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NMR imaging investigations of swelling-controlled drug delivery Blazek, Almira 1998

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N M R I m a g i n g I n v e s t i g a t i o n s o f S w e l l i n g - C o n t r o l l e d D r u g D e l i v e r y by Almira Blazek B . S c , University of Vic tor ia , 1992 A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the Faculty of Graduate Studies Department of Chemistry We accept this thesis as conforming to the required standard. T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A July 31, 1998 © A l m i r a Blazek, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date DE-6 (2/88) A b s t r a c t Important current developments in pharmaceutical science are in the area of formulation technology where the ultimate goal is to control the rate and duration of drug release. Swelling-controlled drug delivery systems utilize the swelling of a hydrophilic polymer to control drug release. N M R spectroscopy and N M R imaging are presented as non-invasive and non-destructive techniques that can provide both chemical and spatial information during the swelling of such controlled release systems. The tablet system chosen for this study contained hydroxypropylmethylcellulose ( H P M C ) as the hydrophilic polymer and one of two fluorinated compounds, triflupromazine-H C 1 or 5-fluorouracil, as model drugs. The geometry for the tablet swelling was chosen to simplify the system to one where the transport processes were one-dimensional. Water distributions were determined by one-dimensional 1 H N M R imaging. H P M C distributions were not measured directly but were calculated from the calibration of the T2 relaxation times of the water as a function of H P M C concentration. The presence of air bubbles in the swollen tablet resulted in experimentally determined polymer distributions which contained up to 45% more H P M C than the known weight of H P M C in the tablet. When the air in the tablet was removed under vacuum prior to the imaging experiment, the total weight of H P M C from the experimental distributions was much closer to the actual weight of H P M C in the tablet. The comparison of the polymer distribution and the drug distributions, obtained from one-dimensional 1 9 F N M R imaging investigations of tablets containing model drugs, showed that most of the triflupromazine-HCl remained within the swollen polymer tablet while more of the 5-fluorouracil was able to escape. The critical condition for drug release i i from the tablet was the relationship between the diffusivity of the drug and the expansion rate of the tablet. For triflupromazine-HCl, the required rate of diffusion was not reached unt i l the region of tablet erosion. In contrast, the diffusion coefficient of 5-fluorouracil in 30% H P M C was large enough that the drug diffused faster than the polymer expanded. Prel iminary modelling calculations assuming Fickian diffusion and a segmented-tablet model were performed. i n C o n t e n t s Abstract i i Table of Contents iv List of Tables v i i i List of Figures x List of Abbreviations x i i i Acknowledgments x iv 1 Introduction 1 1.1 Controlled Release Formulations 1 1.1.1 Advantages of Controlled Drug Release 1 1.1.2 Methods of Attaining Controlled Drug Release 5 1.1.3 Swelling-Controlled Drug Delivery 8 1.1.4 Analy t ica l Methods for Investigating Swelling Polymer Systems 10 1.1.5 N M R Imaging in the Investigation of Controlled Release Systems . 12 1.2 Nuclear Magnetic Resonance Spectroscopy 14 1.2.1 The N M R Phenomenon 14 1.2.2 Pulsed Fourier-Transform N M R and Relaxation Processes 16 1.2.3 Diffusion Measurements by N M R 23 1.2.4 Z-Spectroscopy 24 1.3 Nuclear Magnetic Resonance Imaging 26 1.3.1 One-dimensional Imaging 26 1.3.2 Slice Selection 29 1.3.3 Two-dimensional Imaging 31 1.4 Goals of the Thesis Research 34 2 Spectroscopic Investigations of Mixtures Containing HPMC, Model Drugs, and Water 37 2.1 Introduction 37 2.2 Experimental 38 2.2.1 Preparation of Mixtures 38 iv 2 . 2 . 2 N M R M e a s u r e m e n t s 4 0 2 . 3 R e s u l t s a n d D i s c u s s i o n 4 2 2 .3 .1 1 H T i a n d T2 R e l a x a t i o n T i m e s f o r W a t e r i n t h e M i x t u r e s 4 2 2 . 3 . 2 1 9 F T i a n d T2 R e l a x a t i o n T i m e s f o r t h e T r i f l u p r o m a z i n e - H C l a n d 5 - F l u o r o u r a c i l i n t h e m i x t u r e s 4 4 2 . 3 . 3 S e l f - d i f f u s i o n C o e f f i c i e n t s f o r W a t e r , T r i f l u p r o m a z i n e - H C l a n d 5 - F l u o r o -u r a c i l i n t h e M i x t u r e s 50 2 . 3 . 4 M o b i l i t y C h a n g e s i n t h e P o l y m e r as D e t e r m i n e d b y N M R S p e c t r o s c o p y 5 3 2 .4 S u m m a r y 59 3 One-dimensional 1H NMR Imaging Investigations of Water and Polymer in Swelling HPMC Tablets 61 3.1 I n t r o d u c t i o n 61 3 .2 E x p e r i m e n t a l 6 3 3 .2 .1 P r e p a r a t i o n o f H P M C T a b l e t s 6 3 3 . 2 . 2 E x p e r i m e n t a l S e t u p f o r S w e l l i n g I n v e s t i g a t i o n s 6 3 3 . 2 . 3 O n e - d i m e n s i o n a l I m a g i n g 66 3 . 2 . 4 P r o c e s s i n g o f I m a g e D a t a 68 3 . 3 R e s u l t s a n d D i s c u s s i o n 72 3.3 .1 W a t e r P e n e t r a t i o n i n t o H P M C T a b l e t s 72 3 . 3 . 2 D i s t r i b u t i o n o f H P M C i n t h e S w e l l i n g T a b l e t 86 3 . 3 . 3 T o t a l W e i g h t o f H P M C f r o m C a l c u l a t e d P o l y m e r D i s t r i b u t i o n s 91 3 . 3 . 4 P o s s i b l e E f f e c t s o f W a t e r D i f f u s i o n o n t h e I m a g i n g R e s u l t s 9 2 3 .4 S u m m a r y 94 4 Detection of Air Spaces in the Swollen HPMC Tablet 95 4.1 I n t r o d u c t i o n 9 5 4 . 2 E x p e r i m e n t a l 96 4 . 2 . 1 V a c u u m T r e a t m e n t t o R e m o v e A i r f r o m t h e T a b l e t 96 4 . 2 . 2 O n e - a n d T w o - d i m e n s i o n a l I m a g i n g 96 4 . 3 R e s u l t s a n d D i s c u s s i o n 99 4 . 3 . 1 T w o - d i m e n s i o n a l I m a g e s o f U n t r e a t e d a n d V a c u u m - T r e a t e d T a b l e t s 99 4 . 3 . 2 T o t a l W e i g h t o f P o l y m e r i n U n t r e a t e d a n d V a c u u m - T r e a t e d T a b l e t s 104 4 . 3 . 3 W a t e r D i s t r i b u t i o n s i n t h e V a c u u m - T r e a t e d T a b l e t s 105 4 . 3 . 4 H P M C D i s t r i b u t i o n s i n t h e V a c u u m - T r e a t e d T a b l e t s 108 4 . 4 S u m m a r y 112 v 5 One-Dimensional 1 9 F NMR Imaging Investigations of Model Drugs in Swelling HPMC Tablets 113 - 5.1 Introduction 113 5.2 Experimental 114 5.2.1 Preparation of Tablets Containing Fluorinated Drug 114 5.2.2 One-dimensional Imaging 114 5.2.3 Calibration of Fluorine Signal 115 5.3 Results and Discussion 119 5.3.1 Distributions of Triflupromazine-HCl and 5-Fluorouracil in the Swelling Tablet 119 5.3.2 H P M C Concentration Distributions Calculated from Images of the Model Drugs ° 122 5.3.3 Discussion of Drug Release Mechanism 129 5.4 Summary 137 6 Evaluation of Theoretical Models of Transport Processes in Swelling HPMC Tablets 140 6.1 Introduction 140 6.2 Theory 141 6.2.1 Fickian Diffusion 141 6.2.2 Segmented Tablet Model 144 6.3 Notes on the Calculations 146 6.4 Results and Discussion 148 6.4.1 F ick ian Diffusion Calculations 148 6.4.2 Segmented Tablet Calculations 161 6.5 Summary 165 7 Conclusions and Suggestions for Future Work 166 7.1 Conclusions 166 7.2 Suggestions for Future Work 167 Bibliography 169 Appendices A Processing of Image Data 177 A . l A S C I I output from W I N - N M R 177 A . 2 Converter Program for Batch-Processing Files 178 A . 3 Calculating (Frequency, Intensity) Data Points 181 A . 4 T 2 Calculat ion from the Variable-T^ Image Files 184 vi A . 5 C o r r e c t i n g I m a g e I n t e n s i t y f o r T 2 D e p h a s i n g 193 A . 6 C a l c u l a t i n g P o l y m e r W e i g h t P e r c e n t D i s t r i b u t i o n s f r o m T2 D i s t r i b u t i o n s . 195 B Calculating Theoretical Concentration Distributions 198 B . l C a l c u l a t i o n o f E r r o r F u n c t i o n V a l u e s 198 B . 2 F i c k i a n D i s t r i b u t i o n s 2 0 2 B . 3 S e g m e n t e d T a b l e t M o d e l 2 0 9 v i i 1 L i s t o f T a b l e s 2.1 Measured 1 H Tx and T2 relaxation parameters for the water component in mixtures of H P M C and water 43 2.2 Measured 1 9 F T i and T2 relaxation parameters for the tr i f lupromazine-HCl component of mixtures of H P M C , triflupromazine-HCl and water 46 2.3 Measured 1 9 F T i and T2 relaxation parameters for the 5-fluorouracil com-ponent of mixtures of H P M C , 5-fluorouracil, and water 49 2.4 Measured self-diffusion coefficients for the water component of mixtures of H P M C and water 50 2.5 Measured self-diffusion coefficients for the tr if lupromazine-HCl ( 1 9 F ) com-ponent of mixtures of H P M C , triflupromazine-HCl and water 52 2.6 Measured self-diffusion coefficients for the 5-fluorouracil ( 1 9 F ) component of mixtures of H P M C , 5-fluorouracil and water 52 2.7 Width-at-half-height values for z-spectra of H P M C mixtures 59 3.1 Definition of H P M C tablet types and summaries of their characteristics . . 63 3.2 Typica l values for parameters used in the spin-echo pulse sequence for ac-quiring the one-dimensional images 67 3.3 Summary of average water penetration distances for each tablet type and experimental variation 84 3.4 Average total weights of H P M C calculated from the one-dimensional imaging studies of a Type 1 tablet 92 4.1 Typica l parameters used in the spin warp imaging sequence to acquire the two-dimensional images of swelling H P M C tablets 98 4.2 Total weights of H P M C calculated from one-dimensional imaging experi-ments at various times during the swelling of vacuum-treated tablets. . . . 105 5.1 Parameters for the H P M C tablets containing the fluorinated model drugs. 114 5.2 Sequence of experiments for calibration of 1 9 F signal at various times during the swelling of the drug-containing tablet 116 vin 5.3 The total detectable moles 1 9 F in the T 2 corrected one-dimensional images of H P M C tablets containing triflupromazine-HCl and 5-fluorouracil 119 5.4 The total weight of H P M C calculated from the H P M C distributions obtained from the 1 9 F imaging experiments of H P M C tablets containing triflupromazine-H C l 126 5.5 Distances of various concentration regions in the H P M C concentration dis-tributions calculated from the imaging experiments of Chapter 4 134 5.6 Drug inside and outside the H P M C tablets as determined from the 1 9 F imag-ing experiments 135 6.1 Equations and ini t ia l parameters used in the Fickian fitting calculations. . 146 6.2 The results of one-dimensional Fickian fitting to the water distributions in the swelling tablet 149 6.3 The results of one-dimensional Fickian fitting to the H P M C distributions in the swelling tablet 152 6.4 The results of one-dimensional Fickian fitting to the t r i f lupromazine-HCl distributions in the swelling tablet 155 6.5 The results of one-dimensional Fickian fitting to the 5-fluorouracil distribu-tions in the swelling tablet 158 B . l The value of the error function 199 ix L i s t o f F i g u r e s 1.1 The variation of drug concentrations in the body wi th conventional drug delivery methods 3 1.2 Schematic representations of the various methods of controlling drug release. 6 1.3 Nuclear spins depicted as precessing vectors 16 1.4 The free induction decay of a sample after an rf pulse 18 1.5 The inversion recovery experiment for measuring T i 20 1.6 The spin-echo experiment for measuring T 2 21 1.7 The pulse sequence for the P G S E experiment 24 1.8 The pulse sequence for the z-spectroscopy experiment 25 1.9 A n example of a one-dimensional imaging experiment 27 1.10 The spin-echo pulse sequence used to acquire one-dimensional images. . . . 28 1.11 The slice-selection process in N M R imaging 30 1.12 Phase and frequency encoding 32 1.13 The pulse sequence for the two-dimensional Fourier imaging experiment. . 33 1.14 The pulse sequence for the two-dimensional spin-warp imaging experiment. 35 2.1 Structures of the materials used in this thesis 39 2.2 Variat ion of 1 H relaxation times of the water resonance in H P M C mixtures at equil ibrium 45 2.3 Variat ion of 1 9 F relaxation times of the tr if lupromazine-HCl component in H P M C mixtures at equilibrium 48 2.4 Variat ion of 1 9 F relaxation times of the 5-fluorouracil component in H P M C mixtures at equil ibrium 51 2.5 Self-diffusion coefficients of water, tr if lupromazine-HCl, and 5-fluorouracil in selected H P M C mixtures 54 2.6 The inverse of the T 2 of the water component in H P M C mixtures as a function of H P M C weight percent 55 2.7 * H N M R Z-spectra for selected H P M C mixtures 58 3.1 Tablet arrangement for swelling (a) upwards and (b) downwards 64 3.2 Pulse sequence used to acquire the one-dimensional projections 67 x 3.3 A n example of a one-dimensional image showing normalized water penetra-t ion into an H P M C tablet and the resulting tablet swelling at a t ime of 4 hours 73 3.4 *H images obtained from a tablet swelling in D 2 0 74 3.5 The variation of the signal intensity in the water images as a function of the TE and the corresponding T 2 values after 25 hours of swelling 76 3.6 Water images showing both the 2 ms image and the T 2 -corrected distribu-tions at various swelling times 78 3.7 Water distributions from upwards and downwards swelling experiments at various swelling times 79 3.8 Corrected average water distributions for the Type 1 and Type 2 tablets at various swelling times 80 3.9 Corrected average water distributions for the Type 2 and Type 3 tablets at various swelling times 82 3.10 The water penetration distance as a function of the square root of t ime. . . 85 3.11 Average H P M C weight percent curves obtained from corresponding T 2 curves calculated from one-dimensional images of water 87 3.12 H P M C weight percent distributions from upwards and downwards swelling experiments at various swelling times 88 3.13 Average H P M C weight percent distributions for the Type 1 and Type 2 tablets at various swelling times 89 3.14 Corrected average H P M C weight percent distributions for the Type 2 and Type 3 tablets at various swelling times 90 4.1 A schematic representation of the experimental set-up for vacuum-treating the H P M C tablets 97 4.2 Longitudinal images of the water distribution in an untreated and a vacuum-treated tablet taken at various swelling times approximately the same posi-tion in the two swelling tablet systems 101 4.3 Cross-sectional images of the water distribution in an untreated tablet and a vacuum-treated tablet taken at approximately the same position in the middle of the swollen tablet at a swelling time of 43 hours 103 4.4 Water distributions of the untreated and vacuum-treated tablets at various swelling times 106 4.5 H P M C weight percent distributions of the Tria l 2 vacuum-treated tablet as calculated and diffusion-corrected at various swelling times 109 4.6 Average H P M C weight percent distributions of the untreated and vacuum-treated tablets at various swelling times 110 xi 5.1 Calibrat ion plots relating 1 9 F concentration determined from the internal reference to the total signal in the 2 ms image acquired at the same times during the swelling of an H P M C tablet containing drug 118 5.2 Molar distributions of 1 9 F in swollen H P M C tablets containing triflupromazine-H C l and 5-fluorouracil 120 5.3 The variation of the signal intensity in the tr if lupromazine-HCl images as a function of T# and the corresponding T 2 values after 19 hours of swelling. 123 5.4 The variation of the signal intensity in the 5-fluorouracil images as a function of TE and the corresponding T 2 values after 19 hours of swelling 125 5.5 H P M C distributions calculated from water and tr if lupromazine-HCl images. 127 5.6 Molar 1 9 F distributions of triflupromazine-HCl overlapped wi th H P M C dis-tributions calculated from the water images 130 5.7 Molar 1 9 F distributions of 5-fluorouracil overlapped wi th H P M C distribu-tions calculated from the water images 132 5.8 The distance of various regions in the swelling H P M C tablet as a function of the square root of the swelling time 136 5.9 Fraction of drug released as a function of the square-root of the swelling t ime. 138 6.1 Init ial conditions for one-dimensional Fickian diffusion 143 6.2 Description of the segmented tablet model 145 6.3 Comparison of water distributions from the vacuum-treated tablet and the theoretical distributions assuming one-dimensional F ick ian diffusion 150 6.4 Comparison of the average H P M C distributions from the vacuum-treated tablet and the theoretical distributions assuming one-dimensional F ick ian diffusion 153 6.5 Comparison of the triflupromazine-HCl distributions from the vacuum-treated tablet and the theoretical distributions assuming one-dimensional F ick ian diffusion 156 6.6 Comparison of the 5-fluorouracil distributions from the vacuum-treated tablet and the theoretical distributions assuming one-dimensional F ick ian diffusion. 159 6.7 Example of the theoretical H P M C distribution obtained using 1/(1-0:0^) as the segment swelling factor • 161 6.8 Average H P M C distributions of the vacuum-treated tablet and the theoret-ical distribution calculated using the segmented tablet model 163 xn L i s t o f A b b r e v i a t i o n s 5 f l u 5 - F l u o r o u r a c i l FID F r e e I n d u c t i o n D e c a y G G a u s s HPMC 2 - H y d r o x y p r o p y l m e t h y l c e l l u l o s e i . d . i n n e r d i a m e t e r MRI M a g n e t i c R e s o n a n c e I m a g i n g NMR N u c l e a r M a g n e t i c R e s o n a n c e o . d . o u t e r d i a m e t e r rf r a d i o f r e q u e n c y TE T h e t i m e - t o - e c h o i n a s p i n - e c h o p u l s e s e q u e n c e , t h e t i m e f r o m t h e m i d d l e o f t h e 90° p u l s e t o t h e m a x i m u m a m p l i t u d e o f t h e e c h o . TGA T h e r m a l G r a v i m e t r i c A n a l y s i s TR T h e r e p e t i t i o n t i m e , t h e d e l a y b e t w e e n r e p e a t s o f a n N M R e x p e r i m e n t , t r i f l u T r i f l u p r o m a z i n e - H C l X l l l A c k n o w l e d g m e n t s I w o u l d l i k e t o e x t e n d m y g r a t i t u d e t o P r o f . C o l i n A . F y f e f o r t h e o p p o r t u n i t y t o j o i n h i s r e s e a r c h g r o u p a n d w o r k w i t h N M R . H i s g u i d a n c e a n d s u p p o r t d u r i n g t h e c o u r s e o f m y P h . D . r e s e a r c h a n d t h e p r e p a r a t i o n o f t h i s t h e s i s h a v e b e e n i n v a l u a b l e . I a l s o w i s h t o t h a n k D r s . H i l t r u d G r o n d e y , S t e p h a n i e I s b e l l a n d Z h i m i n g M e i f o r t h e i r k n o w l e d g e a n d p a t i e n c e d u r i n g t h e e a r l y s t a g e s o f m y r e s e a r c h . I w i s h t o t h a n k t h e m e m b e r s o f t h e E l e c t r i c a l a n d M e c h a n i c a l E n g i n e e r i n g S e r v i c e s a t U B C C h e m i s t r y , e s p e c i a l l y M r . T o m M a r k u s a n d M r . O s k a r G r e i n e r , f o r t h e i r m u c h n e e d e d a s s i s t a n c e . D r . P i n g G a o o f U p J o h n - P h a r m a c i a i s t h a n k e d f o r t h e g i f t o f t h e H P M C a n d D r . R o b e r t M i l l e r a n d M r . R a n d y O a t e s o f t h e D e p a r t m e n t o f P h a r m a c e u t i c a l S c i e n c e s a r e t h a n k e d f o r t h e i r h e l p w i t h t h e p r e p a r a t i o n o f t h e H P M C t a b l e t s . I w o u l d a l s o l i k e t o t h a n k D r . M a r k W e l s h o f R e t r o l o g i c S y s t e m s f o r d e v e l o p i n g s o f t w a r e ( l i s t e d i n A p p e n d i x A . 2 ) w h i c h g r e a t l y r e d u c e d t h e t i m e s p e n t o n d a t a p r o c e s s i n g . I w i s h t o t h a n k t h e p a s t a n d p r e s e n t m e m b e r s o f t h e F y f e g r o u p f o r m a k i n g m y t i m e a t U B C m e m o r a b l e . T h e p a s t f e w y e a r s w o u l d n o t h a v e b e e n as m u c h f u n w i t h o u t t h e i r f r i e n d s h i p a n d s u p p o r t . I a l s o a p p r e c i a t e t h e s u p p o r t o f f r i e n d s , m a n y o f w h o m h a v e c o m p l e t e d o r a r e i n t h e p r o c e s s o f c o m p l e t i n g t h e i r o w n P h . D . p r o g r a m s . I t h a n k m y m o t h e r , M a r i a , a n d m y t w o b r o t h e r s , R o b e r t a n d D e n n i s , f o r t h e i r l o v e a n d s u p p o r t t h r o u g h o u t m y a c a d e m i c c a r e e r . M y g r e a t e s t t h a n k s g o t o M a r k , m y b e s t f r i e n d s i n c e t h e d a y w e m e t , w h o h a s a l w a y s e n c o u r a g e d m e t o b e m y b e s t . xiv C h a p t e r 1 I n t r o d u c t i o n 1.1 Controlled Release Formulations 1.1.1 A d v a n t a g e s o f C o n t r o l l e d D r u g R e l e a s e O r a l i n g e s t i o n o f s o l i d d o s a g e f o r m s s u c h as t a b l e t s a n d c a p s u l e s h a s h i s t o r i c a l l y b e e n t h e m o s t c o n v e n i e n t a n d c o m m o n l y u s e d m o d e o f d r u g d e l i v e r y [ 1 , 2 ] . I n t h e 1 9 8 0 s , f o r e x a m p l e , m o r e t h a n h a l f o f t h e $ 2 0 0 b i l l i o n U S d r u g m a r k e t c o n s i s t e d o f s o l i d o r a l d o s a g e f o r m s [1]. T h e m a n y r e a s o n s d r u g s a r e g i v e n i n t a b l e t a n d c a p s u l e f o r m r a t h e r t h a n as a l i q u i d i n c l u d e t h e e a s e o f u s e b y t h e p a t i e n t , t h e p r e d e t e r m i n e d u n i t d o s e o f t h e d r u g , t h e g r e a t e r s t a b i l i t y o f t h e d r u g i n t h e s o l i d v e r s u s t h e l i q u i d s t a t e a n d t h e r e l a t i v e e a s e , w h e n n e c e s s a r y , o f p r o t e c t i n g t h e d r u g f r o m t h e s t o m a c h o r vice versa t h r o u g h t h e u s e o f c o a t i n g s [2]. A l t h o u g h e a s y t o a d m i n i s t e r , t h e s e d o s a g e f o r m s a r e s t i l l o n l y e f f e c t i v e w h e n u s e d p r o p e r l y . A 1 9 7 9 s t u d y e s t i m a t e d t h a t 5 0 % o f t h e 1.8 b i l l i o n p r e s c r i p t i o n m e d i c a t i o n s d i s p e n s e d a n n u a l l y i n t h e U S a r e n o t t a k e n c o r r e c t l y [3]. S u c h n o n c o m p l i a n c e w i t h i n s t r u c t i o n s h a s a n e g a t i v e i m p a c t o n t h e t r e a t m e n t o u t c o m e s a n d m a y r e s u l t i n d i s e a s e c o m p l i c a t i o n s t h a t l e a d t o h o s p i t a l i z a t i o n o r e v e n d e a t h [4]. T h e n e g a t i v e e f f e c t s a s s o c i a t e d w i t h i n c o r r e c t u s e o f m e d i c a t i o n s a r e r e l a t e d t o t h e o v e r d o s e - u n d e r d o s e c y c l e o f d r u g c o n c e n t r a t i o n t h a t c o n v e n t i o n a l , r a p i d - r e l e a s e f o r m u l a -t i o n s p r o d u c e i n t h e b o d y [1, 2 , 5 , 6] . A f t e r i n g e s t i o n o f t h e s o l i d d o s a g e f o r m , t h e d r u g c o n c e n t r a t i o n i n t h e b o d y i n c r e a s e s r a p i d l y , i n s o m e c a s e s t o a t o x i c l e v e l . A s t h e d r u g i s c o n s u m e d o r d e - a c t i v a t e d b y t h e b o d y , t h e c o n c e n t r a t i o n d e c r e a s e s a n d e n t e r s t h e r a n g e w h e r e t h e t h e r a p e u t i c e f f e c t s o f t h e d r u g a r e o b s e r v e d . T h e d r u g c o n c e n t r a t i o n c o n t i n u a l l y 1 decreases and eventually drops below therapeutic levels, rendering the drug treatment in-effective. A t this t ime another dose is required and the cycle begins again. As can be seen in Figure 1.1, the drug levels in the body depend strongly on the regularity of the dosing. Infrequent dosing would decrease the effectiveness of the drug i f the concentrations are not maintained at therapeutic levels while too-frequent dosing would lead to highly toxic drug levels resulting in harmful effects. The dosing profile wi l l vary for different medications depending on the biological half-life of the drug. One negative aspect of conventional drug delivery is the inabili ty to use agents that are degraded too quickly by the body. Conven-tional methods result in the exclusion of a large number of attractive synthetic drugs and almost the entire family of mammalian biochemicals [2]. W i t h i n the past 30 years pharmaceutical research has become increasingly focussed on the development of novel systems for drug delivery that overcome the disadvantages of conventional methods of drug treatment. A controlled release device, designed to release enough drug ini t ia l ly to reach therapeutic levels and then continue releasing at a constant rate to replace used or de-activated drug, would reduce or eliminate the overdose-underdose cycle in the drug concentration and maximize the efficiency of the drug. Targetted or site-specific release in the body would also improve the efficiency of treatment and l imi t drug exposure to unnecessary areas that may result in side-effects [1, 5]. Also , controlled release devices provide a protective barrier to the metabolic processes in the body, thus enabling the delivery of the short half-life drugs that were previously unusable wi th conventional methods. In addition, new delivery methods may circumvent the oral administration route for drugs and provide constant drug release from implantable devices. The use of controlled release formulations in disease treatment provides several advantages over rapid-release counterparts. Patients generally exhibit fewer side effects because the drug concentrations are kept under the toxic levels that cause adverse reac-tions [1, 5, 7]. The disease treatment is often more effective because therapeutic drug levels are maintained for longer periods of time compared to conventional methods [1, 5, 7]. Also, the activity of a drug can be extended throughout the night allowing the patient to sleep 2 (a) Drug Concentration Toxic Level Therapeutic Time (b) Drug Concentration i Toxic Level / \ / \ f \ / I Therapeutic / V / V / V / VLevel 1 v i V .1 \ l V „ Time (c) Drug Concentration Toxic Level Therapeutic Time Figure 1.1: The variation of drug concentrations in the body wi th conventional drug de-livery methods. Four hypothetical doses are administered at (a) the prescribed intervals, (b) longer intervals and (c) shorter intervals. The beneficial effects are observed when the drug concentration remains in the therapeutic range as in (a) and (c). However, harmful effects are observed when the drug concentration reaches toxic levels as in (c). 3 u n d i s t u r b e d [7]. T h e d e c r e a s e i n t h e f r e q u e n c y o f d o s i n g , f r o m t a b l e t s e v e r y f e w h o u r s f o r c o n v e n t i o n a l m e d i c a t i o n t o t y p i c a l l y o n e d a i l y d o s e w i t h a c o n t r o l l e d r e l e a s e f o r m u -l a t i o n , l e a d s t o b e t t e r p a t i e n t c o m p l i a n c e w i t h t h e m e d i c a t i o n r e g i m e n [1, 5] . A l s o , t h e d e v e l o p m e n t o f i m p l a n t a b l e d e v i c e s f o r a p a r t i c u l a r m e d i c a t i o n r e m o v e s t h e i s s u e o f p a t i e n t c o m p l i a n c e a l t o g e t h e r . C o n t r o l l e d r e l e a s e t e c h n o l o g y a l s o p r o v i d e s p o t e n t i a l e c o n o m i c b e n e f i t s f o r t h e p h a r -m a c e u t i c a l i n d u s t r y , t h e p a t i e n t , a n d t h e h e a l t h c a r e s y s t e m . A l t h o u g h t h e d e v e l o p m e n t o f a c o n t r o l l e d r e l e a s e f o r m u l a t i o n is t y p i c a l l y m o r e c o s t l y t h a n a c o n v e n t i o n a l f o r m u l a t i o n , i m p r o v i n g t h e e f f i c i e n c y o f a c u r r e n t d r u g is g e n e r a l l y l e s s e x p e n s i v e t h a n d e v e l o p i n g a n e n t i r e l y n e w o n e [8]. T h e a b i l i t y t o m a i n t a i n m a r k e t s h a r e a n d p r o l o n g t h e e f f e c t i v e p e r i o d o f p a t e n t p r o t e c t i o n f o r a g i v e n d r u g b y r e f o r m u l a t i o n o f t h e d r u g as a c o n t r o l l e d r e l e a s e o r t a r g e t t e d d e l i v e r y s y s t e m h a s b e e n r e c o g n i z e d as a n i m p o r t a n t r e a s o n f o r t h e i n t e r e s t o f t h e p h a r m a c e u t i c a l i n d u s t r y i n a d v a n c e d d r u g d e l i v e r y d e v i c e s [9]. A l t h o u g h t h e c o s t p e r d o s e f o r a c o n t r o l l e d r e l e a s e f o r m u l a t i o n is u s u a l l y h i g h e r t h a n f o r a c o n v e n t i o n a l f o r m u l a t i o n , t h e t r e a t m e n t m a y b e m o r e e c o n o m i c a l f o r t h e p a t i e n t a n d t h e h e a l t h c a r e s y s t e m . T h e r e d u c e d a d v e r s e r e a c t i o n s t h a t o c c u r w i t h t h e u s e o f c o n t r o l l e d d r u g d e l i v e r y r e s u l t s i n l e s s h o s p i t a l i z a t i o n a n d f e w e r v i s i t s t o t h e p h y s i c i a n , a s u b s t a n t i a l s a v i n g i n t e r m s o f t i m e a n d m o n e y [4, 6 ] . T h e d e v e l o p m e n t o f s e l f - a d m i n i s t e r e d c o n t r o l l e d r e l e a s e d o s a g e f o r m s f o r m e d i c a t i o n s t h a t w o u l d o t h e r w i s e r e q u i r e p r o f e s s i o n a l a s s i s t a n c e w o u l d r e d u c e t h e t i m e h e a l t h c a r e p r o f e s s i o n a l s s p e n d o n d i s e a s e t r e a t m e n t , a n a d d i t i o n a l s a v i n g f o r t h e h e a l t h c a r e s y s t e m [4]. T h e u l t i m a t e g o a l f o r c o n t r o l l e d r e l e a s e t e c h n o l o g y i s t o i m p r o v e d i s e a s e m a n a g e -m e n t b y t a i l o r i n g d r u g t r e a t m e n t t o t h e n e e d s o f e a c h p a t i e n t o r c l a s s o f p a t i e n t s [7]. T o a c h i e v e t h i s a i m , d i r e c t c o n t r o l o v e r t h e r a t e , l o c a t i o n a n d t i m i n g o f d r u g r e l e a s e w i l l b e n e c e s s a r y . T h e s o l u t i o n i n v o l v e s t h e d e v e l o p m e n t o f m u l t i c o m p o n e n t s y s t e m s i n w h i c h t h e d r u g i s b u t o n e c o m p o n e n t [2]. 4 1.1.2 Methods of Attaining Controlled Drug Release The various methods for controlling the release of drugs have been discussed elsewhere in great detail [1, 5, 6, 9, 10, 11]. A brief description of each technique, focussing on the mechanism of release control, wi l l be provided here. Examples of the three main classes of delivery devices—diffusion-controlled systems, chemically-controlled systems and water penetration-controlled systems—are depicted in Figure 1.2. Each type uses polymers to provide some form of barrier to drug release. Polymers are uniquely suited as materials in controlled delivery systems because their properties can be modified and controlled [10]. The two types of diffusion-controlled systems, reservoir devices and monoli thic de-vices, differ widely in their properties and performance. In reservoir systems, the active agent is surrounded by a permeable membrane. In monolithic systems, the drug is dissolved or dispersed in an insoluble polymer which is then formed into a tablet or slab. Drug release from a reservoir device depends on the rate of drug diffusion through the membrane and is constant as long as the concentration of drug in contact with the inner side of the mem-brane is constant. The release from a monolithic device declines wi th t ime and depends on the drug loading of the device. The mechanism of drug release from a monoli thic device changes from diffusion through the polymer matrix at low drug loadings ( < 5 % by volume) to diffusion of the drug through water-filled channels left behind by previously escaped drug at higher drug loadings (>20% by volume). The choice between the two diffusion-controlled systems depends on factors such as expense, safety and the desired drug-release profile. The rate of drug release from reservoir devices depends on the. thickness, area and permeability of the membrane and the control of these factors in production leads to higher manufacturing costs. These devices are also susceptible to catastrophic failure if the membrane ruptures, leading to the immediate release of high concentrations of drug. The major advantage of reservoir devices is that they can provide long-term constant release profiles. O n the other hand, monolithic systems release drugs at a declining rate but are inexpensive to manufacture and are relatively safe from dose-dumping. Diffusion-controlled devices are widely used as implants and in transdermal applications. 5 Reservoir Monolithic (b) O o Surface biodegradation Bulk biodegradation (c) drug solution water elementary osmotic pump water T A drug solution mini-osmotic pump gel layer swelling hydrophilic matrix Figure 1.2: Schematic representations of the various methods of controlling drug release, (a) diffusion-controlled, (b) chemically-controlled, and (c) water-penetration controlled. The drug is represented by the dark colour and the lighter a region, the lower the drug concentration. The open-edged, dotted circles indicate drug released from the device. Chemically-controlled systems release drugs by chemical processes such as polymer degradation or erosion. The earliest of these systems used slowly dissolving polymer coat-ings or matrices to retard the dissolution of the drug. Sustained release could be obtained by coating individual particles with polymer layers of varying thickness, thereby altering the dissolution rate for each particle and extending drug release over longer periods of t ime. Attempts were made to develop monolithic devices that released drug by controlled biodegradation of the polymer rather than dissolution. The hope was that the active agent in these systems would be released by slow surface, or heterogeneous, degradation of the polymer matr ix. Unfortunately, the biodegradation of most polymers is not constant and is rarely confined to the surface of the polymer. Most polymers degrade by a homogeneous mechanism, where there is an ini t ial ly slow bulk degradation and then at a cri t ical stage when the entire polymer is degraded to the same extent, the polymer matr ix quickly erodes. Often the release of active agent by diffusion prior to degradation is quite significant lead-ing to complicated release patterns. Recently, biodegradable polymers have been used in conjunction with implantable diffusion-controlled devices to ensure that the spent reservoir or matr ix degrades after drug release is complete. Water penetration-controlled systems include osmotically driven and swelling sys-tems. Osmotic systems utilize osmotic forces to pump drug out of a reservoir-like device. These systems contain osmotic agents surrounded by a membrane permeable only to water. As water penetrates and dissolves the osmotic agents, the osmotic pressure in the interior of the device increases and forces a drug solution out of the device. There are two types of osmotic devices, the elementary osmotic pump and the mini-osmotic pump. In the elemen-tary device, the drug and osmotic agent form the core of the device which is coated with a semi-permeable membrane. As water penetrates and dissolves the interior core, osmotic pressure forces the drug solution out of the device through one or more small holes in the membrane. In the mini-osmotic pump, the osmotic agent and the drug are separated into two compartments by a movable partition. The water enters the osmotic agent compart-ment and the increased osmotic pressure moves the partition, forcing drug out of the drug 7 compartment. W i t h constant reservoir volume, these devices deliver a volume of drug solu-tion equal to the volume of osmotic water uptake within the same time interval. The rate of water influx and drug delivery wi l l be constant as long as a constant thermodynamic activity is maintained across the membrane. In the mini-osmotic pump system, delivery of the drug can be zero-order because of the separate compartmental design. In the elemen-tary pump system, the delivery is only constant as long as there is excess solid present. Osmotic delivery systems are capable of providing prolonged zero-order release at a delivery rate much higher than achievable by a diffusion mechanism. Elementary osmotic pumps are used as oral dosage forms whereas mini-osmotic pumps are often used as controlled release implants in experimental studies into the effects of continuous administration of drugs. Swelling hydrophilic matrices, the focus of this thesis, wi l l be discussed in detail in the following section. 1.1.3 Swelling-Controlled Drug Delivery The term swelling-controlled drug delivery is used tp describe drug release from monolithic devices prepared with hydrophilic polymers whose dimensions change wi th the absorption of water [5]. These hydrophilic matrix tablets are pr imari ly used in oral drug delivery. The tablet is ingested and as the hydrophilic polymer swells, a gel layer is formed around the tablet that inhibits the release of drug. The rate of drug release from the hydrophilic matr ix is a function of water absorption, polymer hydration, and drug diffusion through the swollen polymer gel [5]. When water penetrates a hydrophilic polymer, relaxation of the polymer chains oc-curs once the water concentration is high enough to decrease the glass-to-rubber transition temperature of the system below the temperature of the experiment [12]. The mechanism of water penetration into the polymer wi l l vary depending on the relative rates of the wa-ter diffusion and polymer-chain relaxation [5, 12, 13, 14]. When the diffusion rate of the water is the controlling factor in water uptake, the penetration behaviour follows Fick 's laws of diffusion. When the rate of water or solvent uptake is largely determined by the rate of swelling and relaxation of the polymer chains, then non-Fickian Case II diffusion 8 behaviour is observed. The time-dependence, t", of the penetration front in a matr ix slab is a convenient method of determining the nature of the diffusion process. The diffusion process is F ick ian when the front movement is proportional to the square-root of time (n=0.5) but, i f the front changes are linear with time, then the penetration process follows Case II diffusion [13]. A time-dependence of the penetration front between n=0.5 and 1 suggests that there is a mixture of the two penetration mechanisms. The drug release behaviour also varies with the mechanism of water penetration [5]. In the case of F ick ian water diffusion, the drug release wi l l depend on the rate of drug diffusion through different polymer concentrations. In systems that exhibit Case II water diffusion, drug release fol-lows the swelling of the matrix. The rate of relaxation of the polymer chains is affected by parameters such as polymer orientation, molecular weight, molecular weight distribution and temperature [14]. Thus, the water diffusion mechanism and subsequent drug release behaviour for a controlled release system wi l l depend on the nature of the polymer used in the formulation. Cellulose ethers are a broad class of polymers commonly used in hydrophilic ma-tr ix tablets [15]. These derivatives of cellulose have functional group substitutions such as methyl, ethyl, hydroxypropyl and carboxymethyl, and their chemical properties can be tailored by the choice and degree of substitution of the cellulose chain. Cellulosic polymers, such as hydroxypropylmethylcellulose ( H P M C ) , are chosen because of their wide availabil-ity, cost-effectiveness, compatibility with conventional techniques and low toxicity [12, 15]. The hydrophilic matr ix formulation is prepared by mixing the drug wi th the polymer and pressing the mixture into a tablet or capsule. Water penetration into the polymer leads to the formation of a gelatinous layer containing regions that vary in polymer concen-tration [15]. In the area near 100% polymer, the gel is a wetted mass of powders that have swollen. Towards the outside of the tablet, as the polymer concentration decreases, the layer consistency becomes one of a true gel. A t very low concentrations, the polymer chains dissolve and the erosion of the hydrophilic matrix in these regions is an additional mechanism of drug release. 9 1 . 1 . 4 A n a l y t i c a l M e t h o d s f o r I n v e s t i g a t i n g S w e l l i n g P o l y m e r S y s t e m s T h i s s e c t i o n i s a r e p r e s e n t a t i v e r e v i e w o f t h e a n a l y t i c a l m e t h o d s t h a t h a v e b e e n u s e d t o i n v e s t i g a t e s w e l l i n g - c o n t r o l l e d r e l e a s e s y s t e m s . T h e t e c h n i q u e s h a v e b e e n d i v i d e d i n t o t h r e e c a t e g o r i e s — b u l k m e a s u r e m e n t s , d i s s e c t i o n , a n d i m a g i n g — b a s e d o n t h e a p p r o a c h u s e d t o s t u d y t h e p o l y m e r d e v i c e a n d d r u g r e l e a s e b e h a v i o u r . M a n y r e s e a r c h e r s h a v e u s e d a c o m b i n a t i o n o f t e c h n i q u e s t o p r o v i d e a n e x t e n s i v e d e s c r i p t i o n o f t h e r e l e a s e s y s t e m u n d e r s t u d y . S e l e c t e d r e f e r e n c e s a r e p r o v i d e d f o r e a c h t e c h n i q u e , h o w e v e r , i n g e n e r a l , n u m e r o u s o t h e r e x a m p l e s a r e a v a i l a b l e i n t h e l i t e r a t u r e . T h e d i s c u s s i o n h e r e w i l l f o c u s o n t h e d a t a o b t a i n e d f r o m e a c h m e t h o d o r c l a s s o f m e t h o d s a n d o n p o s s i b l e l i m i t a t i o n s . T h e a n a l y t i c a l m e t h o d s t h a t f a l l i n t o t h e c l a s s i f i c a t i o n o f b u l k m e a s u r e m e n t s a r e t h o s e t h a t d e t e r m i n e o v e r a l l c h a n g e s i n a s p e c i e s c o n c e n t r a t i o n r a t h e r t h a n s p e c i f i c c o n c e n -t r a t i o n d i s t r i b u t i o n s . I n t h e s t u d y o f t a b l e t s w e l l i n g , t h e r a t e o f w a t e r u p t a k e i s m o n i t o r e d t h r o u g h t h e w e i g h t c h a n g e s o f t h e t a b l e t [13, 16] . I n a s i m i l a r m a n n e r t o t h a t d e s c r i b e d i n S e c t i o n 1 .1 .3 , t h e t i m e - d e p e n d e n c e o f t h e w e i g h t i n c r e a s e i s u s e d t o d e t e r m i n e t h e n a t u r e o f t h e w a t e r p e n e t r a t i o n p r o c e s s . A s q u a r e - r o o t t i m e - d e p e n d e n c e o f t h e t a b l e t w e i g h t i s p r o o f o f F i c k i a n d i f f u s i o n w h e r e a s a l i n e a r d e p e n d e n c e o n t i m e p o i n t s t o n o n - F i c k i a n C a s e I I d i f f u s i o n [14]. T h e p o l y m e r b e h a v i o u r i s i n f e r r e d f r o m t h e d i m e n s i o n a l c h a n g e s o f t h e s w e l l i n g t a b l e t s u c h as a n i n c r e a s e i n t h e t h i c k n e s s o r d i a m e t e r o f a t a b l e t [17, 18 ] . S e v e r a l r e s e a r c h e r s h a v e u s e d t h e o r i e s o f p o l y m e r s w e l l i n g b a s e d o n w a t e r p e n e t r a t i o n t o d e v e l o p m o d e l s t o f i t t h i c k n e s s c h a n g e s i n s y s t e m s w h e r e t h e s w e l l i n g is r e s t r i c t e d t o t h e a x i a l d i r e c -t i o n [19, 2 0 ] . T h e m o s t c o m m o n b u l k t e c h n i q u e f o r s t u d y i n g d r u g r e l e a s e i s t h e d i s s o l u t i o n m e t h o d o u t l i n e d i n t h e U S P h a r m a c o p e i a [21]. T h e t a b l e t s a r e s u s p e n d e d i n w a t e r b a t h s , o r flow-cells, a n d t h e d r u g c o n c e n t r a t i o n r e l e a s e d i n t o s o l u t i o n i s m o n i t o r e d b y U V - V i s s p e c t r o p h o t o m e t r y o r o t h e r s u i t a b l e t e c h n i q u e [18, 2 2 , 2 3 , 2 4 , 25 ] . W h e n t h e f r a c t i o n a l d r u g r e l e a s e i s l i n e a r w i t h t h e s q u a r e - r o o t o f t i m e t h e n d r u g d i f f u s i o n i s t h e s i g n i f i c a n t o m e c h a n i s m o f r e l e a s e a n d t h e p r o c e s s i s F i c k i a n [26]. A f r a c t i o n a l r e l e a s e t h a t i s l i n e a r l y d e p e n d e n t o n t i m e i n d i c a t e s t h a t t h e p o l y m e r r e l a x a t i o n i s t h e c o n t r o l l i n g f a c t o r i n t h e 10 drug release. Bu lk measurements of swelling tablets are a general method of characterizing the tablet and drug release behaviours but are unable to directly detect concentrations of 5 water, polymer or drug within the tablet. The dissection of a swollen tablet is a basic technique used to obtain concentration distributions in a hydrogel. For each time point, a fresh tablet is left to swell for the required duration and then the gel is sliced into sections of known dimension. The water and polymer concentrations in each slice are determined by drying to a constant weight. The drug concentration in each slice is determined by a suitable assay that can detect the drug without interference from the polymer. In this manner, the time-dependent concentration distributions for each species in the swelling tablet can be determined. In one example of this method, the distributions for polymer, drug and water in a swelling H P M C tablet containing KC1 were obtained by freezing the swollen gel prior to dissection to stop the diffusion of the KC1 [27]. Another common use of the dissection technique is to determine the diffusion coefficient from the drug distribution within swollen gels of known polymer concentration [28]. The advantages of the dissection method, low expense and ease of execution, are countered by the labour-intensive nature of the experiment. There is also the added risk of experimental variations due to the handling of the swollen tablet. In situ imaging during the tablet swelling process allows for the detailed analysis of the system without disturbing the polymer gel layer. The various imaging techniques can be divided into two categories, those that provide only a pictographic record of the swelling hydrophilic matr ix tablet and those capable of providing concentration distributions wi thin the swollen polymer. The most basic form of imaging is photography which is useful to monitor the dimensional changes of the tablet during swelling [17, 18, 29]. Polarized-light microscopy, in conjunction with photography, permits the detection of the water penetration front and measurement of the gel layer thickness [14, 22, 23, 24], parameters that provide information on the nature of the water penetration process and polymer hydration. X-ray photography has also been used to monitor water penetration into H P M C tablets [30]. H P M C tablets containing sodium sulphate were placed in dissolution media 11 c o n t a i n i n g b a r i u m c h l o r i d e r e s u l t i n g i n t h e f o r m a t i o n o f X - r a y o p a q u e b a r i u m s u l p h a t e w h e r e w a t e r h a d p e n e t r a t e d t h e t a b l e t . I n t h e X - r a y p h o t o g r a p h s , t a k e n u s i n g d e n t a l f i l m , d a r k r i n g s i n d i c a t e d t h e s w o l l e n g e l l a y e r . T h e i n f o r m a t i o n a t t a i n a b l e w i t h p h o t o g r a p h i c m e t h o d s i s l i m i t e d b y t h e l a c k o f c o n c e n t r a t i o n i n f o r m a t i o n f o r t h e w a t e r o r t h e p o l y m e r i n t h e s w e l l i n g t a b l e t . A l s o , t h e s e t e c h n i q u e s c a n n o t p r o b e t h e d r u g r e l e a s e b e h a v i o u r u n l e s s t h e l o s s o f d r u g f r o m t h e d e -v i c e l e a d s t o a d d i t i o n a l o p t i c a l c h a n g e s t h a t c a n b e d e t e c t e d a p a r t f r o m t h o s e c a u s e d b y w a t e r p e n e t r a t i o n . I m a g i n g t e c h n i q u e s t h a t c a n p r o v i d e c o n c e n t r a t i o n i n f o r m a t i o n i n c l u d e o p t i c a l i m a g i n g , c o n f o c a l l a s e r s c a n n i n g m i c r o s c o p y , a n d N M R i m a g i n g . I n o n e m e t h o d o f o p t i c a l i m a g i n g , l i g h t s c a t t e r i n g w a s u s e d t o o b t a i n in situ o p t i c a l i m a g e s o f t h e g e l l a y e r o f a s w e l l i n g H P M C t a b l e t [31]. T h e i n t e n s i t y o f t h e s c a t t e r i n g , c a l i b r a t e d w i t h r e s p e c t t o t h e H P M C c o n c e n t r a t i o n i n H P M C - w a t e r m i x t u r e s , w a s u s e d t o c a l c u l a t e p o l y m e r c o n -c e n t r a t i o n d i s t r i b u t i o n s a t v a r i o u s t i m e s d u r i n g t h e t a b l e t s w e l l i n g . T h i s o p t i c a l i m a g i n g t e c h n i q u e c o u l d e a s i l y b e a p p l i e d i n t h e s t u d y o f o t h e r s w e l l i n g p o l y m e r s y s t e m s . T h e t e c h -n i q u e , u n f o r t u n a t e l y , d o e s n o t p r o v i d e d r u g c o n c e n t r a t i o n d i s t r i b u t i o n s b u t u s e s t h e d i s -s o l u t i o n m e t h o d t o d e t e r m i n e d r u g r e l e a s e b e h a v i o u r . C o n f o c a l l a s e r s c a n n i n g m i c r o s c o p y h a s b e e n u s e d t o s t u d y b o t h p o l y m e r s w e l l i n g b e h a v i o u r a n d d r u g r e l e a s e i n m o n o l i t h i c d e v i c e s [32, 3 3 ] . T h e t e c h n i q u e p r o d u c e s s p a t i a l l y - r e s o l v e d m a p s o f a f l u o r e s c e n t s p e c i e s a n d c a n p r o v i d e i n f o r m a t i o n o n t h e c o n c e n t r a t i o n d i s t r i b u t i o n s o f a f l u o r e s c e n t d r u g . N M R i m a g i n g h a s b e e n u s e d i n s e v e r a l i n s t a n c e s t o s t u d y s w e l l i n g - c o n t r o l l e d c o n t r o l l e d r e l e a s e s y s t e m s . A s t h e t e c h n i q u e is t h e f o c u s o f t h i s t h e s i s , t h e e x p e r i m e n t s p e r f o r m e d b y o t h e r i n v e s t i g a t o r s w i l l b e d i s c u s s e d i n d e t a i l i n t h e f o l l o w i n g s e c t i o n . 1.1.5 N M R Imaging in the Investigation of Controlled Release Systems T h e f i r s t e x p e r i m e n t s u s i n g a n N M R m e t h o d t o o b t a i n i m a g e s w e r e r e p o r t e d i n 1 9 7 3 w h e r e i m a g i n g w a s u s e d t o s t u d y t w o t u b e s o f w a t e r [34] a n d a s o l i d l a y e r e d s a m p l e [35]. I n b o t h t h e s e e x p e r i m e n t s , a m a g n e t i c field g r a d i e n t w a s a p p l i e d t o t h e s a m p l e a n d t h e r e s u l t i n g N M R ' s p e c t r u m ' , o r o n e - d i m e n s i o n a l i m a g e , s h o w e d f r e q u e n c y b r o a d e n i n g r e l a t e d 12 to the position of the sample within the gradient. In the study of two tubes of water, magnetic fields were applied along various axes and the one-dimensional N M R images were mathematically back-projected into a two-dimensional image of the original sample. In the second study, a model sample consisting of plates of solid camphor was imaged using a magnetic field applied perpendicular to the plane of the plates. The spacings of the layers derived from the images were similar to the actual spacings of the sample within the 10% accuracy of the magnetic field calibration. The earliest reports of the use of N M R imaging to monitor solvent ingress into polymers were in the mid-1980s [36, 37, 38]. In recent years, numerous investigators have util ized this technique to monitor, for example, the N M R relaxation and diffusion properties of acetone and methanol in poly(methylmethacrylate) [39] and the absorption and desorption of water in Ny lon 6,6 [40]. The number of reported N M R imaging investigations of drug delivery systems has been l imited. The earliest application of the technique was in 1988 when the release of a paramagnetic contrast agent from an osmotic pump was monitored [41]. A later imaging study of osmotic pump tablets found that the degree of water penetration through the tablet membrane visible in the two-dimensional images, was greater for 'fast' release than for 'slow' release versions of the tablets [42]. N M R imaging of silicone oi l wi thin intact tablets was recently presented as a novel method of determining tablet porosity [43]. Other investigators have reported the use of N M R imaging in the development of drug release formulations. Researchers at Glaxo Wellcome Inc. changed the coat material of their reg-ulated release tablets based on evidence from N M R images obtained in our laboratory that the process of water absorption in the coat was altering the expected drug release behaviour [44]. Proctor & Gamble modified the preparation of a tablet containing two active agents, from a monolayer tablet containing a mixture of the two drugs to a bilayer tablet where the drugs are separated, when N M R imaging experiments indicated that the mixture of drugs lead to the formation of a gel that hindered drug release [45]. The most extensive N M R imaging analysis has been performed on swelling hy-drophilic matr ix systems containing H P M C or similar polymers. During the course of this 13 thesis research, one group used two-dimensional imaging to determine the degree of tablet swelling, the gel layer thickness and the diffusivity of water in the polymer at various times during the swelling of an H P M C tablet [46, 47, 48]. Another imaging study of hydrox-ypropylcellulose capsules revealed that the rate of the hydration penetration front is not the rate-limiting step in drug release as determined by the dissolution method [49]. The work performed to date on hydrophilic matrix tablets has not exploited the advantages of N M R imaging. N M R imaging is a non-invasive, non-destructive technique that can provide quantitative concentrations distributions for species wi th in the swollen polymer tablets, data useful in developing models to explain swelling and drug release. Also, other N M R active nuclei apart from *H can be imaged allowing for the independent monitoring of drug species in an aqueous environment. Al though N M R imaging has been used to obtain concentration distributions to determine diffusion coefficients of a drug within a hydrogel [50], the technique has not been applied to monitor water, polymer and drug distributions from an ini t ial ly dry hydrophilic matrix tablet unt i l the work reported in this thesis [51, 52]. 1.2 Nuclear Magnetic Resonance Spectroscopy Nuclear magnetic resonance was first reported in 1946 [53, 54]. From 1949, wi th the discovery of the chemical shift effect, to the present day, N M R has proven to be one of the most important tools for investigating chemical structures. The theory of the phenomenon has been extensively discussed in several books [55, 56, 57, 58]. The description here wi l l be a brief review of the basic concepts underlying the experiments of this thesis. 1.2.1 T h e N M R P h e n o m e n o n Nuclei contain protons and neutrons which are both s p i n - | species. The coupling of the angular momenta of the individual nucleons leads to a total nuclear spin that can have an integral, half-integral or zero value. A nucleus of spin I has (21+1) spin states, m j , which take on values - I , -1+1, up to +1. A n 1=0 nucleus has only one spin state and exhibits no N M R properties. 14 A moving charged body has an associated magnetic moment. For the nucleus, the magnetic moment, fl, is related to its angular momentum, P, by 7, the nuclear gyromagnetic constant (Equation 1.1). In the absence of an external magnetic field, al l the spin states of the nucleus are degenerate in energy. However, when a magnetic field Bo is applied in the z-direction, as in the N M R experiment, the energy levels for the spin states separate in relation to the strength of the magnetic field, the value of 7, Planck's constant h over 2ir (h) and the spin state quantum number, m / , as shown in Equation 1.2. t = lP (LI) E = - 7 ^ m / 5 o (1-2) For the simplest case of a sp in - | nucleus, there are two energy levels separated by a AE of I •yhBo |. Transitions between these two states can be induced by an oscillating magnetic field when its frequency corresponds to AE, as in Equation 1.3. Often the strength of a magnet used in an N M R experiment is quoted in terms of the frequency for the *H transition in the magnet, e.g. 400 M H z rather than 9.4 T . AE = hp =| 7SB0 I (1-3) v = \ £ \ B 0 Another method of regarding the N M R experiment is to use a vector formalism. The magnetic field, B, exerts a torque on the magnetic moment vector, fl, causing it to precess about the axis of the main magnetic field, usually defined as the z-axis. The induced angular velocity, cu, of this Larmor precession is equal to —7Bo and u is equal to | 7/27r | Bo as before. A sample under investigation contains an ensemble of s p i n - | nuclei in one of the two possible spin states each representable by a vector as shown in Figure 1.3(a). The net magnetization in the systems depends on the population difference between the two energy states which can be determined from the Boltzmann equation. The resulting total 15 (a) Bo (b) Bo mi = +1/2 mi = -1/2 Figure 1 .3 : (a) Nuclear spins depicted as precessing vectors. Spins with m/=+l/2 are at lower energy than m/=-l/2 spins, hence the larger number of +1/2 vectors, (b) The net magnetization vector, M, with magnitude given by Equation 1.4. magnetization vector M , shown in Figure 1.3(b), is directed along the z-axis and has the magnitude given in Equation 1.4 where N is the total number of spins, kT is the thermal energy and k is Boltzmann's constant. The diagnostic structural information available from NMR is due to the additional phenomenon of local electronic shielding. The motion of electrons in a magnetic field results in an induced magnetic moment opposed to the primary applied field. The decrease in the apparent magnetic field experienced by the nucleus causes a shift in the resonance frequency for that nucleus. An empirical database of chemical shifts for different nuclei in specific molecular environments has been developed over the past 50 years. This database makes possible structure determinations of unknown molecules from their N M R spectra . 1.2.2 Pulsed Fourier-Transform NMR and Relaxation Processes The earliest manner of performing an NMR experiment was the continuous wave method where the sample was placed in a fixed magnetic field and the radiofrequency (rf) field was 2kT 16 s c a n n e d t h r o u g h a r a n g e o f v a l u e s ( o r vice versa). W h e n t h e r e s o n a n c e f r e q u e n c y f o r e a c h t y p e o f n u c l e u s i n t h e s a m p l e w a s m a t c h e d , a n a b s o r p t i o n p e a k w a s o b s e r v e d i n t h e N M R s p e c t r u m . M o d e r n N M R e x p e r i m e n t s a r e p e r f o r m e d w i t h r f p u l s e s t h a t h a v e a b r o a d e x c i t a t i o n r a n g e a n d s i m u l t a n e o u s l y s a t i s f y t h e r e s o n a n c e c o n d i t i o n f o r a l l t h e d i f f e r e n t n u c l e i i n t h e s a m p l e w i t h i n t h a t r a n g e . T h e N M R s p e c t r u m is o b t a i n e d b y o b s e r v a t i o n o f t h e d e c a y o f t h e e x c i t e d s t a t e as t h e p e r t u r b e d s y s t e m s r e l a x t o w a r d e q u i l i b r i u m . F o u r i e r t r a n s f o r m a t i o n o f t h e s i g n a l i n t e n s i t y as a f u n c t i o n o f t i m e y i e l d s t h e N M R s p e c t r u m , a m a p o f i n t e n s i t y as a f u n c t i o n o f f r e q u e n c y . T h e d e s c r i p t i o n o f t h e e f fec t o f a n r f p u l s e o n t h e n e t m a g n e t i z a t i o n i s a i d e d b y t h e d e f i n i t i o n o f a n e w f r a m e o f r e f e r e n c e . I n t h e l a b o r a t o r y f r a m e , t h e a x e s a r e s t a t i c a n d t h e n u c l e i a n d r f p u l s e m o v e w i t h r e s p e c t t o t h e a x e s . B y d e f i n i n g a r o t a t i n g f r a m e , w h e r e o n l y t h e z - a x i s i s s t a t i c a n d t h e x a n d y - a x e s r o t a t e a t t h e s a m e f r e q u e n c y as t h e r f p u l s e , b o t h t h e r f m a g n e t i z a t i o n a n d t h e s p i n v e c t o r s c a n b e s t a t i c w i t h r e s p e c t t o t h e f r a m e . I n t h e r o t a t i n g f r a m e , t h e B\ m a g n e t i c field g e n e r a t e d b y t h e p u l s e c a u s e s t h e n e t m a g n e t i z a t i o n t o r o t a t e a b o u t t h e d i r e c t i o n o f t h e a p p l i e d p u l s e . T h e a n g l e o f r o t a t i o n d e p e n d s o n t h e s t r e n g t h a n d d u r a t i o n o f t h e p u l s e a n d t h e g y r o m a g n e t i c r a t i o o f t h e n u c l e u s . A '90°' p u l s e t i p s t h e m a g n e t i z a t i o n f r o m t h e z - a x i s i n t o t h e x , y - p l a n e . W h e n t h e f r e q u e n c y o f t h e p u l s e i s e x a c t l y e q u a l t o t h e L a r m o r p r e c e s s i o n f r e q u e n c y , t h e n e t m a g n e t i z a t i o n w i l l b e s t a t i c w i t h r e s p e c t t o t h e f r a m e . T h e r e t u r n t o e q u i l i b r i u m w i l l g e n e r a t e a f r e e i n d u c t i o n d e c a y ( F I D ) as i n F i g u r e 1 .4 (a ) . W h e n t h e f r e q u e n c y o f t h e p u l s e i s n o t e q u a l t o t h e L a r m o r f r e q u e n c y , t h e r e s u l t i s a n o s c i l l a t i n g F I D ( F i g u r e 1 .4 (b ) ) b e c a u s e t h e L a r m o r p r e c e s s i o n f r e q u e n c y i s f a s t e r o r s l o w e r t h a n t h e r o t a t i n g f r a m e f r e q u e n c y w h i c h i s d e f i n e d b y t h e f r e q u e n c y o f t h e p u l s e . T h e F I D i s r e c o r d e d b y c o m p u t e r a n d m u l t i p l e r e p e t i t i o n s o f t h e s a m e e x p e r i m e n t c a n b e a d d e d t o g e t h e r t o i m p r o v e t h e s i g n a l - t o - n o i s e r a t i o i n t h e r e s u l t i n g N M R s p e c t r u m . T h e r e a r e t w o r e l a x a t i o n t i m e s t o c o n s i d e r w h e n p e r f o r m i n g b a s i c p u l s e F T - N M R e x p e r i m e n t s b e c a u s e a n r f p u l s e d i s t u r b s t h e p o p u l a t i o n b a l a n c e i n t h e s p i n s t a t e s a n d g e n e r a t e s a t e m p o r a r y p h a s e - c o h e r e n c e i n t h e s p i n s . A f t e r t h e p u l s e , t h e s y s t e m p o p u l a t i o n s 17 (a) Amplitude (b) Amplitude Time Time Figure 1.4: The free induction decay (FID) of a sample after an (a) on-resonance rf pulse and (b) off-resonance rf pulse. w i l l revert back to the Bol tzmann equilibrium populations. This relaxation is described by the Bloch equation for Bol tzmann relaxation, Equation 1.5, where Ti is the spin-lattice, or longitudinal, relaxation constant. The second time, spin-spin or transverse relaxation, is responsible for the decay of the F I D . The nuclear spins, phase-coherent during the rf pulse, begin to dephase again, resulting in a decrease from the maximum intensity. The time constant of the decay, as shown in Equation 1.6, is T 2 , the spin-spin relaxation parameter. The Ti and T 2 relaxation times are characteristic for a nuclear species in its environment. These parameters should be known prior to performing more complex N M R studies as their values wi l l determine which experiments are feasible. dMz dt dMa dt (Mz - Mo) Ma T 2 ' a (1.5) (1.6) The knowledge of the Ti relaxation time is important for obtaining quantitative signals as the delay (TR) between successive repetitions of a pulse sequence should be five times Ti to ensure complete recovery to Bol tzmann equilibrium. Ti values are typically 18 m e a s u r e d b y t h e i n v e r s i o n - r e c o v e r y s e q u e n c e s h o w n i n F i g u r e 1.5 [59]. T h e 180° p u l s e i n v e r t s t h e m a g n e t i z a t i o n f r o m t h e + z t o t h e - z d i r e c t i o n s a n d r e l a x a t i o n t o B o l t z m a n n e q u i l i b r i u m o c c u r s d u r i n g t h e r d e l a y . T h e 90° p u l s e t i p s t h e m a g n e t i z a t i o n i n t h e x , y - p l a n e s o t h a t t h e s i g n a n d m a g n i t u d e o f t h e m a g n e t i z a t i o n c a n b e d e t e c t e d . T h e m a g n e t i z a t i o n c h a n g e s f r o m - M 0 t o +M0 f o l l o w i n g E q u a t i o n 1.7 w h i c h i s t h e i n t e g r a t e d f o r m o f t h e B l o c h e q u a t i o n . F i g u r e 1.5 s h o w s p l o t s o f t h i s e q u a t i o n w i t h r e l a t i v e l y s h o r t a n d l o n g Ti v a l u e s . Mz = M0(l-2e~t) (1.7) T h e T 2 r e l a x a t i o n t i m e d i c t a t e s t h e l e n g t h o f t i m e t h a t t h e m a g n e t i z a t i o n c a n b e m a n i p u l a t e d a n d d e t e c t e d i n a n N M R e x p e r i m e n t . A l t h o u g h T 2 r e l a x a t i o n c a u s e s t h e d e c a y o f t h e F I D , a d d i t i o n a l f a c t o r s , s u c h as m a g n e t i c f i e l d i n h o m o g e n e i t i e s , i n c r e a s e t h e r a t e o f t h e d e c a y a n d t h u s , t h e t r u e T 2 v a l u e c a n n o t b e m e a s u r e d d i r e c t l y f r o m t h e F I D e n v e l o p e . T h e s e q u e n c e u s e d t o m e a s u r e t h i s r e l a x a t i o n p a r a m e t e r , t h e s p i n - e c h o s h o w n i n F i g u r e 1 .6 , r e f o c u s s e s t h e m a g n e t i c f i e l d i n h o m o g e n e i t i e s b u t h a s n o e f f e c t o n T 2 r e l a x a t i o n . T h e 90° p u l s e i n t h e s e q u e n c e t i p s t h e z - m a g n e t i z a t i o n i n t o t h e x , y - p l a n e . T h e i n d i v i d u a l v e c t o r s f a n o u t d u e t o f i e l d i n h o m o g e n e i t i e s t h a t c a u s e L a r m o r p r e c e s s i o n a l f r e q u e n c i e s f a s t e r o r s l o w e r t h a n t h e a v e r a g e . A f t e r a d u r a t i o n r t h e 180° p u l s e r o t a t e s t h e v e c t o r s t o a n e w p o s i t i o n so t h a t t h e f a s t e r v e c t o r s l a g b e h i n d t h e s l o w e r o n e s a n d t h e d i f f e r e n t p r e c e s s i o n f r e q u e n c i e s c a u s e t h e v e c t o r s t o r e f o c u s a f t e r a n o t h e r r d e l a y . T h e r e f o c u s s e d v e c t o r , h o w e v e r , h a s d e c r e a s e d i n m a g n i t u d e as a r e s u l t o f t r u e T 2 d e p h a s i n g a c c o r d i n g t o E q u a t i o n 1.8 w h e r e t h e t i m e - t o - e c h o (T#) i s e q u a l t o 2 r . MX)y = M0e~^ (1.8) T h e m e c h a n i s m s f o r Ti a n d T 2 r e l a x a t i o n a r e l i m i t e d t o t h o s e t h a t p r o d u c e f l u c -t u a t i n g m a g n e t i c f i e l d s t o i n d u c e t r a n s i t i o n s b e t w e e n n u c l e a r s p i n l e v e l s . F o r s p i n - | n u -c l e i , t h e r e a r e a n u m b e r o f p h y s i c a l m e c h a n i s m s w h i c h p r o v i d e t h e a p p r o p r i a t e c o n d i t i o n s . 19 (a) 180c 90c T R (b) x dela^  90c (c) Relative Intensity 1.0 i 0.5 H 0.0 -0.5 i •1.0 x(s) Figure 1.5: The inversion recovery experiment for measuring T i , (a) the pulse sequence, (b) the vector description of the effect of (a) on the net magnetization vector, and (c) Equation 1.7 plotted with Ti values of one second (thick line) and five seconds (thin line). 20 (a) 90c 180c (b) 90c az ( c ) 1.0 0.8 Relative Intensity 0.6 0.4 0.2 0.0 F i g u r e 1.6: T h e s p i n - e c h o e x p e r i m e n t f o r m e a s u r i n g T 2 , (a ) t h e p u l s e s e q u e n c e , ( b ) t h e v e c t o r d e s c r i p t i o n o f t h e e f fec t o f (a ) o n t h e n e t m a g n e t i z a t i o n a n d o n t h e i n d i v i d u a l m a g n e t i z a t i o n v e c t o r s i n t h e x , y - p l a n e f o r a n o n - r e s o n a n c e e x p e r i m e n t , a n d (c ) E q u a t i o n 1.8 p l o t t e d w i t h T 2 v a l u e s o f f i v e m i l l i s e c o n d s ( t h i c k l i n e ) a n d t w e n t y - f i v e m i l l i s e c o n d s ( t h i n l i n e ) . 21 D i p o l e - d i p o l e i n t e r a c t i o n s a r e t h e m o s t i m p o r t a n t r e l a x a t i o n m e c h a n i s m f o r m o l e c u l e s i n s o l u t i o n . T h e y m a y b e m o d u l a t e d b y m o l e c u l a r t u m b l i n g o r b y t r a n s l a t i o n a l d i f f u s i o n . D i p o l a r i n t e r a c t i o n s w i t h u n p a i r e d e l e c t r o n s a r e a n o t h e r r e l a x a t i o n m e c h a n i s m w h i c h is o f t e n d e l i b e r a t e l y p r o m o t e d b y t h e u s e o f p a r a m a g n e t i c s a l t s , s u c h as C U S O 4 , t o d e c r e a s e t h e r e l a x a t i o n t i m e s . D i p o l a r i n t e r a c t i o n s w i t h e l e c t r o n s a r e m u c h l a r g e r t h o s e w i t h n u c l e i b e c a u s e t h e m a g n e t i c m o m e n t s o f e l e c t r o n s a r e v e r y l a r g e i n c o m p a r i s o n t o t h o s e o f n u c l e i . A n o t h e r m e c h a n i s m o f r e l a x a t i o n is t h r o u g h s c a l a r c o u p l i n g . W h e n o n e s p i n , I, i s c o u p l e d t o a n o t h e r s p i n , S , t h e r e a r e t w o p a t h w a y s w h i c h c a n l e a d t o r e l a x a t i o n o f t h e I s p i n . T h e T y p e 1 s c a l a r r e l a x a t i o n m e c h a n i s m f o r I o c c u r s w h e n t h e s c a l a r c o u p l i n g w i t h S i s t i m e -d e p e n d e n t , s u c h as i n a r a p i d c h e m i c a l e x c h a n g e p r o c e s s , w h i c h r e s u l t s i n t h e g e n e r a t i o n o f a f l u c t u a t i n g f i e l d . T h e T y p e 2 s c a l a r r e l a x a t i o n o c c u r s w h e n S h a s a v e r y s h o r t r e l a x -a t i o n t i m e . A t h i r d m e c h a n i s m o f r e l a x a t i o n is c h e m i c a l s h i e l d i n g a n i s o t r o p y ( C S A ) . A s m e n t i o n e d p r e v i o u s l y , e l e c t r o n s i n a m o l e c u l e s h i e l d t h e n u c l e u s f r o m t h e a p p l i e d m a g n e t i c f i e l d . W h e n t h e s h i e l d i n g i s n o t s y m m e t r i c a l , m o l e c u l a r t u m b l i n g l e a d s t o f l u c t u a t i n g l o c a l m a g n e t i c f i e l d s a n d i n c r e a s e d r e l a x a t i o n r a t e s . C o h e r e n t m o l e c u l a r r o t a t i o n c a n a l s o g e n e r -a t e a m a g n e t i c f i e l d , d u e t o t h e m o t i o n s o f t h e e l e c t r o n s , w h i c h c a n c o u p l e w i t h t h e n u c l e a r s p i n a n d p r o v i d e a n o t h e r r e l a x a t i o n p a t h w a y . T h e o v e r a l l r e l a x a t i o n r a t e f o r a p a r t i c u l a r s p e c i e s i s a s u m o f t h e r e c i p r o c a l r e l a x a t i o n r a t e s f o r t h e v a r i o u s m e c h a n i s m s . T h e d o m i n a n t m e c h a n i s m o f r e l a x a t i o n f o r s p i n - | n u c l e i , d i p o l a r c o u p l i n g , i s m o d -u l a t e d b y r e o r i e n t a t i o n d u e t o m o l e c u l a r m o t i o n s . T h e r e l a x a t i o n r a t e s , 1/Ti a n d 1 / T 2 , c a n b e d e t e r m i n e d f r o m t h i s r e l a x a t i o n m e c h a n i s m a n d a r e e x p r e s s e d i n t h e B l o e m b e r g e n -P u r c e l l - P o u n d e q u a t i o n s , 1.9 a n d 1.10 [60], w h e r e r i s t h e i n t e r n u c l e a r d i s t a n c e , LOQ i s t h e p r e c e s s i o n f r e q u e n c y a n d r c i s t h e c h a r a c t e r i s t i c c o r r e l a t i o n t i m e , a m e a s u r e o f t h e r a t e o f m o l e c u l a r r e o r i e n t a t i o n . r c c a n b e r e g a r d e d as t h e " t i m e b e t w e e n j u m p s " s o as t h e m o l e c -u l a r m o t i o n d e c r e a s e s , t h e v a l u e o f TC i n c r e a s e s . T h e t w o r e l a x a t i o n t i m e s e x h i b i t d i f f e r e n t b e h a v i o u r s w i t h r e s p e c t t o m o l e c u l a r m o t i o n c h a n g e s i n t h e s y s t e m . I n a l o g - l o g p l o t o f t h e r e l a x a t i o n t i m e as a f u n c t i o n o f t h e r c , t h e T i t i m e e x h i b i t s a V - s h a p e d b e h a v i o u r w i t h t h e m i n i m u m g i v e n b y u0rc ?»0.62. T o t h e f a s t e r m o t i o n s i d e o f t h e m i n i m u m , T i i n c r e a s e s 22 as the motion increases. However, on the slower motion side of the min imum, T i increases wi th decreasing motion. In contrast, the T 2 value decreases fairly regularly wi th decreasing motion. ± = A 2 ^ r rc 4re Ti 10 r 6 L l + u;0\2 1 + ^ f a 2 1 j 7^ = 2 0 ^ ^ + ITa^ + IT^? ] ( L 1 0 ) 1.2.3 Diffusion Measurements by N M R The effect of diffusion in an inhomogeneous magnetic field on the spin-echo experiment was described in the pioneering work of N M R by Hahn [61], Carr and Purcel l [62]. After a 90° pulse, the nuclear spins dephase due to a spread of Larmor precession frequencies caused by irregularities in the main magnetic field. The 180° pulse of the spin-echo experiment refocusses the magnetization but only for spins whose Larmor precession frequencies have remained constant for the duration of the experiment [63]. When a spin diffuses in an inhomogeneous magnetic field, it may enter a region where the local magnetic field is different and thus, its precessional frequency wi l l change. The magnetization of this spin, and al l others that have diffused in a similar manner, wi l l not be refocussed completely by the 180° pulse and the overall echo amplitude wi l l decrease as a result. The effect of diffusion on the echo amplitude can be used to measure the self-diffusion coefficient in an experiment where a magnetic field gradient is deliberately applied to cause incomplete refocussing of the echo. The most efficient method, the pulsed-gradient spin-echo ( P G S E ) technique, was introduced in the mid-1960s [64]. In this experiment, shown in Figure 1.7, the magnetic field gradient is applied in two pulses. The spacing, A , and duration, 5, of the two pulses can be varied while maintaining a constant T#, thus keeping the T 2 dephasing constant between experiments. Assuming a Gaussian model for diffusion, the echo attenuation at constant T E is given by Equation 1.11 where AG(TE) is the amplitude at T# when the gradient is applied, A 0 ( T E ) is the amplitude at T# in 23 rf pulses 90 c T R 180 c gradient pulses T E F i g u r e 1.7: T h e p u l s e s e q u e n c e f o r t h e P G S E e x p e r i m e n t . t h e a b s e n c e o f t h e g r a d i e n t , G is t h e s t r e n g t h o f t h e a p p l i e d m a g n e t i c field g r a d i e n t a n d D i s t h e s e l f - d i f f u s i o n c o e f f i c i e n t . T h e e c h o a m p l i t u d e c a n b e a l t e r e d b y c h a n g i n g a n y o r a l l o f A , 5, o r G . T h e P G S E e x p e r i m e n t d e t e r m i n e s t h e s e l f - d i f f u s i o n c o e f f i c i e n t f r o m t h e d i s p l a c e m e n t o f t h e s p i n s i n t h e d i r e c t i o n o f t h e m a g n e t i c f i e l d g r a d i e n t d u r i n g a d i f f u s i o n t i m e o f (A-5/3) [63]. MTE) = -Dj2S2(A - f)G72 MTE) (1.11) 1.2.4 Z-Spectroscopy N M R s t u d i e s o f p o l y m e r s a r e d i f f i c u l t t o p e r f o r m b e c a u s e t h e r i g i d e n v i r o n m e n t o f t h e p o l y m e r c h a i n s l e a d s t o v e r y b r o a d s p e c t r a l l i n e s . Z - s p e c t r o s c o p y i s a t e c h n i q u e t h a t u t i l i z e s d i p o l a r c o u p l i n g b e t w e e n t h e m o b i l e p r o t o n s o f a l i q u i d a n d t h e r i g i d p r o t o n s o f a s e m i - s o l i d m a t e r i a l t o g a i n i n f o r m a t i o n a b o u t t h e m a t e r i a l [65]. T h e p u l s e s e q u e n c e , s h o w n i n F i g u r e 1 .8 , h a s a l o n g , w e a k r f p u l s e t h a t s a t u r a t e s o r p a r t i a l l y s a t u r a t e s t h e p r o t o n s o f 24 90° weak rf pulse A the semi-solid in the system. Because of the dipolar coupling between the protons of the liquid and the semi-solid, the amplitude of the spectrum of the liquid protons, acquired by the on-resonance 90° pulse, depends on the T\ and T 2 relaxation times of the protons of the semi-solid, as well as on the ratio of the number of semi-solid to liquid protons and the magnetization transfer rate between them. The effect of the pulse on the spins of the semi-solid material will vary with the resonance offset of the preparation pulse and hence, the amplitude of the spectrum of the liquid spins will also vary. The z-spectrum is the plot of the normalized signal amplitude of the liquid component as a function of the off-set frequency. The inverse of the z-spectrum is similar in shape to the wide-line 1 H N M R spectrum of the solid-like component and reflects the internal mobility of the solid-like component in the sample [65]. The liquid-solid system can be modelled as a pair of spin baths, A and B , interacting via intermolecular dipole-dipole interactions. The system can be described in the rotating frame by a set of six coupled Bloch equations for spins in the presence of an rf field [66]. If the rf field is assumed to partially saturate the B spins without directly affecting the A spins, then the transverse components of A may be neglected. This assumption is only valid when the preparation pulse frequency is far from the A spin resonance frequency. The steady state solution of the remaining four equations is given by Equation 1.12 [66]. In these equations, A is the offset of the rf field from the A resonance, / is the ratio of the number of B spins to the number of A spins, u>i is the amplitude of the rf field of the preparation pulse, R^ and R# are the spin-lattice relaxation rates for the A and B spins, RBA is the rate of cross-relaxation between the A and B spins, and M^° is the equilibrium 25 l o n g i t u d i n a l m a g n e t i z a t i o n i n t h e a b s e n c e o f a n y r f f i e l d s . I n t h e l i m i t w h e r e RBA/RA ^ 1, t h e e q u a t i o n c a n b e r e d u c e d t o E q u a t i o n 1.13 w h i c h i s v e r y s i m i l a r t o t h e e x p r e s s i o n f o r s t e a d y s t a t e z - m a g n e t i z a t i o n f o r t h e B s p i n s e x c e p t f o r t h e TIB/JTIA t e r m . I n t h e c a s e % w h e r e /TIA ^> TIB, MA i s e x a c t l y t h e s t e a d y - s t a t e m a g n e t i z a t i o n o f s p i n B i n a n r f f i e l d . T h u s , t h e z - s p e c t r u m w o u l d , u n d e r c e r t a i n c o n d i t i o n s , y i e l d t h e s p e c t r u m o f t h e B s p i n s y s t e m [66]. < = pzw; (1-12) a _ fRBAT2B^] 2RARB 7= T | f l [ ^ + / ( ^ + l)] W Z Mf-Mj(t) U\T\BT2B (1 + 4 T T 2 T | 5 A 2 ) ( 1 + ^ ) + U J \ T I B T W J ( 1 . 1 3 ) 1.3 Nuclear Magnetic Resonance Imaging 1.3.1 One-dimensional Imaging O n e - d i m e n s i o n a l N M R i m a g i n g w a s f i r s t i n t r o d u c e d i n 1 9 7 3 [34, 35] as a n e x t e n s i o n o f t h e N M R e x p e r i m e n t w h e r e a m a g n e t i c f i e l d g r a d i e n t w a s u s e d t o b r o a d e n t h e f r e q u e n c y o f t h e N M R s i g n a l i n t h e d i r e c t i o n o f t h e a p p l i e d g r a d i e n t . I n F i g u r e 1 .9 , a n e x a m p l e w i t h t w o t u b e s o f w a t e r i s p r e s e n t e d . I n t h e t r a d i t i o n a l N M R e x p e r i m e n t , t h e m a g n e t i c f i e l d i s h o m o g e n e o u s , a n d t h e N M R s p e c t r u m c o n t a i n s a s i n g l e p e a k a t t h e r e s o n a n c e f r e q u e n c y f o r w a t e r . I n t h e o n e - d i m e n s i o n a l i m a g i n g e x p e r i m e n t , a l i n e a r m a g n e t i c field g r a d i e n t i s a p p l i e d t o t h e s a m p l e t o i n t r o d u c e a c o n t r o l l e d m a g n e t i c field i n h o m o g e n e i t y . T h e w a t e r 26 (b) -•x (c) frequency F i g u r e 1.9: A n e x a m p l e o f a o n e - d i m e n s i o n a l i m a g i n g e x p e r i m e n t , (a ) t w o t u b e s o f w a t e r i n t h e r f c o i l , ( b ) t h e a p p l i e d m a g n e t i c field g r a d i e n t , G ^ , w h i c h a d d s t o t h e m a i n m a g n e t i c field a n d (c ) t h e r e s u l t i n g N M R s p e c t r u m w h i c h r e f l e c t s t h e p o s i t i o n o f t h e t u b e s i n t h e g r a d i e n t . 27 90° 180° A rf pulses T R T E frequency-encoding gradient pulses F i g u r e 1.10: T h e s p i n - e c h o p u l s e s e q u e n c e u s e d t o a c q u i r e o n e - d i m e n s i o n a l i m a g e s . i n e a c h o f t h e t u b e s n o w e x p e r i e n c e s d i f f e r e n t a p p l i e d m a g n e t i c f i e l d s a n d t h e L a r m o r f r e q u e n c y f o r a p a r t i c u l a r w a t e r m o l e c u l e i n t h e s a m p l e v a r i e s as g i v e n b y E q u a t i o n 1.14, w h e r e uo i s t h e a n g u l a r m o m e n t u m g e n e r a t e d b y t h e m a i n m a g n e t i c f i e l d , Gx i s t h e g r a d i e n t s t r e n g t h a n d x i s t h e p o s i t i o n i n t h e g r a d i e n t . I n e a r l y N M R i m a g i n g e x p e r i m e n t s , t h e m a g n e t i c f i e l d g r a d i e n t w a s a p p l i e d d u r i n g t h e a c q u i s i t i o n o f t h e F I D i n a b a s i c 9 0 ° p u l s e e x p e r i m e n t . R e c e n t m e t h o d s h a v e i n c o r -p o r a t e d t h e s p i n - e c h o t o s e p a r a t e d a t a a c q u i s i t i o n f r o m t h e p u l s e s a n d g r a d i e n t s w i t c h i n g p o s i t i o n s . A t y p i c a l s e q u e n c e u s e d t o a c q u i r e o n e - d i m e n s i o n a l i m a g e s i s s h o w n i n F i g -u r e 1.10. B e c a u s e t h e s e q u e n c e i s s y m m e t r i c a l a b o u t t h e 1 8 0 ° p u l s e , t h e e n t i r e e c h o c a n b e r e c o r d e d r a t h e r t h a n j u s t t h e F I D , r e s u l t i n g i n a y/2 g a i n i n s i g n a l - t o - n o i s e . T h e r e l a -t i o n s h i p b e t w e e n t h e c o n c e n t r a t i o n o f s p i n s , p(x) a n d t h e s i g n a l o b t a i n e d w i t h t h e i m a g i n g e x p e r i m e n t , S ( x ) , w h e r e x i s t h e p o s i t i o n i n a n x - g r a d i e n t , i s g i v e n i n E q u a t i o n 1.15. T o o b t a i n a q u a n t i t a t i v e N M R s i g n a l d i r e c t l y r e l a t a b l e t o c o n c e n t r a t i o n , t h e e x p e r i m e n t a l p a -r a m e t e r s TR a n d TE m u s t b e c h o s e n s u c h t h a t TR T i ( x ) a n d T E <C T 2 ( X ) i s t r u e f o r t h e e n t i r e s a m p l e . I n p r a c t i c e , t h e TR t i m e s h o u l d b e f i v e t i m e s t h e m a x i m u m T i v a l u e p r e s e n t to = CJQ + ^Gxx 28 i n t h e s a m p l e a n d t h e T E t i m e s h o u l d b e as s h o r t as p o s s i b l e c o m p a r e d t o t h e m i n i m u m T 2 v a l u e p r e s e n t i n t h e s a m p l e . A n i m a g i n g e x p e r i m e n t c a n a l s o b e u s e d t o m e a s u r e t h e T2 ( o r T i ) d i s t r i b u t i o n i n a s a m p l e i n t h e d i r e c t i o n o f t h e g r a d i e n t b y v a r y i n g T # ( o r TR) w i t h a l l o t h e r f a c t o r s k e p t c o n s t a n t . A s t h e f r e q u e n c y d i s t r i b u t i o n i n a o n e - d i m e n s i o n a l i m a g e i s d e s c r i b e d b y a f i n i t e n u m b e r o f p o i n t s , e a c h p o i n t r e p r e s e n t s t h e s i g n a l f r o m a r e g i o n o f w i d t h Ax, r a t h e r t h a n a fixed p o s i t i o n , x , i n t h e s a m p l e . T h e p a r a m e t e r A a ; i s t h e r e s o l u t i o n o f t h e e x p e r i m e n t a n d i s a f u n c t i o n o f t h e n u m b e r o f p o i n t s , t h e s t r e n g t h o f t h e g r a d i e n t a n d t h e g y r o m a g n e t i c r a t i o o f t h e n u c l e u s . S(x) = C p(x) (1 - e W ) ( e w ) (1.15) 1.3.2 Slice Selection D i s c u s s i o n s o f N M R i m a g i n g e x p e r i m e n t s , a l s o k n o w n as m a g n e t i c r e s o n a n c e i m a g i n g ( M R I ) , o f t e n i n c l u d e t h e c o n c e p t o f s l i c e s e l e c t i o n . T h e s e s l i c e s a r e n o t p h y s i c a l d i s s e c t i o n s o f t h e s a m p l e b u t a r e s e l e c t e d p l a n e s o f t h e s a m p l e f r o m w h i c h t h e N M R s i g n a l i n t e n s i t y i s m e a s u r e d . S l i c e s e l e c t i o n i n c o r p o r a t e s t w o c o m p o n e n t s , a l i n e a r m a g n e t i c field g r a d i e n t a n d a f r e q u e n c y - s e l e c t i v e r f p u l s e . W h e n t h e s e l e c t i v e p u l s e i s a p p l i e d a t t h e s a m e t i m e as t h e m a g n e t i c f i e l d g r a d i e n t s p r e a d s o u t t h e r e s o n a n c e f r e q u e n c i e s o f t h e s a m p l e , a l i m i t e d r e g i o n o f t h e s a m p l e , as s h o w n i n F i g u r e 1.11, i s e x c i t e d b y t h e r f p u l s e . A s m a l l n e g a t i v e g r a d i e n t i s u s e d i m m e d i a t e l y a f t e r t h e s l i c e - s e l e c t i o n p r o c e d u r e t o r e f o c u s t h e m a g n e t i z a t i o n i n t h e s l i c e . O n l y t h e s i g n a l f r o m t h i s p l a n e o f t h e s a m p l e w i l l b e a f f e c t e d b y f u r t h e r p u l s e s a n d a p p e a r i n t h e r e s u l t i n g N M R i m a g e . T h e s l i c e t h i c k n e s s , u s u a l l y q u o t e d i n m i c r o m e t r e s , i s c a l c u l a t e d b y d i v i d i n g t h e e x c i t a t i o n b a n d w i d t h o f t h e p u l s e b y t h e p r o d u c t o f t h e g r a d i e n t s t r e n g t h a n d t h e g y r o m a g n e t i c r a t i o o f t h e n u c l e u s . T r a d i t i o n a l r f p u l s e s , m e a n t t o e x c i t e a w i d e f r e q u e n c y r a n g e , a r e r e c t a n g u l a r s t e p f u n c t i o n s w h e r e t h e r f p o w e r is s w i t c h e d o n f o r m i c r o s e c o n d s a n d t h e n s w i t c h e d off. T h e r e i s a F o u r i e r t r a n s f o r m r e l a t i o n s h i p b e t w e e n t h e s h a p e a n d d u r a t i o n o f a p u l s e a n d i t s e x c i t a t i o n 29 F i g u r e 1.11: T h e s l i c e - s e l e c t i o n p r o c e s s i n N M R i m a g i n g , (a ) t h e a p p l i e d z - g r a d i e n t , ( b ) a s a m p l e i n t h e g r a d i e n t , (c ) t h e s p r e a d o f f r e q u e n c i e s f r o m s a m p l e ( b ) as a r e s u l t o f t h e a p p l i e d g r a d i e n t , a n d (d ) t h e e x c i t a t i o n w i d t h , A w , o f t h e s e l e c t i v e p u l s e w h i c h c o r r e s p o n d s t o a p a r t i c u l a r r e g i o n o f t h e o r i g i n a l s a m p l e , as i n d i c a t e d b y t h e s h a d e d b o x i n ( b ) . 30 frequency. A short rectangular pulse has a wide excitation range and a sine shape (sinx/x) after Fourier transformation. B y the same relationship, the original pulse must be long and shaped similarly to a sine function to obtain a narrow rectangular excitation profile. 1 . 3 . 3 T w o - d i m e n s i o n a l I m a g i n g The first two-dimensional imaging technique was part of the pioneering work of N M R imaging [34] where the two-dimensional image of two tubes of water was obtained by the mathematical back-projection of a series of one-dimensional images taken along different axes. In contrast, the two-dimensional Fourier imaging technique, developed in 1975 [67], incorporated an additional magnetic field gradient directly in the pulse sequence to spatially resolve the N M R signal in a second dimension. In a one-dimensional imaging experiment, the gradient encodes spatial information in the frequencies of the detected signal and is therefore called a frequency-encoding gradient. The second gradient in the two-dimensional experiment encodes spatial information in the phase of the detected signal and is termed the phase-encoding gradient. The scheme in Figure 1.12 shows how the combined phase-and frequency-encoding can uniquely characterize a specific region of the sample. The phase angle acquired at a position in the sample is given by Equation 1.16 where UJQ is the precessional frequency, Gy is the strength of a y-gradient, and y is the position wi th in the gradient and t i is the duration of the gradient. The second dimension of the N M R imaging experiment is obtained by modulating the phase angle in the experiment. The Fourier imaging method, shown in Figure 1.13, obtained the phase modulation by increasing the t i time in successive experiments. How-ever, the method also introduced the problem of increased T 2 relaxation wi th increasing t j . The spin-warp modification circumvented this problem by varying the gradient strength in Equation 1.16 while keeping the t i time constant [69]. A spin-echo was also introduced into the sequence for the same reasons as in the one-dimensional experiment, to move the 31 (a) (c) I \ L \ I \ I \ L \ L \ L \ I \ t L \ L \ I \ I \ L \ L \ I \ < r = i i i A t t t - • x (d) r < ? V •<fv f t A t t t <3= «7 t X F i g u r e 1 .12 : P h a s e a n d f r e q u e n c y e n c o d i n g o f a s a m p l e d i v i d e d i n t o 16 v o x e l s , (a ) t h e n u c l e a r s p i n s i n t h e x , y - p l a n e a f t e r t h e 90° p u l s e , ( b ) t h e d i f f e r e n t i a l p r e c e s s i o n o f t h e s p i n s d u r i n g t h e a p p l i c a t i o n o f t h e y - g r a d i e n t , (c ) t h e r e s u l t i n g p h a s e - e n c o d i n g o f t h e v o x e l s o n c e t h e y - g r a d i e n t i s r e m o v e d , a n d (d ) t h e f r e q u e n c y - e n c o d i n g o f t h e s p i n s as t h e x - g r a d i e n t i s a p p l i e d . E a c h v o x e l i n ( d ) i s u n i q u e l y i d e n t i f i e d b y t h e c o m b i n e d p h a s e a n d p r e c e s s i o n f r e q u e n c y o f t h e s p i n . 3 2 selective 90° A rf pulses A A A A A / V V V V V slice-selection gradient phase-encoding gradient frequency-encoding gradient F i g u r e 1 .13 : T h e p u l s e s e q u e n c e f o r t h e t w o - d i m e n s i o n a l F o u r i e r i m a g i n g e x p e r i m e n t . T h e F I D r e f l e c t s t h e l o c a l f r e q u e n c i e s i n d u c e d b y e a c h g r a d i e n t [68]. 3 3 a c q u i s i t i o n a w a y f r o m t h e p u l s e s a n d t o i n c r e a s e t h e s i g n a l - t o - n o i s e r a t i o b y y/2. T h e final t w o - d i m e n s i o n a l i m a g e i s o b t a i n e d b y p e r f o r m i n g a F o u r i e r t r a n s f o r m a t i o n o n b o t h t h e f r e q u e n c y a n d p h a s e d o m a i n s o f t h e t w o - d i m e n s i o n a l d a t a s e t . T h e s p i n - w a r p i m a g i n g p u l s e s e q u e n c e , s h o w n i n F i g u r e 1 .14 , i s u s u a l l y p e r f o r m e d w i t h a s e l e c t i v e 90° p u l s e t o o b t a i n t h e i m a g e . T h e c h o i c e o f g r a d i e n t d i r e c t i o n f o r e a c h o f t h e s l i c e - s e l e c t i v e , p h a s e - e n c o d i n g a n d f r e q u e n c y - e n c o d i n g g r a d i e n t s d e p e n d s o n t h e r e g i o n o f t h e s a m p l e d e s i r e d f o r t h e i m a g e . A s i n t h e o n e - d i m e n s i o n a l i m a g i n g , t h e e x p e r i m e n t s a r e p e r f o r m e d w i t h a finite n u m b e r o f p o i n t s i n t h e f r e q u e n c y d o m a i n a n d a n e q u a l n u m b e r o f i n c r e m e n t s o f t h e p h a s e - e n c o d i n g g r a d i e n t p r o d u c i n g a n N x N p i x e l i m a g e . E a c h p i x e l c o n t a i n s t h e N M R s i g n a l f r o m a v o l u m e e l e m e n t , o r v o x e l , g i v e n b y t h e p r o d u c t o f t h e s l i c e t h i c k n e s s a n d t h e s q u a r e o f t h e r e s o l u t i o n . T h e s i g n a l i n t e n s i t y , S ( x , y ) , f r o m e a c h v o x e l i s a l s o r e l a t e d t o t h e c o n c e n t r a t i o n o f s p i n s , p(x,y), b y E q u a t i o n 1 .15 . T h e s i g n a l w i l l b e q u a n t i t a t i v e w h e n TR ^> T i ( x , y ) a n d T E <C T 2 ( x , y ) . T h e v a r i a t i o n o f t h e T R a n d TE; p a r a m e t e r s c a n a l s o b e u s e d t o o b t a i n a t w o - d i m e n s i o n a l m a p o f t h e T i a n d T 2 d i s t r i b u t i o n i n t h e s l i c e . 1.4 Goals of the Thesis Research T h e g r o w i n g u s e o f s w e l l i n g - c o n t r o l l e d d r u g d e l i v e r y n e c e s s i t a t e s a d e t a i l e d u n d e r s t a n d i n g o f t h e s w e l l i n g a n d d r u g r e l e a s e b e h a v i o u r f o r t h e s e s y s t e m s . N M R i m a g i n g , i n c o m b i n a t i o n w i t h N M R s p e c t r o s c o p y , i s p r e s e n t e d as a n i d e a l t o o l t o g a i n n e w i n s i g h t i n t o t h e b e h a v i o u r o f s w e l l i n g h y d r o p h i l i c m a t r i c e s . T h e a b i l i t y o f t h e t e c h n i q u e t o p r o v i d e c o n c e n t r a t i o n i n f o r m a t i o n f o r d i f f e r e n t c h e m i c a l s p e c i e s i s f u l l y e x p l o i t e d . T h e h y d r o p h i l i c m a t r i x t a b l e t c h o s e n f o r t h e s t u d y c o n t a i n e d H P M C as t h e h y -d r o p h i l i c p o l y m e r a n d o n e o f t w o fluorinated c o m p o u n d s , t r i f l u p r o m a z i n e - H C l o r 5 - f l u o r o -u r a c i l , as m o d e l d r u g s . S p e c t r o s c o p i c s t u d i e s o f p r e p a r e d m i x t u r e s o f t h e p o l y m e r , w a t e r , a n d d r u g s a r e p r e s e n t e d i n C h a p t e r 2. T h e s e p r e l i m i n a r y i n v e s t i g a t i o n s p r o v i d e a d e t a i l e d u n d e r s t a n d i n g o f t h e d e p e n d e n c e o f t h e d i f f u s i v i t y o f t h e s p e c i e s a n d t h e T i a n d T 2 n u c l e a r r e l a x a t i o n t i m e s o n t h e c o n c e n t r a t i o n o f H P M C i n t h e s y s t e m . T h i s c h a p t e r a l s o d i s c u s s e s 34 180° selective 90° I I rf pulses slice-selection gradient _ ti phase-encoding I gradient frequency-encoding gradient F i g u r e 1 .14: T h e p u l s e s e q u e n c e f o r t h e t w o - d i m e n s i o n a l s p i n - w a r p i m a g i n g e x p e r i m e n t . 35 the mobil i ty changes in the H P M C as a function of its concentration in the mixtures. Chapters 3 and 4 develop the N M R imaging protocol required to obtain quantitative species distributions within a swelling polymer tablet. A simple geometrical arrangement for the swelling tablet is introduced that allows quantitative distributions for the water and polymer to be obtained rapidly. Chapter 3 focusses on the water in the system and tests various factors that may influence the swelling behaviour of the tablet. The method of calculating the polymer concentration from one-dimensional imaging data is presented and the polymer distributions are compared for different systems. A i r bubbles in the swollen gel, the most significant factor affecting the polymer distribution results, are discussed separately in Chapter 4 where a method for removing air from the dry tablet is presented. Chapter 5 contains the results of drug imaging studies performed in a similar manner to Chapters 3 and 4. The model drugs chosen for this study both contained fluorine so that their N M R signal could be observed without interference from the abundant water signal. Fluorine is an ideal nucleus for these imaging studies because of its high sensitivity, second only to water, and the lack of background signal from other species in the system. The distributions of the two drugs are compared to gain an understanding of the factors that affect drug release. The drug images are also used to calculate polymer distributions which are then compared with the distributions obtained from the water images. Chapter 6 describes preliminary modelling investigations of the quantitative water, polymer and drug distributions obtained in Chapters 4 and 5. The in i t ia l modelling cal-culations assumed that the movement of all three species could be described by Fick ian diffusion equations. A segmented tablet model for describing the polymer movement was also investigated. In this second model, the tablet is divided into segments, each of which swell according to the amount of water present, and the sum of the individual swellings results in the overall swelling of the tablet. The final chapter provides conclusions and suggestions for future work. 36 C h a p t e r 2 S p e c t r o s c o p i c I n v e s t i g a t i o n s o f M i x t u r e s C o n t a i n i n g H P M C , M o d e l D r u g s , a n d W a t e r 2.1 Introduction O n e o f t h e a i m s o f t h e t h e s i s r e s e a r c h w a s t o o b t a i n q u a n t i t a t i v e c o n c e n t r a t i o n d i s t r i b u -t i o n s f o r t h e c o m p o n e n t s o f a s w e l l i n g h y d r o p h i l i c m a t r i x t a b l e t i n o r d e r t o g a i n a b e t t e r u n d e r s t a n d i n g o f t h e f a c t o r s t h a t g o v e r n c o n t r o l l e d d r u g r e l e a s e f r o m t h e s e s y s t e m s a t t h e m o l e c u l a r l e v e l . T o e n s u r e t h a t t h e N M R i m a g i n g e x p e r i m e n t s p r o v i d e d t h e d e s i r e d i n -f o r m a t i o n , a d e t a i l e d k n o w l e d g e o f t h e N M R r e l a x a t i o n t i m e s o f e a c h c o m p o n e n t o f t h e m a t r i x w a s r e q u i r e d . I n a d d i t i o n , t h e n a t u r e o f t h e h y d r o p h i l i c m a t r i x w a s e x p e c t e d t o d e p e n d o n t h e a m o u n t o f w a t e r p r e s e n t a n d t h e d e g r e e o f t a b l e t s w e l l i n g . T h u s , a s t u d y o f t h e e f f e c t o f d i f f e r e n t H P M C c o n c e n t r a t i o n s o n t h e N M R r e l a x a t i o n p a r a m e t e r s , as w e l l as o n t h e d i f f u s i v i t y o f t h e w a t e r a n d t h e m o d e l d r u g s t h r o u g h t h e p o l y m e r m a t r i x , w a s a l s o n e c e s s a r y . T h e w a t e r a n d d r u g c o m p o n e n t s i n t h e m a t r i x c a n b e m e a s u r e d d i r e c t l y b u t N M R s t u d i e s o f h y d r a t e d H P M C a n d o t h e r p o l y m e r s i n t h e g e l s t a t e a r e h a m p e r e d b y t h e i r b r o a d s p e c t r a l l i n e s a n d s h o r t r e l a x a t i o n t i m e s . H o w e v e r , as w i l l b e s h o w n , t h e c h a r -a c t e r i s t i c s o f t h e p o l y m e r c a n b e i n f e r r e d i n d i r e c t l y t h r o u g h t h e i n f l u e n c e o f t h e p o l y m e r o n o t h e r c o m p o n e n t s i n t h e s y s t e m . I n m i x t u r e s o f p o l y m e r , d r u g a n d w a t e r , t h e d r u g a n d t h e w a t e r c a n e x i s t i n v a r i o u s s t a t e s w h i c h a r e d e f i n e d i n t e r m s o f t h e i r i n t e r a c t i o n s w i t h t h e p o l y m e r . A s p e c i e s i n a f r e e 37 state has no interaction with the polymer and its movement is not hindered by the polymer in any way. When there is a bonding interaction with the polymer, the species is in a bound state which can vary in degree from a minor interaction to complete immobil izat ion. Also, there may be multiple distinct bound states which introduces the possibility of exchange between states. N M R relaxation times depend strongly on the mobil i ty of a species, as discussed in Section 1.2.2, and, therefore, the different states for a species would exhibit different N M R properties. Self-diffusion coefficients would also be affected by the nature of different states because the overall translational motion of a species would decrease as a result of the residency time in the less-mobile bound states. When there are free and bound states for a particular species, the rate of exchange between the different states has a significant effect on the resulting T 2 properties of the system. If the rate of exchange is fast with respect to the rate of relaxation of the species in the N M R experiment then the measured T 2 parameter is an average of the values for the different states weighted by the fraction of time the species resides in each state as shown in Equation 2.1 where p,- is the fraction residing in the i t h state [70]. When the rate of exchange is slow compared to the relaxation, then the N M R properties of the separate states are not averaged and the value of the parameter for each state is apparent in the experimental results. The latter system is st i l l straightforward to interpret i f there are only a few distinct states. When there are multiple states with a range of different relaxation rates, the analysis of the multiexponential decay behavior becomes more complex and requires non-linear least-squares calculations. 2.2 Experimental 2 . 2 . 1 P r e p a r a t i o n o f M i x t u r e s The structures for the materials used in this t h e s i s—H P M C [71], triflupromazine-1 = E pi T2,i 38 o F i g u r e 2 . 1 : S t r u c t u r e s o f t h e m a t e r i a l s u s e d i n t h i s t h e s i s , (a ) h y d r o x y p r o p y l m e t h y l c e l l u l o s e ( H P M C ) , ( b ) t r i f l u p r o m a z i n e - H C l , a n d (c ) 5 - f l u o r o u r a c i l . 39 H C l [72] and 5-fluorouracil [72]— are shown in Figure 2.1. Hydroxypropylmethylcellulose ( H P M C 2208, Methocel K 4 M Premium) was obtained from Dow Chemical Co . as a free-flowing white powder. The molecular weight for H P M C was 90000 g m o l - 1 , the methyl substitution was 19-24% and the hydroxypropyl substitution was 7-12% [73]. The moisture content of the powder was determined by T G A to be 5.4%. The moisture content remained constant so the powder was used as-supplied. Trif lupromazine-HCl ( F . W . = 388.9 g m o l - 1 ) was purchased from Aldr i ch Chemical company. The compound, commonly used as a tran-quilizer in veterinary practice [72], was chosen because of its water solubility and because it contained a C F 3 moiety. The second model drug, 5-fluorouracil ( F . W . = 130.1 g m o l - 1 ) , was obtained from Sigma. This drug is used as a chemotherapy agent [72]. It was chosen because of its smaller size compared to triflupromazine-HCl and because it is uncharged. Each mixture was prepared by weighing the appropriate amounts of H P M C , drug and disti l led water into a via l . The total weight of the mixtures varied from one to two grams and representative weight ranges for each component, with an error of ±0 .00005 grams, are 0.01000 to 0.06000 grams for the model drug materials, 0 to 0.60000 grams for the polymer and >0.40000 grams for the water. Although the materials were weighed to five decimal places, the calculated concentrations were quoted wi th less precision due to the possibility of material loss during mixing. The components in each v ia l were mixed, the v ia l was capped, sealed with parafilm and stored in a refrigerator to allow the mixture to equilibrate. The vials were mixed a second time after several days of equilibration. The concentrations of polymer and drug in these mixtures are expressed as weight percent (w/w% or just %) which is the ratio of the weight of the specified component to the total weight of the mixture. 2.2.2 N M R Measurements The relaxation times for the water ( X H) and drug ( 1 9 F ) components in the H P M C mixtures were measured using a Bruker MSL400 (9.4 T) spectrometer with a Bruker micro-imaging probe incorporating a 15 m m vertical coil tuned to either X H or 1 9 F . The N M R measure-ments were performed on the mixtures in the same vials in which they were prepared. 40 T h e t e m p e r a t u r e , as d e t e r m i n e d b y a v a r i a b l e - t e m p e r a t u r e u n i t , w a s 2 2 ± 1 ° C . T h e T i r e l a x a t i o n t i m e s i n t h e m i x t u r e s w e r e d e t e r m i n e d b y t h e i n v e r s i o n r e c o v e r y s e q u e n c e ( 1 8 0 -r - 9 0 - a c q u i r e ) [59]. T h e s i g n a l i n t e n s i t y (S ) v a r i a t i o n w i t h r e s p e c t t o t h e r v a l u e w a s f i t t o E q u a t i o n 2 . 2 , w h e r e a a n d b a r e c o n s t a n t s , u s i n g n o n l i n e a r l e a s t - s q u a r e s f i t t i n g i n t h e M a t h e m a t i c a p r o g r a m [74]. T h e T 2 t i m e s w e r e d e t e r m i n e d u s i n g t h e s p i n - e c h o s e q u e n c e ( 9 0 - T - 1 8 0 - r - a c q u i r e ) [62]. T h e s i g n a l i n t e n s i t y ( S ) v a r i a t i o n w i t h r e s p e c t t o 2 r o r t h e t i m e - t o - e c h o ( T # ) w a s p l o t t e d u s i n g E q u a t i o n 2 .3 a n d t h e v a l u e o f T 2 w a s e x t r a c t e d f r o m t h e s l o p e o f t h e s t r a i g h t l i n e . T h e n o n l i n e a r i t y o f t h e p l o t o f E q u a t i o n 2 . 3 f o r s o m e 1 9 F m e a s u r e m e n t s s u g g e s t e d t h a t t h e r e w e r e m u l t i p l e T 2 s p e c i e s i n m i x t u r e s o f h i g h H P M C c o n c e n t r a t i o n . I n t h e s e c a s e s , E q u a t i o n 2 .4 w a s u s e d i n M a t h e m a t i c a t o f i t t h e d a t a t o p r o -d u c e t w o T 2 v a l u e s w i t h t h e r e l a t i v e r a t i o s o f e a c h s p e c i e s d e t e r m i n a b l e f r o m t h e c o n s t a n t s c a n d d . S = a + 6 e x p ^ (2.2) ln(S) = ^TE + constant (2.3) S = c e x p — ^ + d e x p — ^ (2.4) -*2,1 1-2,2 T 2 r e l a x a t i o n t i m e s m e a s u r e d u s i n g t h e s p i n - e c h o m e t h o d c a n b e a f f e c t e d b y d i f f u -s i o n o f t h e n u c l e a r s p e c i e s t h r o u g h r e g i o n s o f m a g n e t i c f i e l d i n h o m o g e n e i t y [61 , 6 2 , 7 5 , 63 ] . I n a p l o t o f E q u a t i o n 2 . 3 , d i f f u s i o n c a u s e s a n a d d i t i o n a l d e c r e a s e i n l n ( S ) , a b o v e t h a t o f T 2 d e p h a s i n g , l e a d i n g t o a d o w n w a r d s t u r n f r o m t h e e x p e c t e d l i n e a r b e h a v i o r w i t h t h e g r e a t -es t e f f e c t s e e n a t t h e l a r g e s t v a l u e s o f T ^ . F o r m i x t u r e s w h e r e t h e p l o t o f E q u a t i o n 2 . 3 e x h i b i t e d t h i s e f f e c t , t h e TE v a l u e s f o r t h e T 2 m e a s u r e m e n t w e r e r e s t r i c t e d t o t h e v a l u e s u s e d i n t h e i m a g i n g e x p e r i m e n t s t h u s e n s u r i n g t h a t t h e c a l i b r a t i o n c o n d i t i o n s r e f l e c t e d t h o s e o f i m a g i n g e x p e r i m e n t s d i s c u s s e d i n l a t e r c h a p t e r s . T h e s e l f - d i f f u s i o n c o e f f i c i e n t s ( D ) o f t h e w a t e r a n d d r u g c o m p o n e n t s o f t h e m i x t u r e s w e r e m e a s u r e d b y t h e P u l s e d - G r a d i e n t - S p i n - E c h o ( P G S E ) m e t h o d u s i n g t h e z - g r a d i e n t o f 41 a Doty Scientific micro-imaging probe. The diffusion coefficient of water in l O m M C U S O 4 solution, 2.35 x 1 0 - 5 c m 2 s - 1 , .was used to calibrate the z-gradient for the diffusion mea-surements up to the maximum gradient strength of 60 G / c m . The self-diffusion coefficients were calculated from the slopes of the plots of ln (Ao) versus the gradient strength squared ( G 2 ) as shown in Equation 2.5 where 7 is the gyromagnetic ratio of the nucleus and 5 and A variable time parameters in the P G S E experiment. The 8 and A times in the sequence were varied for some samples resulting in self-diffusion coefficients which were consistent wi th the values presented in this thesis. ln(AG) = -72S\A-6-)DG2 + ln(A0) (2.5) . slope = ~72<S2(A-f) Cross-relaxation or z-spectroscopy experiments were performed for selected mixtures of H P M C and water. In these experiments, a weak off-resonance preparation pulse, with an excitation width of 500 Hz , was applied for 5 s before the spectrum of water was observed. As the offset of the preparation pulse was varied, the intensity of the water signal decreased from a maximum value at offsets far from the resonance frequency of water, to a min imum value at zero offset. The z-spectra for the mixtures were prepared by plott ing the normalized signal intensity versus the offset of the preparation pulse [66]. The width-at-half-height for each z-spectrum was taken as the difference between the two offset frequencies that decreased the water signal intensity to 50% of the maximum. 2.3 Results and Discussion 2 . 3 . 1 X H T i a n d T2 R e l a x a t i o n T i m e s f o r W a t e r i n t h e M i x t u r e s The * H spin-lattice and spin-spin relaxation times, T i and T 2 , respectively, were measured for the water resonance in equilibrated H P M C mixtures. Only one relaxation time was observed for each mixture, even at concentrations as high as 60% H P M C , indicating that there is rapid exchange between free water and polymer-bound water. The single relaxation 42 T a b l e 2 . 1 : M e a s u r e d 1 H T i a n d T 2 r e l a x a t i o n p a r a m e t e r s f o r t h e w a t e r c o m p o n e n t i n m i x t u r e s o f H P M C a n d w a t e r . t HPMC° / w / w % Ti / B T 2 / m s 0 2 . 7 4 1 2 4 7 2 . 3 4 2 .31 4 7 2 4 .71 2 .20 2 2 4 7 .05 2 .18 186 9 .44 1.82 145 1 4 . 3 1.67 6 7 . 4 18 .7 1.48 4 5 . 5 2 3 . 6 1.28 3 0 . 6 2 8 . 5 1.11 2 5 . 6 3 8 . 3 0 . 8 9 0 15.1 4 7 . 8 0 . 7 7 7 8 . 8 3 5 6 . 6 0 . 6 6 3 6 . 5 2 a Corrected for 5.4% moisture content 6 Measured by the Inversion-Recovery method, error ± 5 % c Measured by the Spin-Echo method, error ± 5% t i m e a l s o s u g g e s t s t h a t t h e * H s i g n a l f r o m m o b i l e p o l y m e r p r o t o n s i n t h e m i x t u r e s i s l o w . T h e T 2 r e l a x a t i o n t i m e s f o r p r o t o n s i n a s o l i d p o l y m e r a r e t y p i c a l l y s e v e r a l o r d e r s o f m a g n i t u d e s h o r t e r t h a n t h e v a l u e s f o r w a t e r . I n t h e H P M C m i x t u r e s , h o w e v e r , t h e p o l y m e r c h a i n s a r e h y d r a t e d a n d t h e i n c r e a s e d m o b i l i t y o f t h e h y d r o x y l g r o u p s m a y l e a d t o T 2 v a l u e s t h a t a r e c o m p a r a b l e t o t h o s e o f w a t e r . A t 6 0 % H P M C , u s i n g 9 0 0 0 0 g m o l - 1 as t h e m o l e c u l a r w e i g h t , 2 0 0 g m o l - 1 as t h e m o l e c u l a r w e i g h t o f e a c h g l u c o s e u n i t , a n d t h r e e h y d r o x y l g r o u p s p e r g l u c o s e u n i t , t h e s i g n a l i n t e n s i t y f o r w a t e r w o u l d b e a b o u t 5 t i m e s l a r g e r t h a n t h e i n t e n s i t y f o r t h e h y d r o x y l . A t 4 0 % H P M C , t h e w a t e r s i g n a l i s a b o u t 11 t i m e s g r e a t e r t h a n t h e h y d r o x y l s i g n a l . T h e s e c a l c u l a t i o n s a s s u m e t h a t a l l o f t h e h y d r o x y l s i g n a l w o u l d b e d e t e c t a b l e a n d t h e y d o n o t t a k e t h e ~ 2 0 % m e t h y l s u b s t i t u t i o n o f t h e h y d r o x y l p r o t o n i n t o a c c o u n t . I n s e c t i o n 3 . 3 . 1 , i m a g i n g e x p e r i m e n t s p e r f o r m e d w i t h D 2 0 c o n f i r m t h a t t h e 1 H s i g n a l f r o m t h e p o l y m e r i s a n i n s i g n i f i c a n t c o m p o n e n t o f t h e o b s e r v e d * H s i g n a l . T h e r e l a x a t i o n t i m e s o f t h e w a t e r c o m p o n e n t i n t h e H P M C m i x t u r e s a r e d e p e n d e n t o n t h e m o b i l i t y o f t h e w a t e r w i t h i n t h e p o l y m e r m a t r i x a n d a r e e x p e c t e d t o d e c r e a s e w i t h 4 3 i n c r e a s i n g p o l y m e r c o n c e n t r a t i o n . T h e r e l a x a t i o n t i m e s g i v e n i n T a b l e 2 .1 s h o w t h a t b o t h T i a n d T 2 d e c r e a s e d as t h e w e i g h t p e r c e n t o f H P M C i n c r e a s e d , r e f l e c t i n g t h e d e c r e a s e i n t h e t u m b l i n g f r e q u e n c y o f w a t e r d u e t o t h e i n c r e a s e i n t h e n u m b e r o f h y d r o g e n b o n d i n g i n t e r a c t i o n s t o t h e p o l y m e r c h a i n h y d r o x y l s . C a l c u l a t i o n s d i s c u s s e d i n C h a p t e r 3 r e q u i r e d a c a l i b r a t i o n e q u a t i o n r e l a t i n g t h e T 2 r e l a x a t i o n p a r a m e t e r a n d t h e H P M C c o n c e n t r a t i o n . E q u a t i o n s 2 .6 a n d 2 .7 w e r e g e n e r a t e d f r o m n o n - l i n e a r l e a s t - s q u a r e s f i t t i n g t o t h e r e l a x -a t i o n d a t a u s i n g t h e M a t h e m a t i c a p r o g r a m . T h e p h e n o m e n o l o g i c a l e q u a t i o n s d e s c r i b e t h e d e p e n d e n c e o f t h e r e l a x a t i o n t i m e s o n H P M C c o n c e n t r a t i o n s as s h o w n i n F i g u r e 2 . 2 . [HPMC] = 136.7 e " 1 - 2 7 4 Tl-H - 3.395 (2.6) [HPMC] = 54.86 e - ° - 0 7 1 1 9 T>* + 21.52 e - ° - 0 0 6 0 2 8 T ^ (2.7) 2 . 3 . 2 1 9 F T i a n d T2 R e l a x a t i o n T i m e s f o r t h e T r i f l u p r o m a z i n e -H C l a n d 5 - F l u o r o u r a c i l i n t h e m i x t u r e s T h e m o d e l d r u g s c h o s e n f o r t h i s s t u d y b o t h c o n t a i n e d f l u o r i n e , a n i d e a l n u c l e u s f o r N M R s t u d i e s , s e c o n d o n l y t o p r o t o n s i n s e n s i t i v i t y . D e t e c t i o n o f fluorine r a t h e r t h a n p r o t o n s a l l o w s f o r t h e o b s e r v a t i o n o f t h e m o d e l d r u g s i n d e p e n d e n t l y w i t h o u t i n t e r f e r e n c e f r o m t h e a b u n d a n t w a t e r s i g n a l . T h e d e p e n d e n c e o f t h e r e l a x a t i o n t i m e s o n t h e H P M C c o n c e n t r a t i o n a n d o n t h e d r u g c o n c e n t r a t i o n w a s i n v e s t i g a t e d f o r e a c h m o d e l d r u g . T h e c o n c e n t r a t i o n r a n g e s c h o s e n f o r t h e d r u g s i n t h e s e m i x t u r e s w e r e b a s e d o n t h e 5 % d r u g c o m p o s i t i o n o f t h e H P M C t a b l e t s u s e d i n t h e N M R i m a g i n g e x p e r i m e n t s o f C h a p t e r 5 . A s w a t e r p e n e t r a t e s t h e t a b l e t a n d t h e t a b l e t s w e l l s , t h e d r u g c o n c e n t r a t i o n d r o p s f r o m t h e m a x i m u m 5 % . T h e c o n c e n t r a t i o n s o f 3 % , 1 % a n d 0 . 5 % w e r e c h o s e n t o r e p r e s e n t h i g h , m e d i u m a n d l o w d r u g c o n c e n t r a t i o n s , r e s p e c t i v e l y . A l s o , t h e r e i s a n e x p e c t e d c o r r e l a t i o n b e t w e e n d r u g a n d H P M C c o n c e n t r a t i o n s w i t h t h e h i g h e r d r u g c o n c e n t r a t i o n s f o u n d i n t h e . m o r e p o l y m e r - c o n c e n t r a t e d r e g i o n s o f t h e s w o l l e n t a b l e t . T h u s , t h e c h o s e n c o n c e n t r a t i o n s f o r t h e p r e p a r e d m i x t u r e s a r e n o t r e q u i r e d 4 4 HPMC (w/w %) F i g u r e 2 . 2 : V a r i a t i o n o f * H r e l a x a t i o n t i m e s o f t h e w a t e r r e s o n a n c e i n H P M C m i x t u r e s a t e q u i l i b r i u m (a) T i v a l u e s a n d (b ) T 2 v a l u e s . T h e filled c i r c l e s a r e t h e e x p e r i m e n t a l p o i n t s a n d t h e l i n e s a r e t h e c u r v e s c a l c u l a t e d u s i n g E q u a t i o n s 2 .6 a n d 2 . 7 , r e s p e c t i v e l y . 4 5 Table 2.2: Measured 1 9 F T i and T 2 relaxation parameters for the tr i f lupromazine-HCl component of mixtures of H P M C , triflupromazine-HCl and water. D r u g / w/w% H P M C / w/w% T j / s Tc2 / ms 0.50 0 1.19 682 0.50 2.14 1.11 274 0.50 4.76 0.998 120 0.50 9.56 0.874 92.6 0.50 13.6 0.803 63.3 0.50 20.2 0.748 43.0 1.0 0 1.12 600 1.0 2.53 1.03 276 1.0 4.48 0.981 147 1.0 15.2 0.833 64 1.0 19.9 0.771 49.1 1.0 24.2 0.730 35.9 1.0 30.8 0.700 23.4 (54%)d, 8.0 (46%) 1.0 39.2 0.673 9.1 (63%), 2.0 (37%) 1.0 46.3 0.623 5.5 (50%), 1.02 (50%) 1.0 60.0 — 5.9 (21%), 0.75 (79%) 3.0 0 0.884 206 3.0 2.49 0.867 162 3.0 5.23 0.838 111 2.9 10.2 0.803 75.7 3.0 16.0 0.776 57.9 3.0 21.4 0.760 45.2 3.0 29.7 0.674 25.1 (54%), 9.2 (46%) 3.0 40.3 0.690 12.8 (51%), 1.77 (49%) 3.0 46.2 0.671 5.0 (58%), 1.18 (42%) 3.0 58.4 — 2.41 (28%), 0.74 (72%) a Corrected for 5/. % moisture content b Measured by the Inversion-Recovery method, error ± 5% c Measured by the Spin-Echo method, error ± 5% d Percentage of the species with the preceding T 2 value 46 t o c o v e r a l l t h e p o s s i b l e c o m b i n a t i o n s o f d r u g a n d H P M C c o n c e n t r a t i o n . T r i f l u p r o m a z i n e - H C l w a s t h e first m o d e l d r u g s t u d i e d . T h e m e a s u r e d 1 9 F r e l a x a t i o n t i m e s f o r i t i n t h e H P M C m i x t u r e s a r e g i v e n i n T a b l e 2 .2 a n d d i s p l a y e d i n F i g u r e 2 . 3 . T h e r e l a x a t i o n t i m e s d e c r e a s e d w i t h i n c r e a s i n g H P M C c o n c e n t r a t i o n as e x p e c t e d . T h e r e l a x a t i o n t i m e s a l s o e x h i b i t e d a d e p e n d e n c e o n t h e t r i f l u p r o m a z i n e - H C l c o n c e n t r a t i o n a t l o w H P M C c o n c e n t r a t i o n s . T h e p o l y m e r i n f l u e n c e o n t h e r e l a x a t i o n t i m e s b e c a m e t h e d o m i n a n t e f f e c t a t c o n c e n t r a t i o n s a b o v e 1 0 % as l i t t l e d i f f e r e n c e w a s o b s e r v e d b e t w e e n t h e r e l a x a t i o n t i m e s o f m i x t u r e s o f v a r y i n g d r u g c o m p o s i t i o n . U n l i k e t h e w a t e r m e a s u r e m e n t s , t w o T 2 r e l a x a t i o n s p e c i e s w e r e o b s e r v e d f o r t r i -flupromazine-HCl a t p o l y m e r c o n c e n t r a t i o n s 3 0 % a n d a b o v e . T h e o b s e r v a t i o n o f t h e d i s -t i n c t s p e c i e s s u g g e s t s t h a t t h e b o n d i n g i n t e r a c t i o n s b e t w e e n t r i f l u p r o m a z i n e - H C l a n d t h e p o l y m e r l e a d t o a n e x c h a n g e r a t e b e t w e e n s t a t e s s l o w e r t h a n t h e T 2 r e l a x a t i o n r a t e c o r -r e s p o n d i n g t o e a c h s t a t e . T h e r e l a t i v e a b u n d a n c e o f t h e s h o r t T 2 s p e c i e s i n d i c a t e s t h a t t h e r e w i l l b e s o m e s i g n a l l o s t f r o m t r i f l u p r o m a z i n e - H C l i n t h e i m a g i n g e x p e r i m e n t s , e v e n a t t h e s h o r t e s t T # t i m e s . T h e i m a g i n g e x p e r i m e n t s o f t h e d r u g w i l l r e q u i r e a n e x t e r n a l s i g n a l c a l i b r a t i o n t o c o r r e c t f o r t h e l o s s o f s i g n a l i n h i g h H P M C r e g i o n s i n o r d e r t o o b t a i n c o n c e n t r a t i o n d i s t r i b u t i o n s t h a t a r e q u a n t i t a t i v e t h r o u g h o u t t h e s w o l l e n t a b l e t . T h e T 2 v a l u e s o f t h e t r i f l u p r o m a z i n e - H C l w e r e u s e d t o o b t a i n a n a v e r a g e r e l a t i o n s h i p b e t w e e n t h e r e l a x a t i o n t i m e o f t h e 1 9 F a n d t h e H P M C c o n c e n t r a t i o n . T h e r e s u l t i n g E q u a t i o n 2 .8 w a s o b t a i n e d b y n o n - l i n e a r l e a s t - s q u a r e s f i t t i n g o f a s u b s e t o f t h e d a t a i n T a b l e 2 . 2 . T h e r e l a x -a t i o n t i m e s o f t h e 3 % m i x t u r e s b e l o w « 2 0 % H P M C w e r e n o t u s e d i n t h e fit b e c a u s e t h e s e c o n c e n t r a t i o n c o m b i n a t i o n s a r e u n l i k e l y t o b e p r e s e n t i n t h e s w o l l e n t a b l e t . I n t h e m i x -t u r e s w h e r e t w o d i s t i n c t T 2 s p e c i e s w e r e p r e s e n t , t h e r e l a t i v e a m o u n t s o f e a c h s p e c i e s a n d t h e r a n g e o f TE v a l u e s f o r t h e i m a g i n g e x p e r i m e n t s o f C h a p t e r 5 w e r e u s e d t o d e t e r m i n e e f f e c t i v e T 2 v a l u e s . F o r a l l b u t t w o o f t h e m i x t u r e s , t h e a p p a r e n t T 2 v a l u e s w e r e t h e s a m e as t h o s e i n T a b l e 2 . 2 . F o r t h e s p e c i f i c c o n d i t i o n s o f 1 9 F i m a g i n g e x p e r i m e n t s o f t h i s t h e s i s , t h e c a l c u l a t e d a p p a r e n t T 2 v a l u e s f o r t h e 3 0 . 8 % a n d 3 9 . 2 % m i x t u r e s w e r e 1 3 . 9 m s a n d 8 .87 m s r e s p e c t i v e l y . T h e s e l a t t e r v a l u e s w e r e u s e d t o d e t e r m i n e d E q u a t i o n 2 . 8 , t h e c a l i b r a t i o n 4 7 (a) 1.4T 1.2i T l (s) 1.0 0 . 8 0 . 6 1 A • O 0 . 4 H 0.2-(b) o.o-0 8 0 0 1 -> r -10 2 0 — i — 3 0 — i — 4 0 HPMC(w/w%) 5 0 6 0 HPMC(w/w%) F i g u r e 2 . 3 : V a r i a t i o n o f 1 9 F r e l a x a t i o n t i m e s o f t h e t r i f l u p r o m a z i n e - H C l c o m p o n e n t i n H P M C m i x t u r e s a t e q u i l i b r i u m (a ) T i v a l u e s a n d ( b ) T 2 v a l u e s . T h e c o n c e n t r a t i o n s o f t h e d r u g a r e 0 . 5 % ( f i l l e d c i r c l e s ) , 1 % ( o p e n c i r c l e s ) , a n d 3 % ( o p e n t r i a n g l e s ) . T h e l i n e i n ( b ) i s t h e c u r v e c a l c u l a t e d f r o m E q u a t i o n 2 .8 . 4 8 e q u a t i o n r e l a t i n g T 2 v a l u e s c a l c u l a t e d f r o m t h e 1 9 F i m a g i n g e x p e r i m e n t s o f C h a p t e r 5 t o H P M C c o n c e n t r a t i o n . [HPMC] = 38.18 e - 0 - 0 1 4 8 9 T 2.<«y /« + 87.09 e " 0 - 2 8 6 9 T2,tnfiu ( 2 . 8 ) T a b l e 2 . 3 : M e a s u r e d 1 9 F T i a n d T 2 r e l a x a t i o n p a r a m e t e r s f o r t h e 5 - f l u o r o u r a c i l c o m p o n e n t o f m i x t u r e s o f H P M C , 5 - f l u o r o u r a c i l , a n d w a t e r . D r u g / w / w % H P M C 8 / w / w % T \ / s T 2 / m s 0 .50 0 3 .64 3 9 0 0 . 5 4 10 .6 2 . 2 6 2 0 0 0 .50 2 0 . 4 1.51 9 3 . 2 1.0 0 . 9 0 9 3 . 3 3 3 0 6 1.0 9 . 9 3 2 . 2 6 2 0 5 1.1 18 .0 1.61 130 1.0 3 0 . 0 1.06 2 5 . 4 3 .0 19 .9 1 .43 7 4 . 3 3 .0 3 1 . 5 1.01 2 0 . 2 3 .0 3 9 . 7 0 . 8 2 2 7.1 2 . 9 4 6 . 7 0 . 7 3 4 «9 -30 ( « 1 3 % ) d , «2 .9 ( « 8 7 % ) a C o r r e c t e d fo r 5 . 4 % m o i s t u r e c o n t e n t b M e a s u r e d by t h e I n v e r s i o n - R e c o v e r y m e t h o d , e r r o r ± 5 % c M e a s u r e d by t h e S p i n - E c h o m e t h o d , e r r o r ± 5 % P e r c e n t a g e o f t h e spec ies w i t h t h e p r e c e d i n g T 2 va lue T h e d a t a g i v e n i n T a b l e 2 . 3 s h o w t h e c o m b i n a t i o n s o f H P M C a n d 5 - f l u o r o u r a c i l c o n c e n t r a t i o n s t h a t w e r e p r e p a r e d i n t h e s t u d y o f t h e r e l a x a t i o n s t i m e s o f t h e s e c o n d m o d e l d r u g . T h e t r e n d s i n r e l a x a t i o n t i m e s , c l e a r l y s h o w n i n F i g u r e 2 . 4 , a r e s i m i l a r t o t h o s e o f t r i f l u p r o m a z i n e - H C l . B o t h t h e T x a n d T 2 r e l a x a t i o n t i m e s d e c r e a s e w i t h i n c r e a s i n g H P M C c o n c e n t r a t i o n . T h e r e i s a s l i g h t i n d i c a t i o n i n t h e p l o t s t h a t t h e r e l a x a t i o n t i m e s a r e d e p e n d e n t o n t h e 5 - f l u o r o u r a c i l c o n c e n t r a t i o n as w e l l . I n c o n t r a s t t o t h e t r i f l u p r o m a z i n e -H C l r e s u l t s , s i n g l e T 2 r e l a x a t i o n s p e c i e s w e r e o b s e r v e d f o r 5 - f l u o r o u r a c i l u p u n t i l 5 0 % . T h e r e s u l t s o f t h e d o u b l e - e x p o n e n t i a l fits t o t h e i n t e n s i t y d a t a f o r t h i s c o n c e n t r a t i o n y i e l d e d a s m a l l p e r c e n t a g e o f a v a r i a b l e , o d d l y - l a r g e , T 2 s p e c i e s , i n c o m b i n a t i o n w i t h a s p e c i e s 49 o f a m o r e r e a s o n a b l e T 2 v a l u e . T h e r e l a x a t i o n t i m e s f o r 5 - f l u o r o u r a c i l s u g g e s t t h a t t h e s i g n a l o b t a i n e d f o r t h i s d r u g i n t h e i m a g i n g e x p e r i m e n t s w i l l b e e s s e n t i a l l y q u a n t i t a t i v e i n a l l r e g i o n s o f t h e s w o l l e n t a b l e t a n d w i l l n o t n e e d t o b e c o r r e c t e d as e x t e n s i v e l y as i n t h e t r i f l u p r o m a z i n e - H C l e x p e r i m e n t s . T h e d a t a o f T a b l e 2 .3 w e r e f i t t o E q u a t i o n 2 .9 u s i n g n o n - l i n e a r l e a s t - s q u a r e s f i t t i n g . [HPMC] = 20.72 e - ° - 1 0 1 7 T2,5fiu +47.92 e-0.002902 T 2 i 5/z„ _ 1 6 6 1 (2.9) 2 . 3 . 3 S e l f - d i f f u s i o n C o e f f i c i e n t s f o r W a t e r , T r i f l u p r o m a z i n e - H C l a n d 5 - F l u o r o u r a c i l i n t h e M i x t u r e s T h e d i f f u s i o n b e h a v i o r s o f t h e w a t e r a n d d r u g w i t h i n t h e s w o l l e n g e l a r e m a j o r f a c t o r s i n t h e r a t e o f d r u g r e l e a s e f r o m a h y d r o p h i l i c m a t r i x t a b l e t . T h e r a t e o f g e l f o r m a t i o n d e p e n d s s t r o n g l y o n h o w r a p i d l y w a t e r c a n m o v e i n t o d r y a n d c o n c e n t r a t e d p o l y m e r r e g i o n s . O n c e t h e g e l i s f o r m e d , t h e d r u g c a n e s c a p e t h e t a b l e t e i t h e r b y t h e e r o s i o n o f t h e g e l o r b y d i f f u s i o n t h r o u g h t h e g e l . T a b l e 2 . 4 : M e a s u r e d s e l f - d i f f u s i o n c o e f f i c i e n t s f o r t h e w a t e r c o m p o n e n t o f m i x t u r e s o f H P M C a n d w a t e r . H P M C / w / w % D 6 / n r 5 c m 2 s - 1 0 2 . 1 7 4 .71 1.95 9 .44 1.83 18 .7 1.4 2 8 . 5 0 .96 3 8 . 3 0 .51 a Corrected for 5.4% moisture 6 P G S E method, error ±0.05 T h e m e a s u r e d s e l f - d i f f u s i o n c o e f f i c i e n t s f o r w a t e r , g i v e n i n T a b l e 2 . 4 , d e c r e a s e s m o o t h l y as t h e H P M C c o n c e n t r a t i o n i s i n c r e a s e d , d r o p p i n g t o a p p r o x i m a t e l y o n e q u a r t e r o f t h e d i f f u s i o n v a l u e f o r d i s t i l l e d w a t e r . T h e d i f f u s i o n c o e f f i c i e n t s f o r t h e m o d e l d r u g s , 50 F i g u r e 2 . 4 : V a r i a t i o n o f 1 9 F r e l a x a t i o n t i m e s o f t h e 5 - f l u o r o u r a c i l c o m p o n e n t i n H P M C m i x t u r e s a t e q u i l i b r i u m (a) T i v a l u e s a n d (b ) T 2 v a l u e s . T h e c o n c e n t r a t i o n s o f t h e d r u g a r e 0 . 5 % ( f i l l e d c i r c l e s ) , 1 % ( o p e n c i r c l e s ) , a n d 3 % ( o p e n t r i a n g l e s ) . T h e l i n e i n ( b ) i s t h e c u r v e c a l c u l a t e d f r o m E q u a t i o n 2 .9 . 51 Table 2.5: Measured self-diffusion coefficients for the tr if lupromazine-HCl ( 1 9 F ) component of mixtures of H P M C , triflupromazine-HCl and water. D r u g / w / w % H P M C / w / w % D b / IO" 6 c m 2 s " 1 0.50 0 4.53 1.0 0 3.67 1.0 4.61 1.81 1.0 9.66 1.02 1.0 19.3 0.36 3.0 0 1.94 3.0 4.11 1.31 3.0 9.64 0.94 3.0 19.3 0.60 a Corrected for 5.4% moisture 6 P G S E method, error ±0.05 Table 2.6: Measured self-diffusion coefficients for the 5-fluorouracil ( 1 9 F ) component of mixtures of H P M C , 5-fluorouracil and water. D r u g / w / w % H P M C a / w / w % D 6 / I O - 5 c m 2 s " 1 0.50 0 1.01 0.54 10.6 0.86 0.50 20.4 0.28 1.0 0.909 0.92 1.0 9.93 0.86 1.1 18.0 0.32 1.0 30.0 0.34 1.1 37.5 0.17 3.0 31.5 0.27 3.0 39.7 0.15 a Corrected for 5.4% moisture 6 P G S E method, error ±0.05 52 T a b l e s 2 . 5 a n d 2 . 6 , i n d i c a t e t h a t 5 - f l u o r o u r a c i l s e l f - d i f f u s e s a b o u t t w i c e as q u i c k l y as t r i f l u p r o m a z i n e - H C l i n s o l u t i o n s c o n t a i n i n g o n l y 0 . 5 % d r u g . A s t h e H P M C c o n c e n t r a -t i o n i n c r e a s e d , t h e d i f f u s i o n c o e f f i c i e n t s o f b o t h d r u g s d e c r e a s e d b u t n o t a t t h e s a m e r a t e . T h e d i f f u s i o n o f t r i f l u p r o m a z i n e - H C l a p p e a r s t o b e m o r e s t r o n g l y a f f e c t e d b y t h e i n c r e a s i n g p o l y m e r c o n c e n t r a t i o n . T h e s e l f - d i f f u s i o n c o e f f i c i e n t s f o r a l l t h r e e s p e c i e s a r e s h o w n i n F i g u r e 2 . 5 . T h e d i f f u -s i o n c o e f f i c i e n t s m e a s u r e d f o r t h e w a t e r a n d m o d e l d r u g s i n t h e m i x t u r e s s h o u l d r e f l e c t t h e v a l u e s f o r t h e s a m e s p e c i e s i n r e g i o n s o f t h e t a b l e t w i t h s i m i l a r c o m p o s i t i o n . A c o m p a r i s o n o f t h e m e a s u r e d d i f f u s i o n c o e f f i c i e n t s t o t h e a p p a r e n t d i f f u s i o n p a r a m e t e r s d e t e r m i n e d f r o m t h e m o d e l i n g c a l c u l a t i o n s o f C h a p t e r 6 w i l l b e o f g r e a t i n t e r e s t . 2 . 3 . 4 M o b i l i t y C h a n g e s i n t h e P o l y m e r a s D e t e r m i n e d b y N M R S p e c t r o s c o p y I n t h e s i m p l e s t d e s c r i p t i o n o f a s w o l l e n p o l y m e r - w a t e r s y s t e m , t h e w a t e r c a n b e c o n s i d e r e d t o e x i s t i n o n e f r e e a n d o n e b o u n d s t a t e . T h e f a c t t h a t o n l y o n e r e l a x a t i o n c o m p o n e n t i s o b s e r v e d f o r t h e w a t e r n u c l e i i n d i c a t e s t h a t t h e s e s t a t e s a r e i n r a p i d e q u i l i b r i u m . T h e f r e e w a t e r h a s a l o n g e r T 2 v a l u e t h a n t h e b o u n d w a t e r a n d t h e r e s u l t i n g a v e r a g e i n t h e f a s t -e x c h a n g e l i m i t i s a c o m b i n a t i o n o f t h e t w o T 2 v a l u e s as s h o w n b y E q u a t i o n 2 . 1 , y i e l d i n g E q u a t i o n 2 . 1 0 . A p l o t o f t h e i n v e r s e o f t h e o b s e r v e d T 2 as a f u n c t i o n o f t h e f r a c t i o n o f b o u n d w a t e r s h o u l d y i e l d a s t r a i g h t l i n e w i t h a n i n t e r c e p t o f 1 / T 2 j r e e , i n t h i s c a s e t h e i n v e r s e o f t h e T 2 o f d i s t i l l e d w a t e r . 1 Pfree . Pbound 1 . / 1 1 \ icy - i r\\ rp rp i rp ~ rp ~T Vbound\rp rp ) \6.i.V)) -*2,o6s J-2, free J-2,bound ±2,free •>-2)bound 12, free F o r t h e v a r i o u s H P M C m i x t u r e s , t h e f r a c t i o n o f b o u n d w a t e r i s u n k n o w n b u t s h o u l d b e r e l a t e d t o t h e c o n c e n t r a t i o n o f t h e p o l y m e r . F i g u r e 2 .6 s h o w s t h e p l o t o f 1 / T 2 j 0 6 s v e r s u s H P M C w e i g h t p e r c e n t . T h e d a t a i n F i g u r e 2 .6 a p p e a r t o s e p a r a t e i n t o t h r e e d i s t i n c t l i n e a r r e g i o n s . T h e d a t a f r o m 0 % t o 1 0 % H P M C f a l l o n o n e l i n e , t h e d a t a f r o m 1 0 % t o 3 0 % f a l l 5 3 2.5-1 2 . 0 -1 .5 -D ( 1 0 - 5 c m 2 s _ 1 ) i .o • 0 . 5 -k • o.o-0 — I — 10 ^ — 2 0 — i — 3 0 1 4 0 HPMC(w/w%) F i g u r e 2 . 5 : S e l f - d i f f u s i o n c o e f f i c i e n t s o f w a t e r ( o p e n s q u a r e s ) , t r i f l u p r o m a z i n e - H C l ( f i l l e d c i r c l e s ) , a n d 5 - f l u o r o u r a c i l ( o p e n t r i a n g l e s ) i n s e l e c t e d H P M C m i x t u r e s . N o d i s t i n c t i o n h a s b e e n m a d e b e t w e e n m i x t u r e s o f v a r y i n g d r u g c o n c e n t r a t i o n . 5 4 0 . 2 01 0 . 1 5 H 1 / T 2 ( m s -1) o.ioH 0 . 0 5 i 0 . 0 0 3 0 4 0 HPMC(w/w%) 6 0 F i g u r e 2 .6 : T h e i n v e r s e o f t h e T 2 o f t h e w a t e r c o m p o n e n t i n H P M C m i x t u r e s as a f u n c t i o n o f H P M C w e i g h t p e r c e n t i n d i c a t i n g d i s c o n t i n u i t i e s a t « 1 2 % a n d « 3 5 % H P M C . 5 5 o n a s e c o n d l i n e , a n d t h e v a l u e s f r o m 4 0 % t o 6 0 % a p p e a r t o f a l l o n a t h i r d l i n e . T h e s l o p e f o r e a c h l i n e i s h{l/T2,bound — l/T/^./ree} w h e r e t h e f r a c t i o n o f b o u n d w a t e r i s t h e p r o d u c t o f t h e c o n s t a n t h a n d t h e w e i g h t p e r c e n t H P M C . T h e i n t e r c e p t f o r t h e 0 - 1 0 % l i n e y i e l d s l/T/2,/ree as e x p e c t e d a c c o r d i n g t o E q u a t i o n 2 . 1 0 , b u t t h e i n t e r c e p t s f o r t h e s e c o n d a n d t h i r d l i n e s a r e f a r r e m o v e d f r o m t h a t v a l u e . T h e r e a r e t w o p o s s i b l e e x p l a n a t i o n s f o r t h e d i s c o n t i n u i t i e s t h a t o c c u r a t a p p r o x i -m a t e l y 1 2 % H P M C a n d 3 5 % H P M C [76]. T h e h y d r a t i o n o f t h e p o l y m e r m a y h a v e c h a n g e d , t h u s a l t e r i n g t h e b o u n d w a t e r f r a c t i o n a n d t h e c o e f f i c i e n t h i n t h e s l o p e . A n o t h e r e x p l a -n a t i o n i s t h a t t h e T 2 o f t h e b o u n d w a t e r h a s c h a n g e d . S i n c e t h e T 2 o f t h e b o u n d w a t e r d e p e n d s o n t h e m o b i l i t y o f t h e p o l y m e r t o w h i c h i t i s b o u n d , a s u b s t a n t i a l c h a n g e i n t h e m o b i l i t y o f t h e p o l y m e r c h a i n s i n t h e p o l y m e r - w a t e r m i x t u r e w o u l d c a u s e a s i g n i f i c a n t c h a n g e i n t h e T2,f>0tmd- T h e f i r s t d i s c o n t i n u i t y i n F i g u r e 2 .6 a p p e a r s i n t h e s a m e , s e m i -d i l u t e c o n c e n t r a t i o n r e g i o n w h e r e t h e m i x t u r e w o u l d f i r s t b e c l a s s i f i e d as a g e l r a t h e r t h a n as a v i s c o u s s o l u t i o n . T h e p o l y m e r c h a i n s i n t h e g e l s t a t e w o u l d b e e x p e c t e d t o b e m o r e r e s t r i c t e d t h a n i n s o l u t i o n b u t m o r e m o b i l e t h a n i n t h e s o l i d p o l y m e r . T h u s , t h e first d i s c o n t i n u i t y i s p r o b a b l y d u e t o a s u b s t a n t i a l d e c r e a s e i n c h a i n m o b i l i t y w h e n t h e p o l y m e r b e c o m e s c o n c e n t r a t e d e n o u g h t o f o r m t h e p h y s i c a l e n t a n g l e m e n t s r e q u i r e d f o r t h e g e l s t a t e . T h e s e c o n d d i s c o n t i n u i t y o c c u r s i n t h e c o n c e n t r a t i o n r e g i o n w h e r e t h e m i x t u r e s l o s e t h e i r t r a n s p a r e n c y a n d r e s e m b l e w e t t e d p o w d e r s r a t h e r t h a n g e l s . T h e d i s c o n t i n u i t y a t h i g h e r H P M C c o n c e n t r a t i o n m a y b e d u e t o d e h y d r a t i o n b e l o w t h e w a t e r c o n c e n t r a t i o n n e c e s s a r y f o r o p t i m u m w a t e r - m e d i a t e d , i n t e r c h a i n H - b o n d , c r o s s - l i n k i n g . W h e n t h e H - b o n d i n g i n t e r -a c t i o n o c c u r s d i r e c t l y b e t w e e n t h e p o l y m e r c h a i n s , r o t a t i o n a l m o t i o n w o u l d b e c o m e g r e a t l y r e s t r i c t e d . I n o r d e r t o c h e c k t h i s i n t e r p r e t a t i o n o f t h e d a t a o f F i g u r e 2 . 6 , t h e m o b i l i t y o f t h e p o l y m e r c o m p o n e n t i n t h e p o l y m e r - w a t e r m i x t u r e s w a s p r o b e d w i t h t h e t e c h n i q u e o f c r o s s - r e l a x a t i o n o r z - s p e c t r o s c o p y . T h i s e x p e r i m e n t r e q u i r e s w a t e r t o b e i n t h e p r e s e n c e o f a p o l y m e r w h i c h p r o v i d e s s o - c a l l e d s o l i d - l i k e p r o t o n s t o i n t e r a c t w i t h t h e b o u n d w a t e r c o m p o n e n t . A n o f f - r e s o n a n c e p u l s e , a p p l i e d t o . s a t u r a t e t h e r e s o n a n c e s o f t h e s o l i d - l i k e 56 c o m p o n e n t . A n o f f - r e s o n a n c e p u l s e , a p p l i e d t o s a t u r a t e t h e r e s o n a n c e s o f t h e s o l i d - l i k e p r o t o n s i n t h e s y s t e m , i n d i r e c t l y a f f e c t s t h e m a g n e t i z a t i o n o f t h e w a t e r b e c a u s e , d u r i n g t h e l e n g t h o f t h e p u l s e , c r o s s - r e l a x a t i o n t h r o u g h d i p o l a r c o u p l i n g o c c u r s b e t w e e n t h e p r o t o n s o f t h e b o u n d w a t e r a n d t h o s e o f t h e p o l y m e r . W h e n t h e s p e c t r u m o f t h e w a t e r is a c q u i r e d a f t e r t h e o f f - r e s o n a n c e p u l s e , t h e i n t e n s i t y o f t h e s i g n a l w i l l d e c r e a s e r e l a t i v e t o t h e i n t e n s i t y i n t h e a b s e n c e o f t h e p r e p a r a t i o n p u l s e , r e f l e c t i n g t h e a m o u n t o f c r o s s - r e l a x a t i o n t h a t h a s o c c u r r e d . T h e z - s p e c t r u m i s t h e p l o t o f t h e n o r m a l i z e d s i g n a l i n t e n s i t y , M / M o , v e r s u s t h e o f f se t o f t h e p r e s a t u r a t i o n p u l s e . F i g u r e 2 .7 s h o w s t h e z - s p e c t r a f o r s o m e o f t h e H P M C m i x t u r e s . I n g e n e r a l , t h e s e z - s p e c t r a p r o v i d e d i r e c t e v i d e n c e t h a t s u b s t a n t i a l i n t e r a c t i o n o c c u r s b e t w e e n t h e w a t e r a n d t h e p o l y m e r p r o t o n s . O n l y w a t e r n u c l e i i n c l o s e p r o x i m i t y t o t h e p o l y m e r , i.e. b o u n d w a t e r , c a n p a r t i c i p a t e i n c r o s s - r e l a x a t i o n w i t h t h e p o l y m e r p r o t o n s b e c a u s e t h e m a g n i t u d e o f t h e d i p o l a r c o u p l i n g i n t e r a c t i o n is i n v e r s e l y p r o p o r t i o n a l t o t h e i n t e r n u c l e a r d i s t a n c e c u b e d . E x c h a n g e b e t w e e n t h e h y d r o x y l s o f t h e H P M C a n d t h e h y d r o x y l s o f t h e w a t e r w o u l d b e a n a d d i t i o n a l m e c h a n i s m f o r m a g n e t i z a t i o n t r a n s f e r b e t w e e n t h e w a t e r a n d t h e p o l y m e r . T h e z - s p e c t r u m o f d i s t i l l e d w a t e r i s i n c l u d e d t o s h o w t h e r e s u l t o f t h e s a m e e x p e r i m e n t o n a s a m p l e w h e r e t h e p o s s i b i l i t y f o r c r o s s - r e l a x a t i o n i s a b s e n t a n d i n d i c a t e s t h a t d i r e c t s a t u r a t i o n f r o m t h e o f f - r e s o n a n c e p u l s e i s m i n i m a l f o r m o d e r a t e o f f s e t s . A n i m p o r t a n t f e a t u r e o f t h e s e p l o t s is t h a t t h e w i d t h - a t - h a l f - h e i g h t , Ai/2, o f t h e z - s p e c t r u m i s r e l a t e d t o t h e w i d t h o f t h e s p e c t r a l l i n e f o r t h e s o l i d - l i k e p r o t o n s , e v e n w h e r e , as i n t h e p r e s e n t c a s e , t h e p r o t o n s p e c t r u m o f t h e s o l i d c o m p o n e n t i s n o t o b s e r v e d d i r e c t l y . T h e b r o a d l i n e s o f s o l i d s a r e d u e t o t h e p r e s e n c e o f d i p o l a r c o u p l i n g s t h a t a r e n o t a v e r a g e d t o z e r o b y m o t i o n . T h u s , t h e less m o b i l e t h e p o l y m e r c h a i n s , t h e b r o a d e r t h e l i n e f o r t h e p o l y m e r p r o t o n s a n d t h e b r o a d e r t h e c o r r e s p o n d i n g z - s p e c t r u m f o r t h e w a t e r i n t h e p o l y m e r . T a b l e 2 .7 s h o w s t h a t t h e w i d t h s o f t h e z - s p e c t r a i n c r e a s e w i t h i n c r e a s i n g p o l y m e r c o n c e n t r a t i o n . T h e w i d t h - a t - h a l f - h e i g h t f o r t h e 2 0 % m i x t u r e w a s a l m o s t f i v e t i m e s t h a t f o r t h e 1 0 % m i x t u r e . N o o t h e r d o u b l i n g i n p o l y m e r c o n c e n t r a t i o n r e s u l t e d i n s u c h a n i n c r e a s e i n t h e w i d t h o f t h e z - s p e c t r u m ; w i d t h s d o u b l e d f o r a l l o t h e r c o m p a r i s o n s . T h e s e r e s u l t s 57 - 3 0 - 2 0 - 1 0 0 10 2 0 3 0 Offset of preparation pulse (kHz) F i g u r e 2 . 7 : 1 H N M R Z - s p e c t r a f o r s e l e c t e d H P M C m i x t u r e s f r o m o b s e r v a t i o n s o f t h e * H s i g -n a l o f H 2 0 . T h e m i x t u r e s s h o w n a r e w a t e r ( l i n e ) , 9 . 4 % ( f i l l e d c i r c l e s ) , 1 4 . 2 % ( o p e n c i r c l e s ) , 1 8 . 7 % ( f i l l e d s q u a r e s ) , 3 8 . 3 % ( o p e n s q u a r e s ) a n d 5 6 . 6 % ( f i l l e d t r i a n g l e s ) . A p r e p a r a t i o n p u l s e w i t h a n e x c i t a t i o n w i d t h o f 5 0 0 H z w a s a p p l i e d a t d i f f e r e n t o f f s e t f r e q u e n c i e s f o r five s e c o n d s p r i o r t o t h e a c q u i s i t i o n o n t h e w a t e r s i g n a l . ( O n l y t h e r a n g e o f o f f s e t s o f - 3 0 k H z t o + 3 0 k H z i s s h o w n . ) 58 T a b l e 2 .7 : W i d t h - a t - h a l f - h e i g h t v a l u e s f o r z - s p e c t r a o f H P M C m i x t u r e s . H P M C / w / w % A i / 2 / k H z R e l a t i v e A j / 2 4 .71 1.42 1 9 .44 3 .18 2 . 2 4 14 .3 7 .45 5 . 2 5 18 .7 14 .3 10 .1 2 8 . 5 18 .5 1 3 . 0 3 8 . 3 2 2 . 0 1 5 . 5 5 6 . 6 2 8 . 8 2 0 . 3 a Corrected for 5.4% moisture content b Relative to the of the 4.71% mixture s u g g e s t t h a t t h e r e i s a s i g n i f i c a n t c h a n g e i n t h e m o b i l i t y o f t h e p o l y m e r w h e n t h e p o l y m e r c o n c e n t r a t i o n p a s s e s b e t w e e n 1 0 % a n d 2 0 % . T h u s , t h e r e s u l t s o f t h e z - s p e c t r o s c o p y s u p p o r t t h e i n t e r p r e t a t i o n t h a t t h e d i s c o n t i n u i t y a t ~ 1 2 % i n F i g u r e 2 .6 i s t h e r e s u l t o f a c h a n g e i n t h e p o l y m e r m o b i l i t y . S i n c e t h e r e w a s n o t a c o r r e s p o n d i n g l y l a r g e c h a n g e i n t h e z - s p e c t r u m a r o u n d 3 5 % H P M C , t h e s e c o n d d i s c o n t i n u i t y i n F i g u r e 2 .6 w a s i n t e r p r e t e d as a c h a n g e i n t h e h y d r a t i o n c h a r a c t e r i s t i c s o f t h e p o l y m e r . 2.4 Summary T h e d e p e n d e n c e s o f t h e r e l a x a t i o n t i m e s f o r t h e w a t e r a n d t h e m o d e l d r u g s o n H P M C c o n c e n t r a t i o n w e r e d e t e r m i n e d . T h e s e v a l u e s a r e a s s u m e d t o b e r e p r e s e n t a t i v e o f t h e p o l y m e r e n v i r o n m e n t i n t h e s w o l l e n t a b l e t i n r e g i o n s o f s i m i l a r c o m p o s i t i o n . T h e c a l i b r a t i o n o f t h e w a t e r T 2 v a l u e s a n d H P M C c o n c e n t r a t i o n w i l l b e u s e d i n C h a p t e r 3 t o c a l c u l a t e H P M C c o n c e n t r a t i o n s f r o m T 2 v a l u e s m e a s u r e d f r o m t h e X H N M R i m a g i n g e x p e r i m e n t s . S i m i l a r p h e n o m e n o l o g i c a l e q u a t i o n s r e l a t i n g t h e T 2 r e l a x a t i o n t i m e s o f t h e f i u o r i n a t e d d r u g s t o t h e p o l y m e r c o n c e n t r a t i o n w e r e a l s o d e t e r m i n e d . T h e u s e o f t h e s e e q u a t i o n s i n t h e 1 9 F i m a g i n g e x p e r i m e n t s o f C h a p t e r 5 w i l l a l l o w f o r a l t e r n a t e c a l c u l a t i o n s o f t h e p o l y m e r d i s t r i b u t i o n w h i c h c a n b e c o m p a r e d w i t h t h e o n e o b t a i n e d f r o m t h e i m a g i n g s t u d i e s o f w a t e r . T h e m o b i l i t y c h a n g e s o f t h e p o l y m e r w e r e s t u d i e d b y r e l a x a t i o n t i m e m e a s u r e m e n t s 59 a n d z - s p e c t r o s c o p y . B o t h e x p e r i m e n t s s u g g e s t e d t h a t t h e m o b i l i t y o f t h e p o l y m e r d e c r e a s e s s u b s t a n t i a l l y w h e n t h e H P M C c o n c e n t r a t i o n p a s s e s b e t w e e n 1 0 % a n d 2 0 % . T h e f o r m a t i o n o f a g e l s t a t e i n t h i s c o n c e n t r a t i o n r e g i o n is b e l i e v e d t o b e t h e c a u s e o f t h e m o b i l i t y c h a n g e . T h e p o s i t i o n o f t h e g e l - s o l u t i o n t r a n s i t i o n p o i n t i n t h e s w o l l e n t a b l e t , a n i m p o r t a n t f a c t o r i n t h e d r u g r e l e a s e p r o c e s s , c a n n o w b e m o n i t o r e d . . 60 C h a p t e r 3 O n e - d i m e n s i o n a l 1 H N M R I m a g i n g I n v e s t i g a t i o n s o f W a t e r a n d P o l y m e r i n S w e l l i n g H P M C T a b l e t s 3.1 Introduction T h e s w e l l i n g o f h y d r o p h i l i c p o l y m e r s s u c h as H P M C d e p e n d s o n a n u m b e r o f d i f f e r e n t p r o -c e s s e s s u c h as w a t e r p e n e t r a t i o n , p o l y m e r h y d r a t i o n a n d t h e s u b s e q u e n t i n c r e a s e s i n p o l y -m e r c h a i n m o b i l i t y . T r a d i t i o n a l l y , t h e s w e l l i n g b e h a v i o r o f t a b l e t s p r e p a r e d f r o m H P M C a n d s i m i l a r p o l y m e r s h a s b e e n s t u d i e d b y e x a m i n i n g b u l k c h a n g e s i n t h e t a b l e t b y d i r e c t p h y s i c a l m e a s u r e m e n t o r w i t h o p t i c a l m i c r o s c o p y a n d p h o t o g r a p h y as d e s c r i b e d i n S e c -t i o n 1 .1 .4 . C h a n g e s i n t a b l e t d i m e n s i o n s a n d t h e w a t e r p e n e t r a t i o n f r o n t i n t o t h e t a b l e t h a v e b e e n u s e d t o d r a w c o n c l u s i o n s r e g a r d i n g t h e n a t u r e o f t h e w a t e r a n d p o l y m e r t r a n s -p o r t p r o c e s s e s . A n i n - d e p t h u n d e r s t a n d i n g o f t h e s e s w e l l i n g s y s t e m s , h o w e v e r , r e q u i r e s a n e x a c t k n o w l e d g e o f t h e w a t e r a n d p o l y m e r c o n c e n t r a t i o n s as f u n c t i o n s o f p o s i t i o n a n d s w e l l i n g t i m e . S u c h c o n c e n t r a t i o n d i s t r i b u t i o n s a r e n e c e s s a r y t o d e v e l o p a n d t e s t m o d e l s f o r t h e s w e l l i n g b e h a v i o r o f t h e p o l y m e r . N M R i m a g i n g i s a n i d e a l t e c h n i q u e f o r s t u d y i n g t h e s e s y s t e m s b e c a u s e i t c a n p r o v i d e s p a t i a l l y - r e s o l v e d c o n c e n t r a t i o n s f o r i n d i v i d u a l c h e m -i c a l s p e c i e s a n d c a n m o n i t o r c h a n g e s i n t h e i r c o n c e n t r a t i o n s w i t h i n a s i n g l e s a m p l e d u r i n g t h e e n t i r e s w e l l i n g p r o c e s s i n a n o n - i n v a s i v e a n d n o n - d e s t r u c t i v e m a n n e r . S o m e p r e v i o u s i n v e s t i g a t o r s h a v e u s e d N M R i m a g i n g t o p r o b e t h e p e n e t r a t i o n o f w a t e r i n t o h y d r o p h i l i c p o l y m e r t a b l e t s [46, 4 7 , 4 8 , 49 ] . I n t h e s e s t u d i e s , t a b l e t s w e r e 61 p l a c e d i n w a t e r t o s w e l l a n d , a t v a r i o u s i n t e r v a l s , t h e w a t e r w a s c a r e f u l l y r e m o v e d a n d t w o - d i m e n s i o n a l , s l i c e - s e l e c t i v e i m a g e s o f t h e w a t e r w i t h i n t h e t a b l e t w e r e a c q u i r e d . T h e i m a g e s s h o w e d w a t e r p e n e t r a t i o n i n t o t h e t a b l e t ; c o r e a n d o v e r a l l d i m e n s i o n a l i n c r e a s e s o f t h e t a b l e t d u e t o t h e s w e l l i n g . T h e s e s t u d i e s , h o w e v e r , y i e l d e d o n l y a q u a l i t a t i v e d e s c r i p t i o n o f t h e s w e l l i n g p r o c e s s b e c a u s e t h e i m a g e s w e r e n o t a c q u i r e d w i t h e x p e r i m e n t a l p a r a m e t e r s t h a t g u a r a n t e e d q u a n t i t a t i v e s i g n a l i n t e n s i t i e s . T h u s , t h e s i g n a l s i n t h e i m a g e s c o u l d n o t b e d i r e c t l y r e l a t e d t o t h e c o n c e n t r a t i o n s o f w a t e r i n t h e s y s t e m . A l s o , t h e s e s t u d i e s w e r e l i m i t e d t o t h e w a t e r i n t h e t a b l e t ; t h e p o l y m e r c o n c e n t r a t i o n d i s t r i b u t i o n s i n t h e s w e l l i n g t a b l e t w e r e n o t i n v e s t i g a t e d d i r e c t l y a l t h o u g h t h e o v e r a l l s w e l l i n g b e h a v i o r o f t h e t a b l e t w a s d i s c u s s e d i n t e r m s o f t h e c h a n g e s i n t h e a p p a r e n t t a b l e t ' d i m e n s i o n s ' t h a t w e r e v i s i b l e i n t h e i m a g e s . T h e a c q u i s i t i o n o f q u a n t i t a t i v e c o n c e n t r a t i o n d i s t r i b u t i o n s i n r e a s o n a b l y s h o r t t i m e s , a n d a t f r e q u e n t i n t e r v a l s , d u r i n g t h e c o u r s e o f t h e e x p e r i m e n t i s a n e s s e n t i a l r e q u i r e m e n t f o r t h e d e t a i l e d s t u d y o f s w e l l i n g p o l y m e r t a b l e t s . T w o - d i m e n s i o n a l i m a g i n g t e c h n i q u e s g e n e r a l l y d o n o t m e e t t h i s c r i t e r i o n . T h e t o t a l e x p e r i m e n t a l t i m e t o a c q u i r e o n e q u a n t i t a -t i v e t w o - d i m e n s i o n a l i m a g e o f w a t e r i s o f t h e o r d e r o f h o u r s r a t h e r t h a n o f m i n u t e s d u e t o t h e r e l a t i v e l y l o n g T i r e l a x a t i o n t i m e o f w a t e r . T h e u n r e s t r i c t e d s w e l l i n g o f a t a b l e t i s a l s o a v e r y c o m p l e x s y s t e m t o a n a l y s e b e c a u s e t h e p r o c e s s e s o f w a t e r d i f f u s i o n a n d p o l y m e r e x p a n s i o n o c c u r i n t h r e e d i m e n s i o n s . T h e s e t w o e x p e r i m e n t a l c o n s i d e r a t i o n s n e c e s s i t a t e a n a l t e r n a t e s y s t e m f o r t h e i m a g i n g s t u d i e s f r o m t h o s e p r e s e n t e d i n t h e l i t e r a t u r e . I n t h e p r e s e n t w o r k , a f l a t - f a c e d , d i s k - s h a p e d p o l y m e r t a b l e t w a s p l a c e d i n a t u b e s u c h t h a t o n l y o n e o f i t s f a c e s w a s e x p o s e d t o w a t e r . T h e d i f f u s i o n a n d e x p a n s i o n p r o c e s s e s i n t h i s s y s -t e m o c c u r a l o n g o n e d i m e n s i o n o n l y , t h e l o n g a x i s o f t h e t u b e . B e c a u s e o f t h e c y l i n d r i c a l s y m m e t r y , t h e c o n c e n t r a t i o n d i s t r i b u t i o n s o f t h e w a t e r a n d p o l y m e r c a n b e d e t e r m i n e d b y u s i n g a s i n g l e g r a d i e n t a l o n g t h e a x i s o f t h e t u b e t o p r o d u c e o n e - d i m e n s i o n a l i m a g e s . T h e m a j o r a d v a n t a g e s o f t h e l a t t e r i m a g i n g t e c h n i q u e c o m p a r e d t o t w o - d i m e n s i o n a l i m a g i n g a r e t h e g r e a t l y d e c r e a s e d e x p e r i m e n t a l t i m e r e q u i r e d t o o b t a i n q u a n t i t a t i v e i m a g e s a n d t h e s i m p l i c i t y o f t h e s u b s e q u e n t a n a l y s i s . 6 2 3.2 Experimental 3 . 2 . 1 P r e p a r a t i o n o f H P M C T a b l e t s T a b l e t s w e r e p r e p a r e d b y d i r e c t c o m p r e s s i o n o f t h e a s - s u p p l i e d H P M C p o w d e r u s i n g a r o -t a r y t a b l e t p r e s s m o d i f i e d t o d e t e c t c o m p r e s s i o n a l f o r c e s . T h e H P M C p o w d e r w a s w e i g h e d o n a t o p - l o a d i n g b a l a n c e a n d t h e n t r a n s f e r r e d t o t h e d i e o f a B e t a M a n e s t y r o t a r y t a b l e t p r e s s . T h e t h i c k n e s s o f t h e t a b l e t a n d t h e p e a k f o r c e o f c o m p r e s s i o n w e r e c o n t r o l l e d b y a n a d j u s t a b l e s c r e w t h a t v a r i e d t h e p o s i t i o n o f t h e u p p e r c o m p r e s s i o n w h e e l o f t h e p r e s s a n d t h u s t h e p o s i t i o n o f t h e u p p e r p u n c h d u r i n g c o m p r e s s i o n . E a c h t a b l e t w a s w e i g h e d a f t e r c o m p r e s s i o n a n d i t s d i m e n s i o n s r e c o r d e d . D i f f e r e n t t y p e s o f t a b l e t w e r e p r e p a r e d b y v a r y i n g t h e a m o u n t o f H P M C a n d t h e f o r c e o f c o m p r e s s i o n . T h e p r o p e r t i e s o f e a c h t a b l e t t y p e a r e s u m m a r i z e d i n T a b l e 3 . 1 . T a b l e 3 . 1 : D e f i n i t i o n o f H P M C t a b l e t t y p e s a n d s u m m a r i e s o f t h e i r c h a r a c t e r i s t i c s C o m p r e s s i o n a l D i a m e t e r 6 T h i c k n e s s 6 T y p e H P M C ( m g ) F o r c e ( M P a ) ( m m ± 0 . 0 1 ) ( m m ± 0 . 0 1 ) 1 162 ± 1 6 2 ± 3 1 2 . 7 5 1 .33 2 3 2 3 ± 3 60 ± 1 1 2 . 7 5 2 . 6 6 3 3 2 3 103 1 2 . 7 5 2 . 4 6 a corrected for 5.4% w/w in as-supplied material water content 6 as m e a s u r e d w i t h d i g i t a l c a l i p e r s 3 . 2 . 2 E x p e r i m e n t a l S e t u p f o r S w e l l i n g I n v e s t i g a t i o n s T h e s w e l l i n g e x p e r i m e n t s w e r e c a r r i e d o u t w i t h t h e t a b l e t a n d w a t e r i n a 15 m m o . d . ( 1 2 . 8 m m i . d . ) N M R t u b e h e l d v e r t i c a l i n t h e r f c o i l . F i g u r e 3.1 s h o w s t h e t w o v a r i -a t i o n s o f t h e e x p e r i m e n t a l s e t u p u s e d i n t h e s e s t u d i e s . T h e u p w a r d - s w e l l i n g a r r a n g e m e n t , F i g u r e 3 . 1 ( a ) , w a s u s e d f o r t h e m a j o r i t y o f t h e e x p e r i m e n t s . I n t h i s e x p e r i m e n t a l v a r i a t i o n , t h e H P M C t a b l e t w a s p l a c e d o n a s u p p o r t a t t h e e n d o f t h e t u b e w i t h o n l y o n e f a c e e x p o s e d t o w a t e r . T h e b o t t o m f a c e a n d t h e e d g e s o f t h e t a b l e t w e r e s e a l e d w i t h a s m a l l a m o u n t o f f l u o r i n a t e d g r e a s e t o p r e v e n t l e a k a g e o f w a t e r b e t w e e n t h e t a b l e t a n d t h e t u b e w a l l . T h e s e c o n d v a r i a t i o n o f t h e s e t u p , d e p i c t e d i n F i g u r e 3 . 1 ( b ) , w a s u s e d t o o b t a i n d a t a f o r 63 D D (a) ( b ) F i g u r e 3 . 1 : T a b l e t a r r a n g e m e n t f o r s w e l l i n g (a ) u p w a r d s a n d (b ) d o w n w a r d s . T h e a r r o w s i n d i c a t e t h e d i r e c t i o n o f i n c r e a s i n g d i s t a n c e as m e a s u r e d f r o m t h e b a c k f a c e o f t h e t a b l e t r e s t i n g a g a i n s t t h e s o l i d s u p p o r t . 64 d o w n w a r d - s w e l l i n g t o t e s t f o r p o s s i b l e e f f e c t s d u e t o g r a v i t y . I n t h i s s y s t e m , t h e t o p f a c e o f t h e t a b l e t w a s h e l d a g a i n s t t h e s u p p o r t a n d t h e b o t t o m f a c e w a s e x p o s e d t o w a t e r . T h e t o p f a c e a n d e d g e s o f t h e t a b l e t w e r e s e a l e d w i t h g r e a s e w h i c h , i n a d d i t i o n t o p r e v e n t i n g w a t e r p e n e t r a t i o n a l o n g t h e t a b l e t e d g e s , a d h e r e d t h e t a b l e t t o t h e s u p p o r t . T h e p r e p a r a t i o n o f t h e t a b l e t f o r i m a g i n g o f u p w a r d s - s w e l l i n g w a s s t r a i g h t f o r w a r d . F i r s t , t h e g l a s s s u p p o r t w a s p l a c e d i n t h e N M R t u b e . T h e n , F l u o r o l u b e G R - 9 0 , a fluo-r o c a r b o n g r e a s e m a n u f a c t u r e d b y F i s h e r S c i e n t i f i c , w a s a p p l i e d b e t w e e n t h e e d g e s o f t h e g l a s s s u p p o r t a n d t h e w a l l o f t h e t u b e u s i n g a l o n g h o m e - m a d e ' s y r i n g e ' c o m p o s e d o f a p i e c e o f t u b i n g a n d a p l a s t i c r o d . T h e t a b l e t w a s t h e n a d d e d t o t h e t u b e a n d c a r e f u l l y p r e s s e d i n t o t h e g r e a s e . A m a r k e r , c o n s i s t i n g o f a g l a s s b u l b a t t h e e n d o f a t h i n r o d , w a s p o s i t i o n e d i n t h e t u b e a n d t h e d i s t a n c e b e t w e e n t h e c e n t r e o f t h e b u l b a n d t h e b o t t o m f a c e o f t h e t a b l e t w a s m e a s u r e d . T h i s d i s t a n c e , t y p i c a l l y 1 c m , p r o v i d e d a n a d d i t i o n a l r e f e r e n c e f o r t h e c a l i b r a t i o n o f t h e d i s t a n c e s c a l e i n t h e s w e l l i n g e x p e r i m e n t s as w i l l b e d i s c u s s e d i n S e c t i o n 3 . 2 . 3 . T h e p r e p a r a t i o n f o r t h e d o w n w a r d s - s w e l l i n g w a s s i m i l a r e x c e p t t h a t t h e p o s i t i o n m a r k e r w a s n o t u s e d . T h e s w e l l i n g o f t h e H P M C t a b l e t w a s i n i t i a t e d b y t h e a d d i t i o n o f w a t e r t o a n i n i t i a l l y d r y t u b e . W h e n t h e u p w a r d - s w e l l i n g o f t h e t a b l e t w a s i n v e s t i g a t e d , 5 m L o f d i s t i l l e d w a t e r w e r e a d d e d t o t h e N M R t u b e t o e n s u r e t h a t a l a r g e e n o u g h e x c e s s o f w a t e r w a s p r e s e n t t o h a v e a s e m i - i n f i n i t e e x p a n s i o n o f t h e p o l y m e r t a b l e t . F o r t h e d o w n w a r d -s w e l l i n g v a r i a t i o n , o n l y 2 m L o f w a t e r w e r e u s e d b e c a u s e o f i m a g i n g c o n s t r a i n t s . A l a r g e r v o l u m e o f w a t e r w o u l d r e q u i r e t h a t t h e t a b l e t b e p l a c e d h i g h e r i n t h e t u b e w h i c h c o u l d r e s u l t i n t h e t a b l e t r e s i d i n g a t t h e e d g e o f t h e c o i l a n d t h e r e f o r e o u t s i d e t h e r e l i a b l e i m a g e f i e l d o f v i e w . B e c a u s e o f t h e l i m i t e d v o l u m e o f w a t e r , t h i s s e t u p w a s o n l y u s e d w i t h T y p e 1 t a b l e t s w h i c h c o n t a i n e d t h e l e a s t a m o u n t o f H P M C a n d w o u l d b e l e a s t a f f e c t e d b y a l i m i t e d s o u r c e o f w a t e r . F o r t h i s s y s t e m , t h e g l a s s s u p p o r t , g r e a s e , t a b l e t , a n d w a t e r w e r e a d d e d w h i l e t h e t u b e w a s i n v e r t e d w i t h r e s p e c t t o t h e a r r a n g e m e n t i n F i g u r e 3 . 1 ( b ) . A g r e a s e d r u b b e r s e p t u m w a s u s e d t o s t o p p e r t h e o p e n e n d o f t h e t u b e . W h e n t h e s e p t u m w a s p u t i n p l a c e , i t w a s p u n c t u r e d w i t h a n e e d l e t o a l l o w p r e s s u r e e q u i l i b r a t i o n a n d e s c a p e 6 5 o f a i r b u b b l e s t h a t w o u l d r e s t a g a i n s t t h e t a b l e t w h e n t h e t u b e w a s i n v e r t e d a n d d i s t o r t t h e N M R i m a g e s . 3 . 2 . 3 O n e - d i m e n s i o n a l I m a g i n g T h e o n e - d i m e n s i o n a l i m a g i n g e x p e r i m e n t s w e r e p e r f o r m e d o n a B r u k e r M S L 4 0 0 ( 9 . 4 T ) s p e c t r o m e t e r w i t h a B r u k e r m i c r o i m a g i n g p r o b e i n c o r p o r a t i n g a 15 m m v e r t i c a l c o i l t u n e d t o 4 0 0 . 1 2 M H z , t h e J H r e s o n a n c e f r e q u e n c y . T h e N M R t u b e c o n t a i n i n g t h e t a b l e t w a s s u s p e n d e d i n t h e c e n t r e o f t h i s c o i l f o r t h e e n t i r e d u r a t i o n o f t h e s w e l l i n g e x p e r i m e n t . T h e z - g r a d i e n t o f t h e B r u k e r m i c r o i m a g i n g p r o b e w a s a l o n g t h e s a m e d i r e c t i o n as t h e m a i n m a g n e t i c f i e l d a n d t h e l o n g a x i s o f t h e N M R t u b e . A t u b e c o n t a i n i n g a 10 m M C U S O 4 s o l u t i o n w a s u s e d t o d e t e r m i n e t h e 180° a n d 90° p u l s e t i m e s a n d t o a d j u s t t h e s h i m m i n g t o e n s u r e a h o m o g e n o u s m a g n e t i c f i e l d . O n e - d i m e n s i o n a l * H i m a g e s w e r e o b t a i n e d f o r t h i s s y s t e m u s i n g t h e s p i n - e c h o p u l s e s e q u e n c e g i v e n i n F i g u r e 3 .2 . A l l i m a g e s w e r e a c q u i r e d w i t h q u a d r a t u r e p h a s e c y c l i n g w h i c h r e q u i r e s t h a t t h e n u m b e r o f s c a n s b e a m u l t i p l e o f 4 . T h e r e l a t i o n s h i p b e t w e e n t h e c o n c e n t r a t i o n o f p r o t o n s p i n s , p , a n d t h e s i g n a l o b t a i n e d w i t h t h e i m a g i n g e x p e r i m e n t , S ( T E ) , w a s g i v e n p r e v i o u s l y i n E q u a t i o n 1.15. T a b l e 3 .2 g i v e s t h e t y p i c a l p a r a m e t e r s u s e d i n t h e e x p e r i m e n t s p r e s e n t e d i n t h i s c h a p t e r . T h e e x p e r i m e n t a l t i m e p e r i m a g e w a s a b o u t 3 m i n u t e s a n d t h e t e n i m a g e s w i t h TE v a r i a t i o n w e r e o b t a i n e d i n a b o u t 3 0 m i n u t e s . T h e d a t a s e t s w e r e a c q u i r e d a t 3 h o u r i n t e r v a l s d u r i n g a n a p p r o x i m a t e l y 37 h o u r s w e l l i n g e x p e r i m e n t . T h e r e p e t i t i o n d e l a y ( T R ) o f 20 s w a s m o r e t h a n f i v e t i m e s t h e m a x i m u m T i v a l u e f o r w a t e r i n t h e s y s t e m , g u a r a n t e e i n g n o s i g n a l l o s s i n t h e i m a g e s d u e t o T i e f f e c t s . T h e t i m e - t o - e c h o ( T # ) i n t h e s p i n - e c h o s e q u e n c e w a s v a r i e d f r o m 2 m s t o 128 m s , i n t h e o r d e r 2 m s , 4 m s , 16 m s , 3 2 m s , 96 m s , 128 m s , 6 4 m s , 24 m s , 8 m s , a n d 3 m s , b y a d j u s t i n g t h e v a r i a b l e d e l a y ( V D ) . T h i s T # v a r i a t i o n m a d e p o s s i b l e t h e m e a s u r e m e n t o f t h e T 2 r e l a x a t i o n t i m e s a t e a c h p o s i t i o n i n t h e i m a g e . T h e s i g n a l i n t e n s i t i e s i n t h e s h o r t e s t T # i m a g e (2 m s ) w e r e e s s e n t i a l l y q u a n t i t a t i v e b u t c o u l d b e i m p r o v e d f o r a n y s i g n a l l o s s d u e t o T 2 d e c a y b y u s i n g t h e T 2 d i s t r i b u t i o n a n d E q u a t i o n 3.1 w h i c h is a r e a r r a n g e m e n t o f E q u a t i o n 1.8. A l l o f t h e w a t e r s i g n a l s h o u l d b e v i s i b l e i n t h e c o r r e c t e d i m a g e s . H o w e v e r , t h e i m a g i n g e x p e r i m e n t 66 90 c 180 c T R rf pulses v D RA-T E z-gradient A Q / 2 A Q Figure 3.2: Pulse sequence used to acquire the one-dimensional projections. The variable experimental parameters are defined as follows: TR is the delay between successive exper-iments, 90° and 180° labels are rf pulses, G 2 is the strength of the z-gradient, A Q is the acquisition time, V D is a variable delay and T g is the time-to-echo. Table 3.2: Typ ica l values for parameters used in the spin-echo pulse sequence for acquiring the one-dimensional images. Parameter Value 90° radiofrequency pulse (/xs) 18-19 180° radiofrequency pulse (//s) 36-38 Spectral W i d t h , Sw (Hz) 83333.33 Number of points acquired, T p (Words 0 ) 128 Number of points in F T , S/ (Words) 256 Acquisi t ion Time, A Q ( / / S ) 768 Z-gradient, GZ (G /cm) 9.8 ± 0.2 Repetit ion delay, TR (s) 20 Number of Scans 8 Time-to-echo, TE (ms) variable a On the Bruker M S L Aspect3000 computer, one Word equals 24 bits 67 u s e d i n t h i s c h a p t e r d e t e c t s o n l y m o b i l e w a t e r . T h u s , a n y t i g h t l y b o u n d , i m m o b i l i z e d w a t e r c o u l d b e i n v i s i b l e i n t h e s e m e a s u r e m e n t s d u e t o i t s a n t i c i p a t e d e x t r e m e l y s h o r t T 2 v a l u e . 3 . 2 . 4 P r o c e s s i n g o f I m a g e D a t a E a c h o n e - d i m e n s i o n a l i m a g e w a s i n i t i a l l y o b t a i n e d i n t h e f o r m o f a n e c h o w h e r e t h e N M R s i g n a l w a s e n c o d e d i n i n t e n s i t y as a f u n c t i o n o f t i m e . F o u r i e r t r a n s f o r m a t i o n a n d m a g n i -t u d e c a l c u l a t i o n w e r e p e r f o r m e d o n t h e A s p e c t 3 0 0 0 c o m p u t e r o f t h e M S L 4 0 0 s p e c t r o m e t e r t o c o n v e r t e a c h i m a g e i n t o a m a p o f s i g n a l i n t e n s i t y as a f u n c t i o n o f f r e q u e n c y . O n e i m a g e i n t h e d a t a se t f o r a p a r t i c u l a r s w e l l i n g e x p e r i m e n t w a s c h o s e n as a n a b s o l u t e i n t e n s i t y re f -e r e n c e a n d t h e i n t e n s i t i e s o f t h e r e s t o f t h e i m a g e s i n t h e d a t a set w e r e s c a l e d w i t h r e s p e c t t o i t s i n t e n s i t y . F o r f u r t h e r p r o c e s s i n g , t h e i m a g e f i l e s w e r e t r a n s f e r r e d t o a M a c i n t o s h C e n t r i s 6 5 0 c o m p u t e r v i a B r u k e r N M R L i n k s o f t w a r e . T h e f i l e s w e r e c o n v e r t e d t o I B M f o r m a t a n d t h e n B r u k e r W I N - N M R w a s u s e d t o e x p o r t a n A S C I I file, a n e x a m p l e o f w h i c h i s g i v e n i n A p p e n d i x A . l , t h a t c o n t a i n e d i m a g i n g p a r a m e t e r s s u c h as t h e n u m b e r o f d a t a p o i n t s , t h e s t a r t a n d e n d f r e q u e n c y v a l u e s , t h e f r e q u e n c y i n c r e m e n t , a n d t h e l i s t o f N M R s i g n a l i n t e n s i t i e s . I n l a t e r e x p e r i m e n t s , a c o n v e r t e r p r o g r a m , w r i t t e n i n J a v a a n d r u n o n a M a c i n t o s h L C 4 7 5 c o m p u t e r , w a s u s e d t o e x t r a c t t h e s a m e p a r a m e t e r s f r o m F o u r i e r t r a n s -f o r m e d o n e - d i m e n s i o n a l i m a g e f i l e s . T h e s e c o n d c o n v e r t e r p r o g r a m , l i s t e d i n A p p e n d i x A . 2 , i n c r e a s e d t h e s p e e d o f i m a g e p r o c e s s i n g as i t c o u l d c o n v e r t i m a g e files i n b a t c h e s w h e r e a s w i t h W I N - N M R , t h e f i l e s h a d t o b e p r o c e s s e d i n d i v i d u a l l y . T h e f r e q u e n c y s c a l e w a s c a l c u -l a t e d u s i n g a c o m p u t e r p r o g r a m t h a t r e a d i n t h e f i l e s , c a l c u l a t e d t h e f r e q u e n c y l i s t u s i n g t h e s t a r t f r e q u e n c y a n d t h e f r e q u e n c y i n c r e m e n t a n d t h e n w r o t e n e w i m a g e files i n t h e f o r m o f ( f r e q u e n c y , i n t e n s i t y ) d a t a p a i r s . T h i s p r o g r a m is l i s t e d i n A p p e n d i x A . 3 . I n a t y p i c a l e x p e r i m e n t , t h e f r e q u e n c y s c a l e e x t e n d e d f r o m - 4 1 6 6 6 . 6 6 H z t o + 4 1 6 6 6 . 6 6 H z . T h e i m a g e o f t h e w a t e r i n t h e t a b l e t w a s n o t a l w a y s i n t h e s a m e p o s i -t i o n i n t h i s f r e q u e n c y r a n g e b e c a u s e t h e p o s i t i o n o f t h e s a m p l e w i t h r e s p e c t t o t h e c o i l M0 = MXtyeT2 68 w a s r a r e l y d u p l i c a t e d e x a c t l y . T h e i n t e r p r e t a t i o n a n d c o m p a r i s o n o f d a t a f r o m s e p a r a t e e x p e r i m e n t s w a s m a d e e a s i e r b y r e l a t i n g t h e i n t e n s i t y o f w a t e r t o t h e m o r e m e a n i n g f u l s c a l e o f d i s t a n c e . I n o r d e r t o c o n v e r t t h e f r e q u e n c y s c a l e i n t o a d i s t a n c e s c a l e , t w o t e r m s n e e d e d t o b e d e f i n e d . T h e f i r s t w a s t h e p o s i t i o n o f t h e o r i g i n , t h e r e f e r e n c e p o s i t i o n f r o m w h i c h a l l d i s t a n c e s w o u l d b e m e a s u r e d . I n t h e s w e l l i n g t a b l e t s y s t e m , t h e l o g i c a l c h o i c e f o r t h e o r i g i n w a s t h e p o s i t i o n o f t h e t a b l e t f a c e t h a t r e s t s a g a i n s t t h e g l a s s s u p p o r t i n t h e t u b e . N e x t , i n c r e a s i n g d i s t a n c e w a s d e f i n e d as t h e d i r e c t i o n a w a y f r o m t h e s u p p o r t t o w a r d s t h e b u l k w a t e r as i n d i c a t e d i n F i g u r e 3 . 1 . T h i s d e f i n i t i o n a l l o w e d f o r e a s y c o m p a r i s o n o f d a t a s e t s r e g a r d l e s s o f w h e t h e r t h e t a b l e t w a s s w e l l i n g u p w a r d s o r d o w n w a r d s . D i s t a n c e i n t h e i m a g e w a s r e l a t e d t o f r e q u e n c y b y E q u a t i o n 3 .2 w h e r e D t i s t h e d i s t a n c e , i n c m , f r o m t h e o r i g i n f o r t h e ith. p o i n t , ft- i s t h e f r e q u e n c y o f t h e ith p o i n t , f 0 i s t h e f r e q u e n c y o f t h e o r i g i n , 7// i s t h e g y r o m a g n e t i c r a t i o o f 1 H i n H z / G , a n d Gz i s t h e g r a d i e n t s t r e n g t h i n G / c m . W i t h t h i s e q u a t i o n , t h e i m a g e s w e r e c o n v e r t e d f r o m a f r e q u e n c y s c a l e i n t o a d i s t a n c e s c a l e . T h e r e w a s a ±750 H z e r r o r i n d e t e r m i n i n g t h e p o s i t i o n o f t h e o r i g i n f r o m t h e i m a g e s w h i c h c o r r e s p o n d s t o a n e r r o r o f a b o u t ±0.02 c m i n e a c h d i s t a n c e v a l u e . B e c a u s e o f t h e n a t u r e o f t h e c a l c u l a t i o n , t h e e r r o r w a s s y s t e m a t i c a n d t h e e n t i r e d i s t a n c e s c a l e w o u l d b e s h i f t e d e i t h e r t o s l i g h t l y l a r g e r d i s t a n c e s o r t o s l i g h t l y s m a l l e r o n e s . A n a d d i t i o n a l r e f e r e n c e f o r t h e d i s t a n c e s w a s t h e p o s i t i o n o f a m a r k e r w h i c h a p p e a r e d as a d i p i n t h e i m a g e i n t e n s i t y a r o u n d 1 c m . T h e d i s t a n c e t o t h i s m a r k e r w a s k n o w n a n d w a s u s e d t o v e r i f y t h e d i s t a n c e s c a l e . E a c h i n t e n s i t y v a l u e i n t h e o n e - d i m e n s i o n a l i m a g e r e p r e s e n t e d t h e a v e r a g e N M R s i g n a l f r o m a s p e c i f i c v o l u m e e l e m e n t i n t h e s a m p l e w h o s e s i z e w a s d e t e r m i n e d b y t h e r e s o l u t i o n o f t h e i m a g i n g e x p e r i m e n t a n d t h e d i a m e t e r o f t h e N M R t u b e t h a t c o n t a i n s t h e t a b l e t . F o r t h e e x p e r i m e n t s p r e s e n t e d i n t h i s c h a p t e r , t h e r e s o l u t i o n w a s 0 . 0 1 6 c m a n d t h e c r o s s - s e c t i o n a l a r e a f o r t h e N M R t u b e w a s 1 .287 c m 2 . T h e r e f o r e , e a c h d a t a p o i n t i n Di = fi — fo 1H Gz 69 t h e w a t e r i m a g e w a s t h e N M R s i g n a l f r o m w a t e r i n a v o l u m e o f 0 . 0 2 0 c m 3 . T h e i n t e n s i t y v a l u e s i n t h e i m a g e s , as t h e y w e r e o r i g i n a l l y o b t a i n e d , w e r e a r b i t r a r y a n d v a r i e d b e t w e e n e x p e r i m e n t s . I n N M R s p e c t r o s c o p y , t h e s i g n a l f r o m a n i n t e r n a l o r e x t e r n a l r e f e r e n c e o f k n o w n c o n c e n t r a t i o n i s o f t e n u s e d t o c a l i b r a t e t h e s i g n a l o f a s p e c i e s w h o s e c o n c e n t r a t i o n i s u n k n o w n . T h e s a m e p r o c e d u r e c a n b e u s e d i n N M R i m a g i n g . I n t h e o n e - d i m e n s i o n a l i m a g e s o f w a t e r , c a r e w a s t a k e n t o e n s u r e t h a t b o t h w a t e r i n t h e t a b l e t r e g i o n a n d w a t e r i n t h e b u l k r e g i o n w e r e v i s i b l e . T h e c o n c e n t r a t i o n o f w a t e r i n t h e b u l k i s k n o w n a n d c a n b e u s e d t o c a l i b r a t e t h e i n t e n s i t i e s i n a l l r e g i o n s o f t h e t a b l e t . T h e i m a g e s p r e s e n t e d i n S e c t i o n 3 .3 .1 a r e s h o w n w i t h t h e i n t e n s i t i e s o f w a t e r i n t h e t a b l e t r e g i o n s n o r m a l i z e d b y t h e b u l k w a t e r c o n c e n t r a t i o n . I n t h e i m a g i n g e x p e r i m e n t p e r f o r m e d w i t h D 2 0 , t h e 1 H s i g n a l f r o m t h e s w o l l e n p o l y m e r t a b l e t w a s r e f e r e n c e d i n a s i m i l a r m a n n e r t o t h e i n t e n s i t y o f w a t e r s i g n a l f r o m a 5 m m o . d . (4 .2 m m i . d . ) t u b e . U s i n g t h e s q u a r e o f r a t i o o f t h e i n n e r d i a m e t e r s ( 1 2 . 8 2 / 4 . 2 2 ) , w h i c h is t h e s a m e as t h e r a t i o o f t h e c r o s s - s e c t i o n a l a r e a s o f t h e l a r g e a n d s m a l l t u b e , t h e i n t e n s i t y o f 1 H s i g n a l f r o m t h e s m a l l t u b e is 9 . 3 t i m e s l e s s t h a n f r o m t h e l a r g e t u b e w h e n t h e r e s o l u t i o n is t h e s a m e . T h u s , t h e i n t e n s i t y o f t h e 1 H s i g n a l f r o m t h e t a b l e t s w o l l e n i n D 2 0 c a n b e d i r e c t l y r e l a t e d t o t h e s i g n a l i n t e n s i t y o b t a i n e d i n t h e i m a g i n g e x p e r i m e n t s w i t h d i s t i l l e d w a t e r . S e v e r a l f u r t h e r c a l c u l a t i o n s w e r e p e r f o r m e d w i t h t h e i m a g e d a t a f i l e s . T h e f i r s t w a s t h e c a l c u l a t i o n o f t h e T 2 d i s t r i b u t i o n i n t h e s w e l l i n g p o l y m e r f r o m t h e t e n f i l e s t h a t c o m p o s e d t h e 2 m s t o 128 m s T # v a r i a t i o n a t e a c h d a t a c o l l e c t i o n i n t e r v a l . T h e T 2 v a l u e w a s d e t e r m i n e d b y t a k i n g t h e i n v e r s e o f t h e s l o p e o f t h e p l o t o f L n ( s i g n a l i n t e n s i t y ) v e r s u s T ^ , t h e s a m e p r o c e d u r e u s e d t o c a l c u l a t e t h e T 2 v a l u e s f o r t h e c a l i b r a t i o n e q u a t i o n i n C h a p t e r 2 . A c o m p u t e r p r o g r a m , l i s t e d i n A p p e n d i x A . 4 , w a s w r i t t e n t o p e r f o r m t h e l e a s t -s q u a r e s c a l c u l a t i o n o n t h e s i g n a l i n t e n s i t y d a t a i n t h e TE v a r i a t i o n f i l e s t o d e t e r m i n e t h e s l o p e a n d h e n c e t h e T 2 v a l u e f o r e a c h p o i n t i n t h e i m a g e . T h e p r o g r a m r e a d i n t h e i m a g e f i l e s a n d t h e c o r r e s p o n d i n g T^ ; v a l u e s f o r e a c h o f t h e t e n f i l e s o f t h e T ^ - v a r i a t i o n d a t a s e t a n d c o m b i n e d t h e d a t a i n t o a n a r r a y i n o r d e r o f i n c r e a s i n g T # . T h e c a l c u l a t i o n p r o c e d u r e w a s t o d e t e r m i n e t h e s l o p e a n d t h e e r r o r i n t h e s l o p e f o r s u b s e t s o f t h e d a t a , s t a r t i n g f r o m 70 the four shortest TE files and then adding one file at a time to the calculation up to the max imum number of ten files. Thus for each distance, seven separate slopes were computed using 4, 5, 6, 7, 8, 9, and 10 data pairs, respectively. The calculation that resulted in the lowest relative error in the slope was chosen as the best result and its slope was used to compute T 2 . The slope calculated from all 10 data pairs was chosen as the default result when its relative error was no more than 50% greater than the lowest relative error. This method of calculating the T 2 distribution was chosen because of the range of T 2 values in the swollen polymer and the range of.Te values used to characterize them. The measurements of the T 2 values in mixtures of H P M C and water presented in Section 2.3.1 showed that the T 2 of the water component can vary between about 10 ms and 1000 ms. For species whose T 2 values are greater than 50 ms, there is st i l l visible signal in the image acquired wi th the longest TE of 128 ms. However, in the regions of the swollen tablet where T 2 is shorter than 50 ms, the N M R signal from these regions essentially disappears in the long TE images, resulting in one or more data points where the signal intensity is zero. If these zero points are included in the least-squares calculation, the slope is heavily skewed towards them and the error in the slope increases substantially. Thus, by starting wi th the short TE data points and using the relative error in the slope as the criterion for how many data points should be used in the final calculation, the T 2 values can be determined from the appropriate subset of data. W i t h this method, the majority of T 2 values in the system were calculated using the default number of 10 data pairs and only those in the most concentrated polymer regions with the much shorter T 2 values were determined from fewer data pairs. The resulting T 2 distributions were needed in two additional calculations. They were used to correct the signal intensities of the 2 ms projections for any signal loss due to T 2 . They were also converted into H P M C weight distributions through Equat ion 2.7 which describes the relationship between the T 2 of water and the H P M C concentration in H P M C - w a t e r mixtures. The Pascal programs that performed these functions are listed in Appendices A . 5 and A . 6 , respectively. The H P M C weight percent distributions were also 71 p r o c e s s e d f u r t h e r t o c o n v e r t t h e u n i t s o f t h e d i s t r i b u t i o n i n t o g r a m s p e r c e n t i m e t r e c u b e d . T h e c o n v e r s i o n w a s p e r f o r m e d b y m u l t i p l y i n g e a c h w e i g h t f r a c t i o n v a l u e b y 0 . 0 2 0 1 c m 3 , t h e r e s u l t o f E q u a t i o n 3 .3 w h e r e p i s t h e d e n s i t y , a s s u m e d t o b e 1, A i s t h e c r o s s - s e c t i o n a l a r e a o f t h e N M R t u b e , 7 i s t h e g y r o m a g n e t i c r a t i o a n d a n d Sw, T o , a n d G 2 a r e e x p e r i m e n t a l p a r a m e t e r s l i s t e d i n T a b l e 3 .2 . Factor = PA S w (3.3) 7 J-D 3.3 Results and Discussion 3 . 3 . 1 W a t e r P e n e t r a t i o n i n t o H P M C T a b l e t s T h e p e n e t r a t i o n o f w a t e r i n t o t h e H P M C t a b l e t b e g a n i m m e d i a t e l y u p o n i t s a d d i t i o n t o t h e d r y t a b l e t a n d c o n t i n u e d f o r t h e d u r a t i o n o f t h e s w e l l i n g e x p e r i m e n t . F i g u r e 3 . 3 s h o w s a o n e - d i m e n s i o n a l i m a g e o f t h e w a t e r d i s t r i b u t i o n t a k e n w i t h t h e s h o r t e s t p o s s i b l e TE o f 2 m s a t a s w e l l i n g t i m e o f 4 h o u r s . T h e t a b l e t i n t h i s s y s t e m w a s o f t h e T y p e 1 v a r i e t y w i t h a n o r i g i n a l t h i c k n e s s o f 0 . 1 3 3 c m , as i n d i c a t e d i n t h e figure b y t h e d a s h e d v e r t i c a l l i n e . B o t h t h e p e n e t r a t i o n o f w a t e r i n t o t h e t a b l e t a n d t h e e x p a n s i o n o f t h e H P M C a r e v i s i b l e i n t h i s i m a g e . T h e i n c r e a s e d * H N M R s i g n a l i n t h e t a b l e t r e g i o n c l e a r l y s h o w s t h a t w a t e r h a s m o v e d a f a i r d i s t a n c e i n t o t h e t a b l e t f r o m t h e o r i g i n a l w a t e r - t a b l e t i n t e r f a c e . T h e d i s p l a c e m e n t e f f ec t o f t h e p o l y m e r e x p a n s i o n is a p p a r e n t as a d e c r e a s e o f w a t e r s i g n a l a w a y f r o m t h e i n i t i a l t a b l e t p o s i t i o n i n w h a t w a s o r i g i n a l l y a b u l k w a t e r r e g i o n . W a t e r a p p e a r s n o t t o h a v e p e n e t r a t e d t h e t a b l e t c o m p l e t e l y a t t h i s s w e l l i n g t i m e as t h e r e i s a r e g i o n o f t h e t a b l e t t h a t e x h i b i t s n o * H s i g n a l . T h e s i g n a l i n t e n s i t y o f F i g u r e 3 .3 is a s s u m e d t o a r i s e s o l e l y f r o m t h e w a t e r p r o t o n s . H o w e v e r , t h e p r o t o n s o f t h e s w o l l e n p o l y m e r m a y c o n t r i b u t e t o t h e o v e r a l l s i g n a l . T o t e s t t h e e x t e n t o f t h i s c o n t r i b u t i o n , a X H i m a g i n g e x p e r i m e n t w a s p e r f o r m e d o n a t a b l e t s w e l l i n g i n D2O r a t h e r t h a n H 2 0 . T h e 1R s i g n a l i n t h i s s y s t e m c o u l d a r i s e f r o m m o b i l e f u n c t i o n a l i t i e s o n t h e p o l y m e r c h a i n s u c h as h y d r o x y l a n d m e t h y l g r o u p s a n d a l s o f r o m H D O w h i c h w o u l d b e t h e r e s u l t o f e x c h a n g e b e t w e e n t h e p o l y m e r h y d r o x y l s a n d D 2 0 . F i g u r e 3 .4 s h o w s t h a t 72 -F i g u r e 3 . 3 : A n e x a m p l e o f a o n e - d i m e n s i o n a l i m a g e s h o w i n g n o r m a l i z e d w a t e r p e n e t r a t i o n i n t o a n H P M C t a b l e t a n d t h e r e s u l t i n g t a b l e t s w e l l i n g a t a t i m e o f 4 h o u r s . T h e o r i g i n a l w a t e r - t a b l e t i n t e r f a c e is i n d i c a t e d b y t h e d a s h e d v e r t i c a l l i n e a t 0 . 1 3 3 c m . 73 Relative Intensity (a) Swelling in D2O, 7 hours 1.001 0.80 H (b) Swelling in H2O, 7 hours H2O in 4.2 i.d. tube H2O in 12.8 00000000000000 mm i.d. tube 0.60 0.40 H 0.20 0.00 0.25 0.50 0.75 1.00 1.25 i 0.00 i 1.50 0.0 0.1 polymer protons andHDO ^ 0.2 0.3 0.4 0.5 0.6 0.7 (c) Swelling in D 2 0, 37 hours <d) S w e U i n S i n H 2 ° > 3 7 h o u r s H2O in 4.2 1.001 0.801 0.60 0.401 0.20 H i.d. tube 0.00 0.00 0.25 0.50 0.75 l.OO 1.00' 0.80' 0.60 0.401 0.201 ' — 1 0.00 1.25 1.50 0.0 H2O in 12.8 ooooooooo i.d. tube polymer protons and HDO tyyMEiii | iHlHiHiiiFii|iHiMiH 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Distance (cm) F i g u r e 3 .4 : 1 H i m a g e s o b t a i n e d f r o m a t a b l e t s w e l l i n g i n D 2 0 , (a ) 7 h o u r s ( c ) 3 7 h o u r s . T h e a x e s l a b e l s f o r t h e f o u r p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e i m a g e i n t e n s i t i e s i n (a ) a n d (c ) a r e r e l a t i v e t o t h e m a x i m u m s i g n a l i n t e n s i t y f r o m t h e 4 . 2 m m i . d . t u b e , s e e n as a s i g n a l p l a t e a u a b o v e 1 c m . I n (b ) a n d ( d ) , t h e p r o t o n s i g n a l s f r o m t h e D 2 0 e x p e r i m e n t a r e r e n o r m a l i z e d t o t h e s i g n a l i n t e n s i t y f r o m a 1 2 . 8 m m i . d . t u b e a n d o v e r l a p p e d w i t h i m a g e s f r o m a s w e l l i n g e x p e r i m e n t u s i n g H 2 0 . T h e d i s t a n c e s c a l e i n ( b ) a n d ( d ) i s e x p a n d e d t o f o c u s o n t h e r e g i o n c o n t a i n i n g t h e s w o l l e n p o l y m e r t a b l e t . 74 t h e m e a s u r e d p r o t o n s i g n a l f r o m t h i s s y s t e m is q u i t e l o w . A t t h e s w e l l i n g t i m e o f 7 h o u r s , t h e t a b l e t h a s b e e n p e n e t r a t e d c o m p l e t e l y b y w a t e r a n d t h e m a j o r i t y o f p r o t o n e x c h a n g e b e t w e e n t h e p o l y m e r a n d t h e D 2 0 h a s o c c u r r e d . T h e a p p e a r a n c e o f X H s i g n a l i n r e g i o n s a w a y f r o m t h e p o l y m e r t a b l e t a t s u c h a n e a r l y s w e l l i n g t i m e s u g g e s t e d t h a t d i f f u s i o n o r r e p e a t e d c h e m i c a l e x c h a n g e h a d s p r e a d H D O t h r o u g h o u t t h e s y s t e m . T h e s i g n a l i n t e n s i t i e s f r o m t h e s w e l l i n g e x p e r i m e n t i n D 2 0 a r e o r i g i n a l l y r e f e r e n c e d t o t h e s i g n a l i n t e n s i t y i n a 4 . 2 m m i . d . t u b e c o n t a i n i n g w a t e r . T o c o m p a r e t h e s i g n a l i n t e n s i t i e s f r o m t h e s w e l l i n g e x p e r i m e n t i n D 2 0 t o t h o s e o f t h e s w e l l i n g e x p e r i m e n t s i n H 2 0 , t h e s i g n a l f r o m t h e D 2 0 e x p e r i m e n t m u s t b e r e f e r e n c e d t o t h e s a m e i n t e n s i t y as i n t h e H 2 0 e x p e r i m e n t s , t h e w a t e r s i g n a l i n a 12 .8 i . d . t u b e . T h e r e f o r e , t h e s i g n a l i n F i g u r e 3 . 4 ( a ) a n d (c ) i s d i v i d e d b y 0 . 1 0 7 , t h e r a t i o o f t h e s q u a r e s o f t h e d i a m e t e r s o f t h e t w o r e f e r e n c e t u b e s , ( 4 . 2 ) 2 / ( 1 2 . 8 ) 2 . T h e c o n t r i b u t i o n o f t h e p o l y m e r p r o t o n s t o t h e o v e r a l l p r o t o n s i g n a l , c l e a r l y s e e n i n F i g u r e 3 . 4 ( b ) a n d ( d ) , i s n e g l i g i b l e u n d e r t h e c o n d i t i o n s o f t h e s e i m a g i n g e x p e r i m e n t s . T h e q u a n t i t a t i v e r e l i a b i l i t y o f t h e N M R s i g n a l i n i m a g e s s u c h as F i g u r e 3 . 3 d e p e n d s o n t h e d e g r e e o f s i g n a l d e p h a s i n g d u e t o T 2 r e l a x a t i o n t h a t o c c u r s d u r i n g t h e i m a g i n g T # o f 2 m s . T h e T 2 v a l u e s o f t h e X H o f w a t e r w e r e p r e s e n t e d i n S e c t i o n 2 .3 .1 a n d s h o w n t o d e p e n d s t r o n g l y o n t h e c o n c e n t r a t i o n o f H P M C i n a n H P M C - w a t e r m i x t u r e . T h e r e f o r e , t h e l o s s o f s i g n a l f r o m d i f f e r e n t r e g i o n s o f t h e s w o l l e n t a b l e t s h o u l d v a r y w i t h t h e a m o u n t o f p o l y m e r t h a t i s p r e s e n t . T h e i m a g e s a c q u i r e d w i t h a TE o f 2 m s c a n b e m a d e q u a n t i t a t i v e b y c o r r e c t i n g f o r t h e T 2 - d e p h a s i n g w i t h E q u a t i o n 3 . 1 . T o c o r r e c t a l l r e g i o n s o f t h e i m a g e , t h e T 2 r e l a x a t i o n t i m e d i s t r i b u t i o n w a s d e -t e r m i n e d b y v a r y i n g t h e TE p a r a m e t e r i n t h e s p i n - e c h o p u l s e s e q u e n c e as d e s c r i b e d i n S e c t i o n 3 . 2 . 3 . T h e e f f ec t o f T E o n * H s i g n a l i n t e n s i t y i s s e e n i n F i g u r e 3 . 5 ( a ) . A s T ^ i s i n c r e a s e d , t h e w a t e r s i g n a l f r o m t h e m o r e c o n c e n t r a t e d p o l y m e r r e g i o n s d e c r e a s e s m o r e r a p i d l y t h a n t h a t f r o m t h e less c o n c e n t r a t e d p o l y m e r r e g i o n s . T h e T 2 v a l u e f o r e a c h d i s -t a n c e p o i n t c a n b e c a l c u l a t e d f r o m t h e s l o p e o f a l i n e a r l e a s t - s q u a r e s f i t t i n g o f L n ( s i g n a l i n t e n s i t y ) as a f u n c t i o n o f T ^ . F i g u r e 3 . 5 ( b ) s h o w s t h e r e s u l t i n g T 2 d i s t r i b u t i o n w h i c h c a n b e u s e d t o c o r r e c t t h e s i g n a l s i n t h e 2 m s p r o j e c t i o n . S i g n i f i c a n t d i f f e r e n c e s b e t w e e n t h e 75 0 . 0 0 .1 0 . 2 0 . 3 0 . 4 Distance (cm) 0 . 5 0 . 6 (b) 5 0 0 4 0 0 1 T2 (ms) 3 0 0 " 2 0 0 " 1 0 0 -0 T 1 r -> r 0 . 0 0 .1 0 . 2 0 . 3 0 . 4 Distance (cm) 0 . 5 0 . 6 Figure 3.5: The variation of the signal intensity in the water images as a function of the T s (a) and the corresponding T 2 values (b) calculated from the data in (a) after 25 hours of swelling. The dashed vertical line indicates the ini t ial position of the water-tablet interface at 0.133 cm. The T# values are 2 ms (dotted open squares), 3 ms (filled triangles), 4 ms (dotted filled squares), 8 ms (filled diamonds), 16 :ms (filled squares), 24 ms (open squares), 32 ms (filled circles), 64 ms (open triangles), 96 ms (open crossed squares) and 128 ms (open circles). 76 measured and corrected water images are clearly visible in Figure 3.6 which shows various stages of water penetration into the 0.133 cm thick tablet. The shapes of the corrected distributions match the measured ones except at the swelling time of 1 hour. For that time, there appears to be no adjustment in signal intensity for the water that has penetrated most deeply into the tablet. When the water concentration is relatively low and the T 2 relaxation parameter is relatively short compared to other regions of the system, the error in the signal intensity makes the determination of a T 2 value extremely difficult. Thus, because certain intensity values in the distribution are not corrected, the distribution ap-parently changes shape. The signal intensities in the corrected images are quantitatively reliable and are directly proportional to water concentrations in all regions of the system. The water penetration behaviors of several variations of H P M C tablets were studied to determine which factors were important. The effects of three factors were tested: the direction of swelling with respect to gravity, the thickness of the tablet, and the peak compressional force in the tablet preparation. When the results from tablets of different thickness were compared, the distances for the thinner tablet were adjusted by a constant shift to larger values to allow the initial water-tablet interfaces of the two tablet systems to coincide. The imaging data from experiments performed with the tablet swelling upward and those performed with the tablet swelling downward were compared to test the effect of the force on gravity on the mechanical stability of the gel. The force of gravity would cause viscous polymer solutions, about 10% H P M C and below, to flow. In the system where the tablet is allowed to swell downward, the flow of polymer in solution may result in a different water distribution than for a system that swells in the upwards direction. Figure 3.7 shows the similarity of the water distributions for the two systems indicating that gravity has no discernible influence on the swelling tablet in this system. The elimination of all air bubbles from the downward-swelling system was problematic and the effect of such an air bubble is visible in Figure 3.7. The next variation of the swelling experiment was a comparison of similarly prepared 77 Relative Intensity (a) 4 hours 1.00 H 0.80 H 0.60 H 0.40 H 0.20 1 0.00 (c) 25 hours l.OO 0.80 0.60 0.40 0.20 0.00 (b) 16 hours 1.00 -I (d) 37 hours 1.00 0.80 H 0.60 -f 0.40 H 0.20 H ~ i — < — i — < — i — 1 1 o.oo - | — i — i — H — i — i r 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 1 1 1 1 1 0.4 0.5 0.6 Distance (cm) Figure 3.6: Water images showing both the 2 ms image (open circles) and the T2-corrected distributions (filled circles) at different swelling times, (a) 4 hours, (b) 16 hours, (c) 25 hours, (d) 37 hours. The axes labels for the four plots are the same and are defined by the arrows. The intensities in the images are relative to the bulk water intensity. 78 Relative Intensity ^ (a) 1 hour 1.00 Oi 0.60 0.40 0.20 ••8* (b) 7 hours oogo Q • i I i • 0.60 0.40 0.20 0.00 o° oo0o$lboo0 -QQQQgQOQQQ o • • i 0 • i • c* • I • I I y i p. - i — i — i — i — i — i — i — i — i 0.00 -I ' 1— 1 1 r 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • 0.0 0.1 0.2 0.3 0.4 0.5 0.6 (c) 13 hours (d) 19 hours 1.00 0.80 0.60 0.40 0.20 0.00 • < f • / • i 0.0 0.1 • i i i i i . i . i 0.2 0.3 0.4 0.5 0.6 too H 0.60 0.40 0.20 i 0.00 •••So*8 o^ogejoooo0^ o o jr 4& Distance (cm) F i g u r e 3 . 7 : W a t e r d i s t r i b u t i o n s f r o m u p w a r d s ( f i l l e d c i r c l e s ) a n d d o w n w a r d s ( o p e n c i r c l e s ) s w e l l i n g e x p e r i m e n t s , 2 m s i m a g e s t a k e n a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 7 h o u r s , (c ) 13 h o u r s , a n d ( d ) 19 h o u r s . T h e a x e s l a b e l s f o r t h e f o u r p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e i n t e n s i t i e s i n t h e i m a g e s a r e r e l a t i v e t o t h e b u l k w a t e r i n t e n s i t y . T h e m a r k e d d e v i a t i o n f r o m a s m o o t h c u r v e v i s i b l e i n t h e d o w n w a r d s s w e l l i n g d a t a i s t h e r e s u l t o f a n a i r b u b b l e . 79 Relative Intensity Distance (cm) F i g u r e 3 . 8 : C o r r e c t e d a v e r a g e w a t e r d i s t r i b u t i o n s f o r t h e T y p e 1 t a b l e t ( f i l l e d c i r c l e s , n = 2 ) a n d t h e T y p e 2 t a b l e t ( o p e n c i r c l e s , n = 3 ) a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 4 h o u r s a n d (c ) 7 h o u r s . T h e a x e s l a b e l s f o r t h e f o u r p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e i n t e n s i t i e s i n t h e i m a g e s a r e r e l a t i v e t o t h e b u l k w a t e r i n t e n s i t y . T h e d i s t a n c e v a l u e s f o r t h e T y p e 1 t a b l e t d a t a h a v e b e e n s h i f t e d b y + 0 . 1 3 3 c m , t h e d i f f e r e n c e i n t h i c k n e s s b e t w e e n t h e t w o t a b l e t s . T h e d a s h e d v e r t i c a l l i n e a t 0 . 2 6 6 c m i n d i c a t e s t h e i n i t i a l w a t e r -t a b l e t i n t e r f a c e f o r t h e T y p e 2 t a b l e t a n d t h e s o l i d v e r t i c a l l i n e a t 0 . 1 3 3 c m m a r k s t h e z e r o p o s i t i o n f o r t h e T y p e 1 t a b l e t . 80 t a b l e t s w i t h d i f f e r e n t t h i c k n e s s e s . T y p e 2 t a b l e t s c o n t a i n e d t w i c e t h e a m o u n t o f H P M C a n d , w h e n c o m p r e s s e d w i t h t h e s a m e p e a k f o r c e , w e r e t w i c e as t h i c k as T y p e 1 t a b l e t s . T h e u p w a r d s s w e l l i n g e x p e r i m e n t w a s p e r f o r m e d f o r b o t h o f t h e s e t a b l e t s . A f t e r 1 h o u r , t h e w a t e r i m a g e s f o r t h e t w o t a b l e t s w e r e i d e n t i c a l as s e e n i n F i g u r e 3 . 8 . A t 4 h o u r s , t h e d i s t r i b u t i o n s a r e q u i t e s i m i l a r , a l t h o u g h t h e m i d d l e s e c t i o n o f t h e t w o d i s t r i b u t i o n s a p p e a r s t o d e v i a t e s l i g h t l y . A f t e r 7 h o u r s o f s w e l l i n g , t h e t w o t a b l e t s y s t e m s a r e n o l o n g e r d i r e c t l y c o m p a r a b l e b e c a u s e w a t e r h a s p e n e t r a t e d t h e t h i n n e r t a b l e t c o m p l e t e l y b u t h a s o n l y p e n e t r a t e d h a l f - w a y i n t o t h e t h i c k e r t a b l e t . B e c a u s e t h e w a t e r d i s t r i b u t i o n s f o r b o t h t a b l e t t y p e s a t 1, 4 a n d 7 h o u r s h a v e s i m i l a r s h a p e s , t h e d e v i a t i o n s b e t w e e n t h e t w o s y s t e m s m a y b e t h e r e s u l t o f t h e e r r o r i n s e t t i n g t h e z e r o p o s i t i o n w h i c h i s ^ 0 . 0 2 c m f o r e a c h e x p e r i m e n t . T h e s i m i l a r i t y b e t w e e n t h e w a t e r d i s t r i b u t i o n s a t e a r l y t i m e s s u g g e s t s t h a t t h e t h i n t a b l e t c a n b e r e g a r d e d as t h e o u t e r l a y e r o f t h e t h i c k t a b l e t . T h e f i n a l c o m p a r i s o n w a s b e t w e e n T y p e 2 a n d T y p e 3 t a b l e t s , b o t h o f s i m i l a r w e i g h t a n d t h i c k n e s s b u t p r e p a r e d w i t h d i f f e r e n t p e a k c o m p r e s s i o n a l f o r c e s . T h e s e t a b l e t s s h o w e d t h e s a m e w a t e r p e n e t r a t i o n b e h a v i o r f o r m o s t o f t h e s w e l l i n g e x p e r i m e n t as s h o w n i n F i g u r e 3 . 9 . A t a s w e l l i n g t i m e o f a p p r o x i m a t e l y 30 h o u r s , t h e s l i g h t l y t h i n n e r T y p e 3 t a b l e t w a s c o m p l e t e l y p e n e t r a t e d b y w a t e r w h e r e a s t h e T y p e 1 t a b l e t w a s c o m p l e t e l y p e n e t r a t e d a f e w h o u r s l a t e r . T h e d i s t r i b u t i o n s a t 37 h o u r s i n F i g u r e 3 .9 a p p e a r t o d e v i a t e b e c a u s e o f t h i s d i f f e r e n c e i n c o m p l e t e p e n e t r a t i o n t i m e s . M a t e r i a l s s u c h as H P M C c o m p r e s s e a s i l y b u t o f t e n e x p a n d s l i g h t l y o n c e t h e f o r c e o f c o m p r e s s i o n i s r e m o v e d . T a b l e t s p r e p a r e d w i t h d i f f e r e n t c o m p r e s s i o n a l f o r c e s m a y e x p a n d b y v a r y i n g d e g r e e s t o t h e s a m e ' e q u i l i b r i u m ' s t a t e w h i c h c o u l d e x p l a i n h o w t h e t a b l e t t h i c k n e s s e s r e m a i n v e r y s i m i l a r u n d e r d i f f e r e n t c o m p r e s s i o n a l f o r c e s a n d w h y t h e w a t e r p e n e t r a t i o n b e h a v i o r s a r e s i m i l a r . I n o r d e r t o c o m p a r e t h e i m a g i n g r e s u l t s f r o m a l l t h e e x p e r i m e n t a l v a r i a t i o n s , t h e w a t e r p e n e t r a t i o n d i s t a n c e ( W P D ) w a s d e f i n e d . T h i s p a r a m e t e r i s t h e f u r t h e s t d i s t a n c e t h a t w a t e r h a s p e n e t r a t e d i n t o t h e t a b l e t as d e t e c t e d i n t h e N M R i m a g e a n d i s m e a s u r e d f r o m t h e o r i g i n a l w a t e r - t a b l e t i n t e r f a c e p o s i t i o n . T h e m a g n i t u d e o f t h e W P D t h u s r a n g e s f r o m 0 w h e n n o w a t e r h a s p e n e t r a t e d t h e t a b l e t t o t h e i n i t i a l t a b l e t t h i c k n e s s w h e n w a t e r 81 HPMC(w/w%) A (a) 1 hour (b) 16 hours 1.00 0.801 0.60 0.40 0.20 o.oo i — 1 — I — « — i — r J - i — « — I — 1 — I — ' — i — > — I — 1 — I 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. (c) 25 hours T ' 1 r ~ - I ' 1 ' 1 ' 1 ' 1 1 1 .0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Distance (cm) F i g u r e 3 .9 : C o r r e c t e d a v e r a g e w a t e r d i s t r i b u t i o n s f o r t h e T y p e 2 t a b l e t ( f i l l e d c i r c l e s , n = 3 ) a n d t h e T y p e 3 t a b l e t ( o p e n c i r c l e s , n = l ) a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 16 h o u r s , (c ) 2 5 h o u r s , a n d ( d ) 37 h o u r s . T h e a x e s l a b e l s f o r t h e f o u r p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e i n t e n s i t i e s i n t h e i m a g e s a r e r e l a t i v e t o t h e b u l k w a t e r i n t e n s i t y . T h e d i s t a n c e v a l u e s f o r t h e T y p e 3 t a b l e t d a t a h a v e b e e n s h i f t e d b y + 0 . 0 2 c m , t h e d i f f e r e n c e i n t h i c k n e s s b e t w e e n t h e t w o t a b l e t s . T h e d a s h e d v e r t i c a l l i n e a t 0 . 2 6 6 c m i n d i c a t e s t h e i n i t i a l w a t e r - t a b l e t i n t e r f a c e f o r t h e T y p e 2 t a b l e t . 82 has penetrated to the far side of the tablet. Table 3.3 lists the average penetration distance for each experimental variation for different times in the swelling experiment. There was a small variability in the swelling times for repetitions of the same experiment which is quoted as a standard deviation of the time. The error in the water penetration distance is wi th in the error of setting the zero, position from the imaging experiments. The linearity of a plot of the water penetration distance as a function of the square root of t ime is the standard proof for a Fickian water penetration process [13]. However, the test gives no details regarding the specific mechanism of the water penetration. Figure 3.10 shows that all the data points from Table 3.3 fall on the same straight line suggesting that the water penetration process into H P M C tablets is Fickian regardless of the direction of swelling, tablet thickness and compression force. The negative intercept of the straight line fit may indicate that the water penetration visible in the one-dimensional images is slightly behind the true penetration front of the water into the polymer, the in i t ia l water molecules being immobil ized by strong bonding to the polymer. 83 Table 3.3: Summary of average water penetration distances ( W P D ) for each tablet type and experimental variation. Tablet T ime (min) St. Dev . a W P D (cm) St. Dev. Type 1, upwards (n=2) 40 9 0.03 0.01 220 11 0.09 0.01 399 11 0.12 0.02 570 — 0.13 — Type 1, downwards (n=2) 44 4 0.03 0.01 224 4 0.07 0.02 404 4 0.12 0.02 Type 2 (n=3) 36 3 0.03 0.01 218 5 0.07 0.02 578 6 0.15 0.02 938 7 0.20 0.01 1297 6 0.22 0.02 1656 7 0.25 0.02 Type 3 (n= l ) 38 — 0.02 — 218 — 0.07 — 399 — 0.12 — 579 — 0.14 — 759 — 0.16 — 940 — 0.18 — 1119 — 0.21 — 1299 — 0.22 — a Measure of the variability of the swelling time between repetitions of the same experiment. 84 0.30 -\ 0.25 H 0.20 H WPD (cm) o.i5 H 0.10 H 0.05 H 0.00 0 10 20 30 40 50 Time172 (min1/2) F i g u r e 3 . 1 0 : T h e w a t e r p e n e t r a t i o n d i s t a n c e ( W P D ) as a f u n c t i o n o f t h e s q u a r e r o o t o f t i m e f o r T y p e 1 u p w a r d s s w e l l i n g ( o p e n c i r c l e s ) , T y p e 1 d o w n w a r d s s w e l l i n g ( f i l l e d t r i a n g l e s ) , T y p e 2 ( f i l l e d c i r c l e s ) a n d T y p e 3 ( o p e n s q u a r e s ) t a b l e t s . T h e s t a n d a r d d e v i a t i o n s i n t h e W P D a r e c o m p a r a b l e t o t h e e r r o r i n s e t t i n g t h e z e r o p o s i t i o n f o r e a c h e x p e r i m e n t . T h e d e v i a t i o n s i n t h e e x p e r i m e n t a l t i m e a r e t o o s m a l l t o b e e v i d e n t i n t h e p l o t . T h e l e a s t -s q u a r e s s t r a i g h t l i n e f i t , r 2 o f 0 . 9 9 4 , g i v e s a s l o p e o f 0 . 0 0 6 7 9 4 c m m i n 1 / 2 a n d a n i n t e r c e p t o f - 0 . 0 2 3 6 c m . 85 3 . 3 . 2 D i s t r i b u t i o n o f H P M C i n t h e S w e l l i n g T a b l e t A s d i s c u s s e d p r e v i o u s l y , d i r e c t N M R i m a g i n g o f t h e H P M C i n t h e s w e l l i n g t a b l e t c o u l d n o t b e p e r f o r m e d w i t h t h e i m a g i n g t e c h n i q u e s o f t h i s t h e s i s . I n s t e a d , t h e H P M C d i s t r i b u t i o n w a s c a l c u l a t e d f r o m t h e w a t e r i m a g e s a c q u i r e d d u r i n g t h e c o u r s e o f t h e s w e l l i n g . A s d i s c u s s e d p r e v i o u s l y , t h e p o l y m e r h a s a s i g n i f i c a n t i n f l u e n c e o n t h e T2 r e l a x a t i o n t i m e o f t h e w a t e r c o m p o n e n t i n m i x t u r e s o f H P M C a n d w a t e r , a n e f fec t w h i c h w a s e v i d e n t i n t h e v a r i a t i o n o f t h e s i g n a l i n t e n s i t y o f t h e w a t e r i m a g e s w i t h v a r i a t i o n o f T # i n t h e s p i n - e c h o p u l s e s e q u e n c e . T h i s s i g n a l v a r i a t i o n w a s u s e d t o c a l c u l a t e T 2 d i s t r i b u t i o n s as s h o w n i n F i g u r e 3 . 5 . I n S e c t i o n 2 . 3 . 1 , a c a l i b r a t i o n r e l a t i n g t h e T 2 r e l a x a t i o n t i m e o f w a t e r w i t h t h e w e i g h t p e r c e n t o f H P M C w a s d e v e l o p e d f r o m m i x t u r e s c o n t a i n i n g v a r y i n g r a t i o s o f H P M C a n d w a t e r . W i t h t h e a s s u m p t i o n t h a t t h e r e l a x a t i o n t i m e s o f w a t e r i n t h e s w o l l e n t a b l e t a r e t h e s a m e as t h o s e i n t h e m i x t u r e s w i t h e q u i v a l e n t c o n c e n t r a t i o n s , t h i s c a l i b r a t i o n ( E q u a t i o n 2 .7 ) c a n b e u s e d t o c o n v e r t t h e T 2 d i s t r i b u t i o n s d e t e r m i n e d f r o m t h e i m a g i n g d a t a i n t o H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s . T h i s m e t h o d c a n b e u s e d t o c a l c u l a t e H P M C d i s t r i b u t i o n s a t a n y t i m e d u r i n g t h e s w e l l i n g o f t h e p o l y m e r t a b l e t . T h e a v e r a g e H P M C d i s t r i b u t i o n s f o r a 0 . 1 3 3 c m t a b l e t a r e s h o w n i n F i g u r e 3 . 1 1 . I n t h e s e d i s t r i b u t i o n s , H P M C c o n c e n t r a t i o n s a b o v e 4 0 % a r e c o n s i d e r e d t o b e o n l y s e m i -q u a n t i t a t i v e b e c a u s e o f t h e v e r y l i m i t e d d e p e n d e n c e o f T 2 o n t h e w e i g h t p e r c e n t H P M C b e t w e e n 4 0 % a n d 6 0 % H P M C . B e c a u s e t h e H P M C d i s t r i b u t i o n i s c a l c u l a t e d f r o m t h e w a t e r i m a g e s , H P M C c o n c e n t r a t i o n s c a n o n l y b e o b t a i n e d w h e r e t h e r e i s s u f f i c i e n t w a t e r p r e s e n t t o a l l o w f o r t h e e x p e r i m e n t a l d e t e r m i n a t i o n o f a T 2 v a l u e . T h u s , t h e c a l c u l a t e d H P M C p o i n t s d o n o t e x t e n d as f a r i n t o t h e o r i g i n a l t a b l e t p o s i t i o n as t h e w a t e r u n l e s s t h e e n t i r e t a b l e t h a s b e e n s u f f i c i e n t l y w e t t e d . A f t e r 37 h o u r s o f s w e l l i n g , t h e t a b l e t h a s e x p a n d e d t o f o u r t i m e s i t s o r i g i n a l t h i c k n e s s w i t h a c o n c e n t r a t i o n g r a d i e n t f r o m a p p r o x i m a t e l y 4 0 % H P M C i n i t s m o s t c o n c e n t r a t e d r e g i o n d o w n t o z e r o . P o l y m e r d i s t r i b u t i o n s f o r t h e d i f f e r e n t e x p e r i m e n t a l v a r i a t i o n s w e r e a l s o c a l c u l a t e d t o d e t e r m i n e w h e t h e r t h e r e w e r e a n y s i g n i f i c a n t d i f f e r e n c e s i n t h e H P M C c o n c e n t r a t i o n g r a d i e n t s . T h e i m a g i n g r e s u l t s f r o m t h e t h r e e v a r i a t i o n s — d i r e c t i o n o f s w e l l i n g w i t h r e s p e c t 86 H P M C (w / w %) ^ (a) 1 hour 100 • 80 60 40 20 1 0 (b) 16 hours 100 3 i 1 • 1 1 1 " 1 1 1 01 ' 1 ' 1 " T ' 1 ' 1 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 (c) 25 hours 100 (d) 37 hours 100 • Distance (cm) F i g u r e 3 . 1 1 : A v e r a g e H P M C w e i g h t p e r c e n t c u r v e s o b t a i n e d f r o m c o r r e s p o n d i n g T 2 c u r v e s c a l c u l a t e d f r o m o n e - d i m e n s i o n a l i m a g e s t a k e a t d i f f e r e n t T # as i n F i g u r e 3 . 5 , a t m e d i a n s w e l l i n g t i m e s o f (a ) 1 h o u r , (b ) 16 h o u r s , (c ) 25 h o u r s , a n d ( d ) 37 h o u r s . T h e a x e s l a b e l s f o r t h e f o u r p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e e r r o r b a r s r e p r e s e n t s t a n d a r d d e v i a t i o n s a n d t h e d a s h e d v e r t i c a l l i n e s i n d i c a t e t h e p o s i t i o n o f t h e i n i t i a l w a t e r -t a b l e t i n t e r f a c e . T h e s o l i d h o r i z o n t a l l i n e s i n t h e figure m a r k t h e u p p e r l i m i t f o r q u a n t i t a t i v e r e l i a b i l i t y o f t h e H P M C w e i g h t p e r c e n t . 87 H P M C ( w / w % ) ^ (a) 1 hour 60 40 20 0» %hMU1XUD (b) 7 hours 60H 40 H 20 0.0 0.2 0.4 0.6 - i 0 0.8 0.0 Ot o» 0.2 ,'HHOOO r-0.4 0.6 (c) 13 hours 60 40 20 \ 8. U V o* • (d) 19 hours 401 201 60- ; 0.0 0.2 0.4 0.6 - i 0 0.8 0.0 \ Oi, °2r 0.2 - i 1 r 0.4 0.6 Distance (cm) F i g u r e 3 . 1 2 : H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s f r o m u p w a r d s ( f i l l e d c i r c l e s ) a n d d o w n -w a r d s ( o p e n c i r c l e s ) s w e l l i n g e x p e r i m e n t s , 2 m s i m a g e s t a k e n a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 7 h o u r s , ( c ) 13 h o u r s , a n d (d ) 19 h o u r s . T h e a x e s l a b e l s f o r t h e f o u r p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e d a s h e d v e r t i c a l l i n e a t 0 . 1 3 3 c m i n d i c a t e s t h e i n i t i a l p o s i t i o n o f t h e w a t e r - t a b l e t i n t e r f a c e . 88 HPMC (w / w %) ^ (a) 1 hour 1001 (b) 4 hours 100 1 60 H 40 H 201 0.0 — r 0.1 —r~ 0.2 —t— 0.6 - r -0.7 (c) 7 hours 100 • F i g u r e 3 . 1 3 : A v e r a g e H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s f o r t h e T y p e 1 t a b l e t ( f i l l e d c i r c l e s , n = 2 ) a n d t h e T y p e 2 t a b l e t ( o p e n c i r c l e s , n = 3 ) a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 4 h o u r s a n d (c ) 7 h o u r s . T h e a x e s l a b e l s f o r t h e f o u r p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e d i s t a n c e v a l u e s f o r t h e T y p e 1 t a b l e t d a t a h a v e b e e n s h i f t e d b y + 0 . 1 3 3 c m , t h e d i f f e r e n c e i n t h i c k n e s s b e t w e e n t h e t w o t a b l e t s . T h e d a s h e d v e r t i c a l l i n e a t 0 . 2 6 6 c m i n d i c a t e s t h e i n i t i a l w a t e r - t a b l e t i n t e r f a c e f o r t h e T y p e 2 t a b l e t a n d t h e s o l i d v e r t i c a l l i n e a t 0 . 1 3 3 c m m a r k s t h e z e r o p o s i t i o n f o r t h e T y p e 1 t a b l e t . 89 H P M C ( w / w % ) D i s t a n c e ( c m ) F i g u r e 3 . 1 4 : C o r r e c t e d a v e r a g e H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s f o r t h e T y p e 2 t a b l e t ( f i l l e d c i r c l e s , n = 3 ) a n d t h e T y p e 3 t a b l e t ( o p e n c i r c l e s , n = l ) a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 16 h o u r s , ( c ) 25 h o u r s , a n d (d ) 37 h o u r s . T h e a x e s l a b e l s f o r t h e f o u r p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e d i s t a n c e v a l u e s f o r t h e T y p e 3 t a b l e t d a t a h a v e b e e n s h i f t e d b y + 0 . 0 2 c m , t h e d i f f e r e n c e i n t h i c k n e s s b e t w e e n t h e t w o t a b l e t s . T h e d a s h e d v e r t i c a l l i n e a t 0 . 266 c m i n d i c a t e s t h e i n i t i a l w a t e r - t a b l e t i n t e r f a c e f o r t h e T y p e 2 t a b l e t . 90 t o g r a v i t y , t a b l e t t h i c k n e s s , a n d p e a k c o m p r e s s i o n a l f o r c e d u r i n g t a b l e t p r e p a r a t i o n — w e r e c o n v e r t e d i n t o H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s a n d c o m p a r e d . F i g u r e 3 . 1 2 p r e s e n t s t h e c o m p a r i s o n o f t h e c a l c u l a t e d H P M C d i s t r i b u t i o n s f o r s w e l l i n g - u p w a r d s a n d s w e l l i n g - d o w n w a r d s v a r i a t i o n s o f t h e i m a g i n g e x p e r i m e n t . T h e s e d i s t r i b u t i o n s a p p e a r v e r y s i m i l a r a t a l l s w e l l i n g t i m e s s u g g e s t i n g t h a t t h e g r a v i t y - i n d u c e d f l o w o f H P M C s o l u t i o n s h a s l i t t l e e f fec t o n t h e r e s u l t i n g H P M C d i s t r i b u t i o n . T h e p r e s e n c e o f t h e a i r b u b b l e i n t h e s w e l l i n g - d o w n w a r d s e x p e r i m e n t s e e m s t o h a v e o n l y a s m a l l i n f l u e n c e o n t h e c a l c u l a t e d T 2 v a l u e s a n d t h e r e s u l t i n g H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s as t h e r e i s o n l y a s l i g h t l o w e r i n g o f t h e H P M C % i n t h e v i c i n i t y o f t h e a i r b u b b l e . F i g u r e 3 . 1 3 s h o w s a s i m i l a r c o m p a r i s o n o f t h e b e h a v i o r s o f t h e s i m i l a r l y p r e p a r e d T y p e 1 a n d T y p e 2 t a b l e t s ( t h i c k n e s s e s o f 0 . 1 3 3 c m a n d 0 .266 c m r e s p e c t i v e l y ) . T h e c a l c u l a t e d H P M C d i s t r i b u t i o n s h a v e s i m i l a r s h a p e s a t t h e t h r e e s w e l l i n g t i m e s s h o w n i n t h e f i g u r e b u t a p p e a r t o b e o f fset f r o m e a c h o t h e r . A s t h e o f fset i s w i t h i n t h e c o m b i n e d e r r o r o f s e t t i n g t h e z e r o p o s i t i o n f o r t h e t w o i m a g i n g e x p e r i m e n t s , t h e c a l c u l a t e d H P M C d i s t r i b u t i o n i s a s s u m e d n o t t o d e p e n d o n t a b l e t t h i c k n e s s . F i g u r e 3 .14 s h o w s t h a t t h e H P M C d i s t r i b u t i o n s f o r t a b l e t s p r e p a r e d w i t h d i f f e r e n t c o m p r e s s i o n a l f o r c e s a r e a l s o s i m i l a r s u g g e s t i n g t h a t t h e p o l y m e r d i s t r i b u t i o n i s n o t a f f e c t e d b y t h e c o m p r e s s i o n f o r c e u s e d i n t h e t a b l e t p r e p a r a t i o n . 3.3.3 T o t a l W e i g h t o f H P M C f r o m C a l c u l a t e d P o l y m e r D i s t r i b u t i o n s T h e u l t i m a t e g o a l o f t h e i m a g i n g i n v e s t i g a t i o n s o f H P M C t a b l e t s w a s t o p a r a m e t e r i z e t h e e x p a n s i o n o f t h e t a b l e t i n t e r m s o f p o l y m e r c o n c e n t r a t i o n as f u n c t i o n s o f b o t h t i m e a n d d i s t a n c e i n o r d e r t o t e s t v a r i o u s p o s s i b l e m o d e l s f o r t h e s w e l l i n g p r o c e s s . E a c h d a t a p o i n t i n t h e H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s o f S e c t i o n 3 .3 .2 r e p r e s e n t s t h e a m o u n t o f p o l y m e r i n a c e r t a i n r e g i o n , a d i s k o f v o l u m e 0 .0201 c m 3 . I f t h e v o l u m e a n d d e n s i t y a r e k n o w n , t h e w e i g h t p e r c e n t p r o f i l e s a r e e a s i l y c o n v e r t e d i n t o c o n c e n t r a t i o n u n i t s s u c h as g c m - 3 w h i c h d e s c r i b e t h e a m o u n t o f p o l y m e r a t e a c h l o c a t i o n . W h e n t h e t a b l e t i s f u l l y h y d r a t e d , a c o m p l e t e H P M C d i s t r i b u t i o n i n g c m - 3 u n i t s c a n b e c a l c u l a t e d . T h e s u m o f t h e p o l y m e r w e i g h t s o v e r e a c h v o l u m e r e g i o n p r o v i d e s 91 T a b l e 3 .4 : A v e r a g e t o t a l w e i g h t s o f H P M C c a l c u l a t e d f r o m t h e o n e - d i m e n s i o n a l i m a g i n g s t u d i e s o f a T y p e 1 t a b l e t . T h e p e r c e n t d e v i a t i o n s a r e c a l c u l a t e d f r o m t h e k n o w n w e i g h t o f 166 m g H P M C i n t h e t a b l e t . T i m e ( h r s ) T o t a l H P M C " ( m g ) E r r o r ( m g ) % d e v 6 19 2 2 0 18 3 3 2 5 2 3 9 18 4 4 31 241 20 4 5 3 7 2 4 0 21 4 5 ° T h e assumec d e n s i t y was 1 g c m 3 6 % d e v = 1 0 0 % x ( H P M C - 166) / 166 a n e x p e r i m e n t a l m e a s u r e o f t h e t o t a l a m o u n t o f p o l y m e r i n t h e s y s t e m w h i c h s h o u l d b e c o m p a r a b l e , w i t h i n e x p e r i m e n t a l e r r o r , t o t h e k n o w n w e i g h t o f t h e H P M C i n t h e t a b l e t . W h e n t h i s t o t a l w e i g h t c a l c u l a t i o n w a s p e r f o r m e d f o r t h e H P M C d i s t r i b u t i o n s c a l c u l a t e d f r o m t h e T y p e 1 t a b l e t , t h e a p p a r e n t a m o u n t o f p o l y m e r , g i v e n i n T a b l e 3 . 4 w a s f o u n d t o b e u p t o 4 5 % l a r g e r t h a n t h e k n o w n w e i g h t o f H P M C i n t h e t a b l e t . T h i s o v e r - e s t i m a t i o n o f w e i g h t o c c u r r e d e v e n w h e n a l l t h e c a l c u l a t e d w e i g h t p e r c e n t s i n t h e p o l y m e r d i s t r i b u t i o n w e r e b e l o w 4 0 % a n d t h e r e f o r e c o n s i d e r e d r e l i a b l e . T h i s d i s c r e p a n c y , d i s c u s s e d i n g r e a t e r d e t a i l i n C h a p t e r 4 , w a s f o u n d t o b e c a u s e d b y t h e p r e s e n c e o f a i r b u b b l e s i n t h e s w o l l e n g e l w h i c h o c c u p y a f r a c t i o n o f t h e v o l u m e a s s u m e d t o b e c o m p o s e d o n l y o f H P M C a n d w a t e r . 3.3.4 Possible Effects of Water Diffusion on the Imaging Results T h e p u l s e s e q u e n c e f o r t h e o n e - d i m e n s i o n a l i m a g i n g e x p e r i m e n t s i s v e r y s i m i l a r t o t h e p u l s e s e q u e n c e p r e s e n t e d i n S e c t i o n 1 .2 .3 w h i c h w a s u s e d t o m e a s u r e t h e s e l f - d i f f u s i o n c o e f f i c i e n t o f t h e w a t e r . T h i s r a i s e s t h e c o n c e r n t h a t t h e i m a g e s o f w a t e r m a y b e a f f e c t e d b y t h e d i f f u s i o n t h a t o c c u r s d u r i n g t h e t i m e t h e g r a d i e n t s a r e a p p l i e d . F a s t d i f f u s i o n o f w a t e r c a u s e s t h e a p p a r e n t T 2 v a l u e m e a s u r e d f r o m a n i m a g i n g e x p e r i m e n t t o b e l e s s t h a n t h e t r u e T 2 v a l u e a n d t h e d i f f e r e n c e b e t w e e n t h e m e a s u r e d a n d t r u e T 2 v a l u e s b e c o m e s g r e a t e r as t h e s p a t i a l r e s o l u t i o n i n t h e i m a g e s i n c r e a s e s [77]. U s i n g E q u a t i o n 3 . 4 w i t h a r e s o l u t i o n , Ax, o f 0 . 0 1 6 c m a n d a d i f f u s i o n c o e f f i c i e n t o f 2 . 3 5 x l 0 - 5 c m 2 s _ 1 ( t h e v a l u e f o r f r e e w a t e r ) , 92 t h e m e a s u r e d v a l u e f o r t h e t r u e T 2 o f 5 0 0 m s w o u l d b e 371 m s w h e n T ^ i s 2 m s a n d 341 m s w h e n TE i s 128 m s . A l t h o u g h t h i s ~ 3 2 % d e c r e a s e i n t h e a p p a r e n t T 2 i s s i g n i f i c a n t f o r f r e e w a t e r , t h e e f f ec t o f d i f f u s i o n o n t h e T 2 v a l u e s m e a s u r e d f o r t h e s w o l l e n p o l y m e r t a b l e t i s m u c h l e s s s i g n i f i c a n t b e c a u s e t h e d e v i a t i o n d e c r e a s e s s u b s t a n t i a l l y as t h e t r u e T 2 v a l u e d e c r e a s e s a n d as t h e d i f f u s i o n c o e f f i c i e n t d e c r e a s e s . F o r t h e H P M C - w a t e r m i x t u r e s b e t w e e n 5 % a n d 1 0 % , t h e T 2 v a l u e s a r e a p p r o x i m a t e l y 2 0 0 m s a n d a b o v e 1 0 % H P M C , t h e T 2 v a l u e s d r o p b e l o w 100 m s . T h e d e c r e a s e i n t h e a p p a r e n t T 2 v a l u e d r o p s t o ~ 1 6 % a n d ~ 9 % , r e s p e c t i v e l y f o r t h e s e t w o l i m i t s a n d m a y b e e v e n l o w e r b e c a u s e t h e d i f f u s i o n c o e f f i c i e n t d e c r e a s e s w i t h i n c r e a s i n g H P M C w e i g h t p e r c e n t (cf . S e c t i o n 2 . 3 . 3 ) . T h e T 2 v a l u e s d e t e r m i n e d f r o m t h e i m a g i n g e x p e r i m e n t s a r e u s e d i n t w o s e p a r a t e c a l c u l a t i o n s w h i c h c o u l d b e i n f l u e n c e d b y t h e d i f f u s i o n a t t e n u a t i o n o f t h e m e a s u r e d T 2 r e l a x a t i o n t i m e . T h e f i r s t c a l c u l a t i o n is t h e c o r r e c t i o n o f s i g n a l i n t e n s i t y u s i n g E q u a t i o n 3 . 1 . R e p l a c i n g t h e t r u e T 2 v a l u e s i n t h i s e q u a t i o n w i t h t h e d i f f u s i o n a t t e n u a t e d v a l u e s l e a d s t o a n a v e r a g e i n c r e a s e o f 0 . 2 % i n t h e e x p o n e n t i a l t e r m o f E q u a t i o n 3 . 1 . T h e r e f o r e , t h e e f f ec t o f d i f f u s i o n o n t h e T 2 v a l u e s h a s n o e f fec t o n t h e c o r r e c t i o n o f t h e s i g n a l i n t e n s i t y . T h e s e c o n d c a l c u l a t i o n i n v o l v e s t h e c o n v e r s i o n o f T 2 v a l u e s t o H P M C w e i g h t p e r c e n t u s i n g t h e c a l i b r a t i o n o f E q u a t i o n 2 .7 . W h e n t h e a p p a r e n t T 2 v a l u e s a r e u s e d i n s t e a d o f t h e t r u e v a l u e s , t h e c a l c u l a t e d H P M C w e i g h t p e r c e n t is a b o u t 1 % h i g h e r . F o r e x a m p l e , i f t h e t r u e T 2 i s 1 0 0 m s , t h e n t h e a p p a r e n t T 2 o f 91 m s p r o d u c e s a H P M C w e i g h t p e r c e n t o f 1 2 . 4 % i n s t e a d o f 1 1 . 8 % . T h i s c o n v e r t s i n t o a p e r c e n t d e v i a t i o n o f + 5 . 5 % . F o r t r u e T 2 v a l u e s o f 2 0 0 m s a n d 5 0 0 m s , t h e H P M C c o n c e n t r a t i o n s a r e 7 . 8 % c o m p a r e d t o 6 . 5 % a n d 2 . 8 % c o m p a r e d t o 1 . 1 % . T h e s e a r e ' w o r s t c a s e ' e s t i m a t e s b a s e d o n t h e f a s t d i f f u s i o n i n p u r e w a t e r ; t h e d e v i a t i o n s i n t h e s w o l l e n H P M C t a b l e t w i l l b e l o w e r b e c a u s e t h e d i f f u s i o n o f w a t e r t h r o u g h t h e p o l y m e r g e l i s s l o w e r t h a n i n p u r e w a t e r . T h e e r r o r t h a t t h e d i f f u s i o n a t t e n u a t i o n o f t h e T 2 v a l u e i n t r o d u c e s i n t o t h e H P M C w e i g h t p e r c e n t d i s t r i b u t i o n i s s m a l l 9 3 a n d f a l l s w i t h i n t h e e r r o r c a u s e d b y o t h e r f a c t o r s . T h e d i s t r i b u t i o n s i n t h i s c h a p t e r w e r e n o t c o r r e c t e d f o r t h e d i f f u s i o n e f fec t b e c a u s e t h e r e i s a n o t h e r m u c h l a r g e r f a c t o r t h a t c a u s e s d i s c r e p a n c i e s i n t h e H P M C w e i g h t p e r c e n t , n a m e l y t h e p r e s e n c e o f a i r b u b b l e s . 3.4 Summary T h e o n e - d i m e n s i o n a l i m a g i n g s t u d i e s p e r f o r m e d o n t h e H P M C t a b l e t p e r m i t t e d t h e r a p i d d e t e r m i n a t i o n o f b o t h t h e w a t e r a n d p o l y m e r d i s t r i b u t i o n s a t v a r i o u s t i m e s d u r i n g t h e s w e l l i n g p r o c e s s . T h e r e p e t i t i o n o f t h e e x p e r i m e n t u n d e r v a r i o u s c o n d i t i o n s s h o w e d t h a t t h e r e s u l t s w e r e r e p r o d u c i b l e a n d d i d n o t d e p e n d s t r o n g l y o n s u c h f a c t o r s as s w e l l i n g d i r e c t i o n w i t h r e s p e c t t o g r a v i t y , t h e t h i c k n e s s o f t h e t a b l e t , o r t h e c o m p r e s s i o n f o r c e u s e d d u r i n g t a b l e t p r e p a r a t i o n . T h e p e n e t r a t i o n o f w a t e r i n t o t h e H P M C t a b l e t a p p e a r e d t o b e t h e s a m e r e g a r d l e s s o f t h e e x p e r i m e n t a l v a r i a t i o n a n d e x h i b i t e d a l i n e a r r e l a t i o n s h i p w i t h t h e s q u a r e r o o t o f t i m e , i n d i c a t i n g F i c k i a n d i f f u s i o n . T h e p o l y m e r d i s t r i b u t i o n s o b t a i n e d i n t h i s c h a p t e r o v e r - e s t i m a t e t h e a m o u n t o f p o l y m e r p r e s e n t . T h i s d i s c r e p a n c y h a s b e e n t r a c e d t o t h e p r e s e n c e o f n u m e r o u s s m a l l a i r b u b b l e s i n t h e s w o l l e n g e l w h i c h o c c u p y v o l u m e a s s u m e d t o b e f i l l e d b y p o l y m e r a n d w a t e r o n l y . 94 C h a p t e r 4 D e t e c t i o n o f A i r S p a c e s i n t h e S w o l l e n H P M C T a b l e t 4.1 Introduction T a b l e t s a r e g e n e r a l l y p r e p a r e d b y t h e c o m p r e s s i o n o f g r a n u l e s o b t a i n e d f r o m e i t h e r a w e t o r d r y g r a n u l a t i o n m e t h o d o r b y d i r e c t c o m p r e s s i o n o f a n u n t r e a t e d p o w d e r m i x t u r e [78]. D u r i n g t h e c o m p r e s s i o n , a i r b e t w e e n t h e p a r t i c l e s c a n b e t r a p p e d w i t h i n t h e t a b l e t . T h e p o r o s i t y o f a t a b l e t d e p e n d s o n f a c t o r s s u c h as t h e s i z e o f t h e p a r t i c l e s , t h e f o r c e o f c o m -p r e s s i o n a n d t h e s p e e d o f c o m p r e s s i o n [79]. W h e n t h e t a b l e t p r e p a r a t i o n c o n d i t i o n s r e s u l t i n a l a r g e v o l u m e o f a i r t r a p p e d w i t h i n t h e t a b l e t , t h e r e s u l t i n g i n t e r n a l p r e s s u r e c a n c a u s e t h e t a b l e t t o r u p t u r e i n a n o c c u r r e n c e t e r m e d ' c a p p i n g ' [80]. D u r i n g t h e s w e l l i n g o f a h y d r o p h i l i c m a t r i x t a b l e t , t h e m o v e m e n t o f t h e p o l y m e r r e d u c e s t h e p r e s s u r e e x e r t e d o n t h e t r a p p e d a i r r e s u l t i n g i n t h e f o r m a t i o n o f a i r b u b b l e s . T h e s e b u b b l e s w i l l o c c u p y s p a c e w h i c h m i g h t o t h e r w i s e b e f i l l e d b y t h e s w o l l e n p o l y m e r a n d m a y r e s u l t i n a d i f f e r e n t a p p a r e n t i n c r e a s e i n t h e t a b l e t s i z e t h a n t h a t d u e t o p o l y m e r s w e l l i n g a l o n e . A n a l y s i s m e t h o d s t h a t r e q u i r e k n o w l e d g e o f t h e v o l u m e o c c u p i e d b y t h e s w o l l e n g e l w i l l b e s t r o n g l y i n f l u e n c e d b y t h e p r e s e n c e o f t h e s e b u b b l e s . S u c h a n e f f e c t w a s o b s e r v e d i n S e c t i o n 3 . 3 . 3 w h e r e e s t i m a t e s o f t h e t o t a l p o l y m e r w e i g h t i n t h e s w o l l e n t a b l e t e x c e e d e d t h e k n o w n p o l y m e r w e i g h t b y u p t o 4 5 % . T h e r e a r e t w o b a s i c a p p r o a c h e s t o e l i m i n a t i n g t h e e f f ec t o f t h e a i r b u b b l e s : m e a s u r -i n g a n d c o r r e c t i n g f o r t h e v o l u m e o c c u p i e d b y t h e a i r o r r e m o v i n g t h e a i r f r o m t h e t a b l e t p r i o r t o t h e i m a g i n g e x p e r i m e n t . T h i s c h a p t e r d e s c r i b e s t h e s e c o n d a p p r o a c h i n w h i c h a n 9 5 ; H P M C t a b l e t i s t r e a t e d u n d e r v a c u u m t o r e m o v e a i r f r o m t h e p o r e s o f t h e t a b l e t . 4.2 Experimental 4 . 2 . 1 V a c u u m T r e a t m e n t t o R e m o v e A i r f r o m t h e T a b l e t T y p e 1 t a b l e t s w e r e p r e p a r e d f r o m t h e a s - s u p p l i e d H P M C p o w d e r a n d p l a c e d i n a n N M R t u b e as d e s c r i b e d i n S e c t i o n s 3 .2 .1 a n d 3 . 2 . 2 , r e s p e c t i v e l y . P r i o r t o e a c h i m a g i n g s t u d y , t h e t a b l e t w a s t r e a t e d w i t h v a c u u m t o r e m o v e a n y a i r w h i c h m i g h t b e t r a p p e d i n t h e p o r e s o f t h e t a b l e t . T h e t u b e c o n t a i n i n g t h e t a b l e t w a s p l a c e d i n s i d e a l o n g S c h l e n k t u b e , as s h o w n i n F i g u r e 4 . 1 , a n d k e p t u n d e r a v a c u u m o f a p p r o x i m a t e l y 12 m m H g f o r 5 m i n u t e s . G l a s s r o d s w e r e r e q u i r e d t o p r e v e n t t h e t a b l e t f r o m r i s i n g u p i n t h e t u b e d u r i n g t h e v a c u u m t r e a t m e n t w h i c h t e n d e d t o c a u s e w a t e r l e a k a g e b e t w e e n t h e t a b l e t a n d t u b e w a l l . A f t e r t h e t r e a t m e n t , w a t e r w a s a l l o w e d t o e n t e r t h e s y s t e m t o b r e a k t h e v a c u u m a n d p r e v e n t t h e r e i n c o r p o r a t i o n o f a i r i n t o t h e t a b l e t . T h e w a t e r d r a w n i n t o t h e t u b e w a s r e p l a c e d b y 5 m L o f f r e s h w a t e r t o m a k e t h e r e m a i n d e r o f t h e s w e l l i n g e x p e r i m e n t o f t h e v a c u u m - t r e a t e d t a b l e t as s i m i l a r as p o s s i b l e t o t h a t o f t h e u n t r e a t e d t a b l e t . 4 . 2 . 2 O n e - a n d T w o - d i m e n s i o n a l I m a g i n g T h e t w o - d i m e n s i o n a l i m a g e s o f t h e w a t e r d i s t r i b u t i o n w e r e a c q u i r e d w i t h t h e s l i c e - s e l e c t i v e s p i n w a r p s e q u e n c e s h o w n i n F i g u r e 1.14. T w o v a r i a t i o n s o f t h e i m a g i n g e x p e r i m e n t w e r e p e r f o r m e d f o r b o t h t h e u n t r e a t e d a n d t h e v a c u u m - t r e a t e d t a b l e t s . I n o n e v e r s i o n o f t h e e x p e r i m e n t , t h e t w o d i m e n s i o n a l w a t e r s i g n a l i n t e n s i t y w a s a c q u i r e d f r o m a s l i c e p a r a l l e l t o t h e l o n g a x i s o f t h e t u b e . T h e s e c o n d v e r s i o n r e c o r d e d t h e t w o d i m e n s i o n a l s i g n a l i n t e n s i t y i n a p l a n e o r t h o g o n a l t o t h e l o n g a x i s o f t h e t u b e . T h e t a b l e t s y s t e m s f o r t h e t w o -d i m e n s i o n a l i m a g i n g e x p e r i m e n t w e r e p r e p a r e d w i t h a s o l u t i o n c o n t a i n i n g 10 m M C u S C ^ , r a t h e r t h a n d i s t i l l e d w a t e r , t o s h o r t e n t h e T i r e l a x a t i o n t i m e o f t h e w a t e r p r o t o n s a n d t h u s s h o r t e n t h e t i m e r e q u i r e d t o o b t a i n s e m i - q u a n t i t a t i v e t w o - d i m e n s i o n a l i m a g e s o f t h e s w e l l i n g t a b l e t s . T a b l e 4.1 g i v e s t h e p a r a m e t e r s f o r e a c h o f t h e t w o - d i m e n s i o n a l i m a g i n g v a r i a t i o n s . T h e o n e - d i m e n s i o n a l i m a g i n g s t u d i e s o f t h e v a c u u m - t r e a t e d t a b l e t w e r e p e r f o r m e d 96 vacuum line glass rods tablet solid support F i g u r e 4 . 1 : A s c h e m a t i c r e p r e s e n t a t i o n o f t h e e x p e r i m e n t a l s e t - u p f o r v a c u u m - t r e a t i n g t h e H P M C t a b l e t s . G l a s s r o d s a r e u s e d t o h o l d d o w n t h e t a b l e t i n t h e N M R t u b e w h i c h i s t h e n p l a c e d i n a l o n g S c h l e n k t u b e a n d c o n n e c t e d b y a t h r e e - w a y v a l v e t o a v a c c u m l i n e a n d a s o u r c e o f w a t e r . T h e t a b l e t i s s u b j e c t e d t o a v a c u u m o f 1 2 m m H g f o r 5 m i n u t e s a n d t h e n w a t e r i s d r a w n i n t o t h e S c h l e n k t u b e t o b r e a k t h e v a c u u m . B e f o r e t h e t a b l e t i s p l a c e d i n t h e m a g n e t f o r i m a g i n g , t h e g l a s s r o d s a r e r e m o v e d a n d t h e w a t e r d r a w n i n b y t h e v a c u u m i s r e p l a c e d b y f r e s h w a t e r . 97 T a b l e 4 . 1 : T y p i c a l p a r a m e t e r s u s e d i n t h e s p i n w a r p i m a g i n g s e q u e n c e t o a c q u i r e t h e t w o -d i m e n s i o n a l i m a g e s o f s w e l l i n g H P M C t a b l e t s . T h e V e r s i o n 1 v a l u e s a r e f o r t h e l o n g i t u d i n a l i m a g e s a n d t h e V e r s i o n 2 v a l u e s a r e f o r t h e c r o s s - s e c t i o n a l i m a g e s . P a r a m e t e r V e r s i o n 1 V e r s i o n 2 S e l e c t i v e 90° p u l s e S h a p e s i n c 2 s i n c 2 D u r a t i o n ( m s ) 2 2 S l i c e - s e l e c t i o n g r a d i e n t D i r e c t i o n y z S t r e n g t h ( G / c m ) 7 .3 16 D u r a t i o n ( m s ) 2 .8 2 . 2 P h a s e - e n c o d i n g g r a d i e n t D i r e c t i o n X y S t r e n g t h ( G / c m ) - 9 . 9 t o + 9 . 9 - 2 8 . 8 t o + 2 8 . 8 D u r a t i o n ( / /s ) 6 6 0 6 0 0 I n c r e m e n t s 2 5 6 2 5 6 F r e q u e n c y - e n c o d i n g g r a d i e n t D i r e c t i o n z X S t r e n g t h ( G / c m ) 8.1 1 6 . 9 D u r a t i o n " (/xs) 6 6 0 6 0 0 S p e c t r a l W i d t h , Sw ( k H z ) 5 0 1 2 5 N u m b e r o f p o i n t s i n f r e q u e n c y d o m a i n , T r j ( W o r d s ) 2 5 6 2 5 6 N u m b e r o f p o i n t s i n t h e F T , S / ( W o r d s ) 5 1 2 5 1 2 T i m e - t o - e c h o , T # ( m s ) 2 . 5 2 . 5 R e p e t i t i o n d e l a y , TR ( S ) 0 . 5 1 N u m b e r o f r e p e a t s 16 3 2 T i m e t o a c q u i r e i m a g e ( m i n ) 34 136 S l i c e t h i c k n e s s ( ^ m ) 6 5 0 3 0 0 I n - p l a n e r e s o l u t i o n (/im) 6 0 70 ° The frequency encoding gradient remains on longer during the acquisition of the echo in the second half of the spin warp sequence. 98 in the same manner as for the untreated tablet in Chapter 3. Processing of the imaging data for the vacuum-treated tablet was the same as that described in Section 3.2.4. The additional processing of the data to correct for the effects of diffusion during the gradient pulses of the imaging experiment was performed in an iterative manner. Equat ion 4.1, determined from a Mathematica fit to water diffusivity the data in Section 2.3.3, was used to interpolate the diffusion coefficient for H P M C weight percents, [ H P M C ] , in between those of the prepared mixtures. The diffusion coefficient of 0.51 x l O - 5 c m 2 s _ 1 was used as the min imum value for H P M C concentrations above 40%. The in i t ia l T 2 values were converted into H P M C weight percents which were then used to determine the in i t ia l dif-fusion coefficients for the correction. The diffusion-corrected T 2 values were calculated using Equation 4.2 which is a rearrangement of Equation 3.4 where the (TE — 2/3AQ)/TE term is assumed to be unity in order to determine the maximum effect of diffusion. The new T 2 values are converted into a second set of H P M C weight percent values which in turn are used to determine the second set of diffusion coefficients. The calculation with Equat ion 4.2 was repeated with the new set of diffusion coefficients to obtain a th i rd set of H P M C weight percents. Further iterations were not required as the second and third sets of weight percents were identical to the 2nd decimal place. DH = 2.164 - 0.03785[#PMC] - 0.0001423[#PMC] 2 (4.1) 1 1 D IT2 ^ 2 , true ^2, obs 0.0162 ( 4 . 2 ) 4.3 Results and Discussion 4.3.1 Two-dimensional Images of Untreated and Vacuum-Treated Tablets The two-dimensional imaging experiments were performed to determine the extent of air present throughout the tablet and to monitor the changes in the air distribution in the 99 t a b l e t as i t s w e l l s . T w o - d i m e n s i o n a l i m a g i n g e x p e r i m e n t s w i t h t h e v a c u u m - t r e a t e d t a b l e t w e r e p e r f o r m e d t o d e t e r m i n e h o w s u c c e s s f u l l y t h e v a c u u m t e c h n i q u e r e m o v e d t h e a i r f r o m t h e p o r e s w i t h i n t h e t a b l e t . T h e s e r i e s o f l o n g i t u d i n a l i m a g e s f o r b o t h t a b l e t s y s t e m s a r e s h o w n i n F i g u r e 4 . 2 . I n t h e s e g r e y - s c a l e i m a g e s , t h e l i g h t r e g i o n s i n d i c a t e t h e p r e s e n c e o f w a t e r a n d t h e d a r k o r b l a c k r e g i o n s i n d i c a t e a l o w c o n c e n t r a t i o n o r t h e c o m p l e t e a b s e n c e o f w a t e r . T h e a i r b u b b l e s i n t h e u n t r e a t e d t a b l e t a r e v i s i b l e as d a r k b l o b s s u r r o u n d e d b y w a t e r . T h e y a p p e a r e d as e a r l y as 4 h o u r s a f t e r t h e b e g i n n i n g o f t a b l e t s w e l l i n g a n d f o r m e d c o n t i n u o u s l y as t h e w a t e r p e n e t r a t i o n a n d s w e l l i n g c o n t i n u e d . A t l a t e r t i m e s , t h e s w o l l e n t a b l e t h a s q u a d r u p l e d i t s o r i g i n a l t h i c k n e s s a n d e s s e n t i a l l y f i l l s t h e t w o - d i m e n s i o n a l i m a g e i n F i g u r e 4 . 2 ( h ) . A t t h e s e l a t e r t i m e s , t h e r e a p p e a r e d t o b e a f a i r l y e v e n d i s t r i b u t i o n o f b u b b l e s t h r o u g h o u t t h e g e l . I n c o n t r a s t , t h e i m a g e s f r o m t h e v a c u u m - t r e a t e d s y s t e m a r e a l m o s t c o m p l e t e l y f r e e o f a i r b u b b l e s i n d i c a t i n g t h a t t h e v a c u u m t e c h n i q u e r e m o v e d t h e a i r f r o m t h e t a b l e t p o r e s . T h e t r u e a i r b u b b l e v o l u m e c a n n o t b e d e t e r m i n e d f r o m t h e i m a g e s o f F i g u r e s 4 . 2 a n d 4 . 3 b e c a u s e t h e c h a n g e s i n m a g n e t i c s u s c e p t i b i l i t y a c r o s s t h e a i r - w a t e r i n t e r f a c e c a u s e t h e a i r b u b b l e s t o a p p e a r l a r g e r t h a n t h e i r a c t u a l s i z e . A l t h o u g h , t h e s e i m a g e s a r e o n l y o f o n e l o n g i t u d i n a l s l i c e t h r o u g h t h e s a m p l e , t h e a i r b u b b l e d i s t r i b u t i o n s v i s i b l e i n t h e m c a n b e a s s u m e d t o b e r e p r e s e n t a t i v e o f t h e d i s t r i b u t i o n t h r o u g h o u t t h e s w o l l e n t a b l e t . T h e c r o s s - s e c t i o n a l i m a g e t h r o u g h t h e m i d d l e o f t h e u n t r e a t e d t a b l e t i n F i g u r e 4 . 3 c o n f i r m s t h a t a i r b u b b l e s o c c u p y a n e x t e n s i v e v o l u m e i n t h e s w o l l e n t a b l e t . T h e i m a g e o f t h e v a c u u m - t r e a t e d t a b l e t s h o w s o n l y a f e w s m a l l a i r b u b b l e s i n d i c a t i n g t h a t t h e m a j o r i t y o f a i r i n t h e t a b l e t p o r e s w a s r e m o v e d i n t h e e x p o s u r e t o v a c u u m . T h i s e f f e c t i s a l s o s o m e w h a t v i s i b l e i n t h e l o n g i t u d i n a l i m a g e s o f t h e u n t r e a t e d t a b l e t . W a t e r l e a k a g e b e t w e e n t h e t a b l e t a n d t h e t u b e w a l l d o e s n o t a p p e a r t o b e t h e c a u s e o f t h i s e f f e c t as t h e w a t e r p e n e t r a t i o n f r o n t i n t o b o t h t h e u n t r e a t e d a n d v a c u u m - t r e a t e d t a b l e t s , as s e e n i n F i g u r e 4 . 2 , r e m a i n e d s t r a i g h t t h r o u g h o u t t h e e x p e r i m e n t . T h e a i r t r a p p e d i n t h e o u t e r r e g i o n s o f a n e w l y c o m p r e s s e d t a b l e t c a n e q u i l i b r a t e t o a t m o s p h e r i c p r e s s u r e m o r e e a s i l y t h a n a i r t r a p p e d d e e p w i t h i n t h e t a b l e t a n d p e r h a p s t h e l o w e r a i r p r e s s u r e r e s u l t s i n f e w e r b u b b l e s i n t h e s e 100 Figure 4.2: Longitudinal images of the water distribution in an untreated tablet ((a) through (h)) and a vacuum-treated tablet ( (A) through ( H ) ) taken at approximately the same position in the two swelling tablet systems. The images show the bottom portion of the N M R tube. The times for the eight sets of images are (a, A ) 1 hour, (b, B ) 4 hours, (c, C) 7 hours, (d, D) 13 hours, (e, E) 19 hours, (f, F) 25 hours, (g, G) 31 hours, and (h, H ) 37 hours. The relationship between distance in the image and distance in the tablet is 1:0.22. The parameters for the imaging experiment are indicated in Table 4.1. (The figure is continued on the next page.) 1 0 1 Figure 4.2 continued: images (e) to (h) and (E) to ( H ) . 102 Figure 4.3: Cross-sectional images of the water distribution in an untreated tablet (A) and a vacuum-treated tablet (B) taken at approximately the same position in the middle of the swollen tablet at a swelling time of 43 hours. The relationship between distance in the image and distance in the tablet is 1:0.20. The parameters for the imaging experiment are indicated in Table 4.1. 103 r e g i o n s o f t h e s w o l l e n t a b l e t . 4 . 3 . 2 T o t a l W e i g h t o f P o l y m e r i n U n t r e a t e d a n d V a c u u m - T r e a t e d T a b l e t s A c o m p a r i s o n b e t w e e n t h e k n o w n w e i g h t o f p o l y m e r i n t h e s y s t e m a n d t h e t o t a l p o l y m e r w e i g h t c a l c u l a t e d f r o m a p o l y m e r d i s t r i b u t i o n d e t e r m i n e d e x p e r i m e n t a l l y i s a v e r y d i r e c t a n d i n c i s i v e t e s t o f t h e a c c u r a c y o f t h e e x p e r i m e n t a l l y d e t e r m i n e d p o l y m e r d i s t r i b u t i o n . T h e i m a g i n g s t u d i e s o f C h a p t e r 3 p r o d u c e d d i s t r i b u t i o n s w h o s e t o t a l p o l y m e r c o n t e n t d e v i a t e d g r e a t l y f r o m t h e k n o w n t a b l e t w e i g h t (cf . T a b l e 3 . 4 ) . A s i m i l a r c o m p a r i s o n w a s m a d e w i t h t h e d a t a f r o m t h e v a c u u m - t r e a t e d s a m p l e s t o d e t e r m i n e i f t h e a i r b u b b l e s p r e s e n t i n t h e s w o l l e n g e l w e r e t h e c a u s e o f t h e t o t a l w e i g h t d e v i a t i o n . T a b l e 4 . 2 s h o w s t h e r e s u l t s o f t h e t o t a l w e i g h t c a l c u l a t i o n f o r t w o s e p a r a t e i m a g -i n g e x p e r i m e n t s w i t h v a c u u m - t r e a t e d t a b l e t s , b e f o r e a n d a f t e r c o r r e c t i n g t h e m e a s u r e d T 2 v a l u e s f o r d i f f u s i o n e f f e c t s . T h e t o t a l w e i g h t c a l c u l a t i o n w a s n o t p e r f o r m e d f o r d i s t r i b u -t i o n s e a r l i e r t h a n 19 h o u r s b e c a u s e t h e w a t e r e i t h e r h a d n o t p e n e t r a t e d r e g i o n s o f t h e t a b l e t o r h a d p e n e t r a t e d s u c h t h a t i t s c o n c e n t r a t i o n l e v e l w a s n o t h i g h e n o u g h t o c a l c u l a t e H P M C w e i g h t p e r c e n t s . T h e d i f f e r e n c e s b e t w e e n t h e o r i g i n a l p o l y m e r d i s t r i b u t i o n s a n d t h e d i f f u s i o n - c o r r e c t e d d i s t r i b u t i o n s w a s o n a v e r a g e o n l y 5 m g o r a b o u t 3 % o f t h e k n o w n t a b l e t w e i g h t . T h e a v e r a g e e r r o r o f e a c h o f t h e c a l c u l a t e d p o l y m e r w e i g h t s i s a b o u t 14 m g w h i c h i n c l u d e s e r r o r s f r o m t h e w e i g h t p e r c e n t c a l c u l a t i o n a n d p a r a m e t e r s u s e d i n d e t e r m i n i n g t h e v o l u m e o f e a c h s e g m e n t s u c h as t h e c r o s s - s e c t i o n a l a r e a o f t h e t u b e a n d t h e g r a d i e n t s t r e n g t h . T h e t w o v a c u u m t r i a l s p r o d u c e d p o l y m e r w e i g h t s t h a t w e r e m u c h c l o s e r t o t h e a c t u a l w e i g h t o f H P M C i n t h e t a b l e t t h a n t h o s e d e t e r m i n e d f r o m t h e u n t r e a t e d s y s t e m w h i c h i n d i c a t e d t h a t t h e r e m o v a l o f a i r a f f e c t s t h e t o t a l p o l y m e r w e i g h t c a l c u l a t i o n . H o w e v e r , t h e t o t a l w e i g h t s f r o m b o t h v a c u u m t r i a l s w e r e g r e a t e r t h a n t h e a c t u a l w e i g h t o f t h e t a b l e t s u g g e s t i n g e i t h e r t h a t t h e v a c u u m - t r e a t m e n t d o e s n o t r e m o v e a l l t h e a i r f r o m t h e p o r e s o f t h e t a b l e t s o r t h a t t h e i m a g i n g m e t h o d f o r d e t e r m i n i n g H P M C c o n c e n t r a t i o n s u f f e r s f r o m a s m a l l s y s t e m a t i c e r r o r t o w a r d s h i g h e r H P M C c o n c e n t r a t i o n . 104 T a b l e 4 . 2 : T o t a l w e i g h t s o f H P M C c a l c u l a t e d f r o m o n e - d i m e n s i o n a l i m a g i n g e x p e r i m e n t s a t v a r i o u s t i m e s d u r i n g t h e s w e l l i n g o f v a c u u m - t r e a t e d t a b l e t s . T h e o r i g i n a l r e s u l t s a r e t h o s e c o m p u t e d f r o m d i s t r i b u t i o n s c a l c u l a t e d as i n C h a p t e r 3 . T h e c o r r e c t e d r e s u l t s h a v e b e e n a d j u s t e d f o r a n y d i f f u s i o n e f f e c t s . T i m e ( h r s ) T r i a l 1 T r i a l 2 O r i g i n a l C o r r e c t e d O r i g i n a l C o r r e c t e d H P M C % d e v f t H P M C % d e v H P M C % d e v H P M C % d e v 19 179 8 175 5 184 11 1 8 0 8 2 5 188 . 13 183 10 189 14 186 12 31 190 14 185 ' 11 192 ' 16 188 13 3 7 188 13 182 10 193 16 188 13 a H P M C is the total weight of polymer in milligrams with an average error of ± 1 4 mg. 6 Percent deviation from the known polymer weight of 166 mg, 100% X ( H P M C — 1 6 6 ) / 1 6 6 4.3.3 Water Distributions in the Vacuum-Treated Tablets T h e w a t e r d i s t r i b u t i o n s f o r t h e v a c u u m t r e a t e d t a b l e t s w e r e d e t e r m i n e d u s i n g t h e * H i m a g -i n g p r o c e d u r e p r e v i o u s l y d e s c r i b e d i n C h a p t e r 3 . T h e y a r e d i s p l a y e d i n F i g u r e 4 . 4 i n c o m -p a r i s o n w i t h t h e w a t e r d i s t r i b u t i o n s f r o m t h e u n t r e a t e d t a b l e t s y s t e m s . T h e d i s t r i b u t i o n s a r e q u i t e s i m i l a r a t a l l s w e l l i n g t i m e s , a l t h o u g h i t a p p e a r s as i f t h e a m o u n t o f w a t e r i n t h e c o n c e n t r a t e d r e g i o n o f t h e s w o l l e n t a b l e t i s c o n s i s t e n t l y l a r g e r i n t h e v a c u u m - t r e a t e d s y s t e m t h a n i n t h e u n t r e a t e d s y s t e m s u g g e s t i n g t h a t m o r e w a t e r p e n e t r a t e s t h e t a b l e t i n t h e a b s e n c e o f t r a p p e d a i r . T h e d i f f e r e n c e s i n w a t e r c o n c e n t r a t i o n a r e g e n e r a l l y s m a l l , h o w e v e r , a n d m a y b e w i t h i n t h e c o m b i n e d e r r o r s o f t h e t w o e x p e r i m e n t s . T h e r e w a s a c o n c e r n t h a t t h e v a c u u m t r e a t m e n t o f t h e t a b l e t w o u l d r e s u l t i n w a t e r d r a w n d e e p i n t o t h e t a b l e t t o r e p l a c e t h e a i r i n t h e p o r e s o f t h e t a b l e t . H o w e v e r , t h e e x t e n t o f w a t e r p e n e t r a t i o n i n t o t h e t a b l e t f o r t h e v a c u u m - t r e a t e d s y s t e m i s t h e s a m e as f o r t h e u n t r e a t e d s y s t e m a n d t h e w a t e r p e n e t r a t i o n d i s t a n c e ( W P D ) d a t a f r o m t h e v a c u u m - t r e a t e d s y s t e m w o u l d a l s o f a l l o n t h e s t r a i g h t l i n e o f t h e p l o t o f W P D as a f u n c t i o n o f t h e s q u a r e -r o o t o f t i m e , p r e s e n t e d i n F i g u r e 3 .10 . T h u s , t h e v a c u u m - t r e a t m e n t d i d n o t c h a n g e t h e F i c k i a n n a t u r e o f t h e w a t e r p e n e t r a t i o n p r o c e s s . 105 Relative Intensity A (a) 1 hour 1.00 H 0.80 H 0.60 H 0.40 0.20 H 0.00 0.20 i (b) 4 hours 1.00 0.80 0.60 0.40 H 0.20 H -I • 1 1 1 0.00 0.4 0.5 0.6 (d) 13 hours 1.00 0.80 0.60 0.40 0.20 -U-1 1 1 1 1 0.4 0.5 0.6 i 1 • 1 • 1 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Distance (cm) F i g u r e 4 . 4 : W a t e r d i s t r i b u t i o n s o f t h e u n t r e a t e d ( o p e n c i r c l e s , n = 2 ) a n d v a c u u m - t r e a t e d ( f i l l e d c i r c l e s , T r i a l 2 ) t a b l e t s a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 4 h o u r s , ( c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 2 5 h o u r s , (g) 31 h o u r s a n d ( h ) 3 7 h o u r s . T h e e r r o r b a r s f o r t h e u n t r e a t e d t a b l e t s y s t e m i n d i c a t e t h e s t a n d a r d d e v i a t i o n s d e t e r m i n e d f r o m t h e a v e r a g i n g w h i l e t h e e r r o r b a r s f o r t h e v a c u u m - t r e a t e d t a b l e t a r e fixed a t ±0.02. T h e a x e s i n t h e e i g h t p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e i n t e n s i t i e s i n t h e d i s t r i b u t i o n s a r e r e l a t i v e t o t h e i n t e n s i t y o f t h e b u l k w a t e r . T h e d a s h e d v e r t i c a l l i n e i n t h e figure i n d i c a t e s t h e i n i t i a l p o s i t i o n o f t h e w a t e r - t a b l e t i n t e r f a c e . ( T h e figure i s c o n t i n u e d o n t h e n e x t p a g e ) 106 Relative Intensity A(e) 19 hours 1.00 0.80 H 0.60 H 0.40 H 0.20 0.00 (1) 25 hours 1.00 -0.80 -0.60 0.40 0.20 H - i 1 — — | 1 1 1 1 — i 1 1 1 u.uu - | 1 1 — ~ T — i 1 1 ' 1—' 1 ' 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 —i 1 1 1 1 0.4 0.5 0.6 Distance (cm) F i g u r e 4.4 c o n t i n u e d : p l o t s (e) t o ( h ) . 107 4.3.4 HPMC Distributions in the Vacuum-Treated Tablets As was apparent in Table 4.2, the correction for the diffusion of water during the imaging ex-periment was very small . Figure 4.5 shows the difference between the H P M C distributions calculated from the measured T 2 values and those calculated from the diffusion-corrected T 2 values. The H P M C weight percent scale is expanded to allow the differences between the two distributions to be seen clearly. The result of the diffusion correction is a slight lowering of H P M C weight percents in the dilute region of the swollen tablet. The water in this region has larger T 2 values and faster diffusion than the more concentrated regions that show lit t le or no change after the correction for water diffusion is applied. The diffusion corrected H P M C distributions are shown again in Figure 4.6 compared wi th the polymer distributions from the untreated tablet system. A t al l swelling times, the H P M C weight percents calculated from the imaging experiments of the vacuum-treated system are less than those from the untreated system in most regions of the swollen tablet. The most significant differences between the two distributions occurs in the concentrated polymer regions where there are numerous air bubbles present. In the less concentrated regions, the two distributions are very similar because the air has either escaped the gel or dissolved in the more abundant water. The extent of tablet swelling was the same in both tablet systems which was not the expected result. The presence of the air bubbles in the untreated tablet was expected to cause a larger apparent tablet swelling than that due to the polymer alone. 108 F i g u r e 4 . 5 : H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s o f t h e T r i a l 2 v a c u u m - t r e a t e d t a b l e t as c a l c u l a t e d ( o p e n c i r c l e s ) a n d d i f f u s i o n - c o r r e c t e d ( f i l l e d c i r c l e s ) a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 13 h o u r s , (c ) 2 5 h o u r s , a n d (d ) 37 h o u r s . T h e a x e s i n t h e p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e d a s h e d v e r t i c a l l i n e i n t h e f i g u r e i n d i c a t e s t h e i n i t i a l p o s i t i o n o f t h e w a t e r - t a b l e t i n t e r f a c e . 109 HPMC(w/w %) i(ai) 1 hour 100 - i 80 H 60 H (b) 4 hours 100 -\ 80 H 60 H 40 H 20 H —r -0.4 —r~ 0.6 0.8 40 H 20 H (c) 7 hours 100 (d) 13 hours 100 -\ 0.6 — I 0.8 Distance (cm) F i g u r e 4 . 6 : A v e r a g e H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s o f t h e u n t r e a t e d ( o p e n c i r c l e s , n = 2 ) a n d v a c u u m - t r e a t e d ( f i l l e d c i r c l e s , n = 2 ) t a b l e t s a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 4 h o u r s , ( c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 2 5 h o u r s , (g) 31 h o u r s a n d ( h ) 3 7 h o u r s . T h e e r r o r b a r s f o r b o t h t a b l e t s y s t e m s a r e t h e s t a n d a r d d e v i a t i o n s f r o m t h e a v e r a g i n g . T h e a x e s i n t h e p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e d a s h e d v e r t i c a l l i n e i n t h e f i g u r e i n d i c a t e s t h e i n i t i a l p o s i t i o n o f t h e w a t e r - t a b l e t i n t e r f a c e . ( T h e figure i s c o n t i n u e d o n t h e n e x t p a g e ) 110 H P M C ( w / w % ) A ( e ) 1 9 h o u r s ( f ) 2 5 h o u r s D i s t a n c e ( c m ) F i g u r e 4 . 6 c o n t i n u e d : p l o t s (e) t o ( h ) . I l l 4.4 Summary T h e v a c u u m - t r e a t m e n t o f H P M C t a b l e t s p r i o r t o t h e i m a g i n g e x p e r i m e n t w a s s h o w n t o r e m o v e t h e a i r b u b b l e s a n d d e c r e a s e t h e c a l c u l a t e d t o t a l p o l y m e r w e i g h t f r o m t h e e x p e r i -m e n t a l H P M C w e i g h t p e r c e n t d i s t r i b u t i o n s . T h e v a c u u m - t r e a t m e n t w a s s h o w n t o v a r y i n e f f i c i e n c y a n d t h e t o t a l p o l y m e r w e i g h t w a s u s e d as a c r i t e r i o n f o r d e t e r m i n i n g t h e a c c u r a c y o f t h e H P M C d i s t r i b u t i o n s f r o m a n i m a g i n g e x p e r i m e n t . T h e w a t e r a n d p o l y m e r d i s t r i -b u t i o n s o b t a i n e d f r o m t h e v a c u u m - t r e a t e d t a b l e t a r e n o w s u i t a b l e f o r c o m p a r i s o n w i t h t h e o r e t i c a l m o d e l s . 112 C h a p t e r 5 O n e - D i m e n s i o n a l i y F N M R I m a g i n g I n v e s t i g a t i o n s o f M o d e l D r u g s i n S w e l l i n g H P M C T a b l e t s 5.1 Introduction D r u g r e l e a s e f r o m s w e l l i n g - c o n t r o l l e d d e l i v e r y s y s t e m s h a s b e e n s t u d i e d p r i m a r i l y b y t h e U S P d i s s o l u t i o n m e t h o d s w h e r e t h e t a b l e t i s s u s p e n d e d i n a m e d i a b a t h , o r f l o w - c e l l , a n d t h e a m o u n t o f d r u g r e l e a s e d i n t o s o l u t i o n i s m e a s u r e d as a f u n c t i o n o f t i m e [21]. T h e r e l a t i o n s h i p b e t w e e n t h e f r a c t i o n o f d r u g r e l e a s e d a n d t i m e i s u s e d t o d e t e r m i n e w h e t h e r t h e d r u g r e l e a s e p r o c e s s f o l l o w s F i c k i a n o r n o n - F i c k i a n k i n e t i c s w h i c h i s r e l a t e d t o t h e w a t e r p e n e t r a t i o n p r o c e s s as d i s c u s s e d i n S e c t i o n 1 .1 .3 . D i s s o l u t i o n t e s t s , h o w e v e r , c a n n o t p r o b e t h e d r u g p r e s e n t w i t h i n t h e s w o l l e n t a b l e t a n d d o n o t p r o v i d e i n f o r m a t i o n o n t h e r e l a t i v e i m p o r t a n c e o f t h e t w o m e c h a n i s m s o f d r u g r e l e a s e f r o m s w e l l i n g - c o n t r o l l e d d e v i c e s , n a m e l y d i f f u s i o n t h r o u g h t h e s w o l l e n p o l y m e r o r , i n c a s e s o f s l o w d i f f u s i o n , t h e r e l e a s e o f d r u g a t t h e e d g e s o f t h e t a b l e t t h r o u g h e r o s i o n . I n C h a p t e r 3 , a s i m p l e g e o m e t r y w a s p r e s e n t e d t o s t u d y t h e s w e l l i n g o f a n H P M C t a b l e t a n d N M R i m a g i n g o f * H w a s u s e d t o d e t e r m i n e t h e d i s t r i b u t i o n s o f w a t e r a n d p o l y m e r as t h e t a b l e t s w e l l e d . I n a s i m i l a r e x p e r i m e n t , u s i n g a t a b l e t t h a t c o n t a i n s a m o d e l d r u g , N M R i m a g i n g o f a n u c l e u s s p e c i f i c t o t h e d r u g , i n t h i s c a s e 1 9 F , p e r m i t s t h e i n d e p e n d e n t m o n i t o r i n g o f t h e d r u g d i s t r i b u t i o n w i t h i n t h e p o l y m e r t a b l e t as i t s w e l l s . T h e r e l a t i o n s h i p b e t w e e n , t h e d i s t r i b u t i o n s o f t h e d r u g a n d p o l y m e r m a k e s i t p o s s i b l e t o 113 d i s t i n g u i s h b e t w e e n d r u g s t h a t a r e r e l e a s e d o n l y b y e r o s i o n o f t h e t a b l e t a n d t h o s e t h a t a r e a l s o r e l e a s e d b y d i f f u s i o n t h r o u g h t h e p o l y m e r g e l . T h e m e c h a n i s m o f r e l e a s e i n a n y s p e c i f i c c a s e w i l l d e p e n d o n t h e p r o p e r t i e s o f t h e d r u g a n d t a b l e t s y s t e m . 5.2 Experimental 5.2.1 Preparation of Tablets Containing Fluorinated Drug T h e t a b l e t s f o r t h e 1 9 F i m a g i n g e x p e r i m e n t s w e r e s i m i l a r t o t h e T y p e 1 t a b l e t s o f S e c -t i o n 3 . 2 . 1 . T h e t a b l e t s w e r e c o m p r e s s e d f r o m m i x t u r e s o f H P M C a n d d r u g c o n t a i n i n g 5 . 3 0 % a n d 5 . 2 5 % b y w e i g h t o f t r i f l u p r o m a z i n e - H C l a n d 5 - f l u o r o u r a c i l , r e s p e c t i v e l y . T h e t a b l e t p a r a m e t e r s , g i v e n i n T a b l e 5 . 1 , i n d i c a t e t h a t t h e t w o t a b l e t s a r e e s s e n t i a l l y i d e n t i c a l . T h e t a b l e t s c o n t a i n e d a p p r o x i m a t e l y t h e s a m e c o n c e n t r a t i o n o f fluorine b e c a u s e t h e l a r g e r m o l e c u l a r w e i g h t f o r t r i f l u p r o m a z i n e - H C l c o m p a r e d t o 5 - f l u o r o u r a c i l i s c o m p e n s a t e d b y t h e l a r g e r n u m b e r o f 1 9 F a t o m s i n t h e f o r m e r d r u g . T a b l e 5 . 1 : P a r a m e t e r s f o r t h e H P M C t a b l e t s c o n t a i n i n g t h e fluorinated m o d e l d r u g s . W e i g h t " T h i c k n e s s D r u g 1 9 F ( I O " 5 ) D r u g i n T a b l e t ( m g ± 0 . 0 1 ) ( m m i O . O l ) ( m g i O . O l ) ( m o l e s ± 0 . 0 4 ) t r i f l u p r o m a z i n e - H C l 174 1.30 9 . 2 2 7 .11 5 - f l u o r o u r a c i l 176 1.31 9 . 2 4 7 . 1 0 °The weight of the H P M C component, once corrected for moisture content, was 156 mg for the triflupromazine-HCl tablet and 158 mg for the 5-fluorouracil tablet. 5.2.2 One-dimensional Imaging T h e o n e - d i m e n s i o n a l i m a g i n g s t u d i e s o f t h e d r u g - c o n t a i n i n g t a b l e t s w e r e p e r f o r m e d i n a s i m i l a r m a n n e r t o t h o s e o f C h a p t e r 3 w i t h t h e a d d i t i o n a l v a c u u m - t r e a t m e n t s t e p d e s c r i b e d i n C h a p t e r 4 . T h e r e w e r e a f e w s i g n i f i c a n t d i f f e r e n c e s f o r t h e 1 9 F v e r s i o n o f t h e i m a g i n g e x p e r i m e n t s . T h e r f c o i l w a s t u n e d t o 3 7 6 . 4 5 M H z , t h e f r e q u e n c y o f 1 9 F i n a 9 . 4 T m a g n e t . T h e s p e c t r a l w i d t h w a s i n c r e a s e d t o 100 k H z t o i n c l u d e m o r e o f t h e r e g i o n o u t s i d e t h e t a b l e t , a n d t h u s , t h e r e s o l u t i o n i n c r e a s e d t o 0 . 0 2 0 c m . T h e n u m b e r o f s c a n s f o r t h e e x p e r i m e n t w a s i n c r e a s e d b e c a u s e o f t h e l o w e r c o n c e n t r a t i o n , a n d h e n c e l o w e r s i g n a l , o f t h e fluorinated 114 d r u g s c o m p a r e d t o w a t e r . B e c a u s e o f t h e i n c r e a s e d n u m b e r o f s c a n s , t h e TE r a n g e f o r t h e v a r i a b l e - T ^ s e r i e s w a s s h o r t e n e d t o a m a x i m u m v a l u e o f 64 m s , a c q u i r e d i n t h e o r d e r 2 m s , 4 m s , 16 m s , 3 2 m s , 6 4 m s , 2 4 m s , 8 m s , a n d 3 m s , t o d e c r e a s e t h e t i m e r e q u i r e d t o o b t a i n t h e se t o f i m a g e s . A l s o , a c a l i b r a t i o n s t e p t o q u a n t i f y t h e 1 9 F s i g n a l w a s a d d e d t o t h e p r e v i o u s l y d e s c r i b e d i m a g i n g p r o c e d u r e . 5 . 2 . 3 C a l i b r a t i o n o f F l u o r i n e S i g n a l T h e s i g n a l i n t h e 1 9 F i m a g e s o f t h e fluorinated d r u g s w a s o b t a i n e d o n a n a r b i t r a r y s c a l e t h a t v a r i e d f r o m e x p e r i m e n t t o e x p e r i m e n t . T o o b t a i n c o n c e n t r a t i o n i n f o r m a t i o n , t h e s i g n a l f r o m t h e d r u g s i n t h e t a b l e t w a s r e f e r e n c e d t o t h e s i g n a l f r o m a n o t h e r fluorinated c o m p o u n d o f k n o w n c o n c e n t r a t i o n . 3 - F l u o r o - 4 - n i t r o t o l u e n e ( F . W . 1 5 5 . 1 3 g m o l - 1 ) w a s o b t a i n e d f r o m A l d r i c h C h e m i c a l C o . a n d w a s c h o s e n b e c a u s e i t s r e s o n a n c e f r e q u e n c y w a s w e l l r e m o v e d f r o m t h e f r e q u e n c i e s o f t r i f l u p r o m a z i n e - H C l a n d 5 - f l u o r o u r a c i l a n d i t s s i g n a l d i d n o t a p p e a r i n t h e 1 9 F i m a g e s o f t h e s w o l l e n t a b l e t . T h e Ti a n d T 2 r e l a x a t i o n t i m e s f o r t h e 1 9 F i n 3 - f l u o r o - 4 - n i t r o t o l u e n e i n CDCI3 w e r e a p p r o x i m a t e l y 3 s a n d 3 5 0 m s , r e s p e c t i v e l y , so a s p i n - e c h o s p e c t r u m a c q u i r e d w i t h a TR o f 15 s a n d a T E o f 2 m s w o u l d b e q u a n t i t a t i v e . A s m a l l a m o u n t o f t h i s c o m p o u n d , 10 .7 m g , w a s w e i g h e d i n t o a 5 m m o . d . N M R t u b e a n d d i s s o l v e d i n CDCI3. T h e 5 m m t u b e w a s t h e n s u s p e n d e d i n t h e l a r g e r t u b e c o n t a i n i n g t h e t a b l e t . T h e c a l i b r a t i o n f o r t h e d r u g s w a s p e r f o r m e d b y a c q u i r i n g s p e c t r a a n d i m a g e s as l i s t e d i n T a b l e 5 . 2 . T h e p r o c e d u r e f o r t h e t a b l e t s w i t h 5 - f l u o r o u r a c i l w a s a d j u s t e d s l i g h t l y b e c a u s e t h e Ti o f t h e d r u g i n d i l u t e s o l u t i o n s i s a b o u t 4 s. I f t h e TR i n t h e T ^ - v a r i a t i o n s e r i e s w a s c h o s e n t o a v o i d a n y Ti d e p h a s i n g , t h e n t h e 8 i m a g e s w o u l d t a k e 3 - 4 h o u r s t o a c q u i r e w h i c h w a s d e e m e d t o b e t o o l o n g . A n a l t e r n a t e p r o c e d u r e , w h e r e t h e 2 m s i m a g e w a s a c q u i r e d w i t h a TR o f 20 s a n d t h e n t h e T# v a r i a t i o n w a s p e r f o r m e d w i t h a s h o r t e r TR, a l l o w e d f o r t h e q u a n t i t a t i v e d e t e r m i n a t i o n o f t h e 5 - f l u o r o u r a c i l c o n c e n t r a t i o n s a n d a l s o a m e a s u r e m e n t o f t h e T 2 d i s t r i b u t i o n . T o e n s u r e c o m p l e t e d e t e c t i o n o f t h e s i g n a l i n t e n s i t y f r o m a p a r t i c u l a r s p e c i e s , t h e o f fset o f t h e e x c i t a t i o n p u l s e w a s a d j u s t e d f o r e a c h e x p e r i m e n t i n t h e s e q u e n c e s u c h t h a t t h e s p e c i e s o f i n t e r e s t w a s o n r e s o n a n c e . T h e s i g n a l i n t e n s i t y o f a s p i n - e c h o s p e c t r u m o f t h e d r u g w a s q u a n t i f i e d i n r e l a t i o n 115 , T a b l e 5 . 2 : S e q u e n c e o f e x p e r i m e n t s f o r c a l i b r a t i o n o f 1 9 F s i g n a l a t v a r i o u s t i m e s d u r i n g t h e s w e l l i n g o f t h e d r u g - c o n t a i n i n g t a b l e t . T h e p a r a m e t e r s f o r e a c h e x p e r i m e n t , as w e l l as t h e t i m e f o r a c q u i s i t i o n , a r e i n d i c a t e d . T r i f l u p r o m a z i n e - H C l : 1. S p i n - e c h o s p e c t r u m o f 3 - f l u o r o - 4 - n i t r o t o l u e n e TE = 2 m s , TR = 15 s , 80 s c a n s , 20 m i n u t e s 2 . S p i n - e c h o s p e c t r u m o f t r i f l u p r o m a z i n e - H C l TE — 2 m s , TR = 7 s , 80 s c a n s , 9 . 5 m i n u t e s 3 . 8 v a r i a b l e - T ^ ; o n e - d i m e n s i o n a l i m a g e s TE = 2 - 6 4 m s , TR = 7 s , 80 s c a n s , 7 5 m i n u t e s 5 - F l u o r o u r a c i l : 1. S p i n - e c h o s p e c t r u m o f 3 - f l u o r o - 4 - n i t r o t o l u e n e TE — 2 m s , TR = 15 s , 64 s c a n s , 16 m i n u t e s 2. S p i n - e c h o s p e c t r u m o f 5 - f l u o r o u r a c i l TE = 2 m s , T R = 20 s , 64 s c a n s , 2 2 m i n u t e s 3. Q u a n t i t a t i v e i m a g e o f 5 - f l u o r o u r a c i l T E = 2 m s , TR = 20 s , 6 4 s c a n s , 2 2 m i n u t e s 4. 8 v a r i a b l e - T ^ o n e - d i m e n s i o n a l i m a g e s TE = 2 - 6 4 m s , TR = 10 s , 6 4 s c a n s , 8 6 m i n u t e s 116 t o t h e s i g n a l i n t e n s i t y o f t h e s p i n - e c h o s p e c t r u m o f 3 - f l u o r o - n i t r o t o l u e n e t a k e n u n d e r t h e s a m e e x p e r i m e n t a l c o n d i t i o n s . T h e s i g n a l i n t h e , s p i n - e c h o s p e c t r u m o f t h e d r u g w a s t h e n a s s u m e d t o b e t h e s a m e as t h e t o t a l s i g n a l i n t h e o n e - d i m e n s i o n a l i m a g e w i t h a T E o f 2 m s as a n y s i g n a l l o s s d u e t o T 2 d e p h a s i n g w o u l d a f f ec t b o t h e x p e r i m e n t s e q u a l l y . T h e c a l i b r a t i o n f o r t h e t r i f l u p r o m a z i n e - H C l r e q u i r e d 20 m i n u t e s t o o b t a i n t h e s p i n - e c h o s p e c t r u m a n d t h e 2 m s i m a g e . T h e s a m e p r o c e d u r e f o r t h e 5 - f l u o r o u r a c i l r e q u i r e d a b o u t 4 5 m i n u t e s . T h e c a l i b r a t i o n e q u a t i o n s , r e l a t i n g t h e a r b i t r a r y i n t e n s i t y s c a l e o f t h e i m a g e s t o c o n c e n t r a t i o n s o f d r u g , w e r e o b t a i n e d b y p l o t t i n g t h e c o n c e n t r a t i o n s o f 1 9 F d e t e r m i n e d f r o m t h e i n t e r n a l r e f e r e n c e as a f u n c t i o n o f t h e t o t a l s i g n a l i n t h e i m a g e s a t v a r i o u s t i m e s d u r i n g t h e s w e l l i n g o f t h e t a b l e t . S u c h p l o t s f o r t r i f l u p r o m a z i n e - H C l a n d 5 - f l u o r o u r a c i l , u s i n g d a t a f r o m s w e l l i n g t i m e s o f 7 h o u r s t o 3 7 h o u r s , a r e s h o w n i n F i g u r e 5 . 1 . T h e l e a s t - s q u a r e s f i t s t o t h e s e d a t a s e t s r e s u l t e d i n E q u a t i o n s 5.1 a n d 5 . 3 , w i t h a n r 2 o f 0 . 9 9 7 i n b o t h c a s e s . T h e y -i n t e r c e p t i s t h e o f f se t f r o m t h e z e r o c o n c e n t r a t i o n a t z e r o t i m e a n d w a s a s s u m e d t o b e s p r e a d e v e n l y o v e r a l l t h e p o i n t s i n t h e d i s t r i b u t i o n . W h e n t h e v a l u e o f t h e y - i n t e r c e p t w a s d i v i d e d e q u a l l y b e t w e e n t h e n u m b e r o f r e l e v a n t d a t a p o i n t s i n e a c h 1 9 F d i s t r i b u t i o n , 101 f o r t r i f l u p r o m a z i n e - H C l a n d 96 f o r 5 - f l u o r o u r a c i l , t h e n e w c a l i b r a t i o n s , E q u a t i o n s 5 .2 a n d 5 . 4 , r e s p e c t i v e l y , c o u l d b e u s e d t o c o n v e r t t h e s i g n a l i n t e n s i t i e s i n t h e T 2 - c o r r e c t e d i m a g e s o f t h e d r u g s t o m o l e s 1 9 F . A s e a c h p o i n t i n t h e 1 9 F i m a g e s r e p r e s e n t s t h e s i g n a l f r o m a v o l u m e o f 0 . 0 2 5 6 c m 3 , a d i s t r i b u t i o n o f 1 9 F i n u n i t s o f m o l a r i t y c a n b e c a l c u l a t e d . W h e n t h e n u m b e r o f 1 9 F n u c l e i p e r m o l e c u l e i s t a k e n i n t o a c c o u n t , t h e d i s t r i b u t i o n c a n a l s o b e e x p r e s s e d i n m o l a r i t y o f t h e d r u g . Total moles 19F = 5 . 0 2 4 4 x 1 0 " (Total Signalirijiu) - 1 . 0 6 7 3 x 1 0 " 5 (5 .1 ) moles 1 9 F = 5 . 0 2 4 4 x 10-13(Signaltrijiu) - 1 .0567 x 1 0 ~ 7 (5 .2 ) Total moles 1 9 F = 2 . 6 1 1 9 x !Q-13(Total Signakflu) + 5 . 7 2 0 4 x 1 0 - 6 (5 .3 ) moles 1 9 F = 2 . 6 1 1 9 x 10~13(SignalsJ l u) + 5 . 9 5 8 7 x l Q - : (5 .4 ) 117 (a) 7.0e-5"| 6 . 0 e - 5 H Moles 1 9 F 5.0e-5-4.0e-5" 3.Ue-51 ' 1 1 1 ' 1 ' 1 ' 1 1 1 1 i 8.0e+7 9.0e+7 1.0e+8 l.le+8 1.2e+8 1.3e+8 1.4e+8 1.5e+8 Total signal (b) 7.0e-5 6.0e-5H Moles 1 9 F 5.0e-5H 4.0e-5l 3.0e-5 1.0e+8 1.2e+8 T 1 1 1 r 1.4e+8 1.6e+8 1.8e+8 2.0e+8 2.2e+8 Total signal F i g u r e 5 . 1 : C a l i b r a t i o n p l o t s r e l a t i n g 1 9 F c o n c e n t r a t i o n d e t e r m i n e d f r o m t h e i n t e r n a l r e f -e r e n c e t o t h e t o t a l s i g n a l i n t h e 2 m s i m a g e a c q u i r e d a t t h e s a m e t i m e s d u r i n g t h e s w e l l i n g o f a n H P M C t a b l e t c o n t a i n i n g d r u g , (a ) t r i f l u p r o m a z i n e - H C l a n d ( b ) 5 - f l u o r o u r a c i l . T h e l i n e i n e a c h p l o t i s t h e r e s u l t o f a l e a s t - s q u a r e s fit t o t h e d a t a , ( a ) E q u a t i o n 5.1 a n d (b ) E q u a t i o n 5 . 3 . 118 5.3 Results and Discussion 5.3.1 Distributions ofTriflupromazine-HCl and 5-Fluorouracil in the Swelling Tablet T h e o n e - d i m e n s i o n a l i m a g i n g s t u d i e s o f d r u g - c o n t a i n i n g H P M C t a b l e t s w e r e u s e d t o d e -t e r m i n e t h e d i s t r i b u t i o n s o f t h e m o d e l d r u g s i n t h e s w o l l e n t a b l e t . T h e H P M C t a b l e t s , p r e p a r e d w i t h e i t h e r t r i f l u p r o m a z i n e - H C l o r 5 - f l u o r o u r a c i l , c o n t a i n e d e s s e n t i a l l y t h e s a m e w e i g h t s o f t h e d r u g a n d , c o i n c i d e n t a l l y , t h e s a m e m o l e s o f 1 9 F . T h u s , t h e c o m p a r i s o n b e t w e e n t h e t r i f l u p r o m a z i n e - H C l a n d 5 - f l u o r o u r a c i l d i s t r i b u t i o n s i n t h e t w o s y s t e m s , F i g -u r e 5 . 2 , i s p r e s e n t e d i n c o n c e n t r a t i o n o f 1 9 F r a t h e r t h a n d r u g so t h a t t h e c o m p a r i s o n b e t w e e n t h e i m a g i n g r e s u l t s f o r t h e t w o d r u g s w i l l b e c l e a r e r . ( T h e 5 - f l u o r o u r a c i l c o n c e n -t r a t i o n d i s t r i b u t i o n w i l l b e i d e n t i c a l t o i t s 1 9 F d i s t r i b u t i o n b e c a u s e t h e d r u g m o l e c u l e h a s o n e 1 9 F g r o u p w h e r e a s t h e t r i f l u p r o m a z i n e - H C l c o n c e n t r a t i o n d i s t r i b u t i o n w o u l d b e 1 / 3 o f i t s 1 9 F d i s t r i b u t i o n b e c a u s e t h e d r u g m o l e c u l e h a s t h r e e 1 9 F f r o m a C F 3 g r o u p . ) T a b l e 5 . 3 : T h e t o t a l d e t e c t a b l e m o l e s 1 9 F i n t h e T 2 c o r r e c t e d o n e - d i m e n s i o n a l i m a g e s o f H P M C t a b l e t s c o n t a i n i n g t r i f l u p r o m a z i n e - H C l a n d 5 - f l u o r o u r a c i l . T i m e ( h o u r s ) m o l e s 1 9 F ( ± 0 . 0 5 x l O ~ 5 ) T r i f l u p r o m a z i n e - H C l % a 5 - f l u o r o u r a c i l % a 1 2 .20 31 2 . 0 6 2 9 4 3 .46 49 1 .67 2 4 7 4 . 1 8 59 3 .86 5 4 13 5 .29 75 5 .08 7 2 19 5 .81 8 2 5 . 7 7 81 2 5 6 .18 87 6 . 1 2 8 6 31 6 .42 90 6 . 3 0 8 9 3 7 6 .52 9 2 6 . 3 5 8 9 a P e r c e n t a g e r a t i o o f d e t e c t e d versus k n o w n mo les o f 1 9 F i n t a b l e t T h e t o t a l d e t e c t a b l e a m o u n t o f e a c h d r u g as a f u n c t i o n o f s w e l l i n g t i m e i s g i v e n i n T a b l e 5 . 3 . I n b o t h t h e s e s y s t e m s , t h e d e t e c t a b l e 1 9 F i n t h e i m a g e s i n c r e a s e d s l o w l y w i t h s w e l l i n g t i m e . A t e a r l y t i m e s , a l a r g e p o r t i o n o f t h e d r u g w i t h i n t h e t a b l e t w a s i m m o b i l e a n d i n v i s i b l e t o t h e i m a g i n g t e c h n i q u e . A s w a t e r p e n e t r a t e d f u r t h e r a n d f u r t h e r i n t o t h e t a b l e t , t h e d r u g w a s d i s s o l v e d a n d i t s h i g h r e s o l u t i o n N M R s i g n a l g r e w . H o w e v e r , t h e 119 1 9 F (moles L-i) i (a) 1 hour 0.10 - i 0.08 H 0.06 H 0.04 H 0.02 H 0.00 (b) 4 hours o.io n j j 0.08 H 0.06 H 0.04 H 0.02 H E i • i • i ooo i I J 1 1 1 1 [ » 1 1 — T » 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 (c) 7 hours 0.10 -I 0.08 13 hours 0.06 H 0.04 H 0.02 ooo H— I— i — • — i — • — — i ^ • " • " T ooo H—I—i—.—i—i—i—•—i —•—i 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 Distance (cm) F i g u r e 5 . 2 : M o l a r d i s t r i b u t i o n s o f 1 9 F i n s w o l l e n H P M C t a b l e t s c o n t a i n i n g t r i f l u p r o m a z i n e -H C l ( f i l l e d c i r c l e s ) a n d 5 - f l u o r o u r a c i l ( o p e n c i r c l e s ) . T h e s w e l l i n g t i m e s i n t h e figure a r e (a ) 1 h o u r , ( b ) 4 h o u r s , (c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 2 5 h o u r s , (g ) 31 h o u r s , a n d ( h ) 3 7 h o u r s . T h e a x e s a r e t h e s a m e i n a l l 8 p l o t s a n d a r e d e f i n e d b y t h e a r r o w s . T h e d a s h e d v e r t i c a l l i n e a t 0 . 1 3 0 c m i n d i c a t e s t h e i n i t i a l p o s i t i o n o f t h e w a t e r - t a b l e t i n t e r f a c e . ( T h e figure i s c o n t i n u e d o n t h e n e x t p a g e . ) 120 19F (moles L - i ) ^ (e) 1 9 hours o.io 0.08 H 0.06 0.04 0.02 ( f ) 2 5 h o u r s 0.10 -i 0.08 H 0.06 0.04 0.02 H o.oo H — i — i — i — i — i — i — i — i — i — f ^ * i o.oo H—i—i—'—i—•—i—>—i— 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 ( g ) 3 1 h o u r s 0.10 0.08 -f 0.06 0.04 H 0.02 H (h) 3 7 hours 0.10 - i 0.08 0.06 H 0.04 H 0.02 H 0.00 -I 1 r 1 • 1 • 1—' i 1 1 0.00 H 1 1 • — i 1 1 1 1—i r 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 D i s t a n c e ( c m ) F i g u r e 5 . 2 c o n t i n u e d : p l o t s (e) t h r o u g h ( h ) . 121 k n o w n c o n c e n t r a t i o n o f (7 .11 ± 0 .04 ) x l O - 5 m o l e s 1 9 F w i t h i n b o t h t a b l e t s w a s n o t r e a c h e d f o r e i t h e r s y s t e m . E v e n a t t h e l o n g e s t s w e l l i n g t i m e s , o n l y a b o u t 9 0 % o f t h e t o t a l 1 9 F s i g n a l w a s d e t e c t a b l e . I n t h e t r i f l u p r o m a z i n e - H C l d i s t r i b u t i o n s , i t i s b e l i e v e d t h a t t h e s h o r t T 2 s p e c i e s t h a t a r e p r e s e n t i n H P M C c o n c e n t r a t i o n s a b o v e ~ 3 0 % c a u s e s u c h a l a r g e s i g n a l l o s s i n t h e 2 m s i m a g e t h a t t h e T 2 v a l u e s c a l c u l a t e d f o r r e g i o n s o f t h e p o l y m e r a b o v e « 3 0 % d o n o t a d e q u a t e l y c o r r e c t f o r t h e s e s p e c i e s . I n t h e 5 - f l u o r o u r a c i l s y s t e m , d i f f u s i o n o f t h e 5 - f l u o r o u r a c i l o u t s i d e t h e r e g i o n o f t h e c o i l , a n d h e n c e o u t o f t h e i m a g i n g field o f v i e w , i s t h e m o s t l i k e l y e x p l a n a t i o n f o r t h e m i s s i n g 1 0 % o f s i g n a l a t 37 h o u r s . A t e a r l i e r t i m e s , t h e p r e s e n c e o f w h i t e flecks i n t h e s w o l l e n g e l s u g g e s t e d t h a t t h e 5 - f l u o r o u r a c i l w a s n o t c o m p l e t e l y d i s s o l v e d w h i c h w o u l d a c c o u n t f o r t h e l a c k o f h i g h - r e s o l u t i o n N M R s i g n a l . F i g u r e 5 . 2 c l e a r l y s h o w s t h a t t h e 5 - f l u o r o u r a c i l w a s a b l e t o d i f f u s e m o r e f r e e l y t h a n t h e t r i f l u p r o m a z i n e - H C l . A p r o p o r t i o n o f t h e 5 - f l u o r o u r a c i l a p p e a r e d t o h a v e d i f f u s e d o u t o f t h e field o f v i e w o f t h e i m a g i n g e x p e r i m e n t s as e a r l y as 13 h o u r s . T h e d i f f e r e n c e s i n t h e s e d i s t r i b u t i o n s w i l l b e d i s c u s s e d f u r t h e r i n S e c t i o n 5 . 3 . 3 . 5 . 3 . 2 H P M C C o n c e n t r a t i o n D i s t r i b u t i o n s C a l c u l a t e d f r o m I m a g e s o f t h e M o d e l D r u g s T h e T 2 d i s t r i b u t i o n s c a l c u l a t e d f r o m t h e v a r i a b l e - T # i m a g e s o f t h e m o d e l d r u g s i n t h e s w o l l e n H P M C t a b l e t c a n b e u s e d t o c a l c u l a t e H P M C d i s t r i b u t i o n s i n t h e s a m e m a n n e r as d e s c r i b e d i n C h a p t e r 3 . T h e c a l i b r a t i o n r e l a t i o n s h i p s b e t w e e n t h e T 2 v a l u e s o f t h e m o d e l d r u g s a n d H P M C w e i g h t p e r c e n t w e r e g e n e r a t e d i n C h a p t e r 2 , r e s u l t i n g i n E q u a t i o n s 2 .8 a n d 2 . 9 f o r t r i f l u p r o m a z i n e - H C l a n d 5 - f l u o r o u r a c i l , r e s p e c t i v e l y . T h e T 2 v a l u e s d e t e r m i n e d f r o m t h e i m a g i n g e x p e r i m e n t s o f t h e d r u g s w e r e n o t c o r r e c t e d f o r d i f f u s i o n - e f f e c t s b e c a u s e t h e d i f f u s i o n c o e f f i c i e n t s o f t h e d r u g s a r e m u c h l o w e r t h a n t h o s e o f w a t e r . T h e c o r r e c t i o n f o r t h e d r u g s w o u l d t h e r e f o r e b e m u c h s m a l l e r t h a n t h a t f o r w a t e r w h i c h w a s s h o w n , i n S e c t i o n 4 . 3 . 4 , t o b e m i n i m a l . O n e e x a m p l e o f t h e v a r i a t i o n o f t h e 1 9 F s i g n a l i n t e n s i t y o f t r i f l u p r o m a z i n e - H C l as a f u n c t i o n o f T g is s h o w n i n F i g u r e 5 .3 w h e r e t h e s i g n a l i n t e n s i t y d e c r e a s e d as t h e T g i n c r e a s e d . T h e m o s t s i g n i f i c a n t s i g n a l c h a n g e s o c c u r r e d i n t h e c o n c e n t r a t e d r e g i o n s o f 122 (a) Relative Intensity 1.00 1.50 T 2 (ms) 800 H 600 1 400 H 200 H Distance (cm) 0.25 0.50 0.75 1.00 1.25 1.50 Distance (cm) F i g u r e 5 . 3 : T h e v a r i a t i o n o f t h e s i g n a l i n t e n s i t y i n t h e t r i f l u p r o m a z i n e - H C l i m a g e s as a f u n c t i o n o f T g (a ) a n d t h e c o r r e s p o n d i n g T 2 v a l u e s ( b ) c a l c u l a t e d f r o m t h e d a t a i n (a ) a f t e r 19 h o u r s o f s w e l l i n g . T h e T # v a l u e s a r e 2 m s ( f i l l e d c i r c l e s ) , 3 m s ( o p e n c i r c l e s ) , 4 m s ( f i l l e d t r i a n g l e s ) , 8 m s ( o p e n s q u a r e s ) , 16 m s ( o p e n t r i a n g l e s ) , 2 4 m s ( c r o s s e s ) , 3 2 m s ( o p e n d i a m o n d s ) a n d 64 m s ( f i l l e d d i a m o n d s ) . 123 t h e t a b l e t . A t d i s t a n c e s a b o v e «0 .6 c m , t h e r e w a s v e r y l i t t l e c h a n g e i n i n t e n s i t y w i t h i n c r e a s i n g T E . T h e a c c u r a t e d e t e r m i n a t i o n o f T 2 v a l u e s a b o v e 2 0 0 m s i s t h e r e f o r e d i f f i c u l t w i t h a m a x i m u m TE o f o n l y 64 m s . T h e c a l c u l a t e d T 2 d i s t r i b u t i o n i s c o n s i d e r e d t o b e a p p r o x i m a t e d u e t o t h e 75 m i n u t e s o f e x p e r i m e n t a l t i m e r e q u i r e d t o o b t a i n t h e c o m p l e t e se t o f i m a g e s f o r t h e c a l c u l a t i o n . F i g u r e 5 .4 s h o w s a n e x a m p l e o f t h e 1 9 F s i g n a l v a r i a t i o n o f 5 - f l u o r o u r a c i l as a f u n c t i o n o f T & . T h e s e i m a g e s a r e a f f e c t e d b y T i r e l a x a t i o n b e c a u s e t h e TR o f 10 s d o e s n o t a l l o w d r u g i n d i l u t e p o l y m e r r e g i o n s t o r e l a x c o m p l e t e l y b e t w e e n s u c c e s s i v e r e p e t i t i o n s o f t h e p u l s e s e q u e n c e . H o w e v e r , t h e d e g r e e o f T i d e p h a s i n g s h o u l d r e m a i n c o n s t a n t i n t h e s e t o f i m a g e s a c q u i r e d a t e a c h t i m e i n t e r v a l , n o t a f f e c t i n g t h e c a l c u l a t i o n o f T 2 v a l u e s f r o m t h e i n t e n s i t y c h a n g e s . T h e c a l c u l a t e d T 2 d i s t r i b u t i o n , t h e a v e r a g e o v e r 86 m i n u t e s o f e x p e r i m e n t a l t i m e , a p p e a r s r e a s o n a b l e . H o w e v e r , t h e r a n g e o f T 2 v a l u e s e x t e n d s f a r b e y o n d t h e m a x i m u m T 2 v a l u e o f a b o u t 4 0 0 m s d e t e r m i n e d f r o m t h e 0 .5 w / w %, o r 0 . 0 3 8 M , s o l u t i o n o f 5 - f l u o r o u r a c i l i n d i s t i l l e d w a t e r . T h e T 2 r e l a x a t i o n t i m e f o r a 0 . 1 % , o r 0 . 0 0 7 7 M , m i x t u r e w a s m e a s u r e d t o d e t e r m i n e i f t h e h i g h T 2 v a l u e s c o r r e s p o n d t o 5 - f l u o r o u r a c i l i n c o n c e n t r a t i o n s l o w e r t h a n t h o s e p r e v i o u s l y m e a s u r e d . T h e T 2 v a l u e s f o r t h e 0 . 1 % m i x t u r e w e r e 4 9 7 m s w h e n t h e TR w a s 3 0 s a n d 4 4 9 w h e n t h e TR w a s 10 s , as i n t h e i m a g i n g e x p e r i m e n t s . A l t h o u g h t h e T 2 v a l u e d o e s r i s e as t h e 5 - f l u o r o u r a c i l c o n c e n t r a t i o n d e c r e a s e s , t h e m e a s u r e d v a l u e f o r t h e m i x t u r e d o e s n o t r e a c h t h e 700 m s v a l u e d e t e r m i n e d i n t h e i m a g i n g e x p e r i m e n t s i n a s i m i l a r c o n c e n t r a t i o n r e g i o n . A l s o , t h e l o s s o f s i g n a l d u e t o t h e s h o r t e n e d TR a p p e a r s t o l o w e r t h e m e a s u r e d T 2 v a l u e r a t h e r t h a n r a i s e i t . T h u s , t h e a n o m a l o u s l y h i g h T 2 v a l u e s m u s t b e t h e r e s u l t o f t h e d i f f u s i o n o f 5 - f l u o r o u r a c i l d u r i n g t h e a c q u i s i t i o n o f t h e v a r i a b l e - T ^ d a t a s e t . T h e m o v e m e n t o f t h e 5 - f l u o r o u r a c i l d u r i n g t h e 86 m i n u t e s o f t h e e x p e r i m e n t c a u s e s a s l i g h t i n c r e a s e i n t h e s i g n a l i n t e n s i t y i n d i l u t e r e g i o n s o f t h e p o l y m e r . T h e i n c r e a s e i n i n t e n s i t y i s q u i t e s i g n i f i c a n t b e c a u s e t h e r e l a t i v e l y l a r g e T 2 v a l u e s i n t h e s e r e g i o n s r e s u l t i n o n l y a s l i g h t l o s s o f s i g n a l e v e n a t t h e m a x i m u m T E o f 6 4 m s . T h u s , t h e r e s u l t i n g a p p a r e n t T 2 v a l u e i s l a r g e r t h a n t h e t r u e T 2 v a l u e b e c a u s e t h e s i g n a l i n t e n s i t y a p p e a r s t o d e c r e a s e s less r a p i d l y w i t h i n c r e a s i n g TE. 124 (a) Relative Intensity 0.00 (b) 1 0 ° o 0.25 800 H 600 1 T 2 (ms) 400 H 200 1 0.50 0.75 1.00 Distance (cm) 1.25 1.50 0.25 0.50 0.75 1.00 Distance (cm) 1.25 1.50 F i g u r e 5 .4 : T h e v a r i a t i o n o f t h e s i g n a l i n t e n s i t y i n t h e 5 - f l u o r o u r a c i l i m a g e s as a f u n c t i o n o f TJS (a ) a n d t h e c o r r e s p o n d i n g T 2 v a l u e s ( b ) c a l c u l a t e d f r o m t h e d a t a i n (a ) a f t e r 19 h o u r s o f s w e l l i n g . T h e TE v a l u e s a r e 2 m s ( f i l l e d c i r c l e s ) , 3 m s ( o p e n c i r c l e s ) , 4 m s ( f i l l e d t r i a n g l e s ) , 8 m s ( o p e n s q u a r e s ) , 16 m s ( o p e n t r i a n g l e s ) , 2 4 m s ( c r o s s e s ) , 3 2 m s ( o p e n d i a m o n d s ) a n d 6 4 m s ( f i l l e d d i a m o n d s ) . 125 T h e H P M C d i s t r i b u t i o n s c a l c u l a t e d f r o m t h e T 2 d i s t r i b u t i o n s d e t e r m i n e d f r o m t h e w a t e r a n d t r i f l u p r o m a z i n e - H C l i m a g i n g e x p e r i m e n t s a r e s h o w n i n F i g u r e 5 . 5 . T h e H P M C d i s t r i b u t i o n s f r o m t h e 5 - f l u o r o u r a c i l d a t a w e r e s i m i l a r t o t h o s e o b t a i n e d f r o m t h e w a t e r a n d t r i f l u p r o m a z i n e - H C l d a t a b u t s h o w e d m a r k e d d e v i a t i o n s i n r e g i o n s o f l o w e r H P M C c o n c e n t r a t i o n d u e t o t h e e r r o n e o u s l y l a r g e T 2 v a l u e s o b t a i n e d i n t h e s e r e g i o n s as d i s c u s s e d p r e v i o u s l y . T h e t w o s e t s o f d i s t r i b u t i o n s i n F i g u r e 5 .5 a r e f a i r l y s i m i l a r a n d i n d i c a t e t h e s a m e d e g r e e o f p o l y m e r s w e l l i n g a t a l l e i g h t m e a s u r e m e n t i n t e r v a l s . T h e t o t a l w e i g h t s c a l c u l a t e d f r o m t h e t r i f l u p r o m a z i n e - H C l d i s t r i b u t i o n s a r e g i v e n i n T a b l e 5 .4 a n d a g r e e q u i t e w e l l w i t h t h e k n o w n w e i g h t o f H P M C i n t h e t a b l e t . T a b l e 5 .4 : T h e t o t a l w e i g h t o f H P M C c a l c u l a t e d f r o m t h e H P M C d i s t r i b u t i o n s o b t a i n e d f r o m t h e 1 9 F i m a g i n g e x p e r i m e n t s o f H P M C t a b l e t s c o n t a i n i n g t r i f l u p r o m a z i n e - H C l . T i m e ( h o u r s ) H P M C ( ± 2 0 m g ) % d e v a 19 162 3 .8 2 5 166 6 .4 31 164 5.1 3 7 173 10 .9 Percent deviation, 100% X ( H P M C - 1 5 6 ) / 1 5 6 T h e d i f f e r e n c e s b e t w e e n t h e p r o c e d u r e s f o r t h e : H a n d 1 9 F i m a g i n g e x p e r i m e n t s s u g g e s t t h a t t h e H P M C c o n c e n t r a t i o n s i n t h e d i s t r i b u t i o n s o b t a i n e d f r o m t h e w a t e r i m a g i n g e x p e r i m e n t s a r e m o r e r e l i a b l e t h a n t h o s e f r o m t h e d r u g e x p e r i m e n t s . T h e l o w e r s i g n a l i n t e n s i t y i n t h e d r u g i m a g i n g e x p e r i m e n t s d o u b l e s t h e e x p e r i m e n t a l t i m e n e c e s s a r y t o o b t a i n t h e d a t a s e t f o r c a l c u l a t i n g t h e H P M C w e i g h t p e r c e n t s f r o m 3 0 m i n u t e s f o r t h e w a t e r e x p e r i m e n t s t o 75 a n d 86 m i n u t e s , f o r t r i f l u p r o m a z i n e - H C l a n d 5 - f l u o r o u r a c i l r e s p e c t i v e l y , a n d r e s u l t s i n m o r e v a r i a b i l i t y i n t h e c a l c u l a t e d H P M C v a l u e s . T h e r a n g e o f T # v a l u e s u s e d i n t h e d r u g a n d w a t e r e x p e r i m e n t s i s a n o t h e r c r i t e r i o n f a v o u r i n g t h e H P M C d i s t r i b u t i o n s f r o m t h e w a t e r e x p e r i m e n t s . T h e n u m b e r o f T # v a l u e s f o r t h e d r u g e x p e r i m e n t s w a s 8 c o m p a r e d t o t h e 10 u s e d i n t h e w a t e r e x p e r i m e n t s a n d t h e m a x i m u m v a l u e o f T # w a s o n l y 6 4 m s f o r t h e d r u g e x p e r i m e n t s c o m p a r e d t o 128 m s f o r t h e w a t e r e x p e r i m e n t s . T h e c h a n g e s w e r e m a d e t o r e d u c e t h e t i m e t o a c q u i r e t h e d a t a n e c e s s a r y t o c a l c u l a t e t h e H P M C 126 HPMC (w/w %) ^ (a) 1 hour 100 -i 80 H —r -0.6 O O - r - —I 0.6 (b) 4 hours 100 -\ (d) 13 hours 100 80 60 40 20 —1 0 0.8 0.0 — i -0.6 0.8 —I 0.8 Distance (cm) F i g u r e 5 . 5 : H P M C d i s t r i b u t i o n s c a l c u l a t e d f r o m t h e w a t e r i m a g e s ( f i l l e d c i r c l e s ) , a n d t r i f l u p r o m a z i n e - H C l i m a g e s ( o p e n c i r c l e s ) . T h e s w e l l i n g t i m e s i n t h e f i g u r e a r e (a ) 1 h o u r , ( b ) 4 h o u r s , (c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 2 5 h o u r s , (g) 31 h o u r s , a n d ( h ) 3 7 h o u r s . T h e a x e s a r e t h e s a m e i n a l l 8 p l o t s a n d a r e d e f i n e d b y t h e a r r o w s . T h e v e r t i c a l d a s h e d l i n e i n d i c a t e s t h e o r i g i n a l p o s i t i o n o f t h e w a t e r t a b l e t i n t e r f a c e . ( T h e f i g u r e i s c o n t i n u e d o n t h e n e x t p a g e . ) 127 HPMC(w/w%) ^(e) 19 hours 100 0.0 (g) 31 hours 100 80 60 (f) 25 hours 100 -i 0.8 0.0 0.2 (h) 37 hours 100 80 H 60 H 1 0.8 Distance (cm) F i g u r e 5.5 c o n t i n u e d : p l o t s (e) t h r o u g h ( h ) . 128 w e i g h t p e r c e n t s . T h e r e d u c t i o n i n t h e T # r a n g e , h o w e v e r , m a y h a v e r e d u c e d t h e a c c u r a c y o f t h e r e s u l t i n g H P M C v a l u e s , e s p e c i a l l y i n r e g i o n s w i t h l o w e r H P M C c o n c e n t r a t i o n . T h u s , e v e n t h o u g h t h e d i s t r i b u t i o n s f r o m t h e i m a g i n g e x p e r i m e n t s p e r f o r m e d o n w a t e r c o n t a i n a b o u t 5 % m o r e p o l y m e r t h a n t h o s e o b t a i n e d f r o m t h e i m a g i n g e x p e r i m e n t s p e r f o r m e d o n t h e d r u g , t h e f o r m e r a r e d e e m e d t o b e t h e m o s t a c c u r a t e d i s t r i b u t i o n s w h i c h d e s c r i b e t h e s w e l l i n g - c o n t r o l l e d d r u g r e l e a s e s y s t e m . I n g e n e r a l , p o l y m e r d i s t r i b u t i o n s o b t a i n e d f r o m w a t e r - b a s e d d a t a w i l l a l w a y s b e t h e m o s t a c c u r a t e b e c a u s e o f t h e g r e a t e r s i g n a l - t o - n o i s e i n t h e e x p e r i m e n t s a n d t h e s h o r t e r e x p e r i m e n t a l t i m e s r e q u i r e d t o o b t a i n t h e T 2 d a t a s e t s . 5.3.3 Discussion of Drug Release Mechanism T h e m e c h a n i s m o f d r u g r e l e a s e f r o m h y d r o p h i l i c m a t r i x t a b l e t s c a n b e d e d u c e d f r o m a c o m p a r i s o n o f t h e d r u g a n d p o l y m e r d i s t r i b u t i o n s . T h e H P M C d i s t r i b u t i o n s o b t a i n e d f r o m t h e w a t e r i m a g i n g d a t a o f C h a p t e r 4 w e r e c o n s i d e r e d t o b e t h e m o s t a c c u r a t e o f t h e t h r e e s e t s o f d a t a a n d w e r e u s e d f o r t h e c o m p a r i s o n . W h e n t h e d i s t r i b u t i o n s o f t r i f l u p r o m a z i n e - H C l a n d H P M C a r e o v e r l a p p e d , as i n F i g u r e 5 . 6 , o n e c a n c l e a r l y see t h a t t h e m a j o r i t y o f t h e d r u g i s s t i l l c o n t a i n e d w i t h i n t h e p o l y m e r t a b l e t . I n e a c h o f t h e p l o t s o f t h i s figure, t h e H P M C c o n c e n t r a t i o n s a r e g i v e n b y t h e s c a l e o n t h e l e f t a n d t h e 1 9 F m o l a r i t i e s o f t h e d r u g a r e g i v e n b y t h e s c a l e o n t h e r i g h t . T h e r e l a t i v e a m o u n t s o f t h e d r u g a n d p o l y m e r i n t h e d r y t a b l e t w a s a b o u t 4 . 5 6 x l O - 4 m o l e s 1 9 F p e r g r a m . T h e p a r a l l e l s l o p e s f o r t h e t r i f l u p r o m a z i n e - H C l a n d H P M C d i s t r i b u -t i o n s s u g g e s t e d t h a t t h e r a t i o o f t r i f l u p r o m a z i n e - H C l t o H P M C c o n c e n t r a t i o n r e m a i n e d f a i r l y c o n s t a n t a n d i n f a c t , t h e c a l c u l a t e d r a t i o s i n t h i s r e g i o n w e r e w i t h i n 2 0 % o f t h e o r i g -i n a l r a t i o . T h e s i m i l a r i t y b e t w e e n t h e d r u g a n d p o l y m e r d i s t r i b u t i o n s s u g g e s t e d t h a t t h e m a j o r i t y o f t h e d r u g m o v e m e n t i s t h e r e s u l t o f t h e s w e l l i n g o f t h e p o l y m e r . D r u g r e l e a s e o n l y o c c u r r e d w h e n t h e p o l y m e r c o n c e n t r a t i o n d r o p p e d b e l o w a b o u t 1 0 % H P M C . A t t h i s p o i n t t h e H P M C i s n o l o n g e r i n t h e g e l f o r m a n d i s s l o w l y d i s s o l v i n g i n s o l u t i o n , r e s u l t i n g i n t h e e r o s i o n o f t h e t a b l e t . T h u s , t h e d o m i n a n t m e c h a n i s m f o r t r i f l u p r o m a z i n e - H C l r e l e a s e a p p e a r s t o b e t a b l e t e r o s i o n . T h e d i f f u s i o n c o e f f i c i e n t s m e a s u r e d f o r t r i f l u p r o m a z i n e - H C l i n t h e H P M C c o n c e n t r a t i o n s o f t h i s e r o d i n g r e g i o n r a n g e f r o m 2 x l 0 - 6 t o 4 x l 0 - 6 c m 2 s _ 1 . 129 H P M C ( w / w % ) A ( a ) 1 h o u r 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1 9 F ( m o l e s L " 1 ) ( b ) 4 h o u r s A 0.00 0.25 0.50 0.75 1.00 1.25 1.50 D i s t a n c e ( c m ) F i g u r e 5 . 6 : M o l a r 1 9 F d i s t r i b u t i o n s o f t r i f l u p r o m a z i n e - H C l ( o p e n c i r c l e s ) o v e r l a p p e d w i t h H P M C d i s t r i b u t i o n s ( f i l l e d c i r c l e s ) c a l c u l a t e d f r o m t h e w a t e r i m a g e s . T h e s w e l l i n g t i m e s i n t h e figure a r e (a ) 1 h o u r , ( b ) 4 h o u r s , (c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 2 5 h o u r s , (g ) 31 h o u r s , a n d (h ) 37 h o u r s . T h e a x e s a r e t h e s a m e i n a l l 8 p l o t s a n d a r e d e f i n e d b y t h e l a r g e a r r o w s . T h e p o s i t i o n o f t h e 5 % H P M C c o n c e n t r a t i o n r e g i o n i s i n d i c a t e d b y t h e filled a r r o w . ( T h e f i g u r e is c o n t i n u e d o n t h e n e x t p a g e . ) 130 HPMC (w/w %) • (e) 19 hours 50 -i 40 H 30 H (f) 25 hours 0.10 50 hO.08 40 H 20 H 10 H T — 1 — r 0.00 0.25 0.50 0.75 1.00 1.25 1.50 (g) 31 hours 50 -i 1 9 F (moles L 1 ) A h 0.06 30 H 0.04 20 H h 0.02 10 H rO.10 0.08 0.06 h0.04 hO02 0.00 0 - |— i— i— i — r 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 (h) 37 hours rO.io 50 n h 0.08 40 A h 0.06 30 0.04 20 H h 0 .02 io H rO.io hO.08 h0.06 r-0.04 0.02 - i — • — i —>— T —•— i — > — i — • — r ooo o -\—i—i—•—i—• T '— i — • — i — > — h ooo 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 Distance (cm) F i g u r e 5 .6 c o n t i n u e d : p l o t s (e) t h r o u g h ( h ) . 131 H P M C ( w / w % ) A ( a ) 1 h o u r 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1 9 F ( m o l e s L 1 ) D i s t a n c e ( c m ) F i g u r e 5 .7 : M o l a r 1 9 F d i s t r i b u t i o n s o f 5 - f l u o r o u r a c i l ( o p e n c i r c l e s ) o v e r l a p p e d w i t h H P M C d i s t r i b u t i o n s ( f i l l e d c i r c l e s ) c a l c u l a t e d f r o m t h e w a t e r i m a g e s . T h e s w e l l i n g t i m e s i n t h e f i g u r e a r e (a ) 1 h o u r , ( b ) 4 h o u r s , (c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 2 5 h o u r s , (g) 31 h o u r s , a n d ( h ) 3 7 h o u r s . T h e a x e s a r e t h e s a m e i n a l l 8 p l o t s a n d a r e d e f i n e d b y t h e l a r g e a r r o w s . T h e p o s i t i o n o f t h e 5 % H P M C c o n c e n t r a t i o n r e g i o n i s i n d i c a t e d b y t h e f i l l e d a r r o w . ( T h e f i g u r e i s c o n t i n u e d o n t h e n e x t p a g e . ) 132 HPMC(w/w %) A(e) 19 hours 50 -i 1 9 F (moles L 1 ) (1) 25 hours 40 30 20 10 rO.lO 50 h 0.08 40 H h 0.06 30 h 0.04 20 0.02 10 ->—i— 1 —r 0.00 0 rO.10 hO.08 hO.06 h 0.04 h0.02 - > — i — 1 — r 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 (g) 31 hours 50 (h) 37 hours rO.10 50 n 0.08 40 -1 20 H h 0.06 30 H h 0.04 20 H h 0.02 10 H 0.00 0 0.10 hO.08 h0.06 0.04 hO.02 i 1 1 1—i- 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 Distance (cm) F i g u r e 5 .7 c o n t i n u e d : p l o t s (e) t h r o u g h ( h ) . 133 T a b l e 5 . 5 : D i s t a n c e s o f v a r i o u s c o n c e n t r a t i o n r e g i o n s i n t h e H P M C c o n c e n t r a t i o n d i s t r i b u -t i o n s c a l c u l a t e d f r o m t h e i m a g i n g e x p e r i m e n t s o f C h a p t e r 4 . T i m e ( h o u r s ) D i s t a n c e ( ± 0 . 0 1 c m ) s a 0 % H P M C 5% H P M C 1 0 % H P M C 0 0 . 1 3 a — — 1 0 . 2 5 0 .20 0 . 1 9 4 0 .36 0 .31 0 . 2 8 7 0 .40 0 .37 0 . 3 3 13 0 . 5 2 0 .46 0 . 4 0 19 0 .60 0 .52 0 . 4 6 2 5 0 .66 0 .58 0 .51 31 0 . 7 3 0 .63 0 . 5 4 37 0 .79 0 .67 0 . 5 7 a O n l y the 0% region should coincide with the tablet thickness at zero t ime. S i m i l a r c o m p a r i s o n s f o r 5 - f l u o r o u r a c i l i n F i g u r e 5 .7 s u g g e s t t h a t t h e d r u g i s d i f f u s i n g f r e e l y f r o m t h e t a b l e t f r o m t h e s t a r t o f t h e s w e l l i n g . T h e m a x i m u m o f t h e e x p o n e n t i a l l y -s h a p e d c o n c e n t r a t i o n g r a d i e n t a p p e a r s t o c o i n c i d e w i t h a p o l y m e r c o n c e n t r a t i o n o f « 3 0 % a t a l l s w e l l i n g t i m e s . T h e m e a s u r e d d i f f u s i o n c o e f f i c i e n t o f 5 - f l u o r o u r a c i l i n 3 0 % H P M C w a s 3 . 4 x l O - 6 c m 2 s _ 1 f o r t h e 1 % d r u g m i x t u r e a n d 2 . 7 x l 0 ~ 6 c m 2 s _ 1 f o r t h e 3 % d r u g m i x t u r e . T h i s i s t h e s a m e d i f f u s i o n c o e f f i c i e n t r a n g e o b s e r v e d f o r t r i f l u p r o m a z i n e - H C l i n 0 % t o 1 0 % H P M C , s u g g e s t i n g t h a t a d i f f u s i o n c o e f f i c i e n t o f a b o u t 3 x l 0 - 6 c m 2 s _ 1 i s r e q u i r e d t o e s c a p e t h e s w e l l i n g t a b l e t a n d t h a t t h e r a t e o f t h e s w e l l i n g m u s t b e c o m p a r a b l e t o , o r l e s s t h a n , t h a t v a l u e . A n e s t i m a t e o f t h e r a t e o f t a b l e t e x p a n s i o n c a n b e o b t a i n e d b y t r a c k i n g t h e p o s i -t i o n o f t h e t a b l e t t h i c k n e s s as a f u n c t i o n o f s w e l l i n g t i m e . T h e e d g e o f t h e t a b l e t c a n b e d e f i n e d b y a p a r t i c u l a r H P M C c o n c e n t r a t i o n s f r o m t h e H P M C d i s t r i b u t i o n s . T h r e e d i f -f e r e n t c o n c e n t r a t i o n r e g i o n s w e r e c o n s i d e r e d as r e p r e s e n t i n g t h e ' e d g e o f t h e t a b l e t ' : « 0 % H P M C w o u l d b e t h e t a b l e t e d g e m e a s u r e d b y b u l k m e t h o d s , 1 0 % H P M C w a s d i s c u s s e d i n S e c t i o n 2 . 3 . 4 as t h e t r a n s i t i o n c o n c e n t r a t i o n f o r g e l f o r m a t i o n , a n d 5 % H P M C w a s c h o s e n as a n i n t e r m e d i a t e c o n c e n t r a t i o n b e t w e e n t h e t w o e x t r e m e s . T h e d i s t a n c e s o f t h e « 0 % , 5 % a n d 1 0 % c o n c e n t r a t i o n r e g i o n s as a f u n c t i o n o f t i m e a r e p r e s e n t e d i n T a b l e 5 . 5 . T h e s e d i s t a n c e s e x h i b i t e d l i n e a r r e l a t i o n s h i p s w i t h t h e s q u a r e r o o t o f t i m e , as s h o w n i n F i g u r e 5 . 8 , 134 r e s u l t i n g i n d i f f e r e n t s l o p e s f o r e a c h c o n c e n t r a t i o n r e g i o n . I n o r d e r t o c o m p a r e t h e s w e l l i n g o f t h e t a b l e t w i t h t h e d i f f u s i o n c o e f f i c i e n t s o f t h e d r u g s , a p p a r e n t r a t e c o n s t a n t s f o r t a b l e t e x p a n s i o n w e r e d e t e r m i n e d b y s q u a r i n g t h e s l o p e s , r e s u l t i n g i n 3 . 1 6 x l 0 - 6 c m 2 s _ 1 f o r 0 % r e g i o n , 2 . 3 4 x l 0 ~ 6 c m 2 s _ 1 f o r t h e 5 % r e g i o n a n d 1 . 5 9 x l 0 - 6 c m 2 s _ 1 f o r t h e 1 0 % r e g i o n . A s w i l l b e s h o w n i n C h a p t e r 6 , t h e s e a p p a r e n t e x p a n s i o n r a t e s a r e n o t t h e s a m e as t h e a p p a r e n t d i f f u s i o n c o e f f i c i e n t d e t e r m i n e d f o r t h e p o l y m e r b u t a r e a s i m p l e m e a s u r e o f t h e m o v e m e n t o f t h e t a b l e t f r o n t . I t w a s s u g g e s t e d p r e v i o u s l y t h a t d r u g w o u l d n o t b e r e l e a s e d f r o m t h e H P M C t a b l e t u n t i l t h e d i f f u s i o n c o e f f i c i e n t o f t h e d r u g w a s a p p r o x i m a t e l y 3 x l 0 - 6 c m 2 s _ 1 . T h e a p p a r e n t e x p a n s i o n r a t e s o f t h e t a b l e t e d g e a r e w i t h i n t h e s a m e r a n g e as t h e d i f f u s i o n c o e f f i c i e n t r e q u i r e d f o r d r u g r e l e a s e s u g g e s t i n g ' t h a t t h e r e l a t i o n s h i p b e t w e e n t h e d i f f u s i o n c o e f f i c i e n t s o f t h e d r u g i n a p o l y m e r a n d t h e a p p a r e n t e x p a n s i o n r a t e o f t h e p o l y m e r , as d e t e r m i n e d b y p l o t s s u c h as F i g u r e 5 . 8 , c o u l d b e u s e d i n o t h e r s y s t e m s t o d e -t e r m i n e d r u g r e l e a s e b e h a v i o r . T h e a v e r a g e o f t h e t h r e e a p p a r e n t r a t e c o n s t a n t s f o r t a b l e t e x p a n s i o n i s ( 2 . 4 ± 0 . 8 ) x l 0 - 6 c m 2 s _ 1 . T a b l e 5 . 6 : D r u g i n s i d e a n d o u t s i d e t h e H P M C t a b l e t s as d e t e r m i n e d f r o m t h e 1 9 F i m a g i n g e x p e r i m e n t s . T h e e d g e o f t h e s w e l l i n g t a b l e t , d e f i n e d as 5 % H P M C , i s d e t e r m i n e d f r o m t h e H P M C d i s t r i b u t i o n s o b t a i n e d f r o m t h e * H i m a g i n g e x p e r i m e n t s o f C h a p t e r 4 . S w e l l i n g m o l e s 1 9 F ( ± 0 . 0 5 x l O " 5 ) T i m e T a b l e t e d g e T r i f l u p r o m a z i n e - H C l 5 - f l u o r o u r a c i l ( h o u r s ) ( c m ) I n s i d e O u t s i d e I n s i d e O u t s i d e 1 0 .20 1.57° 0 . 6 3 a 0 . 7 5 a 1.30° 4 0 .31 2 . 9 2 a 0.53° 0 . 4 6 a 1.21° 7 0 .37 3 .46 0 . 7 2 2 . 1 3 1 .73 13 0 .46 4 . 3 4 0 .94 2 . 9 5 2 . 1 3 19 0 . 5 2 4 . 7 2 1.09 3 . 4 2 2 . 3 5 2 5 0 .58 5 .02 1.17 3 .68 2 . 4 4 31 0 . 6 3 5 .18 1.24 3 .81 2 . 4 9 3 7 0 .67 5 .14 1.39 3 . 8 7 2 . 4 8 ( 3 . 2 4 ) 6 a T h e d e v i a t i o n s a t e a r l y t i m e s are t ie resu l t o f t h e huj $her r e l a t i v e no ise l e v e l , e s p e c i a l l y a t l a r g e r d i s t a n c e s . A m o u n t re leased i f t h e 1 0 % m i s s i n g f r o m t h e m a x i m u m a m o u n t o f 1 9 F is a s s u m e d t o be o u t s i d e o f t h e i m a g i n g f ie ld o f v i e w T h e s i g n a l i n t h e 1 9 F i m a g e s o f t h e d r u g s c a n b e d i v i d e d i n t o t w o r e g i o n s , d r u g 135 ( a ) 0 % A b ) 5 0 / o ( c ) 1 0 % D i s t a n c e ( c m ) 0 . 4 H 0 . 2 1 0 . 0 H • 1 • 1 ' 1 • 1 0 2 4 6 8 T i m e 1 / 2 ( h o u r s 1 7 2 ) F i g u r e 5 . 8 : T h e d i s t a n c e o f v a r i o u s r e g i o n s i n t h e s w e l l i n g H P M C t a b l e t as a f u n c t i o n o f t h e s q u a r e r o o t o f t h e s w e l l i n g t i m e . T h e t h r e e se ts o f d a t a a r e (a ) « 0 % ( f i l l e d s q u a r e s ) a n d l e a s t s q u a r e s f i t l i n e t o t h e d a t a w i t h s l o p e 0 . 1 0 6 6 c m h 1 / 2 , i n t e r c e p t 0 . 1 3 4 c m a n d r 2 0 . 9 9 9 (b ) 5 % ( o p e n t r i a n g l e s ) a n d l e a s t s q u a r e s f i t l i n e t o t h e d a t a w i t h s l o p e 0 . 0 9 1 7 0 c m h 1 / 2 , i n t e r c e p t 0 .121 c m a n d r 2 0 . 9 9 9 a n d (c ) 1 0 % ( f i l l e d c i r c l e s ) a n d l e a s t s q u a r e s fit l i n e t o t h e d a t a w i t h s l o p e 0 . 0 7 5 7 0 c m h 1 / 2 , i n t e r c e p t 0 . 1 2 4 c m a n d r 2 0 . 9 9 5 . 136 i n s i d e t h e t a b l e t a n d d r u g o u t s i d e t h e t a b l e t . T h e l a t t e r r e p r e s e n t s t h e d r u g r e l e a s e d f r o m t h e d e v i c e a t e a c h s w e l l i n g t i m e . T h e i n t e r m e d i a t e 5 % H P M C r e g i o n w a s c h o s e n as t h e d i v i d i n g l i n e b e t w e e n t h e i n s i d e a n d o u t s i d e o f t h e t a b l e t . T h e c o n c e n t r a t i o n s o f d r u g i n t h e t w o r e g i o n s o f t h e s y s t e m a r e g i v e n i n T a b l e 5 .6 . T h e a m o u n t o f d r u g r e l e a s e d f r o m t h e t r i f l u p r o m a z i n e - H C l t a b l e t s i n c r e a s e d s l o w l y w i t h t i m e . T h e a m o u n t o f 5 - f l u o r o u r a c i l r e l e a s e d b e c a m e d i f f i c u l t t o d e t e r m i n e a t l o n g e r s w e l l i n g t i m e s b e c a u s e s o m e o f t h e d r u g h a d d i f f u s e d o u t o f t h e i m a g i n g f i e l d o f v i e w . A t 37 h o u r s , i t w a s a s s u m e d t h a t t h e m i s s i n g 1 0 % o f t h e t o t a l 1 9 F s i g n a l w a s t h e r e s u l t o f t h i s d i f f u s i o n a n d s h o u l d c o u n t as d r u g r e l e a s e d f r o m t h e t a b l e t . F o r b o t h o f t h e d r u g s , t h e f r a c t i o n o f d r u g r e l e a s e d w a s a l i n e a r f u n c t i o n o f t h e s q u a r e - r o o t o f t i m e i n d i c a t i n g t h a t d r u g r e l e a s e f r o m t h e s w e l l i n g H P M C t a b l e t w a s F i c k i a n . T h e r a t i o o f t h e s q u a r e o f t h e s l o p e s i n d i c a t e s t h a t t h e r a t e o f 5 - f l u o r o u r a c i l r e l e a s e f r o m t h e s e H P M C t a b l e t s w a s a b o u t f i v e t i m e s f a s t e r t h a n t h e r a t e o f t r i f l u p r o m a z i n e - H C l r e l e a s e . 5.4 Summary N M R i m a g i n g o f t h e 1 9 F i n t h e m o d e l d r u g s w a s u s e d t o m o n i t o r t h e d r u g d i s t r i b u t i o n s w i t h i n t h e s w e l l i n g t a b l e t s . T h e H P M C d i s t r i b u t i o n s c a l c u l a t e d f r o m v a r i a b l e - T ^ e x p e r i -m e n t s o f b o t h d r u g s a g r e e d r e a s o n a b l y w e l l w i t h t h e H P M C d i s t r i b u t i o n s c a l c u l a t e d f r o m t h e w a t e r e x p e r i m e n t s . A c o m p a r i s o n o f t h e d i s t r i b u t i o n s o f d r u g a n d p o l y m e r s h o w e d t h a t t h e m a j o r i t y o f t r i f l u p r o m a z i n e - H C l r e m a i n e d w i t h i n t h e s w o l l e n t a b l e t e v e n a t l a t e r s w e l l i n g t i m e s . I n c o n t r a s t , t h e 5 - f l u o r o u r a c i l d i f f u s e d w i t h i n t h e t a b l e t s y s t e m a t e a r l y t i m e s a n d m o r e o f t h i s d r u g w a s r e l e a s e d . T h e c o n d i t i o n f o r d r u g r e l e a s e f r o m t h e t a b l e t r e q u i r e s t h a t t h e d i f f u s i o n c o e f f i c i e n t o f t h e d r u g b e g r e a t e r t h a n t h e e x p a n s i o n r a t e o f t h e t a b l e t , e s t i m a t e d t o b e ( 2 . 4 ± 0 . 8 ) x l 0 - 6 c m 2 s - 1 . F o r t r i f l u p r o m a z i n e - H C l , t h i s c o n d i t i o n w a s o n l y m e t a t t h e e d g e o f t h e s w e l l i n g t a b l e t w h e r e l o w H P M C c o n c e n t r a t i o n s r e s u l t e d i n t a b l e t e r o s i o n . T h e d i f f u s i o n c o e f f i c i e n t o f 5 - f l u o r o u r a c i l i n 3 0 % H P M C w a s l a r g e e n o u g h t o s a t i s f y t h e c o n d i t i o n f o r d r u g r e l e a s e a n d t h i s d r u g e s c a p e d t h e t a b l e t t h r o u g h d i f f u s i o n a t t h i s H P M C c o n c e n t r a t i o n . T h e f r a c t i o n o f d r u g r e l e a s e d f o r b o t h d r u g s w a s l i n e a r w i t h 137 (a) 0.5 0.4 i 0.3 -Fraction Released o.o - i — • — i — 1 — i — • — i — • — i — « — i — • — i — • — i 0 1 2 3 4 5 6 7 Time 1 / 2 (hours172) 0.0 i—> 1 1 1 1 1 > 1 • 1 1 1 ' 1 0 1 2 3 4 5 6 7 Time 1 / 2 (hours172) Figure 5.9: Fraction of drug released as a function of the square-root of the swelling time. The two plots are (a) fraction triflupromazine-HCl released and least squares fit line to the data wi th slope 0.02573 / i 1 / 2 , intercept 0.03644 and r 2 0.983 and (b) fraction 5-fluorouracil released and least squares fit line to the data with slope 0.06152 h1/2, intercept 0.07555 and r 2 0.990. 138 the square-root of time indicating that the drug release was Fickian. 139 C h a p t e r 6 E v a l u a t i o n o f T h e o r e t i c a l M o d e l s o f T r a n s p o r t P r o c e s s e s i n S w e l l i n g H P M C T a b l e t s 6.1 Introduction P r e v i o u s t h e o r e t i c a l t r e a t m e n t s o f s w e l l i n g - c o n t r o l l e d d r u g d e l i v e r y s y s t e m s h a v e b e e n b a s e d o n c h a n g e s i n b u l k p r o p e r t i e s o f t h e s y s t e m s u c h as c h a n g e s i n t h i c k n e s s [19, 2 0 ] , w e i g h t o f a b s o r b e d w a t e r [81] o r f r a c t i o n o f r e m a i n i n g d r u g i n t h e m a t r i x [82]. S o m e t h e -o r e t i c a l w o r k h a s b e e n p r e s e n t e d t o m o d e l t h e c o n c e n t r a t i o n d i s t r i b u t i o n s o f w a t e r a n d d r u g i n t h e g e l l a y e r o f a s w e l l i n g h y d r o p h i l i c m a t r i x t a b l e t u s i n g a p s e u d o - s t e a d y s t a t e o n e - d i m e n s i o n a l s i n g l e - f a c e d i f f u s i o n m e t h o d [27]. T h e l i m i t e d w o r k o n m o d e l l i n g t h e c o n -c e n t r a t i o n d i s t r i b u t i o n s o f w a t e r , d r u g a n d p o l y m e r i n a l l r e g i o n s o f a s w e l l i n g c o n t r o l l e d d r u g d e l i v e r y s y s t e m h a s r e s u l t e d f r o m t h e l a c k o f a c o m p l e t e se t o f t h e s e c o n c e n t r a t i o n d a t a p r i o r t o t h e N M R i m a g i n g s t u d y p r e s e n t e d i n t h i s t h e s i s . A l t h o u g h t h e p r e v i o u s t h e o r e t i c a l t r e a t m e n t s a r e n o t d i r e c t l y a p p l i c a b l e t o t h e c o n c e n t r a t i o n d a t a o b t a i n e d f r o m t h e N M R i m a g i n g , t h e g e n e r a l a p p r o a c h e s o f t h e a u t h o r s a r e u s e f u l i n d e v e l o p i n g a s i m p l e m o d e l t o f i t t h e c o n c e n t r a t i o n c h a n g e s t h a t a r e s e e n as t h e H P M C t a b l e t s w e l l s . T h e g e o m e t r y c h o s e n f o r t h e t a b l e t s w e l l i n g e x p e r i m e n t s o f C h a p t e r s 3 - 5 r e s t r i c t e d t h e m o v e m e n t o f t h e c o m p o n e n t s o f t h e t a b l e t t o o n e d i m e n s i o n , t h a t p e r p e n d i c u l a r t o t h e f a c e o f t h e t a b l e t . T h i s s l a b g e o m e t r y i s t h e s i m p l e s t c a s e f o r m o d e l l i n g t h e t r a n s p o r t o f w a t e r , p o l y m e r a n d d r u g . I n t h e i n i t i a l s t a g e o f t h e c a l c u l a t i o n s , t h e c o m p o n e n t s o f 140 t h e h y d r o p h i l i c m a t r i x t a b l e t w e r e a s s u m e d t o d i f f u s e v i a a F i c k i a n d i f f u s i o n m e c h a n i s m r e s u l t i n g i n e f f e c t i v e d i f f u s i o n p a r a m e t e r s . F u r t h e r i n v e s t i g a t i o n s e x a m i n e d a s e g m e n t e d t a b l e t m o d e l t o d e s c r i b e t h e p o l y m e r d i s t r i b u t i o n . I n t h i s m o d e l , t h e o v e r a l l t a b l e t s w e l l i n g i s r e g a r d e d as t h e s u m o f t h e s w e l l i n g o f i n d i v i d u a l s e g m e n t s o f t h e o r i g i n a l d r y t a b l e t . 6.2 Theory 6 . 2 . 1 F i c k i a n D i f f u s i o n A b r i e f d e s c r i p t i o n o f F i c k i a n d i f f u s i o n t h e o r y f o r o n e - d i m e n s i o n a l d i f f u s i o n i s p r e s e n t e d h e r e . M o r e e x t e n s i v e d e s c r i p t i o n s o f t h e t h e o r y a n d t r e a t m e n t s o f o t h e r g e o m e t r i e s a r e a v a i l a b l e i n t h e l i t e r a t u r e [83]. F i c k ' s 1st a n d 2 n d l a w s f o r d i f f u s i o n b a s e d o n r a n d o m m o l e c u l a r m o t i o n s a r e g i v e n i n E q u a t i o n s 6.1 a n d 6 . 2 , r e s p e c t i v e l y , w h e r e J is t h e f l u x , C i s t h e c o n c e n t r a t i o n o f t h e d i f f u s i n g s p e c i e s , x i s t h e p o s i t i o n , t i s t h e t i m e a n d D i s t h e c o n s t a n t d i f f u s i o n c o e f f i c i e n t . T h e s o l u t i o n s t o F i c k ' s 2 n d l a w d e p e n d o n t h e i n i t i a l c o n d i t i o n s f o r t h e d i f f u s i n g s u b s t a n c e . E x a m p l e s o f d i f f e r e n t d i f f u s i n g s y s t e m s a r e s h o w n i n F i g u r e 6 . 1 . J - D * (6.1) 9C „ d2C "dt = 9a? ( 6 - 2 ) E q u a t i o n 6 .3 i s t h e r e s u l t i n g s o l u t i o n t o F i c k ' s 2 n d l a w w h e n t h e d i f f u s i n g s u b s t a n c e o r i g i n a t e s f r o m a p l a n e s h e e t a t x = 0 as i n F i g u r e 6 . 1 ( a ) . W h e n t h e i n i t i a l r e g i o n i s e x t e n d e d t o i n f i n i t e d i m e n s i o n a n d t h e s p e c i e s d i f f u s e s i n t o a n a d j a c e n t r e g i o n a l s o o f i n f i n i t e d i m e n -s i o n , as i n F i g u r e 6 . 1 ( b ) , t h e n t h e c o m b i n a t i o n o f G a u s s i a n d i f f u s i o n f r o m a l l t h e p o s i t i o n s i n t h e e x t e n d e d r e g i o n r e s u l t s i n E q u a t i o n 6 .4 w h e r e t h e e r r o r - f u n c t i o n c o m p l e m e n t ( e r f c ) a n d t h e e r r o r f u n c t i o n ( e r f ) a r e d e f i n e d b y E q u a t i o n s 6 .5 a n d 6 .6 , r e s p e c t i v e l y . C = ,C° e -Wi (6.3) 141 C^ = Y erfcvm (6-4) erfc z = 1 — erf z (6-5) erf z = -= [Ze~4Dt dy (6.6) y 7T • ' U W h e n t h e s p e c i e s d i f f u s e f r o m o r i n t o a r e g i o n o f l i m i t e d s i z e , - h < x < h , as s h o w n i n F i g u r e 6 . 1 ( c ) a n d ( d ) , t h e n E q u a t i o n s 6 .7 a n d 6 .8 , r e s p e c t i v e l y , c a n b e u s e d t o d e t e r m i n e t h e c o n c e n t r a t i o n d i s t r i b u t i o n o f t h e s p e c i e s . T h e s e e q u a t i o n s a r e s y m m e t r i c a l a b o u t z e r o a n d c a n a l s o b e u s e d t o d e s c r i b e t h e s y s t e m w h e r e 0 < x < h . C ( M ) = f { « * ^ § + «**5|} (6.8) T h e g i v e n s o l u t i o n s t o F i c k ' s 2 n d l a w u n d e r t h e i n i t i a l c o n d i t i o n s s h o w n i n F i g u r e 6.1 a l l r e q u i r e t h a t c e r t a i n r e g i o n s e x t e n d t o i n f i n i t e d i m e n s i o n s . I n p r a c t i c e , t h i s r e q u i r e m e n t is m e t b y a s e m i - i n f i n i t e s y s t e m w h e r e t h e d i f f u s i n g s p e c i e s d o e s n o t r e a c h t h e e x t e r n a l b o u n d a r i e s . 142 (a) (b) (c) 0 0 -h 0 h (d) •h 0 h F i g u r e 6 . 1 : I n i t i a l c o n d i t i o n s f o r o n e - d i m e n s i o n a l F i c k i a n d i f f u s i o n , (a ) f r o m a p l a n e s h e e t , ( b ) f r o m o n e i n f i n i t e r e g i o n t o a n o t h e r , (c ) f r o m a l i m i t e d r e g i o n , - h < x < h , i n t o a n i n f i n i t e r e g i o n a n d ( d ) f r o m a n i n f i n i t e r e g i o n i n t o a l i m i t e d r e g i o n , - h < x < h . T h e a r r o w s i n d i c a t e t h e d i r e c t i o n o f d i f f u s i o n i n e a c h c a s e . 143 6.2.2 Segmented Tablet Model T h e s e g m e n t e d t a b l e t m o d e l w a s p r e s e n t e d i n t h e l i t e r a t u r e as a m e t h o d o f f i t t i n g t h e c h a n g e i n t h i c k n e s s o f a s w e l l i n g t a b l e t [19]. T h e m o d e l c a n b e e x t e n d e d t o a l s o p r e d i c t t h e p o l y m e r c o n c e n t r a t i o n d i s t r i b u t i o n i n t h e s w o l l e n t a b l e t . I n t h e m o d e l , a d r y p o l y m e r t a b l e t , o f t h i c k n e s s h , i s d i v i d e d i n t o s e g m e n t s o f e q u a l s i z e , d x o , as s h o w n i n F i g u r e 6 . 2 ( a ) . T h e s w e l l i n g o f t h e t a b l e t a t e a c h t i m e i s t h e r e s u l t o f t h e c o m b i n a t i o n o f t w o p r o c e s s e s , t h e h y p o t h e t i c a l F i c k i a n w a t e r p e n e t r a t i o n i n t o t h e d r y s e g m e n t s a n d s u b s e q u e n t s e g m e n t s w e l l i n g r e s u l t i n g i n F i g u r e 6 . 2 ( b ) . E a c h s e g m e n t s w e l l s i n r e l a t i o n t o t h e a m o u n t o f w a t e r p r e s e n t g i v e n b y E q u a t i o n 6 .9 w h i c h e n s u r e s t h a t t h e w a t e r c o n c e n t r a t i o n a t t h e w a t e r - t a b l e t i n t e r f a c e f o r t h e d r y t a b l e t i s C o , t h e i n i t i a l w a t e r c o n c e n t r a t i o n i n t h e s u r r o u n d i n g m e d i u m . T h e a m o u n t o f s w e l l i n g o f e a c h s e g m e n t i s g i v e n b y E q u a t i o n 6 . 1 0 . ( T h e f a c t o r , g i v e n as d x o / ( l - a Cw) i n t h e l i t e r a t u r e , w a s m o d i f i e d f o r t h e c a l c u l a t i o n s p r e s e n t e d h e r e f o r r e a s o n s t h a t a r e d i s c u s s e d i n S e c t i o n 6 .4 .2 . ) T h e o v e r a l l s w e l l i n g o f t h e t a b l e t i s t h e c o m b i n a t i o n o f t h e i n d i v i d u a l s w e l l i n g s as i n d i c a t e d b y E q u a t i o n 6 . 1 1 . T h e i n t e g r a t i o n o f E q u a t i o n 6 .11 i s n o t s t r a i g h t f o r w a r d a n d r e q u i r e s s h o r t a n d l o n g t i m e a p p r o x i m a t i o n s [19]. T h e d i s c r e t e m e t h o d o f c a l c u l a t i o n , w h e r e a s u m r e p l a c e s t h e i n t e g r a l , i s m o r e p r a c t i c a l f o r t h e c a l c u l a t i o n s o f t h i s t h e s i s . 4 C 0 ~ (-1)" (2n + l)7ra; - ( 2 " + | ) a a ' a ^ f R Q , CW = C0 £ c o s ^ — e w 6.9 TT n = 0 (2n + 1) 2h cx dx' = dxo - —— (6.10) 1 ~ C-U, A x = x' - x 0 = (dx' - dx0) =• / dxQ ( 1) (6.11) JV 1 C u ; T h e g e n e r a t i o n o f a p o l y m e r c o n c e n t r a t i o n d i s t r i b u t i o n r e q u i r e s t h e c a l c u l a t i o n o f d i s t a n c e s a n d p o l y m e r c o n c e n t r a t i o n s f o r t h e s w o l l e n s e g m e n t s . T h e n e w d i s t a n c e f o r a p a r t i c u l a r s w o l l e n s e g m e n t i s g i v e n b y t h e s u m o f t h e t h i c k n e s s i n c r e a s e s i n e a c h o f t h e p r e v i o u s s e g m e n t s as i n E q u a t i o n 6 .12 . E a c h s e g m e n t a l s o c o n t a i n s a n a m o u n t o f 144 F i g u r e 6 . 2 : D e s c r i p t i o n o f t h e s e g m e n t e d t a b l e t m o d e l . T h e d r y t a b l e t i n (a ) i s d i v i d e d i n t o s e g m e n t s e a c h o f t h i c k n e s s d x o a n d t h e w a t e r c o n c e n t r a t i o n d i s t r i b u t i o n ( s o l i d l i n e ) i s c a l c u l a t e d b a s e d o n t h e o r i g i n a l t a b l e t t h i c k n e s s , t h e t i m e a n d a h y p o t h e t i c a l d i f f u s i o n c o e f f i c i e n t f o r t h e w a t e r i n g r e s s i n t o a n o n - s w e l l i n g t a b l e t . E a c h s e g m e n t o f t a b l e t i s t h e n s w e l l e d b a s e d o n t h e a m o u n t o f w a t e r p r e s e n t , r e s u l t i n g i n a n e w t h i c k n e s s a n d p o s i t i o n . A s e a c h s e g m e n t c o n t a i n s a f i x e d a m o u n t o f p o l y m e r , t h e c o n c e n t r a t i o n o f p o l y m e r d e c r e a s e s i n v e r s e l y w i t h t h e i n c r e a s e i n v o l u m e . 145 p o l y m e r g i v e n b y t h e i n i t i a l v o l u m e o f t h e s e g m e n t . A s a s e g m e n t s w e l l s , t h e a m o u n t o f p o l y m e r r e m a i n s c o n s t a n t b u t t h e c o n c e n t r a t i o n o f p o l y m e r d e c r e a s e s b e c a u s e t h e v o l u m e o f t h e s e g m e n t i n c r e a s e s . T h e n e w c o n c e n t r a t i o n f o r t h e s w o l l e n s e g m e n t i s g i v e n b y E q u a t i o n 6 . 1 3 . x\ = xi + ±dx,(-^—-l) (6.12) o i — cw C p ( * ; , t ) = C „ , p ^ = C „ , p < i ^ (6.13) 6.3 Notes on the Calculations T h e c o n c e n t r a t i o n d i s t r i b u t i o n s f r o m t h e v a c u u m - t r e a t e d s y s t e m s o f C h a p t e r s 4 a n d 5 w e r e u s e d f o r c o m p a r i s o n w i t h t h e t h e o r e t i c a l d i s t r i b u t i o n s . T h e t h e o r e t i c a l d i s t r i b u t i o n s b a s e d o n F i c k i a n d i f f u s i o n w e r e c a l c u l a t e d w i t h t h e p r o g r a m l i s t e d i n A p p e n d i x B . 2 . I n t h i s p r o g r a m , t h e t i m e , t , a n d t h i c k n e s s , h , w e r e f i x e d a n d t h e d i f f u s i o n c o e f f i c i e n t , D , w a s i n c r e m e n t e d t h r o u g h a s e r i e s o f v a l u e s . T h e x 2 v a l u e s , t h e s u m o f t h e s q u a r e s o f t h e d i f f e r e n c e s b e t w e e n t h e m e a s u r e d a n d t h e o r e t i c a l c o n c e n t r a t i o n s f o r e a c h p o s i t i o n i n t h e m e a s u r e d c o n c e n t r a t i o n d i s t r i b u t i o n , w e r e u s e d as g o o d n e s s - o f - f i t p a r a m e t e r s a n d m i n i -m i z e d t o p r o v i d e t h e b e s t - f i t r e s u l t s . T h e o v e r a l l b e s t - f i t w a s d e t e r m i n e d b y m i n i m i z i n g t h e s u m o f t h e x2 v a l u e s f o r t h e i n d i v i d u a l f i t s a t v a r i o u s s w e l l i n g t i m e s . T a b l e 6.1 p r o v i d e s s p e c i f i c d e t a i l s r e g a r d i n g t h e f i t t i n g c a l c u l a t i o n s f o r e a c h s p e c i e s i n t h e s w e l l i n g t a b l e t . T a b l e 6 . 1 : E q u a t i o n s a n d i n i t i a l p a r a m e t e r s u s e d i n t h e F i c k i a n f i t t i n g c a l c u l a t i o n s . S p e c i e s E q . C o h ( c m ) T i m e s ( h r s ) F o c u s a w a t e r 6 .8 1 0 . 1 0 5 1 , 4 , 7 , 1 3 , 1 9 , 2 5 , 3 1 , 3 7 0 . 1 — 0 . 6 c m H P M C 6 .7 97%b 0 . 1 3 3 1 , 4 , 7 , 1 3 , 1 9 , 2 5 , 3 1 , 3 7 a l l t r i f l u p r o m a z i n e - H C l 6 .7 0 .42 M 0 . 1 3 3 1 9 , 2 5 , 3 1 , 3 7 ' s t e e p ' s l o p e 5 - f l u o r o u r a c i l 6 .7 0 .42 M 0 . 1 3 3 1 9 , 2 5 , 3 1 , 3 7 a l l a The specific region of the measured distribution used in the x2 calculation. 6 Polymer concentration expressed in w/w% to be consistent with previously presented data. 146 T h e C o v a l u e f o r e a c h s p e c i e s w a s d e t e r m i n e d b y t h e i n i t i a l c o n c e n t r a t i o n i n t h e d r y t a b l e t a n d t h e r e q u i r e m e n t t h a t e a c h t h e o r e t i c a l d i s t r i b u t i o n c o n s e r v e t h e t o t a l a m o u n t o f t h e s p e c i e s . T h e w a t e r i n t e n s i t i e s h a v e b e e n p r e s e n t e d r e l a t i v e t o t h e b u l k w a t e r c o n c e n -t r a t i o n , h e n c e t h e C o v a l u e o f 1. F o r t h e p o l y m e r , t h e C o v a l u e o f 9 7 w / w % w a s c h o s e n t o e n s u r e t h a t e a c h t h e o r e t i c a l c o n c e n t r a t i o n c u r v e c o n t a i n e d t h e k n o w n w e i g h t o f 166 m g o f H P M C . T h e r a t i o o f 166 m g H P M C t o t h e v o l u m e o f t h e t a b l e t , 1 .287 c m 2 x 0 . 1 3 3 c m o r 171 c m 3 , i s t h e s a m e as t h e C o v a l u e s u g g e s t i n g t h a t t h e d e n s i t y o f t h e t a b l e t i s 1 g c m - 3 . E a c h o f t h e d r u g - c o n t a i n i n g t a b l e t s h a d 7 .11 x l 0 ~ 5 m o l e s o f 1 9 F i n t h e s a m e v o l u m e o f t a b l e t , r e s u l t i n g i n a n i n i t i a l 1 9 F c o n c e n t r a t i o n o f 0 . 4 2 M . T h e v a l u e s f o r h i n t h e e q u a t i o n s w a s t h e d r y t a b l e t t h i c k n e s s f o r a l l t h e s p e c i e s a p a r t f r o m w a t e r . I n t h e i n i t i a l c a l c u l a t i o n s f o r w a t e r w i t h h = 0 . 1 3 3 c m , i t b e c a m e a p p a r e n t t h a t t h e r e w a s m o r e w a t e r p r e s e n t i n t h e t a b l e t t h a n c o u l d b e a c c o u n t e d f o r b y t h e o r y . T h e w a t e r d i s t r i b u t i o n a f t e r 1 h o u r s u g g e s t e d t h a t t h e v a c u u m - t r e a t m e n t h a d p u l l e d w a t e r i n t o t h e o u t e r m o s t l a y e r s o f t h e t a b l e t . T h e w a t e r - t a b l e t i n t e r f a c e f o r t h e w a t e r c a l c u l a t i o n w a s m o v e d i n t o t h e p o l y m e r t o 0 . 1 0 5 c m , t h e p o s i t i o n w i t h 5 0 % H P M C c o n c e n t r a t i o n i n t h e m e a s u r e d 1 h o u r d i s t r i b u t i o n . T h i s e x t r a w a t e r p e n e t r a t i o n a t e a r l y t i m e s r e s u l t s i n a s m a l l i n c r e a s e i n t h e m o b i l i t y o f t h e p o l y m e r a n d d r u g i n t h i s r e g i o n o f t h e t a b l e t . T h e v a r i a b l e m o b i l i t i e s o f t h e p o l y m e r a n d d r u g s p e c i e s d u r i n g w a t e r p e n e t r a t i o n a n d p o l y m e r s w e l l i n g a r e a l r e a d y a s s u m e d t o b e a v e r a g e d i n t h e F i c k i a n m o d e l , t h u s , t h e a d d i t i o n a l m o b i l i t i e s a t e a r l y t i m e s a r e a c c o u n t e d f o r b y t h e a p p a r e n t F i c k i a n d i f f u s i o n p a r a m e t e r . V a r i o u s t i m e s w e r e u s e d i n t h e c a l c u l a t i o n o f t h e t h e o r e t i c a l c o n c e n t r a t i o n d i s t r i -b u t i o n s . O n l y t h e l a t e r t i m e s w e r e u s e d f o r t h e d r u g c a l c u l a t i o n s b e c a u s e t h e m e a s u r e d d i s t r i b u t i o n s a t e a r l y t i m e s d o n o t s h o w a l l o f t h e d r u g c o n t a i n e d i n t h e s y s t e m . T h e x2 c o m p a r i s o n s f o r t h e w a t e r a n d t r i f l u p r o m a z i n e - H C l d i s t r i b u t i o n s w e r e r e s t r i c t e d t o c e r t a i n r e g i o n s o f t h e m e a s u r e d d i s t r i b u t i o n s t o p r e v e n t o t h e r r e g i o n s f r o m d i s t o r t i n g t h e r e s u l t -i n g t h e o r e t i c a l d i s t r i b u t i o n . T h e d i s t a n c e s f r o m 0 - 0 . 1 c m i n t h e w a t e r d i s t r i b u t i o n s w e r e n o t u s e d i n t h e x2 c a l c u l a t i o n b e c a u s e , a t e a r l y t i m e s , t h e v i s i b l e s i g n a l m a y n o t h a v e r e p r e s e n t e d t h e a m o u n t o f w a t e r i n t h a t r e g i o n o f t h e t a b l e t . F o r t h e t r i f l u p r o m a z i n e -147 H C 1 d i s t r i b u t i o n s , t h e r e g i o n o f i n t e r e s t w a s t h e ' s t e e p ' s l o p e t h a t m i r r o r e d t h e p o l y m e r d i s t r i b u t i o n a n d t h e c a l c u l a t i o n s w e r e f o c u s s e d t o f i t t h i s r e g i o n b e s t . T h e s e g m e n t e d t a b l e t c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g t h e p r o g r a m l i s t e d i n A p -p e n d i x B . 3 . I n t h e c a l c u l a t i o n s , t h e t a b l e t w a s d i v i d e d i n t o 133 s e g m e n t s o f w i d t h 0 .001 c m . T h e C o v a l u e s w e r e 1 f o r t h e w a t e r a n d 9 7 % f o r t h e p o l y m e r . I n t h i s p r o g r a m , t h e o r e t -i c a l w a t e r d i s t r i b u t i o n s w e r e c a l c u l a t e d u s i n g E q u a t i o n 6 .9 w i t h f i x e d t i m e a n d t h i c k n e s s , 0 . 1 3 3 c m , a n d v a r i a b l e d i f f u s i o n c o e f f i c i e n t s . T h e w a t e r d i s t r i b u t i o n s w e r e t h e n u s e d t o c a l c u l a t e t h e n e w t h i c k n e s s , d i s t a n c e a n d p o l y m e r c o n c e n t r a t i o n f o r e a c h s e g m e n t b a s e d o n E q u a t i o n s 6 . 1 2 a n d 6 . 1 3 w h e r e a w a s v a r i a b l e . T h e m i n i m u m s u m o f t h e x2 v a l u e s f o r e a c h t i m e w a s u s e d t o d e t e r m i n e t h e o v e r a l l b e s t - f i t . 6.4 Results and Discussion 6.4.1 Fickian Diffusion Calculations A s w e l l i n g h y d r o p h i l i c m a t r i x t a b l e t i s a c o m p l e x s y s t e m w h e r e t h e t r a n s p o r t o f t h e w a t e r , p o l y m e r a n d d r u g c o m p o n e n t s a r e r e l a t e d . I n t h i s s y s t e m , t h e p o l y m e r a n d d r u g h a v e l i m i t e d m o b i l i t y i n t h e t a b l e t u n t i l t h e w a t e r c o n c e n t r a t i o n r e a c h e s s o m e c r i t i c a l l e v e l . A l s o , t h e w a t e r a n d d r u g m o b i l i t i e s d e p e n d s t r o n g l y o n t h e p o l y m e r c o n c e n t r a t i o n . T h e a t t e m p t t o m o d e l t h i s s y s t e m b a s e d o n a s i m p l e F i c k i a n d i f f u s i o n m o d e l d i s r e g a r d s t h e c o m p l e x i t y o f t h e s y s t e m i n t h e h o p e s t h a t a n a v e r a g e , e f f e c t i v e d i f f u s i o n p a r a m e t e r c a n a d e q u a t e l y d e s c r i b e t h e t i m e - d e p e n d e n t c o n c e n t r a t i o n d i s t r i b u t i o n s f o r e a c h s p e c i e s . T h e r e s u l t s o f f i t t i n g t h e w a t e r d i s t r i b u t i o n s t o E q u a t i o n 6 .8 a r e p r e s e n t e d i n T a -b l e 6 . 2 . T h e w a t e r p e n e t r a t i o n i n t o t h e t a b l e t a t t h e e a r l i e s t t i m e o f o n e h o u r s u g g e s t e d t h a t t h e v a c u u m - t r e a t m e n t d r e w w a t e r i n t o t h e o u t e r l a y e r s o f t h e t a b l e t . T h e c o m p a r i s o n b e t w e e n t h e o r e t i c a l d i s t r i b u t i o n s c a l c u l a t e d w i t h t h e o r i g i n a l t a b l e t t h i c k n e s s o f 0 . 1 3 3 c m a n d t h e r e g i o n t h i c k n e s s o f 0 . 1 0 5 c m s u g g e s t e d b y t h e 1 h o u r i m a g e i n d i c a t e d t h a t t h e l a t t e r w e r e b e t t e r f i t s t o t h e m e a s u r e d w a t e r d i s t r i b u t i o n s . T h e b e s t - f i t d i f f u s i o n c o e f f i c i e n t t o e a c h i n d i v i d u a l t i m e i n c r e a s e d a t l o n g e r s w e l l i n g t i m e s r e f l e c t i n g t h e i n c r e a s i n g m o b i l i t y o f t h e w a t e r i n t h e s w o l l e n p o l y m e r t a b l e t . 148 T a b l e 6 . 2 : T h e r e s u l t s o f o n e - d i m e n s i o n a l F i c k i a n f i t t i n g t o t h e w a t e r d i s t r i b u t i o n s i n t h e s w e l l i n g t a b l e t . T h e t h e o r e t i c a l w a t e r d i s t r i b u t i o n s w e r e c a l c u l a t e d u s i n g E q u a t i o n 6 .8 w i t h h = 0 . 1 0 5 c m . T i m e D (± 0 . 0 5 x l 0 - 7 ) a x2 ( h r s ) ( c m 2 s _ 1 ) 1 1.30 0 . 0 0 3 3 7 6 4 2 .00 0 . 0 6 5 6 8 7 2 . 8 5 0 . 0 7 0 8 4 13 3 .50 0 . 0 3 8 9 1 19 3 .90 0 . 0 2 3 4 6 2 5 4 . 0 0 0 . 0 0 8 9 9 8 31 4 . 0 0 0 . 0 0 4 9 1 7 37 4 . 0 5 0 . 0 0 3 1 0 8 o v e r a l l 3 . 35 0 . 2 8 7 5 6 a The given error in the apparent diffusion coefficient results in a change in the last quoted digit of the \ 2 value b Minimum sum of x2 values from the individual fits T h e t h e o r e t i c a l d i s t r i b u t i o n s c a l c u l a t e d w i t h t h e o v e r a l l b e s t - f i t d i f f u s i o n c o e f f i c i e n t o f 3 . 3 5 x l O - 7 c m 2 s _ 1 a r e p r e s e n t e d i n F i g u r e 6 .3 i n c o m p a r i s o n w i t h t h e m e a s u r e d w a t e r d i s t r i b u t i o n s f r o m C h a p t e r 4. T h e a v e r a g e d i f f u s i o n c o e f f i c i e n t p r o d u c e s g r e a t e r w a t e r p e n e t r a t i o n i n t o t h e t a b l e t a t e a r l y s w e l l i n g t i m e s a n d l e s s a t l a t e r t i m e s w h e n c o m p a r e d t o t h e m e a s u r e d d i s t r i b u t i o n s . T h e a v e r a g e t h e o r e t i c a l d i s t r i b u t i o n s , h o w e v e r , a r e f a i r l y g o o d a p p r o x i m a t i o n s o f t h e w a t e r d i s t r i b u t i o n a t a l l t i m e s . T h e d i f f u s i o n p a r a m e t e r s o b t a i n e d f r o m t h e o n e - d i m e n s i o n a l d i f f u s i o n m o d e l a r e o f a l o w e r o r d e r o f m a g n i t u d e t h a n t h e m e a s u r e d s e l f - d i f f u s i o n c o e f f i c i e n t s f o r w a t e r g i v e n i n T a b l e 2 .4 . T h e l o w e s t s e l f - d i f f u s i o n c o e f f i c i e n t m e a s u r e d w a s 5.1 x l O - 6 c m 2 s _ 1 f o r w a t e r i n 4 0 % H P M C . M e a s u r e m e n t s f o r w a t e r d i f f u s i o n i n h i g h e r c o n c e n t r a t i o n s o f H P M C w e r e n o t p e r f o r m e d d u e t o e x p e r i m e n t a l l i m i t a t i o n s . T h e m a x i m u m g r a d i e n t s t r e n g t h a v a i l a b l e f o r t h e P G S E e x p e r i m e n t w a s n o t s u f f i c i e n t t o m e a s u r e t h e d e c r e a s e d d i f f u s i o n c o e f f i c i e n t s w i t h o u t u s i n g l o n g g r a d i e n t p u l s e s . T h e r e s u l t i n g T E v a l u e s i n t h e e x p e r i m e n t w e r e t o o l o n g t o o b s e r v e s i g n a l i n t h e c o n c e n t r a t e d H P M C m i x t u r e s w h o s e T 2 v a l u e s w e r e o f t h e o r d e r o f 10 m s . T h e r e s u l t s o f t h e F i c k i a n fitting s u g g e s t t h a t t h e d i f f u s i o n o f w a t e r i n r e g i o n s o f H P M C c o n c e n t r a t i o n m u c h g r e a t e r t h a n 4 0 % i s a n o r d e r o f m a g n i t u d e l o w e r 149 Relative Intensity A (a) 1 hour (b) 4 hours (c) 7 hours 1.00 H 0.80 H 0.60 H 0.40 H 0.20 H 0.00 Distance (cm) F i g u r e 6 . 3 : C o m p a r i s o n o f w a t e r d i s t r i b u t i o n s f r o m t h e v a c u u m - t r e a t e d t a b l e t ( d o t s , T r i a l 2 ) a n d t h e t h e o r e t i c a l d i s t r i b u t i o n s a s s u m i n g o n e - d i m e n s i o n a l F i c k i a n d i f f u s i o n ( s o l i d l i n e ) c a l c u l a t e d u s i n g E q u a t i o n 6.8 w i t h t h e t a b l e t t h i c k n e s s o f 0 . 1 0 5 c m a n d a n a p p a r e n t d i f -f u s i o n c o e f f i c i e n t o f 3 . 3 5 x l O - 7 c m 2 s _ 1 a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 4 h o u r s , ( c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 25 h o u r s , (g) 31 h o u r s a n d ( h ) 3 7 h o u r s . T h e a x e s i n t h e e i g h t p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . T h e i n t e n s i t y i n t h e i m a g e s a r e r e l a t e d t o t h e i n t e n s i t y o f t h e b u l k w a t e r . ( T h e figure i s c o n t i n u e d o n t h e n e x t p a g e ) 150 Relative Intensity A(e) 19 hours 1.00 B.80 10.60 10.40 10.20 10.00 0.60 -{ 0.40 i 0.20 i T — ^ — i — 1 — r T — ' — i 0.00 H—i—|—*->—r — I — 1 — I — ' — I — ' — I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 (g) 31 hours 1.00 -b.80 -P.60 H 10.40 10.20 H 10.00 (h) 37 hours 1.00 -0.80 -0.60 0.40 0.20 H 1—-1 1 1 1 1 1 1 1 1 1 u.uu -| 1 1— 1 1 1 1 1 • 1 1 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 Distance (cm) F i g u r e 6 .3 c o n t i n u e d : p l o t s (e) t o ( h ) . 151 T a b l e 6 . 3 : T h e r e s u l t s o f o n e - d i m e n s i o n a l F i c k i a n f i t t i n g t o t h e H P M C d i s t r i b u t i o n s i n t h e s w e l l i n g t a b l e t . T h e t h e o r e t i c a l p o l y m e r d i s t r i b u t i o n s w e r e c a l c u l a t e d u s i n g E q u a t i o n 6 .7 w i t h h = 0 . 1 3 3 c m . T i m e D ( ± 0 . 0 5 x l ( r 7 ) a x2 ( h r s ) ( c m 2 s _ 1 ) 1 4 . 9 5 2 0 5 5 . 9 4 4 . 6 0 4 4 8 . 3 7 4 . 2 0 2 6 9 . 9 13 3 .40 2 8 5 . 8 19 3 .10 3 8 8 . 4 2 5 3 . 0 5 4 7 6 . 7 31 3 . 1 5 4 7 2 . 5 3 7 3 . 2 0 3 9 9 . 1 o v e r a l l 3 . 4 0 5 2 6 8 . 5 b a The given error in the apparent diffusion coefficient results in a change in the last quoted digit of the x 2 value b Sum of x2 values from the individual fits t h a n t h e m e a s u r e d v a l u e f o r 4 0 % H P M C . T h e d i f f u s i o n p a r a m e t e r r e s u l t f r o m t h e fitting f o r t h e 1 h o u r t i m e i n t e r v a l , 1.30 x l O - 7 c m 2 s _ 1 , a p p r o x i m a t e s t h e d i f f u s i o n c o e f f i c i e n t o f w a t e r i n t o « 1 0 0 % H P M C . T h e r e s u l t s o f t h e fitting o f t h e H P M C d i s t r i b u t i o n s b y E q u a t i o n 6 .7 a r e g i v e n i n T a b l e 6 . 3 . T h e a d d i t i o n a l w a t e r p e n e t r a t i o n i n t o t h e o u t e r m o s t l a y e r s o f t h e H P M C t a b l e t c a u s e d b y t h e v a c u u m - t r e a t m e n t w o u l d r e s u l t i n a i n c r e a s e d m o b i l i t y f o r t h e p o l y m e r i n t h i s r e g i o n a t e a r l y t i m e s . T h e r a n g e o f p o l y m e r m o b i l i t i e s t h r o u g h o u t t h e t a b l e t a r e a s s u m e d t o b e a v e r a g e d b y fitting t o F i c k i a n d i f f u s i o n t h e o r y a n d t h i s a v e r a g e w o u l d a l s o i n c l u d e t h e e f f e c t o f i n c r e a s e d m o b i l i t y f o r t h e p o l y m e r a t e a r l y t i m e s . T h e t h e o r e t i c a l d i s t r i b u t i o n s c a l c u l a t e d w i t h t h e e f f e c t i v e d i f f u s i o n p a r a m e t e r o f 3 . 4 0 x l 0 ~ 7 c m 2 s _ 1 s h o w r e a s o n a b l e a g r e e m e n t w i t h t h e H P M C d i s t r i b u t i o n s a t v a r i o u s s w e l l i n g t i m e s as s h o w n i n F i g u r e 6 .4 . S o m e o f t h e d e v i a t i o n s b e t w e e n t h e t h e o r e t i c a l a n d m e a s u r e d p o l y m e r d i s t r i b u t i o n s a t l o n g e r s w e l l i n g t i m e s m a y b e r e l a t e d t o t h e s l i g h t o v e r e s t i m a t i o n i n t h e m e a s u r e d p o l y m e r d i s t r i b u t i o n s w h i c h c o n t a i n 5 - 1 0 % m o r e p o l y m e r t h a n t h e k n o w n w e i g h t o f 166 m g H P M C i n t h e d r y t a b l e t . W h e n t h e s a m e p a r a m e t e r s a r e u s e d , E q u a t i o n s 6 .7 a n d 6 .8 a r e c o m p l e m e n t s o f e a c h o t h e r a n d t h e i r s u m w o u l d r e s u l t i n C o - T h e s i m i l a r i t y 152 H P M C ( w / w % ) ^ (a) 1 hour 100 -i 80 H 60 H 40 H 20 H (c) 7 hours 100 n 80 H 60 H 40 H 20 H —I— 0.4 - r~ 0.6 0.6 0.8 (b) 4 hours 100 -\ 80 -i 60 4 40 H 20 H 0.8 0.0 0.6 - I 0.8 (d) 13 hours 100 - i 0.6 —I 0.8 Distance (cm) F i g u r e 6 .4 : C o m p a r i s o n o f a v e r a g e H P M C d i s t r i b u t i o n s f r o m t h e v a c u u m - t r e a t e d t a b l e t ( d o t s ) a n d t h e t h e o r e t i c a l d i s t r i b u t i o n s a s s u m i n g o n e - d i m e n s i o n a l F i c k i a n d i f f u s i o n ( s o l i d l i n e ) c a l c u l a t e d u s i n g E q u a t i o n 6 .7 w i t h t h e t a b l e t t h i c k n e s s o f 0 . 1 3 3 c m a n d a n a p p a r e n t d i f f u s i o n c o e f f i c i e n t o f 3 . 4 0 x l O - 7 c m 2 s - 1 a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 4 h o u r s , (c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 2 5 h o u r s , (g) 31 h o u r s a n d ( h ) 3 7 h o u r s . T h e a x e s i n t h e e i g h t p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . ( T h e figure i s c o n t i n u e d o n t h e n e x t p a g e ) 153 H P M C ( w / w % ) A (e) 1 9 h o u r s 100 -i ( i ) 2 5 h o u r s 100 F i g u r e 6 .4 c o n t i n u e d : p l o t s (e) t o ( h ) . 154 T a b l e 6 .4 : T h e r e s u l t s o f o n e - d i m e n s i o n a l F i c k i a n f i t t i n g t o t h e t r i f l u p r o m a z i n e - H C l d i s -t r i b u t i o n s i n t h e s w e l l i n g t a b l e t . T h e t h e o r e t i c a l d r u g d i s t r i b u t i o n s w e r e c a l c u l a t e d u s i n g E q u a t i o n 6 .7 w i t h h = 0 . 1 3 3 c m . T i m e ( h r s ) D ( ± 0 . 0 5 x l 0 - 7 ) a ( c m 2 s _ 1 ) X2 19 2 5 31 3 7 7 .20 8 .60 9 . 0 5 9 . 9 0 0 . 0 0 4 1 0 2 0 . 0 0 2 8 1 0 0 . 0 0 1 6 5 3 0 . 0 0 2 2 5 2 o v e r a l l 8 .80 0 . 0 1 1 2 0 b a T h e g i v e n e r r o r i n t h e a p p a r e n t d i f u s i o n coef f ic ient r e s u l t s in a change in the last quoted digit of the \ 2 value 6 Sum of x2 values from the individual fits b e t w e e n t h e o v e r a l l e f f e c t i v e d i f f u s i o n p a r a m e t e r s f o r p o l y m e r a n d w a t e r s u g g e s t s t h a t t h e p o l y m e r a n d w a t e r d i s t r i b u t i o n s , w h e n p r e s e n t e d i n t h e s a m e u n i t s , a r e c o m p l e m e n t s o f e a c h o t h e r . T h e d r u g d i s t r i b u t i o n s w e r e d i f f i c u l t t o fit a t e a r l y t i m e s b e c a u s e n o t a l l t h e d r u g w a s v i s i b l e i n t h e 1 9 F i m a g e s . T h u s , t h e o r e t i c a l d r u g d i s t r i b u t i o n s w e r e o n l y c a l c u l a t e d f o r t h e l o n g e r s w e l l i n g t i m e s a n d t h e o v e r a l l b e s t - f i t t o t h e e n t i r e d a t a s e t w a s a l s o d e t e r -m i n e d f r o m t h e s e c a l c u l a t i o n s . T h e a v e r a g e d i f f u s i o n c o e f f i c i e n t d e t e r m i n e d f r o m t h e l a t e r t i m e s w a s t h e n u s e d t o c a l c u l a t e t h e o r e t i c a l d r u g d i s t r i b u t i o n s f o r t h e e a r l y t i m e s . T h e g o o d n e s s - o f - f i t t e s t w a s f o c u s s e d o n t h e ' s t e e p ' s l o p e o f t h e t r i f l u p r o m a z i n e - H C l d i s t r i b u -t i o n , t h e r e g i o n b e t w e e n a b o u t 0 . 2 5 a n d 0 .75 c m . T h e r e s u l t s o f t h e fitting c a l c u l a t i o n s a r e p r e s e n t e d i n T a b l e 6 .4 . T h e o v e r a l l b e s t - f i t t h e o r e t i c a l c o n c e n t r a t i o n d i s t r i b u t i o n m a t c h e s t h e t r i f l u p r o m a z i n e - H C l c o n c e n t r a t i o n q u i t e w e l l a t t h e l a t e r t i m e s as s h o w n i n F i g u r e 6 .5 . A t e a r l y s w e l l i n g t i m e s , t h e s l o p e s o f t h e m e a s u r e d a n d t h e o r e t i c a l d i s t r i b u t i o n s a r e e s s e n -t i a l l y p a r a l l e l b u t o t h e r c o m m e n t s a b o u t t h e q u a l i t y o f t h e fit c a n n o t b e m a d e . T h e t o t a l p e r c e n t s o f d e t e c t a b l e m o l e s o f 1 9 F f r o m t h e i m a g e s , as g i v e n b y T a b l e 5 . 3 , w e r e 9 2 % a t 3 7 h o u r s , 8 2 % a t 19 h o u r s , b u t o n l y 3 1 % a t 1 h o u r . T h u s , t h e d e v i a t i o n s v i s i b l e b e t w e e n t h e t h e o r e t i c a l a n d m e a s u r e d t r i f l u p r o m a z i n e - H C l d i s t r i b u t i o n s m a y b e d u e , i n p a r t , t o t h e l o w e r t o t a l d r u g p r e s e n t i n t h e m e a s u r e d d r u g d i s t r i b u t i o n s . 155 19F (moles L-i) A (a) 1 hour (b) 4 hours 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 (c) 7 hours (d) 13 hours 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1 • Distance (cm) F i g u r e 6 . 5 : C o m p a r i s o n o f t h e t r i f l u p r o m a z i n e - H C l d i s t r i b u t i o n s f r o m t h e v a c u u m - t r e a t e d t a b l e t ( d o t s ) a n d t h e t h e o r e t i c a l d i s t r i b u t i o n s a s s u m i n g o n e - d i m e n s i o n a l F i c k i a n d i f f u s i o n ( s o l i d l i n e ) c a l c u l a t e d u s i n g E q u a t i o n 6 .7 w i t h t h e t a b l e t t h i c k n e s s o f 0 . 1 3 3 c m a n d a n a p p a r e n t d i f f u s i o n c o e f f i c i e n t o f 8 . 8 0 x l O - 7 c m 2 s - 1 a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 4 h o u r s , (c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 25 h o u r s , (g) 31 h o u r s a n d ( h ) 3 7 h o u r s . T h e a x e s i n t h e e i g h t p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . ( T h e f i g u r e i s c o n t i n u e d o n t h e n e x t p a g e ) 156 19F (moles L-i) A(e) 19 hours (f) 25 hours 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 (g) 31 hours (h) 37 hours 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 Distance (cm) F i g u r e 6 . 5 c o n t i n u e d : p l o t s (e) t o ( h ) . 157 T a b l e 6 . 5 : T h e r e s u l t s o f o n e - d i m e n s i o n a l F i c k i a n f i t t i n g t o t h e 5 - f l u o r o u r a c i l d i s t r i b u t i o n s i n t h e s w e l l i n g t a b l e t . T h e t h e o r e t i c a l d r u g d i s t r i b u t i o n s w e r e c a l c u l a t e d u s i n g E q u a t i o n 6 .7 w i t h h = 0 . 1 3 3 c m . T i m e ( h r s ) D ( ± 0 . 0 5 x l 0 - 6 ) a ( c m 2 s _ 1 ) x2 19 2 5 31 37 4 . 7 5 3 .75 3 .25 3 .00 0 . 0 0 5 8 1 1 0 . 0 0 3 8 7 8 0 . 0 0 2 5 0 9 0 . 0 0 1 7 5 3 o v e r a l l 3 . 65 0 . 0 1 5 4 3 3 7 6 a T h e g i ven e r r o r in t h e a p p a r e n t d i f u s i o n coef f ic ient r e s u l t s i n a c h a n g e in the las t q u o t e d d i g i t o f t h e x2 va lue 6 S u m of x 2 va lues f r o m t h e i n d i v i d u a l f i t s T h e e f f e c t i v e d i f f u s i o n c o e f f i c i e n t o f 8 . 80 x l O - 7 c m 2 s _ 1 f r o m t h e F i c k i a n d i f f u -s i o n c a l c u l a t i o n s i s w i t h i n t h e r a n g e o f m e a s u r e d s e l f - d i f f u s i o n c o e f f i c i e n t s d e t e r m i n e d f o r t r i f l u p r o m a z i n e - H C l a n d p r e s e n t e d i n T a b l e 2 .5 . T h e d i f f u s i o n c o e f f i c i e n t s f o r t h e d r u g i n 1 0 % H P M C w a s 1 0 . 2 x l O - 7 a n d 9 . 4 x l O - 7 c m 2 s " 1 f o r 1 % a n d 3 % d r u g , r e s p e c t i v e l y . I n 2 0 % H P M C , t h e v a l u e s d r o p p e d t o 3 . 6 x l O - 7 a n d 6 . 0 x l O - 7 c m 2 s " 1 f o r 1 % a n d 3 % r e s p e c t i v e l y . T h e p r e v i o u s F i c k i a n f i t t i n g c a l c u l a t i o n s f o r t h e p o l y m e r a n d t r i f l u p r o m a z i n e - H C l s h o w e d r e a s o n a b l y g o o d a g r e e m e n t w i t h t h e m e a s u r e d d i s t r i b u t i o n s . T h e l a c k o f m o b i l i t y f o r e a c h s p e c i e s i n t h e d r y p o r t i o n s o f t h e t a b l e t a t e a r l y t i m e s d o e s n o t a f f e c t t h e o v e r a l l s h a p e o f t h e d i s t r i b u t i o n b e c a u s e t h e d i f f u s i o n o r m o v e m e n t r a t e f o r t h e t w o s p e c i e s i n t h e w e t t e d p o r t i o n s o f t h e t a b l e t w a s s t i l l r e l a t i v e l y s l o w . T h i s is n o t t h e c a s e f o r t h e d r u g 5 - f l u o r o u r a c i l w h i c h d i f f u s e d f r e e l y a n d r a p i d l y a l m o s t i m m e d i a t e l y a f t e r w a t e r h a d p e n e -t r a t e d t h e t a b l e t . T h e b e s t - f i t r e s u l t s f o r F i c k i a n f i t t i n g t o t h e 5 - f l u o r o u r a c i l d i s t r i b u t i o n s a t t h e l o n g e r s w e l l i n g t i m e s a r e g i v e n i n T a b l e 6 .5 a n d t h e t h e o r e t i c a l c o n c e n t r a t i o n d i s t r i -b u t i o n s f o r t h e s e t i m e s a r e p l o t t e d i n F i g u r e 6 .6 . T h e a g r e e m e n t b e t w e e n t h e t h e o r e t i c a l a n d m e a s u r e d d i s t r i b u t i o n s f o r t h i s d r u g i s n o t v e r y g o o d . T h e s h a p e o f t h e m e a s u r e d d i s -t r i b u t i o n s r e f l e c t s t h e p o r t i o n o f 5 - f l u o r o u r a c i l t h a t w a s n o t d i f f u s i n g f r o m t h e i n i t i a t i o n o f t a b l e t s w e l l i n g . T h e 5 - f l u o r o u r a c i l d i f f u s i o n w a s f a s t e n o u g h t h a t t h e f r e e l y d i f f u s i n g d r u g 158 19F (moles L-i) A (a) 19 hours 0.10 -\ 0.08 H 0.06 -T 0.04 H 0.02 H (b) 25 hours 0.10 -\ 0.08 H 0.06 -i 0.04 H 0.02 H o.oo H—I—i—•—i—i—i—i—i—i—i—i—i ooo H—I—i—•—i—•—i—•—i—•—i—•—i 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 (c) 31 hours 0.10 - I 0.08 H 0.06 0.04 0.02 H (d) 37 hours 0.10 0.08 H 0.06 H 0.04 -\ 0.02 H o.oo - I — I — i — • — i — • — i — • — i — i — i — • — i o.oo H — I — i — • — i — • — i — • — i — • — i — i — i 0.00 0.25 0.50 0.75 1.00 1.25 1.50 0.00 0.25 0.50 0.75 1.00 1.25 1.50 D i s t a n c e ( c m ) F i g u r e 6 .6 : C o m p a r i s o n o f t h e 5 - f l u o r o u r a c i l d i s t r i b u t i o n s f r o m t h e v a c u u m - t r e a t e d t a b l e t ( d o t s ) a n d t h e t h e o r e t i c a l d i s t r i b u t i o n s a s s u m i n g o n e - d i m e n s i o n a l F i c k i a n d i f f u s i o n ( s o l i d l i n e ) c a l c u l a t e d u s i n g E q u a t i o n 6 .7 w i t h t h e t a b l e t t h i c k n e s s o f 0 . 1 3 3 c m a n d a n a p p a r e n t d i f f u s i o n c o e f f i c i e n t o f 3 . 6 5 x l O - 6 c m 2 s _ 1 a t s w e l l i n g t i m e s o f (a ) 19 h o u r s , ( b ) 2 5 h o u r s , (c ) 31 h o u r s a n d ( d ) 3 7 h o u r s . T h e a x e s i n t h e f o u r p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . 159 w a s a b l e t o s e p a r a t e i t s e l f r a p i d l y f r o m t h e less m o b i l e d r u g i n t h e t a b l e t . A l t h o u g h t h e t h e o r e t i c a l d i s t r i b u t i o n s f o r 5 - f l u o r o u r a c i l d o n o t e x a c t l y m a t c h t h e s h a p e s o f t h e m e a s u r e d o n e s , t h e y d o i n d i c a t e h o w f a r t h e d r u g h a s e x t e n d e d f r o m t h e t a b l e t . C o n s i s t e n t w i t h t h i s , t h e o v e r a l l b e s t - f i t d i f f u s i o n p a r a m e t e r f r o m t h e F i c k i a n m o d e l l i n g , 3 . 6 5 x l O - 6 c m 2 s _ 1 , i s a p p r o x i m a t e l y t h e s a m e d i f f u s i o n c o e f f i c i e n t m e a s u r e d f o r t h e d r u g i n 3 0 % H P M C ( T a b l e 2 .6 ) a n d i n t h e s a m e r a n g e as t h a t r e q u i r e d f o r d r u g r e l e a s e f r o m f r o m t h e s w e l l i n g t a b l e t as d i s c u s s e d i n S e c t i o n 5 . 3 . 3 . T h e e f f e c t i v e d i f f u s i o n p a r a m e t e r f o r 5 - f l u o r o u r a c i l i s a b o u t f o u r t i m e s l a r g e r t h a n t h a t f o r t r i f l u p r o m a z i n e - H C l s u g g e s t i n g t h a t t h e f o r m e r d r u g w o u l d b e r e l e a s e d f r o m t h e t a b l e t a b o u t f o u r t i m e s f a s t e r t h a n t h e l a t t e r . I n r e a s o n a b l e a g r e e m e n t , t h e p l o t s o f f r a c t i o n o f d r u g r e l e a s e d as a f u n c t i o n o f t h e s q u a r e - r o o t o f t i m e i n S e c t i o n 5 . 3 . 3 i n d i c a t e d t h a t 5 -f l u o r o u r a c i l w a s r e l e a s e d a b o u t f i v e t i m e s f a s t e r t h a n t r i f l u p r o m a z i n e - H C l . 160 50 40 -\ 30 -H P M C (w/w)% 20 -101 ! 0 H r - 1 1 1 1 1 r 0.0 0.2 0.4 0.6 0.8 Distance (cm) F i g u r e 6.7: E x a m p l e o f t h e t h e o r e t i c a l H P M C d i s t r i b u t i o n ( s o l i d l i n e ) o b t a i n e d u s i n g 1 /(l-aCw) as t h e s e g m e n t s w e l l i n g f a c t o r c o m p a r e d w i t h t h e m e a s u r e d H P M C d i s t r i b u t i o n ( d o t s ) a t 37 h o u r s . T h e t h e o r e t i c a l d i s t r i b u t i o n w a s c a l c u l a t e d w i t h a d i f f u s i o n c o e f f i c i e n t o f 2 x H r 7 c m 2 s - 1 a n d a o f 0.85. 6.4.2 Segmented Tablet Calculations T h e o r i g i n a l f o r m o f t h e s e g m e n t s w e l l i n g m o d e l c o n t a i n e d t h e s w e l l i n g f a c t o r l/(l-aCw) r a t h e r t h a n t h e f a c t o r g i v e n i n E q u a t i o n 6.10. T h e g o a l o f t h e m o d e l , as o r i g i n a l l y p r e s e n t e d i n t h e l i t e r a t u r e [19], w a s t o f i t t h e c h a n g e s i n t h i c k n e s s o f a n a x i a l l y - s w e l l i n g t a b l e t . A s i s e v i d e n t i n F i g u r e 6.7, t h e t h e o r e t i c a l d i s t r i b u t i o n c a l c u l a t e d u s i n g t h i s f a c t o r i n t h e s e g m e n t e d t a b l e t m o d e l c a n b e u s e d t o e f f e c t i v e l y m a t c h t h e t h i c k n e s s o f t h e t a b l e t . H o w e v e r , t h e p o l y m e r c o n c e n t r a t i o n s i n t h e t h e o r e t i c a l d i s t r i b u t i o n d o n o t e v e n c l o s e l y r e s e m b l e t h e a c t u a l p o l y m e r d i s t r i b u t i o n i n t h e s w o l l e n t a b l e t . N o v a l u e o f t h e d i f f u s i o n c o e f f i c i e n t o r a w o u l d r e s u l t i n a b e t t e r m a t c h t o t h e m e a s u r e d c o n c e n t r a t i o n s . W h e n t h e f a c t o r w a s r e a r r a n g e d t o t h e o n e p r e s e n t e d i n E q u a t i o n 6.10, t h e c o n c e n -t r a t i o n d i s t r i b u t i o n s i n t h e s w o l l e n p o l y m e r w e r e m o r e c l o s e l y m a t c h e d b y t h e t h e o r e t i c a l d i s t r i b u t i o n s . T h e d i f f u s i o n c o e f f i c i e n t a n d t h e a f a c t o r w e r e f r e e l y v a r i e d i n t h e f i t t i n g c a l -c u l a t i o n a n d t h e o v e r a l l b e s t - f i t w a s p r o v i d e d b y a w a t e r d i f f u s i o n c o e f f i c i e n t o f 9 . 0 x l O - 8 161 c m 2 s _ 1 a n d a e q u a l t o 1. T h e d i f f u s i o n c o e f f i c i e n t f o r t h e w a t e r i s l o w e r t h a n t h e v a l u e d e t e r m i n e d f r o m t h e F i c k i a n d i f f u s i o n c a l c u l a t i o n s b e c a u s e t h e f o r m e r i s f o r a h y p o t h e t i c a l s i t u a t i o n w h e r e t h e w a t e r i s d i f f u s i n g i n t o a t a b l e t t h a t d o e s n o t s w e l l . T h e x2 v a l u e f o r t h e b e s t - f i t r e s u l t t o t h e s e g m e n t e d t a b l e t m o d e l w a s 1 2 6 6 7 . 3 , a b o u t 2 . 5 t i m e s g r e a t e r t h a n t h e m i n i m u m x2 v a l u e f r o m t h e F i c k i a n f i t t i n g t o t h e s a m e d i s t r i b u t i o n s , s u g g e s t i n g t h a t t h e t h e o r e t i c a l d i s t r i b u t i o n s f r o m t h e s e g m e n t e d t a b l e t m o d e l f i t t h e m e a s u r e d d a t a p o o r l y . T h e c o m p a r i s o n o f t h e t h e o r e t i c a l p o l y m e r d i s t r i b u t i o n s c a l c u l a t e d f r o m t h e s e g m e n t e d t a b l e t m o d e l a n d t h e m e a s u r e d H P M C d i s t r i b u t i o n s s h o w c l e a r l y t h a t t h e s e g m e n t - s w e l l i n g c a l c u l a t i o n , E q u a t i o n s 6 . 1 2 a n d 6 . 1 3 , p r e d i c t s s u b s t a n t i a l l y m o r e s w e l l i n g a t l o n g e r t i m e s t h a n t h e m e a s u r e d p o l y m e r d i s t r i b u t i o n . T h e f i t s a t e a r l y t i m e s m o r e c l o s e l y m a t c h t h e m e a s u r e d p o l y m e r d i s t r i b u t i o n s . T h e s e g m e n t e d t a b l e t m o d e l p r o v i d e s a m o r e p h y s i c a l l y m e a n i n g f u l d e s c r i p t i o n o f t h e t a b l e t s w e l l i n g p r o c e s s t h a n F i c k i a n d i f f u s i o n t h e o r y , as t h e f o r m e r c o n s i d e r s t h e i m -p o r t a n c e o f w a t e r p e n e t r a t i o n i n t h e m o v e m e n t o f t h e p o l y m e r . T h e d i f f e r e n c e s i n t h e t h e o r e t i c a l r e s u l t s a t d i f f e r e n t t i m e s s u g g e s t t h a t t h e d e g r e e o f s e g m e n t s w e l l i n g m a y b e r e l a t e d t o w a t e r c o n c e n t r a t i o n i n a c o m p l e x m a n n e r . N M R s p e c t r o s c o p y e x p e r i m e n t s i n S e c t i o n 2 . 3 . 4 s u g g e s t e d t h a t t h e m o b i l i t y o f H P M C f e l l i n t o t h r e e d i s t i n c t r e g i o n s d e p e n d -i n g o n t h e H P M C c o n c e n t r a t i o n a n d h e n c e , t h e . w a t e r c o n c e n t r a t i o n . T h e s w e l l i n g o f a n H P M C s e g m e n t m a y b e r e l a t e d t o t h e m o b i l i t y o f t h e c o n t a i n e d p o l y m e r w h i c h w o u l d b e d e t e r m i n e d b y t h e a m o u n t o f w a t e r p r e s e n t . F u r t h e r e x p e r i m e n t s w i l l b e n e c e s s a r y t o d e t e r m i n e t h e e x a c t n a t u r e o f t h e r e l a t i o n s h i p b e t w e e n t h e s w e l l i n g o f a p o l y m e r s e g m e n t a r i d a n e q u i l i b r i u m c o n c e n t r a t i o n o f w a t e r . 162 HPMC(w/w %) (^a) 1 hour 100 - i 80 H 60 H 40 H 20 H (b) 4 hours 100 n 0.0 (c) 7 hours 100 -i — r -0.4 0.6 (d) 13 hours 100 - i 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Distance (cm) F i g u r e 6 . 8 : A v e r a g e H P M C d i s t r i b u t i o n s o f t h e v a c u u m - t r e a t e d t a b l e t ( d o t s ) a n d t h e t h e o -r e t i c a l d i s t r i b u t i o n ( s o l i d l i n e ) c a l c u l a t e d u s i n g t h e s e g m e n t e d t a b l e t m o d e l , E q u a t i o n s 6 . 1 2 a n d 6 . 1 3 w i t h t h e t a b l e t t h i c k n e s s o f 0 . 1 3 3 c m a n d a w a t e r d i f f u s i o n c o e f f i c i e n t o f 9 . 0 x l 0 - 8 c m 2 s _ 1 a n d a o f 1, a t s w e l l i n g t i m e s o f (a ) 1 h o u r , ( b ) 4 h o u r s , (c ) 7 h o u r s , ( d ) 13 h o u r s , (e) 19 h o u r s , ( f ) 2 5 h o u r s , (g) 31 h o u r s a n d (h ) 37 h o u r s . T h e a x e s i n t h e e i g h t p l o t s a r e t h e s a m e a n d a r e d e f i n e d b y t h e a r r o w s . ( T h e f i g u r e i s c o n t i n u e d o n t h e n e x t p a g e ) 163 H P M C ( w / w % ) A (e) 1 9 h o u r s 100 -i 80 H 60 H (!) 2 5 h o u r s 100 D i s t a n c e ( c m ) F i g u r e 6 .8 c o n t i n u e d : p l o t s (e) t o ( h ) . 164 6 .5 S u m m a r y T h e m o d e l i n g c a l c u l a t i o n s f o r t h e w a t e r , p o l y m e r a n d d r u g d i s t r i b u t i o n s b a s e d o n o n e -d i m e n s i o n a l F i c k i a n d i f f u s i o n p r o v i d e d r e a s o n a b l e a p p r o x i m a t i o n s t o t h e m e a s u r e d c o n -c e n t r a t i o n d i s t r i b u t i o n s f o r e a c h s p e c i e s . T h e a v e r a g e e f f e c t i v e d i f f u s i o n p a r a m e t e r f o r t h e w a t e r w a s m u c h l o w e r t h a n t h e l o w e s t m e a s u r e d s e l f - d i f f u s i o n c o e f f i c i e n t f o r w a t e r i n 4 0 % p o l y m e r s u g g e s t i n g t h a t t h e d i f f u s i o n o f w a t e r c o n t i n u e s t o d e c r e a s e i n c o n c e n t r a t i o n s o f p o l y m e r g r e a t e r t h a n 4 0 % . T h e e f f e c t i v e d i f f u s i o n p a r a m e t e r s f o r t h e d r u g s w e r e c o m p a r a -b l e t o t h e i r m e a s u r e d s e l f - d i f f u s i o n c o e f f i c i e n t s i n m i x t u r e s o f H P M C . T h e s e g m e n t e d t a b l e t m o d e l r e p r o d u c e d t h e p o l y m e r d i s t r i b u t i o n s i n t h e s w o l l e n H P M C t a b l e t a t e a r l y t i m e s r e a s o n a b l y w e l l b u t p r e d i c t e d g r e a t e r s w e l l i n g a t l a t e r t i m e s t h a n w a s m e a s u r e d e x p e r i m e n t a l l y . T h e c a l c u l a t i o n s w i t h t h i s m o d e l s u g g e s t e d t h a t t h e s w e l l i n g o f a s e g m e n t o f t h e t a b l e t w a s r e l a t e d t o t h e c o n c e n t r a t i o n o f w a t e r i n a m o r e c o m p l e x m a n n e r t h a n o r i g i n a l l y p r o p o s e d , i n a g r e e m e n t w i t h e a r l i e r N M R s p e c t r o s c o p i c r e s u l t s , p r e s e n t e d i n C h a p t e r 2 , t h a t i n d i c a t e d t h a t t h e m o b i l i t y o f H P M C i n a n H P M C -w a t e r m i x t u r e w a s d e p e n d e n t o n t h e a m o u n t o f w a t e r p r e s e n t . 165 C h a p t e r 7 C o n c l u s i o n s a n d S u g g e s t i o n s fo r F u t u r e W o r k 7.1 Conclusions T h e w o r k p r e s e n t e d i n t h i s t h e s i s h a s d e m o n s t r a t e d t h a t N M R s p e c t r o s c o p y a n d N M R i m a g i n g a r e i n v a l u a b l e t e c h n i q u e s i n t h e s t u d y o f s w e l l i n g - c o n t r o l l e d d r u g d e l i v e r y s y s t e m s . T h e d e p e n d e n c e o f p a r a m e t e r s s u c h as T i , T 2 a n d d i f f u s i v i t y o f t h e w a t e r a n d d r u g s p e c i e s o n t h e p o l y m e r c o n c e n t r a t i o n w e r e d e t e r m i n e d i n C h a p t e r 2 w i t h N M R s p e c -t r o s c o p y . T h e s e p a r a m e t e r s p r o v i d e d i n s i g h t i n t o t h e m o b i l i t y c h a n g e s o f t h e w a t e r , d r u g a n d p o l y m e r c o m p o n e n t s i n t h e s w e l l i n g t a b l e t . T h e c h a n g e s i n p o l y m e r m o b i l i t y o b s e r v e d i n t h e z - s p e c t r o s c o p i c s t u d y a l s o i n d i c a t e d t h e p o l y m e r c o n c e n t r a t i o n r a n g e r e q u i r e d t o o b t a i n a g e l r a t h e r t h a n a v i s c o u s s o l u t i o n . T h e d r u g r e l e a s e b e h a v i o r f r o m t h e s w e l l i n g t a b l e t c o u l d b e d i r e c t l y r e l a t e d t o t h e m e a s u r e d d i f f u s i o n c o e f f i c i e n t s o f t h e d r u g s i n v a r i o u s H P M C c o n c e n t r a t i o n s . T h e o n e - d i m e n s i o n a l N M R i m a g i n g p r o t o c o l d e v e l o p e d i n C h a p t e r s 3 a n d 4 m a d e p o s s i b l e t h e d e t e r m i n a t i o n o f q u a n t i t a t i v e c o n c e n t r a t i o n d i s t r i b u t i o n s f o r t h e w a t e r , p o l y -m e r a n d m o d e l d r u g s ( C h a p t e r 5) a t m a n y t i m e i n t e r v a l s d u r i n g t h e s w e l l i n g p r o c e s s . T h e s e d i s t r i b u t i o n s p r o v i d e d a c o m p l e t e d e s c r i p t i o n o f t h e p r o c e s s e s o f w a t e r p e n e t r a t i o n , t a b l e t s w e l l i n g a n d d r u g r e l e a s e . T h e d r u g r e l e a s e b e h a v i o r w a s f o u n d t o d e p e n d o n t h e r e l a t i v e r a t e o f d r u g d i f f u s i o n c o m p a r e d t o t h e r a t e o f e x p a n s i o n o f t h e d e v i c e . T h e d r u g r e l e a s e w a s f a s t e r , as i n t h e c a s e o f t h e d r u g 5 - f l u o r o u r a c i l , w h e n t h e d r u g d i f f u s i o n i n c o n c e n -t r a t e d p o l y m e r r e g i o n s w a s c o m p a r a b l e t o o r l a r g e r t h a n t h e a p p a r e n t t a b l e t e x p a n s i o n 166 r a t e o b t a i n e d f r o m p l o t s o f t h i c k n e s s as a f u n c t i o n o f t h e s q u a r e - r o o t o f t i m e . W i t h s l o w d r u g d i f f u s i o n , as i n t h e c a s e o f t h e d r u g t r i f l u p r o m a z i n e - H C l , t h e d r u g d o e s n o t e s c a p e t h e t a b l e t u n t i l v e r y l o w H P M C c o n c e n t r a t i o n s w h e r e t h e t a b l e t b e g i n s t o e r o d e . T h e p r e l i m i n a r y m o d e l i n g c a l c u l a t i o n s f o r t h e w a t e r , p o l y m e r a n d d r u g d i s t r i b u t i o n s w e r e b a s e d o n o n e - d i m e n s i o n a l F i c k i a n d i f f u s i o n w h i c h p r o v i d e d r e a s o n a b l e a p p r o x i m a t i o n s t o t h e c o n c e n t r a t i o n d i s t r i b u t i o n s f o r e a c h s p e c i e s . A s e g m e n t e d t a b l e t m o d e l w a s a l s o t e s t e d t o p r e d i c t t h e p o l y m e r d i s t r i b u t i o n s i n t h e s w o l l e n H P M C t a b l e t . I n i t i a l c a l c u l a t i o n s w i t h t h i s m o d e l s u g g e s t e d t h a t t h e s w e l l i n g o f a s e g m e n t o f t h e t a b l e t w a s r e l a t e d t o t h e c o n c e n t r a t i o n o f w a t e r i n a m u c h m o r e c o m p l e x m a n n e r t h a n t h e m o d e l o r i g i n a l l y a s s u m e d . 7.2 Suggestions for Future Work T h e w o r k i n t h i s t h e s i s f o c u s s e d o n t h e a x i a l s w e l l i n g o f H P M C t a b l e t s in vitro a t r o o m t e m p e r a t u r e . T h e s t u d y o f t h i s s p e c i f i c c a s e o f a s w e l l i n g - c o n t r o l l e d d r u g d e l i v e r y s y s t e m y i e l d e d c o n c l u s i o n s r e g a r d i n g d r u g r e l e a s e b e h a v i o r a n d p r e l i m i n a r y t h e o r e t i c a l m o d e l s t o d e s c r i b e t h e p o l y m e r d i s t r i b u t i o n . T h e v a c u u m - t r e a t m e n t o f t h e H P M C t a b l e t s p r i o r t o t h e i m a g i n g e x p e r i m e n t s r e -m o v e d c o m p r e s s e d a i r f r o m t h e t a b l e t w h i c h m a d e p o s s i b l e t h e q u a n t i t a t i v e d e t e r m i n a t i o n o f t h e p o l y m e r c o n c e n t r a t i o n d i s t r i b u t i o n s . H o w e v e r , t h e v a c u u m - t r e a t m e n t a p p e a r e d t o c a u s e i n c r e a s e d w a t e r p e n e t r a t i o n i n t o t h e o u t e r m o s t l a y e r s o f t h e t a b l e t . I t w a s n o t e d i n C h a p t e r 4 t h a t a i r p r e s e n t i n t h e t a b l e t a t a t m o s p h e r i c p r e s s u r e d i d n o t r e s u l t i n a i r b u b -b l e s i n t h e s w o l l e n t a b l e t . A m o d i f i c a t i o n o f t h e v a c u u m - t r e a t m e n t , w h e r e a i r i s p e r m i t t e d t o r e - e n t e r t h e t a b l e t a t a t m o s p h e r i c p r e s s u r e m a y m i n i m i z e b o t h t h e e f f e c t s o f a i r b u b b l e s i n t h e s w o l l e n g e l a n d t h e i n c r e a s e d w a t e r p e n e t r a t i o n . F u r t h e r e x p e r i m e n t s o n t a b l e t s w e l l i n g , w h e r e t h e d e g r e e o f s w e l l i n g w i t h a c o n -t r o l l e d c o n c e n t r a t i o n o f w a t e r i s d e t e r m i n e d , w i l l p r o v i d e a b e t t e r u n d e r s t a n d i n g o f h o w t a b l e t s w e l l i n g i s r e l a t e d t o w a t e r c o n c e n t r a t i o n . T h i s i n f o r m a t i o n i s n e c e s s a r y t o i m p r o v e t h e f i t t i n g o f t h e p o l y m e r d i s t r i b u t i o n b a s e d o n t h e s e g m e n t e d t a b l e t m o d e l . T o d e t e r m i n e t h e g e n e r a l i t y o f t h e c o n c l u s i o n s o f t h i s t h e s i s , t h e f o c u s o f s t u d y 167 m u s t b e b r o a d e n e d t o i n c l u d e s y s t e m s w h e r e t h e s w e l l i n g o f t h e t a b l e t i s l e s s r e s t r i c t e d . U l t i m a t e l y , t h e u n r e s t r i c t e d s w e l l i n g o f t h e s y s t e m i n t h r e e d i m e n s i o n s w i l l d e t e r m i n e t h e q u a l i t y o f t h e o r e t i c a l m o d e l s b a s e d o n a x i a l s w e l l i n g . T h e N M R i m a g i n g s t u d i e s o f t h e s e c o m p l e x s y s t e m s w i l l p o s e e x p e r i m e n t a l d i f f i c u l t i e s as t h e y w i l l r e q u i r e t h e u s e o f t w o -o r t h r e e - d i m e n s i o n a l N M R i m a g i n g t e c h n i q u e s r a t h e r t h a n t h e o n e - d i m e n s i o n a l t e c h n i q u e t h a t w a s s u c c e s s f u l l y a p p l i e d i n t h i s t h e s i s . 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The Mathematics of Diffusion. O x f o r d U n i v e r s i t y P r e s s , L o n d o n , U K , 1 9 5 6 . 175 H . S . C a r s l a w a n d J . C . J a e g e r . Conduction of Heat In Solids. C l a r e n d o n P O x f o r d , U K , 1 9 5 9 . A p p e n d i x II. 176 A p p e n d i x A P r o c e s s i n g o f I m a g e D a t a A . l ASCII output from WIN-NMR The following listing is an example of the A S C I I output from the W I N - N M R program which was later reproduced by the Java converter program. The frequency information is given by a start frequency, an end frequency and a frequency interval. The intensity for each frequency is then listed, in arbitrary units, in a column after the header information. To preserve space in this section, the intensities are listed from left to right rather than as one long column. Data f i l e : /MacintoshHD/bhjan21/BHJAN21.001 Starting Point: 0 Ending Point: 127 Point Count: 128 Read Data SF01: 400.12 Hz Sweep Width: 83333.3 Hz Hz/Pt: 651.042 F i r s t Point: 39666.7 Hz Last Point: -43666.7 Hz F i r s t Point: 99.1394 PPM Last Point: -109.137 PPM 484576 485286 486762 488940 492641 497245 500295 501473 503597 508666 515326 522450 530249 538270 545824 554803 566866 579258 588402 596853 610046 627312 643166 657261 674128 693682 710637 723804 736885 751418 766600 785483 810688 835670 851818 863811 881104 895966 887655 845999 755778 546937 151772 659636 1523293 2266984 2678130 2784588 2787366 2850616 2980960 3077309 3088798 3062632 3059069 3072138 3063307 3034434 3018335 3019557 3011146 2989495 2982559 2997201 2999792 2969777 2932773 2918207 2916614 2904164 2883866 2872988 2868824 2856918 2839863 2830495 2825906 2813718 2796714 2787526 2784881 2777351 2765665 2760037 2759387 2754016 2745389 2743128 2744913 2739457 2727660 2721218 2721315 2718006 2710643 2709328 2715010 2717425 2714806 2716650 2724149 2726752 2721761 2717534 2711643 2686006 2632814 2567302 2504828 2442167 2373221 2308210 2263164 2239889 2227888 2219094 2211218 2202104 2190571 2181377 2181059 2188252 2193558 2190366 2182260 2178785 2184815 2195383 177 A .2 Converter Program for Batch-Processing Files B e l o w i s a l i s t i n g o f t h e c o n v e r t e r p r o g r a m u s e d t o b a t c h - p r o c e s s i m a g e f i l e s . I t w a s w r i t t e n b y D r . M a r k W e l s h i n t h e J a v a l a n g u a g e a n d r u n o n a M a c i n t o s h L C 4 7 5 u s i n g t h e M a c i n t o s h J a v a V i r t u a l M a c h i n e . T h e c o m m e n t s , p r e c e d e d b y ' / / ' , e x p l a i n t h e f u n c t i o n o f e a c h s e c t i o n . /** * A c o n v e r t e r f o r A l m i r a ' s MSL b i n a r y f i l e s . * * / impor t j a v a . i o . * ; impor t j a v a . a w t . * ; p u b l i c c l a s s C o n v e r t e r { p u b l i c s t a t i c v o i d main() { / / C rea t e our frame Frame frame = new F r a m e O ; / / S e l e c t a f i l e ( a c t u a l l y the d i r e c t o r y ) F i l e D i a l o g f d = new F i l e D i a l o g ( f r a m e , " S e l e c t a f i l e i n the d i r e c t o r y t o be c o n v e r t e d " , F i l e D i a l o g . L O A D ) ; f d . s h o w ( ) ; / / C rea t e a F i l e ob j ec t f o r the s e l e c t e d d i r e c t o r y F i l e d i r = new F i l e ( f d . g e t D i r e c t o r y O ) ; i f ( ! d i r . i s D i r e c t o r y O ) { S y s t e m . o u t . p r i n t l n ( " P r o b l e m s e l e c t i n g a d i r e c t o r y . " ) ; r e t u r n ; } / / Get a l i s t o f a l l f i l e s i n t h i s d i r e c t o r y S t r i n g f i l e N a m e s [ ] ; t r y { f i l eNames = d i r . l i s t O ; \ c a t c h ( S e c u r i t y E x c e p t i o n e) { S y s t e m . o u t . p r i n t l n ( " P r o b l e m l i s t i n g f i l e s i n d i r e c t o r y . " ) ; r e t u r n ; } / / Fo r each f i l e , perform a c o n v e r s i o n f o r ( i n t i = 0; i < f i l e N a m e s . l e n g t h ; i++) { conve r t ( fd . g e t D i r e c t o r y O , f i l eNames [ i ] ) ; } } 178 // Convert a f i l e from MSL binary to an ASCII dump private sta t i c void convert(String directory, String fileName) byte E0L[] = new byte [2]; E0L[0] = OxOD; E0L[1] = OxOA; try { // Create an MSL input stream directory += "/"; AlsBufferedlnputStream i n F i l e = new AlsBufferedInputStream( new FileInputStream(directory + fileName)); // Create the output f i l e PrintStream outFile = new PrintStream( new FileOutputStream(directory + "X" + fileName)); // Get the header data inFile.skipMSL(43); int tdsize = inFile.readMSL(); inFile.skipMSL(9); int spwidthRaw = in F i l e .readMSLO ; inFile.skipMSL(23); int sfreqRaw = in F i l e .readMSLO ; inFile.skipMSL(103); int offsetRaw = in F i l e .readMSLO ; inFile.skipMSL(74); // munge i t double spwidth = (double)spwidthRaw / 0x40; double sfreq = (double)sfreqRaw / 0x4000; double offset = (double)offsetRaw / 0x80; // and print i t out outFile.print("Data f i l e : " + directory + fileName); outFile.write(EOL); outFile.print("Starting Point: 0"); outFile.write(EOL); outFile.print("Ending Point: " + Integer.toString(tdsize - 1)); outFile.write(EOL); outFile.print("Point Count: " + Integer.toString(tdsize)); outFile.write(EOL); outFile.print("Read Data"); outFile.write(EOL); outFile.print("SF01: " + Double.toString(sfreq) + " Hz"); outFile.write(EOL); outFile.print("Sweep Width: " + Double.toString(spwidth) + " Hz"); outFile.write(EOL); outFile.print("Hz/Pt: " 179 + Double.toString(spwidth/(double)tdsize)); outFile.write(EOL); outFile.print("First Point: " + Double.toString(offset + spwidth) + " Hz"); outFile.write(EOL); outFile.print("Last Point: " + Double.toString(offset) + " Hz"); outFile.write(EOL); outFile.print("First Point: " + Double.toString((offset + spwidth) / (double)sfreq) + " PPM") ; outFile.write(EOL); outFile.print("Last Point: " + Double.toString(offset / (double)sfreq) + " PPM"); outFile.write(EOL); // Print out the real data for (int i = 0; i < tdsize; i++) { outFile.print(Integer.toString(inFile.readMSL())); outFile.write(EOL); inFile.skipMSL(l); } // Release resources i n F i l e . closeO; outFile.closeO ; } catch (Exception e) { System.out.println(e.toString() + ": Problem parsing f i l e " ) ; } f i n a l l y { System.out.println(directory + fileName); } } } class AlsBufferedlnputStream extends BufferedlnputStream { public st a t i c f i n a l int MSL_W0RD = 3; public AlsBufferedlnputStream(InputStream inStream) { super(inStream); } public int skipMSL(int skip) throws IOException { int toSkip = skip * MSL.WORD; i f (super.skip(toSkip) != toSkip) { throw new IOExceptionO ; } return toSkip; } public int readMSL() throws IOException 180 { int value = (read() « 0x10) + (read() « 0x08) + read(); value <<= 8; value >>= 8; return value; } } A.3 Calculating (Frequency, Intensity) Data Points T h e f o l l o w i n g p r o g r a m r e a d s i n t h e A S C I I o u t p u t o f A p p e n d i x A . l , e x t r a c t s t h e n e c e s s a r y f r e q u e n c y i n f o r m a t i o n t o c a l c u l a t e t h e f r e q u e n c y f o r e a c h p o i n t a n d t h e n w r i t e s t h e ( f r e -q u e n c y , i n t e n s i t y ) d a t a t o a n e w f i l e . I t w a s w r i t t e n a n d r u n i n S y m a n t e c ' s T H I N K P a s c a l v e r s i o n 4 . 0 o n a M a c i n t o s h L C 4 7 5 . C o m m e n t s i n t h e p r o g r a m , b r a c k e t e d b y ' ( * ' a n d ' * ) ' , e x p l a i n t h e f u n c t i o n o f v a r i o u s s e c t i o n s . program READ_WIN_NMR; type data = array[1..2028] of real; Firstpart = array[0..9] of string[1]; Secondpart = array[0..99] of string[2]; var F i r s t f i l e E x t , LastfileExt: string[3]; period: string[1]; e x t l : Firstpart; ext2: Secondpart; i n f i l e , o u t f i l e : text; Root, Name, NewRoot, NewName: string; Datafile, Datatype: string; Startpoint, Endpoint, Numpoints: integer; Specfreq, Sweepwidth, Res: real; Startfreq, Endfreq: real; Startppm, Endppm: real; i , j , k: integer; Intensity: data; Frequency: data; (•Runs through the characters in the heading of an acquisition *) (•parameter in the ASCII f i l e up to the semi-colon character *) (*for example, Starting Point: *) procedure ReadToSemicolon; var x: char; begin repeat Read(infile, x); 181 u n t i l Ord(x) = 58; end; (************************^ (•Main Program *) (***********************^  begin (•Introduction to program*) ShowText; Writeln; Writeln('Convert WIN NMR ASCII to data suitable for '); Writeln('Kaleidagraph, Excel etc . '); Writeln; Writeln('This program w i l l ask you to open a WIN NMR ASCII f i l e ' Writeln('and to give a name to save the resulting l i s t ' ) ; Writeln('of frequency and intensity data pairs.'); Writeln; Writeln.('Please note that the MAXIMUM TD for this program i s 2K.' Writeln; Writeln('Hit return to continue . '); Readln; (*The MSL filenames are in the form name.ext where the extension *) (•is a number from 001 to 999. The following sets up strings for • ) ( • f i l e extensions of 000 to 999 so that batch-processing can be*) (•performed on f i l e s that have the same rootname*) Period := '.' ; for i := 0 to 9 do ext l [ i ] := Chr(i + 48); (* Ord('O') = 48, 0rd('9') = 57*) k := 0; for i := 0 to 9 do for j := 0 to 9 do begin ext2[k] := concat(extl[i] , e x t l [ j ] ) ; k := k + 1; end; (•Requests f i l e rootnames and extensions*) Writeln('Please enter in the Root Name of the f i l e s that you'); Writeln('want to convert. Do not include the period'); Writeln; Writeln('format: name of harddrive:folder(:folder etc.):filename Readln(Root); Writeln; Writeln('Please enter in the f i r s t f i l e extension eg 001'); Readln(FirstfileExt); Writeln; Writeln('Please enter the last f i l e extension eg 065'); Writeln('This program can handle f i l e extensions'); Writeln('from 000 to 999'); Readln(LastFileExt); Writeln('Please enter the root name of the f i l e s to save '); Writeln('the data as. The extension for the saved f i l e w i l l ' ) ; Writeln('be the same as that for the f i l e read i n ' ) ; Writeln; Writeln('format: harddrive:folder:filename'); 182 Readln(NewRoot); (•processing starts*) (*the following increments the f i l e extension string to the*) (•value of the f i r s t extension entered*) k := 0; j := 0; while concat(extl[k], ex t2[j]) <> FirstFileExt do begin i f j = 9 9 then begin k := k + 1 ; j := - l ; end; j := j + l ; end; (* need to set j back one to avoid missing the f i r s t f i l e * ) j == j - i ; (*reads through the f i l e s one by one and creates an output f i l e * ) (•of the (frequency.intensity) data points which has a new name*) (•but the same f i l e extension number as the input f i l e * ) while concat(extl[k], e x t 2[j]) <> LastFileExt do begin i f j = 9 9 then begin k := k + 1 ; j := - l ; end; j := j + i ; Name := concat(Root, Period, extl[k], e x t 2[j]); Open(infile, Name); Readln(infile, Datafile); ReadToSemicolon; Readln(infile, Startpoint); ReadToSemicolon; Readln(infile, Endpoint); ReadToSemicolon; Readln(infile, Numpoints); Readln(infile, Datatype); ReadToSemicolon; Readln(infile, Specfreq); ReadToSemicolon; Readln(infile, Sweepwidth); ReadToSemicolon; Readln(infile, Res); ReadToSemicolon; Readln(infile, Startfreq); ReadToSemicolon; Readln(infile, Endfreq); ReadToSemicolon; Readln(infile, Startppm); ReadToSemicolon; Readln(infile, Endppm); i := 0; for i := 1 to Numpoints do 183 begin Read(infile, Intensity[i]); i f i < Numpoints then Readln(infile); end; (•calculation of the frequency value for each point*) (•intensity values are l i s t e d in order of positive to*) (•negative frequency*) Frequency[1] := Startfreq; i := 0; for i := 2 to Numpoints do Frequency[i] := Frequency[(i - 1)] - Res; (*outputting to the new f i l e * ) NewName := concat(NewRoot, Period, extl[k], ext2[j]); 0pen(outfile, NewName); for i := 1 to Numpoints do begin write(outfile, Frequency[i] : 10 : 5); write(outfile, ' '); writeln(outfile, IntensityCi] : 10 : 0) ; end; Cl o s e ( i n f i l e ) ; Close(outfile); end; end A A T 2 Calculation from the Variable-T^ Image Files T h i s p r o g r a m c a l c u l a t e s T 2 a n d e r r o r i n T 2 f r o m t h e d a t a s e t o f o n e - d i m e n s i o n a l i m a g e f i l e s a c q u i r e d a t d i f f e r e n t t i m e s t o e c h o . T h e p r o g r a m w a s w r i t t e n a n d r u n i n S y m a n t e c ' s T H I N K P a s c a l v e r s i o n 4 . 0 a n d r u n o n a M a c i n t o s h L C 4 7 5 . T h e p r o g r a m r e a d s i n t h e o u t p u t f i l e s o f A p p e n d i x A . 3 a n d c a l c u l a t e s t h e c o r r e s p o n d i n g d i s t a n c e f o r e a c h f r e q u e n c y a n d c a n s c a l e t h e i n t e n s i t i e s i f d e s i r e d . T h e e n t i r e d a t a s e t i s s o r t e d i n t o a a r r a y b y o r d e r o f i n c r e a s i n g T E . T h e d a t a s e t i s t h e n u s e d t o c a l c u l a t e t h e s l o p e o f a L n ( i n t e n s i t y ) v e r s u s T E p l o t f o r e a c h f r e q u e n c y p o i n t . T h e p r o g r a m c a l c u l a t e s t h e s l o p e s o f s u b s e t s o f t h e d a t a f i l e s , f r o m t h e f o u r s m a l l e s t T # f i l e s u p t o t h e t o t a l n u m b e r o f f i l e s . T h e s u b s e t t h a t p r o d u c e s t h e s l o p e w i t h t h e l o w e s t r e l a t i v e e r r o r i s c o n s i d e r e d t h e b e s t r e s u l t f o r t h e T 2 c a l c u l a t i o n u n l e s s t h e r e l a t i v e e r r o r o f t h e t o t a l n u m b e r o f f i l e s i s w i t h i n 5 0 % o f t h e l o w e s t r e l a t i v e e r r o r . 184 program filehandling; const Maxnumfiles = 15; (*arbitrary number, usually have 10*) Maxnumpoints = 256; (*arbitrary, usually have 128*) type Manyl = array[1..Maxnumfiles] of string; Many2 = array[1..Maxnumfiles] of text; data = array[1..Maxnumpoints] of real; value = array[1..Maxnumfiles] of real; b u i l t = array[1..Maxnumpoints, 0..Maxnumfiles] of rea l ; var Response, GoAgain, Check: boolean; test: char; Name: Manyl; I n f i l e : Many2; Numfiles, Numpoints, i : integer; Menu: string[100]; freq, i n t : data; TE, sortedTE: value; Hertzpercm, FreqofZero, temp: real; Combined: b u i l t ; (*Reads in the frequency and intensity values from a f i l e *) (*****************************************^  procedure Readfile (Numpoints, i : integer; var freq, i n t : data); var j : integer; begin j := 0; for j := 1 to Numpoints do begin Read(infile[i] , freqCj]); Readln(inf i l e [ i ] , i n t [ j ] ) ; end; end; (•Calculates new (distance, intensity) points by using the *) (•entered scaling factor, zero position and Hertz per cm factor *) procedure Convert (Numpoints: integer; Hertzpercm, FreqofZero: real; var freq: data); var j : integer; tempi: real; begin 185 j := 0; tempi := 0; for j := 1 to Numpoints do begin tempi := (freqCj] - FreqofZero) / Hertzpercm; freq[j] := tempi; end; end; (****************************^ (•Arranges data f i l e s into an array in order of increasing TE *) (***************************************************** procedure Buildarray (Numpoints, i , Numfiles: integer; TE: value; freq, int: data; var sTE: value; var Combined: b u i l t ) ; var j , k: integer; lowTE: real; rank: integer; begin j := 0; i f i = 1 then for j := 1 to Numpoints do Combined [ j , 0] .:= freq[j] ; (•setting ranking of the data based on increasing TE+) rank := 1; k := 0; for k := 1 to Numfiles do i f TE[i] > TE [k] then rank := rank + 1; sTE[rank] := TE[i] ; (•the ranking determines in which column the intensity data goes+) j := 0; for j := 1 to Numpoints do CombinedLj, rank] := i n t [ j ] ; end; i t * * * * * * * * * * * * * * * * * * * * * * * * * * * * * " ) (•This i s the main calculation procedure involved in working out+) (•the T2 value. Temp is the number of f i l e s from 4 •) (• onward that are used to calculate the slope •) (****************************************************************) procedure CalcSlope (temp, j : integer; Combined: b u i l t ; sorTE: value; var slope, denom, int, ErrorlnSlope, Errorpernumpoints: value); var begin n: integer; Xsum, Ysum, X2sum, XYsum: real; TotDiff2, Diff2: real; 186 (•Least-squares procedure for calculating the slope of a straight*) (•line. TE is the x variable and In int i s the y variable*) n := 0; Xsum := 0; Ysum := 0; X2sum := 0; XYsum := 0; for n := 1 to temp do begin Xsum := Xsum + sorTE[n]; Ysum := Ysum + Combined[j, n]; X2sum := X2sum + (sorTE[n]) * (sorTE[n]); XYsum := XYsum + (sorTE[n]) * (Combined[j, n]) ; end; denom[temp] := (X2sum * temp - Xsum * Xsum); slope[temp] := (XYsum * temp - Xsum * Ysum) / denom[temp]; Int[temp] := (X2sum * Ysum - Xsum * XYsum) / denom[temp]; TotDiff2 := 0; n := 0; for n := 1 to temp do begin Diff2 := Sqr((Combined[j, n] - slope[temp] * sorTE[n] - int [temp])); TotDiff2 := TotDiff2 + Diff2; end; ErrorInSlope[temp] := Sqrt((temp * TotDiff2) / ((temp - 2) * denom[temp])); Errorpernumpoints[temp] := ErrorInSlope[temp] / temp; end; ( * $ $ * * * * * * * * * * * * * * * * * * * * * * * * * * * * *********************************) (*The data set may contain points that would ordinarily be *) (•inappropriate to use in the calculation. To simplify the *) (•rejection of points, the following procedure calculates the *) (*slope with subsets of 4 f i l e s minimum to Numfiles maximum. *) (*Since the data has already been sorted based on *) (•increasing TE value, calculations with subsets of the data •) (•eliminate the problem points at higher TE values for regions •) (•of the sample with short T2 values. The best slope i s chosen •) (•by using the relative error in the slope as the selection •) (•criterion. This best slope i s then used to calculate T2 •) (****************************************************************) procedure T2fromSlope (Numfiles, j : integer; Combined: b u i l t ; sorTE: value; var T2, ErrorInT2: re a l ) ; type testcases = array[1..MaxNumfiles] of real; var k, m: integer; slope, denom, int, ErrorlnSlope, Errorpernumpoints: val re l e r r , bestslope, bestErrorlnSlope, reltemp: real; 187 begin (*The minimum number of points that w i l l be used i s 4*) for k := 4 to Numfiles do CalcSlope(k, j , Combined, sorTE, slope, denom, int, ErrorlnSlope, Errorpernumpoints); r e l e r r := 1; bestslope := 1; bestErrorlnSlope := 1; (•Looking for the subset that gives the lowest relative *) (*error in the slope*) for k := 4 to Numfiles do begin reltemp := ABS(Errorpernumpoints[k] / slope[k]); i f reltemp < rele r r then begin bestslope := slope[k]; bestErrorlnSlope := Errorlnslope[k]; r e l e r r := reltemp; end; (*The following lines choose the slope with a l l the points*) (*as the default bestslope when the relative error for the entire*) (*dataset i s s t i l l close to the best error ( i . e . within 50%)*) i f (k = Numfiles) and (reltemp <= 1.5 * relerr) then begin bestslope := slope[Numfiles]; bestErrorlnSlope := Errorlnslope[Numfiles]; writeln('chose this one for', j ) ; end; end; T2 := -1 / bestslope; ErrorInT2 := Abs(bestErrorlnSlope * T2 / bestslope); end; (********************* (*This procedure starts the T2 calculation. It asks for an *) (*outfile name and then c a l l s on other procedures to do the *) (•calculation. At the end, i t writes the T2 data to the o u t f i l e *) (****************************** procedure CalcT2 (Numpoints, Numfiles: integer; stTE: value; var Combined: b u i l t ) ; var j , n: integer; temp, temp2: real; NewName, SaveT2: string; o u t f i l e : text; T2, ErrorInT2: real; begin Writeln; Writeln('You w i l l be asked to enter in the name of the'); Writeln( ' file to save the T2 data. Hit Return to continue.'); 188 Readln; NewName := Newfilename(SaveT2); Open(outfile, NewName); for j := 1 to Numpoints do begin for n := 1 to Numfiles do begin temp := Ln(Combined[j, n]); Combined[j, n] := temp; end; T2fromSlope(Numfiles, j , Combined, stTE, T2, ErrorInT2); Combined [ j , 1] := T2; Combined[j, 2] := ErrorInT2; for n := 3 to Numfiles do Combined[j, n] := 0; Writeln(outfile, Combined[j, 0] : 10 : 5, ' ', Combined [ j , 1] : 10 : 5, ' ', Combined [ j , 2] : 10 : 5); end; Close(outfile); end; (•Main program. Asks for various parameters and does some •) (•checking for responses. Starts the reading in and building •) (•of the dataset array and then ca l l s for CalcT2. •) begin ShowText; (•Requests various parameters^) Writeln; WritelnCPlease enter the number of data points'); Writeln(' ( i . e . the TD value from the experiment)'); Readln(Numpoints); Writeln; writeln('Please enter in the Hertz/cm conversion factor.'); Writeln('(Enter 1 for no conversion)'); Readln(Hertzpercm); Writeln; Writeln('Enter the zero position in Hz.'); Writeln('(Enter 0 for no change in the data.)'); Readln(FreqofZero); Writeln; Writeln('Hit Return to continue'); Readln; (•routine to verify that the entered values are correct^) GoAgain := True; 189 while GoAgain = True do begin Writeln; Writeln('Here are the values that you entered'); Writeln('You may change them i f you w ish'); Writeln; Writeln('l Number of data points = ', Numpoints : 2); Writeln('2 Hertz/cm conversion factor = ', Hertzpercm : 10 : 5); Writeln('3 Frequency of Zero = ', Freqofzero : 10 : 5) ; Writeln; Writeln('Are these values correct?'); repeat Writeln('Enter Y for yes and N for no and then Return'); Readln(test); u n t i l test in ['y', 'Y', 'N', 'n']; while test in ['N', 'n'] do begin Writeln; Writeln('Enter the number of the parameter you wish to change'); repeat Writeln('Numbers go from 1 to 4.'); Readln(i); u n t i l i in [1..3] ; case i of 1: begin ' Writeln('Number of data points = '); Readln(Numpoints); end; 2: begin Writeln('Hertz/cm conversion factor Readln(Hertzpercm); end; 3: begin Writeln('Frequency of Zero = '); Readln(Freqofzero); end; end; Writeln; Writeln('All a l l the values correct?'); repeat Writeln('Enter Y for yes and N for no, then Return'); Readln(test); u n t i l test in ['Y', 'y', 'N', 'n'] ; end; •requests the number of image f i l e s in the TE dataset*) Writeln; Writeln('How many f i l e s do you have to analyse?'); 190 Writeln('(The maximum is set at ', Maxnumfiles : 2, ' ) ' ) ; Readln(Numfiles); Writeln; while Numfiles > Maxnumfiles do begin Writeln; Writeln('You cannot exceed the Maximum number of f i l e s '( Maxnumfiles : 2, ' )!'); Writeln; Writeln('Please enter in a new number of f i l e s . ' ) ; Readln(Numfiles); end; Writeln; Writeln('All your f i l e s w i l l be opened now. Hit Return to continue.'); Readln; (*opens f i l e s using the Macintosh ' f i l e open' window*) for i := 1 to Numfiles do begin Name[i] := Oldfilename(Menu); Open(Inf i l e [ i ] , Name[i]); end; Writeln; Writeln; Writeln('The indicated f i l e s have been opened.'); (*requests the TE value for each f i l e * ) Writeln; writeln('Please enter the time-to-echo (TE in ms)'); Writeln('for each of the f i l e s as indicated.'); Writeln; i := 0; for i := 1 to Numfiles do begin Write('Filename: ', Name[i], ' TE(ms) = ' ) ; Readln(TE[i]); end; Writeln; (*check for correct TE values*) Writeln; i := 0; for i := 1 to Numfiles do Writeln(i : 1, ' F i l e : ', Name[i] , TE(ms) = ' , TE[i] : 3 : 2) ; writeln; Writeln('Are a l l the values correct?'); repeat Write('Enter either Y for yes or N for no, then Return '); Readln(test); u n t i l test in ['Y', 'y', 'N', 'n']; 191 case test of 'Y\ 'y>: Check := true; 'N\ 'n': Check := false; end; i f Check = false then repeat for i := 1 to Numfiles do Writeln(i : 2, ' F i l e : ', Name[i], ' TE(ms) = ' , TE[i] : 3 : 2) ; Writeln; Writeln('Enter the number of the f i l e you wish to change.'); repeat Writeln('Numbers go from 1 to ' , Numfiles : 2); Readln(i); u n t i l i in [1..Numfiles]; Writeln('File:', Name[i], ' TE(ms) = '); "Readln (TE[i]) ; Writeln; Writeln('Are a l l the values correct now?'); repeat Writeln('Enter Y for yes and N for no and then Return'); Readln(test); u n t i l test in ['Y', 'y', 'N', 'n']; case test of 'Y', 'y': Check := true; 'N', 'n': Check := false; end; u n t i l Check = true; (•starts the T2 calculation*) writeln; writeln ( ' CALCULATING . PLEASE WAIT ' ) ; for i := 1 to Numfiles do begin Readfile(Numpoints, i , freq, i n t ) ; Convert(Numpoints, Hertzpercm, FreqofZero, freq); Buildarray(Numpoints, i , Numfiles, TE, freq, int, sortedTE, Combined); end; CalcT2(Numpoints, Numfiles, sortedTE, Combined); 192 for i := 1 to Numfiles do Close ( I n f i l e [ i ] ) ; Writeln; Writeln ('Do you want to analyse another set o f ) ; Writeln('files with the same parameters?'); Writeln; repeat Writeln('Enter Y for yes or N for no, then Return'); Readln(test); u n t i l test in C'Y', 'y', 'N', 'n'] ; case test of 'Y', 'y': GoAgain := true; 'N', 'n': GoAgain := false; end; end; end. A . 5 Correcting Image Intensity for T 2 Dephasing T h e T2 d i s t r i b u t i o n c a l c u l a t e d i n A p p e n d i x A . 4 w a s u s e d t o c o r r e c t t h e i n t e n s i t i e s o f t h e i m a g e a c q u i r e d f o r d e p h a s i n g d u e t o T 2 r e l a x a t i o n d u r i n g t h e T E t i m e . T h e f o l l o w i n g p r o g r a m , w r i t t e n a n d r u n i n S y m a n t e c ' s T H I N K P a s c a l v e r s i o n 4 . 0 o n a M a c i n t o s h L C 4 7 5 , p e r f o r m s t h e c a l c u l a t i o n a n d a l s o a l l o w s f o r s c a l i n g o f t h e i n t e n s i t i e s . program Correct_for_T2; var i n f i l e l , i n f i l e 2 , o u t f i l e : text; Menu, Namel, Name2, NewName: string; i , Numpoints: integer; GoAgain: boolean; T2, ErrorInT2, TE, position, intensity, newintensity, error: real; errT2squared, errlntensitysquared, errlnt, Maxlnt: r e a l ; x: char; begin GoAgain := true; (•requests various parameters*) Writeln('Enter the number of points'); Readln(Numpoints); Writeln; Writeln('What i s the TE value in ms?'); Readln(TE); Writeln; 193 Writeln('Enter in the experimental error in the intensity'); Readln(errlnt); Writeln('Enter in the maximum intensity'); Readln(Maxlnt); (*Main calculation procedure that opens the T2 f i l e and the image*) ( * f i l e to be corrected, performs the correction calculation*) (*and writes the corrected intensities to a new f i l e * ) repeat Writeln('You w i l l be asked to open the T2 f i l e . ' ) ; Namel := Oldfilename(Menu); Writeln('Now open the image f i l e to be corrected'); Name2 := Oldfilename(Menu); (•modified filename for output*) NewName := Concat(Name2, ' corrected'); Open(infilel, Namel); 0pen(infile2, Name2); Open(outfile, NewName); error := 0; for i := 1 to Numpoints do begin (*The image f i l e s t i l l has position in terms of frequency but*) (*the T2 f i l e has the calculated distance. The f i l e s are read*) (*in this order to pass the calculated distances to the*) (*image f i l e with the corrected intensities*) Readln(infile2, position, intensity); Readln(infilel, position, T2, ErrorInT2); (•Scaling to the maximum intensity*) intensity := intensity / Maxlnt; errlnt := errlnt / Maxlnt; (*the following corrects for signal loss due to T2*) newintensity := intensity * Exp(TE / T2); errT2squared := (ErrorInT2 * ErrorInT2) * (intensity * TE * Exp(TE / T2) / (T2 * T2)) * (intensity * TE * Exp(TE / T2) / (T2 * T2)); errlntensitysquared := (errlnt * errlnt) * (Exp(TE / 12)) * (Exp(TE / T2)); error := Sqrt(errT2squared + errlntensitysquared); Writeln(outfile, position : 10 : 5, ' ', newintensity : 5 : 5, ' ', error : 5 : 5); end; C l o s e ( i n f i l e l ) ; Close(infile2); Close(outfile); writeln('Would you like to repeat for another f i l e ? ' ) ; Readln(x); i f x in ['n', 'N'] then GoAgain := false; 194 u n t i l GoAgain = false; end. A . 6 C a l c u l a t i n g P o l y m e r W e i g h t P e r c e n t D i s t r i b u t i o n s f r o m T 2 D i s t r i b u t i o n s T h e f o l l o w i n g p r o g r a m , w r i t t e n a n d r u n i n S y m a n t e c ' s T H I N K P a s c a l v e r s i o n 4 . 0 o n a M a c i n t o s h L C 4 7 5 , r e q u e s t s t h e c o e f f i c i e n t s f r o m t h e n o n - l i n e a r l e a s t - s q u a r e s f i t e q u a t i o n s t h a t d e s c r i b e t h e d e p e n d e n c e o f t h e r e l a x a t i o n t i m e T 2 o n t h e p o l y m e r w e i g h t p e r c e n t . T h e f i t e q u a t i o n i s t h e n u s e d t o c a l c u l a t e t h e p o l y m e r w e i g h t p e r c e n t d i s t r i b u t i o n f o r t h e s y s t e m a t t h a t s w e l l i n g i n t e r v a l . program Calcpolymerpercent; const Maxnumfiles = 100; Maxnumpoints = 256; type namestring = array[1..Maxnumfiles] of string[200]; data = array[1..Maxnumpoints] of real; var alpha, beta, gamma, delta, epsilon: real; Distance, T2, errT2, Poly, errPoly: data; Name: namestring; Menu: string[200]; Numfiles, Numpoints, k: integer; (**********************************^ (•Reads in the coefficients of the non-linear least-squares f i t *) (•equations for the T2 dependence on polymer concentration *) (*****************************^  procedure GetCoefficients (var a, b, c, d, e: real ) ; begin Writeln('The following equations w i l l be used to calculate the'); Writeln('polymer concentration and the error in the polymer concentration'); Writeln; Writeln('polymer0/, = a Exp(-b T2) + c Exp(-d T2) + e'); Writeln; Writeln(' (err polymer °/„)"2 = (err T2)"2{- a b Exp(-b T2) + (- c d Exp(-d T2))}~2'); Writeln; Writeln('Please enter the in values for a, b, c, d, and e.'); Write('a= ' ) ; Readln(a); Write('b= ' ) ; Readln(b); Write('c= ' ) ; 195 Readln(c); Write('d= ' ) ; Readln(d); Write('e= ' ) ; Readln(e); Writeln; end; (****************************************************************) (•Gets a l i s t of f i l e names to process using the Macintosh ' f i l e * ) (*open' window. *) (****************************************************************^ procedure Getfilenames (var NName: namestring; MMenu: string; var NNumfiles: integer); var i : integer; begin Writeln('How many f i l e s w i l l be opened?'); Readln(NNumfiles); i := 0; for i := 1 to NNumfiles do NNameCi] := Oldfilename(MMenu); end; (****************************************************************) (*Reads in a T2 f i l e *) procedure Readfile (Name: namestring; i : integer; Numpoints: integer; var Distance, T2, errT2: data); var j : integer; i n f i l e : text; begin Open(infile, Name[i]); for j := 1 to Numpoints do begin Read(infile, Distance[j]); Read(infile, T2[j]); Readln(infile, errT2[j]); end; C l o s e ( i n f i l e ) ; end; (****************************************************************) (•Uses the f i t equations to calculate the weight percent and error*) (****************************************************************) procedure Calculate (TT2, errTT2: data; var PPoly, errPPoly: data; a, b, c, d, e: real; Numpoints: integer); var j : integer; begin j := 0; for j := 1 to Numpoints do begin PPoly [j] := a * Exp(-b * TT2[j]) + c * Exp(-d * TT2[j] + e) ; 196 errPPoly[j] := errTT2[j] * errTT2[j] * (a * b * Exp(-b * TT2[j]) + c * d * Exp(-d * TT2[j])) * (a * b * Exp(-b * TT2[j]) + c * d * Exp(-d * TT2[j])); errPPolyCj] := Sqrt(errPPoly[j] ); end; end; (******* (•Outputs the polymer weight percent results *) (********************* procedure Writefile (NName: namestring; Numpoints, i : integer; DDistance, PPoly, errPPoly: data); var j : integer; o u t f i l e : text; tempName: string; begin j := 0; tempName := concat(Name[i] , ' poly 0/'); 0pen(outfile, tempName); for j := 1 to Numpoints do Writeln(outfile, DDistance[j] : 5 : 5, ' ' , P P o l y[j] : 5 : 5, ' ', errPPolyEj] : 5 : 5 ) ; Close(outfile); end; (•Main program that c a l l s the procedures*) begin GetCoefficients(alpha, beta, gamma, delta, epsilon); Getfilenames(Name, Menu, Numfiles); Writeln; Writeln('Enter in the number of points for each f i l e ' ) ; Readln(Numpoints); for k := 1 to Numfiles do begin Readfile(Name, k, Numpoints, Distance, T2, errT2); Calculate(T2, errT2, Poly, errPoly, alpha, beta, gamma, delta, epsilon, Numpoints); Writefile(Name, Numpoints, k, Distance, Poly, errPoly); end; end. 197 A p p e n d i x B C a l c u l a t i n g T h e o r e t i c a l C o n c e n t r a t i o n D i s t r i b u t i o n s B . l Calculation of Error Function Values T h e v a l u e o f t h e e r r o r f u n c t i o n , e r f ( x ) , i s n e c e s s a r y f o r c o m p u t i n g c o n c e n t r a t i o n d i s t r i b u -t i o n s f r o m E q u a t i o n s 6 .7 a n d 6 .8 . T a b u l a t e d v a l u e s o f t h e e r r o r f u n c t i o n a r e a v a i l a b l e i n t h e l i t e r a t u r e [84]. T a b l e B . l l i s t s t h e e r r o r f u n c t i o n v a l u e s f o r p o s i t i v e v a l u e s o f x . T h e e r r o r f u n c t i o n f o r n e g a t i v e v a l u e s o f x a r e t h e n e g a t i v e o f t h o s e f o r p o s i t i v e x , i.e. e r f ( — x ) = — e r f ( x ) . A p r o c e d u r e w a s d e v e l o p e d t o i n t e r p o l a t e b e t w e e n t h e v a l u e s l i s t e d i n t h e t a b l e s o t h a t t h e v a l u e o f t h e e r f ( x ) c o u l d b e d e t e r m i n e d f o r a n y x . T h e i n t e r p o l a t i o n m e t h o d u s e d f o r t h e c a l c u l a t i o n s o f t h i s t h e s i s i n v o l v e d d e t e r -m i n i n g c o e f f i c i e n t s f o r c u b i c s p l i n e s t h a t w o u l d d e f i n e d i f f e r e n t s e g m e n t s o f t h e d a t a i n T a b l e B . l . T h e p o i n t s t h a t d e f i n e t h e e n d p o i n t s f o r e a c h s e g m e n t a r e a s s u m e d t o b e t w o p o i n t s j o i n e d b y a c u b i c e q u a t i o n , r e s u l t i n g i n t h e set o f f o u r s i m u l t a n e o u s e q u a t i o n s , B . l t o B . 4 , w h e r e y,- i s t h e e r f ( x 8 ) , w,- i s t h e d e r i v a t i v e o f y,-, a n d a , b , c , a n d d a r e t h e u n k n o w n c o e f f i c i e n t s o f t h e c u b i c e q u a t i o n . T h e c o e f f i c i e n t s a r e d e t e r m i n e d b y s o l v i n g t h e se t o f s i m u l t a n e o u s e q u a t i o n s . T h e s o l u t i o n s , o b t a i n e d b y m a t r i x i n v e r s i o n i n M a t h e m a t i c a , a r e g i v e n i n E q u a t i o n B . 5 . yi = ax3 + bx\ + cxi + d ?/2 = ax3, + bx\ + CX2 + d Wi = Zax\ + 2bxi + c W2 = Sax2, + 26x2 + c ( B . l ) ( B - 2 ) ( B . 3 ) ( B . 4 ) 198 T a b l e B . l : T h e v a l u e o f t h e e r r o r f u n c t i o n . X e r f ( x ) 0.00 0 0.50 0.056372 0.10 0.112463 0.15 0.167996 0.20 0.222703 0.25 0.276326 0.30 0.328627 0.35 0.379382 0.40 0.428392 0.45 0.475482 0.50 0.520500 0.55 0.563323 0.60 0.603856 0.65 0.642029 0.70 0.677801 0.75 0.711156 0.80 0.742101 0.85 0.770668 0.90 0.796908 0.95 0.820891 1.00 0.842701 1.10 0.880205 1.20 0.910314 1.30 0.934008 1.40 0.952285 1.50 0.966105 1.60 0.976348 1.70 0.983790 1.80 0.989091 1.90 0.992790 2.00 0.995322 2.10 0.997021 2.20 0.998137 2.30 0.998857 2.40 0.999311 2.50 0.999593 2.60 0.999764 2.70 0.999866 2.80 0.999925 2.90 0.999959 3.00 0.999978 199 a (xi - x2)3 b (B.5) c d - 2 2 3 ( x i + x2) -3(xi + x2) — 6 x 1 X 2 6xxx 2 X2(3xx — x 2 ) x\(xi — 3x 2 ) ( x i - x 2 ) - ( x i + 2 x 2 ) ( x i - x 2 ) x2(xx - x 2 ) ( 2 x ! + x 2 ) - X i X ^ X i - x 2 ) (xi - x2) - ( 2 x i + x 2 ) ( x x - x 2 ) X i ( x i - x 2 ) ( x i + 2x 2 ) —x\x2(xi — x2) L w2 J yi The program Quadfit was written to determine the coefficients for an arbitrary number of cubic spline interpolations to the error function values. The program was written in Symantec's Think Pascal and run on a Macintosh LC475. The error function for values of x from -3 to +3 were divided into 12 segments and a set of 12 equations were generated to calculate the erf(x) for any value of x. The interpolated values agreed wi th the tabulated values to the fourth decimal place which was a sufficient accuracy for the calculations of this thesis. program Quadfit; type data = array[1..100] of real; coeff = array[1..30] of real; var i n f i l e , o u t f i l e : text; Name, Save, Menu: string; i , j , subdiv: integer; incr, factor: real; x l , x2, y l , y2, wl, w2: real; a, b, c, d: coeff; xpoints, ypoints: data; procedure Searchy (x: real; var y: real; xpts, ypts: data); var k: integer; begin k := 0; repeat k := k + 1; u n t i l xpts[k] = x; y := yptsCk] ; end; procedure Calcderiv (x: real; var w: real); 200 begin w := (2 / Sqrt(Pi)) * Exp(-x * x); end; begin Writeln('This program i s spe c i f i c a l l y written to'); Writeln('fit the erf in the region -3 tb +3'); Writeln('You w i l l be asked to open the appropriate f i l e . ' ) ; Writeln('Hit Return to continue'); Readln; Name := Oldfilename(Menu); Open(infile, Name); for i := 1 to 81 do begin Read(infile, xpoints[i]); Read(infile, ypoints[i]); i f i < 81 then Readln(infile); end; Writeln('How many subdivisions for the quadfit?'); Readln(subdiv); Writeln('You w i l l be asked for a filename to save the data as'); Writeln('File format w i l l be:number of subdivisions followed by the'); Writeln('coefficients for the same number of cubic equations.'); Writeln('Hit Return to continue.'); Readln; Save := Newfilename(Menu); Open(outfile, Save); Writeln(outfile, subdiv); incr := 6 / subdiv; x l := -3; x2 := xl + incr; for j := 1 to subdiv do begin Searchy(xl, y l , xpoints, ypoints); Searchy(x2, y2, xpoints, ypoints); Calcderiv(xl, wl); Calcderiv(x2, w2); Factor := 1 / ((xl - x2) * (xl - x2) * (xl - x2)); a[j] := Factor * (-2 * y l + 2 * y2 + (xl - x2) * (wl) + (xl - x2) * (w2)); b[j] := Factor * (3 * (xl + x2) * y l - 3 * (xl + x2) * y2 - (xl + 2 * x2) * (xl - x2) * wl - (2 * xl + x2) * (xl - x2) * w2); c[j] := Factor * (-6 * xl * x2 * y l + 6 * xl * x2 * y2 + x2 * (xl - x2) * (2 * xl + x2) * wl + x l * (xl - x2) * (xl + 2 * x2) * w2); d[j] := Factor * (x2 * x2 * (3 * xl - x2) * y l 201 + x l * x l * (xl - 3 * x2) * y2 - x l * x2 * x2 * (xl - x2) * wl - x l * xl * x2 * (xl - x2) * w2); Writeln(outfile, a[j] : 5 : 6, ' ', b[j] : 5 : 6, c[j] : 5 : 6, ' \ d[j] : 5 : 6); xl := x2; x2 := x2 + incr; end; C l o s e ( i n f i l e ) ; Close(outfile); end. B.2 Fickian Distributions T h e t h e o r e t i c a l d i s t r i b u t i o n s o f S e c t i o n 6 .4 .1 w e r e c o m p u t e d u s i n g t h e f o l l o w i n g p r o g r a m w r i t t e n i n S y m a n t e c ' s T h i n k P a s c a l a n d r u n o n a M a c i n t o s h L C 4 7 5 . T h e p r o g r a m u s e s t h e c u b i c e q u a t i o n s d e t e r m i n e d i n S e c t i o n B . l t o i n t e r p o l a t e b e t w e e n t h e v a l u e s o f e r f ( x ) g i v e n i n T a b l e B . l a l l o w i n g f o r t h e r a p i d c a l c u l a t i o n o f c o n c e n t r a t i o n s d i s t r i b u t i o n s b a s e d o n E q u a t i o n s 6 .7 o r 6 .8 . T h e p r o g r a m l i s t i n g h e r e i s s p e c i f i c f o r t h e c a s e o f d i f f u s i o n i n t o a l i m i t e d r e g i o n b u t t h e s a m e p r o g r a m c a n b e u s e d f o r t h e c a s e o f d i f f u s i o n o u t o f a l i m i t e d r e g i o n b y s u b s t i t u t i n g E q u a t i o n 6 .7 i n p r o c e d u r e C a l c D i f f . program Diffusion_Curve; type dataarray = array[1..2, 1..128] of real; theoretical = array[l..2, 1..1000] of real; manyl = array[0..9] of string[1]; many2 = array[0..99] of string[2]; coeff = array[1..50] of real; var e x t l : manyl; ext2: many2; incr, D i f f , diner, xprimel, xprime2: real; denom, e r f l , erf2, chi2: real; subdiv, dnum: integer; a, b, c, d: coeff; x, cone, time, thickness, temp: real; segment: real; numpoints, n, m, j , k: integer; data: dataarray; diffcurve, swelled: theoretical; rootname, filename, period: string; 202 (•Require the values of erf(x) to compute the diffusion curves. *) (•Previously computed values of erf(x) are available in tables. •) (•The previously determined cubic splines are incorporated in •) (•this program so that the erf of any value can be rapidly •) (•determined. •) (****************************^  procedure Coefficients (var sd: integer; var aa, bb, cc, dd: coeff); begin (•number of cubic splines used in the interpolation^) sd := 12; (•Coefficients for each cubic spline+) aa[l] = 0.00311; bb[l] = 0.0277; cc[l] = 0.082357; dd[l] = -0.918224; aa[2] = 0.023045; bb [2] = 0.17404; cc[2] = 0.440291; dd [2] = -0.626543; aa [3] = 0.090917; bb [3] = 0.575578; cc [3] = 1.231973; dd [3] = -0.10635; aa[4] 0.161688; bb[4] = 0.902506; cc[4] = 1.735056; dd [4] = 0.151537; aa[5] = 0.020344; bb [5] = 0.509449; cc [5] = 1.372974; dd[5] = 0.041168; aa[6] = -0.299353; bb[6] = 0.025082; cc [6] = 1.128379; dd[6] = 0; aa[7] = -0.299353; bb [7] = -0.025082; cc[7] = 1.128379; dd [7] = 0; aa[8] 0.020344; bb [8] = -0.509449; cc[8] = 1.372974; dd [8] = -0.041168; aa[9] 0.161688; bb[9] : = -0.902506; cc[9] ; = 1.735056; 203 dd[9] : = -0 .151537; aa[10] = 0 .090917; bb[10] - - 0.575578; cc[l0] = 1 .231973; dd[10] = 0 .10635; aa[ll] = 0 .023045; bb[ll] = -0.17404; c c [ l l ] = 0 .440291; dd[ll] = 0 .626543; aa[12] ZZ 0 .00311; bb[l2] ZZ -0.0277; cc[12] = 0 .082357; dd[12] = 0 .918224; end; (********************************^ (•Computes extension strings from 000 to 999 for output f i l e s *) procedure Extensionstrings (var e l : manyl; var e2: many2); var i , j , k: integer; Period: string; begin (*The following prepares arrays to compute*) (* f i l e extensions from 000 to 999 *) for i := 0 to 9 do el [ i ] := Chr(i + 48); (* Ord('O') = 48, 0rd('9') = 57 for the Mac LC475*) k := 0; for i := 0 to 9 do for j := 0 to 9 do begin e2[k] := concat(el[i] , e l [ j ] ) ; k := k + 1; end; end; (********************************^ (•Determines in which segment the distance xx belongs, the cubic*) (•spline for the erf calculation and returns the value of erf(xx)*) function Quad_erf (xx: real; sdv: integer; aaa, bbb, ccc, ddd: coeff): real; var step: r e a l ; lowerlevel, upperlevel: real; j : integer; begin i f (xx < -3) or (xx > 3) then begin i f xx < -3 then 204 quad_erf := -1.0; i f xx > 3 then Quad_erf := 1.0; end else begin step := 6 / sdv; * j := i ; lowerlevel := -3; upperlevel := lowerlevel + step; while upperlevel <= 3 do begin i f (xx >= lowerlevel) and (xx <= upperlevel) then begin Quad_erf := aaa[j] * xx * xx * xx + bbb[j] * xx * xx + ccc[j] * xx + ddd[j] ; end else j := j + i ; lowerlevel := upperlevel; upperlevel := upperlevel + step; end; end; end; (******************************** (•Asks for various parameters such as number of points and the *) (•time and the diffusion coefficients for the calculation •) (***************************^ procedure Getlnfo (var g i d i f f , gidincr, gitime, githick: r e a l ; var ginum, gidnum: integer; var gidata: dataarray; var giname: string); var Name, Menu: string; j : integer; tempi, temp2, temp3: real; i n f i l e : text; begin Writeln('This program calculates a water distribution assuming Fickian diffusion'); Writeln; Writeln('Enter in the number of points in the distribution'); Readln(ginum); Writeln; Writeln('Enter i n : start value for diffusion coefficient (space) increment (space) # increments'); Readln(gidiff, gidincr, gidnum); Writeln; Writeln('Enter in the original thickness of the tablet'); Readln(githick); Writeln('Enter in the time in seconds for the f i l e you are about 2 0 5 to o p e n ' ) ; R e a d l n ( g i t i m e ) ; Name := Oldfilename(menu); 0 p e n ( i n f i l e , Name); f o r j := 1 to ginum do beg in R e a d l n ( i n f i l e , t empi , temp2, temp3); (*temp3 i s the e r r o r * ) i f tempi > 0 then begin g i d a t a [ l , j ] := tempi; (*distance*) g i d a t a [ 2 , j ] := temp2 end; end; W r i t e l n ( ' E n t e r i n the rootname f o r the saved f i l e s . H i t R e t u r n ' ) Readln; giname := Newfilename(menu); end; (*********************************^ ( • C a l c u l a t e s the concentra t ion d i s t r i b u t i o n based on F i c k i a n *) (* into a l i m i t e d r e g i o n f o r the water d i s t r i b u t i o n s or out of a *) ( • l i m i t e d r e g i o n f o r the polymer and drug d i s t r i b u t i o n s *) (**************************^ procedure C a l c D i f f ( c d D i f f , cdt ime, c d t h i c k , cdsegment: r e a l ; cdsubdiv: i n t e g e r ; var c d d i f f c u r v e : t h e o r e t i c a l ; aa , bb, c c , dd: c o e f f ) ; var denom, x, x p r i m e l , e r f l , xprime2, e r f 2 , Co: r e a l ; i : i n t e g e r ; beg in C o : = l ; (*for normal ized water concentrat ions*) denom := S q r t ( 4 * c d D i f f * cdt ime); x := .0; i := 1; repeat beg in x p r i m e l := ( cd th i ck - x) / denom; e r f l := Quad_erf (xpr imel , cdsubdiv , aa , bb, c c , dd) ; xprime2 := ( c d t h i c k + x) / denom; er f2 := Quad_erf(xprime2, cdsubdiv , aa , bb, c c , dd) ; ( •d i s tance*) c d d i f f c u r v e [ l , i ] := x; ( • c o n c e n t r a t i o n f o r the dis tance*) c d d i f f c u r v e [ 2 , i ] := 0.5 * Co * ((1 - e r f l ) + (1 - e r f 2 ) ) ; (*would use c d d i f f c u r v e [ 2 , i ] := 0.5 * Co * ( e r f l + erf2) f o r * ) ( • d i f f u s i o n out of a l i m i t e d region*) x := x + cdsegment; i := i + 1; end; u n t i l x > 1; end; (*******************************^ (•Compares the t h e o r e t i c a l and a c t u a l d i s t r i b u t i o n s and computes*) 206 (•the values of chi2 *) procedure Compare (compnum: integer; cdiffcurve: theoretical; csegment: double; cdata: dataarray; var cchi2: double); var i , j : integer; m, b, cdtest: double; test: boolean; begin cchi2 := 0; cdtest := 0; test := false; for i := 1 to compnum do begin j := 0; repeat j := j + i ; i f (cdata[l, i] >= cdiffcurve[l, j]) and (cdata[1, i] <= cdiffcurve[1, j + 1]) then begin test := true; m := (cdiffcurve[2, j] - cdiffcurve[2, j + 1]) / (cdiffcurve[1, j] - cdiffcurve[1, j + 1]); b := c d i f f curve[2, j] - m • cdif f curved, j] ; cdtest := m • cdata[l, i] + b; end else test := false; u n t i l test = true; cchi2 := cchi2 + (cdata[2, i] - cdtest) • (cdata[2, i] - cdtest); end; end; (************************^ (•Outputs the theoretical concentrations distribution and the •) (•value of the diffusion coefficient and resulting chi2 of the •) (•comparison between the experimental and theoretical distributions^) procedure WriteFile (wfname: string; wfsegment: real; wfdiffcurve: theoretical; wfdiff, wfchi2: r e a l ) ; var k: integer; tempname: string; o u t f i l e : text; temp: re a l ; begin 0pen(outfile, wfname); Writeln(outfile, ' ' ', wfdiff : 10 : 10, ' \ wfchi2 : 10 : 10); k := 1; temp := 0; repeat Writeln (outfile, wfdiff curved, k] : 3 : 3, ' wfdiffcurve[2, k] : 3 : 3); k := k + 1; 207 temp := temp + wfsegment; until temp > 1; Close(outfile); end; (•Main program that c a l l s the procedures • ) (************************** begin (•the following setup various arrays that w i l l be used in the •) (•calculations and the outputting of the data files+) Coefficients(subdiv, a, b, c, d); Extensionstrings(extl, ext2); (•require various parameters to perform the calculation^) Getlnfo(Diff, diner, time, thickness, numpoints, dnum, data, rootname); j := 0; k := 0; period := '. ' ; segment := 0.005; (•loop for incrementing the diffusion coefficient+) for n := 1 to dnum do begin (•calculates the theoretical concentration distribution^) CalcDiff(Diff, time, thickness, segment, subdiv, diffcurve, a, b, c, d); (•determines the chi2 valued) Compare(numpoints, diffcurve, segment, data, chi2); (•increments the extension counters for the output file+) i f j = 99 then begin k := k + 1; j := - i ; end; j := j + i ; (•outputs data to the f i l e and to the screen^) filename := concat(rootname, period, extl[k], ext2[j]); Writeln(filename : 50, ' ', Diff : 12 : 12, ' \ chi2 : 10 : 10); WriteFile(filename, segment, diffcurve, D i f f , chi2); (•increments the diffusion coeff ic ientO D i f f := Diff + diner; end; end. 208 B.3 Segmented Tablet Model T h e t h e o r e t i c a l d i s t r i b u t i o n s o f S e c t i o n 6 . 4 . 2 w e r e c o m p u t e d u s i n g t h e f o l l o w i n g p r o g r a m w r i t t e n i n S y m a n t e c ' s T h i n k P a s c a l a n d r u n o n a M a c i n t o s h L C 4 7 5 . T h e p r o g r a m c a l -c u l a t e s t h e t h e o r e t i c a l w a t e r d i s t r i b u t i o n i n t o t h e d r y t a b l e t u s i n g E q u a t i o n 6 .9 a n d t h e n d e t e r m i n e s t h e d e g r e e o f s w e l l i n g f o r e a c h s e g m e n t , t h e n e w p o s i t i o n o f e a c h s e g m e n t a n d t h e r e s u l t i n g p o l y m e r w e i g h t p e r c e n t c o n c e n t r a t i o n f o r t h e s e g m e n t u s i n g E q u a t i o n s 6 .12 a n d 6 . 1 3 . A n i n i t i a l p o l y m e r c o n c e n t r a t i o n o f 9 7 % ' e n s u r e d t h a t t h e r e s u l t i n g d i s t r i b u t i o n c o n t a i n e d 166 m g o f p o l y m e r r e g a r d l e s s o f t h e d e g r e e o f s w e l l i n g . T h e f a c t o r f o r t h e s w e l l i n g i s i n c l u d e d i n p r o c e d u r e s S w e l l i n g a n d D o S u m a n d c a n b e e a s i l y m o d i f i e d . program cone; type dataarray = array[1..2, 1..128] of double; theoretical = array[1..2, 1..800] of double; manyl = array[0..9] of string[1]; many2 = array[0..99] of string[2]; coeff = array[1..50] of double; var e x t l : manyl; ext2: many2; thickness, time: double; d i f f , d i f f i n c r , distincr, dtemp: double; alpha, alphaincr, atemp: double; chi2: double; diffcurve, swelled: theoretical; numpoints, diffnum, alphanum: integer; a, d, j , k, rat i o : integer; rootname, filename, period: string; data: dataarray; (**********************************^ (•prepares arrays to compute f i l e extensions from 000 to 999 *) (**********************************^  procedure Extensionstrings (var e l : manyl; var e2: many2); var i , j , k: integer; Period: string; begin for i := 0 to 9 do e l [ i ] := Chr(i + 48); (* Ord('O') = 48, 0rd('9') = 57 for the Mac LC475*) k := 0; for i := 0 to 9 do for j := 0 to 9 do begin e2[k] := concat(el [i] , e l [ j ] ) ; k := k + 1; 2 0 9 end; end; (•Reads in the various parameters required for the calculations *) (**************************^  procedure Getlnfo (var g i d i f f , gidincr, gialpha, giaincr, gitime, githick: double; var ginum, gidnum, gianum: integer; var gidata: dataarray; var giname: string); var Name, Menu: string; j : integer; tempi, temp2, temp3: double; i n f i l e : text; begin Writeln('This program calculates a water distribution assuming Fickian diffusion'); Writeln('and then uses i t to calculate the swelling of the polymer' Writeln; Writeln('Enter in the number of points in the distribution'); Readln(ginum); Writeln; Writeln('Enter in the water diffusion coefficient, the increment and the number of increments'); Readln(gidiff, gidincr, gidnum); Writeln; Writeln('Enter in the alpha factor, alpha increment and number of increments'); Readln(gialpha, giaincr, gianum); Writeln; Writeln('Enter in the original thickness of the tablet'); Readln(githick); Writeln; Writeln('Enter in the time in seconds for the f i l e you are about to open'); Readln(gitime); Name := Oldfilename(menu); Open(infile, Name); for j := 1 to ginum do begin Readln(infile, tempi, temp2, temp3); (*temp3 i s the error*) i f tempi > 0 then begin gidata[l, j] := tempi; (•distance^) gidata[2, j] := temp2 end; end; Writeln('Enter in the rootname for the saved f i l e s . Hit Return'); Readln; giname := Newfilename(menu); end; (*****************************^ (•Calculates the theoretical water distribution •) (***************************** 210 procedure Calculation (hh, t t , DD, xincr: double; var tempresults: theoretical; cratio: integer); var x, incr, tempi, temp2, temp3, BigSum, cone, water: double; m, n, posneg, points: integer; begin x := xincr; m := 0; repeat Bigsum := 0; m : = m + 1; (•the sum converged before n=10 under the conditions of *) (*the experiments in this thesis*) for n := 0 to 10 do begin i f n mod 2 = 0 then posneg := 1 else posneg := -1; tempi := posneg / (2 * n + 1); temp2 := cos((2 * n + 1) * Pi * x / (2 * hh)); temp3 := exp(-(2 * n + 1) * (2 * n + 1) * Pi * Pi * dd * t t / (4 * hh * hh)); Bigsum := (tempi * temp2 * temp3) + Bigsum; end; cone := 1 - (4 / Pi) * Bigsum; tempresults[1, m] := x; tempresults[2, m] := cone; x := x + xincr; u n t i l m = cratio; end; (•Performs the sum of the previous segment swellings to compute *) (*the new distance for the current segment *) function DoSum (dssegment, dsalpha: double; d s i : integer; dsdiffcurve: theoretical): double; var m: integer; Sum: double; begin Sum := 0; m := 0; repeat m : = m + 1; Sum := Sum + dssegment * ((dsalpha/ (1 - dsdiffcurve[2, m])) - 1) u n t i l m = dsi; DoSum := Sum; end; ( * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^ (•Calculates the new distance and concentration for each segment*) (*based on the theoretical concentration of water *) 211 procedure Swell (sratio: integer; ssegment, salpha: double; sdiffcurve: theoretical; var sswelled: theoretical); var j : integer; sfactor: double; begin j := 0; repeat j := j + 1; sswelled[1, j] := sdiffcurve[1, j] + DoSum(ssegment, salpha, j , sdiffcurve); sswelled[2, j] := 97 * (1 - sdiffcurve[2, j]) / salpha; u n t i l j = sratio; end; (***************************^ (•Compares the theoretical and actual distributions and computes*) (*the values of chi2 *) (********* procedure Compare (compnum: integer; cdswelled: theoretical; csegment: double; cdata: dataarray; var cchi2: double); var i , j : integer; m, b, cdtest: double; test: boolean; begin cchi2 := 0; cdtest := 0; test := false; for i := 1 to compnum do begin j := 0; repeat j := j + i ; i f (cdataCl, i] >= cdswelledCl, j]) and (cdata[l, i] <= cdswelled[l, j + 1]) then begin test :=' true; m := (cdswelled[2, j] - cdswelled[2, j + 1]) / (cdswelledCl, j] - cdswelled[1, j + 1]); b := cdswelled[2, j] - m * cdswelledCl, j ] ; cdtest := m * cdataCl, i] + b; end else test := false; u n t i l test = true; cchi2 := cchi2 + (cdataC2, i] - cdtest) * (cdataC2, i] - cdtest); end; end; (****************************** (*Writes the swelled distribution and the various parameters *) (*to an output f i l e *) (********************************^  procedure WriteFile (wfname: string; wnumpoints: integer; 212 wfswelled: theoretical; wfdiff, wfalpha, wfchi2: double); var k: integer; o u t f i l e : text; begin Open(outfile, wfname); Writeln(outfile, ' ', ' ', wfdiff : 10 : 10, ' ', wfalpha : 10 : 10, ' wfchi2 : 10 : 10); for k := 1 to wnumpoints do Writeln(outfile, wfswelled[l, k] : 8 : 8, ' wfswelled[2, k] : 6 : 6); Close(outfile); end; (********************************^ (•Main Program. Contains the counters for incrementing the values^) (•of the diffusion coefficient and the swelling factor alpha. • ) (•Calls the procedures required to calculate the theoretical •) (•water distribution and then swell the tablet according to the •) (•amount of water present and the swelling factor •) begin Extensionstrings(extl, ext2); Getlnfo(Diff, d i f f i n c r , alpha, alphaincr, time, thickness, numpoints, diffnum, alphanum, data, roptname); di s t i n c r := 0.001; period :='.'; ratio := Round(thickness / distincr) - 1; Writeln(rootname); WritelnC # ', ' Diff \ ' alpha ', ' chi2 ' ) ; d := 0; repeat dtemp := d i f f + d • d i f f i n c r ; Calculation(thickness, time, dtemp, distincr, diffcurve, r a t i o ) ; a := 0; repeat atemp := alpha + a • alphaincr; Swell(ratio, distincr, atemp, diffcurve, swelled); Compare(numpoints, swelled, distincr,.data, chi2); i f j = 99 then begin k := k + 1; j == - i ; end; j := J + i ; filename := concat(rootname, period, extl[k], ext2[j]); Writeln(concat(ext1[k], ext2[j]), ' ', dtemp : 10 : 10, ' atemp : 3 : 3, ' ', chi2 : 10 : 10); WriteFile(filename, ratio, swelled, dtemp, atemp, chi2) ; a := a + 1; un t i l a = alphanum; d := d + 1; un t i l d = diffnum; end. 213 

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