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Aspects of NMR imaging and in vivo spectroscopy Talagala, Sardha Lalith 1986

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ASPECTS OF NMR IMAGING AND IN VIVO SPECTROSCOPY by SARDHA LALITH TALAGALA B.Sc. (Hons.), U n i v e r s i t y of Peradeniya, S r i Lanka, 1977 M.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of Chemistry) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA December 1986 © Sardha L a l i t h T a l a g a l a 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 1956 Main Mall Vancouver, Canada V6T 1Y3 DF-fin/R-n i i ABSTRACT The work de s c r i b e d i n t h i s t h e s i s deals mainly w i t h aspects r e l a t e d to two- and three-dimensional NMR imaging. A d e t a i l e d d i s c u s s i o n on f r e q u e n c y - s e l e c t i v e e x c i t a t i o n u s i n g amplitude modulated r f pulses i n r e l a t i o n to s l i c e s e l e c t i o n i n NMR imaging has been presented. This i n c l u d e s the a n a l y s i s and implementa-t i o n of the method as w e l l as i l l u s t r a t i v e experimental r e s u l t s . S e v e r a l radiofrequency probe designs s u i t a b l e f o r h i g h f i e l d NMR imaging have been ex p e r i m e n t a l l y evaluated and t h e i r m o d i f i c a t i o n and c o n s t r u c t i o n are a l s o described. The comparative r e s u l t s obtained i n d i c a t e the merits and demerits of d i f f e r e n t designs and provide necessary g u i d e l i n e s f o r s e l e c t i n g the most s u i t a b l e design depending on the a p p l i c a t i o n . P r a c t i c a l aspects of two- and three-dimensional imaging have been discussed and NMR images of s e v e r a l i n t a c t systems have been presented. Experimental methods which enable s l i c e s e l e c t i o n i n the presence of c h e m i c a l l y s h i f t e d species and two-dimensional chemical s h i f t r e s o l v e d imaging have "been described and i l l u s t r a t e d u s i n g phantoms. The use of three-dimensional chemical s h i f t r e s o l v e d imaging as a p o t e n t i a l method to map the pH and temperature d i s t r i b u t i o n w i t h i n an ob j e c t has a l s o been demonstrated. A p r e l i m i n a r y i n v e s t i g a t i o n of the a p p l i c a t i o n of JJ-P NMR spectro-scopy to study the biochemical transformations of the r a t kidney during periods of ischemia and r e p e r f u s i o n has been presented. i i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES v i i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS x i i CHAPTER I: INTRODUCTION 1 1.1 Background 2 1.2 Goals and Format of t h i s Thesis 8 References 10 CHAPTER I I : NMR IMAGING TECHNIQUES 12 2.1 Bas i c Concepts 13 2.1.1 Pulse NMR 13 2.1.2 L i n e a r Magnetic F i e l d Gradient 19 2.1.3 E v o l u t i o n of Magnetization i n the Presence of Gradients 23 2.1.4 S l i c e S e l e c t i o n Methods 26 2.1.4.1 S e l e c t i v e E x c i t a t i o n 27 2.1.4.2 Other Methods 28 i v 2.2 Imaging Methods 29 2.2.1 C l a s s i f i c a t i o n and S e n s i t i v i t y of Imaging Methods 30 2.2.1.1 C l a s s i f i c a t i o n 30 2.2.1.2 S e n s i t i v i t y 32 2.2.2 P r o j e c t i o n - R e c o n s t r u c t i o n Imaging 35 2.2.3 F o u r i e r Imaging 37 2.2.4 Chemical S h i f t Resolved Imaging 47 References 51 CHAPTER I I I : FREQUENCY-SELECTIVE EXCITATION IN NMR IMAGING . . . 54 3.1 Technique of S l i c e S e l e c t i o n 55 3.1.1 Theory of S e l e c t i v e E x c i t a t i o n 55 3.1.1.1 L i n e a r System Approach 56 3.1.1.2 E f f e c t s of Nonlinear Behaviour of Spins 66 3.1.1.3 A n a l y s i s of Bloch Equations . . . . 67 3.1.2 Implementation of the Technique and Experimental R e s u l t s 87 3.2 S l i c e S e l e c t i o n i n the Presence of Chemical S h i f t s . 98 3.2.1 L i m i t a t i o n s of the Current Technique . . . . 98 3.2.2 P o s s i b l e S o l u t i o n s 101 3.2.3 Experimental Demonstration of the Proposed Method 107 3.2.4 I n c o r p o r a t i o n of Imaging and Further Extension I l l References 113 V CHAPTER IV: IMAGING RESULTS 116 4.1 Two-Dimensional Imaging 117 4.1.1 The Method 117 4.1.2 Experimental R e s u l t s 121 4.2 Three-Dimensional Imaging 133 4.2.1 The Method 133 4.2.2 Experimental R e s u l t s 136 4.3 Chemical S h i f t Resolved Imaging 141 4.3.1 Frequency-Selective E x c i t a t i o n and Suppression of S p e c i f i c Resonances 141 4.3.2 A p p l i c a t i o n s of Three-Dimensional Chemical S h i f t Resolved Imaging 148 4.4 Experimental 153 References 155 CHAPTER V: EVALUATION OF RADIOFREQUENCY PROBE DESIGNS SUITABLE FOR NMR IMAGING AT HIGH FIELDS 157 5.1 I n t r o d u c t i o n 158 5.2 Probe Requirements and A s s o c i a t e d Problems . . . . 159 5.3 E f f e c t s of Conducting Samples 164 5.4 A l t e r n a t i v e Probe Designs 167 5.5 Experimental E v a l u a t i o n of Resonator Probe Designs . 170 5.5.1 Probe C o n s t r u c t i o n 174 5.5.2 Probe E v a l u a t i o n 177 5.6 Concluding Remarks 190 v i 5.7 Experimental 191 5.7.1 Method of B x-Mapping 192 References 194 CHAPTER VI; 3 1 P NMR SPECTROSCOPY IN VIVO 197 6.1 I n t r o d u c t i o n 198 6.2 Experimental P r o t o c o l , R e s u l t s and D i s c u s s i o n . . . 200 6.3 Experimental 206 References 208 SUMMARY AND DISCUSSION 210 APPENDIX 216 v i i LIST OF TABLES Table Page 2.1 R e l a t i v e S e n s i t i v i t i e s of NMR Imaging Methods 34 5.1 C h a r a c t e r i s t i c s of D i f f e r e n t r f Probe Designs 178 5.2 90° Pulse Width (to.0°) and S/N Data Obtained Using D i f f e r e n t Probe Designs 182 5.3 B^ Inhomogeneity Parameters of D i f f e r e n t Probe Designs 189 v i i i LIST OF FIGURES Figure Page 2.1 P r e c e s s i o n of s p i n magnetization i n the presence of B Q and f i e l d s 15 2.2 Representation of a l i n e a r f i e l d g radient and the r e l a t i o n s h i p between the s p i n d e n s i t y d i s t r i b u t i o n and the NMR spectrum i n the presence of a gradient 21 2.3 E v o l u t i o n of magnetization i n the r o t a t i n g frame i n the presence of a gradient 24 2.4 S i g n a l r e f o c u s s i n g methods 25 2.5 C l a s s i f i c a t i o n of NMR imaging methods 31 2.6 P r o j e c t i o n - R e c o n s t r u c t i o n imaging method 36 2.7 The b a s i c two-dimensional imaging sequence 39 2.8 The complete spin-warp imaging sequence f o r two-dimensional s l i c e imaging 44 2.9 The b a s i c chemical s h i f t r e s o l v e d imaging sequence . . . 49 3.1 R e l a t i o n s h i p between the input and the output of a l i n e a r system 57 3.2 Normal NMR experiment viewed i n terms of the t r a n s f e r f u n c t i o n of the s p i n system 58 3.3 S e l e c t i v e e x c i t a t i o n experiment viewed i n terms of the t r a n s f e r f u n c t i o n of the s p i n system 60 3.4 Rf modulation f u n c t i o n s and t h e i r F o u r i e r transforms . . 62 3.5 E f f e c t of t r u n c a t i o n of the sine modulating f u n c t i o n on the e x c i t a t i o n spectrum 64 3.6 E f f e c t of t r i a n g u l a r a p o d i z a t i o n of the s i n e f u n c t i o n on the e x c i t a t i o n spectrum 65 i x 3.7 P r e c e s s i o n of s p i n magnetization about heff determined by the o f f s e t b and 70 3.8 P l o t s of M x, My, M x„ and <f> vs Af at the end of a r e c t a n g u l a r r f pulse of 10 ms d u r a t i o n and an on-resonance f l i p angle of 90° 74 3 . 9 Corresponding p l o t s to that given i n F i g . 3.8 f o r a r e c t a n g u l a r pulse of 10 ms d u r a t i o n and an on-resonance f l i p angle of 30° 76 3.10 M o d i f i e d l i n e a r approximation and Bloch equation p r e d i c t i o n f o r a r e c t a n g u l a r r f pulse of 10 ms d u r a t i o n and a f l i p angle of 90° 78 3.11 P l o t of M Xy vs Af f o r a r e c t a n g u l a r r f pulse of 10 ms d u r a t i o n and a f l i p angle of 180° 79 3.12 Magnetization components e x i s t i n g a f t e r a 90° s i n e modulated r f pulse of l e n g t h 8 ms 81 3.13 ^xy> ^ v s ^ a f t e r a 90° sine modulated r f pulse of l e n g t h 4 ms 83 3.14 M x v, <j> vs Af a f t e r a 180" s i n e modulated r f pulse of l e n g t h 8 ms 84 3.15 Block diagram of the experimental setup used to generate amplitude modulated r f pulses 88 3.16 Oscillograms of the r f pulse waveforms 91 3.17 S p e c t r a l s e r i e s showing the e x c i t a t i o n p a t t e r n s of modulated 90° r f pulses 95 3.18 S p e c t r a l s e r i e s showing the e f f e c t of t r i a n g u l a r a p o d i z a t i o n of s i n e r f modulating f u n c t i o n 97 3 . 1 9 E x c i t a t i o n p r o f i l e of a 180° sine modulated r f pulse . . . 98 3.20 I l l u s t r a t i o n of f r e q u e n c y - s e l e c t i v e e x c i t a t i o n and i t s corresponding s p a t i a l s e l e c t i o n f o r two c h e m i c a l l y s h i f t e d species i n the presence of a gradient 1 0 0 3.21 Rf and gradient sequence used to demonstrate the technique described i n the t e x t 104 X 3.22 E v o l u t i o n of magnetization components i n the r o t a t i n g frame during pulse seuqence shown i n F i g . 3.21 105 3.23 S e l e c t i v e e x c i t a t i o n of two frequency bands w i t h a (Cos x Sine) amplitude modulated r f pulse . . . . 108 3.24 80.3 MHz -^H NMR spe c t r a obtained from a s i n g l e chemical s h i f t species u s i n g the sequence shown i n F i g . 3.21 110 3.25 Proposed imaging sequence which enables two ch e m i c a l l y s h i f t e d species to be imaged i n the same s p a t i a l plane I l l 4.1 The two-dimensional imaging sequence used i n the present study 118 4.2 The s l i c e p r o f i l e and i t s p r o j e c t i o n obtained from a 4 cm diameter s p h e r i c a l water phantom 122 4.3 Proce s s i n g of two-dimensional imaging data 124 4.4 1-H NMR images obtained u s i n g a 4 cm diameter s p h e r i c a l water phantom 126 4.5 80.3 MHz -^H NMR image of an i n t a c t orange 128 4.6 80.3 MHz XH NMR image of an i n t a c t lime 129 4.7 80.3 MHz 1H NMR image of a human forearm 131 4.8 80.3 MHz XH NMR image of a r a t head 132 4.9 The pulse and gradient sequence used f o r three-dimensional imaging 135 4.10 Three-dimensional imaging data format and pr o c e s s i n g f l owchart 137 4.11 -*-H NMR images of a phantom (Erlenmayer f l a s k and a round bottom f l a s k c o n t a i n i n g water) obtained from a s i n g l e three-dimensional imaging experiment 139 4.12 80.3 MHz 1H NMR images of a r a t head obtained from a three-dimensional experiment 140 x i 4.13 The pulse and gradient sequence used to demonstrate f r e q u e n c y - s e l e c t i v e e x c i t a t i o n / suppression of resonances i n co n j u n c t i o n w i t h two-dimensional imaging 143 4.14 S p e c t r a l s e r i e s showing the s e l e c t i v e e x c i t a t i o n / s u p p r e s s i o n of s p e c i f i c resonances 145 4.15 Images obtained by s e l e c t i v e e x c i t a t i o n / suppression of s p e c i f i c resonances 146 4.16 Mapping of pH d i s t r i b u t i o n 151 4.17 Mapping of temperature d i s t r i b u t i o n 152 5.1 Schematic diagram of a s i n g l e c o i l NMR probe 159 5.2 O r i e n t a t i o n of the f i e l d i n s o l e n o i d a l and saddle shaped c o i l s 161 5.3 Representation of d i f f e r e n t l o s s mechanisms 165 5.4 The s p l i t - r i n g resonator probe 171 5.5 The H-resonator probe 172 5.6 The bird-cage resonator probe 173 5.7 B-j^-homogeneity maps of the saddle c o i l 185 5.8 B^-homogeneity maps of the i n d u c t i v e l y coupled/tuned H-resonator 186 5.9 B^-homogeneity maps of the i n d u c t i v e l y coupled/tuned bird-cage resonator 187 5.10 B^-homogeneity maps of the s p l i t - r i n g resonator 188 6.1 Schematic diagram of the NMR surface c o i l probe and the animal o r i e n t a t i o n used f o r 3 1 P NMR s t u d i e s of the r a t kidney 201 6.2 32.5 MHz 3 1 P NMR sp e c t r a obtained from a r a t kidney 203 6.3 32.5 MHz 3 1 P NMR spec t r a obtained from a r a t kidney during periods of ischemia and r e p e r f u s i o n . . . 205 ACKNOWLEDGEMENTS I express my deep g r a t i t u d e to Dr. L.D. H a l l f o r h i s guidance and encouragement throughout the course of t h i s work, and f o r i n t r o d u c i n g me to the f i e l d of NMR imaging. I acknowledge the extremely u s e f u l d i s c u s s i o n s w i t h Dr. S. Sukumar, V. Rajanayagam, J . Briand and S.D. Luck. I t i s a l s o a pleasure to thank Drs. M. Comisarow, F.G. H e r r i n g , N. B u r l i n s o n and L.G. H a r r i s o n f o r h e l p f u l d i s c u s s i o n s and comments on the manuscript. Thanks are a l s o extended to Drs. P. Reiner, J . Anderson and D. L i f o r the help i n i n t e r p r e t i n g the images and Drs. A. Autor and N. G u r l l f o r c o l l a b o r a t i o n i n spectroscopy work. I am extremely indebted to T. Markus and C. Neale of the E l e c t r o n i c and Mechanical Shops r e s p e c t i v e l y , without whose expert t e c h n i c a l support, d e d i c a t i o n and enthusiasm t h i s work would not have been p o s s i b l e . I a l s o thank S. Abayakoon f o r the help i n computer c a l c u l a t i o n s , H. G o o n e t i l l e k e f o r some a r t work and B.D.J.P. Munasinghe f o r the help when i t was most needed. The c o n t r i b u t i o n by A. Tse i n proof-reading t h i s t h e s i s i s g r a t e f u l l y acknowledged. I extend my s p e c i a l thanks to Mr. and Mrs. N. Rajapakse f o r t h e i r f r i e n d s h i p and support throughout the production of t h i s t h e s i s . My thanks a l s o go to Mrs. R. Theeparajah f o r the care d i s p l a y e d i n ty p i n g t h i s t h e s i s . - 1 -CHAPTER I INTRODUCTION - 2 -I. INTRODUCTION 1.1 Background Since the f i r s t measurements i n 1946 by Bloch, Hansen and Packard [1] and P u r c e l l , Torrey and Pound [2 ] , Nuclear Magnetic Resonance (NMR) has developed i n t o a s o p h i s t i c a t e d technique w i t h a p p l i c a t i o n s i n a wide v a r i e t y of d i s c i p l i n e s which now i n c l u d e p h y s i c s , chemistry, b i o l o g y and medicine. Over the years i t has proved to be an i n v a l u a b l e spectros-copic t o o l f o r chemical a n a l y s i s , molecular s t r u c t u r e determination and i n v e s t i g a t i o n of molecular motion i n s o l i d s and l i q u i d s . This r a p i d progress of NMR spectroscopy i n t o d i v e r s e research areas can be a t t r i b u t e d to a number of inno v a t i o n s , o f which the development o f pulse F o u r i e r transform (FT) techniques by Ernst and Anderson [3] i s probably the s i n g l e most important example. Use of pulse FT techniques c o n s i d e r a b l y a l l e v i a t e s the problem of low s e n s i t i v i t y of the continuous wave (CW) method thereby enabling l e s s s e n s i t i v e n u c l e i ( n u c l e i w i t h low magnetogyric r a t i o ) , and time dependent phenomena, to be studie d . A d d i t i o n a l impetus f o r the development of the technique was provided by both the advent of h i g h - f i e l d superconducting magnets and advances i n computer technology. More r e c e n t l y , new experimental concepts such as two-dimensional (2D) NMR spectroscopy [4,5] have l e d to methods f o r study i n g molecules of extremely h i g h s t r u c t u r a l complexity, which only a few years ago would have been regarded as e s s e n t i a l l y i mpossible. In i t s l a t e s t development, a p p l i c a t i o n of NMR to s t u d i e s of l i v i n g systems has a t t r a c t e d considerable a t t e n t i o n from the biochemist and the - 3 -c l i n i c i a n a l i k e . These st u d i e s have progressed along two p a r a l l e l and perhaps complementary paths. F i r s t l y , NMR can be used as a spectros-copic method to provide chemical s h i f t i n f o r m a t i o n from s e l e c t e d regions w i t h i n an o b j e c t ; such s p e c t r a from l o c a l i z e d areas of l i v i n g t i s s u e provide v a l u a b l e metabolic i n f o r m a t i o n which i s d i r e c t l y r e l a t e d to the s t a t e of h e a l t h of the t i s s u e and can, i n p r i n c i p l e , be used to monitor i t s response to therapy. In the second area of a p p l i c a t i o n , NMR i s used as an imaging method to map the s p a t i a l d i s t r i b u t i o n of substances w i t h i n an o b j e c t ; i n the c l i n i c a l context, t h i s can provide anatomical i n f o r m a t i o n and a l s o d i s c r i m i n a t e between some p a t h o l o g i c a l t i s s u e s . The use of NMR as an imaging technique, f i r s t demonstrated by Lauterbur i n 1973 [ 6 ] , has opened a completely new area of science. To describe the technique, Lauterbur coined the term "zeugmatography' from the Greek word 'zeugma', meaning 'that which j o i n s together'. The term r e f e r s to the c o u p l i n g of the radiofrequency ( r f ) magnetic f i e l d and the s p a t i a l l y d e f i n e d magnetic f i e l d s by the o b j e c t being imaged. S i m i l a r l y to t h a t of any other imaging technique, the goal of NMR imaging i s to generate a map of a heterogeneous obj e c t showing i t s three-dimensional s t r u c t u r e . Towards t h i s end, NMR imaging e x p l o i t s the s p a t i a l v a r i a t i o n of the NMR s i g n a l i n t e n s i t y or any other NMR parameter i n the sample of i n t e r e s t . Since the nuclear magnetic resonance phenomenon depends on the i n t e r a c t i o n of n u c l e i p l a c e d i n a p o l a r i z i n g magnetic f i e l d (B Q) w i t h radiofrequency ( r f ) r a d i a t i o n , the s p a t i a l i n f o r m a t i o n can be encoded i n t o the NMR s i g n a l by s u i t a b l e manipulation of e i t h e r the B Q f i e l d or the r f f i e l d . This i s accomplished by the use of s p a t i a l l y v a r y i n g B Q or r f f i e l d s i . e . f i e l d g r a d i e n t s . The use of - 4 -p o l a r i z i n g magnetic f i e l d g radients i s s t r a i g h t f o r w a r d and a l s o i s more e a s i l y implemented while the use of r f gradients i s more complicated. Since the Larmor frequency of n u c l e i i s a f u n c t i o n of the p o l a r i z i n g magnetic f i e l d , a p p l i c a t i o n of a magnetic f i e l d g r a d i e n t causes n u c l e i at d i f f e r e n t p o s i t i o n s along the gradient d i r e c t i o n to have d i f f e r e n t resonance frequencies. The encoding of s p a t i a l i n f o r m a t i o n i n t h i s manner was recognized as e a r l y as i n 1951 by G a b i l l a r d , who i n v e s t i g a t e d one dimensional d i s t r i b u t i o n s of the NMR s i g n a l [7,8]. Thus a l l imaging methods depend on the use of f i e l d g r a d i e n t s , i n one form or another, to y i e l d s p a t i a l i n f o r m a t i o n . This i s i n c o n t r a s t to h i g h r e s o l u t i o n s p e c t r o s c o p i c measurements, where a p o l a r i z i n g magnetic f i e l d of high homogeneity (at l e a s t 1 p a r t i n 10^) i s e s s e n t i a l . P r i o r to Lauterbur's r e p o r t of the f i r s t imaging experiment, the d i s c o v e r y by Damadian that the s p i n - l a t t i c e r e l a x a t i o n times (T-^'s) of cancerous t i s s u e are longer than those of analogous h e a l t h y t i s s u e [9] provided an e a r l y b a s i s f o r hope that NMR might provide i n f o r m a t i o n of medical and b i o l o g i c a l value. Thus, immediately a f t e r the c o n t r i b u t i o n by Lauterbur, s e v e r a l a l t e r n a t i v e imaging schemes were devised and demonstrated by other i n v e s t i g a t o r s . Many of these i n i t i a l s t u d i e s were conducted e i t h e r on water f i l l e d phantoms (phantom = a sample f a b r i c a t e d w i t h a s p e c i f i c s p a t i a l s t r u c t u r e designed to t e s t an imaging scheme or device) or s m a l l vegetable samples usi n g m o d i f i e d conventional NMR spectrometers w i t h r e s t r i c t e d sample access of about 1-3 cm. The encouraging r e s u l t s provided by the e a r l y experiments prompted the development of l a r g e s c a l e systems by s e v e r a l groups, and the f i r s t w e l l r e s o l v e d NMR images of the human head were p u b l i s h e d i n 1980 [10,11]. - 5 -Even though the q u a l i t y of these images was poor compared to the current standards, these outstanding t e c h n i c a l achievements generated widespread s c i e n t i f i c and commercial i n t e r e s t . As a r e s u l t , more r e c e n t l y , extremely h i g h q u a l i t y NMR images of c l i n i c a l value have been obtained from a l l p a r t s of the human body. The c u r r e n t i n t e r e s t i n the use of NMR as a sp e c t r o s c o p i c t o o l to probe b i o l o g i c a l systems was s t i m u l a t e d by a study reported by Hoult et a l . i n 1974 [12]. This study demonstrated that h i g h - r e s o l u t i o n 3 1 P NMR sp e c t r a c o u l d be recorded from f r e s h l y e x c i s e d i n t a c t r a t muscle. The predominant resonances i n the spectrum were i d e n t i f i e d as due to the major phosphorus-containing metabolites adenosine triphosphate (ATP), phosphocreatine (PCr) and in o r g a n i c phosphate ( P i ) . Although e x p e r i -ments on a v a r i e t y of organs and t i s s u e s soon f o l l o w e d , s t u d i e s on i n t a c t animals or humans were hindered by the l a c k of both the e x p e r i -mental techniques to o b t a i n NMR s i g n a l s from a s p e c i f i c r e g i o n (as opposed to the whole specimen), and magnets w i t h l a r g e enough bore to accommodate the specimen. The former problem was solved by usi n g a s i n g l e loop of wire as the NMR c o i l . When such a c o i l ( surface c o i l ) i s place d c l o s e to the object under study, only the s i g n a l from the region i n the v i c i n i t y of the c o i l i s detected. This technology was innovated and s u c c e s s f u l l y a p p l i e d by Ackerman et a l . i n 1980 to produce 3^-P sp e c t r a from the l e g muscle and the b r a i n of an i n t a c t r a t [13]. This study s i g n a l l e d the dawn of " i n v i v o NMR spectroscopy" and i s now widely employed to study the metabolic and p h y s i o l o g i c a l s t a t u s of va r i o u s organs and t i s s u e s both i n small animals and i n man. Even though other methods to o b t a i n spectroscopic i n f o r m a t i o n from - 6 -a s p e c i f i c r e g i o n w i t h i n a sample ( l o c a l i z e d spectroscopy) have been developed, surface c o i l s are s t i l l most f r e q u e n t l y employed because of t h e i r s i m p l i c i t y and ease of operation. E a r l y NMR imaging methods ignored the p o s s i b l e e f f e c t s of d i f f e r e n t c h e m i c a l l y s h i f t e d species on the imaging process. Since one chemical s h i f t was not d i s c r i m i n a t e d from another, these imaging methods produced 'composite' images of a l l chemical s h i f t species present i n the object; f o r example, -^H NMR images of human t i s s u e r e f l e c t the s p a t i a l d i s t r i b u -t i o n of both the major c o n t a i n i n g chemical s p e c i e s , water and f a t . Since most of the e a r l y NMR imaging experiments were performed at a low f i e l d s t r e n g t h (-0.2T), presence of c h e m i c a l l y s h i f t e d species d i d not pose a problem. However, i t was soon obvious t h a t the chemical s h i f t e f f e c t s would become important i n ^H imaging at h i g h f i e l d s (>1.5T), as w e l l as i n imaging of n u c l e i such as and ^ 3C. In a d d i t i o n to the co m p l i c a t i o n s of image d i s t o r t i o n due to chemical s h i f t s , the growing i n t e r e s t i n i n v i v o spectroscopic i n f o r m a t i o n independently prompted the m o d i f i c a t i o n of e x i s t i n g imaging techniques to i n c o r p o r a t e chemical s h i f t as an a d d i t i o n a l dimension. With these m o d i f i e d techniques, i n p r i n c i p l e , i t i s p o s s i b l e to image each c h e m i c a l l y s h i f t e d species s e p a r a t e l y or, conversely, to o b t a i n s p e c t r o s c o p i c i n f o r m a t i o n from a given s p a t i a l l o c a t i o n . I t has already been shown r e c e n t l y t h a t images of s i n g l e chemical s h i f t species can be very u s e f u l c l i n i c a l l y i n c e r t a i n s i t u a t i o n s [14]. These experiments, g e n e r i c a l l y known as "chemical s h i f t r e s o l v e d " methods, b r i n g together the separate themes of i n v i v o NMR imaging and spectroscopy to a common focus. A more d e t a i l e d d i s c u s s i o n of these techniques w i l l be given i n the subsequent chapters. - 7 -The noninvasive and apparently hazard-free nature of NMR i n e v i t a b l y l e d to i t s a p p l i c a t i o n i n the study of many b i o l o g i c a l systems and man. E s p e c i a l l y i n c l i n i c a l s t u d i e s , NMR appears to combine the advantages of other c l i n i c a l imaging m o d a l i t i e s (X-ray, Ultrasound and Nuclear Medicine) without s h a r i n g t h e i r disadvantages [15,16]. Advantages of NMR imaging d e r i v e from the f a c t that i t does not use i o n i z i n g r a d i a t i o n and t h a t the observed s i g n a l i s a f u n c t i o n of many parameters such as, s p i n d e n s i t y , s p i n - l a t t i c e (T^) and s p i n - s p i n ( T 2 ) r e l a x a t i o n times, and flow. P a r e n t h e t i c a l l y , i t i s worth n o t i n g t h a t the measurement of blood flow r a t e s by NMR was i n i t i a t e d by Singer [17] as e a r l y as i n 1959. This gives the a b i l i t y to o b t a i n images having d i f f e r e n t c o n t r i b u t i o n s from the i n t r i n s i c t i s s u e parameters such as T]_, T 2 , d i f f u s i o n and flow. As a r e s u l t , e x c e l l e n t s o f t t i s s u e c o n t r a s t and p a t h o l o g i c a l d i s c r i m i n a -t i o n can be obtained by manipulation of experimental parameters without the need f o r a d m i n i s t r a t i o n of c o n t r a s t media. A f u r t h e r d e s i r a b l e f e a t u r e i s the a b i l i t y to o b t a i n NMR images i n any d e s i r e d plane without r e f o r m a t t i n g the p a t i e n t or equipment. This g r e a t l y f a c i l i t a t e s the pe r c e p t i o n o f three-dimensional anatomy over that obtainable from other imaging techniques. Recent NMR imaging i n v e s t i g a t i o n s have demonstrated favorable comparison w i t h the e x i s t i n g imaging techniques, both i n terms of data a c q u i s i t i o n time requirements and s p a t i a l r e s o l u t i o n [18]. C l i n i c a l s t u d i e s u s i n g NMR scanners i n 0.3-0.5T range and 0.8 x 0.8 mm s p a t i a l r e s o l u t i o n , have demonstrated that NMR imaging i s s u p e r i o r to X-ray computed tomography (CT) i n imaging many p a t h o l o g i c a l c o n d i t i o n s i n the b r a i n and thorax [19]. Most imaging e f f o r t s to date have been concen-- 8 -t r a t e d mainly on imaging the proton (^H) d i s t r i b u t i o n (from water and f a t ) because of i t s h i g h n a t u r a l abundance i n l i v i n g t i s s u e s . However, the present t r e n d toward higher magnetic f i e l d s w i l l enable other n u c l e i to be s t u d i e d i n the f u t u r e . Comprehensive accounts on v a r i o u s aspects of NMR imaging and i n v i v o spectroscopy can be found i n Refs. 20-22. 1.2 Goals and Format of This Thesis Most of the o r i g i n a l advances i n NMR imaging technology were accomplished by a small number of s p e c i a l i z e d research groups us i n g prototype systems. The subsequent i n t e r e s t generated i n the commercial s e c t o r has, more r e c e n t l y , l e d to the a v a i l a b i l i t y of NMR imaging systems s u i t a b l e f o r many d i f f e r e n t a p p l i c a t i o n s , and capable of produc-i n g h i g h q u a l i t y images. I n c o n t r a s t to the present technology, at the time of the commence-ment of the s t u d i e s d e s c r i b e d i n t h i s t h e s i s , an i n t e g r a t e d system s u i t a b l e f o r imaging as w e l l as f o r spectroscopy was not a v a i l a b l e . However, the h i g h f i e l d superconducting magnet technology was s u f f i -c i e n t l y advanced that l a r g e bore magnets s u i t a b l e f o r imaging of small animals and human e x t r e m i t i e s were being developed. The s t u d i e s d e s c r i b e d i n t h i s t h e s i s were prompted by the a c q u i s i t i o n of one such magnet w i t h 31 cm diameter h o r i z o n t a l room temperature bore and operat-i n g at a magnetic f i e l d of 1.89 T (80 MHz f o r ^H), together w i t h a h i g h r e s o l u t i o n NMR console. Further c o n t r i b u t i n g f a c t o r s were the growing i n t e r e s t i n t h i s l a b o r a t o r y i n NMR "chemical microscopy" [23], guided - 9 -by the i n i t i a l experiences from a 270 MHz h i g h r e s o l u t i o n spectrometer, coupled w i t h the p o s s i b l e i m p l i c a t i o n s f o r f u t u r e a p p l i c a t i o n s of NMR methods which i n t e g r a t e spectroscopy w i t h imaging. This t h e s i s concentrates on the areas of study undertaken by the author to implement v a r i o u s imaging and i n v i v o s p e c t r o s c o p i c techniques using the above magnet and the h i g h r e s o l u t i o n spectrometer console. W i t h i n t h i s general framework, two p a r t i c u l a r aspects of imaging have been examined i n d e t a i l and are described i n Chapters I I I and V. These s t u d i e s provided the necessary b a s i c i n s i g h t and a l s o generated p r e v i o u s l y unreported experimental data. Further, t h i s t h e s i s a l s o demonstrates novel experimental concepts and a p p l i c a t i o n s r e l a t e d to NMR imaging and i n v i v o spectroscopy. The format of the t h e s i s i s as f o l l o w s : Chapter I I introduces the reader to the b a s i c concepts of NMR imaging and c u r r e n t l y used exper-imental schemes. Chapter I I I i s devoted to frequency s e l e c t i v e e x c i t a -t i o n i n the context of s l i c e s e l e c t i o n . The demonstration of v a r i o u s imaging techniques and the a p p l i c a t i o n s of chemical s h i f t r e s o l v e d imaging forms the b a s i s of Chapter IV. A d e t a i l e d d i s c u s s i o n and experimental e v a l u a t i o n of probes s u i t a b l e f o r NMR imaging i s presented i n Chapter V. F i n a l l y , p r e l i m i n a r y r e s u l t s of s p e c t r o s c o p i c s t u d i e s of r a t kidney i n v i v o are reported i n Chapter VI. The reader w i l l note t h a t the necessary background m a t e r i a l , where a p p r o p r i a t e , i s included at the beginning of each chapter. Since t h i s work was i n i t i a t e d , numerous academic and commercial groups have become a c t i v e i n these areas, and t h e r e f o r e , appropriate c i t a t i o n s are i n c l u d e d throughout t h i s t h e s i s . - 10 -References: Chapter I 1. F. Bloch, W.W. Hansen, and M. Packard, Phys. Rev. 69, 127 (1946). 2. E.M. P u r c e l l , H.C. Torry, and R.V. Pound, Phys. Rev. 69, 37 (1946). 3. R.R. Ernst and W.A. Anderson, Rev. S c i . Instrum. 37, 93 (1966). 4. I . J . Jeener, Ampere I n t e r n a t i o n a l Summer School, Baska, P o l j e , Y u g o s l a v i a , 1971. 5. W.P. Aue, E. B a r t h o l d i , and R.R. Ernst, J . Chem. Phys. 64, 222 (1976). 6. P.C. Lauterbur, Nature 242, 190 (1973). 7. R. G a b i l l a r d , C R. Acad. S c i . ( P a r i s ) 232, 1551 (1951). 8. R. G a b i l l a r d , Phys. Rev. 85, 694 (1952). 9. R. Damadian, Science 171, 1151 (1971). 10. G.N. Holland , R.C. Hawkes, andW.S. Moore, J . Compt. A s s i s t . Tomogr. 4, 429 (1980). 11. R.C. Hawkes, G.N. Holland, W.S. Moore, and B. Worthington, J . Compt. A s s i s t . Tomogr. 4, 527 (1980). 12. D.I. Hoult, S.J.W. Busby, D.G. Gadian, G.K. Radda, R.E. Richards, and P.J. Seeley, Nature (London) 252, 285 (1974). 13. J.J.H. Ackerman, J.H. Grove, G.G. Wong, D.G. Gadian, and G.K. Radda, Nature (London) 283, 169 (1980). 14. J.K.T. Lee, W.T. Dixon, D. L i n g , R.G. L e v i t t , and W.A. Murphy, Radiology 153, 195 (1984). 15. A.R. M a r g u l i s , In " C l i n i c a l Magnetic Resonance Imaging", A.R. Mar g u l i s , C.B. Higgins, L. Kaufman, and L.E. Crooks, Eds., Chapter I , Radiology Research and Education Foundation, San F r a n s i c s o , 1983. 16. A.R. M a r g u l i s , In "Nuclear Magnetic Resonance Imaging i n Medicine", L. Kaufman, L.E. Crooks, A.R. Mar g u l i s , Eds., Chapter 1, Igaku-Shoin, New York-Tokyo, 1981. - 11 -17. J.R. Singer, Science 130, 1652 (1959); see a l s o Ref. 16, Chapter 7. 18. C L . P a r t a i n , E d i t o r , "Nuclear Magnetic Resonance and C o r r e l a t i v e Imaging M o d a l i t i e s " , p. 5, S o c i e t y of Nuclear Medicine Inc. New York, 1984. 19. S.W. Young, "Nuclear Magnetic Resonance Imaging", Chapter 8, Raven Press, New York, 1984. 20. P. M a n s f i e l d and P.G. M o r r i s , "NMR Imaging i n Biomedicine", Aca-demic Press, New York, 1982. 21. D.G. Gadian, "Nuclear Magnetic Resonance and i t s a p p l i c a t i o n s to l i v i n g systems", Clarendon Press, Oxford, 1982. 22. J.R. M a l l a r d , Proc. R. Soc. Lond. B 226, 391 (1986). 23. L.D. H a l l and S. Sukumar, J . Magn. Reson. 50, 161 (1982). - 1 2 -CHAPTER I I NMR IMAGING TECHNIQUES - 13 -I I . NMR IMAGING TECHNIQUES In t h i s Chapter, the reader i s introduced to the d i f f e r e n t e x p e r i -mental methods that have been developed to perform NMR imaging. The d i f f e r e n t techniques vary i n t h e i r approach to determine the NMR s i g n a l i n t e n s i t y from each volume element i n a three dimensional o b j e c t . Of these techniques, emphasis i s placed upon the F o u r i e r imaging methods due to t h e i r g e n e r a l i t y , widespread use and p a r t i c u l a r relevance to t h i s study. In order to l a y the foundation f o r the d i s c u s s i o n to f o l l o w , some b a s i c concepts are i n i t i a l l y reviewed. 2.1 Basic Concepts 2.1.1 Pulse NMR In t h i s S e c t i o n , a b r i e f i n t r o d u c t i o n to pulse F o u r i e r transform NMR [1-3] i s given to ensure that the reader has access to the r e l e v a n t concepts. Consider an ensemble of i d e n t i c a l s p i n 1/2 n u c l e i placed i n a s t a t i c magnetic f i e l d B Q. From quantum mechanical c o n s i d e r a t i o n s i t i s known t h a t the s p i n 1/2 n u c l e i can e x i s t i n one of two energy s t a t e s which d i f f e r i n energy by AE; AE = 7hB0/27r 2.1 - 14 -where, 7 i s the magnetogyric r a t i o and h i s the Planck's constant. At thermal e q u i l i b r i u m , the n u c l e i are d i s t r i b u t e d between the two energy l e v e l s according to the Boltzmann d i s t r i b u t i o n which ensures that a s l i g h t excess of n u c l e i are present i n the lower energy s t a t e . Although many features of NMR can be understood only by the quantum mechanical approach, most of the experiments r e f e r r e d to i n t h i s t h e s i s can be adequately d e s c r i b e d by the s e m i - c l a s s i c a l v e c t o r model. In the s e m i - c l a s s i c a l v e c t o r model, n u c l e i are represented by the nuclear magnetic moment ve c t o r x^. In the presence of an e x t e r n a l magnetic f i e l d B Q, the magnetic moment ve c t o r s of s p i n 1/2 n u c l e i take up one of two p o s s i b l e o r i e n t a t i o n s w i t h respect to the f i e l d ( p a r a l l e l or a n t i - p a r a l l e l ) corresponding to the d i f f e r e n t energy s t a t e s . The i n d i v i d u a l magnetic v e c t o r s precess about B Q w i t h random phase, and at e q u i l i b r i u m , spins o r i e n t e d p a r a l l e l to the f i e l d B Q are i n s l i g h t excess over those opposing i t ( F i g . 2.1a). Therefore, i f B Q i s considered o r i e n t e d along the z - a x i s , i t can be seen that the net magnetization M Q due to a l l the spins at e q u i l i b r i u m , i s a l i g n e d along the z - a x i s . The x and y components of the magnetization are i n d i v i d u -a l l y averaged to zero due to random phase of the magnetic moment vec-t o r s . I f t h i s net magnetization i s d i s p l a c e d from i t s alignment along the z - a x i s , i t e x h i b i t s a p r e c e s s i o n a l motion about B Q due to the torque exerted by the e x t e r n a l f i e l d ( F i g . 2.1b). The angular frequency of pr e c e s s i o n w Q i s given by W o = 7 B 0 2.2 and i s known as the Larmor frequency. 15 -Y F i g . 2.1: (a) Prec e s s i o n of i n d i v i d u a l magnetic v e c t o r s about B Q at e q u i l i b r i u m . (b) Precession of n o n e q u i l i b r i u m magnetization M about B Q i n the l a b o r a t o r y frame. (c) Motion of M i n the r o t a t i n g frame i n the presence of Bj_. (d) Prec e s s i o n of M i n the r o t a t i n g frame f o l l o w i n g a 90° pulse. - 16 In an NMR experiment, the non e q u i l i b r i u m magnetization M ( F i g . 2.1b) i s cre a t e d by the a p p l i c a t i o n of a r o t a t i n g magnetic f i e l d i n the transverse x-y plane. The frequency of r o t a t i o n of Bj_, wr, i s chosen to be near the Larmor frequency of spins i n the r a d i o frequency range. The maximum e f f e c t on the magnetization i s achieved when the frequency of matches the Larmor frequency, corresponding to the resonance c o n d i t i o n ( i . e . o>r = w Q). In p r a c t i c e , the r o t a t i n g B^ f i e l d i s obtained by ap p l y i n g an o s c i l l a t i n g magnetic f i e l d ( r f f i e l d ) d i r e c t e d along a c e r t a i n d i r e c t i o n i n the x-y plane. The o s c i l l a t i n g f i e l d can be decomposed i n t o two counter r o t a t i n g components, and the f i e l d component w i t h the same sense of r o t a t i o n as the p r e c e s s i o n a l magnetization i s r e s p o n s i b l e f o r the c r e a t i o n of the non e q u i l i b r i u m magnetization. The f i e l d component w i t h the opposite sense of r o t a t i o n has n e g l i g i b l e e f f e c t , and t h e r e f o r e , i s ignored [4]. The motion of the macroscopic magnetization M i n the presence of an a p p l i e d magnetic f i e l d i s most conveniently d e s c r i b e d by the Bloch equations [1,5] i n a frame r o t a t i n g at the same frequency w r as the B^ f i e l d (see a l s o Chapter I I I ) . In such a frame o f reference, at reso-nance (w r = w Q), the motion of M i s seen as a p r e c e s s i o n about B^, and the angle of p r e c e s s i o n 9 ( f l i p angle) i s given by 9 = 7 B x t w 2.3 where, t w i s the d u r a t i o n of B^ (pulse l e n g t h ) . Thus, i f the r o t a t i n g frame axes, denoted as x'y'z, are chosen such that B^ l i e s along the x' a x i s , the motion of M i s then i n the zy' plane ( F i g . 2.1c). I f the - 17 -pulse l e n g t h t w i s such that the f l i p angle 6 i s equal to TT/2 (90° p u l s e ) , at the end of the pulse the magnetization w i l l be a l i g n e d along the y' a x i s . The decay of the n o n e q u i l i b r i u m magnetization to the e q u i l i b r i u m value i s governed by the s p i n - l a t t i c e and s p i n - s p i n r e l a x a t i o n pro-cesses [1,2]. The f i r s t order time constants f o r these processes are r e f e r r e d to as T^ and T2 r e s p e c t i v e l y . In the v e c t o r model, T^ c h a r a c t e r i z e s the exponential growth of the l o n g i t u d i n a l magnetization M z to i t s e q u i l i b r i u m value M Q, w h i l e , T2 denotes the decay constant of the t r a n s v e r s e magnetization components and My to t h e i r e q u i l i b r i u m values ( z e r o ) . Once the r f pulse i s terminated, M continues to precess about B Q i n the l a b o r a t o r y frame w i t h an angular frequency equal to the Larmor frequency wQ. In the r o t a t i n g frame, t h i s p r e c e s s i o n i s viewed as of frequency fiQ = w0-wr ( F i g . 2 . l d ) . The frequency Q Q i s commonly r e f e r r e d to as the o f f s e t frequency or the resonance o f f s e t . The transverse magnetization components, M x and My, i n the r o t a t i n g frame a f t e r the pulse can be expressed as, M x ( t ) = M D Sin0 S i n f J D t e x p ( -t/T 2) 2.4 and My(t) = M Q Sin0 CosfJ Qt exp(-t/T 2) 2.5 Here, i t should be noted that even though the r o t a t i n g frame axes were denoted as x' and y', the magnetization components along these axes are expressed without the prime n o t a t i o n . - 18 -In pulse NMR, the s i g n a l i s detected as a time v a r i a t i o n of the volt a g e induced i n a c o i l due to the pre c e s s i n g transverse magnetiza-t i o n [6,7]. This i n i t i a l s i g n a l which i s i n the r f frequency range, i s converted to a low frequency s i g n a l by phase s e n s i t i v e d e t e c t i o n w i t h respect to the frequency of the r f pulse [6,7]. The s i g n a l a f t e r phase s e n s i t i v e d e t e c t i o n ( f r e e i n d u c t i o n decay), except f o r a constant f a c t o r , corresponds to the time e v o l u t i o n of the transverse magnetiza-t i o n components i n the r o t a t i n g frame. In quadrature d e t e c t i o n , both magnetization components M x and My are detected, and t h e r e f o r e the complex output s i g n a l f o l l o w i n g a 90° r f pulse can be w r i t t e n as where i •= 7-1. F o u r i e r t r a n s f o r m a t i o n of the time domain s i g n a l S ( t ) y i e l d s the frequency domain spectrum S(u>) given by S(t) - My + iMx 2.6 and hence, S(t ) = M Q e x p ( i w D t ) exp(-t/T 2) 2.7 S(w) = M D(A(w) + iD(w)} 2.8 where T 2 2(n o-w) A(w) 1 + T 2 2 ( U 0 - u ) 2 and D(w) = 1 + T 2 2 ( U 0 - u > ) 2 The r e a l p a r t of S(u>), A(w) , corresponds to a L o r e n t z i a n absorption l i n e centered a t frequency w = QQ while the imaginary p a r t , D(w), - 19 -corresponds to a d i s p e r s i o n l i n e centered at w = f l 0 . In g eneral, an organic molecule e x h i b i t s a range of resonance frequencies ( d i f f e r e n t fi0 values) due to chemical s h i f t e f f e c t s [2]. Thus the f r e e i n d u c t i o n decay c o n s i s t s of a s u p e r p o s i t i o n of a s e r i e s of s i g n a l s of d i f f e r e n t frequencies. These d i f f e r e n t frequencies are recovered by F o u r i e r transformation. 2.1.2 L i n e a r Magnetic F i e l d Gradient In NMR spectroscopy, the s t a t i c magnetic f i e l d B Q i s homogeneous, corresponding to a s i n g l e Larmor frequency d e f i n e d by Eq. 2.2. Thus, conv e n t i o n a l NMR techniques are i n h e r e n t l y one dimensional i n the sense t h a t the s i g n a l a b s o r p t i o n i s measured as a f u n c t i o n of angular frequency. As mentioned i n Chapter I , s p a t i a l v a r i a t i o n of the NMR s i g n a l can be induced by the use of s t a t i c f i e l d g r a d i e n t s . A magnetic f i e l d g radient represents a v a r i a t i o n of the f i e l d w i t h the s p a t i a l coordinate. A l i n e a r gradient [8] imposes a l i n e a r v a r i a -t i o n of the f i e l d w i t h the s p a t i a l coordinate and can be represented as ^ - constant = G„ 2.9 de e where e represents the s p a t i a l coordinates x, y or z, and B i s the magnetic f i e l d . G e denotes the magnitude of the gradient along e. In p r a c t i c e , a gradient f i e l d (generated by the 'gradient c o i l ' ) i s super-imposed on the s t a t i c f i e l d B D which i s along the z - a x i s . The magnetic - 20 -f i e l d components along the x and y axes generated by the gradient c o i l s can be neglected s i n c e these are much smaller than the s t a t i c f i e l d . Thus the magnetic f i e l d d i r e c t e d along the z-axis (B z) i n the presence of a gra d i e n t f i e l d G x i s represented by B z ( x ) = B Q + G x.x 2 . 1 0 and t h i s i s i l l u s t r a t e d i n F i g . 2 . 2 a . I t should be noted that the f i e l d v a r i a t i o n w i t h i n a plane perpen-d i c u l a r to G x i s zero and the magnitude of the f i e l d i n t h a t plane depends on the x-coordinate. Therefore i n the presence of a grad i e n t , planes of constant f i e l d s t r e n g t h are created p e r p e n d i c u l a r to the gradi e n t d i r e c t i o n . Since the resonance frequency depends on the magnetic f i e l d , a p p l i c a t i o n of a magnetic f i e l d gradient causes the resonance frequen-c i e s to be dependent on the p o s i t i o n according to w x = w o + 7G x.x 2 . 1 1 and the planes of constant f i e l d a l s o become planes of constant reso-nance frequency. This fundamental r e l a t i o n s h i p between the s p a t i a l domain and the frequency domain i n the presence of a grad i e n t forms the b a s i s f o r NMR imaging. I t f o l l o w s that the NMR spectrum obtained i n the presence of a magnetic f i e l d g radient w i l l show a d i s t r i b u t i o n of resonance frequen-c i e s as given by Eq. 2 . 1 1 . The s p e c t r a l amplitude at each frequency - 21 -+• X F i g . 2.2: (a) The v a r i a t i o n of the magnetic f i e l d B z w i t h the s p a t i a l coordinate i n the presence of a l i n e a r f i e l d g r a d i e n t G x. (b) The r e l a t i o n s h i p between the s p i n d e n s i t y d i s t r i b u t i o n of an obj e c t and the NMR spectrum i n the presence of a g r a d i e n t . ( i ) a s i n g l e tube of water, ( i i ) two tubes. - 22 -w i l l be proportional to the spin density i n the corresponding constant frequency plane. Therefore the NMR spectrum of an object placed i n a magnetic f i e l d gradient corresponds to the p r o j e c t i o n of the spin density w i t h i n the object onto the gradient d i r e c t i o n (Fig. 2.2b). From Eq. 2.7, the t o t a l s i g n a l observed i n the presence of a single gradient G x a f t e r phase s e n s i t i v e detection can be w r i t t e n as, S(t) = J K p(x) exp[i(w Q + 7G xx)t] exp(-t/T 2)dx 2.12 where Q 0 i s the o f f s e t frequency, p(x) i s the p r o j e c t i o n of the spin density onto the x-axis, Kp(x).dx i s the magnetization i n length dx and K i s a constant. I f the phase s e n s i t i v e detection i s performed with the Larmor frequency wQ as the reference ( i . e . CiQ = 0), and t « T 2, which allows the second exponential term to be neglected, then the r i g h t hand side of the Eq. 2.12 corresponds to the inverse Fourier transform of p(x). Thus the Fourier transformation of S(t) y i e l d s the spin density p r o j e c t i o n . More p r e c i s e l y , from Eq. 2.12 i t can be shown that the spectrum obtained i n the presence of a gradient corresponds to the convolution of the spectrum i n the absence of the gradient with the scaled spin density p r o j e c t i o n according to the gradient strength employed. Use of magnetic f i e l d gradients to produce projections of the object under i n v e s t i g a t i o n i s a key concept i n NMR imaging and, as w i l l be seen l a t e r , manipulation of gradients i n a l l three d i r e c t i o n s can provide the three dimensional s p a t i a l spin density of the object. - 23 -2.1.3 E v o l u t i o n of Magnetization i n the Presence of Gradients The e v o l u t i o n of magnetization i n the presence of a gradient can be r e a d i l y v i s u a l i z e d i n the r o t a t i n g frame. Consider the e x c i t a t i o n of a sample by a 90° r f pulse f o l l o w e d by the a p p l i c a t i o n of a magnetic f i e l d g r a dient. The t o t a l magnetization from the sample immediately a f t e r a 90° p u l s e , d i r e c t e d along the x ' - a x i s , w i l l be a l i g n e d along the y ' - a x i s ( F i g . 2.3a). Under the i n f l u e n c e of a g r a d i e n t , the i n d i v i d u a l compo-nents of the magnetization corresponding to d i f f e r e n t p o s i t i o n s i n the sample w i l l precess at d i f f e r e n t frequencies as given by Eq. 2.11. Thus, i n the r o t a t i n g frame, the magnetization w i l l be seen to l o s e phase coherence (dephase) about the o f f s e t frequency u 0 ( F i g . 2.3b). In p r a c t i c e , the dephasing of the magnetization w i l l be due to the combined e f f e c t s of both the gradient and the inhomogeneity of the s t a t i c magnetic f i e l d B Q. At t h i s p o i n t i t i s appropriate to consider the p o s s i b l e ways of b r i n g i n g the dephased magnetization back i n t o focus ( r e f o c u s s i n g ) . These r e f o c u s s i n g methods are commonly employed i n imaging pulse sequences as a means of d e l a y i n g the s i g n a l and o b s e r v a t i o n of the same as an echo (see d i s c u s s i o n on spin-warp imaging, Sec. 2.2.3). The r e f o c u s s i n g of the dephased magnetization can be accomplished e i t h e r by a p p l y i n g a 180° pulse ( F i g . 2.4a) or by r e v e r s i n g the gradient ( F i g . 2.4b) at a time a f t e r the 90° pulse. The former method i s the f a m i l i a r spin-echo technique, and i s i l l u s t r a t e d i n F i g s . 2.3a-d. A p p l i c a t i o n of a 180° pulse along the y' a x i s r o t a t e s the magnetiza-t i o n components about the y' a x i s to t h e i r m i r r o r image p o s i t i o n s F i g . 2.3 E v o l u t i o n of magnetization i n the r o t a t i n g frame i n the presence of a gradient. QQ = o f f s e t frequency, w Q ± Aw = frequency i n the presence of a gradient (Aw = 7G x.x). - 25 -(a) 180 RF Gradient 1_ Signal DEFOCUSSING REFOCUSS1NG INTERVAL INTERVAL ( b ) RF 9(f Gradient r Signal DEFOCUSSING REFOCUSSING INTERVAL INTERVAL F i g . 2.4: Signal refocussing methods. (a) Creation of a spin-echo i n the presence of a gradient. (b) Creation of a gradient-echo by the a p p l i c a t i o n of a negative gradient. - 26 -( F i g . 2.3c). At a time r r = l a t e r , a l l magnetization components are refocussed along the y' a x i s , l e a d i n g to a s i g n a l i n the form of an echo ( F i g . 2.3d). I t should be noted t h a t , during t h i s time, the dephasing due to the inhomogeneities of s t a t i c magnetic f i e l d as w e l l as the off-resonance e f f e c t s (due to chemical s h i f t ) are a l s o refocussed. In the second method, r e v e r s i n g the gradient has the e f f e c t of interchang-i n g the p r e c e s s i o n a l frequencies about the o f f s e t frequency fiQ ( F i g . 2.3e). Therefore, provided t h a t the magnitude of the reversed gradient i s the same as before, dephasing due to the gradient i s refocussed at a time T r = T , J . In the more general case the echo time ( r e ) a f t e r the i n i t i a l 90° e x c i t a t i o n i s given by [ 9 ] , J G ( t ) . d t = 0 . 2.13 o In the grad i e n t r e v e r s a l method, the s t a t i c f i e l d inhomogeneities and the chemical s h i f t e f f e c t s are not refocussed ( F i g . 2.3f) and thus the amplitude and the phase of the echo s i g n a l w i l l be d i f f e r e n t from that obtained w i t h the 180° pulse. The echo s i g n a l obtained by gradient r e v e r s a l i s r e f e r r e d to as a gradient-echo i n order to d i s t i n g u i s h from the u s u a l spin-echo. 2.1.4 S l i c e S e l e c t i o n Methods An e s s e n t i a l step i n any imaging technique i s to define an imaging - 27 -plane or a s l i c e i n a three dimensional o b j e c t . In NMR imaging, t h i s i s accomplished by r e s t r i c t i n g the NMR response to a p a r t i c u l a r s l i c e of the o b j e c t . The u n d e r l y i n g concepts of d i f f e r e n t s l i c e s e l e c t i o n methods are d e s c r i b e d i n t h i s s e c t i o n . 2.1.4.1 S e l e c t i v e E x c i t a t i o n S l i c e s e l e c t i o n u s i n g the s e l e c t i v e e x c i t a t i o n technique i s achieved by a p p l y i n g a f r e q u e n c y - s e l e c t i v e r f pulse i n the presence of a l i n e a r magnetic f i e l d g radient [10]. As already discussed i n S e c t i o n 2.1.2, a p p l i c a t i o n of a f i e l d gradient causes the resonance frequency of the spins to be dependent upon the p o s i t i o n according to Eq. 2.11. Uniform e x c i t a t i o n of a l l these frequencies produces a continuous spectrum of resonance frequencies, and each frequency i n the spectrum represents a plane of spins perpendicular to the gradient d i r e c t i o n . I f the spins are subjected to an r f pulse w i t h a narrow frequency spectrum, ( f r e q u e n c y - s e l e c t i v e pulse) i n s t e a d of one w i t h a broad range of frequencies ( n o n s e l e c t i v e p u l s e ) , then only the spins w i t h resonance frequencies w i t h i n the narrow range of the r f spectrum w i l l be stimu-l a t e d . (Such an r f pulse c o n s i s t s of a low power amplitude modulated pulse.) This e f f e c t i v e l y e x c i t e s a s p a t i a l plane ( s l i c e ) of spins p e r p e n d i c u l a r to the d i r e c t i o n of the gradient and the subsequent NMR s i g n a l i s r e c e i v e d e x c l u s i v e l y from t h i s plane. The p a r t i c u l a r s l i c e s e l e c t e d i s determined by the d i r e c t i o n of the a p p l i e d f i e l d gradient and the frequency band e x c i t e d by the pulse. - 28 -D i f f e r e n t planes corresponding to a p a r t i c u l a r s l i c e o r i e n t a t i o n can be e x c i t e d simply by changing the r f pulse spectrum to encompass a d i f f e r e n t frequency range. The s p a t i a l thickness of the s e l e c t e d s l i c e (Ax) i s given by the equation Ax 2TT Af 7G, 2.14 where Af i s the frequency band-width of the p u l s e . For accurate s e l e c t i o n of a s p a t i a l plane, uniform e x c i t a t i o n of spins w i t h i n the s l i c e and n e g l i g i b l e (zero) e x c i t a t i o n o u t side the s l i c e i s needed. This r e q u i r e s an r f pulse which has a r e c t a n g u l a r p r o f i l e i n the frequency domain. T h e o r e t i c a l and p r a c t i c a l aspects of f r e q u e n c y - s e l e c t i v e e x c i t a t i o n i n the presence of a gradient are examined i n Chapter I I I . 2.1.4.2 Other Methods The o s c i l l a t i n g f i e l d gradient method [11,12] of s l i c e s e l e c t i o n r e l i e s upon the a p p l i c a t i o n of a time-dependent l i n e a r f i e l d gradient. I f an a l t e r n a t i n g gradient f i e l d of the form ( x - x Q ) G x C o s ( w x t ) i s used, where x Q , G x and fix are constants denoting p o s i t i o n , gradient amplitude and frequency r e s p e c t i v e l y , an a l t e r n a t i n g magnetic f i e l d i s created everywhere i n the sample except i n the plane at x = x 0 (zero f i e l d plane or s e n s i t i v e p l a n e ) . Therefore, the resonance s i g n a l s d e r i v e d from - 29 -n u c l e i outside the s e n s i t i v e plane are frequency modulated due to the time v a r i a t i o n i n the f i e l d w h i l e the s i g n a l s from w i t h i n the s e n s i t i v e plane are time i n v a r i a n t . S i g n a l averaging over the gradient time dependence removes the s i g n a l from everywhere except t h a t from the s e n s i t i v e plane [12]. Another approach i n v o l v e s the use of s p a t i a l l y dependent r f f i e l d s to s e l e c t i v e l y s a t u r a t e a l l but a s l i c e of spins i n the sample [13]. A p p l i c a t i o n of an r f f i e l d B^, which has a cubic dependence upon the dis t a n c e , - s a t u r a t e s the magnetization as the s i x t h power of the distance [13]. This allows the s e l e c t i o n of a plane of spins p e r p e n d i c u l a r to the s p a t i a l v a r i a t i o n of the B^ f i e l d and centered about the o r i g i n . The width of the s e l e c t e d s l i c e i s c o n t r o l l e d by a l t e r i n g the f u n c t i o n a l dependence of B]_. 2 . 2 Imaging Methods Since the i n c e p t i o n of NMR imaging, s e v e r a l d i f f e r e n t imaging methods have been proposed. In the e a r l y developmental stages, the s e q u e n t i a l - p o i n t and - l i n e methods (see c l a s s i f i c a t i o n below) were prominently used due to t h e i r s i m p l i c i t y . But c u r r e n t l y , these methods have been re p l a c e d by the s u p e r i o r F o u r i e r imaging method which o f f e r s s e v e r a l advantages. Therefore f o r a d e s c r i p t i o n of the s e q u e n t i a l - p o i n t and - l i n e methods, the reader i s r e f e r r e d to the e a r l y reviews on the subje c t [8,14]. In t h i s s e c t i o n , a c l a s s i f i c a t i o n of the a v a i l a b l e methods as w e l l as a d e t a i l e d d e s c r i p t i o n of the F o u r i e r imaging method - 30 -w i l l be presented. The p r o j e c t i o n - r e c o n s t r u c t i o n method i s a l s o d e s c r i b e d b r i e f l y due to i t s h i s t o r i c a l importance. 2.2.1 C l a s s i f i c a t i o n and S e n s i t i v i t y of Imaging Methods 2.2.1.1 C l a s s i f i c a t i o n NMR imaging techniques can be c l a s s i f i e d [15] i n t o four groups depending on the type of the volume that i s chosen f o r ob s e r v a t i o n at any i n s t a n t ; i . e . a p o i n t , a l i n e , a plane or a volume ( F i g . 2.5). Consider t h a t the sample volume to be imaged i s d i v i d e d i n t o n volume elements (voxels) along each a x i s . Thus n 3 independent values are r e q u i r e d to f u l l y c h a r a c t e r i z e the sample volume and to c o n s t r u c t a complete image. These values may be obtained from N experiments where N < n 3 . The number of experiments, N, necessary to o b t a i n s u f f i c i e n t i n f o r m a t i o n f o r c o n s t r u c t i o n of the complete image depends on the technique used. In the s i m p l e s t type of imaging methods, each volume element i s observed s e l e c t i v e l y by one of the N experiments ( F i g . 2.5a). Thus N = n 3 , and these methods are termed as " s e q u e n t i a l - p o i n t " techniques. Imaging methods known as the s e n s i t i v e - p o i n t method [11] and the f i e l d f o c u s s i n g n uclear magnetic resonance (FORNAR) [16,17] belong to t h i s category. These two methods d i f f e r i n the procedure by which a p a r t i c u -l a r volume element i s defined f o r observation. A l t e r n a t i v e l y , i f a l l the volume elements along a s e l e c t e d l i n e are 31 -(a) (b) (c) (d) F i g . 2.5: C l a s s i f i c a t i o n of NMR imaging methods: (a) S e q u e n t i a l - p o i n t , (b) S e q u e n t i a l - l i n e , (c) Sequential-plane and (d) Simulta-neous methods. observed and r e s o l v e d simultaneously ( F i g . 2.5b), then N = n 2 , and the technique i s r e f e r r e d to as a " s e q u e n t i a l - l i n e " measurement. The m u l t i p l e - s e n s i t i v e - p o i n t [18] method, the l i n e - s c a n method [19] and i t s v a r i a n t s [20,21] f a l l i n t o t h i s c l a s s . In a 'sequential-plane' measurement, an e n t i r e plane of volume elements i s observed simultaneously ( F i g . 2.5c). In t h i s case N = n. Simultaneous o b s e r v a t i o n and r e s o l u t i o n of a l l volume elements i n a plane i n a s i n g l e experiment can be achieved by e i t h e r the planar imaging method [22,23] or the echo-planar imaging method [24]. These - 32 -methods c a l l f o r s t r i n g e n t demands on instrumentation. More f a m i l i a r s e q u e n t i a l - p l a n e measurements r e q u i r e , f o r example, n experiments to r e s o l v e a l l the volume elements i n a plane while observing the s i g n a l from the e n t i r e plane i n a l l the experiments. Thus the t o t a l number of experiments N = n^. Experimental techniques such as p r o j e c t i o n -r e c o n s t r u c t i o n [25], F o u r i e r imaging [26] and r o t a t i n g frame zeugmatog-raphy [27] f a l l i n t o t h i s category. I n 'simultaneous (volume)' methods the NMR s i g n a l from the whole three dimensional o b j e c t i s observed i n every measurement ( F i g . 2.5d). These methods are d e r i v e d from the extension of the sequential-plane methods i n t o three dimensions. Even though the three-dimensional v e r s i o n of the echo-planar method i s t h e o r e t i c a l l y p o s s i b l e , i t has so f a r not been demonstrated. In t h i s case, the t o t a l number of e x p e r i -ments r e q u i r e d to completely c h a r a c t e r i z e the e n t i r e o b j e c t would be reduced to one. On the other hand, the three-dimensional v e r s i o n s of the p r o j e c t i o n - r e c o n s t r u c t i o n and F o u r i e r imaging methods have been imple-mented, but r e q u i r e n^ separate experiments, while observing the s i g n a l from a l l the volume elements i n a l l experiments. 2.2.1.2 S e n s i t i v i t y At t h i s j u n c t u r e , i t i s appropriate to d i s c u s s q u a l i t a t i v e l y the s e n s i t i v i t y of d i f f e r e n t techniques; i . e . t h i s d i s c u s s i o n ignores the d i f f e r e n c e s i n the data a c q u i s i t i o n procedure i n each method. A more rig o r o u s a n a l y s i s i s given i n Ref. 15. The r e l e v a n t q u a n t i t y f o r .33 -comparison of s e n s i t i v i t i e s i s the s i g n a l - t o - n o i s e r a t i o (S/N) achiev-able from a s i n g l e volume element i n a given time. Let the S/N obtained from a s i n g l e volume element i n a s i n g l e a c q u i s i t i o n be a r b i t r a r i l y assigned to u n i t y . Thus, i f the s i g n a l from a p a r t i c u l a r volume element i s accumulated by only one of the N experiments needed to f u l l y charac-t e r i z e the image, the S/N i n the f i n a l image w i l l a l s o be u n i t y . This a p p l i e s to s e q u e n t i a l p o i n t and l i n e methods as w e l l as the planar (PI) and echo p l a n a r (EPI) imaging methods. The above case should be con-t r a s t e d to the p r o j e c t i o n - r e c o n s t r u c t i o n (PR) and F o u r i e r imaging (FI) methods i n which, each volume element i s observed by n or n^ experiments depending on the type of the experiment (s e q u e n t i a l - p l a n e or s i m u l t a -neous) performed. Thus w i t h PR and FI methods, the S/N i n the f i n a l image w i l l be p r o p o r t i o n a l to Jn or n [28,29]. The S/N and the t o t a l experimental time ( T t o t ) of each method are t a b u l a t e d i n Table 2.1. The r e l a t i v e S/N when a l l the methods are performed f o r an equal d u r a t i o n n 3T, (S/N)3 , i s given i n the l a s t row of Table 2.1. From t h i s a n a l y s i s n T i t can be seen that the maximum s e n s i t i v i t y i s produced by the s i m u l t a -neous methods, and the decreasing d i m e n s i o n a l i t y of the method produces p r o g r e s s i v e l y lower S/N. I t should be emphasized t h a t the s e n s i t i v i t y r a t i o s given by t h i s q u a l i t a t i v e p i c t u r e i s a l t e r e d s i g n i f i c a n t l y by the experimental procedure used [15]. This i s e s p e c i a l l y true i n PI which produces markedly lower S/N than other s e q u e n t i a l plane and simultaneous methods [15]. But the general trend p r e d i c t e d by the above a n a l y s i s i s observed. I t i s of i n t e r e s t to examine the r e l a t i o n s h i p between the parame-t e r s such as r e s o l u t i o n (the number of voxels i n each dimension), - 34 -Table 2.1: R e l a t i v e s e n s i t i v i t i e s of NMR Imaging Methods Seq u e n t i a l Sequential Sequential Plans (2D) Simultaneous (3D) P o i n t l i n e (ID) P I , EPI PR, F l P I , EPI PR, F l S/N 1 1 1 Jn 1 7n2=n T t o t n 3T n 2T nT n.(n.T)=n 2T T n 2T (S/N) 1 Jn 7n2=n Jn.Jn=n yn3=n7n n7n n 3T PI - Planar Imaging EPI - Echo Planar Imaging PR - P r o j e c t i o n R e c o n s t r u c t i o n F l - F o u r i e r Imaging n - # of p i x e l s i n each dimension T - average time f o r a s i n g l e experiment (scan) ID, 2D, 3D - Dime n s i o n a l i t y of the experiment - 35 -imaging time and S/N of the image. Consider that i t i s d e s i r e d to improve the r e s o l u t i o n by a f a c t o r of 2 i n a l l dimensions, i . e . an objec t p r e v i o u s l y represented by n x n x n voxels i s now defined by 2n x 2n x 2n v o x e l s . The volume of each v o x e l i n the h i g h r e s o l u t i o n image i s reduced by a f a c t o r of 8 and hence the S/N obtained i s a l s o reduced by the same amount. Thus the time r e q u i r e d to o b t a i n the high r e s o l u t i o n image w i t h same S/N as i n the low r e s o l u t i o n image i s increased by a f a c t o r of 64. I n f a c t the imaging time increases as a^ where, 'a' i s the f a c t o r by which the r e s o l u t i o n i s increased. I f i t i s merely d e s i r e d to improve the r e s o l u t i o n i n the image plane while the same s l i c e t h i c k n e s s i s r e t a i n e d , the imaging time increases as aV In e i t h e r case, the image a c q u i s i t i o n time and the S/N are d r a s t i c a l l y a f f e c t e d by the increase i n r e s o l u t i o n . 2.2.2 P r o j e c t i o n - R e c o n s t r u c t i o n Imaging [25] As a l r e a d y seen i n the beginning of t h i s Chapter, the NMR absorp-t i o n l i n e shape i n a magnetic f i e l d gradient corresponds to the s p i n d e n s i t y p r o j e c t i o n of the three-dimensional o b j e c t i n a d i r e c t i o n normal to the gr a d i e n t . I n the p r o j e c t i o n - r e c o n s t r u c t i o n method, a s e r i e s of such p r o j e c t i o n s of the object i s obtained at d i f f e r e n t angles by changing the gradient d i r e c t i o n w i t h respect to the obje c t ( F i g . 2.6). These p r o j e c t i o n s , taken together, uniquely define the shape of the ob j e c t , and t h e r e f o r e an image of the object can be re c o n s t r u c t e d by a s u i t a b l e procedure. The problem of r e c o n s t r u c t i o n of the shape of the - 36 -Y F i g . 2.6: P r o j e c t i o n - R e c o n s t r u c t i o n method. The image i s constructed by o b t a i n i n g s e v e r a l one-dimensional p r o j e c t i o n s of the ob j e c t at d i f f e r e n t d i r e c t i o n s ( i n d i c a t e d by arrows) defined by the f i e l d g radient (from Ref. 25). ob j e c t from i t s p r o j e c t i o n s i s a general one, and a review of recon-s t r u c t i o n methods can be found i n Ref. 30. This method a l s o forms the b a s i s of the h i g h l y s u c c e s s f u l X-ray computed tomography pioneered by H o u n s f i e l d [31]. In Lauterbur's o r i g i n a l experiment [25], p r o j e c t i o n s of the object (2 tubes of water) at d i f f e r e n t angles were recorded by the CW NMR method by r o t a t i n g the obje c t w i t h respect to the gradient d i r e c t i o n . These p r o j e c t i o n s were then subjected to a standard r e c o n s t r u c t i o n 37 -al g o r i t h m to generate the image. However, use of FT methods to record the p r o j e c t i o n s o f f e r s i g n i f i c a n t advantages, and are g e n e r a l l y used. In a d d i t i o n to the w e l l known improvement i n s e n s i t i v i t y , many of the a n a l y t i c r e c o n s t r u c t i o n methods r e q u i r e F o u r i e r transforms of the p r o j e c t i o n s to be c a l c u l a t e d , and these are d i r e c t l y a v a i l a b l e as f r e e i n d u c t i o n s decays i n the case of FT techniques. The F o u r i e r p r o j e c t i o n -r e c o n s t r u c t i o n imaging method represents the best method f o r a t t a i n i n g the maximum s i g n a l - t o - n o i s e r a t i o [15]. Moreover, r e o r i e n t a t i o n of the gradi e n t d i r e c t i o n i s p r e f e r r e d over obj e c t r o t a t i o n and can be e a s i l y accomplished by changing the magnitudes of the gradient v e c t o r compo-nents. For a n x n p i x e l image, a number of p r o j e c t i o n s of order n i n it radians i s r e q u i r e d w i t h each p r o j e c t i o n c o n t a i n i n g n p o i n t s . Extension of t h i s method i n t o a l l three dimensions has a l s o been demonstrated [32,33], but has the drawback of r e q u i r i n g powerful computing f a c i l i t i e s to a t t a i n reasonable e f f i c i e n c y . 2.2.3 F o u r i e r Imaging [26] The F o u r i e r imaging method represents an extension of the concept of two-dimensional NMR spectroscopy to provide s p a t i a l i n f o r m a t i o n . This method u t i l i z e s m u lti-dimensional F o u r i e r transformations to con-s t r u c t the e n t i r e image without r e s o r t i n g to r e c o n s t r u c t i o n algorithms. I t o f f e r s considerable computational and experimental s i m p l i c i t y over the p r o j e c t i o n - r e c o n s t r u c t i o n method. Further, the F o u r i e r imaging method i s l e s s s u s c e p t i b l e to magnetic f i e l d inhomogeneity and motional - 38 -a r t i f a c t s [34], and a l s o can be e a s i l y adapted i n a v a r i e t y of ways. These advantages outweigh the decrease i n s e n s i t i v i t y compared to the p r o j e c t i o n - r e c o n s t r u c t i o n method due to the f a c t that the s i g n a l i s not observed during the e n t i r e a v a i l a b l e time [26], and thus has become the imaging method of choice. In general, the F o u r i e r imaging experiment c o n s i s t s of three time p e r i o d s ; p r e p a r a t i o n , e v o l u t i o n and d e t e c t i o n (see F i g . 2.7). The p r e p a r a t i o n p e r i o d c o n s i s t s of a delay time, during which the s p i n system i s allowed to reach the e q u i l i b r i u m c o n d i t i o n , f o l l o w e d by e x c i t a t i o n of the magnetization i n a s u i t a b l e manner. During the e v o l u t i o n p e r i o d , the n o n e q u i l i b r i u m magnetization c r e a t e d during the p r e p a r a t i o n p e r i o d i s allowed to evolve i n the presence of magnetic f i e l d g r a d ients to encode s p a t i a l i n f o r m a t i o n . F i n a l l y , the d e t e c t i o n p e r i o d represents the a c q u i s i t i o n of the s i g n a l under s u i t a b l e c o n d i t i o n s . The b a s i c experimental sequence proposed by Kumar et a l . [26] f o r two-dimensional imaging (encoding of two s p a t i a l axes) i s shown i n F i g . 2.7. The sequence c o n s i s t s of a 90° pulse which e x c i t e s a l l the spins i n the plane, f o l l o w e d by the a p p l i c a t i o n of the G x gradient f o r a time t x . At the end of t h i s p e r i o d , the G x gradient i s switched o f f and the Gy g r a d i e n t i s a p p l i e d . The f r e e i n d u c t i o n s i g n a l i s observed during t y i n the presence of the Gy gradient. The observed s i g n a l i s then a f u n c t i o n of both time p e r i o d s , t x and t y . The experiment i s repeated f o r a s e r i e s of t x values by incrementing t x by a constant, amount. This generates a data m a t r i x S ( t x , t y ) , which upon double F o u r i e r transforma-t i o n gives a frequency domain data matrix S(u>x,Wy), corresponding to the 39 -RF 90" Signal — • PREPARATION EVOLUTION DETECTION PHASE ENCODE FREQUENCY ENCODE F i g . 2.7: The b a s i c 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 sequence. s p a t i a l d i s t r i b u t i o n o f the s p i n s w i t h i n t h e p l a n e . I n o r d e r t o u n d e r s t a n d t h e above sequence, c o n s i d e r t h e s i g n a l from a volume element l o c a t e d a t s p a t i a l c o o r d i n a t e s x,y. I n t h e p r e s e n c e o f G x, t h e a n g u l a r p r e c e s s i o n a l f r e q u e n c y o f t h e m a g n e t i z a t i o n i n the r o t a t i n g frame i s g i v e n by fix = QQ + 7G xx, where M 0 i s t h e o f f s e t f r e q u e n c y i n t h e absence o f t h e g r a d i e n t . Thus, d u r i n g t x , t h e t r a n s v e r s e m a g n e t i z a t i o n from t he volume element a t x,y a c q u i r e s a phase - 40 -angle <f>K given by ^x = (fio + 7 G x - x ) t x • 2 - 1 5 Therefore the phase of the s i g n a l detected during t y r e f l e c t s the p o s i t i o n of the volume element along x. During t y , the p r e c e s s i o n a l frequency i s changed to Qy = 0 o + 7Gy.y, and the s i g n a l observed i s t h e r e f o r e given by S ( t x , t y ) = Kp(x,y) exp i (W 0+ 7G x.x)t x + (u 0+7G y.y)ty exp • ( t +t ) _ x _ _ Y T 2 2.16 where p(x,y) i s the s p i n d e n s i t y at p o i n t x,y. The F o u r i e r trans-formation of the data matrix S ( t x , t y ) w i t h respect to t y produces the data m a t r i x S ( t x , W y ) , i n which the resonance l i n e i s centered at W y = fiQ + 7Gy.y. The phase of t h i s resonance l i n e w i l l be modulated depending on t x according to the Eq. 2.15. The frequency of t h i s modulation i s determined by F o u r i e r t r a n s f o r m a t i o n of S ( t x , W y ) w i t h respect to t x , A c r o s s - s e c t i o n p a r a l l e l to the t x a x i s i n the data m a t r i x S ( t x , W y ) at W y = u 0 + yGy.y i s described by S ( t x , f l 0 + 7 G y . y ) - KT 2p(x,y) exp 1 ( f i 0 + 7 G x . x ) t x exp (-t x/T 2) 2.17 The F o u r i e r t r a n s f o r m a t i o n of t h i s cross - s e c t i o n w i t h respect to t x y i e l d s a resonance l i n e at w x = WQ + 7G x.x. Thus, F o u r i e r trans-formation of a l l the c r o s s - s e c t i o n s through S ( t x , W y ) y i e l d s the data m a t r i x S(wx,o>y), i n which the resonance l i n e i s centered at coordinates - 41 -QQ + 7G x.x, n o + 7G y.y. From the above d i s c u s s i o n i t i s c l e a r that the p o s i t i o n and the amplitude of the resonance l i n e i n the two-dimensional spectrum S ( w x , W y ) i s d i r e c t l y r e l a t e d r e s p e c t i v e l y to the s p a t i a l coordinates and the s p i n d e n s i t y of the volume element. Thus the data matrix S ( w x , W y ) , derived from a l l the volume elements w i t h i n the plane corresponds to an image of the plane. I t should be noted that the s p a t i a l coordinates x and y were encoded i n t o S ( t x , t y ) by making the phase and the frequency of the s i g n a l dependent upon the r e s p e c t i v e coordinates. Consequently, the r e s p e c t i v e gradients used f o r these f u n c t i o n s are r e f e r r e d to as the phase-encoding and frequency-encoding gr a d i e n t s . Several noteworthy aspects of t h i s experiment w i t h regard to the image obtained should be mentioned. F i r s t , the s p a t i a l l y encoded frequencies are dependent upon the o f f s e t frequency ( 0 o ) i n both dimensions. The consequence of t h i s i s t h a t the images of d i f f e r e n t chemical s h i f t species ( i . e . d i f f e r e n t o f f s e t frequencies) are s h i f t e d w i t h respect to each other by the corresponding chemical s h i f t d i f f e r -ence. Second, i n a s i m i l a r manner, the inhomogeneity of the s t a t i c magnetic f i e l d B Q a l s o causes the resonance frequencies to be d i s t o r t e d i n both dimensions over that imposed by the gradients [35]. Both these problems can be a l l e v i a t e d by the use of la r g e enough gradient magni-tudes so that the frequency d i s p e r s i o n due to the grad i e n t (7G xx and 7Gyy) dominates over the chemical s h i f t d i f f e r e n c e and the magnetic f i e l d inhomogeneity. - 42 -Spin-Warp Imaging [36] A v a r i a t i o n on the F o u r i e r imaging procedure of Kumar et a l . [26] i s the spin-warp method [36]. In the method of Kumar et a l . . the phase-encoding of the s i g n a l was achieved by the a p p l i c a t i o n of a constant g r a d i e n t over an incremented time p e r i o d ; i . e . the phase angle <£x i n Eq. 2.15 was v a r i e d by incrementing t x . A l t e r n a t i v e l y , the same e f f e c t can be r e a l i z e d by the v a r i a t i o n of the magnitude of the f i e l d g r a d i e n t (G x) while keeping the phase-encoding time t x constant. This forms the b a s i s of the spin-warp method. Therefore, the b a s i c spin-warp imaging sequence f o r a two-dimensional case consis.ts of the same sequence shown i n F i g . 2.7, except that the amplitude of G x i s v a r i e d l i n e a r l y i n successive experiments while keeping the phase-encoding time p e r i o d constant. The b a s i c spin-warp sequence can be analyzed i n a s i m i l a r manner as d e s c r i b e d p r e v i o u s l y f o r the method of Kumar et a l . Assuming G x i s used as the phase-encoding gra d i e n t , the i n i t i a l data matrix, now represented by S ( G x , t y ) , i s given by Eq. 2.16, and a c r o s s - s e c t i o n p a r a l l e l to the G x a x i s i s given by Eq. 2.17, i n which t x i s a constant. F o u r i e r t r a n s f o r m a t i o n of Eq. 2.17 w i t h respect to G x y i e l d s a reasonance l i n e centered at 7Xt x, r e f l e c t i n g the x - a x i s p o s i t i o n of the volume element. This i s independent of the resonance o f f s e t QQ, and hence, the chemical s h i f t . Thus, as a consequence of keeping the phase-encoding time p e r i o d constant, i n spin-warp imaging, the e f f e c t s of chemical s h i f t as w e l l as of s t a t i c magnetic f i e l d inhomogeneity are e l i m i n a t e d from the phase-encoding dimension. D i s t o r t i o n s due to the s t a t i c magnetic f i e l d - 43 -inhomogeneities w i l l s t i l l be observed along the frequency-encoding dimension y, but can be overcome by i n c r e a s i n g the s t r e n g t h of G y. Furthermore, the s e n s i t i v i t y of the spin-warp method i s s i g n i f i c a n t l y d i f f e r e n t from the method of Kumar et a l . [26] s i n c e the s i g n a l i s sampled during a f i x e d time p e r i o d . This s e n s i t i v i t y f a c t o r can be d e r i v e d i n combination w i t h the a n a l y s i s presented elsewhere [28,29,37], and can a l s o be seen by i n s p e c t i o n of Eq. 2.17. When t x i s constant (G x v a r i a b l e , s p i n warp method), Eq. 2.17 represents a constant amplitude s i n u s o i d a l wave, w h i l s t when t x i s the v a r i a b l e (method of Kumar et a l . [26]) i t represents an e x p o n e n t i a l l y damped si n e f u n c t i o n . Since the peak i n t e n s i t y of a frequency domain s i g n a l i s p r o p o r t i o n a l to the area under the corresponding time domain s i g n a l [37], F o u r i e r t r a n s f o r m a t i o n of Eq. 2.17 i n the spin-warp case produces a s i g n a l of higher amplitude. In p r a c t i c e , the s e n s i t i v i t y achieved w i l l be lower than the maximum due to a p o d i z a t i o n ^ of the s i g n a l to a v o i d undesirable l i n e shapes [29] and the f i n i t e value of the phase-encoding p e r i o d . A more s u b t l e s e n s i t i -v i t y l o s s mechanism which i s present i n both methods has been analyzed r e c e n t l y [38]. Further, the v a r i a t i o n of the amplitude of G x allows the maximum use of the a v a i l a b l e gradient s t r e n g t h , s i n c e both the p o s i t i v e and negative gradient magnitudes can be used to sample the Eq. 2.17. The complete spin-warp sequence used i n p r a c t i c e f o r two-dimen-s i o n a l s l i c e imaging d e r i v e s from that shown i n F i g . 2.8 [36]. In F i g . 2.8, the gradients and the d i f f e r e n t time periods have been named according to t h e i r f u n c t i o n s during the sequence, and the r f pulse i s drawn so as to i n d i c a t e that i t i s amplitude modulated. During the 1 M u l t i p l i c a t i o n of the s i g n a l by a weighting f u n c t i o n [ 2 ] . 44 RF G-Slice \ G-Phase G-Read Signal time < SLICE PHASE SELECTION ENCODE FREQUENCY ENCODE F i g . 2.8: The complete spin-warp imaging sequence f o r two-dimensional s l i c e imaging. - 45 -s l i c e s e l e c t i o n p e r i o d , a s l i c e i n a three-dimensional o b j e c t i s e x c i t e d by a p p l y i n g a f r e q u e n c y - s e l e c t i v e r f pulse i n the presence of a gradient ( G - s l i c e ) . In the phase-encoding p e r i o d , a l l three gradients are a p p l i e d to accomplish s p e c i f i c f u n c t i o n s . The a p p l i c a t i o n of the negative G - s l i c e gradient refocusses the magnetization which dephased during the r f pulse (see Chapter I I I ) . The negative read-gradient (G-read) dephases the magnetization along the frequency-encoding d i r e c -t i o n which i s subsequently refocussed by the a p p l i c a t i o n of a p o s i t i v e read-gradient during the d e t e c t i o n p e r i o d . This enables the s i g n a l to be observed as an echo a f t e r the read-gradient has s t a b i l i z e d , and avoids the p o s s i b l e s i g n a l d i s t o r t i o n due to the f i n i t e g r a d i e n t r i s e time i f i t was observed as a f r e e i n d u c t i o n decay. The G-phase gra-d i e n t , which i s incremented i n successive experiments, encodes the s p a t i a l d i s t r i b u t i o n of spins along the phase-encoding d i r e c t i o n . During the phase-encoding p e r i o d , time-dependent gradients are normally used to a v o i d both the d i s t o r t i o n s due to eddy c u r r e n t e f f e c t s and the t e c h n i c a l d i f f i c u l t i e s i n v o l v e d i n generating constant amplitude g r a d i e n t p u l s e s . For obvious reasons, the time dependence of the g r a d i e n t s u s u a l l y takes the form of a half-sine-wave. I t should be noted t h a t p r o f i l i n g the gradient magnitudes i n t h i s manner demands consider-able a d d i t i o n a l hardware and software c o n t r o l s . Since the acquired data matrix S(G x,ty) i s sampled at s p e c i f i c values of G x and t x , the maximum s p a t i a l d i s t a n c e ( f i e l d - o f - v i e w ) represented i n the f i n a l image i s determined by the sampling r a t e [ 2 ] . In order to prevent fold-over-'- [ 2 ] , the f i e l d - o f - v i e w should be s l i g h t l y g r e a t e r than the dimensions of the o b j e c t . The f i e l d - o f - v i e w (FOV) i n M i s r e p r e s e n t a t i o n of frequencies due to inadequate sampling. - 46 -the phase-encoding (PE) and frequency-encoding (FE) dimensions are r e l a t e d to the experimental parameters v i a , 2ir 2ix ( F O V ) p E = and ( F O V ) F E = 2.18 7 ( A G p ) t p 7G r(At) where AGp i s the phase-encoding gradient increment, tp i s the phase encoding p e r i o d , G r i s the magnitude of the read-gradient, and At i s the time between two sampled p o i n t s i n the d i g i t i z e d s i g n a l (dwell time). I n the case where the phase-encoding gradient i s time-dependent, the (FOV)pE i s given by 2TT ( F O V ) p E = 2.19 where J G„(t).dt = G Q.n, and n i s an i n t e g e r . The phase-encoding o v g r a d i e n t magnitude i s determined by the value of n which i s v a r i e d as — , — + 1 .... -1, 0, +1, .... ^ - 1, where N defi n e s the t o t a l number 2 2 2 of g r a d i e n t increments. The value of N i s important f o r two reasons. I t determines the s p a t i a l r e s o l u t i o n obtained i n the phase-encoding dimension given by (F0V)pg/N, and a l s o the t o t a l imaging time given by TR.N, where TR ( r e p e t i t i o n time) i s the time d u r a t i o n between i n d i v i d u a l experiments. Therefore, higher s p a t i a l r e s o l u t i o n [smaller (F0V)pg/N] along the phase-encoding dimension c a l l s f o r p r o p o r t i o n a t e increase i n imaging time. S i m i l a r l y , the s p a t i a l r e s o l u t i o n along the frequency-encoding dimension i s given by (F0V)p E/N^, where Nj_ i s h a l f the number - 47 -of sampled p o i n t s i n the d i g i t i z e d s i g n a l . Extension of F o u r i e r imaging methods i n t o three dimensions i n v o l v e s the use of two phase-encoding gradients and a frequency-encoding gra-d i e n t [26, 39-41]. Since a l l combinations of the two phase-encoding gradient magnitudes need to be sampled, the t o t a l experimental time increases to TR.Nx.Ny where N x and Ny are the number of phase-encoding gradient increments i n the r e s p e c t i v e dimensions. In the spin-warp method both phase-encoding gradients can be a p p l i e d simultaneously and t h e r e f o r e the t o t a l d u r a t i o n of a s i n g l e sequence i s u n a l t e r e d . This i s not p o s s i b l e w i t h the method of Kumar et a l . [26]. Further d e t a i l s of the three-dimensional spin-warp sequence are presented i n Chapter IV. 2.2.4 Chemical S h i f t Resolved Imaging Imaging techniques discussed i n the preceding s e c t i o n s ignore the presence of c h e m i c a l l y s h i f t e d s p e c i e s , and p e r t a i n only to the encod-in g of the s p a t i a l s p i n d i s t r i b u t i o n i n t o the frequency domain. T h i s , apart from the degradation of the image q u a l i t y , causes the l o s s of chemical s h i f t i n f o r m a t i o n present w i t h i n the o b j e c t under i n v e s t i g a -t i o n . Chemical s h i f t r e s o l v e d imaging methods preserve t h i s i n f o r m a t i o n by e n a b l i n g each c h e m i c a l l y s h i f t e d species to be imaged s e p a r a t e l y . The o r i g i n a l methods proposed f o r chemical s h i f t r e s o l v e d imaging were based on the p r o j e c t i o n - r e c o n s t r u c t i o n method [42-44]. These approaches [43,44] r e q u i r e the magnitude of the f i e l d g radient to be s u f f i c i e n t l y low so that the frequency spread of the resonances caused - 48 -by the gradient i s smaller than the chemical s h i f t s e p a r a t i o n . This represents a s e r i o u s l i m i t a t i o n , s i n c e the decreased g r a d i e n t magnitudes a l s o l i m i t the achievable s p a t i a l r e s o l u t i o n and hence preclude the general a p p l i c a b i l i t y of the technique. More r e c e n t l y , a method i n which the i n t r i n s i c chemical s h i f t can be used as a component of the magnetic f i e l d g radient i n c o n j u n c t i o n w i t h the p r o j e c t i o n -r e c o n s t r u c t i o n method has been proposed [45,46]. A chemical s h i f t imaging method which employs r f f i e l d gradients i n s t e a d of s t a t i c magnetic f i e l d g radients has a l s o been suggested [47]. This method, which i s based on the p r i n c i p l e of r o t a t i n g frame zeugmatography [27] , has been demonstrated u s i n g the inherent r f f i e l d g r a d i ents produced by a surface c o i l [48]. The most g e n e r a l l y a p p l i c a b l e method developed f o r chemical s h i f t r e s o l v e d imaging [49-54] deri v e s from the spin-warp imaging technique. The b a s i c sequence which enables one-dimensional mapping of c h e m i c a l l y s h i f t e d species i s shown i n F i g . 2.9. The important f e a t u r e of t h i s experiment i s that the s i g n a l i s acquired i n the absence of magnetic f i e l d g r a d i e n t s . This enables the chemical s h i f t spectrum to be d i r e c t l y observed. The s p a t i a l d i s t r i b u t i o n of the chemical s h i f t s i s encoded i n t o the observed s i g n a l by the a p p l i c a t i o n of the phase-encod-in g g r a d i e n t s p r i o r to s i g n a l a c q u i s i t i o n . I n p r a c t i c e , the sequence shown i n F i g . 2.9 i s m o d i f i e d so that the s i g n a l i s observed as an echo by the a p p l i c a t i o n of a 180° pulse at the end of the phase-encoding p e r i o d . The i n i t i a l data matrix S j c ( G x , t 2 ) , obtained from a volume element c o n t a i n i n g a chemical s h i f t species k defined by the angular frequency - 49 -RF 9tf Signal tx PHASE ENCODING OF SPATIAL DISTRIBUTION *2 FREQUENCY ENCODING OF CHEMICAL SHIFT F i g . 2.9: The b a s i c chemical s h i f t r e s o l v e d imaging sequence. i s g i v e n by s k ( G x - t 2 > = K />k<x) e x P 1 l(°k + T^ x-'Otx + " ^ 2 exp ( t + t ) x 2 T 2 k 2.20 where t 2 r e p r e s e n t s t h e s i g n a l a c q u i s i t i o n t i m e i n t h e absence o f any g r a d i e n t s . 50 -F o u r i e r t r a n s f o r m a t i o n of the data matrix S ^ ( G x , t 2 ) w i t h respect to t 2 and G x y i e l d s the two-dimensional spectrum S(w x,W2)> where w x and W2 corresponds p u r e l y to the s p a t i a l a x i s and the chemical s h i f t r e s p e c t i v e l y . At t h i s p o i n t i t i s appropriate to note that the chemical s h i f t r e s o l v e d experiment a l s o provides a convenient means of mapping the d i s t r i b u t i o n of the s t a t i c magnetic f i e l d [55-57]. Extension of the experiment to incorporate a l l s p a t i a l dimensions i n v o l v e s simultaneous a p p l i c a t i o n of three phase-encoding g r a d i e n t s . This corresponds to a four-dimensional experiment. The t o t a l imaging time f o r such an experiment i s given by TR.N xNyN z and i s not a f f e c t e d i n f i r s t order by the s i g n a l a c q u i s i t i o n time. Therefore i n s i t u a t i o n s where low s p e c t r a l r e s o l u t i o n along the chemical s h i f t dimension can be t o l e r a t e d , the t o t a l imaging time can be decreased by phase-encoding the chemical s h i f t p r i o r to s i g n a l d e t e c t i o n [58,59]. In t h i s case the imaging time i s given by TR.N xN yN£, where Ng governs the s p e c t r a l r e s o l u t i o n along the chemical s h i f t dimension l e a d i n g to a r e d u c t i o n i n the imaging time by a f a c t o r of Nz/N^. Another approach to chemical s h i f t r e s o l v e d imaging i s v i a sel e c -t i v e e x c i t a t i o n or suppression of s p e c i f i c resonances. This o f f e r s a consid e r a b l e saving i n experimental time since the d i m e n s i o n a l i t y of the experiment i s reduced by one. A d e t a i l e d d i s c u s s i o n of t h i s technique i s presented i n Chapter IV. - 51 -References: Chapter I I 1. T.C. F a r r a r and E.D. Becker, "Pulse and F o u r i e r Transform NMR", Academic Press, New York, 1971. 2. M.L. M a r t i n , J . - J . Delpuech, and G.J. M a r t i n , " P r a c t i c a l NMR Spec-troscopy", Heyden and Son L t d . , P h i l a d e l p h i a , 1980. 3. D. Shaw, " F o u r i e r Transform NMR Spectroscopy (Second E d i t i o n ) , E l s e v i e r , New York, 1984. 4. J.W. Emsley, J . Feeney, and L.H. S u t c l i f f e , "High R e s o l u t i o n NMR Spectroscopy", Volume 1, Chapter 2, Pergamon Press, New York, 1965. 5. F. Bloch, Phys. Rev. 70, 460 (1946). 6. D.I. Hoult, Prog, i n NMR Spectroscopy, 12, 41 (1978). 7. W.S. Hinshaw and A.H. Lent, Proc. of I.E.E.E. 71, 338 (1983). 8. P. M a n s f i e l d and P.G. M o r r i s , "NMR Imaging i n Biomedicine", Chapter 3, Academic Press, New York, 1982. 9. J.M.S. Hutchison, W.A. E d e l s t e i n , and G. Johnson, J . Phys. E. S c i . Instrum. 13, 947 (1980). 10. A.N. Garroway, P.K. G r a n n e l l , and P. M a n s f i e l d , J . Phys. C. 7, L457 (1974). 11. W.S. Hinshaw, J . Appl. Phys. 47, 3709 (1976). 12. H.R. Brooker and W.S. Hinshaw, J . Magn. Reson. 30, 129 (1978). 13. D.I. Hoult, J . Magn. Reson. 33, 183 (1979). 14. P.A. Bottomley, Rev. S c i . Instrum. 53, 1319 (1982). 15. P. Brunner and R.R. Ernst, J . Magn. Reson. 33, 83 (1979). 16. R. Damadian, L. Minkoff, M. Goldsmith, M. Stanford, and J . Koutcher, P h y s i o l . Chem. Phys. 8, 61 (1976). 17. R. Damadian, M. Goldsmith, and L. Minkoff, P h y s i o l . Chem. Phys. 10, 285 (1978). 18. W.S. Hinshaw, P.A. Bottomley, and G.N. Holland, Nature (London) 270, 722 (1977). 19. P. M a n s f i e l d , A.A. Maudsley, and T. Baines, J . Phys. E. 9, 271 (1976). - 52 -20. R.J. Sutherland and J.M.S. Hutchison, J . Phys. E. 11, 79 (1978). 21. L.E. Crooks, I.E.E.E. Trans. Nucl. S c i . NS-27 , 1239 (1980). 22. P. M a n s f i e l d and A.A. Maudsley, J . Phys. C 9, L409 (1976). 23. P. M a n s f i e l d and A.A. Maudsley, J . Magn. Reson. 27, 101 (1977). 24. P. M a n s f i e l d and I.L. Pykett, J . Magn. Reson. 29, 355 (1978). 25. P.C.- Lauterbur, Nature (London) 242, 190 (1973). 26. A. Kumar, D. W e l t i , and R.R. Ernst, J . Magn. Reson. 18, 69 (1975). 27. D.I. Hoult, J . Magn. Reson. 33, 183 (1979). 28. W.P. Aue, P. Bachmann, A. Wokaun, and R.R. Ernst, J . Magn. Reson. 29, 523 (1978). 29. M.M. L e v i t t , G. Bodenhausen, and R.R. Ernst, J . Magn. Reson. 58, 462 (1984). 30. R.A. Brooks and G. Di Chiro, Phys. Med. B i o l . 21, 689 (1976). 31. G.N. H o u n s f i e l d , Br. J . R a d i o l . 46, 1016 (1973). 32. CM. L a i and P.C. Lauterbur, J . Phys. E. 13, 747 (1980). 33. CM. L a i and P.C. Lauterbur, Phy, Med. B i o l . 26, 851 (1981). 34. D.A. Ortendahl, L.E. Crooks, and L. Kaufmann, I.E.E.E. Trans. Nucl. S c i . NS-30, 692 (1983) . 35. K. Sekihara, M. Kuroda, and H. Kohno, Phy. Med. B i o l . 29, 15 (1984). 36. W.A. E d e l s t e i n , J.M.S. Hutchison, G. Johnson, and T. Redpath, Phy. Med. B i o l . 25, 751 (1980). 37. E.D. Becker, J.A. F e r r e t t i , and P.N. Gambhir, Anal. Chem. 51, 1413 (1979) . 38. A.A. Maudsley, J . Magn. Reson. 68, 363 (1986). 39. G. Johnson, J.M.S. Hutchison, J.W. Redpath, and L.M. Eastwood, J . Magn. Reson. 54, 374 (1983). 40. J.H. den Boef, C.M.J, van U i j e n , and CD. Holzscherer, Phy. Med. B i o l . 29, 857 (1984). - 53 -41. J . Frahm, A. Hasse, and D. Matthaei, J . Comp. A s s i s t . Tomogr. 10, 363 (1986). 42. P.C. Lauterbur, D.M. Kramer, W.V. House, J r . , and C.-N. Chen, J . Am. Chem. Soc. 97, 6866 (1975). 43. P. Bendel, C.-M. L a i , and P.C. Lauterbur, J . Magn. Reson. 38, 343 (1980). 44. L.D. H a l l and S. Sukumar, J . Magn. Reson. 50, 161 (1982). 45. P.C. Lauterbur, D.N. L e v i n , and R.B. Marr, J . Magn. Reson. 59, 536 (1984) . 46. M.L. Bernardo, J r . , P.C. Lauterbur, and L.K. Hedges, J . Magn. Reson. 61, 168 (1985). 47. S.J. Cox and P. S t y l e s , J . Magn. Reson. 40, 209 (1980). 48. A. Hasse, C. Malloy, and G.K. Radda, J . Magn. Reson. 55, 164 (1983) . 49. T.R. Brown, B.M. K i n c a i d , and K. U g u r b i l , Proc. N a t l . Acad. S c i . USA 79, 3523 (1982). 50. A.A. Maudsley, S.K. H i l a l , W.H. Perman, and H.E. Simon, J . Magn. Reson. 51, 147 (1983). 51. J.C. Haselgrove, V.H. Subramanian, J.S. Leigh, J r . , L. G y u l a i , and B. Chance, Science 220, 1170 (1983). 52. I.L. Pykett and B.R. Rosen, Radiology 149, 197 (1983). 53. L.D. H a l l and S. Sukumar, J . Magn. Reson. 56, 314 (1984). 54. L.D. H a l l , V. Rajanayagam, and S. Sukumar, J . Magn. Reson. 61, 188 (1985) . 55. A.A. Maudsley, A. Oppelt, and A. Ganssen, Siemens Forch-u. Ent-w i c k l . - B e r . 8, 326 (1979). 56. A.A. Maudsley, H.E. Simon, and S.K. H i l a l , J . Phys. E. 17, 216 (1984) . 57. K. Sekihara, S. Matsui, and H. Kohno, J . Phy. E. 18, 224 (1985). 58. R.E. Sepponen, J.T. Sipponen, and J . I . Tanttu, J . Comp. A s s i t . Tomogr. 8, 585 (1984). 59. R.E. Sepponen, Magn. Res. Imag. 3, 163 (1985). - 5 4 -CHAPTER III FREQUENCY-SELECTIVE EXCITATION IN NMR IMAGING - 55 -I I I . FREQUENCY-SELECTIVE EXCITATION IN NMR IMAGING Several p o s s i b l e techniques t h a t can be employed to define the s p a t i a l plane ( s l i c e ) to be imaged were introduced i n Chapter I I , S e c t i o n 2.1.4. Of these, the most widely used method i s that of s e l e c t i v e e x c i t a t i o n i n the presence of a magnetic f i e l d g radient [1-6]. This method has the advantage that i t can be implemented more conv e n i e n t l y than the other techniques and the d e f i n i t i o n of the s l i c e s e l e c t e d i s a l s o s u p e r i o r . In t h i s Chapter, the t h e o r e t i c a l and e x p e r i -mental c o n s i d e r a t i o n s as w e l l as the implementation of t h i s technique i s described. Further, a novel method to e l i m i n a t e problems a s s o c i a t e d w i t h s l i c e s e l e c t i o n i n the presence of c h e m i c a l l y s h i f t e d species i s proposed, and i t s f e a s i b i l i t y i s a l s o demonstrated. 3.1 Technique of S l i c e S e l e c t i o n 3.1.1 Theory of S e l e c t i v e E x c i t a t i o n S e l e c t i v e e x c i t a t i o n of a narrow frequency band i n the context of s l i c e s e l e c t i o n i n NMR imaging i s e q u i v a l e n t to a s i m i l a r problem encountered i n NMR spectroscopy, where the e x c i t a t i o n of a group of c h e m i c a l l y s h i f t e d resonances, while not p e r t u r b i n g others, i s d e s i r e d f o r v a r i o u s purposes. These include s o l v e n t suppression f o r improved dynamic range, reducing complexity of crowded s p e c t r a by s p i n decoupling 56 -and s e l e c t i v e e x c i t a t i o n i n p o p u l a t i o n t r a n s f e r , chemical exchange, and r e l a x a t i o n experiments [7]. Thus, e a r l y s t u d i e s done i n r e l a t i o n to spectroscopy [8-11] provide the necessary background to the methodology th a t can be employed. The exact s p i n magnetization e x c i t a t i o n p a t t e r n due to an r f pulse i n general can be determined by c o n s i d e r i n g the Bloch equations [12,13] which d e s c r i b e the motion of magnetization under the i n f l u e n c e of a magnetic f i e l d . However, the form of the time domain r f e x c i t a t i o n needed to achieve a c e r t a i n frequency domain e x c i t a t i o n p a t t e r n i s not immediately obvious v i a the Bloch equations. Therefore, i n i t i a l l y i t i s h e l p f u l to consider the problem i n terms of the l i n e a r systems approach [14,15] i n the frequency domain. 3.1.1.1 L i n e a r Systems Approach [14,15] Consider the response of a l i n e a r system subjected to a d r i v i n g f u n c t i o n ( input) I ( t ) ( F i g . 3.1). The response from the system R(t) i s given by the c o n v o l u t i o n of the d r i v i n g f u n c t i o n , w i t h the system impulse response f u n c t i o n H ( t ) . R(t) = H(t) * I ( t ) 3.1 Using the c o n v o l u t i o n theorem [16] Eq. 3.1 can be w r i t t e n i n the frequency domain as, R ( f ) = H ( f ) . I ( f ) 3.2 - 57 -INPUT I(t) 1(f) Hit) LINEAR SYSTEM Hit) OUTPUT Rlt)s Kt)®H(t) R(f)= 1(f) . Hlf) F i g . 3.1: R e l a t i o n s h i p between the input and output of a l i n e a r system c h a r a c t e r i z e d by H(t) and H ( f ) . where 1 ( f ) and R ( f ) are the frequency domain d r i v i n g f u n c t i o n and the response r e s p e c t i v e l y , and H(f) i s the t r a n s f e r f u n c t i o n of the system. H(f) completely describes the system i n the frequency domain j u s t as H(t) does i n the time domain. I f the d r i v i n g f u n c t i o n I ( t ) i s an impulse (a d e l t a f u n c t i o n ) , then 1 ( f ) i s a constant, s i n c e 1 ( f ) i s the F o u r i e r transform of I ( t ) . In t h i s case, the time and frequency domain response f u n c t i o n s , R ( t) and R ( f ) correspond to the system impulse response f u n c t i o n and the t r a n s f e r f u n c t i o n , H(t) and H(f) r e s p e c t i v e l y . Thus the measurement of the system response to an impulse gives a l l the necessary i n f o r m a t i o n to completely c h a r a c t e r i z e the system. Further, from Eq. 3.2, i t can be seen t h a t the response of a l i n e a r system i n the frequency domain i s p r o p o r t i o n a l to the F o u r i e r transform of the d r i v i n g f u n c t i o n . - 58 -I f the response of a s p i n system to an NMR experiment i s considered l i n e a r , the system t r a n s f e r f u n c t i o n corresponds to the "NMR spectrum", and the impulse response f u n c t i o n corresponds to the f r e e i n d u c t i o n decay s i g n a l observed f o l l o w i n g a narrow r f pulse. With a narrow r f p u l s e , the frequency domain d r i v i n g f u n c t i o n 1 ( f ) i s e s s e n t i a l l y f l a t over the t r a n s f e r f u n c t i o n H(f) and the r e f o r e the frequency domain response R ( f ) corresponds d i r e c t l y to the NMR spectrum. This s i t u a t i o n , shown i n F i g . 3.2, represents the c o n d i t i o n s normally encountered i n NMR spectroscopy. F i g . 3.2: Normal NMR experiment viewed i n terms of the t r a n s f e r f u n c t i o n of the s p i n system. - 59 -I t has been shown t h a t , subjected to c e r t a i n r e s t r i c t i o n s (see S e c t i o n 3.1.1.2), the transverse magnetization ('response' of the s p i n system) cr e a t e d by an r f pulse of a r b i t r a r y shape ( i n the time domain) i s d i r e c t l y p r o p o r t i o n a l to the F o u r i e r transform of the pulse [7] i . e . that Eq. 3.2 i s v a l i d . The inverse of t h i s r e l a t i o n s h i p can be used to produce the pulse sequence (or pulse modulation) necessary f o r a d e s i r e d e x c i t a t i o n p a t t e r n . The method based on t h i s concept i s known as the "synthesized ( t a i l o r e d ) e x c i t a t i o n " technique [10,17]. The ready conceptual l i n k provided by the F o u r i e r transform r e l a t i o n s h i p between the e x c i t a t i o n spectrum and the pulse modulation can be used i n q u a l i t a -t i v e a n a l y s i s and design of f r e q u e n c y - s e l e c t i v e e x c i t a t i o n schemes. From the above d i s c u s s i o n i t i s c l e a r that f r e q u e n c y - s e l e c t i v e e x c i t a t i o n of the magnetization can be obtained most simply by making the frequency spectrum of the d r i v i n g f u n c t i o n narrower than the t r a n s -f e r f u n c t i o n . In the case of a uniform d i s t r i b u t i o n of spins along a magnetic f i e l d g radient i n the context of s l i c e s e l e c t i o n , the t r a n s f e r f u n c t i o n i s e s s e n t i a l l y a constant. Thus the frequency response of the s p i n system corresponds d i r e c t l y to the frequency spectrum ( F o u r i e r transform) of the pulse ( F i g . 3.3). As a r e s u l t , any d e s i r e d frequency e x c i t a t i o n p a t t e r n can be obtained by changing the shape of the r f pulse. At t h i s j u n c t u r e i t i s appropriate to note an i n t e r e s t i n g aspect of t h i s s e l e c t i v e e x c i t a t i o n scheme that has been discussed i n the l i t e r a -t ure [18,19]. The d i r e c t correspondence between the frequency domain d r i v i n g f u n c t i o n and the system response i n the case of a constant t r a n s f e r f u n c t i o n i m p l i e s that the r e s p e c t i v e time domain f u n c t i o n s a l s o - 60 -F i g . 3.3: S e l e c t i v e e x c i t a t i o n experiment viewed i n terms of the t r a n s f e r f u n c t i o n of the s p i n system. have the same r e l a t i o n s h i p ; i . e . the response R ( t ) , i s the same as the d r i v i n g f u n c t i o n I ( t ) . Therefore, since the NMR r e c e i v e r i s normally gated o f f during the a p p l i c a t i o n of the pul s e , the primary response of the s p i n system cannot be observed and n e g l i g i b l e s i g n a l w i l l be detected a f t e r the pulse [18,19]. The p h y s i c a l i n t e r p r e t a t i o n of the - 61 -above argument i s th a t the d i f f e r e n t frequency components of the magne-t i z a t i o n acquire d i f f e r e n t phase angles during the pul s e . Thus, i f the frequency components are completely dephased at the end of the pul s e , no net s i g n a l can be detected. The dephased magnetization can be r e f o -cussed e i t h e r by r e v e r s i n g the gradient d i r e c t i o n or by applying a n o n s e l e c t i v e 180° pulse immediately f o l l o w i n g . the s e l e c t i v e pulse [18,19]. Further, the shape of the echo formed a f t e r the gradient r e v e r s a l (or 180° pulse) c l o s e l y resembles the a p p l i e d pulse [19], and at the maximum of the echo a l l magnetization components have approxi-mately the same phase [21,23]. A d r i v i n g f u n c t i o n w i t h a narrow frequency d i s t r i b u t i o n i s most co n v e n i e n t l y obtained by a long weak r f pulse ('soft p u l s e ' ) . This corresponds to a re c t a n g u l a r modulation of the pul s e . Since the reso-nance s i g n a l r e s u l t i n g from an r f e x c i t a t i o n pulse i s detected w i t h a phase s e n s i t i v e d etector u s i n g the r f c a r r i e r frequency as the r e f e r -ence, the r f c a r r i e r frequency may th e r e f o r e be ignored i n the a n a l y s i s : i . e . the s i g n a l observed represents the behaviour of the s p i n system i n a frame r o t a t i n g at the r f c a r r i e r frequency. The r e c t a n g u l a r modula-t i o n f u n c t i o n and i t s F o u r i e r transform are shown i n F i g . 3.4a. The p r i n c i p a l frequency band-width of a r e c t a n g u l a r modulation i s given by 2/r, where r i s the time d u r a t i o n of the modulation (pulse w i d t h ) . The amplitude of the pulse (B^) i s adjusted to o b t a i n a 90° f l i p angle according to the r e l a t i o n s h i p 7r/2 = yB-^t^, where t w i s the pulse l e n g t h . S o f t r f pulses are commonly used i n NMR spectroscopy [20] but are not s u i t a b l e f o r s l i c e s e l e c t i o n i n NMR imaging because of the secondary e x c i t a t i o n lobes on e i t h e r s i d e of the primary frequency band - 62 -F i g . 3 . 4 : Rf modulation f u n c t i o n s and t h e i r F o u r i e r transforms. (see F i g . 3 . 4 a ) . These side lobes r e s u l t i n e x c i t a t i o n of magnetization i n regions other than the d e s i r e d plane. An r f modulation f u n c t i o n more s u i t a b l e f o r NMR imaging a p p l i c a -t i o n s takes the form of ( s i n wt)/wt [or s i n e wt] which, together w i t h - 63 -i t s F o u r i e r transform, i s shown i n F i g . 3.4b. A sin e f u n c t i o n extending f o r an i n f i n i t e time has a w e l l d e f i n e d r e c t a n g u l a r frequency spectrum but cannot be r e a l i z e d i n p r a c t i c e . Therefore, a s i n e f u n c t i o n trun-cated over a f i n i t e time i n t e r v a l i s commonly used; the e f f e c t of t h i s t r u n c a t i o n on the e x c i t a t i o n spectrum i s shown i n F i g . 3.5. Abrupt t e r m i n a t i o n of the f u n c t i o n causes hig h frequency components on e i t h e r side of the p r i n c i p a l e x c i t a t i o n band as w e l l as uneven i n t e n s i t y w i t h i n the p r i n c i p a l e x c i t a t i o n . The trend towards the t h e o r e t i c a l l i m i t w i t h i n c r e a s i n g width of the sin e f u n c t i o n i s c l e a r l y shown i n F i g . 3.5. The e x c i t a t i o n s p e c t r a shown i n F i g . 3.5 can be improved by apo d i z i n g the truncated s i n e envelope w i t h e i t h e r a Gaussian or a t r i a n g u l a r f u n c t i o n [21]. The e f f e c t of any a p o d i z a t i o n f u n c t i o n i s to decrease the i n t e n s i t y outside the main e x c i t a t i o n band and to produce a more uniform i n t e n s i t y w i t h i n i t . An example of t h i s when u s i n g a t r i a n g u l a r a p o d i z a t i o n f u n c t i o n i s shown i n F i g . 3.6. I t has been shown th a t the t r i a n g u l a r a p o d i z a t i o n performs b e t t e r than the Gaussian a p o d i z a t i o n [21] . A necessary consequence of a p o d i z a t i o n i s the decrease i n the sharpness of the edge d e f i n i t i o n of the p r i n c i p a l band compared to unapodized case. The phase of the frequency components i n the e x c i t a t i o n spectrum has not been addressed i n t h i s d i s c u s s i o n . This i s e a s i l y incorporated by c o n s i d e r i n g both the r e a l and imaginary p a r t s of the F o u r i e r trans-formed f u n c t i o n when the time o r i g i n i s taken at the beginning of the pulse (see S e c t i o n 3.1.1.3, Eq. 3.16 and 3.17). 64 -F i g . 3.5: E f f e c t of t r u n c a t i o n of the sine modulating f u n c t i o n on the e x c i t a t i o n spectrum. P l o t s were obtained by F o u r i e r t r a n s -forming a sine f u n c t i o n ( p e r i o d = 1.8 ms) of v a r y i n g l e n g t h The number of secondary lobes i n the sine f u n c t i o n i s i n d i c a t e d i n the F i g u r e . - 65 -| 1 1 1 1 1 I 1 1 1 1 1 1 1 I j 0 500 1000 1500 Hz F i g . 3 .6 : E f f e c t of t r i a n g u l a r a p o d i z a t i o n of the si n e f u n c t i o n ( p e r i o d 1.8 ms) on the e x c i t a t i o n spectrum. P l o t s were obtained by F o u r i e r transforming the time domain f u n c t i o n shown alongside each e x c i t a t i o n spectrum. The t r i a n g u l a r f u n c t i o n was def-ined by the amplitude and the length of the si n e f u n c t i o n , (a) unapodized case, (b) si n e x ( t r i a n g l e ) , and (c) sine x ( t r i a n g l e ) 2 . - 66 -3.1.1.2 E f f e c t s of Nonlinear Behaviour of Spins From the d i s c u s s i o n i n the preceding s e c t i o n i t i s c l e a r that c o n s i d e r a b l e i n s i g h t to the problem of s e l e c t i v e e x c i t a t i o n can be obtained by c o n s i d e r i n g the l i n e a r response methodology. However, the arguments presented are s t r i c t l y v a l i d only when a p p l i e d to l i n e a r systems. The response of a s p i n system to an r f pulse as governed by Bloch equations, i s n o n l i n e a r , and hence, the r e s u l t s from l i n e a r systems theory are not always a p p l i c a b l e . Nevertheless, l i n e a r approxi-mation can be used to p r e d i c t the frequency response of the spins to an r f p u l s e , provided that the e x c i t a t i o n time i s short compared to the s p i n - l a t t i c e and s p i n - s p i n r e l a x a t i o n times, and a l s o t h a t the net p e r t u r b a t i o n at any frequency i s small ( i . e . small f l i p angles) [7,22]. I t has been shown that the p r e d i c t i o n of transverse magnetization (frequency response) v i a l i n e a r approximation i s v a l i d f o r r f pulses up to f l i p angles of 30°, and the departure from l i n e a r i t y becomes most apparent at f l i p angles c l o s e to 180° [18,22,23]. In the l a t t e r s i t u a t i o n , a n a l y s i s of the Bloch equations should be considered f o r accurate r e s u l t s . An obvious m o d i f i c a t i o n to the l i n e a r approximation theory i s to consider the f l i p angle, r a t h e r than the transverse magnetization, as being p r o p o r t i o n a l to the F o u r i e r transform of the pulse [5,22]. This enables the f l i p angle as a f u n c t i o n of frequency, 6(w), to be expressed as A 0(u>) = 7Bi(») 3.3 - 67 -A where B^(w) i s the F o u r i e r transform of the pulse B ^ ( t ) . Then the transverse and l o n g i t u d i n a l magnetization components (M. and M z r e s p e c t i v e l y ) a f t e r the pulse are given by M x y(w) = M Q sin{ 7B 1(co)} 3.4 and M z(w) A M D cos(7Bj_(co)} 3.5 where M Q i s the e q u i l i b r i u m magnetization. This has been s t u d i e d [22] i n d e t a i l f o r the case of 180° si n e p u l s e , and i t has been shown that the d e v i a t i o n of the s p i n response from l i n e a r approximation becomes apparent when the f l i p angle i s l a r g e and the spins are not on resonance. I t has been shown [19] th a t i n the presence of a gr a d i e n t , an NMR s i g n a l can be observed immediately a f t e r a s e l e c t i v e pulse only when the s p i n system i s d r i v e n i n t o the no n l i n e a r r e g i o n ( i . e . f l i p angle >30°). This response i s a d i r e c t m a n i f e s t a t i o n of the n o n l i n e a r i t y of the s p i n system and bears only a d i s t a n t r e l a t i o n s h i p to the primary response which occurs during the pulse. Both responses can be v i s u a l i z e d by echo formation as mentioned e a r l i e r . A d e t a i l e d account of t h i s i s given i n Ref. 19. 3.1.1.3 A n a l y s i s of Bloch Equations Since NMR experiments are r o u t i n e l y performed i n the no n l i n e a r - 68 -re g i o n , i t i s mandatory that s o l u t i o n of Bloch equations be considered to determine the exact e x c i t a t i o n p a t t e r n . In order to l a y the founda-t i o n f o r the d i s c u s s i o n to f o l l o w , the motion of magnetization under the i n f l u e n c e of a magnetic f i e l d w i l l be b r i e f l y d i s c u s s e d [12,13]. Consider the net macroscopic magnetization M of an ensemble of nucl e a r spins i n a s t a t i c magnetic f i e l d B Q a l i g n e d along the z-axis i n the l a b o r a t o r y frame. At e q u i l i b r i u m , the magnetization (M Q) i s o r i e n t e d along B Q. From c l a s s i c a l c o n s i d e r a t i o n s [24,25], the motion of magnetization M i n a magnetic f i e l d B can be w r i t t e n as, In general, B i n Eq. 3.6 c o n s i s t s of both the s t a t i c magnetic f i e l d B Q a l i g n e d along the z - a x i s , and the r o t a t i n g magnetic v e c t o r of the r f f i e l d B^ i n the x-y plane. I f the motion of the magnetization i s viewed from a frame r o t a t i n g about the z-axis at the same frequency (w r) and dM dt 7M x B 3.6 sense as the B]_ f i e l d , the equation of motion becomes dM = 7M x B e f f 3.7 dt r o t where 3.8 7 - 69 -The r o t a t i n g frame axes (x',y', z) has been chosen so th a t the l i e s along the x ' - a x i s of the r o t a t i n g frame, and i and k are the u n i t v e c t o r s i n that frame. B e f f = bk + B-ii l i 3.9 where 7b = w Q - w r 3.10 i n which 3.11 Thus, from Eq. 3.7, the motion of the magnetization M i n the r o t a t i n g frame f o l l o w s a cone of p r e c e s s i o n about B e f f . This i s sketched i n F i g . 3.7. I t can be e a s i l y seen t h a t when the frequency of the r f f i e l d w r equals the Larmor frequency of spins coQ ("on-resonance" c o n d i t i o n ) , the motion i s i n the z-y' plane of the r o t a t i n g frame w h i l s t the motion of the off-resonance magnetization (u>Q ^  w r) i s i n a t i l t e d plane determined by B e f f . This approach i s u s e f u l when c o n s i d e r i n g a r f pulse of constant amplitude B^. When B^ i s time dependent t h i s elementary p i c t u r e may not be employed to advantage s i n c e the angle B e f f makes w i t h the x - a x i s v a r i e s i n time, and i t i s t h e r e f o r e d i f f i c u l t to see how the magnetization precesses about such a f i e l d . From Eqs. 3.7 to 3.11, the Bloch equations [25] i n the r o t a t i n g frame i n c l u d i n g r e l a x a t i o n terms can be d e r i v e d as - 7 0 -z Bo y X F i g . 3.7: P r e c e s s i o n of s p i n magnetization about B_EFF determined by the o f f s e t b and B^ . dM x M x = A w . M„ — — ^ y T 2 3.12a dM,. M, = - A w . M x + 7 B 1 ( t ) . M z  dt T _ 3 .12b dM, dt -yB>l(t). My + Mc-Mz 3.12c - 71 -where Aw = w Q - w r . 3.13 M x, My and M z r e f e r to the components of the magnetization i n the r o t a t i n g frame, and and T 2 are the s p i n - l a t t i c e and s p i n - s p i n r e l a x a t i o n times r e s p e c t i v e l y . The amplitude of the r f magnetic f i e l d B^ i s shown as a time dependent f u n c t i o n . I f the r f magnetic f i e l d B^ i s constant, Eq. 3.12 can be solved a n a l y t i c a l l y or by geometric a n a l y s i s [ 6 , 2 3 , 2 6 ] . The magnetization components M x and My e x i s t i n g at the end of a r e c t a n g u l a r pulse of le n g t h tp d e r i v e d from Bloch equations can be expressed as My = M 0 a 0 s i n c ( 7 t p / B 1 / + b z ) 3.14 and M x = M 0a 0b «j 1 - coS7t p7B 1 z+b 2 ' 3.15 where Q 0 i s the nominal f l i p angle f o r on-resonance magnetization ( i . e . aQ = 7B]_t p) . For comparison, My and M x p r e d i c t e d by the F o u r i e r transform r e l a t i o n s h i p between the e x c i t a t i o n p a t t e r n and the pulse modulation f u n c t i o n i s given below. My - M Q Q q s i n c ( 7 b t p ) 3.16 72 -M x - M o a o 1 - c o s ( 7 b t p ) 7 b t p 3.17 S o l u t i o n of Bloch equations i n the presence of a v a r y i n g B^ f i e l d has been considered [19]. However, i n general, Eq. 3.12 cannot be solved a n a l y t i c a l l y when B^ i s time dependent [27]. Therefore i n t h i s S e c t i o n , the e x c i t a t i o n p a t t e r n due to amplitude modulated r f pulses has been determined by numerical i n t e g r a t i o n of Bloch equations, and the r e s u l t s are compared w i t h that of the l i n e a r approximation theory. S i m i l a r s t u d i e s have been reported i n the l i t e r a t u r e [21,23]. Numerical i n t e g r a t i o n of Bloch equations was performed by d i v i d i n g the time domain r f envelope i n t o n time steps. For each step, the change i n each magnetization component (AM X, AM V and AM Z) was c a l c u l a t e d and added to the e x i s t i n g value. When usin g a r e c t a n g u l a r r f pul s e , the number of times steps n, necessary f o r an accuracy of about 0.01% i n the computed on-resonance magnetization was of the order of 5,000. In these c a l c u l a t i o n s , r e l a x a t i o n during the pulse was assumed to be n e g l i g i b l e . The example of the re c t a n g u l a r r f pulse was taken as one of the t e s t s of the computer program. The d e t a i l s of the program are given i n the Appendix. For each r f p r o f i l e considered, the magnetization components M x and My were c a l c u l a t e d and p l o t t e d as a f u n c t i o n of the o f f s e t frequency Af (= Aco/2n, see Eq. 3.13). In a d d i t i o n , the t o t a l transverse magnetization i n the x-y plane i s a l s o given by means of the p o l a r coordinates M Xy and <f>, where My = M Xy cos<^ and M x = M Xy sin<f>. I t should be mentioned that because of the numerical e r r o r present i n the c a l c u l a -t i o n s , some i r r e g u l a r p o i n t s can be seen i n the p l o t s of ^  vs Af at Af - 73 -values corresponding to very small M x v values. Thus i n order to r e t a i n the c l a r i t y of the p l o t s , i n some cases only a s e l e c t e d r e g i o n of the tf> vs Af i s shown. Figure 3.8 shows the e x c i t a t i o n p a t t e r n (M x, My, M ^ and <j>) , at the end of a r e c t a n g u l a r r f pulse of 10 ms d u r a t i o n and a nominal on-resonance f l i p angle of 90°, obtained by numerical s o l u t i o n of Bloch equations ( s o l i d c urve). The broken curve shows the r e s u l t s obtained by assuming the F o u r i e r r e l a t i o n s h i p between the e x c i t a t i o n p a t t e r n and the pulse modulat i o n f u n c t i o n (Eqs. 3.16 and 3.17). The two curves d i f f e r s i g n i f i c a n t l y near resonance, while at l a r g e r o f f s e t frequencies they tend to c o i n c i d e . When the f l i p angle i s reduced to 30° the curves show very good agreement ( F i g . 3.9), i m p l y i n g that the response of a s p i n system to an r f pulse can be considered l i n e a r as long as the f l i p angle i s s m a l l (<30°). At t h i s p o i n t i t i s worthwhile to compare the two curves where the F o u r i e r r e l a t i o n s h i p i s assumed to h o l d between the f l i p angle ( r a t h e r than magnetization components) and the pulse modulation. This m o d i f i c a -t i o n i s e q u i v a l e n t to t a k i n g the t r i g o n o m e t r i c s i n e of the broken curve i n F i g . 3.8c, and the r e s u l t i s shown i n F i g . 3.10. I t can be seen th a t the m o d i f i e d l i n e a r approximation curve agrees w e l l w i t h that given by Bloch equations even at 90° f l i p angle, and the c a l c u l a t i o n f o r 30° f l i p angle produced i d e n t i c a l curves (not shown). Nevertheless, the m o d i f i e d l i n e a r approximation curve f o r the 180° f l i p angle case shows ( F i g . 3.11) c o n s i d e r a b l e departure from Bloch equations' p r e d i c t i o n . - 74 -F i g . 3.8: ( a ) - ( c ) Normalized p l o t s of M^My and ^ vs Af ( o f f s e t ) , at the end of a r e c t a n g u l a r r f pulse of ID ms d u r a t i o n and an on-resonance f l i p angle of 90°. S o l i d curve: obtained by numerical s o l u t i o n of Bloch equations. Broken curve: obtained by l i n e a r approximation (Eqs. 3.16 and 3.17). -75--F i g . 3.8 continued: ( d ) , the phase diagram corresponding to the s o l i d curve i n ( c ) . - 76 -Fig . 3.9: Corresponding plots to that given in F ig . 3.8, for a rectangular pulse of 10 ms duration and an on-resonance f l i p angle of 3 0 ° . 77 -Fig . 3.9 continued 7 8 -Figure 3.10: Comparison of modified l i n e a r approximation (broken curve) and Bloch equations ( s o l i d curve) p r e d i c t i o n f o r a r e c t a n g u l a r r f pulse of 10 ms d u r a t i o n and a f l i p angle of 90°. The e x c i t a t i o n p a t t e r n s computed f o r sine shaped r f pulses using Bloch equations are shown i n F i g s . 3.12-3.14. The r f modulating f u n c t i o n used i s given by ix B]^(t) = A s i n e [ - ( t - t Q ) ] f o r 0<t<t o 3.18 T and B x ( t ) = 0, f o r 0>t>t o 3.19 - 79 -e l (b) -600 -5)0 -300 - c — -/oo -|*0 o <t>° CD-I S 100 200 300 400 S00 Af(Hz) F i g . 3.11: P l o t of vs Af f o r a r e c t a n g u l a r r f pulse of 10 ms d u r a t i o n and a f l i p angle of 180°. S o l i d curve: Bloch equations p r e d i c t i o n . Broken l i n e : M o d i f i e d l i n e a r pre-d i c t i o n , ( b ) , the phase diagram of the s o l i d curve i n ( a ) . - 80 -where 2r i s the p e r i o d of the sine f u n c t i o n , 2 t Q i s the d u r a t i o n of the pulse and A i s the amplitude. The p l o t s shown i n F i g s . 3.12-3.14 were c a l c u l a t e d w i t h r = 1 ms and 2 t Q = 8 ms (or 4 ms) to conform to the experimental r e s u l t s given i n the next S e c t i o n . The pulse amplitude A was c a l c u l a t e d to give the d e s i r e d on-resonance f l i p angle 8 according to the r e l a t i o n s h i p r2 t o 6 = 7A J s i n e [- ( t - t Q ) ] dt . 3.20 o r Figure 3.12 shows the e x c i t a t i o n p r o f i l e f o r a 90° r f pulse amplitude modulated according to Eq. 3.18 w i t h t Q = 4r; i . e . the pulse c o n s i s t s of 3 s i d e lobes on e i t h e r side of the p r i n c i p a l lobe. The p r o f i l e of the transverse magnetization M Xy ( F i g . 3.12a) shows th a t a h i g h degree of s e l e c t i v e e x c i t a t i o n can be achieved. Nevertheless, the presence of s m a l l e r e x c i t a t i o n lobes on e i t h e r s i d e of the p r i n c i p a l e x c i t a t i o n band i s evident as a consequence of the abrupt t r u n c a t i o n of the s i n e f u n c t i o n . The phase of M^, shown i n F i g . 3.12b suggests t h a t the transverse magnetization i s completely dephased, and as a r e s u l t , at the end of the pulse almost no s i g n a l w i l l be observed. However, i t can be seen t h a t the phase angle i s approximately a l i n e a r f u n c t i o n of the frequency at l e a s t w i t h i n the p r i n c i p a l e x c i t a t i o n band. This enables r e f o c u s s i n g of the e x c i t e d magnetization by the gradient r e v e r s a l method or by a p p l i c a t i o n of a n o n s e l e c t i v e 180° pulse [18,19]. I n d i v i d u a l magnetization components M x and My are a l s o shown i n F i g s . 3.12c and 3.12d. . 81 -Magnet!**** l e n g t n -r £ pulse-2 ms-- 82 -F i g . 3.12 continued - 84 -F i g . 3.14: Transverse magnetization (M^) and phase (<t>) e x i s t i n g a f t e r a 180° sine modulated r f pulse of le n g t h 8 ms. P e r i o d of the sine f u n c t i o n = 2 ms. - 85 -The e f f e c t of f u r t h e r t r u n c a t i o n of the s i n e f u n c t i o n i s shown i n F i g . 3.13 where t Q = 2r, i . e . one s i d e lobe. On comparison w i t h F i g . 3.12a i t can be seen that the p r i n c i p a l magnetization p r o f i l e i s broadened, along w i t h l e s s sharper edge d e f i n i t i o n . The extension of the secondary e x c i t a t i o n lobe to higher frequencies and uneven i n t e n s i t y d i s t r i b u t i o n w i t h i n the p r i n c i p a l e x c i t a t i o n band are a l s o evident w i t h the pulse of s h o r t e r d u r a t i o n . The e x c i t a t i o n p r o f i l e corresponding to a f l i p angle of 180° and t Q = 4r i s shown i n F i g . 3.14. I t can be seen t h a t frequency s e l e c t i v i t y i s not r e a l i z e d and complete i n v e r s i o n of the magnetization i s achieved only at resonance. When the Larmor frequency i s o f f s e t from the frequency of the r f p u l s e , the magnetization i s r o t a t e d by angles greater or l e s s than 180°, thus l e a v i n g a considerable amount of magnetization i n the transverse plane l e a d i n g to poor s e l e c t i v i t y . I t i s h a r d l y s u r p r i s i n g that a sine shaped s e l e c t i v e 180° pulse performs p o o r l y . I t i s a m a n i f e s t a t i o n of the s p i n system being d r i v e n i n t o a r e g i o n where the response i s h i g h l y n o n l i n e a r . Thus, a pulse modulation f u n c t i o n d e r i v e d from c o n s i d e r a t i o n s based upon the l i n e a r i t y of system cannot be expected to produce the d e s i r e d r e s u l t . A d i s c u s s i o n of the p o t e n t i a l problems i n v o l v e d i n u s i n g s e l e c t i v e 180° pulses ( i n r e l a t i o n to T]_ experiments) i n NMR imaging has appeared i n the l i t e r a t u r e r e c e n t l y [22]. From the preceding examples presented i t i s c l e a r t h a t , while 90° pulses w i t h acceptable s e l e c t i v i t y can be obtained by u s i n g modulating f u n c t i o n s d e r i v e d from the F o u r i e r r e l a t i o n s h i p , s e l e c t i v e 180° pulses warrant con s i d e r a b l e improvement. In both cases, improved performance - 86 -can be achieved by t a k i n g i n t o account the n o n l i n e a r i t y e f f e c t s when designing the pulse modulation f u n c t i o n . Two approaches can be used to solve t h i s problem. F i r s t , given the d e s i r e d e x c i t a t i o n p r o f i l e , Bloch equations may be solved i n reverse to y i e l d the c o r r e c t modulation f u n c t i o n . This method has been used to generate a 90° s e l e c t i v e e x c i t a t i o n f u n c t i o n by employing a numerical procedure [28]. The pulse modulating waveform obtained by t h i s approach shows a small time s h i f t compared to the waveform produced by the F o u r i e r transform approach. The e f f e c t of the time s h i f t i s r e f l e c t e d i n the r e d u c t i o n i n the phase e r r o r of the magnetization a f t e r a n o n - s e l e c t i v e 180° r e f o c u s s i n g pulse [28]. An e f f i c i e n t s e l e c t i v e 180° i n v e r s i o n pulse has a l s o been developed r e c e n t l y by u s i n g a pulse modulated i n the form of a complex h y p e r b o l i c secant [27-29]. The second approach depends on the use of an e r r o r m i n i m i z a t i o n procedure [30]. In t h i s method, the d e v i a t i o n from i d e a l i t y of the magnetization response to a multi-parameter modulating f u n c t i o n i s c a l c u l a t e d , and a range of parameter values are explored to f i n d the best envelope shape. A s e l e c t i v e 180° pulse of comparable e f f i c i e n c y to the h y p e r b o l i c secant pulse has been developed by t h i s method. This modulation f u n c t i o n , a modified truncated sine f u n c t i o n , has the d i s t i n c t advantage over the h y p e r b o l i c secant pulse of not r e q u i r i n g simultaneous amplitude and phase modulation. - 87 -3.1.2 Implementation of the Technique and Experimental Results When the present work was i n i t i a t e d , few p r a c t i c a l d e t a i l s of the technique or experimental r e s u l t s such as those documented here were a v a i l a b l e i n the l i t e r a t u r e . Two r e l e v a n t r e p o r t s which describe s e v e r a l u s e f u l p r a c t i c a l aspects have been p u b l i s h e d only r e c e n t l y [31,32]. Therefore the f o l l o w i n g d i s c u s s i o n i s devoted to a d e s c r i p t i o n of the a c t u a l implementation of the technique used i n t h i s study, along w i t h some experimental r e s u l t s . The technique of s e l e c t i v e e x c i t a t i o n d i s c ussed above r e q u i r e s amplitude modulation of the r f c a r r i e r frequency w i t h a s u i t a b l e func-t i o n ( i . e . g e n e r a l l y a modi f i e d s i n e f u n c t i o n ) . This method d i f f e r s from the e a r l i e r s y n t h e s i z e d e x c i t a t i o n technique [10,17] i n that the s p e c t r a l e x c i t a t i o n c h a r a c t e r i s t i c s are contained i n a s i n g l e pulse r a t h e r than i n a s e r i e s of p u l s e s . A b l o c k diagram of the experimental setup used here to generate amplitude modulated r f pulses i s shown i n F i g . 3.15. The component c e n t r a l to the assembly i s the double balanced mixer (Hewlett-Packard model 10514A) which, used as a balanced modulator, combines the r f c a r r i e r frequency and the modulating waveform. The output of the mixer c o n s i s t s of the product of the c a r r i e r and the modulating waveforms i n the time domain, corresponding to the double-s i d e band suppressed c a r r i e r [33] spectrum. The r f c a r r i e r s i g n a l was obtained from the spectrometer frequency s y n t h e s i z e r u n i t and was gated by a g a t i n g pulse from the pulse programmer. The modulating waveform was generated by us i n g an a r b i t r a r y waveform generator (Wavetek model LOW-POWER RF CARRIER FREQUENCY SYNTHESISER RF RECTANGULAR RF PULSE L GATE DOUBLE BALANCED MIXER LOW-POWER MODULATED RF PULSE LINEAR RF POWER AMPLIFIER t GATING PULSE NICOLET 1280 COMPUTER NICOLET 293C PULSE PROGRAMMER TRIGGER ANALOG o SWITCH +5V PULSE PICKUP COIL ANALOG MODULATING WAVEFORM ARBITRARY WAVEFORM GENERATOR 7 NMR PROBE (a) TRANSMIT/ RECEIVER COUPLER OBSERVATION OSCILLOSCOPE NMR SIGNAL RECEIVER F i g . 3 . 1 5 : B l o c k d iag ram o f the e x p e r i m e n t a l s e tup u s e d t o g e n e r a t e a m p l i t u d e modu la ted r f p u l s e s . - 89 -75) capable of generating waveforms w i t h a v e r t i c a l r e s o l u t i o n of 4096 p o i n t s (12 b i t s ) and a h o r i z o n t a l r e s o l u t i o n a d j u s t a b l e from 2 to 8192 p o i n t s . T y p i c a l l y , each complete c y c l e of the waveform was defined by 361 h o r i z o n t a l p o i n t s and the maximum p o s s i b l e v e r t i c a l r e s o l u t i o n . Upon r e c e i v i n g a t r i g g e r s i g n a l , the waveform generator produces an analog v o l t a g e s i g n a l p r o p o r t i o n a l to the values s t o r e d i n the waveform memory between pr e d e f i n e d s t a r t and stop l o c a t i o n s . The time r e s o l u t i o n f o r each memory l o c a t i o n and the amplitude of the analog s i g n a l can be e x t e r n a l l y programmed i n t o the waveform generator anywhere i n the range from 500 ns to 50 s, and 0.01 to 10 Vp.p i n t o a 50 Q l o a d r e s p e c t i v e l y . The waveform generator was i n t e r f a c e d to the Nicolet-1280 computer v i a a RS-232-C s e r i a l data t r a n s f e r channel. The d e s i r e d modulating waveform was i n i t i a l l y generated i n the computer and subsequently t r a n s f e r r e d to the waveform generator memory. The waveform generation and communica-t i o n software necessary to accomplish t h i s procedure was w r i t t e n i n 1280 assembly language by the author. The t r i g g e r pulse necessary to i n i t i -ate the waveform generator was obtained from the pulse programmer. In the experimental c o n f i g u r a t i o n used, the output of the waveform genera-t o r was f i r s t f e d i n t o a d i g i t a l l y c o n t r o l l e d analog switch and the output of the sw i t c h was connected to the c o n t r o l p o r t (X) of the mixer. This c o n f i g u r a t i o n provides the c a p a b i l i t y to generate h i g h amplitude r e c t a n g u l a r r f pulses and low amplitude modulated pulses i n the same pulse sequence. The input to the c o n t r o l p o r t (X) of the mixer i s connected e i t h e r to a constant v o l t a g e source (+5V) or to the low vo l t a g e ( t y p i c a l l y 750 mV) modulating s i g n a l from the waveform generator depending on the p o s i t i on of the switch. The p o s i t i o n of the switch - 90 -i s c o n t r o l l e d by the same c o n t r o l pulse which t r i g g e r s the waveform generator. The modulated r f output from the mixer was a m p l i f i e d by a l i n e a r r f power a m p l i f i e r (100 W ENI) and was f e d i n t o the probe v i a the t r a n s -m i t t e r / r e c e i v e r coupler (Tx/Rx coupler) u n i t of the spectrometer. In a d d i t i o n to the assembly of components shown i n F i g . 3.15, r e s i s t o r s and attenuators of appropriate values were s u i t a b l y i n s e r t e d i n t o the setup to l i m i t the maximum current or v o l t a g e a p p l i e d to a p a r t i c u l a r compo-nent according to i t s s p e c i f i c a t i o n s . The presence of n o n l i n e a r devices (e.g. mixer and Tx/Rx coupler) i n the experimental setup s i g n i f i c a n t l y a l t e r the shape of the modulated r f waveform s u p p l i e d to the probe as compared to t h a t of the o r i g i n a l modulating waveform. Thus i t i s imperative t h a t the r f p r o f i l e be observed at d i f f e r e n t stages u s i n g an o s c i l l o s c o p e . In t h i s study, the r f p r o f i l e was optimized by observing the voltage induced i n a small pickup c o i l (3.0 mm diameter) placed at the center of the probe. The most prominent d i s t o r t i o n to the r f shape was found to be caused by the Tx/Rx coupler due to the cross-diodes present i n the device. The o s c i l l o g r a m s of the a c t u a l waveforms observed, shown i n F i g . 3.16, i l l u s t r a t e the problem. In each case the o r i g i n a l modulating waveform has been superimposed on the r f waveform f o r ready comparison. Figure 3.16a shows the v o l t a g e induced i n the pickup c o i l when the output from the a m p l i f i e r was connected d i r e c t l y to the probe ( F i g . 3.15, dotted l i n e connection ( a ) ) . This s i t u a t i o n was r e a l i z e d when a s i n e shaped modulating waveform of peak amplitude 150 mV was a p p l i e d as the input to the mixer v i a a 490 ft c u r r e n t l i m i t i n g r e s i s t o r . At t h i s input l e v e l F i g . 3.16: Oscillograms of the r f pulse waveforms. The modulating waveform i s superimposed on the r f waveform f o r comparison. - 92 -the mixer and the a m p l i f i e r response i s approximately l i n e a r , and hence, the r f waveform detected by the pickup c o i l f o l l o w s c l o s e l y the a p p l i e d modulating f u n c t i o n . The waveform detected by the pickup c o i l when the output from the a m p l i f i e r was connected to the probe v i a the T x/R x coupler i s shown i n F i g . 3.16b. In t h i s case, gross d i s t o r t i o n of the r f shape i s apparent and t h i s i s a s c r i b e d to the n o n l i n e a r response of the Tx/Rx coupler. The n o n l i n e a r i t y of the Tx/Rx coupler was overcome by i n c r e a s i n g the input l e v e l of the modulating f u n c t i o n to a peak amplitude of 750 mV, as shown i n F i g . 3.16c. A f t e r c o r r e c t i n g f o r the n o n l i n e a r i t i e s i n the system, the r f power l e v e l a p p l i e d to the probe was found to be too l a r g e compared to the d e s i r e d power l e v e l f o r a 90° p u l s e . At t h i s stage, the r f power l e v e l was adjusted by u s i n g an attenuator of appropriate value a f t e r the Tx/Rx coupler. Although the method adopted above to overcome the n o n l i n e a r i t y of the system was found to be convenient and s u i t a b l e f o r p r e l i m i n a r y implementation of the technique, i t i s appropriate to d i s c u s s some p o s s i b l e improvements. The c o n t r o l of r f power a f t e r the Tx/Rx coupler i s u n d e s i r a b l e i n p r a c t i c e s i n c e t h i s a l s o attenuates the r e c e i v e d s i g n a l ; furthermore i t a l s o l i m i t s the power a v a i l a b l e f o r the non-s e l e c t i v e p u l s e s . These d i f f i c u l t i e s can be e l i m i n a t e d by modifying the shape of the modulating waveform to account f o r the n o n l i n e a r nature of the system v i a an experimentally determined c a l i b r a t i o n curve; t h i s s o l u t i o n was not pursued here due to i t s demands on software. There-f o r e , the experimental e x c i t a t i o n p r o f i l e s given i n the next s e c t i o n have been obtained w i t h optimized r f p r o f i l e s according to the procedure d e s c r i b e d e a r l i e r . In the case of the images presented i n Chapter IV, - 93 -the r f p r o f i l e was optimized by v a r y i n g the modulating waveform input l e v e l (without u s i n g a t t e n u a t i o n a f t e r the Tx/Rx coupler u n i t ) while observing the shape of the s e l e c t e d s l i c e . Experimental e v a l u a t i o n of s e v e r a l amplitude modulated r f waveforms w i t h regard to t h e i r e x c i t a t i o n p r o f i l e s was c a r r i e d out u s i n g t h i s c o n f i g u r a t i o n . The experimental r e s u l t s were then compared to the e x c i t a t i o n p r o f i l e s c a l c u l a t e d u s i n g the Bloch equations i n S e c t i o n 3.1.1.3. These experiments were performed on a 1 cm diameter s p h e r i c a l phantom c o n t a i n i n g water, pl a c e d at the center of a NMR probe. In order to determine the e x c i t a t i o n p a t t e r n of an amplitude modulated r f pulse, a s e r i e s of s p e c t r a were obtained i n a homogeneous magnetic f i e l d by v a r y i n g the frequency of the r f pulse w i t h respect to the Larmor frequency of the water resonance. For a p a r t i c u l a r s e r i e s of s p e c t r a , the r f pulse amplitude was adjusted so t h a t the r e q u i r e d f l i p angle was obtained f o r the on-resonance c o n d i t i o n . The s i g n a l was observed as a f r e e i n d u c t i o n decay by i n i t i a t i n g the a c q u i s i t i o n immediately a f t e r the r f pulse. S i g n a l echo formation, as mentioned i n the previous Sections, was not necessary due to the f a c t t h a t only a s i n g l e resonance was being observed. The absolute-value F o u r i e r transformed data are d i s p l a y e d as a s e r i e s of s p e c t r a p l o t t e d on the same h o r i z o n t a l a x i s , showing the r e l a t i v e amplitude of the e x c i t a -t i o n ( t r a nsverse magnetization M x v) as a f u n c t i o n of frequency r e l a t i v e to the c a r r i e r . While the a c t u a l e x c i t a t i o n p r o f i l e i s symmetrical w i t h respect to the c a r r i e r frequency, only the low frequency s i d e w i t h respect to the c a r r i e r i s shown i n the experimental p l o t s . - 94 -Several s e r i e s of experimental e x c i t a t i o n p r o f i l e s are shown i n F i g . 3.17. The e x c i t a t i o n p a t t e r n due to a 2 ms constant amplitude 90° r f pulse ( F i g . 3.17a) shows that the e x c i t a t i o n of the magnetization extends f a r beyond the p r i n c i p a l band (± 500 Hz) to an extent that cannot be neglected. This i s compatible w i t h the d i s c u s s i o n presented e a r l i e r (see F i g . 3.8). Figures 3.17b, c and d show the e x c i t a t i o n p a t t e r n s corresponding to r f pulses modulated according to the Eq. 3.18 w i t h a p e r i o d of 2 ms, and pulse lengths 2, 4 and 8 ms r e s p e c t i v e l y . In each case the amplitude of the r f pulse has been adjusted to give a 90° f l i p angle. The general t r e n d of i n c r e a s i n g s e l e c t i v i t y w i t h i n c r e a s i n g pulse l e n g t h i s c l e a r l y demonstrated. Further, on comparison w i t h F i g s . 3.12 and 3.13, i t can be seen t h a t e x c e l l e n t correspondence has been achieved between the experimental and c a l c u l a t e d p r o f i l e s f o r o f f s e t frequencies below 1000 Hz. I n F i g s . 3.17c and d, spurious e x c i t a t i o n not p r e d i c t e d by Bloch equations, can be seen at o f f s e t frequencies c l o s e to 1500 Hz. This i s a t t r i b u t e d to the t h i r d i n t e r m o d u l a t i o n harmonic generated by the mixer [34]. Intermodulation suppression i s a f u n c t i o n of many parameters and g e n e r a l l y can be minimized by lower input l e v e l s to the mixer. Experimental determination of the e f f e c t of t r i a n g u l a r a p o d i z a t i o n of the s i n e f u n c t i o n i s shown i n F i g . 3.18. Suppression of the second-ary e x c i t a t i o n lobes as w e l l as the decrease i n sharpness of the p r i n c i -p a l e x c i t a t i o n lobes can be c l e a r l y seen from these p l o t s . The poor s e l e c t i v i t y obtained by u s i n g a 180° modulated r f p u l s e , which shows cl o s e correspondence to the c a l c u l a t e d curve ( F i g . 3.13), i s shown i n F i g . 3.19. - 95 -F i g . 3.17: S p e c t r a l s e r i e s showing the e x c i t a t i o n p a t t e r n s of modulated 90° r f p u l s e s . (a) Rectangular modulation of l e n g t h 2 ms. (b) Sine modulation of p e r i o d 2 ms and a pulse l e n g t h of 2 ms. - 96 -F i g . 3.17 continued: ( c ) , Sine modulation of p e r i o d 2 ms and length 4 ms. ( d ) , Same as (c) w i t h l e n g t h 8 ms. - 97 0 0 0 -j I 1 l 1 1 1 I -1 1 1 1 r — 0 - 1 0 0 0 - 2 0 0 0 Hz (a) T i 1 r i r~ - 2 0 0 0 Hz 0 0 0 0 1000 F i g . 3.18: E f f e c t of t r i a n g u l a r a p o d i z a t i o n of the sin e r f modulating f u n c t i o n . (a) Sine modulation of p e r i o d 1.55 ms, pulse l e n g t h 8.53 ms, 90° pulse. (b) A p o d i z a t i o n of the sin e f u n c t i o n i n (a) w i t h a symmetrical t r i a n g u l a r f u n c t i o n of leng t h 8.53 ms. 3.2 S l i c e S e l e c t i o n i n the Presence of Chemical S h i f t s 3.2.1 L i m i t a t i o n s of the Current Technique The f r e q u e n c y - s e l e c t i v e e x c i t a t i o n method of s l i c e s e l e c t i o n r e l i e s upon the d i r e c t correspondence between the frequency d i s p e r s i o n of a resonance caused by the a p p l i e d gradient and the s p a t i a l d i s t r i b u t i o n of the s p i n s . Such a scheme provides e x c i t a t i o n of w e l l d e f i n e d s p a t i a l planes i n the presence of a s i n g l e chemical s h i f t s p e c ies. However, when many chemical s h i f t species are present, the frequency d i s p e r s i o n - 99 -observed i n the presence of a gradient represents the combination of the s p a t i a l s p i n d i s t r i b u t i o n and the corresponding chemical s h i f t d i s p e r -s i o n . I n these circumstances, f r e q u e n c y - s e l e c t i v e s l i c e s e l e c t i o n gives r i s e to improper s e l e c t i o n of the s p a t i a l planes. Figure 3.20 i l l u s -t r a t e s the case f o r two c h e m i c a l l y s h i f t e d s p e c ies. The frequency spread of a resonance i n the presence of a gradient as given by Eq. 2.11 i n Chapter I I can be r e w r i t t e n to i n c l u d e the chemical s h i f t as, "x = "k + 7G x.x 3.21 where fi^ d e f i n e s the frequency of the c h e m i c a l l y s h i f t e d species k i n the r o t a t i n g frame. According to Eq. 3.21, i n the presence of a gra-d i e n t , each c h e m i c a l l y s h i f t e d resonance w i l l be broadened about i t s own chemical s h i f t frequency ( F i g . 3.20a). As a consequence, f o r d i f f e r e n t chemical s p e c i e s , a p a r t i c u l a r frequency 0^ corresponds to a s l i g h t l y d i f f e r e n t s p a t i a l coordinate. Therefore a b a n d - l i m i t e d e x c i t a t i o n pulse ( F i g . 3.20b) s t i m u l a t e s each chemical species i n s l i g h t l y d i f f e r e n t s p a t i a l planes ( F i g . 3.20c). Any subsequent imaging process thus produces a composite image of the two chemical species w i t h each "chemi-c a l image" o r i g i n a t i n g from a d i f f e r e n t l o c a t i o n . The s p a t i a l separa-t i o n between the s e l e c t e d planes i s given by AS = Inhu/yG, where Ai/ (Hz) i s the chemical s h i f t s e p a r a t i o n and G i s the magnetic f i e l d gradient. This l i m i t a t i o n i s a l s o present i n the s p a t i a l l o c a l i z a t i o n techniques such as depth-resolved s u r f a c e - c o i l spectroscopy (DRESS) [35] and v o l u m e - s e l e c t i v e - e x c i t a t i o n (VSE) [36]. W L (a) J 1 ( b ) (d) L W (c) v v 1 1 L 1 AS W + L W o o (e) frequency spatial coordinate (S) F i g . 3.20: I l l u s t r a t i o n of f r e q u e n c y - s e l e c t i v e e x c i t a t i o n and i t s corresponding s p a t i a l s e l e c t i o n f o r two chemically s h i f t e d s p e c i e s , W and L, i n the presence of a gradient, and wg are the r e s p e c t i v e chemical s h i f t s , (a) Frequency spectrum i n the absence ( s o l i d l i n e ) and presence (broken Line) of a gradient. (b) and ( c ) , Frequency domain r f e x c i t a t i o n p r o f i l e o f a conventional s l i c e s e l e c t i o n pulse and i t s s p a t i a l s e l e c t i o n . (d) and ( e ) , Frequency domain r f p r o f i l e needed t o e x c i t e both chemical s h i f t s at the center of the object and i t s s p a t i a l s e l e c t i o n . 101 -The m i s r e g i s t r a t i o n of chemical s h i f t planes can be minimized by i n c r e a s i n g the magnitude of the gradient; however, i t i s important to note t h a t i t i s impossible to achieve p e r f e c t r e g i s t r a t i o n of these planes i n t h i s manner. At low operating f i e l d s , s u f f i c i e n t gradient magnitudes can be employed so that AS i s s m a l l e r than the s l i c e t h i c k n e s s . In t h i s s i t u a t i o n , e f f e c t i v e l y o v e r l a p p i n g s p a t i a l planes of each chemical species are e x c i t e d . But at higher f i e l d s , the problem i s accentuated by the increased chemical s h i f t s e p a r a t i o n , and the exper-imental c o n d i t i o n s (gradient s t r e n g t h and s l i c e t h i c k n e s s ) may be such th a t completely d i f f e r e n t planes are e x c i t e d g i v i n g r i s e to a n o t i c e a b l e image degradation. For example, the chemical s h i f t s e p a r a t i o n between water and l i p i d s i g n a l s of human t i s s u e at 200 MHz i s approximately 700 Hz. Under these c o n d i t i o n s , use of a s l i c e s e l e c t i o n g r a d i e n t of 0.5 G/cm would give r i s e to a s e p a r a t i o n of approximately 3 mm between the s e l e c t e d s p a t i a l planes. I f the s l i c e t hickness i s assumed to be i n the order of 1-2 mm, the s p a t i a l planes s e l e c t e d w i l l be completely separ-ated from each other by at l e a s t 1-2 mm. Such separations which are comparable to the s l i c e t hickness are c l e a r l y u n d e s i r a b l e and cannot be ignored. This problem has already been encountered i n h i g h r e s o l u t i o n imaging of s m a l l animals at 200 MHz [37]. 3.2.2 P o s s i b l e S o l u t i o n s The problem of s l i c e s e l e c t i o n i n the presence of c h e m i c a l l y s h i f t e d species has been mentioned b r i e f l y by s e v e r a l authors [39,42]. 102 -But a s o l u t i o n to t h i s drawback has not been suggested p r e v i o u s l y . Several two-dimensional F o u r i e r imaging techniques have been reported [38-46] to se p a r a t e l y image d i f f e r e n t chemical s h i f t species. The m a j o r i t y of these methods [38,40-45] depend on e i t h e r frequency-s e l e c t i v e e x c i t a t i o n or suppression of s p e c i f i c resonances, w h i l e the others depend on combination of images obtained under d i f f e r e n t exper-imental c o n d i t i o n s [39,46]. Thus i t i s appropriate to consider p o s s i b l e m o d i f i c a t i o n of these techniques i n order to o b t a i n 'composite' images of c h e m i c a l l y s h i f t e d species o r i g i n a t i n g from the same s p a t i a l plane. With a l l above techniques, t h i s r e q u i r e s combination of separate images corresponding to d i f f e r e n t species and o r i g i n a t i n g from the same s p a t i a l plane. This can be accomplished more e a s i l y w i t h some techniques than others. For example, w i t h methods which depend on s e l e c t i v e e x c i t a t i o n and suppression [38,40-45], i t would be necessary to change the r f c a r r i e r frequency w i t h i n a pulse sequence ( e s p e c i a l l y f o r s l i c e s which are o f f - c e n t e r ) . This t e c h n i c a l s o p h i s t i c a t i o n i s a v a i l a b l e only i n h i g h l y f l e x i b l e imaging devices. On the other hand, methods which depend on image combination [39,46] would r e q u i r e proper combination of at l e a s t four separate images i n the case of two c h e m i c a l l y s h i f t e d s p e c i es. A more convenient technique which enables two chemi c a l l y s h i f t e d species to be imaged i n the same s p a t i a l plane i s described below. Consider two chemi c a l l y s h i f t e d species ( h e r e a f t e r r e f e r r e d to as water (W) and l i p i d (L)) to be imaged at the same s p a t i a l plane; f o r example, at the center of the obj e c t . I f the object i s centered w i t h respect to the gradient n u l l p o s i t i o n i n the magnet, t h i s r e q u i r e s a - 103 -frequency domain r f e x c i t a t i o n p r o f i l e c o n s i s t i n g of two bands p o s i -t i o n e d at the r e s p e c t i v e chemical s h i f t frequencies ( F i g . 3.20d). E x c i t a t i o n of s l i c e s other than the center can be achieved by s h i f t i n g the r f e x c i t a t i o n p r o f i l e away from the chemical s h i f t frequencies while m a i n t a i n i n g the frequency s e p a r a t i o n (equal to the chemical s h i f t d i f f e r e n c e ) between the bands. However, i n p r a c t i c e , s i n c e the gradient imposed frequency disper-s i o n of the resonances w i l l be greater than the chemical s h i f t s e p a r a t i o n , each r f e x c i t a t i o n band w i l l s t i m u l a t e both chemical s h i f t species g i v i n g r i s e to a d d i t i o n a l undesired s p a t i a l e x c i t a t i o n as shown i n F i g . 3.20e. The s t r a t e g y suggested here to e l i m i n a t e the c o n t r i -b u t i o n from the unwanted components i n the f i n a l image i s based on the a c q u i s i t i o n of two data sets w i t h proper phase r e l a t i o n s h i p between the d e s i r e d and undesired magnetization components. I f the data a c q u i s i t i o n c o n d i t i o n s are such that i n one data set a l l magnetization components are i n phase, w h i l s t i n the other the magnetization from d e s i r e d and undesired planes are of opposite phase, s u i t a b l e combination of these data sets w i l l r e s u l t e x c l u s i v e l y i n the d e s i r e d image. The frequency domain r f e x c i t a t i o n p r o f i l e shown i n F i g . 3.20d can be generated by amplitude modulation of the r f pulse i n the time domain. By i n v e r s e F o u r i e r t r a n s f o r m a t i o n of the d e s i r e d e x c i t a t i o n p r o f i l e , i t can be shown that the r e q u i r e d amplitude modulation f u n c t i o n , A ^ t ) , i s given by Sin(a>2/2) t A ^ t ) - Cos W ] t ( w 2 / 2 ) t 3.22 104 -This modulating f u n c t i o n generates two frequency bands on e i t h e r side o f the c a r r i e r frequency, o f f s e t by a frequency equal to the frequency of the cosine f u n c t i o n (w^). The width (u>2) and the frequency p r o f i l e of each band i s determined by the frequency and the d u r a t i o n of the s i n e f u n c t i o n : The way i n which the r e q u i r e d in-phase and out-of-phase r e l a t i o n -ship of the magnetization components can be achieved i s discussed w i t h reference to the pulse sequence and the r o t a t i n g frame diagrams shown i n F i g s . 3.21 and 3.22 r e s p e c t i v e l y . The (cos x sine) amplitude modulated (Eq. 3.22) r f pulse e x c i t e s a t o t a l of four magnetization components; 180* cos x sine RF signal -A B C F i g . 3.21: Rf and gradient sequence used to demonstrate the technique described In the t e x t . The dotted p o r t i o n of the gradient a p p l i e s o nly when the data c o l l e c t i o n i s i n i t i a t e d at p o i n t C, otherwise, the gradient i s kept constant during A-C. F i g . 3.22: E v o l u t i o n of magnetization components i n the r o t a t i n g frame during the pulse sequence shown i n F i g . 3.21. - 106 -two d e s i r e d components and two undesired components (see F i g . 3.20e). These components, i n the presence of the grad i e n t , are denoted as W(w A), L(wg) ( d e s i r e d components) and W(wg), L(w A) (undesired components). W(wA) and W(wg) r e f e r to water magnetization e x c i t e d at the frequency bands centered at the chemical s h i f t frequencies and «g r e s p e c t i v e l y and l i k e w i s e f o r the l i p i d magnetization. In the r o t a t i n g frame diagrams, the d e s i r e d magnetization components are i n d i c a t e d by longer v e c t o r s and t h e i r symbols are un d e r l i n e d . The r o t a t i n g frame frequency i s assumed to be equal to the chemical s h i f t frequency of water (w^). The n o n s e l e c t i v e 180° pulse refocusses a l l four magnetization compo-nents a f t e r a time t^/2 ( F i g . 3.21, p o i n t A and F i g . 3.22A), where t w i s the d u r a t i o n of the amplitude modulated pulse. E v o l u t i o n of the magne-t i z a t i o n components f o r a time t = 7r/(w^-u>g) causes wg frequency components to acquire a phase angle of 180° r e l a t i v e to the components ( F i g . 3.21 p o i n t B and F i g . 3.22B"). In order to minimize the dephasing of the magnetization w i t h i n each frequency band during the p e r i o d A-B, the width of the frequency bands should be narrow compared to t h e i r s e p a r a t i o n . At p o i n t B, i f the grad i e n t i s switched o f f , a l l magnetization components w i l l begin to precess a t t h e i r respec-t i v e chemical s h i f t frequencies; i . e . the unwanted components W(wg) and L(w^) w i l l change t h e i r frequencies to w A and wg r e s p e c t i v e l y ( F i g . 3.22B +). Consequent e v o l u t i o n of the magnetization f o r a f u r t h e r time t = 7r/(wA-wg) i n the absence of a gradient causes the undesired components to acquire a 180° phase angle w i t h respect to the d e s i r e d components ( F i g s . 3.21, p o i n t C and F i g . 3.22C"). An intermediate time between p o i n t s B and C i s shown i n F i g . 3.22Bfc. Therefore, a s u i t a b l e combina-- 107 -t i o n of the two data s e t s , acquired w i t h phase r e l a t i o n s h i p s shown i n F i g s . 3.22A and 3.22C +, w i l l r e s u l t i n c a n c e l l a t i o n of the c o n t r i b u t i o n from the unwanted s p a t i a l planes. 3.2.3 Experimental Demonstration of the Proposed Method Figure 3.23 shows the s e l e c t i v e e x c i t a t i o n of two frequency bands u s i n g an r f pulse amplitude modulated according to Eq. 3.22; the pulse sequence used i s t h a t shown i n F i g . 3.21, except f o r the m o d i f i c a t i o n that the g r a d i e n t was kept constant a f t e r the 180° pulse. For the spectrum shown i n F i g . 3.23b, The time domain data were acquired as a f u l l echo by i n i t i a t i n g the a c q u i s i t i o n immediately a f t e r the 180° p u l s e , and the spectrum i s d i s p l a y e d i n the magnitude mode. By a c q u i s i -t i o n of the second h a l f of the echo i n a separate experiment, i t was observed t h a t minimal frequency dependent phase c o r r e c t i o n i s needed to p r o p e r l y phase both frequency bands. This i m p l i e s t h a t the magnetization components of both frequency bands are approximately in-phase at the echo maximum. Experimental v e r i f i c a t i o n of the proposed method was performed u s i n g a phantom c o n t a i n i n g a s i n g l e chemical s h i f t species (4 cm diame-t e r bulb c o n t a i n i n g water) and 15 cm diameter home-built gradient c o i l s [47] w i t h r i s e time l e s s than 300 ps. The data were acquired i n the presence of the s l i c e s e l e c t i o n gradient so t h a t the r e l a t i v e phase of the magnetization components can be determined. The data c o l l e c t i o n was i n i t i a t e d at e i t h e r p o i n t A, B or C ( F i g . 3.21). Since one chemical - 108 -F i g . 3.23: (a) 80.3 MHz iH NMR spectrum of a 4 cm diameter sphere f i l l e d w i t h water measured i n the presence of a g r a d i e n t , (b) S e l e c t i v e e x c i t a t i o n of two frequency bands w i t h a (cos x s i n e ) amplitude modulated r f pulse. Pulse sequence shown i n F i g . 3.21 was used without the time p e r i o d A-C. The s i g n a l was acquired as a f u l l echo, and the spectrum i s d i s p l a y e d i n the magnitude mode. Cosine f u n c t i o n frequency (w^ ) = 1500 Hz; the p r i n c i p a l lobe of the s i n e modulation 4 ms duration) was employed. s h i f t species was used, the e f f e c t of d i f f e r e n t chemical s h i f t s (water and l i p i d ) was simulated by having the chemical s h i f t frequency c o i n c i d e w i t h one or the other r f e x c i t a t i o n bands i n separate experiments. The s e r i e s of s p e c t r a i n F i g . 3.24A show the phase r e l a t i o n s h i p of W(w^) and W(wg) magnetization components at p o i n t s A, B, and C ( F i g . 3.21) i n the pulse sequence. At p o i n t A, both magnetization components - 109 -are i n phase ( F i g . 3.24A(i)). Figures 3.24A(ii) and ( i i i ) show the s p e c t r a obtained when the data c o l l e c t i o n i s i n i t i a t e d at p o i n t s B and C r e s p e c t i v e l y . These s p e c t r a have been subjected to the same phase c o r r e c t i o n t h a t a p p l i e d to F i g . 3.24A(i). The 90° phase r e l a t i o n s h i p of F i g s . 3.24A(i) and ( i i ) i s due to the f a c t that the data are shown with respect to a r o t a t i n g frame frequency of (w^ + wg)/2 ( i . e . c a r r i e r frequency) r a t h e r than as assumed i n F i g . 3.22. Since the s e r i e s of s p e c t r a shown i n F i g . 3.24A was obtained w i t h the chemical s h i f t frequency centered at the w A band, the unwanted magnetization component corresponds to the band of frequencies centered at a>g. Taking the d i f f e r e n c e of data shown i n Figures 3.24A(i) and ( i i i ) w i l l c a n c e l t h i s component w h i l e r e t a i n i n g the r e q u i r e d magnetization centered at O J ^ ; t h i s i s shown i n F i g . 3.24A(iv). Figures 3 . 2 4 B ( i ) - ( i v ) show the s e r i e s of s p e c t r a obtained when the chemical s h i f t frequency i s c o i n c i d e n t w i t h the frequency band at wg, s i m u l a t i n g the phase r e l a t i o n s h i p of L(u>g) and L(w A) magnetization components. Taking the d i f f e r e n c e of F i g s . 3.24B(i) and ( i i i ) cancels the unwanted component, now at w^ , as shown i n F i g . 3.24B(iv). The data shown i n F i g . 3.24 confirm that the proper phase r e l a t i o n s h i p between the d e s i r e d and undesired magnetization components can be achieved by commencing the a c q u i s i t i o n of data at p o i n t A and p o i n t C . 110 -Lg. 3.24: 80.3 MHz iH NMR spect r a obtained from a s i n g l e chemical s h i f t u s i n g the sequence i n F i g . 3.21. A ( i ) - ( i v ) , chemical s h i f t centered at the hig h frequency (w )^ e x c i t a t i o n band and B ( i ) - ( i v ) , chemical s h i f t centered at the low frequency (wB) band. ( i ) , A c q u i s i t i o n of data at p o i n t A ( F i g . 3.21). ( i i ) and ( i i i ) , A c q u i s i t i o n of data at p o i n t s B and C r e s p e c t i v e l y and phase c o r r e c t i o n same as tha t a p p l i e d to ( i ) . ( i v ) , the d i f f e r e n c e of the data shown i n ( i ) and ( i i i ) . Cosine f u n c t i o n frequency (w )^ = 7450 Hz, the p r i n c i p a l lobe of the s i n e modulation (8 ms duration) was employed. Echo time a f t e r 180° pulse = 4.3 ms. Time delay between a c q u i s i t i o n p o i n t s A and B, and, B and C = 337 /zs. - I l l -3.2.4 Incorporation of Imaging and Further Extension The scheme discussed above can be e a s i l y i n c o r p o r a t e d i n t o an imaging sequence as shown i n F i g . 3.25. The d e s i r e d phase r e l a t i o n s h i p of the magnetization components w i l l be obtained at the maximum of the echo created by the read (frequency-encoding) gr a d i e n t . The complete experiment i n v o l v e s a c q u i s i t i o n of two imaging data sets w i t h At = 0 and At = 27r/(w^-wg). Combination of these data se t s w i l l generate an image showing the d i s t r i b u t i o n of the two chemical species i n an i d e n t i -c a l s p a t i a l plane. The complete two-dimensional experiment to i l l u s -t r a t e t h i s technique ( i . e . o b t a i n experimental images s i m i l a r to F i g . 3.20(d) and (e)) i n v o l v e s the use of the s l i c e s e l e c t i o n g r a d i e n t a l s o 180* RF G-s l i ce J \ G—read signal At F i g . 3.25: Proposed imaging sequence which enables two ch e m i c a l l y s h i f t e d species to be imaged i n the same s p a t i a l plane. At r e f e r s to the time d u r a t i o n denoted A-C i n F i g . 3.21. The phase-encoding gradient (not shown) i s a p p l i e d during the time i n t e r v a l between the r f pulses . - 112 -as the phase-encoding gradient during the imaging experiment. This c o u l d not be accomplished due to software l i m i t a t i o n s but the one dimensional v e r s i o n d escribed here corroborates the f e a s i b i l i t y of the method. Proper c a n c e l l a t i o n of unwanted magnetization i d e a l l y r e q u i r e s p h a s e - s e n s i t i v e two-dimensional data and good magnetic f i e l d homogeneity i n the imaging plane so t h a t phase d i s t o r t i o n s that can occur during time At ( F i g . 3.25) are minimized. But when there i s o v e r l a p p i n g of the frequency d i s t r i b u t i o n of the d e s i r e d and undesired magnetization components i n the presence of the read g r a d i e n t , above problems can be p a r t i a l l y overcome by a d d i t i o n o f the magnitude mode data [39] . With the method de s c r i b e d here, the c a n c e l l a t i o n of the unwanted components w i l l occur even when the imaging plane i s moved away from the center. In t h i s d i s c u s s i o n , the well-known e f f e c t of chemical s h i f t along the frequency-encoding dimension [48,49] has not been addressed. The three-dimensional v e r s i o n of the r e c e n t l y proposed refocussed gradient method [50] e l i m i n a t e s the chemical s h i f t and s t a t i c f i e l d inhomogeneity e f f e c t s from a l l s p a t i a l dimensions. However, combination of the method de s c r i b e d here w i t h the refocussed gradient method w i l l remove chemical s h i f t c o n t r i b u t i o n from both the s l i c e s e l e c t i o n and frequency-encoding dimensions w i t h consequent r e d u c t i o n i n experimental time. S t r a i g h t f o r -ward ex t e n s i o n of t h i s technique to m u l t i - c h e m i c a l s h i f t systems w i l l g e n e r a l l y r e s u l t i n incomplete c a n c e l l a t i o n of the unwanted magnetiza-t i o n . Therefore the method de s c r i b e d i s best s u i t e d f o r h i g h f i e l d N M R imaging whenever two w e l l separated c h e m i c a l l y s h i f t e d species are dominant. - 113 -References: Chapter I I I 1. A.N. Garroway, P.K. G r a n n e l l , and P. M a n f i e l d , J . Phys. C. 7, L457 (1974). 2. P.C. Lauterbur, C.S. Dulcey, C.-M. L a i , M.A. F e i l e r , W.V. House, D. Kramer, C.-N. Chen, and R. Dias, Proc. 18th Ampere Congress 1, 27 (1974) . 3. P.C. Lauterbur, D.M. Kramer, W.V. House, and C.-N. Chen, J . Am. Chem. Soc. 97, 6866 (1975). 4. P. M a n s f i e l d , A.A. Maudsley, and T. Baines, J . Phys. E. 9, 271 (1976). 5. R.J. Sutherland and J.M.S. Hutchison, J . Phys. E. 11, 79 (1978). 6. P. M a n s f i e l d , A.A. Maudsley, P.G. M o r r i s , and I.L. Pykett, J . Magn. Reson. 33, 261 (1979). 7. G.A. Mo r r i s and R. Freeman, J . Magn. Reson. 29, 433 (1978). 8. S. Alexander, Rev. S c i . Instrum. 32, 1066 (1961). 9 . A.G. R e d f i e l d and R.K. Gupta, J . Chem. Phys. 54, 1418 (1971). 10. B.L. Tomlinson and H.D.W. H i l l , J . Chem. Phys. 59, 1775 (1973). 11. A.G. R e d f i e l d , S.D. Kunz, and E.K. Ralph, J . Magn. Reson. 19, 114 (1975) . 12. F. Bloch, Phys. Rev. 70, 460 (1946). 13. T.C. F a r r a r and E.D. Becker, "Pulse and F o u r i e r Transform NMR", Academic Press, New York, 1971. 14. B.P. L a t h i , " S i g n a l s , Systems and Communication", Chap. 1, John Wiley and Sons, New York, 1965. 15. D. Shaw, " F o u r i e r Transform N.M.R. Spectroscopy", p. 53, 2nd e d i -t i o n , E l s e v i e r , New York, 1984. 16. E.O. Brigham, "The Fast F o u r i e r Transform", p. 58. P r e n t i c e - H a l l , Englewood C l i f f s , New Jersey, 1974. 17. H.D.W. H i l l , "Topics i n C-13 NMR spectroscopy", V o l . 3, p. 84. G.C. Levy, Ed., John Wiley and Sons, New York, 1979. - 114 -18. D.I. Hoult, J . Magn. Reson. 26, 165 (1977). 19. D.I. Hoult, J . Magn. Reson. 35, 69 (1979). 20. References 45-59, c i t e d i n [7]. 21. A. Caprihan, IEEE Trans. Med. Imag. MI-2, 169 (1983). 22. P.M. Joseph, L. A x e l , and M. O'Donnell, Med. Phys. 11, 772 (1984). 23. P.R. Locher, P h i l . Trans. R. Soc. Lond B 289, 539 (1980). 24. J.W. Emsley, J . Feeney, and L.H. S u t c l i f f e , "High R e s o l u t i o n NMR Spectroscopy", Chap. 2., Pergammon Press, Oxford, 1965. 25. C P . S l i c h t e r , " P r i n c i p l e s of Magnetic Resonance", p. 11. 2nd E d i t i o n , S p r i n g e r - V e r l a g , New York, 1978. 26. L.E. Crooks, IEEE Trans. Nucl. S c i . NS-27, 1239 (1980). 27. M.S. S i l v e r , R.I. Joseph, and D.I. Hoult, Phy. Rev. A 31, 2753 (1985). 28. M.S. S i l v e r , R.I. Joseph, and D.I. Hoult, J . Magn. Reson. 59, 347 (1984). 29. M.S. S i l v e r , R.I. Joseph, C.-N. Chen, V.J. Sank, and D.I. Hoult, Nature 310, 681 (1984). 30. D.J. L a u r i e , Magn. Reson. Imaging. 3, 235 (1985). 31. A.J. Temps and C F . Brewer, J . Magn. Reson. 56, 355 (1984). 32. C. Bauer, R. Freeman, T. F r e n k i e l , J . Keele r , and A.J. Sharka, J . Magn. Reson. 58, 442 (1984). 33. D. Roddy and J . Coolen " E l e c t r o n i c Communications", Chapter 9, 2nd E d i t i o n , P r e n t i c e - H a l l , V i r g i n i a , 1981. 34. Rf S i g n a l Processing Components Manual, p. 592, Watkins-Johnson Company 1983/84. 35. P.A. Bottomley, T.H. Foster, and R.D. Darrow, J . Magn. Reson. 59, 338 (1984). 36. W.P. Aue, S. M u l l e r , T.A. Cross, and J . S e e l i g , J . Magn. Reson. 56, 350 (1984). 37. S. Sukumar, p r i v a t e communication. - 115 -38. P.A. Bottomley, T.H. Foster, and W.M. Leue, Proc. N a t l . Acad. S c i . 81, 6856 (1984). 39. W.T. Dixon, Radiology 153, 189 (1984). 40. L.D. H a l l , S. Sukumar, and S.L. Ta l a g a l a , J . Magn. Reson. 56, 275 (1984). 41. B.R. Rosen, V.J. Wedeen, and T.J. Brady, J . Compt. A s s i s t . Tomogr. 8, 813 (1984). 42. A. Hasse, J . Frahm, W. Hanicke, and D. Matthaei, Phys. Med. B i o l . 30, 341 (1985); J . Frahm, A. Hasse, W. Hanicke, D. Matthaei, H. Bomsdorf, and T. H e l z e l , Radiology 156, 441 (1985). 43. P.M. Joseph, J . Comput. A s s i s t . Tomogr. 9, 651 (1985). 44. C.L. Dumoulin, Magn. Reson. Med. 2, 583 (1985). 45. L. A x e l and L. Dougherty, J . Magn. Reson. 66, 194 (1986). 46. L. A x e l , G. Glover, and N. P e l c , Magn. Reson. Med. 2, 428 (1985). 47. S.D. Luck, unpublished r e s u l t s . 48. A.J. Dwyer, R.H. Knop, and D.I. Hoult, J . Compt. A s s i s t . Tomogr. 9, 16 (1985). 49. E.E. Babcock, L. Brateman, J.C. Weinreb, S.D. Horner, and R.L. Nunnally, J . Compt. A s s i s t . Tomogr. 9, 252 (1985). 50. J.B. M i l l e r and A.N. Garroway, J . Magn. Reson. 67, 575 (1986). - 1 1 6 -CHAPTER IV IMAGING RESULTS - 117 -IV. IMAGING RESULTS The i n t r o d u c t o r y aspects of NMR imaging methods were discussed i n Chapter I I . This chapter serves to demonstrate the implementaton of two-dimensional and three-dimensional imaging methods u s i n g phantoms and i n t a c t systems. Further, the concept of f r e q u e n c y - s e l e c t i v e e x c i t a t i o n and suppression of s p e c i f i c resonances as a means of chemical s h i f t r e s o l v e d imaging i s a l s o introduced. Demonstration of two p o s s i b l e a p p l i c a t i o n s of three-dimensional chemical s h i f t r e s o l v e d imaging are a l s o presented i n the f i n a l s e c t i o n . 4.1 Two Dimensional Imaging 4.1.1 The Method The p a r t i c u l a r pulse and gradient sequence employed i n t h i s study f o r two-dimensional imaging i s shown i n F i g . 4.1. The o p e r a t i o n of the sequence i s most e a s i l y viewed by c o n s i d e r i n g the a c t i o n of each grad i e n t s e p a r a t e l y . F i r s t l y , the s l i c e s e l e c t i o n i s performed i n the u s u a l manner by the a p p l i c a t i o n of a low-power amplitude modulated r f pulse i n the presence of the s l i c e s e l e c t i o n g r a d i e n t , G - S l i c e ( I n t e r v a l I ) . At the end of t h i s i n t e r v a l , the spins w i t h i n the s e l e c t e d s l i c e are dephased c o n s i d e r a b l y i n the r o t a t i n g frame. The r e f o c u s s i n g of these spins i s achieved during i n t e r v a l I I I , by the a p p l i c a t i o n of a - 1 1 8 180° G-Phase G-Read Signal 4 »-4 • 4 • Interval I I IE IV Fig . 4.1: Two-dimensional imaging sequence used in this study. 90" RF G-SI ice - 119 -n o n - s e l e c t i v e 180° pulse f o l l o w e d by G - S l i c e . With i d e a l gradient behavior, maximum r e f o c u s s i n g of spins i s achieved a f t e r the 180° pulse at a time equal to h a l f the d u r a t i o n of the s e l e c t i v e pulse [1]; at t h i s p o i n t i n the sequence, the s l i c e s e l e c t i o n gradient i s turned o f f . The frequency encoding gradient (G-Read) i s a p p l i e d during the time i n t e r -v a l s I I and IV when the G - S l i c e i s i n a c t i v e . A p p l i c a t i o n of G-Read during i n t e r v a l I I i n i t i a l l y dephases the s e l e c t e d plane of spins along the frequency-encoding d i r e c t i o n . This dephasing i s subsequently refocussed a f t e r the 180° pulse by the a c t i v a t i o n of G-Read during i n t e r v a l IV forming a spin-echo. I n t e r v a l IV a l s o c o n s t i t u t e s the s i g n a l d e t e c t i o n p e r i o d . The phase-encoding gr a d i e n t (G-Phase) i s in c o r p o r a t e d i n t o i n t e r v a l I I and provides the r e q u i r e d s p a t i a l d i s c r i -m i nation along the phase-encoding d i r e c t i o n . The complete imaging experiment i n v o l v e s the accumulation of a s e r i e s of echo s i g n a l s w i t h d i f f e r e n t magnitudes of G-Phase. This modified v e r s i o n of the spin-warp experiment was necessary to avo i d the s i g n a l d i s t o r t i o n s observed when u s i n g the grad i e n t i n v e r s i o n procedure w i t h the a v a i l a b l e g r a d i e n t c o i l system. In p r a c t i c e , i t i s important that each aspect of the experiment be v e r i f i e d and optimized to o b t a i n the best r e s u l t s . This a l s o serves to i d e n t i f y any m a l f u n c t i o n i n g or i n a p p r o p r i a t e set-up of the instrumenta-t i o n . The o p t i m i z a t i o n procedure adopted by the author i s described below. The s l i c e s e l e c t i o n aspect of the experiment i s best optimized by us i n g a s l i g h t l y d i f f e r e n t scheme from that shown i n F i g . 4.1. The m o d i f i c a t i o n i n v o l v e s the s i g n a l be acquired immediately a f t e r the 180° - 120 -pulse i n the presence of the s l i c e s e l e c t i o n gradient only. This r e q u i r e s the s e t t i n g of G-Phase and G-Read to zero as w e l l as the extension of G - S l i c e , a f t e r the 180° p u l s e , to match the a c q u i s i t i o n time. The echo s i g n a l observed w i t h t h i s scheme represents the r e f o -c u s s i n g of spins w i t h i n the s e l e c t e d s l i c e , and t h i s s i g n a l , when subjected to F o u r i e r t r a n s f o r m a t i o n and c a l c u l a t i o n of the magnitude spectrum, corresponds to the p r o f i l e of the s e l e c t e d s l i c e . This procedure allows the s l i c e p r o f i l e to be optimized by d i r e c t observa-t i o n , and s u i t a b l e changes to the r f power and/or shape of the s e l e c t i v e pulse c o u l d thus be made. Such adjustments are necessary s i n c e they w i l l be sample dependent. In p r a c t i c e , the time at which the echo i s formed f o l l o w i n g the n o n s e l e c t i v e 180° pulse i s dependent not only on the l e n g t h of the s e l e c t i v e p u l s e , but a l s o on the delay time between the two p u l s e s , due to the f i n i t e r i s e - and f a l l - t i m e s of the gradient. The echo-time observed here gives a very approximate value f o r the time i n t e r v a l I I I i n the imaging sequence (see Fig.4.1). Once the s l i c e s e l e c t i o n i s optimized, the imaging sequence shown i n F i g . 4.1 should be i n i t i a l l y performed without the phase-encoding g r a d i e n t . This enables the p r o j e c t i o n of the s p i n d e n s i t y d i s t r i b u t i o n of the s e l e c t e d s l i c e onto the frequency-encoding d i r e c t i o n to be observed. During t h i s procedure, i t w i l l be noted t h a t the i n t e n s i t y of the echo-signal obtained i s determined by the d u r a t i o n of i n t e r v a l I I I . Non-ideal gradient s w i t c h i n g causes t h i s time d u r a t i o n to be l e s s than t h a t determined e a r l i e r , and thus should be optimized to give the maximum s i g n a l i n t e n s i t y . Improper s e t t i n g of i n t e r v a l I I I r e s u l t s i n - 121 -s u b s t a n t i a l degradation of the s i g n a l - t o - n o i s e r a t i o and a l s o produces a d i s t o r t e d p r o j e c t i o n of the s e l e c t e d s l i c e . Once t h i s i s accomplished, i t was found t h a t the phase-encoding gradient produces minimal e r r o r s and the f i n a l image produced i s a good r e p r e s e n t a t i o n of the o b j e c t . 4.1.2 Experimental Results The procedure discussed i n the previous s e c t i o n i s i l l u s t r a t e d w i t h experimental data obtained from a 4 cm diameter s p h e r i c a l phantom c o n t a i n i n g water. These are shown i n F i g s . 4.2-4.4. Figure 4.2a shows the NMR spectrum of the phantom i n the presence of a l i n e a r magnetic f i e l d gradient of ca. 0.23 G/cm u s i n g an r f pulse of 17.0 usee. This corresponds to the p r o j e c t i o n of the e n t i r e volume of the sample perp e n d i c u l a r to the d i r e c t i o n of the f i e l d g r a dient. Figure 4.2b shows the s l i c e s e l e c t i o n p r o f i l e obtained by u s i n g an amplitude modulated r f pulse f o l l o w e d by a 180° n o n s e l e c t i v e p u l s e . This was obtained by u s i n g the experimental setup described i n Chapter I I I , S e c t i o n 3.1.2 without u s i n g r f a t t e n u a t i o n a f t e r the T x/R x coupler u n i t . A 1 kW l i n e a r a m p l i f i e r (ENI model LPI-10) was used to provide a reasonably short pulse l e n g t h f o r the n o n s e l e c t i v e pulse. The a m p l i f i e r was a c t u a l l y d r i v e n at a much lower power (ca. 400W) than i t s c a p a c i t y and provided a n o n s e l e c t i v e 180° pulse length of 100 fis. The r f modulating f u n c t i o n c o n s i s t e d of a s i n e f u n c t i o n ( p e r i o d — 4 ms), and a modulated pulse l e n g t h of 8.0 ms was employed. However, the r f waveform s u p p l i e d to the probe resembled that of F i g . 3.16b i n Chapter - 122 -T j i i — i — | — i i i — | — i — i — i — | — i — i — i — | — r 4000 2000 0 - 2 0 0 0 - 4 0 0 0 Hz F i g . 4.2: (a) 80.3 MHz iH NMR spectrum of a 4 cm diameter s p h e r i c a l water phantom i n the presence of a gradient of magnitude 0.23 G/cm. (b) The s l i c e p r o f i l e obtained by the use of a sin e modulated r f pulse i n the presence of the grad i e n t used i n (a ) . (c) P r o j e c t i o n of the s l i c e shown i n (b) onto a d i r e c -t i o n p a r a l l e l to the plane of the s l i c e (see t e x t f o r f u r t h e r d e t a i l s ) . - 123 -I I I due to the n o n l i n e a r i t i e s of the system components. The amplitude of the modulated pulse was optimized to provide the best s e l e c t i o n p r o f i l e . The s l i c e s e l e c t i o n p r o f i l e shown i n F i g . 4.2b, obtained w i t h the same gradient s t r e n g t h as used i n F i g . 4.2a and drawn to tbe same h o r i z o n t a l s c a l e , corresponds to a s l i c e t h i c k n e s s of ca. 5 mm. The p r o j e c t i o n of the s p i n d e n s i t y w i t h i n the s e l e c t e d s l i c e , obtained by u s i n g the sequence given i n F i g . 4.1 w i t h the phase encoding g r a d i e n t s et to zero, i s shown i n F i g . 4.2c. The same s l i c e s e l e c t i o n parameters as used f o r F i g . 4.2b, and a read-gradient s t r e n g t h of ca. 0.23 G/cm were employed. The optimum d u r a t i o n of the i n t e r v a l I I I i n the pulse sequence to produce a maximum echo s i g n a l was found to be 7.1 ms when the i n t e r v a l I I was set at 12.0 ms. Thus the echo-time of the s i g n a l d e f i n e d as the time d u r a t i o n between the center of the modulated r f pulse and echo maximum during the d e t e c t i o n p e r i o d , corresponded to 33.1 ms. Very good correspondence between the expected p r o f i l e and that shown i n F i g . 4.2c i n d i c a t e s the proper adjustment of the experimental scheme. The data obtained during a complete imaging experiment i s shown i n F i g . 4.3. F i g . 4.3a shows a p o r t i o n of the t o t a l time domain data s et S(G x,ty) obtained by incrementing the magnitude of the phase-encoding gradient i n successive experiments. The gradient increment used corre-sponded to a value of 2.44 x 10" 3 G/cm as c a l c u l a t e d from the 8 cm t o t a l f i e l d - o f - v i e w obtained along the phase-encoding dimension i n the f i n a l image. Other experimental parameters were unchanged from that used to o b t a i n F i g . 4.2c. A t o t a l of 128 phase-encoding gradient values (N) c o n s i s t i n g of both p o s i t i v e and negative magnitudes p r o p o r t i o n a l to - 124 -F i g . 4.3: Processing of two-dimensional imaging data. (a) O r i g i n a l time domain data S ( G x , t y ) . (b) F i r s t F o u r i e r transform (FT), S(G x,w y). (c) T r a n s p o s i t i o n (TD), S(w y,G x). (d) Second F o u r i e r transform, S(wy,w x). In a l l cases only a s e l e c t e d set of t r a c e s from the r e a l p a r t of the complex data set i s shown. Each t r a c e represents the e n t i r e r e a l p a r t of the data c o n t a i n i n g 128 p o i n t s . The block numbers of the t r a c e s are i n d i c a t e d on the r i g h t of each data s e t . - 125 --—...-1,0,1 Hzl were used. In the i d e a l case, the maximum s i g n a l 2 2 i n t e n s i t y i n the two-dimensional data set should be observed when the phase-encoding gradient i s zero. In F i g . 4.3a t h i s occurs i n block number 66 r a t h e r than 65 due to a small bias, g r a d i e n t generated when i t s magnitude i s set to zero. Figures 4.3b-c represent intermediate data sets obtained during data p r o c e s s i n g (double F o u r i e r transformation) of S ( G x , t v ) . F o u r i e r t r a n s f o r m a t i o n of S(G x,ty) w i t h respect to t y produces the data set S(G x,ojy), of which s e l e c t e d s p e c t r a l t r a c e s are shown i n F i g . 4.3b. I t should be noted that the o s c i l l a t o r y behavior of the s p e c t r a shown i n F i g . 4.3b i s a consequence of the F o u r i e r t r a n s f o r m a t i o n of a whole echo s i g n a l [ 2 ] , and i s u n r e l a t e d to the imaging process. P r i o r to the second F o u r i e r t r a n s f o r m a t i o n w i t h respect to G x, the data m a t r i x S(Gx,Wy) i s transposed to y i e l d S(a>y,Gx), which i s shown i n F i g . 4.3c. The t r a c e s of S(wy,G x) r e s u l t from a s e r i e s of overlapping c o s i n u s o i d a l s i g n a l s (see Chapter 2, Eq. 2.17) of d i f f e r i n g frequency and thus appear as a decaying s i g n a l . F o u r i e r t r a n s f o r m a t i o n of these t r a c e s y i e l d s the data m a t r i x shown i n F i g . 4.3d corresponding to S(wy,w x). The f i n a l image i s obtained by c a l c u l a t i n g the absolute value of S(ojy,w x). The data obtained are shown i n the form of a stacked p l o t and as w e l l as a contour p l o t i n F i g . 4.4. Images shown i n F i g . 4.4 show a uniform s i g n a l i n t e n s i t y corresponding to the s p i n d e n s i t y d i s t r i b u t i o n w i t h i n the s e l e c t e d s l i c e . The s l i g h t decrease i n i n t e n s i t y on the r i g h t s i d e of the images i s due to the small volume of a i r trapped i n s i d e the water phantom. - 1 2 6 -- 127 -Imaging of i n t a c t Systems From the i n i t i a l study w i t h phantoms the experiment was extended to imaging of f r u i t s , human forearm and a small l a b o r a t o r y animal. The images obtained are shown i n F i g s . 4.5-4.9. At t h i s p o i n t i t should be r e c a l l e d that the s i g n a l i n t e n s i t y i n an NMR image i s not only a f u n c t i o n of the s p a t i a l s p i n d e n s i t y d i s t r i b u -t i o n but a l s o of other parameters such as T]^,T2 and flow. Therefore, the c o n t r a s t between d i f f e r e n t s t r u c t u r e s depends h e a v i l y on the exper-imental parameters such as the pulse r e p e t i t i o n time (TR) and t o t a l echo-time of the s i g n a l (TE). These correspond to the time between successive 90° s e l e c t i v e pulses and the sum of the i n t e r v a l s 1/2 + I I + I I I + IV/2 i n F i g . 4.1 r e s p e c t i v e l y . A l l the images shown i n F i g s . 4.5-4.9 have been d i s p l a y e d w i t h a c o l o r s c a l e comprising ten d i f f e r e n t shades of blue ranging from white to dark blue. I n a l l the images, the t o t a l i n t e n s i t y range i s d i s -played, and white corresponds to h i g h s i g n a l i n t e n s i t y and dark blue corresponds to low s i g n a l i n t e n s i t y . The r e l e v a n t experimental parame-t e r s are given i n the Figure c a p t i o n s . The gradient magnitudes quoted correspond to the values c a l c u l a t e d according to the experimentally observed f i e l d - o f - v i e w assuming constant amplitude g r a d i e n t pulses. Images were obtained w i t h e i t h e r a 12 cm ( f o r arm and orange images) or a 7 cm ( f o r lime and r a t images) diameter of i n d u c t i v e l y coupled H-reso-nator probe (see Chapter V). Figures 4.5 and 4.6 show ^H NMR images obtained from an orange and a lime r e s p e c t i v e l y u s i n g the sequence shown i n F i g . 4.1. In both - 1 2 8 -F i g . 4.5: XH NMR image (80.3 MHz) of an i n t a c t orange (diameter 6.5 cm). Imaging parameters: S l i c e t h i c k n e s s 2.5 mm, Image d i g i t i z a t i o n 256 x 256, Image r e s o l u t i o n 0.32 x 0.32 mm/Pt, TE - 46 ms, T o t a l imaging time 13 min, TR = 3.0s, S l i c e s e l e c t i o n gradient 0.48 G/cm, Frequency-encoding gr a d i e n t 0.3 G/cm, Phase-encoding gradient increment 2.8 x IO" 3 G/cm. - 1 2 9 -4.6: XH NMR image (80.3 MHz) of an i n t a c t lime (diameter 4.5 cm) Imaging parameters: S l i c e t hickness 2.0 mm, Image d i g i t i z a t i o n 256 x 256, Image r e s o l u t i o n 0.2 x 0.23 mm/Pt, TE - 52 ms, T o t a l imaging time 11 min, TR = 2.5s, S l i c e s e l e c t i o n g radient 0.57 G/cm, Frequency-encoding g r a d i e n t 0.24 G/cm, Phase-encoding gradient increment 2.1 x 10" 3 G/cm. - 130 -images very f i n e septa are c l e a r l y r e s o l v e d . This i n d i c a t e s the s p a t i a l r e s o l u t i o n obtained. The seed case and i t s i n t e r i o r are c l e a r l y v i s i b l e i n the orange image. Clo s e r examination of the same r e v e a l s the outer l a y e r of the s k i n d i s t i n c t from the inner l a y e r which c o n t r i b u t e s n e g l i g i b l e s i g n a l . This i s due to the d i f f e r e n c e i n ^-H r e l a x a t i o n times between the outer and the inner l a y e r of the s k i n . C r o s s - s e c t i o n a l -^H NMR image of a human forearm i s shown i n F i g . 4.7. In t h i s image, the water as w e l l as f a t c o n t r i b u t e s to the s i g n a l i n t e n s i t y . Due to the short r e p e t i t i o n time (TR - 500 ms) between the experiments, the regions of high s i g n a l i n t e n s i t y (represented by white) correspond mostly to f a t t y t i s s u e because of i t s r a p i d T^ r e l a x a t i o n compared to water [3]. Therefore, the subcutaneous f a t , the bone marrow (surrounded by the bone which c o n t r i b u t e s n e g l i g i b l e i n t e n s i t y ) and a l s o other f a t t y d eposits between the muscles can a l l be e a s i l y v i s u a l i z e d i n the image. The muscle s t r u c t u r e i s represented as a darker blue r e g i o n and cannot be c l e a r l y d i f f e r e n t i a t e d i n t h i s image. I t i s a l s o p o s s i b l e to see s e v e r a l v e i n s which appear as dark regions w i t h i n the f a t l a y e r . F i g ure 4.8 shows a coronal view of the head of a l i v e r a t . In t h i s image, the most intense i s the b r a i n which i s surrounded by a dark o u t l i n e due to the s k u l l . The mandible a l s o appears as dark and i s w e l l r e s o l v e d . The muscles of the jaw and the tongue are of intermediate i n t e n s i t y . The a i r i n the nasopharynx i s a l s o c l e a r l y seen as a dark r e g i o n below the b r a i n . The above i n t e r p r e t a t i o n s of the image are based on that given i n Ref. 3. These r e s u l t s demonstrate that reasonably good q u a l i t y images of small animals and human e x t r e m i t i e s can be obtained w i t h adequate - 1 3 1 -F i g . 4.7: C r o s s - s e c t i o n a l iH NMR image (80.3 MHz) of a human forearm. Imaging parameters: S l i c e t hickness -3 mm, Image d i i g i t i z a -t i o n 256 x 256, Image r e s o l u t i o n 0.45 x 0.34 mm/pt, TE = 30 ms, TR = 500 ms, T o t a l imaging time 2.0 min, S l i c e s e l e c t i o n gradient 0.38 G/cm, Frequency-encoding g r a d i e n t 0.2 G/cm, Phase-encoding gradient increment 2.6 x 1 0 G / c m . - 132 -F i g . 4.8: Coronal iH NMR image (80.3 MHz) of a r a t head. Imaging parameters: S l i c e t hickness -1.5 mm, Image d i g i t i z a t i o n 256 x 256, Image r e s o l u t i o n 0.2 x 0.2 mm/pt, TE = 29 ms, TR -500 ms, T o t a l imaging time 17.0 min, Number of scans = 8, S l i c e s e l e c t i o n gradient 0.75 G/cm, Frequency-encoding gradient 0.5 G/cm, Phase-encoding g r a d i e n t increment 5.2 x 10" 3 G/cm. - 133 -s p a t i a l r e s o l u t i o n u s i n g the c u r r e n t l y a v a i l a b l e equipment i n t h i s l a b o r a t o r y . I n i t i a l l y , i t was hoped that the i n t e r n a l s t r u c t u r e of the r a t b r a i n may i n f a c t be revealed through NMR imaging. But the poor d i s c r i m i n a t i o n obtained between the s o f t t i s s u e s i n the b r a i n ( F i g . 4.8) was d i s a p p o i n t i n g . However, a recent p u b l i c a t i o n [4] , has demonstrated improved c o n t r a s t w i t h i n the r a t b r a i n obtained through v a r i a t i o n of imaging parameters. 4.2 Three-dimensional Imaging Aspects of simultaneous three-dimensional imaging w i t h regard to i t s s e n s i t i v i t y and experimental time were discussed i n Chapter I I . Further to these c o n s i d e r a t i o n s , three-dimensional imaging enables i n v e s t i g a t i o n of very t h i n s l i c e s compared to two-dimensional imaging, and a l s o allows the c o n s t r u c t i o n of images i n any a r b i t r a r y d i r e c t i o n . E l i m i n a t i o n of the need f o r a separate s l i c e s e l e c t i o n scheme reduces the complexity o f the experiment, but at the same time introduces a more demanding data processing procedure. 4.2.1 The Method The pulse and gradient sequence f o r the three-dimensional imaging i s shown i n F i g . 4 .9 . The r f sequence c o n s i s t s of a n o n s e l e c t i v e 90° e x c i t a t i o n pulse f o l l o w e d by a 1 8 0 ° pulse. The formation of the - 134 -spin-echo s i g n a l i n the presence of G-Read, frequency encodes the s p i n along the d i r e c t i o n of the gradient. The s p a t i a l d i s c r i m i n a t i o n i n the other two dimensions i s achieved by means of two p e r p e n d i c u l a r phase-encoding gradients (G-Phase 1 and G-Phase 2) which are a p p l i e d s i m u l t a -neously. A s e r i e s of phase modulated spin-echo s i g n a l s are acquired by systematic v a r i a t i o n of the magnitude of both the phase-encoding g r a d i e n t s s i m i l a r to that i n a two-dimensional experiment. For the two phase-encoding g r a d i e n t s , the incremental gradient magnitude and the t o t a l number of increments can be d i f f e r e n t , and t h e r e f o r e , the f i e l d of view and the r e s o l u t i o n of each dimension can be adjusted independently. I t i s necessary that a l l combinations of the two phase-encoding gradient magnitudes be sampled i n order to e x t r a c t the complete three-dimensional i n f o r m a t i o n . Assuming G x and Gy are used as the phase-encoding gradients and t 2 denotes the s i g n a l d e t e c t i o n p e r i o d , the i n i t i a l data m a t r i x can be represented as S ( G x , G y , t z ) . Three-dimensional F o u r i e r t r a n s f o r m a t i o n of S(G x,Gy,t 2) y i e l d s the m a t r i x S(w x,Wy,w z), which corresponds to the three-dimensional image of the o b j e c t . At t h i s stage i t i s i n s t r u c t i v e to examine how the three-dimensional F o u r i e r t r a n s f o r m a t i o n i s achieved i n p r a c t i c e . The data format of the i n i t i a l time domain data depends on how the two phase-encoding gradients G x and Gy are incremented i n order to provide a l l the combinations of t h e i r magnitudes. This i s most e a s i l y done by keeping one of the g r a d i e n t s (say G x) constant and v a r y i n g the magnitude of the other (say Gy). The whole sequence i s then repeated f o r a l l the values of G x. This generates the three-dimensional data set S(G x,Gy,t z) which can be considered as a s e r i e s of two-dimensional G y , t z b l o c k s of data - 1 3 5 -RF G-Phase 1 G-Phase 2 G-Read Signal 90° 180° PHASE ENCODE -+• 4-FREQUENCY ENCODE Fig . 4.9: Pulse and gradient sequence used for three-dimensional imaging. - 136 -corresponding to d i f f e r e n t values of G x. This i s represented i n F i g . 4.10a. With t h i s o r i g i n a l data format, the three-dimensional F o u r i e r t r a n s f o r m a t i o n can be achieved by a s e r i e s of one-dimensional F o u r i e r transforms and as i n d i c a t e d i n F i g . 4.10b. The data t r a n s p o s i t i o n steps, TD1 and TD2, shown i n F i g . 4.10b, r e q u i r e a d d i t i o n a l software c a p a b i l i t y to that a v a i l a b l e i n standard commercial NMR software packages. From the f i n a l data matrix, S(w z,Wy,w x), i t i s p o s s i b l e to e x t r a c t the image corresponding to any d e s i r e d plane. I t should be noted that the complicated data t r a n s p o s i t i o n steps can be e l i m i n a t e d i f only the images corresponding to d i f f e r e n t x,y planes ( i . e . s p a t i a l coordinates d e f i n e d by the two phase-encoding g r a d i e n t s ) are d e s i r e d . In t h i s case, the e x t r a c t i o n of a s i n g l e data t r a c e corresponding to a p a r t i c u l a r u>z through the data matrix S(G x,Gy,w z) gives the two-dimensional data matrix, S ( G x , G y ) W z > i n one-dimensional format. These data, upon conversion to the two-dimensional format and subsequent two-dimensional F o u r i e r t r a n s f o r m a t i o n produce the data s e t , S ( ( i> x,Wy) W z, which corresponds to the x-y image at a p a r t i c u l a r z coordinate. This process can then be repeated to produce a s e r i e s of x-y images at d i f f e r e n t z l o c a t i o n s . 4.2.2 Experimental Results I n i t i a l demonstration of the three-dimensional experiment was performed u s i n g a phantom comprising of an Erlenmeyer f l a s k (5 ml) and a round bottom f l a s k (5 ml) c o n t a i n i n g water. Figure 4.11 shows the (a) ( b ) t I t 137 S ( G x , G y , t z ) F T ( Z V S(G x,G y,w z) S(G x,w z,G y) FT(y) S(w z,w y,a) x) ^ E I I x l S(w z,Wy,G x) -*--- S(G x,w z,w ) T D 1 T D 2 S(w 2,G x,w y) F i g . 4.10: (a) Data format of the three-dimensional imaging data matrix S ( G x , G y , t z ) . (b) Flow chart of three-dimensional imaging data processing. FT-Fourier transform, TDl and TD2 - Data t r a n s p o s i t i o n steps. 138 -images corresponding to a l l three s p a t i a l planes obtained from a s i n g l e three-dimensional data set. Images show good d e f i n i t i o n of the shape of the phantom used. The software necessary f o r data t r a n s p o s i t i o n during image p r o c e s s i n g was w r i t t e n by the author. The images were constructed from an o r i g i n a l data matrix s i z e of 64 x 64 x 128 and were subsequently z e r o - f i l l e d to 128 x 128 x 128 during data processing. The r e p e t i t i o n time between experiments was 500 ms, corresponding to a t o t a l data a c q u i s i t i o n time of 34 min. The image p r o c e s s i n g took approximately three hours. This data processing time can be reduced c o n s i d e r a b l y by u s i n g f a s t data processors and automated software. In the attempts to reduce the experimental time by reducing the r e p e t i t i o n time, i t was found t h a t the data t r a n s f e r time (ca. 150 ms) between the computer memory and the d i s k was the l i m i t i n g f a c t o r . This corresponds to a minimum data a c q u i s i t i o n time of approximately 10 mins f o r 64 gradient increments i n each phase-encoding dimension. The three-dimensional imaging experiment was then extended to o b t a i n a s e r i e s of coronal images of a r a t head and these are shown i n F i g . 4.12. Each image corresponds to a s l i c e t h ickness of 0.5 mm and a data m a t r i x s i z e of 64 x 64. I n order to confirm the a c t u a l p o s i t i o n of the image planes, a marker (two, 2 cm long c a p i l l a r y tubes c o n t a i n i n g water) was pl a c e d on the r a t ' s head as shown i n F i g . 4.12a; t h i s marker can be seen i n the images B, C and D. The images A and E correspond to s l i c e s taken j u s t i n f r o n t and back of the marker r e s p e c t i v e l y . Out of the p o s s i b l e 40 image s l i c e s which encompass the 2 cm l e n g t h of marker, only the images w i t h d i s t i n c t changes i n the anatomy are shown. 139 (CM) •"•H NMR Images of a phantom (5 ml Erlenmeyer f l a s k and a round bottom f l a s k c o n t a i n i n g water) obtained from a s i n g l e three-dimensional imaging experiment. (a) L o n g i t u d i n a l YZ s l i c e . (b) C r o s s - s e c t i o n a l XZ s l i c e . (c) and (d) Trans-verse XY s l i c e s e x t r a c t e d from d i f f e r e n t p o s i t i o n s along the l o n g i t u d i n a l z - a x i s . - 139a -F i g . 4.12: iH NMR images (80.3 MHz) of a r a t head obtained from a three-dimensional experiment. (a) Photograph of the r a t showing a marker c o n s i s t i n g of two c a p i l l a r y tubes c o n t a i n -in g water. (A)-(E) Selected coronal s e c t i o n s (0.5 mm t h i c k ) taken from the f r o n t to the back end of the marker. Imaging parameters:Image d i g i t i z a t i o n 64 x 64, Image r e s o l u t i o n 0.8 x 0.8 mm, TE = 12 ms, TR = 250 ms. T o t a l experimental time = 17.0 min. - 140 -141 -I n the image A, the most intense r e g i o n corresponds to the b r a i n , and i t s change i n shape can be c l e a r l y seen i n the successive s l i c e s . Other regions i n image A can be i d e n t i f i e d on comparison w i t h the high r e s o l u t i o n image shown i n F i g . 4.8. The two prominent dark regions w i t h zero i n t e n s i t y i n image B ( F i g . 4.12) correspond to the sinuses while the s m a l l e r dark area i n the center i s assigned to the trachea. The dark i n t r u s i o n s i n images C and D are probably due to a combination of the sinuses and the ear bones. The general anatomical change seen i n these images compares w e l l w i t h the e x i s t i n g data [ 5 ] , but r e q u i r e s f u r t h e r experimentation f o r unambiguous assignment. The i n t e r p r e t a t i o n s given above were formulated i n c o n s u l t a t i o n w i t h Dr. J . Andersen (Department of Anatomy, UBC) and Dr. P. Reiner (Department of P s y c h i a t r y , UBC). 4.3 Chemical S h i f t Resolved Imaging 4.3.1 Frequency-Selective E x c i t a t i o n and Suppression of S p e c i f i c Resonances Chemical s h i f t r e s o l v e d imaging methods which incorporate the i n t r i n s i c chemical s h i f t as an a d d i t i o n a l dimension i n t o the b a s i c two-dimensional spin-warp technique demand e x c e s s i v e l y long measuring times due to the increase i n d i m e n s i o n a l i t y of the experiment (see Chapter I I ) . Therefore, i t i s of considerable i n t e r e s t to develop a l t e r n a t i v e techniques to overcome t h i s disadvantage. The method - 142 -proposed and demonstrated here u t i l i z e s the techniques of frequency-s e l e c t i v e e x c i t a t i o n or suppression of s p e c i f i c chemical resonances coupled w i t h conventional two-dimensional imaging. Frequency-selective e x c i t a t i o n allows d i r e c t o b s e r v a t i o n of the image corresponding to a p a r t i c u l a r chemical s h i f t component, while the s e l e c t i v e s a t u r a t i o n method e l i m i n a t e s a p r e s e l e c t e d chemical species from the image. These methods enable the a c q u i s i t i o n of chemical s h i f t images w i t h experimen-t a l times comparable to that of conventional imaging. Further, t h i s approach to chemical s h i f t r e s o l v e d imaging a l l e v i a t e s the dynamic range problems when observing species of low c o n c e n t r a t i o n (or i n t e n s i t y ) i n the presence of more abundant species. The pulse sequence used to demonstrate the technique i s shown i n F i g . 4.13. For s e l e c t i v e suppression of resonances, a low power r f pulse i s used to s e l e c t i v e l y s a t u r a t e an unwanted resonance [6-8] p r i o r to the a p p l i c a t i o n of the n o n s e l e c t i v e 90° pulse. I n the case of s e l e c t i v e e x c i t a t i o n , the s a t u r a t i n g pulse and the n o n s e l e c t i v e 90° pulse are re p l a c e d by a f r e q u e n c y - s e l e c t i v e pulse which acts as a 90° pulse f o r the resonance of i n t e r e s t . Both the resonance s e l e c t i o n methods are performed i n the absence of magnetic f i e l d g radients and p r i o r to the a p p l i c a t i o n of the imaging sequence. Therefore the band-width r e q u i r e d during s e l e c t i v e e x c i t a t i o n or s a t u r a t i o n i s governed by the h i g h - r e s o l u t i o n c o n d i t i o n s . In t h i s p a r t i c u l a r study, s e l e c t i v e e x c i t a t i o n was achieved e i t h e r v i a a long weak r f pulse ( s o f t pulse) [9] or a DANTE pulse [10]. The DANTE pulse c o n s i s t s of a t r a i n of short , s t r o n g , e q u a l l y spaced r f p u l s e s , each w i t h f l i p angle 6 « n/2. Only those resonances that are o f f s e t from the t r a n s m i t t e r by n/r Hz, where r - 143 -90° 180 RF G-Phase G-Read Signal 1_ F i g . 4.13: The r f pulse and gradient sequence used to demonstrate f r e q u e n c y - s e l e c t i v e e x c i t a t i o n / s u p p r e s s i o n of resonances i n con j u n c t i o n w i t h conventional two-dimensional imaging (see a l s o t e x t ) . i s the pulse spacing and n i s an i n t e g e r , are e x c i t e d to a s i g n i f i c a n t extent by the pulse t r a i n . The experimental demonstration of the method was performed us i n g a phantom comprising four glass c a p i l l a r y tubes ( 1 . 2 mm i.d.) l o c a t e d i n s i d e a 5 mm NMR tube. Two of the c a p i l l a r y tubes were f i l l e d w i t h water w h i l e the other two contained ethanol. The experiments were conducted u s i n g a h i g h r e s o l u t i o n , narrow bore 2 7 0 M H z spectrometer and the s e l e c t i v e s a t u r a t i o n and e x c i t a t i o n pulses were obtained from the decoupler. - 144 -A s e r i e s of s p e c t r a of the phantom obtained under d i f f e r e n t e x c i t a -t i o n c o n d i t i o n s are shown i n F i g . 4.14. These s p e c t r a were obtained by i n i t i a t i n g the s i g n a l a c q u i s i t i o n immediately f o l l o w i n g the s i g n a l e x c i t a t i o n without recourse to echo formation. Figures 4.14A and B show r e s p e c t i v e l y the h i g h r e s o l u t i o n spectrum of the phantom and the s p i n d e n s i t y p r o j e c t i o n spectrum i n the presence of the G x gradient. S e l e c t i v e s a t u r a t i o n of water ( F i g . 4.14C) and s e l e c t i v e e x c i t a t i o n of the ethanol resonances ( F i g s . 4.14D-F) are a l l seen to produce the d e s i r e d d i s c r i m i n a t i o n between the water and ethanol resonances. Due to the p a r a l l e l o r i e n t a t i o n of the ethanol tubes (see In s e t F i g . 4.14) w i t h respect to the a p p l i e d gradient ( G x ) , the ethanol resonances appear as two d i s t i n c t peaks i n F i g s . 4.14B-F. Figure 4.15 shows the images of the phantom obtained u s i n g the pulse sequence shown i n F i g . 4.13. The normal image ( F i g . 4.15B) obtained w i t h a 90° n o n s e l e c t i v e pulse e x c i t a t i o n shows only the water tubes, and attempts to s c a l e up the i n t e n s i t y to v i s u a l i z e the ethanol image r e s u l t e d i n gross d i s t o r t i o n of the e n t i r e image. S e l e c t i v e s a t u r a t i o n of water ( F i g . 4.15C) produces a c l e a r view of the ethanol images v i a the methyl resonance w h i l e the water and other ethanol resonances are absent. S e l e c t i v e - e x c i t a t i o n images of the methyl resonance u s i n g e i t h e r a long weak pulse ( F i g . 4.15D) or a DANTE pulse ( F i g . 4.15E) r e s u l t e d i n an almost e x c l u s i v e image of ethanol. However, the s e l e c t i v e - e x c i t a t i o n image of ethanol v i a the methylene resonance was f a r l e s s s e l e c t i v e ( F i g . 4.15F). This i s a t t r i b u t e d to the r e f o -c u s s i n g of the r e s i d u a l water magnetization e x c i t e d during the DANTE pulse (not v i s i b l e i n F i g . 4.14F) by the 180° pulse. - 145 -F i g . 4.14: Inset - the o r i e n t a t i o n of the phantom; W, water, E, ethanol. [A] 270 MHz ^H spectrum of the phantom. [B] Spectrum i n the presence of a s t a t i c magnetic f i e l d gradient of s t r e n g t h ca. 446 Hz/cm d i r e c t e d along the x - a x i s . [C] Spectrum obtained by s a t u r a t i o n of the water w i t h a 1.0 sec continuous i r r a d i a t i o n p r i o r to data a c q u i s i t i o n , w i t h the gradient being a p p l i e d only during the a c q u i s i t i o n time. [D] S e l e c t i v e e x c i t a t i o n of the ethanol -CH3 peak w i t h a weak pulse of 20 ms du r a t i o n from the decoupler, and data a c q u i s i t i o n i n the presence of the grad i e n t . [E] Selec-t i v e e x c i t a t i o n of the ethanol-CH3 peak w i t h a DANTE pulse t r a i n c o n s i s t i n g of 36, 1 pulses and 3 db a t t e n u a t i o n of the main t r a n s m i t t e r , [F] S e l e c t i v e e x c i t a t i o n of the etha-n o l -CH2 peak w i t h a DANTE sequence of 40, 1 ps pulses and 6 db a t t e n u a t i o n . - 146 -5 A - X i 1 1—• AA AA • 1 i — 65 ' 35 ' 20 sTppm) y F i g . 4.15: In s e t - O r i e n t a t i o n of the phantom (W, water, E, e t h a n o l ) . [A] *H spectrum of the phantom l n the presence of a grad i e n t of 446 Hz/cm. [B] Reconstructed *H image of the phantom. (G x-Read = 446 Hz; G y-Phase Increment - 14 Hz/cm; Number of G v-Phase increments = 64, Echo time = 100 ms, R e l a x a t i o n delay 20 s ) . [C] Water saturat e d image ( s a t u r a t i o n 1.0s). [D] Image w i t h a 90° s e l e c t i v e pulse of 20 ms through the decoupler a t the ethanol-CH 3 resonance, [ E ] , [F] Images w i t h s e l e c t i v e 90° DANTE pulse t r a i n s on the ethanol-CH 3 and -CH2 resonances r e s p e c t i v e l y . DANTE pulses are as described f o r F i g . 4.14E and F. - 147 -The r e s u l t s presented above demonstrate the e s s e n t i a l f e a t u r e s of the technique. In t h i s study, the s l i c e thicknesses of the images were determined by the len g t h of the r e c e i v e r c o i l . But i n a p r a c t i c a l a p p l i c a t i o n of the technique, a s l i c e s e l e c t i o n process needs to be in c o r p o r a t e d i n t o the pulse sequence. This can be con v e n i e n t l y accom-p l i s h e d i n the s e l e c t i v e s a t u r a t i o n method by r e p l a c i n g the n o n s e l e c t i v e 90° pulse i n F i g . 4.13 w i t h a s l i c e - s e l e c t i v e pulse ( i . e . a frequency-s e l e c t i v e pulse i n the presence of a g r a d i e n t ) . But f o r the s e l e c t i v e e x c i t a t i o n method i t i s more d i f f i c u l t , and i t has been suggested [11,12] t h a t the s l i c e s e l e c t i o n process be performed at the same time as the s e l e c t i v e e x c i t a t i o n of the chemical resonances. This procedure however, i s only s u i t a b l e when the chemical s h i f t s e p a r a t i o n i s l a r g e r than the frequency spread of the resonances i n the presence of the s l i c e s e l e c t i o n g r a d i e n t . Thus a more appropriate technique to in c o r p o r a t e s l i c e - s e l e c t i o n i n t o the s e l e c t i v e e x c i t a t i o n method i s to convert the n o n s e l e c t i v e 180° r e f o c u s s i n g pulse i n t o a s l i c e - s e l e c t i v e p ulse. This approach, though not p r e f e r r e d due to the d i f f i c u l t y i n o b t a i n i n g such p u l s e s , i s commonly used i n m u l t i - s e c t i o n imaging [13] and i n s i t u a t i o n s s i m i l a r to th a t encountered here [14, 15]. Further, i t has a l s o been a subje c t of a recent p u b l i c a t i o n [16]. I t should be mentioned that the u t i l i t y of s e l e c t i v e s a t u r a t i o n as a means of chemical s h i f t r e s o l v e d imaging has a l s o been recognized by other workers [17,18]. Since the r e p o r t of the concepts developed here [19], s e v e r a l v a r i a t i o n s of the s e l e c t i v e e x c i t a t i o n technique have been suggested and t h e i r a p p l i c a t i o n to human imaging has been demonstrated '[11,14,20,21]. - 148 -4.3.2 A p p l i c a t i o n s of Three-dimensional Chemical S h i f t Resolved Imaging So f a r , the s t u d i e s i n v o l v i n g chemical s h i f t r e s o l v e d imaging have been d i r e c t e d towards the generation and c l i n i c a l assessment of images corresponding to a p a r t i c u l a r chemical s h i f t species [22] . This study demonstrates the a p p l i c a t i o n of the technique to map the s p a t i a l d i s t r i -b u t i o n of parameters such as pH and temperature [23]. The approach pursued here f o r t h i s purpose i s to perform a three-dimensional chemical s h i f t r e s o l v e d experiment while observing a chemical s h i f t species which i s s e n s i t i v e to the changes i n pH or temperature. Though other methods us i n g computed tomography [24] and s p i n - l a t t i c e r e l a x a t i o n v a r i a t i o n s of NMR images [25] have been considered f o r temperature mapping, determina-t i o n of the pH d i s t r i b u t i o n w i t h i n an o b j e c t has not been considered p r e v i o u s l y . The three-dimensional chemical s h i f t r e s o l v e d experiment c o n s i s t s of a v a r i a t i o n of the sequence shown i n F i g . 4.9. The v a r i a t i o n i n v o l v e s the e l i m i n a t i o n of the frequency-encoding g r a d i e n t (G-Read) and o b s e r v a t i o n of the s i g n a l under h i g h r e s o l u t i o n c o n d i t i o n s . This creates a three-dimensional data set i n which two of the coordinates represent the s p a t i a l axes determined by the phase-encoding g r a d i e n t s , w h i l e the t h i r d i s assigned to the c h e m i c a l - s h i f t a x i s . Processing of t h i s data set i n a s i m i l a r manner to t h a t described i n S e c t i o n 4.2.1 allows the e x t r a c t i o n of images corresponding to a p a r t i c u l a r chemical s h i f t or of s p e c t r o s c o p i c data corresponding to a p a r t i c u l a r p o s i t i o n i n the image plane. I f s l i c e s e l e c t i o n i s d e s i r e d along the remaining s p a t i a l dimension, the i n i t i a l 90° pulse ( F i g . 4.9) i s replaced by a - 149 -fr e q u e n c y - s e l e c t i v e pulse i n the presence of the appropriate gradient. When the chemical s h i f t of the observed s i g n a l i s s e n s i t i v e to changes i n e i t h e r the pH or temperature, the s p a t i a l d i s t r i b u t i o n s of these parameters are r e f l e c t e d i n the l i n e - w i d t h of the observed reso-nance. Thus depending on whether the d i s t r i b u t i o n of pH or temperature i s s p a t i a l l y continuous or i s compartmentalized i n t o separate zones, the observed resonance would be merely broadened or s p l i t i n t o d i f f e r e n t peaks. For e i t h e r s i t u a t i o n i t i s p o s s i b l e to e x t r a c t the s p a t i a l d i s t r i b u t i o n corresponding to a c e r t a i n pH/temperature range from the three-dimensional data s e t . I n the present study, the resonances of i n o r g a n i c phosphate ( 3^P) and water (^ "H) were used as the pH and temperature 'probes' respec-t i v e l y . These were chosen because of t h e i r w e l l known chemical s h i f t dependence on the pH and temperature [26,27] as w e l l as t h e i r p o t e n t i a l a p p l i c a b i l i t y to i n v i v o s t u d i e s . The experimental demonstration of the method was performed us i n g phantoms c o n t a i n i n g appropriate s o l u t i o n s . The phantom used f o r the pH st u d i e s comprised three c o n c e n t r i c compartments made of P l e x i g l a s , each f i l l e d to a he i g h t of 1.5 cm w i t h i n o r g a n i c phosphate (0.1 M) adjusted to pH 12.0, 7.0 and 3.0 r e s p e c t i v e l y . The transverse view of the phantom along w i t h i t s dimensions i s shown at the top of F i g . 4.16. The temperature phantom c o n s i s t e d of two glass tubes of diameter 1.0 and 1.6 cm f i l l e d w i t h water to a height of 3.0 cm. The smaller diameter tube was f i t t e d w i t h a condenser type j a c k e t so that water i n s i d e the tube c o u l d be maintained at an el e v a t e d temperature by c i r c u l a t i n g hot a i r through the j a c k e t . The e q u i l i b r a t e d temperatures - 150 -of water i n s i d e the two tubes under the experimental c o n d i t i o n s used were found to be ca. 75°C and 32°C. Both tubes were wrapped w i t h f i b e r g l a s s i n s u l a t i n g m a t e r i a l to keep the temperatures as steady as p o s s i b l e d u ring the course of the experiment. In both experiments the sample depth was used to define the s l i c e t h i c k n e s s along the t h i r d s p a t i a l dimension thereby e l i m i n a t i n g the need f o r s l i c e s e l e c t i o n . Each phase-encoding gradient ( G x and G z) was incremented 32 times and 512 data p o i n t s were acquired f o r each s i g n a l to produce an experimental data set of dimensions 32 x 32 x 512. The data m a t r i x was z e r o - f i l l e d i n the phase-encoding dimensions p r i o r to F o u r i e r t r a n s f o r m a t i o n to produce f i n a l image data s i z e of 128 x 128. In a l l the experiments, only the second h a l f of the echo s i g n a l was c o l l e c t e d by i n i t i a t i n g the s i g n a l a c q u i s i t i o n a t a time ' t ' a f t e r the 180° p u l s e , set equal to the delay between the 90° and 180° p u l s e s . This was done to avoid the a c q u i s i t i o n of an unsymmetrical whole echo s i g n a l . The pH- and t e m p e r a t u r e - d i s t r i b u t i o n maps of the phantoms and t h e i r h i g h r e s o l u t i o n s p e c t r a are shown i n F i g s . 4.16 and 4.17, r e s p e c t i v e l y . The assignments of the s p e c t r a are i n d i c a t e d i n the f i g u r e s . The images d i s p l a y e d were obtained by summing a l l the i n d i v i d u a l images correspond-i n g to a p a r t i c u l a r frequency r e g i o n of i n t e r e s t . In each case, the frequency r e g i o n of i n t e r e s t was defined by the resonances corresponding to d i f f e r e n t pH/temperature compartments. In order to o b t a i n complete s e p a r a t i o n between the images of each c h e m i c a l l y s h i f t e d resonance, i t i s necessary t h a t the frequency s e p a r a t i o n between the resonances be greater than the s t a t i c magnetic f i e l d inhomogeneity i n the imaging 151 F i g . 4.16: Mapping of pH d i s t r i b u t i o n . Top; Transverse view of the three compartment ( I , I I , I I I ) phantom used f o r pH mapping (dimensions i n m i l l i m e t e r s ) and phosphate s o l u t i o n pH v a l -ues. [A] 32.5 MHz 3 1 P spectrum of the phantom f i l l e d w i t h phosphate s o l u t i o n s of d i f f e r e n t pH. Peak l a b e l s correspond to compartments i n d i c a t e d . [B-D] 3^P pH maps of the phan-tom produced by chemical s h i f t r e s o l v e d imaging. Maps were produced from a s i n g l e data set by e x t r a c t i n g data c o r r e s -ponding to frequency ranges d e f i n i n g each peak. - 152 -200 0 -200 Hz -2 0 ~2~ Z(cm) F i g . 4.17: Mapping of temperature d i s t r i b u t i o n . [A] 80.3 MHz AH spectrum of two tubes of water maintained at ca 75° and 32°C r e s p e c t i v e l y . Peak l a b e l s L and H correspond t o low- and high-temperature tubes. [B and C] Separate low- and high-temperature *H images of the tube assembly. [D] image of the phantom w i t h both tubes at room temperature. Image was obtained as a separate experiment w i t h experimen-t a l parameters i d e n t i c a l t o that of [B] and [C]. - 153 -plane. Thus, because the pH range s t u d i e d was r a t h e r l a r g e , each r e g i o n gave w e l l separated peaks i n the spectrum, and the i n d i v i d u a l pH maps coul d be obtained without any i n t e r f e r e n c e from the other regions of the phantom. In c o n t r a s t , i n the temperature experiment where the frequency s e p a r a t i o n between the resonances induced by the d i f f e r e n c e i n tempera-ture of the tubes was small (ca. 40 Hz), separate images co u l d only be obtained by c a r e f u l s e l e c t i o n of the frequency r e g i o n to e x t r a c t each image. This i n t u r n r e s u l t e d i n incomplete s p a t i a l d e f i n i t i o n of the images. The s l i g h t l y lower s i g n a l - t o - n o i s e r a t i o of the high-temperature map i s a t t r i b u t e d to the longer ^H s p i n - l a t t i c e r e l a x a t i o n time of water at e l e v a t e d temperature [28] and hence p a r t i a l s a t u r a t i o n of the s i g n a l under the r a p i d pulse r e p e t i t i o n r a t e s . The r e s u l t s presented here demonstrate t h a t e i t h e r the pH or temperature d i s t r i b u t i o n of a compartmentalized obj e c t can be conve-n i e n t l y mapped u s i n g chemical s h i f t r e s o l v e d imaging. E i t h e r of the probe n u c l e i used here are s u i t a b l e f o r s t u d i e s of systems where the system has a wide d i s t r i b u t i o n of p r o p e r t i e s . 4.4 Experimental The c o n f i g u r a t i o n of the imaging system used i n the s t u d i e s d e s c r i b e d i n t h i s Chapter (except f o r that given i n S e c t i o n 4.3.1) and the r e s t o f the t h e s i s i s as f o l l o w s . The system c o n s i s t s of an Oxford Instruments 1.89 T (80.3 MHz f o r ^H), 31 cm h o r i z o n t a l - b o r e magnet i n t e r f a c e d to a N i c o l e t NT-300 high r e s o l u t i o n console c o n t r o l l e d by a - 154 -Nicolet-1280 computer (256K) and a 293 C pulse programmer. Data acqui-s i t i o n and p r o c e s s i n g are based on the standard NMC-1280 programme. The magnet i s equipped w i t h a gradient c o i l system, s u p p l i e d by Oxford Instruments, and capable of producing up to 1.3 G/cm. The gradients are c o n t r o l l e d v i a the d r i v i n g v o l t a g e s generated by d i g i t a l - t o - a n a l o g converters i n the pulse programmer and are a m p l i f i e d by Crown M-600 a m p l i f i e r s o p e r a t i n g at constant v o l t a g e . Data storage f a c i l i t i e s i n c l u d e a h i g h c a p a c i t y d i s c (96 MByte, CDC-CMD 9448-96) and a N i c o l e t f l o p p y d i s c d r i v e . Images are d i s p l a y e d on a Ramtek c o l o r graphics t e r m i n a l (Model 6211) capable of d i s p l a y i n g 16 c o l o r s at a time out of a t o t a l of 64. The spectrometer system now a l s o i n c l u d e r f pulse t a i l o r i n g capa-b i l i t y (see Chapter I I I ) and a v a r i e t y of home-built r f probes s u i t a b l e f o r imaging (see Chapter V). The software necessary to c o n t r o l the gradients and to d i s p l a y images were e a r l i e r developed and w r i t t e n at UBC by Dr. S. Sukumar. Male Wistar r a t s (250-350 gm) were used f o r a l l r a t imaging e x p e r i -ments. The r a t s were anaesthetized w i t h 10% i n a c t i n i n j e c t e d i n t r a -p e r i t o n e a l l y a t 0.1 mL/100 gm body weight. This was performed by Dr. P. Reiner (Department of P s y c h i a t r y , UBC). Using t h i s a n a e s t h e t i c the r a t s c o u l d be experimented w i t h f o r s e v e r a l hours. 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M a r t i n , " P r a c t i c a l NMR Spec-troscopy", p. 266, Heyden and Son L t d . , P h i l a d e l p h i a , 1980. - 157 -CHAPTER V EVALUATION OF RADIOFREQUENCY PROBE DESIGNS SUITABLE FOR NMR IMAGING AT HIGH FIELDS - 158 -V. EVALUATION OF RADIOFREQUENCY PROBE DESIGNS SUITABLE FOR NMR IMAGING AT HIGH FIELDS 5.1 I n t r o d u c t i o n The probe i s one of the most important components i n an NMR spectrometer s i n c e i t represents the i n t e r f a c e between the magnet, t r a n s m i t t e r , r e c e i v e r and the sample. The probe permits the e x c i t a t i o n of the sample and d e t e c t i o n of the NMR s i g n a l , and t h e r e f o r e improve-ments i n i t s design can g r e a t l y increase the o v e r a l l performance of the spectrometer. By f a r the most common type of probe used i n pulsed NMR i s the " s i n g l e c o i l " probe, where the same c o i l i s used f o r both the trans-m i s s i o n of radiofrequency ( r f ) energy i n t o the sample ( e x c i t a t i o n ) and the r e c e p t i o n of the s i g n a l ( d e t e c t i o n ) from the sample. A schematic diagram of a s i n g l e c o i l probe i s shown i n F i g . 5.1. The radiofrequency c o i l , which i s wrapped around the sample, i s tuned to the d e s i r e d f r e -quency of o p e r a t i o n u s i n g a p a r a l l e l resonance c i r c u i t . This c i r c u i t i s i n t u r n connected to the t r a n s m i t t e r and the r e c e i v e r by s u i t a b l e means. In t h i s Chapter, a t t e n t i o n i s focussed on probe designs s u i t a b l e f o r h i g h f i e l d NMR imaging. In order to provide the background to the s u b j e c t , the probe requirements and a s s o c i a t e d problems are discussed i n i t i a l l y . This i s f o l l o w e d by a b r i e f i n t r o d u c t i o n to s e v e r a l a l t e r n a -t i v e probe designs. The f i n a l S e c t i o n describes the m o d i f i c a t i o n , c o n s t r u c t i o n and experimental e v a l u a t i o n of these designs. 159 -' M TRANSMITTER RECEIVER F i g . 5.1: Schematic diagram of a s i n g l e c o i l NMR probe, the r f c o i l which acts as an ind u c t o r ; t u n i n g and matching c a p a c i t o r s r e s p e c t i v e l y . Crp and CJJ L represents are the 5.2 Probe Requirements and Ass o c i a t e d Problems The general requirements of an NMR probes are e s s e n t i a l l y the same f o r e i t h e r spectroscopy or imaging. However, one important d i f f e r e n c e i s t h a t f o r imaging, probes of much l a r g e r dimensions are g e n e r a l l y r e q u i r e d as compared to those used f o r conventional spectroscopy. This requirement i n t u r n imposes s e v e r a l important c o n s i d e r a t i o n s which are h i g h l i g h t e d i n t h i s s e c t i o n . The fundamental requirement of any NMR c o i l i s th a t the magnetic f i e l d (B^) created by a current passing through i t should predominantly - 160 -be i n a plane p e r p e n d i c u l a r to the main magnetic f i e l d (B Q) produced by the magnet. The c o i l system used to produce the B^ f i e l d i s dependent upon the magnet employed. In an i r o n magnet, the B D f i e l d i s i n an orthogonal plane to the access of the magnet, thus a s o l e n o i d a l c o i l can be used ( F i g . 5.2a). But i n a superconducting s o l e n o i d a l magnet, B Q i s produced along the a x i s of the bore of the magnet. Therefore, a saddle shaped c o i l i s p r e f e r a b l e ( F i g . 5.2b) s i n c e i t does not r e s t r i c t the sample access. However, any c o i l c o n f i g u r a t i o n can be used as long as i t i s o r i e n t e d i n the magnet such t h a t the B^ f i e l d i s orthogonal to the B Q f i e l d , and as mentioned above, the most commonly used c o i l c o n f i g u r a -t i o n s are the s o l e n o i d and saddle shaped c o i l s . The d i r e c t i o n of the B^ f i e l d c r e a t e d by these c o i l s i s shown i n F i g . 5.2. The NMR c o i l i s tuned to the d e s i r e d frequency of o p e r a t i o n w i t h the a i d of a c a p a c i t o r , and the resonance frequency ( f r ) of the c i r c u i t i s given by 1 f r = 5.1 2nJT~C where L i s the inductance of the c o i l , and C i s the t o t a l capacitance of the c i r c u i t . The t o t a l capacitance of the c i r c u i t comprises the exter-n a l t u n i n g c a p a c i t o r (C-p) and the d i s t r i b u t e d capacitance of the c i r c u i t . The d i s t r i b u t e d capacitance of a c i r c u i t i s the capacitance that e x i s t s between the turns of w i r e , between t e r m i n a l leads, and between turns and e l e c t r i c a l ground e t c . [1]. The h i g h e s t frequency to which a c o i l can be tuned ( c a l l e d the self-resonance frequency) i s - 161 -determined by the d i s t r i b u t e d capacitance s i n c e the t o t a l c i r c u i t capacitance cannot be made smaller than t h i s value. In general, r a d i o -frequency c o i l s are operated w e l l below t h i s l i m i t i n g frequency to Somple F i g . 5.2: O r i e n t a t i o n of the f i e l d i n s o l e n o i d a l (a) and saddle shaped (b) c o i l s . - 162 -ensure that e l e c t r i c a l l o s s e s o c c u r r i n g i n the c o i l form, or any other d i e l e c t r i c t h a t may be present i n the e l e c t r i c f i e l d a s s o c i a t e d w i t h the c o i l , are minimized [1]. Furthermore, c l o s e to the self-resonance frequency, c o i l tuning becomes extremely s e n s i t i v e to the changes i n temperature and the sample i t s e l f [ 2]. In NMR imaging, l a r g e diameter c o i l s (ca. 50 cm f o r a whole body c o i l ) are r e q u i r e d , and the t r a d i t i o n a l s o l e n o i d a l or saddle shaped c o i l s of such diameter have a l a r g e inductance ( f o r a s i n g l e l a y e r s o l e n o i d , inductance i s p r o p o r t i o n a l to the diameter of the c o i l and the square of the number of turns [ 3 ] ) . Therefore these c o i l s have a low self-resonance frequency and t h e i r usable frequency range i s g e n e r a l l y l i m i t e d to below 10 MHz. With the present day NMR imaging equipment being manufactured to operate at h i g h f i e l d s (>50 MHz), c o i l s w i t h lower inductance and which can be e a s i l y tuned to the r e q u i r e d frequency are needed. This i s a problem, even f o r somewhat smaller diameter c o i l s , such as those used f o r s t u d i e s of human limbs. A f u r t h e r concern when u s i n g l a r g e diameter c o i l s i s the generation of e l e c t r i c f i e l d s i n s i d e the c o i l , which have the r a m i f i c a t i o n s consid-ered below. When the c o i l dimensions are such that the l e n g t h of the conductor becomes comparable to the r f wavelength, a s u b s t a n t i a l e l e c t r i c p o t e n t i a l d i f f e r e n c e i s created along the c o i l ; t h i s generates an e l e c t r i c f i e l d which penetrates the sample w i t h i n the c o i l [ 4]. With conducting samples, these e l e c t r i c f i e l d s can cause s i g n i f i c a n t energy d i s s i p a t i o n l e a d i n g to undesirable h e a t i n g of the sample [5]. Further-more, detuning of the c o i l can occur upon sample i n t r o d u c t i o n [6]. More imp o r t a n t l y , these e l e c t r i c f i e l d s c o n t r i b u t e to an a d d i t i o n a l noise - 163 -source when studying conducting samples [4]. From the preceding d i s c u s s i o n i t i s evident t h a t the s o l e n o i d a l and saddle shaped c o i l s become i n c r e a s i n g l y i n e f f i c i e n t as NMR r e c e i v e r c o i l s at higher frequencies and large dimensions. This has prompted the cu r r e n t research i n t e r e s t i n a l t e r n a t i v e radiofrequency probe designs. The aspects considered so f a r a l s o apply to conventional spectroscopy, but become prominent only at much higher frequency (>400 MHz), since the c o i l dimensions used are comparatively s m a l l . In a d d i t i o n to the above c o n s i d e r a t i o n s , i t i s necessary that the probe parameters which govern the s i g n a l - t o - n o i s e r a t i o (S/N) a l s o be optimized. The i n f l u e n c e of the probe parameters on S/N can be expressed as (see Ref. 7, Eqs. 8, 21) S B l u , n - a or 5.2 N R l / 2 where R and Q are the r e s i s t a n c e and the q u a l i t y f a c t o r of the c o i l , n i s the f i l l i n g f a c t o r and B^ u i s the magnetic f i e l d (perpendicular to the main f i e l d B 0) produced by a u n i t c u r r e n t f l o w i n g i n the r e c e i v i n g c o i l . Therefore i n general, an NMR probe should s a t i s f y s e v e r a l d i f f e r e n t c r i t e r i a ; i t should provide s t a b l e tuning w i t h minimum e f f e c t s due to sample i n t r o d u c t i o n , have a high Q value, a good f i l l i n g - f a c t o r , a high I$lu v a l u e , minimal e l e c t r i c f i e l d s , and a reasonable B^ homogeneity over a l a r g e volume as p o s s i b l e . - 1 6 4 -5 . 3 E f f e c t s of Conducting Samples The e l e c t r i c a l c o n d u c t i v i t y of b i o l o g i c a l t i s s u e s (approximately equal to tha t of 1 0 0 mM NaCl s o l u t i o n ) has profound e f f e c t s on the s i g n a l - t o - n o i s e r a t i o of the NMR s i g n a l [ 8 , 9 ] . In essence, a conducting sample serves as an a d d i t i o n a l noise source which reduces the obtainable s i g n a l - t o - n o i s e r a t i o . The p r i n c i p a l source of the noise produced by conductive samples i s the c u r r e n t s generated i n the sample. These c u r r e n t s , produced e i t h e r i n d u c t i v e l y by the changing magnetic f i e l d , or d i e l e c t r i c a l l y by the e l e c t r i c f i e l d s (due to the d i s t r i b u t e d capacitance) passing through the sample, d i s s i p a t e energy i n an analogous manner to power l o s s i n a r e s i s t a n c e . Therefore each of these l o s s mechanisms, i n d u c t i v e [ 8 ] and d i e l e c t r i c [ 9 ] , can be represented by r e s i s t a n c e s , RJJ, and R e respec-t i v e l y , i n s e r i e s w i t h the i n t r i n s i c r e s i s t a n c e R c of the c o i l [ 4 ] . This i s shown i n F i g . 5 . 3 . Hence, the combined r e s i s t a n c e of RJJ,, R e and R c c o n t r i b u t e s to the observed n o i s e . Since the i n d u c t i v e l o s s e s o r i g i n a t e from the changes i n r f mag-n e t i c f i e l d , they are c l o s e l y a l l i e d to the r e c e p t i o n of the NMR s i g n a l , and t h e r e f o r e , t h e i r c o n t r i b u t i o n to noise cannot be avoided. However, the d i e l e c t r i c l o s s e s can be reduced by minimizing the e l e c t r i c f i e l d p e n e t r a t i o n i n t o the sample [ 9 , 1 0 ] . The amount of e l e c t r i c f i e l d experienced by the sample i s dependent upon the probe design; thus, probe designs w i t h minimum s t r a y e l e c t r i c f i e l d s are d e s i r a b l e . Both the i n d u c t i v e and d i e l e c t r i c l o s s e s can be modelled by adding appropriate c i r c u i t elements to the b a s i c p a r a l l e l resonance c i r c u i t of - 165 -R e R m R c L vww—M/W—vvvw—^ mm-F i g . 5.3: Representation of d i f f e r e n t l o s s mechanisms. Rjj and R e represent the equivalent r e s i s t a n c e s due t o i n d u c t i v e and d i e l e c t r i c l o s s e s r e s p e c t i v e l y . R c and L are r e s p e c t i v e l y the i n t r i n s i c r e s i s t a n c e and the inductance of the c o i l . - 166 -the r e c e i v i n g c o i l [ 9 - 1 1 ] . However, the c o n t r i b u t i o n from d i f f e r e n t l o s s mechanisms to the observed noise can be estimated e x p e r i m e n t a l l y by determining the e f f e c t s of the sample on the Q - f a c t o r of the c i r c u i t and on i t s resonance frequency. The q u a l i t y f a c t o r ( Q - f a c t o r ) of a c i r c u i t , expressed i n terms of the i n t r i n s i c r e s i s t a n c e R c of the c o i l i s given by Q = R, 5.3 where L i s the c o i l inductance and u>Q i s the resonance frequency. Therefore the Q of the c i r c u i t i s a measure of the r e s i s t a n c e of the c o i l . I f the sample los s e s due to i n d u c t i v e and d i e l e c t r i c e f f e c t s are expressed as r e s i s t a n c e s and R e i n s e r i e s w i t h c o i l , then, QL ( R c + Rm + Re> 5.4 where Q-^  i s the Q of the probe c i r c u i t i n the presence of the sample ( i . e . loaded Q ) . Therefore the e f f e c t of R m and R e i s to reduce the probe Q, and the loaded Q i s a measure of the t o t a l l o s s e s due to the c o i l r e s i s t a n c e as w e l l as the i n d u c t i v e and d i e l e c t r i c e f f e c t s . - 167 From Eqs. 5.3 and 5.4, 1 1 1 QL QUL QS where QTJL I s the Q of the unloaded probe (without the sample) and Qg takes RJJ, and R E i n t o account. Thus Q measurements of loaded and unloaded probes give an estimate of the t o t a l l o s s e s due to the sample. Since sample l o s s e s are unavoidable, the d e s i r e d c o n d i t i o n i s QTJL » QL-In t h i s s i t u a t i o n , the sample l o s s e s dominate over the i n t r i n s i c c o i l l o s s e s due to i t s r e s i s t a n c e , and the observed noise a r i s e s mainly due to the sample. An estimate of the e l e c t r i c f i e l d p e n e t r a t i o n i n t o the sample can be obtained by measuring the s h i f t of the probe resonance frequency ( A f Q ) upon i n t r o d u c t i o n of the sample [9,12]. The d i f f e r i n g d i e l e c t r i c p r o p e r t i e s of the sample compared to a i r a l t e r the d i s t r i b u t e d c apaci-tance of the c o i l and hence i t s resonance frequency (see Eq. 5.1). This measurement i s u s u a l l y c a r r i e d out w i t h pure water as the sample since i t s h i g h d i e l e c t r i c constant causes l a r g e s h i f t s i n the resonace frequency w h i l e having minimal e f f e c t s on the c o i l Q f a c t o r due to i t s low c o n d u c t i v i t y [12]. 5.4 A l t e r n a t i v e Probe Designs Several a l t e r n a t i v e probe designs have been suggested i n recent - 168 -years to overcome the inadequacies of the conventional saddle and s o l e n o i d a l shaped c o i l s . Of these designs, the s i m p l e s t are the e l l i p t i c a l c o i l [13] and s p h e r i c a l c o i l s [14,15]. These c o i l s are t a i l o r e d to match the shape of the p a r t of the body to be imaged and t h e r e f o r e provide an improvement i n the f i l l i n g f a c t o r over that which can be obtained w i t h conventional c o i l s . The reported frequency of o p e r a t i o n of these c o i l s i s l e s s than 10 MHz, and i t i s conceivable that they would a l s o s u f f e r from the same disadvantages as the conventional c o i l s a t h i g h frequencies. The best compromise at h i g h frequencies i s o f f e r e d by "resonator" type probes [1,5,16-24]. I l l u s t r a t i o n s of the designs used i n t h i s work are given i n S e c t i o n 5.5. Of these designs, that of Alderman and Grant [5] ( h e r e a f t e r r e f e r r e d to as the "H-resonator" a f t e r i t s shape of the conductor) i s most widely used f o r h i g h frequency NMR imaging [20,25]. The success of t h i s design i s a t t r i b u t e d p a r t l y to i t s f l e x i b i l i t y i n dimensions which can be v a r i e d to s u i t the space a v a i l a b l e i n the magnet and, more im p o r t a n t l y , to i t s a b i l i t y to minimize the e l e c t r i c f i e l d s i n s i d e the probe. However, the homogeneity of the radiofrequency B^ f i e l d of t h i s design compares l e s s f a v o r a b l y w i t h the other designs (see S e c t i o n 5.5). A v a r i a t i o n on the H-resonator theme i s the "mortarboard" probe design [19] , i n which one end of the H-resonator i s terminated by a conductive plane. In t h i s c o n f i g u r a t i o n , the e f f e c t i v e l ength of the s t r u c t u r e i s approximately doubled and the magnetic f i e l d i s more homogeneous toward the t e r m i n a t i n g plane compared to the H-resonator [19] . - 169 -The ' s p l i t - r i n g ' resonator probe [18], which can be viewed as a low inductance s i n g l e t u r n s o l e n o i d [ 1 ] , was f i r s t used as a magnetic resonance probe f o r the frequency range 200-2000 MHz. The p o t e n t i a l use of t h i s design as an imaging probe at 80 MHz has s i n c e been demonstrated [21] and i s presented as a p a r t of t h i s work l a t e r i n the Chapter. The main advantages of t h i s design are i t s e x c e l l e n t radiofrequency homogeneity (see S e c t i o n 5.5) and very h i g h Q. The s p l i t - r i n g resonator produces a magnetic f i e l d along the a x i s of the resonator and thus needs to be mounted t r a n s v e r s e l y i n a superconducting magnet. This r e s t r i c t s i t s use i n i n v i v o a p p l i c a t i o n s u s i n g small bore magnets. Nevertheless, i t i s w e l l s u i t e d f o r small s c a l e inanimate imaging a p p l i c a t i o n s [21], and i t s easy adaptation as a surface c o i l probe has already been demon-s t r a t e d [12] . A s i g n i f i c a n t improvement i n the transverse r f f i e l d of an a x i a l l y mounted probe can be achieved by the "bird-cage" design [22]; the o r i g i n a l work which l e d to t h i s design i s given i n Refs. 23 and 24. I t depends on the p r i n c i p l e that a very homogeneous transverse magnetic f i e l d i n an i n f i n i t e l y long c y l i n d e r can be generated by a surface c u r r e n t which runs along the l e n g t h of the conductor and i s p r o p o r t i o n a l to Sin0, where 6 i s the c y l i n d r i c a l azimuthal angle [22]. The c o n v e n t i o n a l saddle c o i l approximates t h i s i d e a l s i n u s o i d a l current d i s t r i b u t i o n f o r s i x e q u a l l y spaced values of 9 (0 = 0, 60, 120, 180, 240, 300°). Of these s i x conductors, four c a r r y equal currents whereas no conductors are needed at 6 = 0 and 180° because the currents at these p o i n t s are zero [22]. A f u r t h e r advantage of the bird-cage design i s t h a t i t allows quadrature e x c i t a t i o n and d e t e c t i o n , and thus leads to a - 170 -decrease i n r f power requirements by a f a c t o r of two and an increase i n s i g n a l - t o - n o i s e r a t i o by a f a c t o r of Jl [22, 26-28]. 5.5 Experimental E v a l u a t i o n of Resonator Probe Designs Three resonator probe designs, the H-resonator, the s p l i t - r i n g resonator and the bird-cage resonator were chosen f o r e v a l u a t i o n of t h e i r performance compared to a conventional saddle c o i l . I l l u s t r a t i o n s of the resonator probes used are given i n F i g s . 5.4-5.6. The resonator probes used i n t h i s study have s e v e r a l important f e a t u r e s . F i r s t , they were coupled to the r f t r a n s m i t t e r / r e c e i v e r (Tx/Rx) u s i n g an i n d u c t i v e mechanism r a t h e r than v i a a c a p a c i t o r . In the i n d u c t i v e c o u p l i n g method, Tx/Rx i s d i r e c t l y f e d i n t o a copper r i n g which couples m a g n e t i c a l l y w i t h the main probe body ( F i g s . 5.4-5.6). The maximum c o u p l i n g was achieved by changing the di s t a n c e between the resonator and the co u p l i n g r i n g . I n d u c t i v e l y coupled NMR probes have been used [12,18,21,26] and t r e a t e d i n d e t a i l [29,30] by s e v e r a l groups. Secondly, the f i n e tuning of the H-resonator and the bird-cage designs was achieved by usi n g an unattached copper r i n g on the opposite s i d e of the probe w i t h respect to the co u p l i n g r i n g ( F i g s . 5.5 and 5.6). The movement of the tuning r i n g w i t h respect to the probe s t r u c t u r e a l t e r s the resonance frequency by changing the t o t a l e f f e c t i v e induc-tance of the s t r u c t u r e [12]. The i n d u c t i v e c o u p l i n g and tuning method as a p p l i e d to the H-resonator and the bird-cage resonator has not been desc r i b e d p r e v i o u s l y . - 1 7 1 -F i g . 5.4: S p l i t - r i n g resonator probe. A, copper f o i l ; B, screw threaded holder housing the c o u p l i n g r i n g . Inset shows f i v e l a y e r s of m a t e r i a l ; P l e x i g l a s , copper (0.25 mm), T e f l o n (0.9 mm), copper (0.25 mm), P l e x i g l a s . - 1 7 2 -F i g . 5.5: H-Resonator probe. A, guard r i n g s ; B, H-shaped conductor; C, capacitance; D, c o u p l i n g r i n g ; E, tuning r i n g . - 173 -F i g . 5.6: Bird-cage resonator probe. A, copper s t r i p s ; B, copper end r i n g s ; C, capacitance; D, coupling r i n g ; E, tuning r i n g . - 174 -F i n a l l y , the capacitance needed f o r these s t r u c t u r e s was formed by o v e r l a p p i n g copper f o i l s separated by a d i e l e c t r i c ( T e f l o n ) . These m o d i f i c a t i o n s completely e l i m i n a t e d the need f o r h i g h - c o s t commercial c a p a c i t o r s and r e s u l t e d i n e a s i l y f a b r i c a t e d and low-cost probes. 5.5.1 Probe C o n s t r u c t i o n A l l the probe designs under e v a l u a t i o n were cons t r u c t e d w i t h i d e n t i c a l diameter (7.5 cm) to enable d i r e c t comparison and were mounted on a c y l i n d r i c a l P l e x i g l a s former. The saddle shaped c o i l ( F i g . 5.2b) was f a b r i c a t e d of 2 mm diameter copper wire and c o n s i s t e d of a s i n g l e t u r n . The l e n g t h of the c o i l was equal to the diameter (7.5 cm) and the c i r c u l a r s e c t i o n s of the wire subtended an angle of 120° at the center. This corresponds to the most commonly used c o n f i g u r a t i o n of the saddle c o i l s i n s p i t e of the f a c t t h a t b e t t e r r f homogeneity can be obtained when the c o i l l e ngth i s twice i t s diameter [2]. The s p l i t - r i n g resonator probe (14 cm long, F i g . 5.4) was c o n s t r u c t e d of a s i n g l e copper f o i l (0.25 mm t h i c k , 101 grade, OFHC) wrapped around a P l e x i g l a s former w i t h two f l a p s which p r o j e c t normally from the circumference of the c y l i n d e r . These f l a p s , separated by a 0.7 mm t h i c k sheet of T e f l o n and sandwiched between two P l e x i g l a s p l a t e s , provided the capacitance r e q u i r e d f o r tuning the probe. The capacitance was v a r i e d by f i n e adjustment of the distance across the T e f l o n d i e l e c -t r i c w i t h the a i d of T e f l o n screws. The resonator was i n d u c t i v e l y - 175 -coupled to the t r a n s m i t t e r v i a a s i n g l e copper r i n g (diameter 7.5 cm) attached to the end of a c o a x i a l cable and mounted i n s i d e a screw-threaded h o l d e r which f i t s around the c y l i n d r i c a l former. The whole probe body was f i t t e d i n t o a s u i t a b l y shaped P l e x i g l a s frame so that the probe can be a c c u r a t e l y p o s i t i o n e d i n s i d e the magnet. The probe f a b r i -cated w i t h dimensions shown i n F i g . 5.4 was found to have a tunin g range of 78.0-200.0 MHz. The H-resonator s t r u c t u r e ( F i g . 5.5) was f a b r i c a t e d of 3 l a y e r s of m a t e r i a l . The innermost l a y e r of guard r i n g s was con s t r u c t e d of copper sheet (0.1 mm t h i c k , OFHC) soldered i n t o a r i n g shape. D i r e c t l y above each guard r i n g a l a y e r of T e f l o n d i e l e c t r i c ( t h i c k n e s s 0.5 mm) was place d ( t h i s i s not shown i n F i g . 5.5). The outermost l a y e r of two H-shaped halves of conductor was constructed of 0.1 mm t h i c k copper sheet. The wings of each of the H-shaped halves were made s l i g h t l y longer than necessary and the e x t r a length was bent at the four p o s i t i o n s above the guard r i n g s . The bent p o r t i o n s from each h a l f were separated by T e f l o n ( t h i c k n e s s 0.5 mm) to provide the e x t r a capacitance needed f o r tuning. Each of these c a p a c i t o r s e c t i o n s were sandwiched between two small P l e x i g l a s s e c t i o n s and were secured by T e f l o n screws. The o v e r a l l dimensions of the probe were such t h a t the r e l a t i v e dimen-sions of v a r i o u s s e c t i o n s were those given by the o r i g i n a l authors [5]. This corresponded to a probe le n g t h of 14 cm, diameter of 7.5 cm and a guard r i n g width of 4 cm. The angle subtended at the center by the v e r t i c a l s e c t i o n s of the H-shaped halves was 80°. The p a r t i c u l a r probe de s c r i b e d above was i n d u c t i v e l y coupled and tuned u s i n g copper r i n g s of diameter 7.0 cm and had a tuning range of 80-82 MHz. In a d d i t i o n to - 176 -t h i s , f o r comparative purposes, a second probe was f a b r i c a t e d i n which the H-shaped halves were j o i n e d by chip c a p a c i t o r s . This probe was c a p a c i t i v e l y coupled and tuned i n the standard manner and corresponded to the o r i g i n a l l y proposed c o n f i g u r a t i o n of the s t r u c t u r e [5]. The bird-cage resonator used i n t h i s study was constructed of s i x t e e n , 5 mm wide copper (0.25 m t h i c k ) s t r i p s e q u a l l y spaced around the circumference of a 7.5 cm diameter c o i l former ( F i g . 5.6). The copper s t r i p s were soldered onto two c i r c u l a r copper end r i n g s (width 8 mm) on e i t h e r end. The capacitance needed f o r the s t r u c t u r e was created by c u t t i n g the copper s t r i p s i n the center and o v e r l a p p i n g the corre-sponding s t r i p s by s l i d i n g the two i n d i v i d u a l halves inwards. A t h i n f i l m of T e f l o n was then i n s e r t e d between the overlapping areas of each p a i r of s t r i p s . The copper s t r i p s were h e l d i n place by a cord t i e d around the assembly. This c o n f i g u r a t i o n corresponds to the low pass v e r s i o n of the bird-cage resonator [22]. The coarse t u n i n g of the probe was obtained by changing the area of overlap between the s t r i p s and by u s i n g T e f l o n f i l m of appropriate t h i c k n e s s . The dimensions of the s t r u c t u r e when tuned to ca. 80 MHz corresponded to a t o t a l l e n g t h of approximately 14 cm, length of s t r i p overlap 2 cm and a T e f l o n f i l m t h i c k n e s s of 0.1 mm. The probe was i n d u c t i v e l y coupled and tuned (copper r i n g diameter 7.0 cm). I t was found that the probe tuning was not s t a b l e over long periods due to the changes i n the capacitance formed by the overlapping s t r i p s . This can be overcome by improving the mechanical s t a b i l i t y of the probe. Improved v e r s i o n s of t h i s probe are p r e s e n t l y being i n v e s t i g a t e d . The mechanical c o n s t r u c t i o n and e l e c t r o n i c d e t a i l s of the probes - 177 -were c a r r i e d out by Messrs. C. Neale and T. Markus, r e s p e c t i v e l y , of the UBC Chemistry Department. 5.5.2 Probe Evaluation The probes con s t r u c t e d were exp e r i m e n t a l l y evaluated by measuring s e v e r a l parameters which are d i r e c t l y r e l a t e d to the design of the probe. They are, the probe Q f a c t o r (loaded and unloaded), the e f f e c t of a water sample on the probe resonanace frequency and the homogeneity of the r f magnetic f i e l d i n s i d e the probe. In a d d i t i o n , the s i g n a l - t o -noise r a t i o and the 90° pulse-width f o r a 1 ml water sample pla c e d at the center of probe were a l s o determined. The experimental data obtained f o r the probe Q-factor and the s h i f t i n probe resonance frequency are given i n Table 5.1. The loaded Q values (QL) were measured when a 150 ml b o t t l e c o n t a i n i n g 0.028M KH2PO4 s o l u t i o n was introduced i n t o the probe. Such a s o l u t i o n mimics the e f f e c t of i n v i v o samples (e.g. r a t ) on the probe Q - f a c t o r [20]. The change i n resonance frequency ( A f Q ) of the probe was measured by p l a c i n g a 150 ml b o t t l e of water i n s i d e the probe. In order to f i n d the e f f e c t of a surrounding s h i e l d , the probe Q and A f Q values were measured when the probes were unshielded and as w e l l as when i n s e r t e d i n t o a 22.5 cm diameter copper tube. The upper and lower values given f o r the e n t r i e s i n Table 5.1 correspond to the values obtained when the probe was unshielded and s h i e l d e d r e s p e c t i v e l y . The Q s values given i n Table 5.1 were c a l c u l a t e d u s i n g Eq. 5.5. - 178 -Table 5.1: C h a r a c t e r i s t i c s of d i f f e r e n t probe designs Probe Design QUL3 A f Q c (MHz) 400 650 610 800 250 280 290 300 1.4 1.7 0.18 0.15 491 480 750 890 280 300 0.19 0.19 452 580 800 790 1600 300 320 300 470 0.33 0.35 0.42 0.40 533 665 Probe designs: 1. Saddle c o i l 2. C a p a c i t i v e l y coupled/tuned H-resonator 3. I n d u c t i v e l y coupled/tuned H-resonator 4. I n d u c t i v e l y coupled/tuned bird-cage resonator 5. I n d u c t i v e l y coupled s p l i t - r i n g resonator The upper and lower, Q and A f Q values given i n each e n t r y correspond to the measurements taken w i t h an unshielded probe and a s h i e l d e d probe r e s p e c t i v e l y (see t e x t ) . "Unloaded" Q. Q, when the probes were loaded w i t h 150 ml, 0.028M K H 2 P O 4 . Resonance frequency s h i f t caused by 150 ml of d i s t i l l e d water. C a l c u l a t e d value u s i n g Eq. 5.5. - 179 -From Table 5.1, i t can be seen that the s h i e l d e d probe Q values are g e n e r a l l y higher than the unshielded probe Q's; the most notable being the increase i n the unloaded Q of the s p l i t - r i n g resonator. This i s a t t r i b u t e d to the r e d u c t i o n of r a d i a t i o n l o s s e s when the probes were plac e d i n s i d e the s h i e l d . The same e f f e c t was observed when the probes were i n s e r t e d i n t o the magnet, and hence, the s h i e l d e d probe Q values give a b e t t e r i n d i c a t i o n of the e f f i c i e n c y of the probe during an experiment. On comparison of the Q values obtained w i t h the two c o n f i g u r a t i o n s of the H-resonator design, the i n d u c t i v e l y coupled and tuned v e r s i o n a f f o r d s a s l i g h t l y higher Q. This increase i n e f f i c i e n c y i s most l i k e l y due to the f a c t t h a t the l o s s e s a s s o c i a t e d w i t h the c a p a c i t i v e cou-p l i n g / t u n i n g network are avoided i n the i n d u c t i v e l y coupled/tuned v e r s i o n . Since A f 0 values are an i n d i c a t i o n of the d i e l e c t r i c l o s s e s , Table 5.1 shows th a t the maximum d i e l e c t r i c l o s s e s are a s s o c i a t e d w i t h the saddle c o i l . This i s to be expected w i t h a c o i l c o n f i g u r a t i o n i n which the l e n g t h of the conductor i s a s i g n i f i c a n t f r a c t i o n (-1/6 i n t h i s case) of the r f wavelength [ 4 ] . Comparative A f Q values show the s u p e r i o r performance of the H-resonator w i t h regard to the d i e l e c t r i c l o s s e s . This i s due to the presence of guard r i n g s i n the s t r u c t u r e which keeps the e l e c t r i c f i e l d s to a minimum and removed from the sample [4]. The bird-cage and the s p l i t - r i n g resonators o f f e r intermediate performance compared to the saddle c o i l and the H-resonator. The r e s u l t s given i n Table 5.1 show that the loaded probe Q values (QL) are s u b s t a n t i a l l y lower than the unloaded probe Q's due to the - 180 -l o s s e s introduced by the KH2PO4 s o l u t i o n . In the case of the s p l i t - r i n g resonator probe, QL « QTJT_> i n d i c a t i n g that the sample l o s s e s dominate over the l o s s e s due to the r e s i s t a n c e of the probe. Further, the s p l i t - r i n g resonator probe a f f o r d s the highest s h i e l d e d QL value and hence the best s e n s i t i v i t y under sample loaded c o n d i t i o n s . The c a l c u l a t e d Q S values given i n Table 5.1 i n d i c a t e the sample l o s s e s due to both the i n d u c t i v e and d i e l e c t r i c mechanisms. The Q S values obtained f o r the saddle c o i l and the H-resonator designs i n d i c a t e t h a t the t o t a l sample l o s s e s f o r these two probes are s i m i l a r . Since higher d i e l e c t r i c l o s s e s are encountered w i t h the saddle c o i l , i t i m p l i e s t h a t i n d u c t i v e l o s s e s are greater f o r the H-resonator probes. The Q S and A f Q values obtained f o r the bird-cage resonator probe p o s s i b l y i n d i c a t e s l i g h t l y smaller i n d u c t i v e l o s s e s compared to the H-resonator. The comparatively higher Q S value obtained f o r the s p l i t - r i n g resonator probe suggests lower i n d u c t i v e l o s s e s compared to the H-resonator design. The t r e n d i n the i n d u c t i v e l o s s e s encountered w i t h d i f f e r e n t designs can be q u a l i t a t i v e l y r a t i o n a l i z e d by c o n s i d e r i n g the f a c t o r s determining the i n d u c t i v e l o s s e s . The i n d u c t i v e l o s s e s , represented by a r e s i s t a n c e RJJ i n s e r i e s w i t h the c o i l , f o r a c y l i n d r i c a l sample of diameter d, l e n g t h i and c o n d u c t i v i t y a, immersed i n a uniform a l t e r n a t i n g magnetic f i e l d (frequency w) p a r a l l e l to the c y l i n d e r a x i s i s given by [10] ( V / / - * o > 2 B l u 2 a i d 4 / l 2 8 5.6 - 181 -where B]^ u i s the magnetic f i e l d produced by the c o i l per u n i t c u r r e n t . Thus RJJ, depends on the c o i l design v i a the parameter Bj_ u- Therefore the dependence of i n d u c t i v e l o s s e s on the probe design can be a t t r i b u t e d to the changes i n B]^ u as w e l l as i t s d i s t r i b u t i o n over the sample volume. Another c o n t r i b u t i n g f a c t o r i s the d i r e c t i o n of B^ w i t h respect to the sample. F o l l o w i n g an a n a l y s i s s i m i l a r to th a t given i n Ref. 31 i n which the f o r a re c t a n g u l a r sample b l o c k was c a l c u l a t e d , i t can be shown th a t the r e s i s t a n c e RJJ, when B]_ i s o r i e n t e d p e r p e n d i c u l a r to the a x i s of a conducting c y l i n d e r i s given by ( V , 1 w2 B l u 2 a i 2 d 3 15 (i/d + d/i) 5.7 Comparison of (Rn,)^ and (Rm)^ values f o r a A/Z r a t i o of 2/3 (corresponding to the sample dimensions d = 5.0 cm and £ = 7.5 cm used i n t h i s study) and i d e n t i c a l B]^ u, a and w, shows th a t (RJJ)^ i s greater than (Rm)yy by a f a c t o r of 1.8. Therefore lower i n d u c t i v e l o s s e s are encountered when the c y l i n d e r a x i s i s p a r a l l e l to Bj_. This corresponds to the o r i e n t a t i o n of the sample w i t h i n the s p l i t - r i n g resonator, while w i t h the other probe designs, the B^ i s d i r e c t e d p e r p e n d i c u l a r to the sample a x i s . Therefore i t i s p o s t u l a t e d that the lower i n d u c t i v e l o s s e s f o r the s p l i t - r i n g resonator a r i s e , at l e a s t i n p a r t from the d i f f e r e n c e i n o r i e n t a t i o n of the sample. The 90° pulse width and the S/N af f o r d e d by each design f o r a 1 ml of water sample placed at the center of the probe are given i n Table 5.2. The d e s i r a b l e c h a r a c e r i s t i c s of s m a l l e s t pulse width and highest - 182 -Table 5.2: 90° Pulse Width (t 9 0<>) and S/N d a t a a Probe b t 9 0° (A*s) S/Nc 1 69 650 2 58 740 3 42 1030 4 55 825 5 34 1290 Data were obtained by u s i n g a 1 ml water sample pla c e d at the center of the probe and 140 W of r f power. Numbers i n d i c a t i n g the probe design correspond to that given i n Table 5.1. Average of f i v e measurements. Maximum d e v i a t i o n -1%. - 183 -S/N are given by the s p l i t - r i n g resonator probe. The i n d u c t i v e l y coupled/tuned H-resonator a l s o o f f e r s good performance, and the saddle c o i l produces the longest pulse width and the l e a s t S/N. The observed 9 0 ° pulse width and the S/N values are i n good agreement w i t h the expected inverse r e l a t i o n s h i p [7] between the two parameters. Consider-in g the s h i e l d e d Q values (Table 5.1) and the S/N a f f o r d e d by each design, c a l c u l a t i o n s show th a t the S/N observed w i t h the lower Q probes i s p r o g r e s s i v e l y lower than t h a t p r e d i c t e d by the square root r e l a t i o n -ship i n Eq. 5.2. This i s due to the changes i n the f i l l i n g f a c t o r (r?) which depends on the d i s t r i b u t i o n of and hence the probe design [ 7 ] . The r f magnetic f i e l d p r o f i l e s (B^-maps) f o r each design are shown i n F i g s . 5.7-5.10. D e t a i l s of the experimental procedure adopted are given i n S e c t i o n 5.7. The f i g u r e s show the magnitude of the B^ f i e l d as a f u n c t i o n of the s p a t i a l d i s t ance along the three axes. The z-axis de f i n e s the l o n g i t u d i n a l a x i s of each probe; f o r the s p l i t - r i n g resona-t o r , t h i s corresponds to a p e r p e n d i c u l a r o r i e n t a t i o n compared to other probes when p l a c e d i n s i d e the magnet. Since the B^-maps of the two H-resonator probes were s i m i l a r , only the map corresponding to the i n d u c t i v e l y coupled design i s shown. Due to the i n s t a b i l i t y of the h i g h power a m p l i f i e r used here, no comparison i s intended between the absolute values of 7B1 ( i n F i g s . 5.7-5.10) and the pulse widths quoted i n Table 5.1. This does not present a d i f f i c u l t y s i n c e , only the change i n 7 B ^ w i t h i n each map i s of i n t e r e s t . Comparison between d i f f e r e n t probes was obtained by d e f i n i n g a B^ inhomogeneity parameter AB]_/B^^0^, where AB]_ r e f e r s to the f i e l d d e v i a t i o n at r/2 or i / 4 and 2>l(0) t o t n e f i e l d at the center; r and i. are the r a d i u s and the t o t a l l e n g t h of the - 184 -probe r e s p e c t i v e l y . The approximate inhomogeneity parameters obtained from the maps are given i n Table 5.3. I t should be noted t h a t i n some cases i t i s d i f f i c u l t to measure the AB^ from the maps. I n these instances the inhomogeneity parameter i s given as l e s s than the value c a l c u l a t e d based on the d i g i t a l r e s o l u t i o n along the 7 B ^ a x i s . . Figures 5.7-5.10 show th a t the B^-maps are h i g h l y dependent upon the probe design. In general, the B^ homogeneity i n the transverse xy plane i s b e t t e r than along the l o n g i t u d i n a l a x i s . An i n t e r e s t i n g o b s e r v a t i o n i n F i g s . 5.7-5.9 i s the increase i n B^ along the y a x i s at p o s i t i o n s away from the center. The transverse r f homogeneity of the bird-cage resonator compares l e s s f a v o r a b l y w i t h other designs, while t h a t of the H-resonator i s comparable to the saddle c o i l . The decreased performance of the bird-cage resonator i s probably due to the p a r t i c u l a r f e a t u r e s of the design used i n t h i s study. The H-resonator a f f o r d s poor z-axis homogeneity due to the presence of guard r i n g s , and improved performance i s o f f e r e d by the saddle c o i l and the bird-cage resonator. The s p l i t - r i n g resonator provides e x c e l l e n t B^ homogeneity along a l l three axes. The asymmetry of the z-axis B^-map of t h i s probe i s due to the f a c t t h a t the s i g n a l from the higher negative z-values i s l o s t due to the inhomogeneity of the main B Q f i e l d . (The phantom used to produce t h i s map i s 14 cm long and i s o r i e n t e d p e r p e n d i c u l a r to the B D f i e l d , and hence the d i f f i c u l t y i n shimming). The decrease i n B^ at higher z-values shows the unavoidable r o l l - o f f of f i e l d i n t e n s i t y at the ends of the c o i l . - 185 -(a) L_ 0 (b) (c) _L _L 5000 10000 XBi (Hz) 5000 10000 XBi (Hz) J_ Hi.o 0.5 o.o 7 -0.5 -1.0 - 1.0 0.5 -0.5 -1.0 1.0 0.0 1/2 -1.0 A ( -0 5000 10000 7B, (Hz) F i g . 5.7: I$i-homogeneity maps of the saddle c o i l . The probe o r i e n t a -t i o n i s shown by the end-view ( r i g h t ) . A, c i r c u l a r conductor s e c t i o n s ; B, s t r a i g h t conductor s e c t i o n s . Bj_; d i r e c t i o n of the B^ f i e l d . - 186 -(a) (b) (c) L. 0 -HO X 0.5 o.o r -0.5 -i.o 10000 20000 XB, (Hz) X 1.0 0.5 y. 0.0 r -0.5 -1.0 10000 20000 7B, (Hz) X X 0.5 0.0 1/2 -0.5 10000 20000 XB, (Hz) B F i g . 5.8: B^- homogeneity maps of the i n d u c t i v e l y coupled and tuned H-resonator. Probe o r i e n t a t i o n Is shown by the end-view ( r i g h t ) . Symbols r e f e r t o th a t given In F i g . 5.5 - 187 -(a) (b) (c) _L 1.0 0.5 0.0 r -0.5 -1.0 10000 20000 7B, (Hz) _L 10000 20000 1.0 0.5 y. o.o r -0.5 -1.0 7B, (Hz) _L 10000 0.5 z 00 1/2 -0.5 20000 / \ I - I \ B, / A,B XB, (Hz) F i g . 5.9: Bi-homogeneity maps of the I n d u c t i v e l y coupled and tuned bird-cage resonator. The probe o r i e n t a t i o n i s shown by the end-view ( r i g h t ) . Symbols r e f e r to th a t given i n F i g . 5.6. - 188 -(a) (b) (c) L. 0 l_ 0 X X 1.0 0.5 o.o 2L -0.5 J-I.O 10000 20000 XB 1 (Hz) X X 1.0 0.5 o.o T •0.5 -1.0 10000 20000 7B, (Hz) X X 1.0 H 0.5 0.0 1/2 H-0.5 -1.0 10000 20000 7B< (Hz) F i g . 5.10: -homogeneity maps of the s p l i t - r i n g resonator. The probe o r i e n t a t i o n i s shown by the end-view ( r i g h t ) . A, copper f o i l . - 189 -Table 5.3: B 1 .Jnhomogeneity Parameters 8 of D i f f e r e n t Probe Designs* 5 P r o b e K x ) N *i<o) A/2 'AB K y ) ' J l ( o ) / r / 2 AB K z )  J l ( o ) / V 4 <8 <8 11 <5 <5 30 <5 <6 33 <10 13 20 <4 <4 <4 Values are given as the percentage of the f i e l d at the center, (see a l s o the t e x t ) . Numbers i n d i c a t i n g the probe design correspond to t h a t given i n Table 5.1. - 1 9 0 -5.6 Concluding Remarks The r e s u l t s presented i n t h i s Chapter i n d i c a t e the r e l a t i v e m e r its and demerits of d i f f e r e n t r f probe designs. In summary, i t i s seen that higher Q values are a f f o r d e d by the resonator probe designs and that the s p l i t - r i n g resonator gives the best r e s u l t s . In general, the d i e l e c t r i c l o s s e s a s s o c i a t e d w i t h the resona-t o r probes are lower than that of the saddle c o i l , and the H-resonator provides the best performance w i t h respect to t h i s parameter. Q u a l i t a -t i v e estimates show th a t the resonators generate higher i n d u c t i v e l o s s e s compared to the saddle c o i l . The best r f homogeneity i s provided by the s p l i t - r i n g resonator. The r f homogeneity of the saddle c o i l i s compara-b l e to t h a t of the H-resonator i n the transverse plane and the former o f f e r s b e t t e r performance along the l o n g i t u d i n a l a x i s . The comparative r e s u l t s of d i f f e r e n t probe designs a l s o i n d i c a t e the d i f f i c u l t y i n o p t i m i z i n g a l l the d e s i r a b l e features w i t h a s i n g l e design. Thus compromises are e s s e n t i a l , and the choice of a probe i s best done by g i v i n g p a r t i c u l a r a t t e n t i o n to the d e s i r e d c r i t e r i a depend-in g on the a p p l i c a t i o n . I t can be s t a t e d t h a t , of the designs i n v e s t i -gated here, the s p l i t - r i n g resonator probe provides the best o v e r a l l performance. But u n f o r t u n a t e l y i t s use i s r e s t r i c t e d because of the awkward o r i e n t a t i o n of the probe i n s i d e the magnet. Under severe sample loaded c o n d i t i o n s (QuL > > ^L^ > a n o ' w b e n the sample l o s s e s are mostly due to i n d u c t i v e l o s s e s , the S/N r a t i o i s independent of any probe parameters [22a]. Hence, any f u r t h e r improve-ment of probe design w i l l have l i t t l e e f f e c t on the S/N. But w i t h a - 191 -p a r t i c u l a r sample, the attainment of the above c o n d i t i o n depends on the probe design used. The best i n d i c a t o r of t h i s i s the QUL/QL r a t i o ^ of the probe. From the values given i n Table 5.1, t h i s r a t i o i s highest f o r the s p l i t - r i n g resonator (QUL/QL •= 3.4) and lowest f o r the saddle c o i l (QUL/QL = 2.3). Considering a l s o the f a c t that the d i e l e c t r i c c o n t r i b u t i o n to the sample l o s s e s i s small f o r the resonator designs, use of these probes should be p r e f e r r e d over the saddle c o i l . F u r t h e r , the independence of S/N of probe parameters upon reaching the c o n d i t i o n QUL » QL does not imply t h a t l i t t l e a t t e n t i o n should be d i r e c t e d towards the c h a r a c t e r i s t i c s of the p a r t i c u l a r design used. For example, good homogeneity would s t i l l be r e q u i r e d s i n c e i t determines the u n i f o r m i t y of the image. The B^ homogeneity maps show that H-resonator designs are poor candidates f o r imaging i n the planes which i n c l u d e the l o n g i t u d i n a l a x i s of the probe and t h a t the s p l i t - r i n g resonator i s most s u i t a b l e choice f o r three-dimensional volume imaging. 5.7 Experimental The probe Q values were measured on the bench w i t h the probe tuned and matched approximately to 80 MHz. The experimental setup [32] used was t h a t a v a i l a b l e i n the UBC Chemistry Department E l e c t r o n i c Shop. This i n c l u d e d a s i g n a l generator (Wavetek 3001), a sweep generator 1 Note t h a t these r a t i o s cannot be taken as i n d i c a t i v e of the t o t a l sample l o s s e s when comparing d i f f e r e n t probe designs. - 192 -(Wavetek 2002A), an r f r e f l e x i o n b r i d g e , an r f det e c t o r and an o s c i l l o -scope. The Q values reported f o r each probe are the average values of s e v e r a l independent measurements, taken as the r a t i o of the resonance frequency to the f u l l - w i d t h at half-power p o i n t (70% of the vo l t a g e maximum) of the probe resonance. S/N values were determined u s i n g standard software [33]. For each measurement the magnet was shimmed w i t h a 1 ml water sample so that the t y p i c a l l i n e - w i d t h was approximately 3 Hz. The a c t u a l S/N r a t i o i s higher than the values quoted because of the d e v i a t i o n of the s i g n a l from a true L o r e n t z i a n l i n e shape. 5.7.1 Method of B^-mapping The B^ magnetic f i e l d p r o f i l e s were generated by u s i n g a v a r i a n t of an e x i s t i n g method [34,35]. The pulse sequence used c o n s i s t e d of a spin-echo experiment performed i n the presence of a grad i e n t (see Chapter I I , F i g . 2.4a), and i n which the len g t h of the f i r s t r f pulse ( t ^ ) was made v a r i a b l e . A data matrix, S (t]_, t g ) , was acquired by incrementing t ^ by a constant amount while the second r f pulse was set to 180°; t g corresponds to the s i g n a l a c q u i s i t i o n time, which i s i n i t i a t e d a f t e r the 180° puls e , i n the presence of a grad i e n t . Double F o u r i e r t r a n s f o r m a t i o n of S ( t ^ , t g ) produces S(wi,Wg), where and u>g correspond, r e s p e c t i v e l y , to the magnitude of 7B1 and the s p a t i a l a x i s d e f i n e d by the gradient. Thus the magnitude of the B^ magnetic f i e l d and the l a c k of u n i f o r m i t y thereof are d i r e c t l y obtained from the pro-- 193 -cessed data s e t . I t i s conceivable that t h i s experiment c o u l d be extended to i n c o r -porate a l l three s p a t i a l axes by i n t r o d u c i n g phase-encoding gradients between the two r f p u l s e s . This would enable complete c h a r a c t e r i z a t i o n of the r f magnetic f i e l d i n the whole volume enclosed by the probe. However such an experiment would produce a l a r g e amount of accumulated data which would have to be subjected to a four-dimensional F o u r i e r t r a n s f o r m a t i o n . The r e s u l t s r e p o r t e d i n t h i s Chapter were obtained by u s i n g a 5 mm NMR tube c o n t a i n i n g water as the phantom. The phantom was o r i e n t e d along e i t h e r one of the three p r i n c i p a l axes x, y or z w i t h the c o r r e s -ponding gr a d i e n t being a p p l i e d during the sequence of each experiment. The data matrices t y p i c a l l y c o n s i s t e d of 64 pulse l e n g t h v a l u e s , a pulse l e n g t h increment of 20 usee and an a c q u i s i t i o n b l o c k s i z e of 256. The data were apodized w i t h a s i n e - b e l l f u n c t i o n [33] i n both dimensions p r i o r to F o u r i e r t r a n s f o r m a t i o n and z e r o - f i l l e d once along the t ^ dimension g i v i n g r i s e to a f i n a l r e a l data matrix s i z e of 128 x 128. The l e n g t h of the water phantom was s e l e c t e d depending on whether the a x i a l or the r a d i a l B;L homogeneity was being i n v e s t i g a t e d . For a x i a l homogeneity measurements the phantom le n g t h was approximately equal to the l e n g t h of the probe (14 cm), w h i l e f o r r a d i a l measurements the phantom le n g t h (6.5 cm) was d i c t a t e d by the inner diameter of the probe (7.0 cm). The use of a s i m i l a r procedure f o r B ^ mapping has a l s o been presented at a recent conference [36]. - 194 -References: Chapter V 1. F.E. Terman, " E l e c t r o n i c and Radio Engineering", 4th Edn. pp. 30-31, McGraw-Hill, New York, 1955. 2. D.I. Hoult, Prog, i n NMR Spectroscopy 12, 41 (1978). 3. F.E. Terman, "Radio Engineers Handbook", p. 53, McGraw-Hill, New York, 1943. 4. D.I. Hoult, i n Proc. I n t e r n a t . Symp. on NMR Imaging, Winston-Salem, North C a r o l i n a (R.C. W i c o f s k i , N. Karstaedt and C.L. P a r t a i n , Eds.) p. 33, Department of Radiology, Bowman Gray School of Medicine 1982. 5. D.W. Alderman and D.M. Grant, J . Magn. Reson. 34, 447 (1979). 6. R.A. Assi n k , E. Fukushima, A.A.V. Gibson, A.R. Rath, and S.B.W. Roeder, J . Magn. Reson. 66, 176 (1986). 7. D.I. Hoult and R.E. Richards, J . Magn. Reson. 24, 71 (1976). 8. D.I. Hoult and P.C. Lauterbur, J . Magn. Reson. 34, 425 (1979). 9. D.G. Gadian and F.N.H. Robinson, J . Magn. Reson. 34, 449 (1979). 10. T.W. Redpath and J.M.S. Hutchison, Magn. Reson. Imaging 2, 295 (1984). 11. W.A. E d e l s t e i n , P.A. Bottomley, and L.M. P f e i f e r , Med. Phys. 11, 180 (1984). 12. T.M. G r i s t and J.S. Hyde, J . Magn. Reson. 61, 571 (1985). 13. T.W. Redpath and R.D. S e l b i e , Phys. Med. B i o l . 29, 739 (1984). 14. G.M. Bydder, P.C. Butsen, R.R. Harman, D.J. G i l d e r d a l e , and I.R. Young, J . Comp. A s s i t . Tomog. 9 , 413 (1985). 15. G.M. Bydder, W.L. C u r a t i , D.G. Gadian, A.S. H a l l , R.R. Harman, P.R. Butsen, D.J. G i l d e r d a l e , and I.R. Young, J . Comp. A s s i s t . Tomog. 9 , 987 (1985). 16. S. Kan, P. Gonard, C. Duret, J . S e l s e t , and C. V i b e t , Rev. S c i . Instrum. 44, 1725 (1973). - 195 -17. H.J. Schneider and P. Dullenkopf. Rev. S c i . Instrum. 48, 68 (1977); 48, 832 (1977). 18. W.N. Hardy and L.A. Whitehead, Rev. S c i . Instrum. 52, 213 (1981). 19. A. L e r o y - W i l l i g , L. Darrasse, J . Taquin, and M. Sauzade, Magn. Reson. Med. 2, 20 (1985). 20. T.A. Cross, S. M u l l e r , and W.P. Aue, J . Magn. Reson. 62, 87 (1985) . 21. L.D. H a l l , T. Marcus, C. Neale, B. Powell, J . S a l l o s , and S.L. Ta l a g a l a , J . Magn. Reson. 62, 525 (1985). 22. (a) C E . Hayes, W.A. E d e l s t e i n , J.F. Schenck, O.M. M u e l l e r , and M. Eash. J . Magn. Reson. 63, 622 (1985). (b) A b s t r a c t s , Volume 2, S o c i e t y of Magnetic Resonance i n Medicine, 4th Meeting, London, U.K., August 1985, p. 1094. 23. W.S. Hinshaw and R.C Gauss, U.S. Patent, No. 4,439,733 (1984). 24. P. Roschmann, A b s t r a c t s , S o c i e t y of Magnetic Resonance i n Medicine, 3rd Meeting, New York, August 1984, p. 634. 25. P.A. Bottomley, H.R. Hart J r . , W. E d e l s t e i n , J.F. Schenck, L.S. Smith, W.M. Leue, O.M. Mu e l l e r , and R.W. Reddington, Radiology 150, 441 (1984). 26. C.-N. Chen, D.I. Hoult, and V.J. Sank, J . Magn. Reson. 54, 324 (1983) . 27. D.I. Hoult, C.-N. Chen, and V.J. Sank, Magn. Reson. Med. 1, 339 (1984) . 28. G.H. Glover, C E . Hayes, N.J. P e l c , W.A. E d e l s t e i n , O.M. M u e l l e r , H.R. Hart, C J . Hardy, M. O'Donenll, and W.D. Barber, J . Magn. Reson. 64, 255 (1985). 29. M. Decorps, P. Blondet, H. Reutenauer, J.P. Albrand, and C. Remy, J . Magn. Reson. 65, 100 (1985). 30. W. F r o n c i s z , A. Jesmanowicz, and J.S. Hyde, J . Magn. Reson. 66, 135 (1986). 31. G. S e r g i a d i s , Magn. Reson. i n Med. 2, 328 (1985). 32. P. Daugaard, H.J. Jakobsen, A.R. Garber, and P.D. E l l i s , J . Magn. Reson. 44, 224 (1981). - 196 33. NMC-1280 Software Manual, N i c o l e t Magnetics Corporation, C a l i f o r -n i a , December 1982. 34. D.I. Hoult, J . Magn. Reson. 33, 183 (1979). 35. A . Bax, "Two-Dimensional Nuclear Magnetic Resonance i n L i q u i d s " , p. 22-26, D e l f t U n i v e r s i t y Press, D e l f t , 1982. 36. J . Murphy-Boesch, G. So, and J.L. James, A b s t r a c t s , 27th Ex p e r i -mental NMR Conference, Baltimore, Maryland, A p r i l 1986, p. A63. 197 -CHAPTER VI 3 1 P NMR SPECTROSCOPY IN VIVO - 198 -VI. JJ-P NMR SPECTROSCOPY IN VIVO 6.1 I n t r o d u c t i o n Since the i n i t i a l attempts to detect NMR s i g n a l s from a l i v i n g animal [ 1 ] , i n v i v o 3^P NMR spectroscopy has progressed to a stage where i t s c l i n i c a l u t i l i t y i s beginning to emerge [2]. This r a p i d advancement has been mainly due to the i n t r o d u c t i o n of the surface c o i l (a f l a t loop of wire) [3,4] as an NMR r e c e i v e r c o i l . Surface c o i l s provide a simple method of d e t e c t i n g s i g n a l s from a l o c a l i z e d r e g i o n c l o s e to the surface of a sample. Thus, during the l a s t few years s k e l e t a l muscle d i s o r d e r s have been e x t e n s i v e l y s t u d i e d u s i n g t h i s technology [5,6]. U n l i k e the s k e l e t a l muscle, noninvasive NMR study of the i n t e r n a l organs such as the kidney, l i v e r and the h e a r t present a formidable challenge. In these s i t u a t i o n s d i r e c t use of a surface c o i l or other c o i l types i s not p o s s i b l e due to the unwanted s i g n a l c o n t r i b u t e d by the t i s s u e s around the organ of i n t e r e s t . Several s i g n a l l o c a l i z a t i o n methods have so f a r been proposed to circumvent t h i s problem [4,7]. Most of these methods are e i t h e r inconvenient to use i n a p r a c t i c a l s i t u a t i o n or s t i l l under development [7]. Though i n v i v o 3 l p s p e c t r a from the l i v e r [8] and the kidney [9] have been obtained n o n i n v a s i v e l y v i a the f i e l d p r o f i l i n g technique [ 8 ] , t h i s method i s not r o u t i n e l y used due to i t s complexity and l a c k of f l e x i b i l i t y . Therefore, i n v i v o s p e c t r o s c o p i c s t u d i e s of i n t e r n a l organs u s u a l l y r e l y upon s u r g i c a l i n t e r v e n t i o n to p o s i t i o n the organ i n the NMR r e c e i v e r c o i l , concur-- 199 -r e n t l y removing i t from the surrounding t i s s u e [10,11]. In order to reduce the p o s s i b l e adverse e f f e c t s due to these s u r g i c a l maneuvers a technique f o r i m p l a n t i n g r f c o i l s around the organ of i n t e r e s t has a l s o been report e d [12]. More r e c e n t l y , the use of two c o n c e n t r i c surface c o i l s to o b t a i n r a t l i v e r s p e c t r a without the need f o r surgery has been described [13]. The a p p l i c a t i o n of NMR to study the metabolic processes i n the kidney has a t t r a c t e d wide a t t e n t i o n i n the past decade and a v a r i e t y of kidney p r e p a r a t i o n s have been i n v e s t i g a t e d [14]. Due to the r e s t r i c t i o n of space i n the NMR probe, i n i t i a l s t u d i e s were conducted on i s o l a t e d kidneys, and advances i n magnet design together w i t h the developments noted e a r l i e r have r e c e n t l y enabled such s t u d i e s to be conducted i n v i v o [15-19]. The work described here was i n i t i a t e d to examine by 3^P NMR, the b i o c h e m i c a l transformations of the r a t kidney i n v i v o during (ischemia) and a f t e r ( r e p e r f u s i o n ) a p e r i o d of inadequate blood flow i n t o the organ. Of f u r t h e r i n t e r e s t was the i n f l u e n c e of v a r i o u s agents (drugs) on the r a t e of recovery of r e n a l adenosine triphosphate (ATP) l e v e l s f o l l o w i n g an ischemic p e r i o d . The i n t e r e s t i n these s t u d i e s l i e s i n the f a c t t h a t warm r e n a l ischemia i s commonly encountered i n a number of c l i n i c a l s i t u a t i o n s , and i s p a r t i c u l a r l y important i n t r a n s p l a n t proce-dures [20]. A p p l i c a t i o n of 3^P NMR to study the metabolic changes i n the r a t kidney i n v i v o during ischemia and r e p e r f u s i o n has a l s o been undertaken by other workers [17]. This work was performed i n c o l l a b o r a t i o n w i t h , and f o l l o w i n g an i n i t i a l suggestion by Dr. A.P. Autor (Department of Pathology, UBC), who - 200 -po i n t e d out the importance of such s t u d i e s . The author's e f f o r t s were concentrated on the aspects r e l a t e d to the NMR experiment. A c c o r d i n g l y the p a r t i c u l a r experimental p r o t o c o l adopted and some p r e l i m i n a r y r e s u l t s are discussed i n the next s e c t i o n . 6.2 Experimental P r o t o c o l , R e s u l t s and D i s c u s s i o n P r i o r to performing any experiments, i t was necessary to devise a s u i t a b l e procedure to o b t a i n 3^P NMR sp e c t r a r e p r e s e n t a t i v e of the r a t kidney. The method pursued here was based on the procedures reported e a r l i e r [15-17], and i n v o l v e d the use of a surface c o i l as the NMR c o i l . For t h i s purpose a surface c o i l probe, c o n s i s t i n g of a f l a t bed (31 x 18 cm) made of P l e x i g l a s was constructed so th a t the animal could be l a i d i n a h o r i z o n t a l posture. A schematic diagram of the probe and animal p o s i t i o n i n g i s shown i n F i g . 6.1. The c o i l i t s e l f (diameter 1.5 cm) was const r u c t e d of two turns of copper wire (diameter 1.25 mm) i n s u l a t e d w i t h T e f l o n , and c o n s i s t e d of leads long enough to reach the area to be i n v e s t i g a t e d . The c o i l was supported above the animal w i t h the a i d of T e f l o n bars attached to the si d e of the probe. This support was adjust-able h o r i z o n t a l l y as w e l l as v e r t i c a l l y , and provided the r e q u i r e d f l e x i b i l i t y i n p o s i t i o n i n g the c o i l . The c a p a c i t o r s r e q u i r e d f o r c o i l t u n i n g were mounted underneath the probe bed. The probe con s t r u c t e d i n t h i s manner, when tuned to ca. 32.5 MHz, was found to have a Q value of 150. F i g . 6 . 1 : Schematic diagram of the NMR surface c o i l probe and the animal o r i e n t a t i o n used f o r ^ l p NMR s t u d i e s of the r a t kidney. - 202 -T y p i c a l l y , the a n e s t h e t i z e d animal w i t h i t s abdominal c a v i t y exposed was p l a c e d on the probe bed and the r f c o i l was s u i t a b l y p o s i -t i o n e d . Subsequently, the whole NMR probe w i t h the animal i n p o s i t i o n was i n s e r t e d i n t o the h o r i z o n t a l bore magnet. In order to f i n d the s i g n a l l o c a l i z i n g a b i l i t y of the surface c o i l , an i n i t i a l experiment was performed by p l a c i n g the surface c o i l d i r e c t l y above the l e f t kidney. In t h i s instance s u i t a b l e care was e x e r c i s e d not to d i s t u r b the kidney from i t s n a t u r a l p o s i t i o n except to remove the surrounding f a t to f a c i l i t a t e c o i l placement. The spectrum obtained w i t h t h i s arrangement i s shown i n F i g . 6.2a. The peak assignments are based on t h a t given i n Ref. 17. As the kidney does not c o n t a i n phospho-c r e a t i n e (PCr) [16,17], the s i g n i f i c a n t amount the PCr seen i n t h i s spectrum i n d i c a t e s the c o n t r i b u t i o n from the surrounding muscle to the observed s i g n a l . This s i t u a t i o n was unacceptable, and f u r t h e r the improved s i g n a l l o c a l i z a t i o n a f f o r d e d by the v a r i a t i o n s i n pulse length (and hence the sample r e g i o n detected by the c o i l ) and displacement of surrounding t i s s u e was judged to be inadequate. Guided by t h i s experience i t was subsequently found that the PCr s i g n a l can be c o n v e n i e n t l y e l i m i n a t e d by p a r t i a l l y c l o s i n g the abdominal c a v i t y and suspending the kidney i n an o r i e n t a t i o n as i n d i c a t e d i n F i g . 6.1. The spectrum obtained w i t h t h i s c o i l and organ p o s i t i o n i n g i s shown i n F i g . 6.2b. The e s s e n t i a l features of t h i s spectrum, except f o r the s i g n a l - t o - n o i s e r a t i o , i s i d e n t i c a l to that of the normal kidney r e p o r t e d i n the l i t e r a t u r e [17]. The small amount of PCr seen i n the spectrum i s most probably from the abdominal muscle. I t was found that t h i s method was convenient and the spectrum could be reproduced without - 203 -(a) Peak assignments /3-ATP a-ATP + a-ADP 7-ATP + 0-ADP phosphocreatine phosphodies t e r inorganic phosphate phosphomonoester + NAD/NADH (from muscle) 3 — i 1 1 1 1 1 1 1 1 | ~ i r 0 - 5 0 PPM F i g . 6.2: 32.5 MHz 3 1 P NMR spect r a of the r a t kidney. (a) Surface c o i l p laced d i r e c t l y above the kidney i n i t s n a t u r a l p o s i -t i o n , (b) The kidney i s p o s i t i o n e d as shown i n F i g . 6.1. Experimental parameters: pulse width = 10 , r e l a x a t i o n delay = 500 ms, number of scans = 1000, a c q u i s i t i o n time = 256 ms, l i n e broadening = 20 Hz. - 204 -d i f f i c u l t y . P r i o r to adapting the above c o n f i g u r a t i o n , the method of f l a n k i n c i s i o n and the use of a s o l e n o i d a l c o i l was a l s o t e s t e d [17], but was found to be l e s s convenient due to a more s u b t l e s u r g i c a l procedure i n these cases, s p e c t r a showed an increased i n o r g a n i c phosphate content due to the p a r t i a l ischemic nature of the organ immediately a f t e r the operative procedure. The study was then extended to monitor the changes i n phosphorus metabolite concentrations during ischemia and r e p e r f u s i o n . A f t e r the s u r g i c a l procedure (see l a t e r ) , the v i a b i l i t y of each p r e p a r a t i o n was confirmed by a c q u i s i t i o n of one or two s p e c t r a under normal c o n d i t i o n s . The l e f t kidney was then made ischemic f o r 30 min by o c c l u d i n g the r e n a l v e s s e l s w i t h a small p l a s t i c c l i p , and "ischemic" s p e c t r a were c o l l e c t e d d u r i ng t h i s p e r i o d . A f t e r the ischemic p e r i o d the c l i p was removed and " r e p e r f u s i o n " s p e c t r a were obtained. A s e r i e s of s p e c t r a obtained under such c o n d i t i o n s i s shown i n F i g . 6.3. Each spectrum i n F i g . 6.3 repre-sents the average of the metabolite concentrations during the 12 min o b s e r v a t i o n p e r i o d . During the p e r i o d of ischemia ATP l e v e l s decreased r a p i d l y w i t h concomitant increase i n i n o r g a n i c phosphate. F o l l o w i n g the r e l e a s e of the r e n a l v e s s e l s the reverse process was observed. This trend was reproduced i n a l l animals s t u d i e d . However, the i n t e r e s t i s focussed on the recovery of the ATP l e v e l s to the c o n t r o l (preischemic) values s i n c e i t i n d i c a t e s the p o s s i b l e r e n a l damage due to ischemia and r e p e r f u s i o n [17]. On comparison of the /3-ATP resonance i n the s p e c t r a shown i n F i g . 6.3(i) and ( v i i ) i t can be seen t h a t the recovery of ATP i s incomplete. In the l i m i t e d number of animals s t u d i e d the extent of ATP recovery was found to have a large F i g . 6.3: 32.5 MHz 3 1 P NMR s p e c t r a obtained from a r a t kidney during periods of ischemia and r e p e r f u s i o n . Each spectrum repre-sents 12 min accumulation time. - 206 -v a r i a t i o n . I t was subsequently evident that the changes i n the body temperature of the animal during the experiment was a c o n t r i b u t i n g f a c t o r to t h i s observation. The p r e l i m i n a r y r e s u l t s obtained by t r e a t -i n g the animal w i t h d i f f e r e n t drugs were encouraging but warrant f u r t h e r study. Due to the p r e l i m i n a r y nature of t h i s study, d e f i n i t e conclusions c o u l d not be drawn. I t i s necessary that these experiments be repeated under more c o n t r o l l e d c o n d i t i o n s , i n that the body temperature of the animal be maintained and monitored during the experiment. The f a c i l i -t i e s f o r these c o n t r o l s were not a v a i l a b l e at the time of t h i s study. However, the experiments reported here i n d i c a t e t h a t the p r o t o c o l adopted (NMR and s u r g i c a l ) can be used to study i s c h e m i a / r e p e r f u s i o n models i n the r a t kidney and thus provides the necessary foundation f o r the f u t u r e work to be c a r r i e d out i n t h i s l a b o r a t o r y . 6.3 Experimental The NMR s p e c t r a were recorded u s i n g the spectrometer system d e s c r i b e d i n S e c t i o n 4.4. The magnet was i n i t i a l l y shimmed using a phantom c o n t a i n i n g H3PO2 and constructed to the approximate dimensions of a r a t kidney (2.0 x 1.5 x 1.0 cm). Subsequently, the magnet was f u r t h e r shimmed by observing the ^H s i g n a l from the kidney while the c o i l was tuned to 3^P [21]. 3^P s p e c t r a were recorded by a d j u s t i n g the pulse width to o b t a i n the maximum s i g n a l i n t e n s i t y when usi n g the surface c o i l [22] . - 207 -S u r g i c a l procedure: Male Wistar r a t s weighing 300-350 g were used i n a l l experiments. Anesthesia was induced by i n t r a p e r i t o n e a l i n j e c t i o n of 3.6% c h l o r a l hydrate 1 ml/100 g body weight. A m i d l i n e abdominal i n c i s i o n was made and the v i s c e r a were r e f l e c t e d to the l e f t . The i n f e r i o r vena cava was cannulated w i t h polyethylene tubing (PE 50) f o r a d m i n i s t r a t i o n of drugs and f l u i d s . The l e f t kidney was then m o b i l i z e d i n t o the wound based on i t s v a s c u l a r supply. The kidney was suspended i n the wound by c l o s i n g the l a t t e r w i t h i n t e r r u p t e d sutures of 3-0 s i l k . The kidney was o r i e n t e d w i t h i t s long a x i s i n the same l i n e as the i n c i s i o n and i t s l a t e r a l edge p o i n t i n g a n t e r i o r l y . The v e s s e l s were not kinked or t w i s t e d . The animals were given 2 ml of 0.9% NaCl i n t r a v e -nously every hour and supplemental a n e s t h e t i c as needed. A f t e r the a c q u i s i t i o n of the normal kidney spectrum, the animals were given h e p a r i n (50 u n i t s ) i n t r a v e n e o u s l y , and the r e n a l v e s s e l s were occluded w i t h a small p l a s t i c v a s c u l a r c l i p . F o l l o w i n g the a c q u i s i t o n of "ischemic" s p e c t r a the animals were t r e a t e d i n t r a v e n o u s l y w i t h 1.5 ml 5% dextrose (D5W). Two minutes a f t e r the treatment, the v a s c u l a r c l i p was removed and the " r e p e r f u s i o n " s p e c t r a were obtained. At the end of the experiment the animals were s a c r i f i c e d by c e r v i c a l cord d i s l o c a t i o n . The above s u r g i c a l procedure was performed by Dr. N. G u r l l . - 208 -References - Chapter VI 1. B. Chance, Y. Nakase, M. Bond, J.S. Leigh, J r . , and G. Macdonald, Proc. N a t l . Acad. S c i . USA 75, 4925 (1978). 2. P.J. Bore, Magn. Reson. Imag. 3, 407 (1985). 3. J.J.H. Ackerman, T.H. Grove, G.G. Wong, D.G. Gadian, and G.K. Radda, Nature 283, 167 (1980). 4. M.R. B e n d a l l , B u l l . Magn. Reson. 8, 17 (1986). 5. D.J. Ta y l o r , P.J. Bore, P. S t y l e s , D.G. Gadian, and G.K. Radda, Mol. B i o l . Med. 1, 77 (1983). 6. G.K. Radda and D.J. Taylor , I n t l . Rev. Exp. P a t h o l . 27, 1 (1985). 7. R.J. Ordidge, A. Connelly, and J.A.B. Lohman, J . Magn. Reson. 66, 283 (1986) , and references c i t e d t h e r e i n . 8. R.E. Gordon, P.E. Hanley, D. Shaw, D.G. Gadian, G.K. Radda, P. S t y l e s , P.J. Bore, and L. Chan, Nature 287, 736 (1980). 9. R.S. Balaban, D.G. Gadian, and G.K. Radda, Kidney I n t l . 20, 575 (1981) . 10. T.H. Grove, J.J.H. Ackerman, G.K. Radda, and P.J. Bore, Proc. N a t l . Acad. S c i . USA 77, 299 (1980). 11. R.J. Neurohr, E.J. B a r r e t t , and R.G. Shulman, Proc. N a t l . Acad. S c i . USA 80, 1603 (1983). 12. A.P. Koretsky, S. Wong, J . Murphy-Boesch, M.P. K l e i n , T.L. James, and M.W. Weiner, Proc. N a t l . Acad. S c i . USA 80, 7491 (1983). 13. M.R. B e n d a l l , D. F o x a l l , B.G. N i c h o l s , and J.R. Schmidt, J . Magn. Reson. 70, 181 (1986). 14. B. Ross, D. Freeman, and L. Chan, Kidney I n t l . 29, 131 (1986). 15. L. Chan, J.G.G. Ledingham, J.A. Dixon, K.R. Thulborn, J.C. Water-ton, G.K. Radda, and B.D. Ross, i n Acute Renal F a i l u r e , H.E. E l i a h o u Ed., p. 35, Libbey, London, 1982. 16. A.P. Koretsky, W. Strauss, V. Basus, J . Murphy, P. Bendel, T. James, and M.W. Weiner, i n Acute Renal F a i l u r e , H. E l i a h o u Ed., p. 42, Libbey, London, 1982. - 209 -1 7 . N.J. Si e g e l , M.J. Avison, H.F. Reiley, J.R. Alger, and R.G. Shulman, Am. J . Physiol. 245, F 530 (1983). 18. D.M. Freeman, L. Chan, H. Yahaya, P. Holloway, and B.D. Ross, Kidney I n t l . 30, 35 (1986). 19. P.J. R a t c l i f f e , C.T.W. Moonen, P.A.H. Holloway, J.G.G. Ledingham, and G.K. Radda, Kidney I n t l . 30, 355 (1986). 2 0 . G.L. Barker, R.J. Corry, and A.P. Autor, Annal. Surgery 202, 628 (1985) . 2 1 . J.J.H. Ackerman, D.G. Gadian, G.K. Radda, and G.G. Wong, J . Magn. Reson. 42, 488 (1981). 22. J.L. Evelhoch and J.J.H. Ackerman, J . Magn. Reson. 53, 52 (1983). - 210 -SUMMARY AND DISCUSSION - 211 -SUMMARY AND DISCUSSION This S e c t i o n serves to summarize b r i e f l y the s t u d i e s d e s c r i b e d i n the previous Chapters and to d i s c u s s f u t u r e extension and a p p l i c a t i o n s . At the commencement of t h i s work (September 1982) NMR imaging was mostly b e i n g performed u s i n g the f i r s t generation of whole body imaging systems o p e r a t i n g at low f i e l d s (<0.25T). But the a v a i l a b i l i t y of h o r i z o n t a l bore magnets designed f o r s p e c t r o s c o p i c s t u d i e s at h i g h f i e l d (1 . 8 T ) prompted s e v e r a l groups i n c l u d i n g ours to i n c o r p o r a t e imaging c a p a b i l i t i e s to such devices. One f a c e t of the work d e s c r i b e d i n t h i s t h e s i s was performed w i t h t h i s aim. Chapter I I d e a l t w i t h the b a s i c concepts of NMR imaging w i t h s p e c i a l emphasis on F o u r i e r imaging techniques. In the absence of an account i n the l i t e r a t u r e which concentrates on important aspects of t h i s w i d e l y used imaging method i n d e t a i l , i t i s hoped that t h i s Chapter would f i l l the v o i d . Chapters I I I and V focussed on two e s s e n t i a l i n g r e d i e n t s of NMR imaging. S p e c i f i c a l l y , a systematic study of the theory, implementation and the experiment of the t a i l o r e d e x c i t a t i o n procedure i n r e l a t i o n to s l i c e s e l e c t i o n was presented i n S e c t i o n 3.1. Even though the e s s e n t i a l concepts of t h i s procedure were w e l l known, the p r a c t i c a l d e t a i l s of the use of continuous r f modulation scheme i n NMR remained e l u s i v e . There-f o r e a d e t a i l e d d e s c r i p t i o n of the procedure adopted here i s i n c l u d e d i n S e c t i o n 3.1. Experimental r e s u l t s which correspond c l o s e l y w i t h that p r e d i c t e d by theory were a l s o obtained w i t h the d e s c r i b e d scheme. I t - 212 -should be mentioned that s i n c e i n i t i a t i o n of t h i s study, two reports which describe u s e f u l p r a c t i c a l aspects of the method have been pub-l i s h e d . A d e t a i l e d account of r f probe designs s u i t a b l e f o r h i g h f i e l d imaging, d e s c r i b i n g t h e i r m o d i f i c a t i o n , c o n s t r u c t i o n and performance was presented i n Chapter V. The s u b j e c t was approached from an experimen-t a l i s t ' s p o i n t - o f - v i e w . the probe designs i n v e s t i g a t e d here (H-resona-t o r , bird-cage resonator and s p l i t - r i n g resonator; see S e c t i o n 5.4) were s u i t a b l y m o d i f i e d to produce e a s i l y f a b r i c a t e d and low-cost probes. The m o d i f i c a t i o n s i n v o l v e d the i n c o r p o r a t i o n of i n d u c t i v e c o u p l i n g and tuning mechanisms i n t o the o r i g i n a l l y proposed c o n f i g u r a t i o n s together w i t h e f f i c i e n t use of i n t r i n s i c f e atures of each design to generate the capacitance ( S e c t i o n 5.5). The three resonator probe designs and a c o n v e n t i o n a l saddle c o i l were then evaluated by measuring s e v e r a l parameters d i r e c t l y r e l a t e d to the performance of the probes ( S e c t i o n 5.5). The B^ homogeneity of the probes was e x p e r i m e n t a l l y evaluated by employing the spin-echo v e r s i o n of the r o t a t i n g frame zeugmatography experiment ( S e c t i o n 5.7). This method enables the determination of the magnitude of the B]_ f i e l d and the l a c k of u n i f o r m i t y thereof d i r e c t l y from the experimental p l o t s and hence would be of c o n s i d e r a b l e value f o r f u t u r e s t u d i e s . Comparative r e s u l t s of the probe designs i n v e s t i g a t e d here show th a t the best o v e r a l l performance i s provided by the s p l i t -r i n g resonator probe and that i t would be a more s u i t a b l e choice f o r three-dimensional volume imaging. Though the p e r p e n d i c u l a r o r i e n t a t i o n of t h i s probe i n s i d e the magnet creates some d i f f i c u l t i e s , i t i s never-t h e l e s s w e l l s u i t e d f o r inanimate imaging a p p l i c a t i o n s . P r e v i o u s l y 213 -u n a v a i l a b l e comparative r e s u l t s produced by t h i s study i n d i c a t e the m e r i t s and demerits of d i f f e r e n t probe designs and thus provide some g u i d e l i n e s f o r s e l e c t i n g the most s u i t a b l e design depending on the a p p l i c a t i o n . The c a p a b i l i t i e s a f f o r d e d by the above s t u d i e s were then used to image s e v e r a l i n t a c t systems. Good q u a l i t y images w i t h adequate s p a t i a l r e s o l u t i o n were obtained ( S e c t i o n 4.1.2). Three-dimensional images of a r a t were a l s o presented i n S e c t i o n 4.2.2. I t i s a n t i c i p a t e d t h a t f u r t h e r improvement i n image q u a l i t y can be r e a l i z e d by g i v i n g more c a r e f u l a t t e n t i o n to aspects such as the s i g n a l -t o - n o i s e r a t i o of the spectrometer system and o p t i m i z a t i o n of gradient behavior. Further, a more v e r s a t i l e image d i s p l a y device would be an added asset i n improved data d i s p l a y and hence i n o p t i m i z a t i o n of experimental parameters to o b t a i n the best c o n t r a s t between the s t r u c -t ures of i n t e r e s t . Two experiments which r e l a t e to chemical s h i f t e f f e c t s were desc r i b e d i n Sections 3.2 and 4.3.1. In one, the problem of s l i c e s e l e c t i o n i n the presence of c h e m i c a l l y s h i f t e d species was addressed. A p o s s i b l e s o l u t i o n to t h i s problem based on the use of a s u i t a b l y modulated r f pulse f o l l o w e d by appropriate data a c q u i s i t i o n and manipu-l a t i o n was i l l u s t r a t e d w i t h a simple phantom. This work i s most p e r t i -nent to h i g h f i e l d NMR imaging a p p l i c a t i o n s where images f r e e from chemical s h i f t a r t i f a c t s and of very h i g h s p a t i a l r e s o l u t i o n are d e s i r e d . However i t remains to be e s t a b l i s h e d whether such a r t i f a c t s are best e l i m i n a t e d by the increase i n gradient s t r e n g t h or by other means. - 214 -Techniques which enable two-dimensional chemical s h i f t r e s o l v e d imaging were introduced i n S e c t i o n 4.3.1. The methods i n v o l v e s e l e c t i v e e x c i t a t i o n and suppression of s p e c i f i c resonances p r i o r to the a p p l i c a -t i o n of conventional imaging sequences. This allows chemical s h i f t s e l e c t i o n to be c a r r i e d out under h i g h r e s o l u t i o n c o n d i t i o n s and a l s o the image r e s o l u t i o n , s i g n a l - t o - n o i s e r a t i o and the a c q u i s i t i o n time to be maintained s i m i l a r to that of conventional imaging. Since the report of t h i s approach i t s u t i l i t y has been recognized by other workers and s e v e r a l convenient adaptations of the technique have been suggested and demonstrated. The a p p l i c a t i o n of three-dimensional chemical s h i f t r e s o l v e d imaging to map the s p a t i a l d i s t r i b u t i o n of pH and temperature was demonstrated i n S e c t i o n 4.3.2. The importance of t h i s demonstration l i e s i n the f a c t that a t present there i s no r e l i a b l e means of noninva-s i v e i n v i v o pH and temperature mapping, and that such i n f o r m a t i o n would be extremely v a l u a b l e i n many occasions. For example, temperature maps would be of i n v a l u a b l e help when hyperthemia treatments f o r malignant tumors are considered and s i m i l a r l y pH maps cou l d w e l l provide greater i n s i g h t to the b i o e n e r g e t i c s of human muscle. However, the extension of the present study to i n v i v o systems would be met w i t h more s t r i n g e n t demands, i n th a t mapping of narrower pH/temperature ranges along w i t h f i n e r s p a t i a l r e s o l u t i o n would be r e q u i r e d f o r most a p p l i c a t i o n s . Nevertheless, the present work provides a foundation f o r such s t u d i e s which may best be attempted at higher magnetic f i e l d s and t h e r e f o r e i t s f u l l p o t e n t i a l remains to be explored. - 215 -F i n a l l y , the p r e l i m i n a r y r e s u l t s of NMR s p e c t r o s c o p i c s t u d i e s f the r a t kidney during periods of ischemia and r e p e r f u s i o n were resented i n Chapter VI. - 2 1 6 -APPENDIX - 217 -1 2 C C A Computer Programme t o I n t e g r a t e BLOCH E q u a t i o n s f o r a 3 A C r e c t a n g u l a r p u l s e . *» 5 COMMON YDLRAY(2OO0) 6 DIMENSION DFRE0(21O),AMX(210),AMY(210).AMZ( 210) . 7 1 AMXY(210),PHI(210).IPAK(210).FTMX(210),FTMY(210), 8 2 FTMXY(210) 9 c 10 11 12 C DEFINE VARIABLES C AMO = INITIAL VALUE OF MZ 13 C TPULS = PULS LENGTH (MSEC) 14 c ANGL = FLIP ANGLE (DEGREES) 15 c N = NO. OF TIME STEPS 16 c NM = PLOTTING PARAMETER 17 c 18 READ(5,10) AMO, TPULS.ANGL,N,NM 19 10 F0RMAT(3F10.4,2I6) 20 WRITE(6,20) AMO,TPULS,ANGL.N.NM 21 20 F0RMAT(/,2X,'INITIAL VALUE OF MZ = '.F10.4, 22 1 /,2X,'PULS LENGTH(MSEC) = '.F10.4, 23 2 /,2X,'FLIP ANGLE(DEGREES) = '.F10.4, 24 3 /,2X,'N0. OF TIME STEPS = '.16, 25 4 /.2X,'PLOTTING PARAMETER = ',16) 26 PI = 4 . 0 * ATAN(1.0) 27 ANGLR = PI * ANGL /180. 28 OMEGA 1 = ANGLR * 1000. / TPULS 29 DT = TPULS / 1000. / FLOAT(N) 30 DF = 1000. / TPULS / 20. 31 DFREO(1) = -5. * 1000. / TPULS 32 WRITE(6,30) 33 30 FORMAT(/,10X,'DFREO',8X.'AMX',12X,'AMY',12X,'AMXY',12X,'PHI 34 c 35 C S t a r t DO LOOP t o go through different DFREO v a l u e s 36 C 37 35 DO 500 I = 1, 201 38 AMX(I) = 0 . 0 39 AMY(I) = 0 . 0 40 AMZ(I) = AMO 41 TIME = 0 . 0 42' I J = -1 43 C 44 C S t a r t DO LOOP f o r the Time I n t e g r a t i o n 45 C 46 DO 400 J = 1, N 47 AMX1 = AMX(I) 48 AMY 1 = AMY(I) 49 AMZ1 = AMZ(I) 50 AMX(I) = AMX 1 + DT * AMY 1 * 2. * PI * DFREO(I) 51 AMY(I ) = AMY 1 + DT * OMEGA 1 * AMZ1 52 1 - DT * AMX1 * 2. * PI * DFREO(I) 53 AMZ(I) = AMZ1 - DT * OMEGA 1 * AMY 1 54 TIME = TIME + DT 55 400 CONTINUE 56 AMXY(I) = SORT((AMX(I)*AMX(I)) + (AMY(I)*AMY(I))) 57 PHIR » ATAN(AMX(I) / AMY(I)) 58 PHI(I) = PHIR * 180. / PI 59 IF(AMX(I).GE.O.O) I J = 1 60 IF(AMY(I).GE.O.O) GO to 310 61 PHI(I) = P H I ( I ) + ( I J * 180.0) 2 1 8 -6 2 C 6 3 C L I N E A R A P P R O X . C A L C . 6 4 C 6 5 3 1 0 F T D F » 2 . * P I * T P U L S * D F R E O ( I ) / 1 0 0 0 . 6 6 I F ( A B S ( F T D F ) . G T . 0 . 0 ) GO TO 3 2 0 6 7 F T M X ( I ) « 0 . 0 6 8 F T M Y ( I ) = AMO * ( A N G L R ) 6 9 F T M X Y ( I ) = AMO * S I N ( A N G L R ) 7 0 GO TO 3 3 0 7 1 3 2 0 F T M X ( I ) = AMO * ( 1. - C O S ( F T D F ) ) * A N G L R / F T D F 7 2 F T M Y ( I ) = AMO * A N G L R * S I N ( F T D F ) / F T D F 7 3 F T M X Y ( I ) = S I N ( S O R T ( F T M X ( I ) * F T M X ( I ) + F T M Y ( I ) * F T M Y ( I ) ) ) 7 4 3 3 0 D F R E Q U + 1 ) = D F R E O ( I ) + D F 7 5 5 0 0 C O N T I N U E 7 6 N P T S = 2 0 1 7 7 6 0 0 0 0 7 0 0 1 = 1 , N P T S 7 8 I F ( P H I ( I ) * D F R E 0 ( I ) . G E . O . O ) GO TO 6 1 0 7 9 P H I ( I ) = - P H I ( I ) 8 0 6 1 0 W R I T E ( 6 , 6 2 0 ) D F R E Q ( I ) , A M X ( I ) , A M Y ( I ) , A M X Y ( I ) , P H I ( I ) 8 1 6 2 0 F 0 R M A T ( 5 F 1 5 . 4 ) 8 2 7 0 0 C O N T I N U E 8 3 I F ( N M . E Q . O ) GO TO 9 5 0 8 4 C •85 9 5 0 S T O P 8 6 END 1 C 2 C A C O M P U T E R P R O G R A M M E TO I N T E G R A T E B L O C H E Q U A T I O N S 3 C F O R A S I N C P U L S E 4 C 5 I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) 6 R E A L » 4 D O M E , A M X X , A M Y Y , B M X Y , P H I I 7 D I M E N S I O N W 1 ( 1 0 ) , X 1 ( 1 0 ) , D O M E ( 4 1 0 ) . A M X X ( 4 1 0 ) . 8 1 A M Y Y ( 4 1 0 ) , B M X Y ( 4 1 0 ) . P H I I ( 4 1 0 ) 9 D A T A W1/ 0 . 0 6 6 6 7 1 3 4 4 3 0 8 6 8 8 D 0 , 0 . 1 4 9 4 5 1 3 4 9 1 5 0 5 8 1 D 0 , 1 0 1 0 . 2 1 9 0 8 6 3 6 2 5 1 5 9 8 2 D 0 , O . 2 6 9 2 6 6 7 1 9 3 0 9 9 9 6 D O , 11 2 0 . 2 9 5 5 2 4 2 2 4 7 1 4 7 5 3 D O , 0 . 2 9 5 5 2 4 2 2 4 7 1 4 7 5 3 D 0 , 12 3 0 . 2 6 9 2 6 6 7 1 9 3 0 9 9 9 6 D O , 0 . 2 1 9 0 8 6 3 6 2 5 1 5 9 8 2 D 0 . 1 3 4 0 . 1 4 9 4 5 1 3 4 9 1 5 0 5 8 1 D 0 , O . 0 6 6 6 7 1 3 4 4 3 0 8 6 8 8 D 0 / 14 D A T A X 1 / - 0 . 9 7 3 9 0 6 5 2 8 5 1 7 1 7 2 D O , - 0 . 8 6 5 0 6 3 3 6 6 6 8 8 9 8 5 D 0 , 1 5 1 - 0 . 6 7 9 4 0 9 5 6 8 2 9 9 0 2 4 D 0 . - O . 4 3 3 3 9 5 3 9 4 1 2 9 2 4 7 D 0 , 16 2 - 0 . 1 4 8 8 7 4 3 3 8 9 8 1 6 3 1 D 0 , O . 1 4 8 8 7 4 3 3 8 9 8 1 6 3 1 D 0 , 17 3 0 . 4 3 3 3 9 5 3 9 4 1 2 9 2 4 7 D O , 0 . 6 7 9 4 0 9 5 6 8 2 9 9 0 2 4 D 0 , 18 4 0 . 8 6 5 0 6 3 3 6 6 6 8 8 9 8 5 D 0 . O . 9 7 3 9 0 6 5 2 8 5 1 7 1 7 2 D 0 / 1 9 C 2 0 C R E A D I N I N P U T V A R I A B L E S 2 1 C 2 2 C D E F I N E V A R I A B L E S 2 3 C 2 4 C AMO = I N I T I A L V A L U E OF MZ 2 5 C T A U = 1 S T NODE P T . OF S I N C F U N C T I O N 2 6 C T P U L S » T O T A L L E N G T H OF S I N C F U N C T I O N ( M S ) 2 7 C N = N U M B E R OF T I M E S T E P S N E C E S S A R Y FOR T H E T I M E 2 8 C I N T E G R A T I O N 2 9 C A N G L = F L I P A N G L E ( D E G R E E S ) 3 0 C 3 1 R E A D ( 5 , 1 0 ) AMO, T A U . T P U L S , N , A N G L 3 2 1 0 F 0 R M A T ( 3 F 1 0 4 . I 6 . F 1 O . 4 ) 3 3 W R I T E ( 6 , 2 0 ) AMO, T A U , T P U L S , N , A N G L 3 4 2 0 F 0 R M A T ( / , 2 X . ' I N I T I A L V A L U E OF MZ = ' . F 1 0 . 4 , 3 5 1 / . 2 X , ' 1 S T NODE P T . OF S I N C F U N C T I O N ( M S ) = ' . F 1 0 . 4 , 3 6 2 / , 2 X , ' T O T A L L E N G T H OF S I N C F U N C T I O N ( M S ) = ' . F 1 0 . 4 , 3 7 3 / . 2 X , ' N 0 . OF T I M E S T E P S = ' . 1 6 , 3 8 4 / , 2 X , ' F L I P A N G L E ( D E G R E E S ) « ' . F 1 0 . 4 , / ) 3 9 P I = 4.DO * D A T A N ( 1 . D O ) 4 0 A N G L R = P I * A N G L / 1 8 0 . D O 4 1 SUM = 0 . 0 219 -42 C 43 C NUMERICAL INTEGRATION OF THE SINC FUNCTION 44 C 45 DO 200 1 * 1 . 10 46 ZETA = X1(I) 47 X TPULS * ZETA / 2000.DO 48 XX = PI * 1000.DO * X / TAU 49 FX = DSIN(XX) / XX 50 SUM = SUM + W1(I) * FX 51 200 CONTINUE 52 SUM = SUM * TPULS / 2000.DO 53 C 54 C CALCULATE THE AMPLITUDE AND TIME AND FREQUENCY INTERVALS 55 C 56 AMPL = ANGLR / SUM 57 DT = TPULS / 10OO.D0 / FLOAT(N) 58 DF = 8.00 » 500.DO / TAU / 400.DO 59 DFREO - -4.DO * 500.DO / TAU 60 NPTS = 401 61 C 62 WRITE(6,210) AMPL, DT, DF 63 210 F0RMAT(/,2X,'AMPLITUDE OF THE SINC FUNCTION = '.4X.F10.4, 64 1 /,2X,'TIME STEP = '.F10.8, 65 2 /,2X,'FREQUENCY OFFSET STEP = '.4X,F10.4,/) 66 WRITE(6,30) 67 30 FORMAT(/,10X.'DFREQ',8X,'AMX',12X,'AMY',12X,'AMXY',12X,'PHI',/) 68 C 69 C START DO LOOP TO GO THROUGH OIFFERENT DFREQ VALUES 70 C 71 DO 500 I =1, NPTS 72 AMX = O.DO 73 AMY = O.DO 74 AMZ = AMO 75 TIME = O.O 76 Id = -1 77 C 78 C START DO LOOP FOR THE TIME INTEGRATION 79 C 80 DO 400 d = 1. N 81 TSHIFT = 1000.D0 * (PI / TAU) * ( TIME-TPULS/20O0.DO) 82 IF(DABS(TSHIFT).GE.10.D-4) GO TO 310 83 OMEGA 1 = AMPL 84 GO TO 320 85 310 OMEGA 1 = AMPL * DSIN(TSHIFT) / TSHIFT 86 320 AMX1 =. AMX 87 AMY 1 = AMY 88 AMZ1 = AMZ 89 AMX = AMX1 + DT * AMY 1 * 2.DO * PI * DFREQ 90 AMY = AMY 1 + DT * OMEGA 1 * AMZ1 91 1 - DT * AMX1 * 2.DO * PI * DFREQ 92 AMZ • AMZ1 - DT * OMEGA 1 * AMY 1 93 TIME = TIME + DT 94 40O CONTINUE 95 C 96 C CALCULATE MXY AND THE PHASE ANGLE 97 C 98 AMXY = DSQRT((AMX * AMX) + (AMY * AMY)) 99 PHIR = DATAN(AMX / AMY) 100 PHI • PHIR * 180.DO / PI 101 IF(AMX.GE.O.DO) Id = 1 102 IF(AMY.GE.O.DO) GO TO 410 103 PHI = PHI + (Id * 180.DO) 104 410 DOME(I) = DFREQ 105 AMXX(I) = AMX 106 AMYY(I) = AMY 107 BMXY(I) = AMXY 108 PHII(I) - PHI 109 DFREQ = DFREQ + DF 110 WRITE(6.450) DOME(I), AMXX(I), AMYY ( I ) , BMXY(I). PHII(I) 111 450 F0RMAT(F15.4,3F15.9,F15.4) 112 500 CONTINUE 113 CALL GRAPH(NPTS,DOME,AMXX,AMYY,BMXY,PHI I) 114 STOP 115 END PUBLICATIONS 2. 3. L.D. H a l l , S. Sukumar and S.L. T a l a g a l a . Chemical S h i f t Resolved Tomography Using Frequency-Selective E x c i t a t i o n and Suppression of S p e c i f i c Resonances. J . Magn. Reson. 56, 275 (1984). L.D. H a l l , T. Marcus, C. Neale, B. Powell, J . S a l l o s and S.L. T a l a g a l a . Modified S p l i t - R i n g Resonator Probe f o r NMR Imaging at High F i e l d Strengths. J . Magn. Reson. 62_, 525 (1985). L.D. H a l l and S.L. T a l a g a l a . Mapping of pH and Temperature D i s t r i b u t i o n Using Chemical S h i f t Resolved Tomography. J . Magn. Reson. 6_5, 501 (1985). L.D. H a l l and S.L. T a l a g a l a . S l i c e S e l e c t i o n i n the Presence of Chemically S h i f t e d Species. J . Magn. Reson. 

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