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Mechanical properties of sheep skin in compression Sakata, Kenji 1969

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MECHANICAL PROPERTIES OF SHEEP SKIN IN  COMPRESSION  by  KENJI SAKATA B. Eng., Kyoto U n i v e r s i t y , Kyoto, 1967  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT  FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENGINEERING  We accept t h i s required  t h e s i s as conforming t o the  st^ful^rd  Members o f the Department o f Chemical E n g i n e e r i n g  The  University  of B r i t i s h  February, 1969  Columbia  In  presenting  an  advanced  the  for  thesis  degree  Library  I further  this  shall  agree  scholarly  at the University make  that  purposes  h i s representatives.  of  this  written  may  f u l f i l m e n t of the requirements f o r of British  available  be g r a n t e d  gain  of  University  Vancouver  8,  0 h p m i n>i 1 of British Canada  shall  that  copying  I agree and  thesis  Department or  that  Study.  of this  o f my  n o t be a l l o w e d  TV|gi r i p p r i r.g Columbia  copying  b y t h e Head  It i s understood  for financial  Columbia,  f o r reference  f o r extensive  permission.  Department The  i t freely  permission  by  thesis  in partial  or  publication  without  my  TABLE OF CONTENTS Page ACKNOWLEDGEMENT  i i i  ABSTRACT  iv  LIST OF TABLES  ,  LIST OF FIGURES  v vi  INTRODUCTION  1  EXPERIMENTAL  8  A  General  8  B  Preparation  C  S o l u t i o n s and Enzymes  D  Apparatus  11  E  Procedure  17  a) b) c)  Calibration C y c l i c S t r e s s F a t i g u e Method S t r e s s S t r a i n Method  17 17 19  d)  M e c h a n i c a l Behaviours of D e n t a l Wax  20  o f Sheep S k i n  EXPERIMENTAL RESULTS AND DISCUSSION  9 9  21  A  General  21  B  S t r e s s S t r a i n Method  22  C ' a)  C  Behaviours i n Tyrode S o l u t i o n  22  b) c) d)  Behaviours i n IN.CH^COOH and 0.IN.HC1 Behaviours i n Enzymes E f f e c t of Temperature  26 30 35  e)  Stress Strain Relationship  35  C y c l i c S t r e s s F a t i g u e Method  MODELLING AND SIMULATION OF SKIN BEHAVIOURS A  Modelling  B  Simulation  of S k i n Behaviours by an Analog Computer  38 47  51  CONCLUSIONS  67  RECOMMENDATIONS FOR FURTHER WORK  69  ii.  page LITERATURE CITED  70  APPENDIX A - MECHANICAL BEHAVIOURS OF DENTAL WAX  73  APPENDIX B - CALIBRATION RESULTS  87  APPENDIX C - STEPWISE REGRESSION METHOD  90  APPENDIX D - ONE WAY  95  CLASSIFICATION  APPENDIX E - FIGURES  101  APPENDIX F - SIMULATION CONSTANTS  131  iii.  ACKNOWLEDGEMENT S  I wish t o thank Dr. K. L. P i n d e r whose guidance t h i s study was made, during  t h e course o f t h i s  and Dr. G. J . P a r f i t t ,  under  f o r t h e i r encouragement and a s s i s t a n c e  project.  I a l s o wish t o thank the Workshop S t a f f f o r t h e i r p r o f i c i e n c y i n b u i l d i n g the required  apparatus t o t h e s p e c i f i c a t i o n s .  I am i n d e b t e d  t o the N a t i o n a l Research C o u n c i l o f Canada f o r  f i n a n c i a l a s s i s t a n c e r e c e i v e d and Department o f Chemical E n g i n e e r i n g and F a c u l t y o f D e n t i s t r y a t t h e U n i v e r s i t y o f B r i t i s h Columbia f o r a d d i t i o n a l support o f equipment and m a t e r i a l s .  iv.  ABSTRACT  The  mechanical properties  i n v e s t i g a t e d by  two  of sheep s k i n i n compression were  methods; a s t r e s s s t r a i n method and  a cyclic  stress  f a t i g u e method. I t was material and on  shown t h a t the  for small  loads,  s k i n behaves l i k e a l i n e a r v i s c o e l a s t i c  however, f o r l a r g e loads i t behaves  the s t r a i n i s e s s e n t i a l l y a l o g a r i t h m i c  function  the s k i n of treatment w i t h s e v e r a l s o l u t i o n s  and  of l o a d .  nonlinearly The  effect  enzymes were a l s o  investigated  and  characterized  statistically.  By  the  c y c l i c s t r e s s f a t i g u e method the dependency of sheep  skin on the p r e v i o u s h i s t o r y , which i s a x i o m a t i c f o r b i o l o g i c a l m a t e r i a l s , was  investigated  and  i t was  shown t h a t the  skin i s e s s e n t i a l l y a logarithmic Based on s k i n was  By  the s i m u l a t i o n  time.  of the model was  c a r r i e d out  comparing the e x p e r i m e n t a l d a t a w i t h the  r e s u l t s , the proposed model was results  of  the e x p e r i m e n t a l d a t a , a mechanical model f o r sheep  proposed and  analog computer.  function  f a t i g u e b e h a v i o u r o f sheep  satisfactorily.  shwon t o r e p r e s e n t the  using  simulation  experimental-'  an  V.  LIST OF TABLES  TABLE  Page.  1  The C o n c e n t r a t i o n and the K i n d o f S o l u t i o n s  2  The Composition o f the Tyrode S o l u t i o n  10  3  The S i z e o f Probes  15  4  R e g r e s s i o n C o e f f i c i e n t s i n Tyrode S o l u t i o n  25  5  R e g r e s s i o n C o e f f i c i e n t s i n IN.CR^COOH and i n 0.IN.HC1  29  6  R e g r e s s i o n C o e f f i c i e n t s i n Enzymes  32  7  The Values o f  33  tan,/C  and Enzymes  10  vi.  LIST OF FIGURES  FIGURE  Page  1  Diagram o f T o t a l Apparatus  12  2  Photograph of T o t a l Apparatus  13  3  Main Apparatus  14  4  Photograph o f Main Apparatus  13  5  P h o t o g r a p h i c View of A d d i t i o n a l Apparatus f o r S t r e s s S t r a i n Method  18  6  Load Compression Curves i n Tyrode S o l u t i o n  24  7  Load Compression Curves i n IN.CR^COOH  28  8  Load Compression Curves i n C o l l a g e n a s e  31  9  Stress Strain Relationship  37  10 - 12 F a t i g u e Curves  39 - 41  133  Load S t r a i n Relationship.--in F a t i g u e Method  42  14  F a t i g u e Curve i n IN.CH C00H  45  15  F a t i g u e Curve i n C o l l a g e n a s e  46  16  F a t i g u e Curve  48  17  A M e c h a n i c a l Model o f Sheep S k i n  50  18  Constant g e n e r a t i n g c i r c u i t  52  19  Force Generating C i r c u i t  53  20  Main C i r c u i t  54  21  S i m u l a t i o n o f the Model i n Tyrode S o l u t i o n  56  22  F a t i g u e Curve  57  23 - 24  3  S i m u l a t i o n of the Model i n Tyrode S o l u t i o n  59 - 62  25  S i m u l a t i o n o f the Model i n C o l l a g e n a s e  63  26  S i m u l a t i o n o f the Model f o r Ramp Input  65  vii.  FIGURE  Page  A - l - A-6  F a t i g u e Curves o f Wax  76 - 81  A-7  A M e c h a n i c a l Model o f D e n t a l Wax  82  A-8  Analog C i r c u i t  82  A-9 - A-12  S i m u l a t i o n o f D e n t a l Wax  E-l  Load Compression Curves i n 0.IN.HC1  102  E-2  Load Compression Curves i n P a p a i n  103  E-3  Load Compression Curves i n T r y p s i n  104  E-4  Load Compression Curves i n H y a l u r o n i d a s e  105  E-5 - E-10  F a t i g u e s Curves i n Tyrode S o l u t i o n  f o r Simulation  83-86  106 -  111  E - l l - E-12  F a t i g u e Curves i n IN.CH COOH  112 - 113  E-13 - E-14  F a t i g u e Curves i n 0.IN.HC1  114 - 115  E-15  F a t i g u e Curve i n C o l l a g e n a s e  116  E-16 - E-17  F a t i g u e Curve i n H y a l u r o n i d a s e  117 -  E-18 - E-19  F a t i g u e Curve i n P a p a i n  119 - 120  E-20 - E-21  F a t i g u e Curve i n T r y p s i n  121 -  122  E-22 - E-24  S i m u l a t i o n o f the Model i n Tyrode S o l u t i o n  123 -  128  E-25  S i m u l a t i o n o f the Model i n P a p a i n  118  129  v  INTRODUCTION  There are many problems i n medicine and  d e n t i s t r y , the s o l u t i o n s  of which r e q u i r e a d e t a i l e d knowledge of the m e c h a n i c a l p r o p e r t i e s of tissues involved.  In d e n t i s t r y t h e r e i s an urgent need f o r a d e t a i l e d  knowledge of the m e c h a n i c a l p r o p e r t i e s of the p e r i o d o n t a l membrane other with  the  related tissues.  This present  work was  initiated in  and  cooperation  the F a c u l t y of D e n t i s t r y to i n v e s t i g a t e some of the problems i n t h i s  field. When the term t i s s u e i s used, i t i s a g e n e r i c name of c e r t a i n organs which i n c l u d e s k i n , s k e l e t a l muscle, l u n g s , v e i n s , a r t e r i e s , e t c . , whose forms are determined by connective  tissue.  the presence of the  In s k i n , where the collagenous  s t r e n g t h are c o n d i t i o n e d mainly by  this  collagenous  connective  the g r e a t e r p a r t of the o r g a n i c substance, i t i s e v i d e n t  tendon  t i s s u e forms  that shape  and  component.  When c o n s i d e r i n g the m e c h a n i c a l p r o p e r t i e s of t i s s u e s i n which the c o l l a g e n o u s must be  connective  t i s s u e forms a l a r g e p a r t , t h r e e  components  taken i n t o c o n s i d e r a t i o n ; c o l l a g e n f i b r e s , e l a s t i c t i s s u e  amorphous ground substances combined w i t h n o n - c o l l a g e n  and  proteins.  However,  t h e r e i s great v a r i a n c e  i n the p r o p o r t i o n of these t h r e e  i n the v a r i o u s  For a d e t a i l e d d e s c r i p t i o n of the composition  organs.  s k i n , the book by  Chvapil  (7)  components  i s recommended.  In s k i n i t i s n e c e s s a r y to c o n s i d e r nonhomogeneity and anistropy  (8,  9).  of  Skin i s considered  to be  a complex of three  directional dimensional  meshwork of c o l l a g e n f i b r e s which demonstrate some measure of p r e f e r e n t i a l direction  (10).  However, no q u a n t i t a t i v e proof  of t h i s i s a v a i l a b l e .  2.  I t i s assumed t h a t f o r elements w i t h l i n e a r dimensions i n the order millimeters  the l o c a l nonhomogeneity w i l l be  ignored  the s k i n may  and  When one b o t h e l a s t i c and it  be  considered  considers  viscous  a n i s o t r o p i c i n o n l y two  be  dimensions.  p r o p e r t i e s , although the m a t e r i a l might  of v i s c o e l a s t i c i t y i s s t r i c t l y a p p l i e d Newton's law  the e l a s t i c component.  and may  a v i s c o e l a s t i c m a t e r i a l which possesses  a l s o e x h i b i t s a c e r t a i n storage  can be  averaged out  On  of energy.  The  a p p l i c a b l e only  f o r the v i s c o u s the b a s i s  of the  flow  classical linear  to those m a t e r i a l s  component and  example, f o r the s t a t i c measurements, t h e r e  e t c . , and  l i n e a r theory,  49),  The  are s t r a i n c y c l i c and  51)  hysteresis  forced v i b r a t i o n  etc.  considers  p a t h o l o g i c a l c o n d i t i o n s , an u n d e r s t a n d i n g  abnormal s t r e s s s t r a i n r e l a t i o n s h i p of t i s s u e s  as a t o o l f o r d i f f e r e n t i a l d i a g n o s i s . i n blood  For  s t r e s s s t r a i n r e l a t i o n s h i p i s of fundamental i n t e r e s t .  example, when one the normal and  for  are s t r e s s r e l a x a t i o n methods  methods (51), c y c l i c s t r e s s f a t i g u e method (51) method (48,  to which  many methods  (51), creep d e f o r m a t i o n w i t h f i x e d s t r e s s (50,  f o r the dynamic measurements t h e r e  theory  HookeS law  have been developed t o i n v e s t i g a t e the v i s c o e l a s t i c p r o p e r t i e s .  under f i x e d s t r a i n  of  vessels, d i s t e n s i b i l i t y  (6) may  For of serve  In hemodynamics, wave p r o p a g a t i o n  of a r t e r i e s and  veins  and  the s t r e s s  strain  r e l a t i o n s h i p of t i s s u e s must be measured. A considerable by  i n v e s t i g a t o r s who  tissues  (1, 2,  prevails.  The  3, 4,  amount of e x p e r i m e n t a l d a t a has  been  published  have attempted to measure the m e c h a n i c a l p r o p e r t i e s 5,  16), but  main d i f f i c u l t i e s  a degree o f vagueness and l i e i n the  customary use  of  uncertainty  of the  infinitesimal  3.  theory of e l a s t i c i t y The  to media which n o r m a l l y e x h i b i t  h i g h degree of n o n l i n e a r i t y  tissues  i n the  concepts of the  l i n e a r theory of e l a s t i c i t y  tension  Daly (11)  and  have s t u d i e d  have u t i l i z e d  that  the  Fung (12)  simple e l o n g a t i o n .  He  exponential function have s t u d i e d  (13,  14,  studied the  the  divided  i n t o t h r e e phases  and  e l a s t i c i t y of t i s s u e i n nearly  an Other authors  i n e x t e n s i o n , f o r example, s k e l e t a l muscle,  15).  Similar  r e s u l t s have been found f o r  Therefore, i t  i s meaningless to s t a t e Young's modulus of a p a r t i c u l a r t i s s u e u n l e s s For  it  a n y t h i n g between zero to 5 x 10  i s o b v i o u s l y n e c e s s a r y to s p e c i f y  f o r the number to have any  meaning.  the  example, f o r the m e s e n t e r i c membrane, 6  Young's modulus can be  the  These e x p e r i m e n t a l r e s u l t s  the v a r i a t i o n i n Young's modulus i s v e r y g r e a t .  l e v e l of s t r a i n i s a l s o s t a t e d .  one,,  phase t h r e e ,  lower s t r e s s range.  s t r a i n r e l a t i o n s h i p of these t i s s u e s .  show t h a t  Ridge  of s k i n i n e x t e n s i o n .  t e n s i l e s t r e s s was  s t r a i n i n the  different tissues  h e a r t muscle, e t c . stress  of the  field.  to c o r r e l a t e t h e i r data.  a power f u n c t i o n  has  found t h a t  material  l o a d e x t e n s i o n r e l a t i o n s h i p ; phase  phase two  the  s t r e s s s t r a i n r e l a t i o n s h i p of s k i n i n  the m e c h a n i c a l p r o p e r t i e s  following  an e x p o n e n t i a l f u n c t i o n , mechanical f a i l u r e .  been aroused i n t h i s  e x t e n s i o n p r o c e s s c o u l d be  f o r which they gave the  a p p l i c a t i o n of  presentation.  a power f u n c t i o n  and Weight (9) have s t u d i e d They s t a t e d  the  The  to a h i g h l y n o n l i n e a r  In r e c e n t y e a r s more i n t e r e s t has Kenedi and  of  a t h e o r e t i c a l framework i n which  imbedded i s l a c k i n g .  l e a d to a c e r t a i n inadequacy i n d a t a  deformations.  stress s t r a i n relationship  i s known t o most authors ( 6 ) , but  e x p e r i m e n t a l r e s u l t s can be  finite  on  the  2 dyne/cm ,  the  point  But  on many o c c a s i o n s  and  curve r e f e r r e d  to,  (4, 5 ) , a s i n g l e  n u m e r i c a l Young's modulus i s g i v e n without an accompanying statement  ex-  4.  concerning  the l e v e l s o f s t r e s s and s t r a i n .  An excuse f o r t h i s s i t u a t i o n  perhaps i s t h a t the p h y s i o l o g i s t has a " t y p i c a l o r "average" c o n d i t i o n of the t i s s u e s i n mind and t h e p u b l i s h e d  modulus r e f e r s t o such a s t a t e .  But w i t h o u t a s u i t a b l e q u a n t i t a t i v e d e f i n i t i o n o f the t y p i c a l i n v o l v e d , the vagueness and c o n f u s i o n As  conditions  o f such an approach i s o b v i o u s .  an a l t e r n a t i v e , some.authors (6) p u b l i s h e d  e n t i r e experimental  The  d i f f i c u l t i e s i n t h i s approach a r e t w o f o l d ;  and  no simple way t o c o r r e l a t e the curves w i t h other  curves.  a cumbersome documentation p h y s i c a l or  p h y s i o l o g i c a l parameters. Some i n v e s t i g a t o r s have s t u d i e d i n d i v i d u a l t i s s u e components;  the m e c h a n i c a l p r o p e r t i e s o f  c o l l a g e n f i b r e s (20, 21, 22, 23, 2 4 ) ,  e l a s t i c f i b r e s (27) , and ground substances combined w i t h n o n c o l l a g e n proteins  (25, 2 6 ) . They c h a r a c t e r i z e d t h e c o l l a g e n f i b r e s as h a v i n g poor  e l a s t i c i t y b u t great m e c h a n i c a l s t r e n g t h .  The e l a s t i c  fibres, i n  combination w i t h c o l l a g e n and m u c o p o l y s a c c h a r i d e s , a l l o w a l a r g e range c o n t r o l o f r e v e r s i b l e d e f o r m a b i l i t y o f the s o f t t i s s u e framework o f the body ( 7 ) .  Ground substances a r e c o n s i d e r e d  e l a s t i c i t y of c e r t a i n connective  t o be a d e c i s i v e f a c t o r i n the  tissue structures  (7), p a r t i c u l a r l y  that  of c a r t i l a g e . However, many people r e c o g n i z e d the m e c h a n i c a l f u n c t i o n s reported  that i t i s d i f f i c u l t to separate  o f each component i n s k i n ( 7 ) .  t h a t one p o s s i b l e f u n c t i o n o f h y a l u r o n i c  i s t o produce a combined s t r u c t u r e o f h y a l u r o n i c  F e s s l e r (28)  a c i d i n connective  tissue  a c i d , water and c o l l a g e n  f i b r e s which has a d e f i n i t e r e s i s t a n c e t o compression, and Ogston (29) reported  am' i n t e r a c t i o n between p o l y s a c c h a r i d e s  and other  macromolecules.  5.  B e s i d e the i n t e r a c t i o n of mucopolysaccharides w i t h c o l l a g e n s , e t c . ,  the  ;a:morphous substance of m o l e c u l a r mucopolysaccharides, c o v e r i n g i n d i v i d u a l c o l l a g e n f i b r e s and h a v i n g the same p r o p e r t i e s as g e l or l u b r i c a n t , makes s l i p p a g e between the c o l l a g e n f i b r e s p o s s i b l e ( 7 ) .  Although the  f i b r e s are g e n e r a l l y supposed to be i n s o l u b l e i n o r g a n i c s o l u t i o n s and  only the enzyme, collagenase,.can  Borustein  (30)  reported  peptides,  amides and  or  collagen  inorganic  d i g e s t the c o l l a g e n  fibres,  t h a t the t r y p s i n and p a p a i n , which mainly d i g e s t  e s t e r s of s k i n , a l s o a f f e c t e d c o l l a g e n by  c e r t a i n bonds of the c o l l a g e n m o l e c u l e s .  Some authors (31,  breaking  32)  reported  t h a t t h e r e were a c i d s o l u b l e c o l l a g e n f i b r e s , which d i s s o l v e mainly i n acetic acid.  Partington  and Wood (25)  showed t h a t the h y a l u r o n i d a s e ,  digests m a i n l y the ground substances of s k i n , had mechanical strength  as i n d i c a t e d hy  agree w i t h 'Fessler's s u g g e s t i o n  s t a b i l i z a t i o n of c o l l a g e n f i b r e s .  34,  (17,  18,  c o n d i t i o n s , I.e.  19)  and not w e l l known  /1000 HC1,  N  /10  HC1  s t u d i e d the s w e l l i n g of p r o t e i n f i b r e s under  i n organic  i n s o l u t i o n s which d i d not N  a c i d p a r t i c i p a t e s i n the  35). Lloyd  various  T h i s does not  However, the d e f i n i t e e f f e c t s of each  enzyme on the t i s s u e components are complicated (32,  no i n f l u e n c e upon i t s  s t r e s s s t r a i n curves.  that h y a l u r o n i c  which  and  inorganic solutions.  induce a c o n t r a c t i o n i n f i b r e l e n g t h  + 2k~NaCl, e t c ) the e l o n g a t i o n  i s the same as i n water.  He  With s o l u t i o n s  (such  found t h a t (such  as  of the f i b r e s under l o a d  as ^/100  HC1, IN'JCH^GOOH,  N /20  NaOH, e t c . ) which induce a c o n t r a c t i o n i n l e n g t h , however, t h i s  c o n t r a c t i o n i s always a s s o c i a t e d w i t h an i n c r e a s e i n w i d t h and volume. g a i n i n volume i s brought about by a b s o r p t i o n  of water due  The  to osmotic f o r c e s .  The  first  e f f e c t s of l o a d i n g such water d i s t e n d e d  out  the o s m o t i c a l l y absorbed waters w i t h a r e s u l t a n t g a i n i n l e n g t h  loss i n width. He  Elden  (45)  s t u d i e d .the h y d r a t i o n  f i b r e s i s to squeeze  of c o n n e c t i v e  and  tissue.  s t a t e d t h a t k i n e t i c a n a l y s i s of tendon s w e l l i n g i n water r e v e a l e d  a d i s p e r s i o n f a c t o r and  a cohesive  the v e l o c i t y of s w e l l i n g and  f a c t o r were p r e s e n t  to tendon weight.  He  that  which were, r e l a t e d t  concluded  that  f l e x i b i l i t y of tendon i s very, s e n s i t i v e to s o l u t i o n parameters. Many i n v e s t i g a t o r s have t r i e d to develop mathematical models of b i o l o g i c a l materials.  V. van  del Pol  e q u a t i o n to d e s c r i b e n o n l i n e a r proposed a more g e n e r a l i z e d  (39)  Some authors t r i e d  and  proposed a  "relaxation oscillators".  Subject  the n o n l i n e a r  Becker  to develop the mathematical models of the (40,  41).  t h e i r models on the assumption t h a t the m a t e r i a l s  describe  (39)'  Fitzhugh  on an analog computer by N e l s o n and  of the t i s s u e s of the human eye  viscoelastic solids.  differential  e q u a t i o n f o r t h e o r e t i c a l membrane models.  These e q u a t i o n s were s i m u l a t e d (38) .  (36)  Generally  aorta  However, they based behave l i k e  linear  the d i f f e r e n t i a l e q u a t i o n s or models which  v i s c o e l a s t i c b e h a v i o u r can be  (46,  developed  47).  to the c o r r e c t boundary c o n d i t i o n s , these e q u a t i o n s w i l l g i v e  response of the m a t e r i a l to any real materials the v a l u e s  imposed s t r e s s or s t r a i n .  the e q u a t i o n s are d i f f i c u l t  can be  i d e a l i z e d m e c h a n i c a l models or a n a l o g i e s  However, f o r  to s o l v e , even assuming t h a t  of the r e l e v a n t parameters can be Much q u a l i t a t i v e i n f o r m a t i o n  the  derived derived  from e x p e r i m e n t a l d a t a from a study o f  which are designed to d u p l i c a t e ,  more or l e s s c l o s e l y , the observed b e h a v i o u r of r e a l m a t e r i a l s . b e h a v i o u r i s more e a s i l y v i s u a l i z e d than t h a t of the m a t e r i a l  Thus, t h e i  itself.  7.  Models a r e made up o f combinations o f Hookean s p r i n g s and Newtonian dash-pots.  The s p r i n g s and dash-pots i n a model r e p r e s e n t t h e e l a s t i c  and v i s c o u s p r o p e r t i e s o f t h e ' m a t e r i a l .  The b a s i c element  i n any  mechanical model i s a p a r a l l e l combination o f s p r i n g and dash-pot, known as a V o i g t element, Maxwell element.  and a s e r i e s combination o f these two i s known as a  These b a s i c elements r e p r e s e n t t h e b e h a v i o u r o f  idealized materials.  Real materials w i l l  c o n s i s t o f a more o r l e s s  c o m p l i c a t e d combination o f these b a s i c elements.  R e c e n t l y , Sobtka (43)  proposed n o n l i n e a r V o i g t and Maxwell models t o s i m u l a t e simple second o r d e r effects. However, m e c h a n i c a l s i m u l a t i o n models o f b i o l o g i c a l t i s s u e s a r e scarce.  Alexander  i n muscle.  (42) has proposed  a model f o r t h e m e c h a n i c a l components  H i s approach was, however, o n l y q u a l i t a t i v e .  has proposed a model f o r the p e r i o d o n t a l membrane, which V o i g t elements  o f dash-pot  and s p r i n g .  He attempted  P a r f i t t (44) consisted of three  to simulate h i s  bio'ilogical d a t a by t h i s model on an a n a l o g computer, u s i n g e i g h t parameters.  He a l s o t r i e d s i m i l a r models i n which  parameters had an e x p o n e n t i a l f u n c t i o n .  linear  one o r more o f the  8.  EXPERIMENTAL  A.  General The  objectives  of t h i s study are to measure the n o n l i n e a r  s t r a i n h i s t o r y r e l a t i o n s h i p during s k i n and t o propose was  l a r g e compressive  deformations  a mechanical model of i t s b e h a v i o u r .  stress  i n sheep  The word " h i s t o r y "  added here t o s i g n i f y the dependence o f the s t r a i n on the p r e v i o u s  h i s t o r y of the s t r e s s , as i s u s u a l l y However, i t i s not the purpose data;  the case f o r b i o l o g i c a l m a t e r i a l s .  o f the p r e s e n t work to d e t a i l the b i o l o g i c a l  the scope i s l i m i t e d t o the a n a l y t i c a l a s p e c t s .  the e x p e r i m e n t a l d a t a can be c h a r a c t e r i z e d then these parameters properties  can be t a b u l a t e d  T h i s means t h a t i f  m a t h e m a t i c a l l y by a few  and used  to c o r r e l a t e the  parameters,  mechanical  of sheep s k i n w i t h the c h e m i c a l and enzymic environments  and  temperature. The properties  The  e x p e r i m e n t a l program was  of sheep s k i n i n compression  designed to i n v e s t i g a t e the by the f o l l o w i n g  1)  To get the s t r e s s s t r a i n c u r v e s .  2)  To get the c y l i c s t r e s s f a t i g u e  e x p e r i m e n t a l apparatus was  designed so t h a t  the two  Most o f the p r e v i o u s authors have s t u d i e d  properties  of t i s s u e s i n e l o n g a t i o n  1.  approaches:  curves.  possible.  approach  two  mechanical  approaches  were  the mechanical'  but not i n compression  and have employed  However, the h i s t o r y dependency of sheep s k i n , which i s  axiomatic f o r a l l b i o l o g i c a l materials, T h e r e f o r e , approach  2 was  was  not fourild by t h i s method.  a l s o used t o t e s t the h i s t o r y dependency.  method i s a l s o v e r y convenient  f o r t e s t i n g the model o f the  behaviours on an analog computer.  This  mechanical  B.  P r e p a r a t i o n o f Sheep S k i n A l a r g e sample  o f s k i n from the abdomen o f a sheep was o b t a i n e d  w i t h i n a few hours o f the sheep's death and the f a t was T h i s sample was  f r o z e n i n the deep f r e e z e of the Department  at the U n i v e r s i t y of B r i t i s h Columbia. to remove the wool. 0.1  inches.  sample  of Physiology  A G i l e t t e s a f e t y r a z o r was  The t h i c k n e s s o f the s k i n was  used  on the average about  Samples to be used i n an experiment were cut from the f r o z e n  j u s t p r i o r to use.  These were u s u a l l y 3 - 4  S i n c e the s k i n from one a r e a o f a s i n g l e sheep was all  c a r e f u l l y removed.  c e n t i m e t e r s square. used i n a l l experiments,  t e s t samples were v e r y s i m i l a r w i t h each o t h e r except f o r l o c a l  nonhomogeneities. C.  S o l u t i o n s and Enzymes The c o n c e n t r a t i o n and the k i n d s o f s o l u t i o n s and enzymes used i n  t h i s experiment to t e s t t h e i r s p e c i f i c e f f e c t s , are shown i n T a b l e 1. Tyrode s o l u t i o n i s a m o d i f i e d T a b l e 2.  U s u a l l y samples  Lock's s o l u t i o n , i t s c o m p o s i t i o n i s shown i n  of the s k i n were immersed i n t h i s s o l u t i o n f o r ;  a s p e c i f i e d t time b e f o r e t e s t i n g the e f f e c t s o f o t h e r s o l u t i o n s and enzymes. T h i s s o l u t i o n i s s i m i l a r i n n a t u r e t o the body f l u i d s and i s used to r e t u r n the f r o z e n s k i n t o i t s normal and n a t u r a l S o l u t i o n s o f IN.CH^COOH and 0.1N  state. HC1,  were used to i n v e s t i g a t e  the s w e l l i n g o f p r o t e i n s so t h a t the r e s u l t s c o u l d be compared to those o f Lloyd  (17, 18, 19). The f o l l o w i n g commercial p r e p a r a t i o n o f enzymes produced by  " N u t r i t i o n a l B i o c h e m i c a l s C o r p o r a t i o n " , C l e v e l a n d , Ohio, were used to t e s t the m e c h a n i c a l p r o p e r t i e s of t i s s u e  components.  10.  Collagenase;  Source, CL h i s t o l y t i c u m , and  containing  some p r o t e i n s and  peptides.  Trypsin;  Prepared p e r Kunze e t . r e f . J . Gen. P h y s i o l . , 19, 991, 1936  Papain;  Source, papaya.  Hyaluronidase;  Source, Bovine t e s t e s , Depolymerized h y a l u r o n i c  TABLE 1 The c o n c e n t r a t i o n  and the k i n d s of s o l u t i o n s  Names  and enzymes.  C o n c e n t r a t i o n i n Water  Tyrode s o l u t i o n Acetic  acid  Hydrochloric  1 N acid  0.1 N  Collagenase  0.1 wt.%.  Trypsin  0.05 wt.%.  Papain  0.2 wt.%.  Hyaluronidase  300 u n i t s per m i l l i g r a m  TABLE 2 Composition o f the t y r o d e s o l u t i o n . Components NaCl  Weights i n 10 L i t e r s 80.0 gm.  KC1  2.0  CaCl„  2.0  MgCl,  1.0  i  NaH P0 2  NaHC0„  4  0.5 10.0  acid.  11.  D.  Apparatus The  experimental  equipment;, used f o r t h i s work i s shown  s c h e m a t i c a l l y i n F i g u r e 1, and a photograph i s shown i n F i g u r e 2. main apparatus F i g u r e 4.  was c o n s t r u c t e d as shown i n F i g u r e 3 and i n the photograph  T h i s apparatus  displacement  The  transducer,  i n c l u d e s a f o r c e t r a n s d u c e r , symbol 1, a l i n e a r symbol 2, a h e a t i n g c o i l , symbol 7, an arm,  symbol 4, a v e s s e l , symbol 6, and an arm s u p p o r t , symbol 3 i n F i g u r e 3 respectively. The  P r i n c i p l e o f the f o r c e t r a n s d u c e r , made by D a y t r o n i c  C o r p o r a t i o n model 152A-5, i s as f o l l o w s ;  the d e f l e c t i o n o f a unique  diaphragm s p r i n g , i n t e g r a l l y machined from a l l o y s t e e l , i s measured by a s e n s i t i v e d i f f e r e n t i a l t r a n s f o r m e r element. and  was  o f 51bs.  f o r weights l e s s than Q51hs the s p r i n g movement i s i n the order o f  -3 10  I t has a l o a d l i m i t  -4 - 10  m i l l i m e t e r s and may be c o n s i d e r e d n e g l i g i b l e .  c a r r i e d out w i t h i n t h i s The  The experiment  range.  l i n e a r displacement  t r a n s d u c e r , made by Crescent  Technology  C o r p o r a t i o n type ZT>25, was a e l e c t r o m e c h a n i c a l v a r i a b l e permeance  instrument  i n which the a.c.  c u r r e n t was p r o p o r t i o n a l t o the probe displacement  a null position.  The maximum a l l o w a b l e displacement  The midpoint  probe o f the l i n e a r displacement  of the support  connected  arm.  from  was 0.25 i n c h e s .  t r a n s d u c e r was s e t a t t h e  The probe and the u p r i g h t arm support were  a g a i n by a b a r , symbol 9 i n F i g u r e 3, which was p a r a l l e l and  about 5 m i l l i m e t e r s below the support  arm.  These c o n n e c t i n g p o i n t s  i n c l u d i n g the arm s u p p o r t i n g p o i n t , were moveable and made up the f o u r vertices of a parallelogram.  T h i s arrangement made i t p o s s i b l e t o keep the  Constant Temperature Bath i i J|  Transduce  i i  L  a in  !xc i t e r  Amplifier  Apparatus  Strip  FIGURE  I  Diagram.of  Total  Apparatus  Chart  r  rat  2  FIGURE 2  Photograph o f T o t a l Apparatus  FIGURE 4  Photograph o f Main Apparatus  FIGURE 3  Main Apparatus  15.  probe o f t h e l i n e a r t r a n s d u c e r always v e r t i c a l  ( p a r a l l e l to the upright  support) d u r i n g t h e movement o f the arm. The probes, symbol  5 i n F i g u r e 3, which were used i n t h i s  apparatus a r e l i s t e d i i n T a b l e 3.  Usually, probe  (P-3) was used, but the  o t h e r probes were a l s o used t o t e s t the s t r e s s s t r a i n  relationships.  TABLE 3 The s i z e o f probes. 2 Symbol  Diameter  (mm.)  Area (mm )  P-l  10.02  79.06  P-2  4.94  19.15  P-3  3.97  12.40  P-4  1.98  3.08  The l e n g t h of the arm, i n which c e n t i m e t e r s from the s u p p o r t .  the probe was held,was,about  24  T h i s l e n g t h was long enough t h a t i t was  p o s s i b l e t o n e g l e c t the h o r i z o n t a l displacement o f the probe s i n c e the v e r t i c a l movement o f the probe was always l e s s then 0.2 c e n t i m e t e r s . A r o l l e r b e a r i n g was s e t a t the s u p p o r t i n g p o i n t o f the arm t o reduce the f r i c t i o n o f the arm movement. symbol  A s c r e w - a d j u s t e d counter-weight,  8 i n F i g u r e 3, was used t o c o n t r o l the i n i t i a l  load.  U s u a l l y , • ^ . c a l i b r a t e d a n a l y t i c a l b a l a n c e weights were used f o r f o r c e s s m a l l e r than 100 grams, b u t s p e c i a l weights o f 100 grams, 200 grams, and 500 grams, made from bronze were used i n f a t i g u e experiments when l a r g e f o r c e s were n e c e s s a r y . C e n t e r i n g marks were drawn above the probe on the support arm so t h a t the weights c o u l d be s e t c o n s i s t e n t l y on a d e f i n i t e p o s i t i o n on the..arm.  16.  D u r i n g an experiment a sample o f the sheep s k i n was p l a c e d on the s o l i d base i n t h e v e s s e l o f the main apparatus under the t e s t  solution  at a c o n s t a n t temperature and was h e l d down by a s t a i n l e s s s t e e l r i n g 3 cm. i n t e r n a l diameter by 4 cm. e x t e r n a l diameter, symbol  10 i n F i g u r e 3.  The  compressive movement o f the s k i n and the magnitude o f the a p p l i e d f o r c e were t r a n s m i t t e d both t o the l i n e a r t r a n s d u c e r and the f o r c e t r a n s d u c e r r e s p e c t i v e l y . The s i g n a l d  from the l i n e a r t r a n s d u c e r was a m p l i f i e d by an  a m p l i f i e r , model 85-N-4 made by C r e s c e n t Technology C o r p o r a t i o n .  This  a m p l i f i e r was t r a n s i s t o r i z e d c a r r i e r a m p l i f i e r , maximum output =10vd.c.  An  amplitude s e t t i n g o f one hundred was u s u a l l y used throughout the experiment. The output from the a m p l i f i e r was t r a n s m i t t e d t o a s t r i p c h a r t r e c o r d e r f o r the s t r e s s f a t i g u r e experiments and t o an X Y r e c o r d e r f o r s t r e s s experiment.  strain  The s t r i p c h a r t r e c o r d e r , a HoneywellFJectronik 19, was used w i t h  a c h a r t speed o f 10 s e c / i n c h and a s e n s i t i v i t y o f 50 mv/chart  width.  The s i g n a l from the f o r c e t r a n s d u c e r was t r a n s m i t t e d t o the t r a n s d u c e r e x c i t e r demodulator; model 201B, made by D a y t r o n i c C o r p o r a t i o n . T h i s i s a s o l i d s t a t e s i g n a l c o n d i t i o n i n g instrument which  a l l o w s the  adaptation of d i f f e r e n t i a l transformer transducers to s t r i p chart and X Y r e c o r d e r s r e q u i r i n g d.c. i n p u t  recorders  signals.  The output o f the t r a n s d u c e r e x c i t e r demodulator were t r a n s m i t t e d to an X Y r e c o r d e r , model 7035A, made by the Hewlett Packard Mosely  Division,  Input ranges o f 1 mv - 20 mv/inch were used on the X Y r e c o r d e r . To c o n t r o l the temperature o f the l i q u i d was  i n which a t e s t  sample  immersed, c o n s t a n t temperature water*from a model NB C o l o r a bath was  c i r c u l a t e d through a copper immersion  c o i l i n the l i q u i d . The c o n s t a n t  17.  temperature b a t h was  designed' to m a i n t a i n s e l e c t e d c o n s t a n t temperatures  i n the range between - 6 0 °  c  and 180°  near the body temperature, was  c  .  A temperature of 3 7 . 2 °  C  , which i s  m a i n t a i n e d throughout the experiments.  To get the s t r e s s s t r a i n curves an a d d i t i o n a l e x p e r i m e n t a l instrument was  used.  I t s photograph i s shown i n F i g u r e 5.  up from a s t a n d , a f u n n e l and a beaker. r a t e , f i n e sand  T h i s was  made  To l o a d a specimen at a c o n s t a n t  (Ottawta sand, average mesh 20,  s p e c i f i c g r a v i t y 1.68)  was  poured i n t o the f u n n e l c o n t i n u o u s l y , the sand dropped i n t o the beaker on the support arm c o n t i n u o u s l y to l o a d the specimens: at a c o n s t a n t r a t e .  The  measured 10  found to  r a t e of weight a d d i t i o n was be 3.27 E.  times and the average was  i=0.01 ^ / s e c . i n these experiments.  Procedure a)  Calibration.  The c a l i b r a t i o n o f the l i n e a r t r a n s d u c e r arid the f o r c e t r a n s d u c e r was  c a r r i e d out w i t h a f e e l e r gauge and c a l i b r a t e d weights  The i n p u t v e r s u s output curves were found to be s t r a i g h t e q u a t i o n s were f i t t e d  respectively.  l i n e s so l i n e a r  t o each curve by the l e a s t square f i t t i n g method.  The d a t a and the c a l i b r a t i o n r e s u l t s are shown i n Appendix B b)  S t r e s s c y c l i c f a t i g u e method.  The f o l l o w i n g g e n e r a l procedure was was  used throughout t h i s s e t o f experiments.  displacement t r a n s d u c e r was i)  c a r r i e d out and probe The s i g n a l from the  r e c o r d e d by the s t r i p c h a r t  linear  recorder.  The p r e p a r e d sheep s k i n sample from the r e f r i g i r a t o r  put i n t o the t y r o d e s o l u t i o n at 3s?. 2 ° ^  (P-3)  was  f o r a p p r o x i m a t e l y two  a h a l f hours to a l l o w the s k i n t o r e t u r n to i t s n a t u r a l  and  state.  FIGURE 5  P h o t o g r a p h i c View of A d d i t i o n a l For S t r e s s S t r a i n Method  Apparatus  19.  ii)  The sample was s e t on the main apparatus i n the t y r o d e  s o l u t i o n and i t s t h i c k n e s s was measured by means o f the l i n e a r displacement iii)  transducer.  Watching  the stopwatch, a weight was put on the marked  p o s i t i o n on the support arm f o r f i v e seconds and then removed f o r f i v e seconds r e s p e c t i v e l y iv)  f o r about 15 c y c l e s .  Procedure ( i i i ) was c a r r i e d out w i t h the f o l l o w i n g  5, 10, 20, 30, 40, 50, 60, 80, 100, and 200 grams. of the probe on the s k i n was changed  and the i n i t i a l  weights  The p o s i t i o n t h i c k n e s s was  measured by means o f the l i n e a r t r a n s d u c e r a t the s t a r t o f each test. v)  A f t e r procedure ( i v ) i n t y r o d e s o l u t i o n , the s k i n was immersed  i n one o f the s o l u t i o n s  f o r the s p e c i f i e d times.  Solutions  (IN CR^COOH, 0.1N HC1);  Enzymes ;  12 h o u r s .  vi)  Procedure ( i i ) ,  immersed i n t h e new vii)  A new sample  40 minutes  ( i i i ) arid ( i v ) were c a r r i e d out w i t h t h e s k i n solutions.  o f sheep s k i n on which the t y r o d e b l a n k was  run was used f o r each s o l u t i o n and the p o s i t i o n of the probe" c a r e f u l l y c o n t r o l l e d so as not t o compress  was  the same p o s i t i o n on  which an experiment have a l r e a d y been done. 2.  S t r e s s s t r a i n method A s i m i l a r procedure as d e s c r i b e d i n s e c t i o n  the  loading  procedure ( i i i ) and ( i v ) .  (P-3) was m a i n l y used but o t h e r probes  (b) was used except f o r  They were changed as f o l l o w s . ( P - l , P-2, P-4) were a l s o  Probe  tested.  20.  S i g n a l s from both the displacement t r a n s d u c e r and the f o r c e t r a n s d u c e r were r e c o r d e d on the X Y r e c o r d e r . iii)  U s i n g the a d d i t i o n a l equipment shown i n F i g u r e 5, the  sand was  added c o n t i n u o u s l y to the f u n n e l and dropped  i n t o the  beaker on the l o a d i n g arm at the c o n s t a n t r a t e . iv)  Procedure  solution.  ( i i i ) was  The p o s i t i o n of the probe was  the t h i c k n e s s was d.  c a r r i e d out f o u r or f i v e times f o r each  measured by means of the l i n e a r t r a n s d u c e r .  M e c h a n i c a l b e h a v i o u r s of d e n t a l S i m i l a r procedures  d e n t a l wax behaviour.  to t e s t  wax.  (i) - (iv) i n section  h e l d c o n s t a n t except f o r the temperature  the sample of wax  was  immersed.  m e c h a n i c a l b e h a v i o u r and o f the s i m u l a t i o n of wax Appendix  A.  (b) were c a r r i e d out f o r  the apparatus and a l s o to i n v e s t i g a t e i t s m e c h a n i c a l  The environment was  the water i n which  changed each time and  R e s u l t s of both the model are shown i n  of  21.  EXPERIMENTAL RESULTS AND  A.  DISCUSSION  General A l l the r e s u l t s were o b t a i n e d i n g r a p h i c a l form by r e c o r d i n g the  displacement w i t h time f o r the c y c l i c s t r e s s f a t i g u e method and displacement  the  and l o a d f o r the s t r e s s - s t r a i n method.  B e f o r e t a l k i n g about  e x p e r i m e n t a l r e s u l t s , however, one  thing  which must always be kept i n mind i s t h a t i n b i o l o g i c a l experiments, i t i s very d i f f i c u l t  to get r e p r o d u c i b l e data.  i n the l o a d compression of s k i n to the next.  Rather wide v a r i a t i o n s  curves f o r sheep s k i n were found  from one p i e c e  T h i s f a c t would p r e c l u d e any p r e c i s e assessment of  the e f f e c t o f any treatment w i t h a p a r t i c u l a r  solution.  T h e r e f o r e , s t a t i s t i c a l a n a l y s i s has been employed to c h a r a c t e r i z e the e f f e c t s o f any s o l u t i o n .  Two  methods were used  f o r a n a l y s i n g the  data:  The  1)  Stepwise  2)  One way  r e g r e s s i o n method (52,  53)  c l a s s i f i c a t i o n method w i t h a n a l y s i s of v a r i a n c e (54).  computing program f o r the stepwise r e g r e s s i o n method i s a v a i l a b l e at the  U n i v e r s i t y o f B r i t i s h Columbia  computing c e n t e r .  stepwise r e g r e s s i o n (U.C.L.A.).  T h i s program was  I t i s c a l l e d BMD02R o r i g i n a l l y w r i t t e n at  the Department o f P r e v e n t i v e M e d i c i n e , U.C.L.A., and m o d i f i e d f o r use at the U.B.C. computing c e n t e r .  T h i s method does a l e a s t squares  f i t on  any  s e t of d a t a and c a l c u l a t e s r e g r e s s i o n c o e f f i c i e n t s by a stepwise method. A t y p i c a l i n p u t and output o f t h i s program i s shown i n Appendix C.  22  The observations  one  way  c l a s s i f i c a t i o n method i s a way  according  to one  to c l a s s i f y a s e t of  c r i t e r i o n , so t h a t the t o t a l v a r i a t i o n  between the numbers of the s e t can be broken up  i n t o components which  can be a t t r i b u t e d to the d i f f e r e n t c r i t e r i a of c l a s s i f i c a t i o n . d i s t r i b u t i o n i s used to t e s t the s i g n i f i c a n c e l e v e l . about t h i s method, see B.  Stress  the book by Bennet and  The  F  For more d e t a i l s  Franklin  (54).  S t r a i n Method a)  Behaviours i n Tyrode S o l u t i o n  S k i n i s supposed to r e t u r n to i t s n a t u r a l s t a t e when soaked i n tyrode  s o l u t i o n (P.H.  p r o p e r t i e s i n tyrode  = 8.6).  Therefore,  the a n a l y s i s of the  s o l u t i o n i s most important and  skin's  fundamental.  Typical  o l o a d compression curves of a sample a t 37.2 at v a r i o u s  p o i n t s are shown i n F i g u r e  v a r i a t i o n i n l o a d compression c u r v e s , thickness  6.  C with s i m i l a r  One  can  allowing  thicknesses  see a r a t h e r wide  f o r the f a c t t h a t  the  of s k i n i n each experiment i s s l i g h t l y d i f f e r e n t . However, there were some i n t e r e s t i n g p o i n t s which were common  f o r a l l of the curves. experimental curves, lOg.  One  p o i n t was  t h a t w i t h i n the a c c u r a c y of  a s t r a i g h t l i n e r e g i o n i s found to a l o a d of about  Hence the s k i n approximates a constant But  are no  longer  f o r weights l a r g e r than 10g.,  Young's modulus i n t h i s  the l o a d compression curves  s t r a i g h t l i n e s , i . e . , the Young's modulus i s not  To a n a l y s e the b e h a v i o u r s of curves between lOg. and r e g r e s s i o n method has  been used.  r e g i o n have been chosen and the i n i t i a l various  thickness  Eighteen  points  225g. the  constant. stepwise  on curves w i t h i n  the displacement at each p o i n t was  of the s k i n .  e q u a t i o n was  this  divided  A f t e r t r i a l s on the computer,  f u n c t i o n s , the f o l l o w i n g g e n e r a l  region.  using  found to f i t the  by  23.  set  of points best w i t h i n t h i s y =  where:  y:  A l  /lo = a + b in x  the  16:  displacement  initial  x:  weight  a,b:  thickness (g)  constants  Equation  (1) shows t h a t the s t r a i n of the s k i n i n compression i s  essentially a logarithmic  and  (1)  the s t r a i n i n compression  Al:  very  region:  f u n c t i o n o f the l o a d a p p l i e d .  s i m i l a r to t h a t found by Fung (12)  other authors such as Ridge and Weight  i n the form of the f u n c t i o n r e l a t i n g the s t r a i n and  although t h e i r experiments were c a r r i e d out a p p l i e d the f o l l o w i n g f u n c t i o n s 0 - lOOg.  where:  This r e s u l t i s  f o r load extension  load,  Ridge and  Weight  curves of s k i n :  E = X + Y log L  100  - lOOOg.  E = C + K  E:  extension  (inches)  L:  load  X, Y,  i n tension.  !  L  b  (g)  C, K, b are  constants.  Fung found t h a t i n simple e l o n g a t i o n n e a r l y an e x p o n e n t i a l  the t e n s i l e s t r e s s  f u n c t i o n of the s t r a i n i n the lower s t r a i n  However, both authors d i d not mention t h a t there was the s t r a i n - l o a d r e l a t i o n s h i p at low  was range.  a l i n e a r region i n  loads.  R e g r e s s i o n c o e f f i c i e n t s a and b f o r the curves as found by s t e p w i s e r e g r e s s i o n method are t a b u l a t e d a statistical has  term ' t which d e f i n e s  been e x p l a i n e d .  (9)  Therefore,  i n T a b l e 4.  Here RSQ  the  (R square) i s  the percentage of the v a r i a t i o n which  the h i g h e r  the v a l u e  of R S Q ,  the b e t t e r i s  FIGURE  6  Load Compression  Curves i n Tyrode  Solution  25.  the f i t .  An i n t e r e s t i n g p o i n t from Tableia4 i s t h a t although  some v a r i a t i o n s i n the v a l u e o f a, the v a l u e o f b i s almost  there are constant and  the v a r i a t i o n from the mean v a l u e a i s w i t h i n 2 percentage:. . shows i n some sense not o n l y the l i m i t  of the e x p e r i m e n t a l  This  result  accuracy but  a l s o shows t h a t i t i s p o s s i b l e to c h a r a c t e r i z e some e f f e c t s o f treatment i n a s o l u t i o n by the s l o p e 'b'.  T h i s approach i s the same as t h a t used  by P a r t i n g t o n and Wood ( 2 6 ) , who i n v e s t i g a t e d the mechanical the n o n - c o l l a g e n  components i n tendon f i b r e s .  p r o p e r t i e s of  They s a i d / ' S i n c e the s l o p e s  of the s u c c e s s i v e l o a d e x t e n s i o n curves up t o a c e r t a i n s t r a i n were r e p r o d u c i b l e , i t was c o n s i d e r e d l i k e l y  t h a t the e f f e c t o f enzymes might be  assayed by i n t e r p o s i n g an enzymic treatment  between the d e t e r m i n a t i o n o f  two s u c c e s s i v e c u r v e s , then any change o f s l o p e c o u l d be a t t r i b u t e d t o the e f f e c t o f the enzyme. TABLE 4 Regression  c o e f f i c i e n t s i n tyrode  a  b  solution.  standard e r r o r 0.002  99.74  -0.160  0.00186  99,79  0.282  -0.164  0.0096  99.95  4  0.223  -0.165  0.00198  99.77  5  0.249  -0.163  0.00202  99.75  1  0.303  -0.157  2  0.256  3  (The c o r d i n a t e was  .  rRSQ  taken i n the f o u r t h quadrant)  26  b.  Behaviour i n IN.CH <IOOH and 3  The  0.IN.HC1 S o l u t i o n s .  t e c h n i q u e used to f i n d the e f f e c t of v a r i o u s  s o l u t i o n s were  to compare the behaviour i n tyrode s o l u t i o n w i t h t h a t i n the s o l u t i o n using  the same sample to f i n d the r e g r e s s i o n c o e f f i c i e n t s  statistically. two  The  s o l u t i o n s was  main reason f o r t e s t i n g the s k i n b e h a v i o u r i n these  to i n v e s t i g a t e p r o t e i n s w e l l i n g , which had  i n v e s t i g a t e d p r e v i o u s l y by L l o y d and  Marriott  (17,  18,  s o l u t i o n s are shown i n F i g u r e  7 and  modulus a g a i n a p p l i e d f o r loads  Figure  l e s s than lOg.  to 225g., the curves were a l s o f i t t e d by 'a' and  'b'  E-l.  i n tyrode,  For  equation  loads  (1).  IN.CH^OOH and  Experiments were c a r r i e d out  i n each s o l u t i o n w i t h  the same sample.  regression  c o e f f i c i e n t s have been compared, as was (a).  The  one  way  to t e s t whether the s e t of s l o p e s  To has  way  Regression  slope  times  'b' of  suggested i n  c l a s s i f i c a t i o n method has  the  the  been used  i n tyrode s o l u t i o n i s d i f f e r e n t from Example  c l a s s i f i c a t i o n method are shown i n Appendix  D.  t e s t the s i g n i f i c a n c e l e v e l , the 5 percentage l e v e l of the F - d i s t r i b u t i o n been u t i l i z e d . T h i s a n a l y s i s shows t h a t there  the s l o p e s it  lOg.  f o u r or f i v e  t h a t i n a IN.CH^COOH s o l u t i o n or i n a 0.IN.HC1 s o l u t i o n . c a l c u l a t i o n s f o r the one  from  0.IN.HC1 s o l u t i o n s  i n v e s t i g a t e each s o l u t i o n ' s e f f e c t , the  previous section  0.IN.HC1  A c o n s t a n t Young's  a r e shown i n T a b l e 5.  To  been  19).  T y p i c a l l o a d compression curves i n IN.CH^COOH and  coefficients  second  'b'  i n t y r o d e s o l u t i o n and  a l s o shows t h a t t h e r e  s o l u t i o n and  i s no  i s a d e f i n i t e d i f f e r e n c e between  i n IN.CH^COOH s o l u t i o n .  d i f f e r e n c e between the s l o p e s  t h a t i n 0.IN.HC1 s o l u t i o n .  However, 'b'  i n tyrode  I t should be noted a g a i n t h a t  each  s e t o f t e s t s was c a r r i e d out on a s i n g l e sample o f s k i n t o reduce the d i f f e r e n c e s i n s k i n c o n d i t i o n and composition. These r e s u l t s agree g e n e r a l l y w i t h those o f L l o y d and coworkers, who i n v e s t i g a t e d the s w e l l i n g o f p r o t e i n f i b r e s . i n f o r m a t i o n was not g i v e n  they e x p l a i n e d  Even though q u a n t i t a t i v e  the s w e l l i n g as f o l l o w s ;  "In s o l u t i o n s such as C I N ^ H C l , e t c . , which do n o t induce i n the f i b r e l e n g t h but cause an i n c r e a s e f i b r e under l o a d i s the same as i n water.  contraction  i n width, elongation  o f the  Some l o s s o f water occurs  over and above t h a t squeezed out by the s t r e t c h i n g of the f i b r e s . water may have simply  d i f f u s e d f r e e l y i n between the f i b r e s .  This  With  s o l u t i o n s such as IN.CH^COOH, e t c . , which induce a c o n t r a c t i o n i n l e n g t h , however, t h i s c o n t r a c t i o n i s always a s s o c i a t e d w i t h an i n c r e a s e and  volume.  The g a i n i n volume i s brought about by a b s o r p t i o n  due  to the osmotic f o r c e " . From these c o n s i d e r a t i o n s  o f width of water  and the e x p e r i m e n t a l r e s u l t s , i t was  confirmed t h a t the manner i n which s k i n s w e l l s i n IN.CH^COOH s o l u t i o n and i n 0.IN.HC1 s o l u t i o n i s d i f f e r e n t . the p r e s e n t  However, i t i s out of the scope o f  work t o d e t a i l the b i o l o g i c a l d a t a ,  component changes a f t e r s w e l l i n g e t c . mechanical p r o p e r t i e s  f o r example, how each s k i n  T h i s study i s l i m i t e d to the  caused by the s w e l l i n g .  29.  TABLE 5 REGRESSION COEFFICIENTS IN CH COOH AND IN HC1 3  Solution  1  b  Standard Errors  R.S.9>,  0.158  -0.134  0.0037  98.79  2  II  0.018  -0.147  0.0058  97.55  3  II  0.078  SO.131  0.0051  97.65  4  II  0.127  -0.145  0.0041  98.76  5  Tyrode  a  IN CH COOH  0.256  -0.166  0.0015  99.87  6  II  0.301  -0.172  0.0034  99.39  7  II  0.223  -0.179  0.0035  99.76  8  II  0.204  -0.160  0.0020  98.87  9  II  0.227  -0.155  0.0041  99.17  11  Tyrode  3  >  0.137  -0.132  0.0022  99.56  12  II  0.150  -0.123  0.0018  99.64  13  II  0.173  -0.130  0.0024  99.44  14  II  0.123  -0.133  0.0029  99.23  0.205  -0.142  0.0015  99.82  0.082  SO.120  0.0028  99.15  15 16  0.IN.HC1 II  17  0.052  -0.114  0.0057  96.14  18  II  0.199  -0.156  0.0040  98.93  19  II  0.170  -0.149  0.0019  99.74  30.  c\  Behaviour The  i n Enzymes. r a t h e r wide v a r i a t i o n i n the l o a d compression  curves f o r  sheep s k i n a l s o precludes any p r e c i s e assessment of the e f f e c t o f enzymic treatment untreated s k i n .  based on a comparison o f the b e h a v i o u r  T h e r e f o r e , i t was a l s o c o n s i d e r e d t h a t any change i n the  s l o p e s of the curves  c o u l d be a t t r i b u t e d to the e f f e c t o f the enzymes.  T y p i c a l l o a d compression and  curves i n enzymes are shown i n F i g u r e 8  F i g u r e s E-2 t o E-4 i n Appendix E.  F i g u r e 8 shows a l s o t h a t t h e r e i s  a l i n e a r r e g i o n f o r loads l e s s than l O g . Equation The  of t r e a t e d and  (1) was f i t t e d  For loads from l O g . t o 225g.,  to these curves by the stepwise  regression coefficients  r e g r e s s i o n method.  'a' and 'b' i n tyrode s o l u t i o n and i n enzymic  s o l u t i o n s a r e shown i n T a b l e 6.  The comparison of the s l o p e s 'b' i n  t y r o d e s o l u t i o n and i n enzymic s o l u t i o n s by the one way  classification  method shows t h a t t h e r e are d i f f e r e n c e s between the s l o p e s o o f the curves i n t y r o d e s o l u t i o n and i n c o l l a g e n a s e , i n t y r o d e s o l u t i o n and i n papain> and i n t y r o d e s o l u t i o n and i n t r y p s i n at the 5 percentage distribution. curves  l e v e l o f the F  However, t h e r e i s no d i f f e r e n c e between the s l o p e s of the  i n t y r o d e s o l u t i o n and i n H y a l u r o n i d a s e .  The r e s u l t i n h y a l u r o n i d a s e  agrees w i t h the r e s u l t s o f P a r t i n g t o n and Wood (25) , who showed the e f f e c t of non=collagenous p r o t e i n s on the s t r e n g t h o f c o l l a g e n f i b r e s from a r a t t a i l  tendon.  In t h e i r experimental  study  isolated  they showed t h a t  s u b j e c t i n g the f i b r e s t o pure h y a l u r o n i d a s e had no i n f l u e n c e upon the mechanical /  s t r e n g t h o f the f i b r e s i n t e n s i o n .  T h i s r e s u l t d i d not take  into  account the p a r t i c i p a t i o n o f h y a l u r o n i c a c i d i n the s t a b i l i z a t i o n o f collggen fibres.  However, a q u a n t i t a t i v e e x p l a n a t i o n f o r t h i s e f f e c t  s t i l l not a v a i l a b l e .  rirS  FIGURE 8  Load Compression Curves i n C o l l a g e n a s e  32.  TABLE 6 REGRESSION COEFFICIENTS Solution 1  IN ENZYMES  a  b  Standard Error  R.S.Q:  0.213  -0.123  0.0012  99.85  2  it  0.147  -0.120  0.0005  99.99  3  II  0.155  -0.119  0.0039  98.5  4  II  0.153  -0.132  0.0025  99.41  0.368]  -0.163  0.0054  98,29  Tyrode  5  Collagenase  6  II  0.321  -0.154  0.0051  98.85  7  II  0.290  -0.154  0.0052  98.2  8  II  0.343  -0.164  0.0041  99.00  9  II  0.346  -0.167  0.0035  99.31  0.243  -0.144  0.0023  99.59  1  Tyrode  2  II  0.244  -0.154  0.0038  99.02  3  II  0.276  -0.166  0.0044  98.89  4  II  0.215  -0.132  0.0017  99.73  5  Hyaluronidase  0.266  -0.146  0.0032  99.22  6  II  0. 2f74  -0.147  0.0019  99.73  7  II  0.223  -0.131  0.0015  99.8  8  ii  0.281  -0.155  0.0022  99.66  9.  ii  0.302  -0.158  0.0018  99.79  1  0.076  -0.110  0.0026  99.14  2  II  0.192  -0.130  0.0013  99.84  3  II  0.015  -0.111  0.0034  98.54  4  II  0.153  -0.128  0.0018  99.68  5  M  0.163  -0.121  0.0015  99.75  6  Tyrode  0.290  -0.166  0.0019  99.79  7  II  0.254  -0.152  0.0008  99.95  8  II  0.270  -0.155  0.0015  99.86  9  II  0.294  -0.161  0.0023  99.68  LO  II  0.242  -0.160  0.0008  99.96  Papain  33.  TABLE 6  -1 Solution  (continued)  a  , b  Standard „ Error  „ „ ~ R.S.Ql  1  Tyrode  0.148  -0.132  0.0032  99.07  2  "  0.143  -0.122  0.0025  99.32  3  "  0.185  -0.129  0.0022  99.54  4  "  0.179  -0.139  0.0034  99.06  5  11  0.143  -0.132  0.0027  99.34  6  Trypsin  0.227  -0.145  0.0016  99.81  7  "  0.231  -0.150  0.0010  99.93  8  "  0.263  -0.155  0.0007  99.97  9  "  0.254  -0.148  0.0018  99.77  0.262  -0.145  0.0016  99.81  10  11  34.  The papain and  r e s u l t s w i t h the o t h e r enzymes show t h a t c o l l a g e n a s e ,  t r y p s i n have a t t a c k e d o r digested, the s k i n .  To i n v e s t i g a t e  the e f f e c t of d i g e s t i o n , the f o l l o w i n g c o n s i d e r a t i o n s were made.  In  T a b l e 6 the mean v a l u e of the s l o p e s f o r each s o l u t i o n have been e v a l u a t e d . Suppose the mean v a l u e of the s l o p e s i n t y r o d e s o l u t i o n i s Ct, or e q u i v a l e n t l y t a n ^ , and mean v a l u e of the s l o p e s i n c o l l a g e n a s e is^Q, tan$2> the  then the angle  'y'  between the two  s l o p e s can be c a l c u l a t e d  or  by  equation  I t a n v l = tan j & -  0,1 =1 t®0?. ~ I 1 + tan#  1  2  t a n  ^  tan^,  i  + •(2)  The  v a l u e s of j t a n y j h a v e been t a b u l a t e d i n T a b l e  systems, t y r o d e - h y a l u r o n i d a s e , tyrode-papain.  7 f o r the  t y r o d e - c o l l a g e n a s e , t y r o d e - t r y p s i n and  The magnitudeSof ^ t a n / j a r e an i n d i c a t i o n of the  extent  of the enzyme a t t a c k even though they have no q u a n t i t a t i v e meaning. T h e r e f o r e , from T a b l e 7, i t i s p o s s i b l e to say t h a t c o l l a g e n a s e and have a g r e a t e r d i g e s t i o n e f f e c t than does t r y p s i n . TABLE 7 The v a l u e of  |tan"y[  System  Mean Value  1.  Tyrode Collagenase  Ot -0.124 ft -0.160  2.  Tyrode Papain  ft -0.159  3.  Tyrode Trypsin  GU-0.131 ^ -0.148  4.  Tyrode Hyaluronidase  a -0.149 P -0.147  a  -0.120  tan/ 0.0287  0.0301  0.0038  0.00014  papain  35.  I t has  a l r e a d y been mentioned t h a t c o l l a g e n a s e  the c o l l a g e n f i b r e s and amides.  p a p a i n and  t r y p s i n attacked  However, b i o l o g i c a l i n f o r m a t i o n  attacked  mainly  mainly p e p t i d e s  and  about s k i n d i g e s t i o n I s v. not  a v a i l a b l e , t h e r e f o r e i t i s d i f f i c u l t to c h a r a c t e r i z e each enzyme's s p e c i f i c d i g e s t i v e e f f e c t on the s k i n from t h i s experiment. discussed d.  This w i l l  f u r t h e r i n t h i s s s e c t i o n of t h i s t h e s i s .  E f f e c t of  temperature.  E f f e c t . : o f temperature on the l o a d compression curve has i n v e s t i g a t e d u s i n g a s i n g l e probe (P-3) However, i t was on the e.  be  not  at 25°  c  , 30°  c  , 37.2°  p o s s i b l e to f i n d a c o n s i s t e n t e f f e c t of  c  and  been 45°  c  .  temperature  curves.  Stress S t r a i n Relationship. In the p r e v i o u s  been d i s c u s s e d ,  sections  the l o a d - s t r a i n r e l a t i o n s h i p has  i . e . , the r e l a t i o n s h i p between X and Y i n E q u a t i o n  However, f o r e n g i n e e r s i t i s more important and  general  mainly (1).  t o r e l a t e the  curves i n a s t r e s s - s t r a i n r e l a t i o n s h i p r a t h e r than i n l o a d - s t r a i n relationship. With t h i s diameter probes. was  f a c t i n mind, experiments were c a r r i e d out u s i n g d i f f e r e n t  The  same i n i t i a l  c a l c u l a t e d as l o a d d i v i d e d by  experiment are shown i n F i g u r e a s e t of e i g h t p o i n t s the f o l l o w i n g  y =  and  probe area. The  The  Stress  r e s u l t s from t h i s using  on each curve shows t h a t the p o i n t s were f i t t e d  g.  strain  ^2 = s t r e s s c,d = are  l o a d ranges were used.  stepwise r e g r e s s i o n a n a l y s i s  equation:  y = c + d im where  9.  loads  constants  (3)  by  36.  The  v a r i a n c e e x p l a n a t i o n term RSQwas  87.8 p e r c e n t a g e .  E q u a t i o n (3) w i t h c o n s t a n t c = -0.185 and d = 0.08156 has been drawn i n F i g u r e 9 as a d o t t e d l i n e . seems p o s s i b l e  From t h i s f i g u r e and the v a l u e of RSQ , i t  t o t a l k about these curves i n terms o f s t r e s s and s t r a i n .  Many authors e s p e c i a l l y p h y s i o l o g i s t s  p r e s e n t e d t h e i r data i n  a form o f a f o r c e displacement or a f o r c e e x t e n s i o n .  T h e i r way o f  p r e s e n t i n g d a t a i s not g e n e r a l , b u t o f t e n i t i s d i f f i c u l t the  stress  from b i o l o g i c a l experiments. B o n i n i q u e (56)  calculated  d i e and gave the f o l l o w i n g cr= / 2 7 T a V a P  where  /  2  the s t r e s s d i s t r i b u t i o n under a r i g i d  equation:  - r  (4)  ~~  2  p = l o a d on the d i e a = radius  o f the d i e  r = distance  from c e n t e r o f d i e t o p o i n t  CT = i n t e n s i t y o f s t r e s s p e r u n i t The The  to c a l c u l a t e  stress  under  consideration  area.  i s minimum a t the c e n t e r where r = o a n d ^ m i n / 2 7 T a . P  2  s t r e s s i s maximum a t the boundary of the d i e where r = a, 0"max =  infinity. localized  He s a i d the i n f i n i t e s t r e s s f a i l u r e o f the m a t e r i a l  a t the boundary w i l l  i n this  produce  region.  I f t h i s s o l u t i o n i s v a l i d , the simple c a l c u l a t i o n of s t r e s s ( f o r c e d i v i d e d by area) i s no l o n g e r v a l i d .  S i n c e t h e r e was no i n d i c a t i o n  of l o c a l f a i l u r e due t o the i n f i n i t e s t r e s s , t h i s e q u a t i o n p r e d i c t s edge, t h e r e i s some doubt about the accuracy o f e q u a t i o n ( 4 ) . f o r the a n a l y s i s used r a t h e r  a t the  Therefore,  o f p r e s e n t work, the l o a d - s t r a i n r e l a t i o n s h i p was mainly  than the s t r e s s  strain relationship.  ,0 tg  10  Z  b  Stress ( g/mm ) 20 30 2  »  FIGURE 9  .  Stress S t r a i n  —s—  Relationship  40 &  50  r~  38.  C.  C y c l i c Stress Fatigue  Method.  These r e s u l t s were o b t a i n e d recorder load.  by  r e c o r d i n g on a s t r i p  chart  the displacement w i t h time f o r an i n t e r m i t t e n t a p p l i c a t i o n of  Figures 10 and  11 are the r e s u l t s i n tyrode  solution fortthe  small  C weights 5g.  and  lOg. u s i n g probe (P-3)  at 37.2° .  Figure  10 shows a  b e h a v i o u r s i m i l a r to t h a t f o r l i n e a r v i s c o e l a s t i c m a t e r i a l s when the input  f o r c e i s a p p l i e d i n square wave form, F i g u r e  b e h a v i o u r , a l t h o u g h some s m a l l n o n l i n e a r and  Figures  E-5  to E-10  11 shows a l s o the same  e f f e c t s are observed.  Figure  i n Appendix E are t y p i c a l r e s u l t s measured i n  s o l u t i o n f o r l a r g e r loads by  t h i s method.  One  can r e c o g n i s e  discussed  i n more d e t a i l i n the next  In a p r e v i o u s r e l a t i o n s h i p was was  obtained  by  e s s e n t i a l l y a logarithmic  weight was and was  t h i s method. read  The  p o i n t s were f i t t e d  13 by  the i n i t i a l  of  a solid line.  load.  a l s o by  found to be  as measured by  function.  also v a l i d  magnitude of the  skin thickness.  c a l c u l a t i o n are shown i n F i g u r e  the R S © was  confirmed t h a t the l o a d  first  The  13.  By  a logarithmic  94.6  percentage.  From F i g u r e  will  The  strain  f o l l o w i n g approach  f o r the r e s u l t s response f o r each  from s t r i p c h a r t s c a l e , based on i n i t i a l pen  d i v i d e d by  this  chapter.  s e c t i o n ( a ) , i t was  used to t e s t whether t h i s r e s u l t was  tyrode  i n these  curves the n o n l i n e a r b e h a v i o u r s of s k i n , i . e . , time dependency, but be  12  position,  r e s u l t s of  this  a stepwise r e g r e s s i o n method these function l i k e equation The  (1)  and  f u n c t i o n i s shown i n f F i g u r e  13 i t i s p o s s i b l e to say  t h a t the  c y c l i c s t r e s s f a t i g u e method f o l l o w s a l o g a r i t h m i c  strain function  FIGURE 10  F a t i g u e Curve i n Tyrode  Solution  Time  (sec)  90  a  o CO  50  a J Z  O  eight  I0 g  T h i c k n e s s 1.81 mni  o  100 FIGURE  11  F a t i g u e Curve i n Tyrode S o l u t i o n  Time  [ I  W  V  Weight  (sec)  50 g  Thickness 1.81 mm 1  a  a FIGURE 12  I  _ S o l u t iL_ F a t i g uae Curve i n Tyrode on  L_  i  FIGURE 13  Load S t r a i n Relationship i n Fatigue Method  43.  T y p i c a l r e s u l t s i n IN.CH^COOH and 0.IN.HC1 s o l u t i o n s are shown i n Figure  14 and  Figures  to f i n d d i s t i n c t  E - l l to E-14.  From these f i g u r e s i t i s d i f f i c u l t  d i f f e r e n c e s i n the b e h a v i o u r of b o t h s o l u t i o n s i n comparison  w i t h the b e h a v i o u r i n t y r o d e s o l u t i o n except t h a t the displacement i n both s o l u t i o n s has caused by  become b i g g e r  the s w e l l i n g of the  than i n tyrode s o l u t i o n , which  was  skin.  T y p i c a l r e s u l t s i n enzymic s o l u t i o n s are shown a l s o i n F i g u r e and  Figures  E-15  to E-21.  I t has  15  been found t h a t the b e h a v i o u r shown by  t h i s method of measurement of s k i n a f t e r treatment w i t h h y a l u r o n i d a s e was  not  d i f f e r e n t from t h a t i n t y r o d e s o l u t i o n .  r e s u l t s i n the p r e v i o u s s e c t i o n .  T h i s agrees w i t h  However, i t has  been shown t h a t  were some d i f f e r e n c e s i n the s k i n b e h a v i o u r a f t e r treatment w i t h papain and  trypsin.  I t was  i n t h i s case a l s o d i f f i c u l t  d i f f e r e n c e s between these t h r e e b e h a v i o u r s and (Some minor d i f f e r e n c e s w i l l be These o b s e r v a t i o n s mechanical f u n c t i o n s e d i t e d by  Chvapil  considering  discussed  i n the s i m u l a t i o n  show t h a t i t i s d i f f i c u l t  mentioned t h a t i t was  mucopolysaccharides of ground substances and  complex manner and  there collagenase,  distinct  that i n tyrode s o l u t i o n .  collagen  section).?•  to s e p a r a t e  not  t i s s u e f u n c t i o n to study, f o r example, the  T h i s means t h a t the  to f i n d  of each chemical component i n t i s s u e .  ( 7 ) , i t was  the  the  In the book  p o s s i b l e when function  fibres  of  separately.  components i n t i s s u e or s k i n a f f e c t e d each o t h e r i n a as F e s s l e r  combined m e c h a n i c a l f u n c t i o n s  (28)  mentioned i n h i s work, there  produced by  the  components.  are  44.  ]  Each enzyme was expected to p r e f e r e n t i a l l y d i g e s t one s p e c i f i c  component o f t i s s u e .  However, B o r n s t e i n  papain a l s o digested  the c o l l a g e n f i b r e s .  reported  (30) r e p o r t e d  t h a t t r y p s i n and  F r a n k l a n d and coworkers (31)  t h e r e was a c i d s o l u b l e c o l l a g e n f i b r e s i n r a t l i v e r .  r e p o r t s i i n d i c a t e that i t i s nearly impossible  t o i n v e s t i g a t e the m e c h a n i c a l  p r o p e r t i e s of each component i n s k i n by u s i n g enzymes. and what the enzymes a t t a c k enzymology.  These  Furthermore, how  i n the s k i n i s not well-known even i n  FIGURE 14  F a t i g u e Curve l n IN.CH^COOH  0  Time  (sec)  50  9<  47.  MODELLING AND  A.  SIMULATION OF SKIN'S MECHANICAL BEHAVIOUR  Modelling In the p r e v i o u s  separate  s e c t i o n s i t was  shown t h a t i t i s i m p o s s i b l e  the m e c h a n i c a l f u n c t i o n s of each component of s k i n .  new  components had  to be  and  ground s u b s t a n c e s .  considered  f o r a change from s m a l l loads I f one  looks  ments, i n F i g u r e 16,  to l a r g e  to change from l i n e a r to  fibres nonlinear  loads.  at the r e s u l t s of the c y c l i c s t r e s s f a t i g u e measure-  i t i s p o s s i b l e to f i n d the f o l l o w i n g three  r a t c h e t or c o n t r a c t i l e element, e l a s t i c element and all  Therefore,  r a t h e r than c o l l a g e n , e l a s t i c  A l s o a model had  to  of which are f u n c t i o n s of time.  The  viscoelastic  elements; element,  r a t c h e t or c o n t r a c t i l e element  expresses the degree to which the probe s i n k s i n t o the s k i n on each l o a d i n g . The  e l a s t i c element means the s t r a i g h t l i n e p a r t s of the response when the  weight i s suddenly a p p l i e d or removed. the delayed  and  curved  a p p l i e d or removed.  The  v i s c o e l a s t i c element means  movements o f theresponse a f t e r the l o a d i s suddenly  I t i s now  are taken i n t o account by  nesessary  to c o n s i d e r how  these t h r e e  elements  the model.  To i n v e s t i g a t e the b e h a v i o u r of the c o n t r a c t i l e element i n F i g u r e 16,  the c h a r t s c a l e s f o r the p o i n t of minimum compression f o r each response,  p o i n t s A i n F i g u r e 16, based on i n i t i a l pen  p o s i t i o n , were read.  p o i n t s were f i t t e d i n the f o l l o w i n g e q u a t i o n method. p = c'o + d o l m n o o r  (5)  by  the stepwise  These  regression  49.  where:  p = the c h a r t s c a l e based n = i n t e g e r number unloaded,  on i n i t i a l pen p o s i t i o n .  n = 1  n (numbers of c y c l e of loaded and  i . e . , each c y c l e takes f i v e seconds so a c t u a l l y  t h i s means time) c , d n  are constants.  n  In t h i s case p = 0 when n = 1, t h e r e f o r e c The response,  n  = 0  c h a r t s c a l e s f o r the p o i n t o f maximum compression  f o r each  p o i n t B i n F i g u r e 16, were a l s o read and f i t t e d by E q u a t i o n (5)  w i t h c o n s t a n t c ^ and d^. viscoelastic  The boundary p o i n t s of the e l a s t i c element and the  element, p o i n t C i n F i g u r e 16, when the l o a d was  suddenly  a p p l i e d ; were read and f i t t e d by the same e q u a t i o n w i t h c o n s t a n t s  A^'  and  S i m i l a r l y the boundary p o i n t s of the e l a s t i c element and the v i s c o -  e l a s t i c element when l o a d was suddenly read and f i t t e d by E q u a t i o n  removed, p o i n t D i n F i g u r e 16, were  (5) w i t h c o n s t a n t s c^ and d^.  t h i s i n v e s t i g a t i o n of s p e c i f i c p o i n t s f o l l o w s .  The summary of  The c o n s t a n t s i n each e q u a t i o n  a r e r e l a t e d g e n e r a l l y by the f o l l o w i n g e q u a t i o n s :  i ii>M>N>l o i • c  c  | oi^i 3l^l 2l^! i I d  d  d  d  >=  0  0  (The c o - o r d i n a t e was taken i n f o u r t h quadrant,  ( 6 )  ( 7 )  t h e r e f o r e each c o e f f i c i e n t has  a negative v a l u e ) . In E q u a t i o n linear.  (7) the e q u a l s i g n i s v a l i d when the behaviour i s  From these o b s e r v a t i o n s i t i s p o s s i b l e to say t h a t a l l the elements  follow Equation  (5) and hence a r e f u n c t i o n s of time.  The model shown i n F i g u r e 17 has been proposed.  The c o n s t a n t s  A, B, C and D a r e l o g a r i t h m i c f u n c t i o n s of time a c c o r d i n g t o the f o l l o w i n g equations:  50.  V  Elastic Element  A  Vi s c o elastic  v  A  Element  Ratchet  FIGURE. 17  A M e c h a n i c a l M o d e l o f Sheep  Skin  2  51.  A = a^ + b ^ l i r t B = a  + b 1  C = a  In -t . (8)  1  + b  3  3  In. t .  D = b. i n . t 4 a , bj, a > (  2  D  2» 3 ' ^3 a  a n c  ^ ^4  a  r  e  constants  and parameters f o r the  simulation. B.  Simulation  o f S k i n Behaviour by Analog Computer  In F i g u r e .Is X^, ^2 and X  3 >  F = AX  X  F = CX  2  X  3  17, i f t h e movement o f each element when a l o a d F i s a p p l i e d the f o l l o w i n g three e q u a t i o n s can be d e r i v e d : (9)  + BX  (10)  2  = D  (11)  where: A,B,C and D are f u n c t i o n s X^ means the f i r s t and  o f time as shown i n E q u a t i o n (8) and  d e r i v a t i v e with respect  t o time.  (11), an>' analog c i r c u i t has been c o n s t r u c t e d .  PACE 231R, i n the Department o f E l e c t r i c a l  From E q u a t i o n ( 9 ) , (10) The analog computer,  Engineering,  was used f o r t h i s  study. The F i g u r e 18. function. The  circuit  f o r generating  A function generator  the v a r i a b l e s A,, B, C and D i s shown i n  was used to generate a l o g a r i t h m i c  Parameters a^,b^, a^, b^, a^,  and b ^ were s e t on p o t e n t i o m e t e r s .  time s c a l e f o r the f u n c t i o n g e n e r a t o r was c o n t r o l l e d by p o t e n t i o m e t e r  "0011". The  circuit  f o r generating  In the experiments the i n p u t .wave.  the i n p u t  f o r c e F i s shown i n F i g u r e 19.  f u n c t i o n had been only approximately a square  Hence, i t was found t h a t b e t t e r s i m u l a t i o n  c o u l d be got i f the i n p u t  wave form was t r a p e z o i d a l r a t h e r than square because o f damping of the pen movement i n s t r i p  chart recorder  and because t h i s form more n e a r l y  52.  FIGURE 18  Constant G e n e r a t i n g  Circuit  FIGURE 19  Force G e n e r a t i n g  Circuit  FIGURE 20  Main  Circuit  55.  approximated the e x p e r i m e n t a l l o a d i n g f u n c t i o n . generated from a s i n e wave u s i n g a comparator.  The square wave was The t r a p e z o i d a l wave was  generated from the square wave by u s i n g the l o g i c a l u n i t , i . e . , r e l a y and r e l a y comparators i n the analog computer.  coils  The s l o p e of the t r a p e z o i d a l  wave was c o n t r o l l e d by the p o t e n t i o m e t e r "Q33" i n F i g u r e 19.  The amplitude  of t h e wave was c o n t r o l l e d by t h e p o t e n t i o m e t e r "Q42". The main c i r c u i t  f o r E q u a t i o n ( 9 ) , (10) and (11) i s shown i n  F i g u r e 20. A t y p i c a l r e s u l t o f the b e h a v i o u r o f the model i s shown i n F i g u r e 21.  I n F i g u r e 21, Channel 2 i s the exact square wave, Channel 3 i s the  t r a p e z o i d a l wave, Channel 4 i s the movement o f the e l a s t i c element,  Channel  6, i s the movement o f the r a t c h e t element, Channel 7 i s the movement o f v i s c o e l a s t i c element and Channel 8 i s the b e h a v i o u r o f t o t a l model o f the skin.  The v a l u e o f each p o t e n t i o m e t e r s e t t i n g i s shown i n Appendix F. The t o t a l model response can be compared t o t h e a c u t a l response  of sheep s k i n i n t y r o d e s o l u t i o n by comparing Channel 8 t o the F i g u r e 22. Good agreement  can be seen.  By r e d u c i n g the parameters b^, b^* b ^ and b^  which c o n t r o l the degree o f n o n l i n e a r i t y , a l i n e a r  viscoelastic  b e h a v i o u r o f s k i n , which was a l s o o b t a i n e d f o r e x p e r i m e n t a l r e s u l t s , was o b t a i n e d and i s shown i n F i g u r e 23.  Other t y p i c a l r e s u l t s a r e shown i n  F i g u r e 24 and F i g u r e s E-22 t o E-24. S i n c e each f a t i g u e r e p r e s e n t s o n l y one e x p e r i m e n t a l r e s u l t of a system which can o n l y be r e p r e s e n t e d by a s t a t i s t i c a l w e i g h i n g o f a l a r g e number o f e x p e r i m e n t a l r e s u l t s , no attempt was made t o f i n d the model parameters f o r a l l the systems s t u d i e d .  However, the testswwhich were made  on the model i n d i c a t e d t h a t a l l the types o f b e h a v i o u r found c o u l d be s i m u l a t e d by t h i s  model.  FIGURE 21-a  S i m u l a t i o n of the Model i n Tyrode  Solution  57.  UJ  > ID O  ( - ) 3 1 V 0 S 1HVH0  FIGURE 21-b  S i m u l a t i o n of the Model i n Tyrode S o l u t i o n  F I G U R E 23-  S i m u l a t i o n o f t h e Model i n Tyrode  Solution  FIGURE 24-a  S i m u l a t i o n of the Model i n Tyrode  Solution  FIGURE 24-b  S i m u l a t i o n o f the Model i n Tyrode  Soluti  on  FIGURE 25-a  S i m u l a t i o n of the Model i n C o l l a g e n a s e  FIGURE  25-b  Simulation  of  the Model  in  Collagenase  FIGURE 26  S i m u l a t i o n o f the Model f o r Ramp I n p u t  66.  Observing the same elements which were used i n the s i m u l a t i o n model, i t was p o s s i b l e t o f i n d some enzyme e f f e c t s which had not p r e v i o u s l y been n o t e d . (i)  I n collagenase,  the s l o p e o f the v i s c o e l a s t i c element i s s t e e p e r  than t h a t i n tyrode  s o l u t i o n and a l s o the movement o f the r a t c h e t  element was l a r g e r than t h a t i n tyrode (ii)  solution.  In p a p a i n , the magnitude o f t h e movement o f the e l a s t i c became s m a l l e r  than t h a t i n tyrode  It i s d i f f i c u l t  element  solution.  t o f i n d any d i f f e r e n c e s i n t r y p s i n and i n h y a l -  uronidase.  Based on the o b s e r v a t i o n  ( i ) and ( i i ) ,  collagenase  and p a p a i n have been s i m u l a t e d  the b e h a v i o u r s i n  and a r e shown i n F i g u r e  25 and  F i g u r e E-25 i n Appendix E. I t was found p r e v i o u s l y  t h a t the b e h a v i o u r o f s k i n i s a l o g a r i t h m i c  f u n c t i o n when the f o r c e was a p p l i e d as a ramp i n p u t .  The b e h a v i o u r o f s k i n  when the f o r c e was a p p l i e d as a ramp f u n c t i o n i n p u t was a l s o s i m u l a t e d  by  the model and i s shown i n F i g u r e 26. In summary  from these s i m u l a t i o n  r e s u l t s , the advantages of t h i s  model are the f o l l o w i n g . (i)  Changing the parameters of constants t o go from a l i n e a r t o a n o n l i n e a r  (ii)  By s e t t i n g the v a l u e simulate  any k i n d s  A,B,C, and D, i t i s p o s s i b l e  behaviour.  o f the seven parameters, i t i s p o s s i b l e t o  o f b e h a v i o u r o f s k i n i n c l u d i n g permanent  s t i f f e n i n g e e l a s t i c element e t c .  strain,  f  67  CONCLUSIONS  1.  By the s t r e s s s t r a i n method and c y c l i c s t r e s s f a t i q u e method, i t was found t h a t f o r the l o a d g r e a t e r  than a p p r o x i m a t e l y 10g., the s t r a i n  of sheep s k i n i n compression i s e s s e n t i a l l y a l o g a r i t h m i c applied load.  However, f o r l o a d s  smaller  f u n c t i o n of  than 10g., the s t r a i n  approximates a l i n e a r f u n c t i o n o f l o a d . 2.  I t was a l s o confirmed t h a t p r o t e i n s s w e l l d i f f e r e n t l y i n IN. CH^COOH and (18)  3.  i n O.IN. HC1.  T h i s f a c t had been r e p o r t e d  from t e n s i o n s t u d i e s on p r o t e i n  Enzymes such as c o l l a g e n a s e ,  by L l o y d and co-workers  fibres.  t r y p s i n and p a p a i n a t t a c k e d  the sheep  s k i n and t h e i r e f f e c t s have been observed on l o a d compression curves of s k i n .  However, i t was observed t h a t h y a l u r o n i d a s e  upon the l o a d compression c u r v e s ,  which agreed w i t h  had no e f f e c t Partington's  work ( 2 5 ) . 4.  I t was expected t h a t by the enzymic treatments the m e c h a n i c a l f u n c t i o n s of each component c o u l d be v i s u a l i z e d , however, i t was found d i f f i c u l t It i s evident  t o s e p a r a t e the m e c h a n i c a l f u n c t i o n s of components.  t h a t t i s s u e components a f f e c t e d each other  a manner to a l l o w 5.  this  i n too complex  simplification.  By the c y c l i c s t r e s s f a t i g u e method i t was found t h a t the h i s t o r y dependent b e h a v i o u r of sheep s k i n i n compression was e s s e n t i a l l y a l o g a r i t h m i c f u n c t i o n of time.  68.  6.  A m e c h a n i c a l model has been proposed and s i m u l a t e d on an a n a l o g computer.  I t was c o n f i r m e d t h a t t h e s i m u l a t i o n r e s u l t s o f t h e  model agreed w e l l w i t h t h e e x p e r i m e n t a l d a t a .  69.  RECOMMENDATIONS FOR  The  FURTHER WORK!  l i n e a r v i s c o e l a s t i c theory has been w e l l developed  workers, however, the n o n l i n e a r v i s c o e l a s t i c it  i s not too w e l l known.  develop theory.  theory i s so c o m p l i c a t e d  T h e r e f o r e a mechanical  the a n a l y s i s of the p r e s e n t work.  I t may  to t e s t  v i s c o e l a s t i c m a t e r i a l s by o t h e r methods.  interesting  Inc.  proposed f o r  and p o s s i b l e to  of the l i n e a r  viscoelastic  the m e c h a n i c a l  p r o p e r t i e s of  For example, a machine, which i s  c a l l e d a dynamic modulus t e s t e r PPM-5R, i s now Morgan Co.  that,  i s recommended.  I t would a l s o be i n t e r e s t i n g  H.M.  model was  be i n t e r e s t i n g  a mathematical model u s i n g some analogy F u r t h e r work i n t h i s f i e l d  by many  commercially  available  With t h i s machine, the dynamic modulus and  from  other  e l a s t i c d a t a can be o b t a i n e d by measuring the s o n i c v e l o c i t y  in  the sample. B i o l o g i c a l m a t e r i a l s are so complex i n composition quite d i f f i c u l t interesting  to get r e p r o d u c i b l e data.  to c o r r e l a t e the mechanical  the type of components remaining  a f t e r treatment  enzymology, p h y s i o l o g y , anatomy and  i f p o s s i b l e , i t may  be  behaviour w i t h i n f o r m a t i o n about  However, f o r t h i s comparison the d e t a i l e d  c o o p e r a t i o n between people who  But,  that i t i s  with d i f f e r e n t  solutions.  knowledge of b i o c h e m i s t r y ,  engineering i s necessary.  Therefore,  are working i n these f i e l d s i s needed.  70,  LITERATURE CITED  1.  BERGEL, D.H., J . o f P h y s i o l . London. 156, 415, 1961.  2.  BERGEL, D.H., J . P h y s i o l . London. 156, 458, 1961.  3.  FUNG, Y.C., Doundations  o f S o l i d Mechanics, Englewood C l i f f s , N.J.,  P r e n t i c e - H a l l , 1965. 4.  PERTERSON, L.H. P h y s i o l . Rev. 42, Suppl. 5, 309, 1962.  5.  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BENNET, C H . and FRANKLIN, N.C S t a t i s t i c a l A n a l y s i s i n Chemistry Chemical I n d u s t r y . N.Y. John Wiley and Sons. I n c .  55.  H.M. MORGAN CO. INC. T e c h n i c a l B u l l e t i n " D e t e r m i n a t i o n of Dynamic Modulus of E l a s t i c i t y i n M a t e r i a l s by Measurement o f S o n i c V e l o c i t y " .  56.  TIMOSHENKO and GOODIER "Theory  of E l a s t i c i t y "  McGraw H i l l , 1951.  and the  APPENDIX A  THE MECHANICAL BEHAVIOUR OF DENTAL WAX  74.  A-l  General The main purpose of t h i s experiment was  as a p r e p a r a t o r y  experiment b e f o r e u s i n g sheep s k i n t o check whether the apparatus worked well. The d e n t a l wax which was  t e s t e d i s mainly used as a model of  p e r i o d o n t a l membranes o r t i s s u e s i n D e n t i s t r y .  Sheets of wax were o b t a i n e d  from the F a c u l t y of D e n t i s t r y at the U n i v e r s i t y of B r i t i s h t h i c k n e s s was  about 0.096 i n c h e s .  whose diameter was the t e s t  A sheet of wax  about 3 c e n t i m e t e r s .  was  Columbia.  cut i n t o s m a l l  Their circles  These sheets of c i r c u l a r wax  were  samples. A probe whose diameter was  throughout t h i s experiment. f o r t h i s experiment.  about 0.864 m i l l i m e t e r s was  Only the c y c l i c s t r e s s f a t i g u e method was  The procedure f o r t h i s method was  the c h a p t e r on " E x p e r i m e n t a l " s e c t i o n " E - ( b ) " .  used  same as shown i n  However, the temperature  was  c  c changed i n s t e p s from 10°  used  to 40° .  The span 50 mv  and the c h a r t  10 s e c / i n c h of the s t r i p c h a r t r e c o r d e r were u t i l i z e d  throughout  speed this  experiment. A-2  Experimental Results The wax w i l l be dependent  more on i t s past h i s t o r y .  on a m i c r o s c o p i c s c a l e a c t u a l c y s t a l s are not p e r f e c t , they may m i c r o c r y s t a l l i n e 'domains bounded by good c y r s t a l s . i r r e g u l a r i t i e s may i t s e l f may  For example, c o n s i s t of  The c y s t a l .  i n v o l v e e x t r a or m i s s i n g l a y e r s w h i l e the s o l i d  be v e r y e a s i l y contaminated.  the p r e v i o u s h i s t o r y of the wax  surface  T h e r e f o r e , f o r a d e t a i l e d study,  has t o be c o n s i d e r e d .  75.  However, these s o r t of c o n s i d e r a t i o n s are not w i t h i n the scope of t h i s Appendix, which i s l i m i t e d to the p r e s e n t a t i o n of the r e s u l t s found d u r i n g the i n i t i a l equipment T y p i c a l r e s u l t s of wax measured by  behaviours  , i t was  60 grams, t h e r e was a l o a d o f 500  temperatures  as  arid F i g u r e A-4  i t i s shown t h a t at h i g h e r  than  independent of weight.  grams, the probe s t a r t e d s i n k i n g through the wax.  F i g u r e A-6  at  behaved l i k e a l i n e a r  for large loads, greater  a l i m i t i n g s t r a i n which was  s t a r t e d s i n k i n g i n t o the wax  In  For  Figure  temperatures the probe  at lower l o a d s .  Model Based on the o b s e r v a t i o n s  f o l l o w i n g simple wax  f o r the b e h a v i o u r of wax  circuit  u s i n g a diode  i n p u t wave form was F i g u r e 17.  a limiter.-,  before  has  s e c t i o n , the  been proposed.  It  However, t h i s model i s only  the probe s t a r t e d s i n k i n g .  The  analog  to c o n t r o l the l i m i t e r i s shown i n F i g u r e A-8.  t r a p o z o i d a l and was  produced by  the exact  channel 4 represents  The  the c i r c u i t shown i n  T y p i c a l r e s u l t s are shown i n F i g u r e A-9.,  Channel 2 r e p r e s e n t s f o r c e and  r e p o r t e d i n the p r e v i o u s  model shown i n F i g u r e A-7  c o n s i s t s of a V o i g t c element and valid  F i g u r e A-3  found t h a t the wax  v i s c o e l a s t i c m a t e r i a l f o r s m a l l l o a d s , but  A-3  at d i f f e r e n t  From F i g u r e , A - l , F i g u r e A-2,  a temperature of 10°  and  test.  the c y c l i c s t r e s s f a t i g u e method are shown from F i g u r e A - l  to F i g u r e A-6.  A-5  experimental  to Figure  A-12.  square wave, channel 3 r e p r e s e n t s  the  the b e h a v i o u r of the model.  these  r e s u l t s , the model appears to r e p r e s e n t  the e x p e r i m e n t a l  From  input  results well.  FIGURE A - l  F a t i g u e Curve  Time  (sec)  0  ibo'k  50  —— a  !  8  —  h  i  FIGURE A-2  •—i  —  2  F a t i g u e Curve  °  •  FIGURE  A-3  F a t i g u e Curve  Time  a o  CO  (sec)  c  50  50  O  height  O  Temp.  500 g 10°  c  1-  I00  1  FIGURE A-5  Fatigue  Curve  Time  (sec)  0  50  FIGURE A-6  Fatigue  90  Curve  FIGURE A-7  A M e c h a n i c a l Model of D e n t a l Wax  O  DIODE ~ OUTPUT  1 0 0 -  FIGURE A-8  Analog C i r c u i t  f o r Simulation  FIGURE A-9  S i m u l a t i o n o f the M o d e l  ON  FIGURE A-12  Simulation  o f the Model  APPENDIX B  CALIBRATION OF THE LINEAR DISPLACEMENT TRANSDUCER AND THE FORCE TRANSDUCER  88.  X FIGURE B - l  WEIGHT [ g ] Force T r a n s d u c e r C a l i b r a t i o n  89.  -8  L  — I  :—i  y  E q u a t i o n F i t t e d For Span IOO mv.  Z  Displacement [inch] FIGURE B-2  L i n e a r Displacement Transducer  Calibration  APPENDIX C  STEPWISE REGRESSION METHOD. EXAMPLE OF THE INPUT AND THE OUTPUT.  v -| J  " 9 L 8 "  PROBLM  6 01  CARD  '"ll  PR.06LM  5ANA~  3  " c l  YES  TRNSGENER^  TRi\'Ofc'N... 4-17  1  XAR f A B L E  FORNlA7  CARD  13F1D.5) " •  D A T A ~  "  ~  '  SEND  S U BP R 08 LE.Vj CAR D  SUBPRO  J ! 0  YES  YES  Y£S  YES  YES  Y£S  CONTROL DELETE CARP  1 2 j  2.  C0js DEL1112. :  9  SUBPRO 3 CO(\iDEL 1 1 1 2 IfVlSl-i  ^ t" 1  Input Program f o r Stepwise Regression Method  BMD02R - STEPWISE REGRESSION - VERSION OF JULY 27 UNIVERSITY OF PENNSYLVANIA COMPUTER CENTER PROBLEM CODE SAKAT NUMBER OF ORIGINAL VARIABLES 5 NUMBER OF VARIABLES ADDED 1 TOTAL NUMBER OF VARIABLES 6 NUMBER OF SUB-PROBLEMS 4 NUMBER OF CASES  VARIABLE 1 37.4 2 45. 3 4 30.8 20.8 5 6  11  MEAN 106.72727 0.29331 0.329_09 0.3395 5 0.31191 4.35407  STANDARD DEVIATION 73.69917 0.11469 0.12195 0.12800 0.11520 0.93791  •  A T y p i c a l Output  bfgRegr.ess.ib'n-Met'hod  1965  92.  SU3-PR0BLM 1 DEPENDENT VARIABLE M A X I M U M NUMBER OF S T E P S F - L E V E L FOR I N C L U S I O N F - L E V E L FOR D E L E T I O N TOLERANCE LEVEL  2 12 O.OIOOOO 0.005COO O.OOIOOO  S T F P NUMBER 1 VARIABLE ENTERED MULTIPLE R S T D . ERROR OF A N A L Y S I S . OF  0.  EST.  998'*  0.0069  VARIANCE OF  i)F  SUM  i  REGRESSION RESIDUAL  SQUARES 0.131 0.000  9  VARIABLES VAR I A B L E  COEFFICIENT  (CONSTANT 6  -0.23826 0.12209  IN  MEAN S Q U A R E F RATIO 0.131 2747.338 0.000  EQUATION STD.  VARIABLES  ERROR  F  TO  REMOVE  VAR I A B L E  PARTIAL  I N S U F F I C I E N T FOR  SUMMARY S  T  E  P  NUMBER  CORR.  IN.EQUATION TOLERANCE  F  TO  ENTER  ) 0.00233  2747.3379  0.49650 0.78362 0.93908 0.87365  45. 30.B 20.8  F-LEVEL  NOT  FURTHER  0.1188 0.0024 0.0030 0.0007  2.6173 12.7288 59.7266 25.7930  COMPUTATION  TABLE VARIABLE ENTERED REMOVED  MULTIPLE .  ,R  0.9984  RSQ  INCREASE . I N RSQ  F V A L U E TO ' E N T E R OR REMOVE  0.9967  0.9967  2747.3379  NUMBER OF I N D E P E N D E N T VARIABLES JNCLUSES  f L I S T OF  ^ >  CASE 1 2 3 4 5 6 7 8 9 10 11  94.  RESIDUALS  RESIDUAL 0.01431 -0.00972 -0.00892 -0.00434 0.00016 0.00003 0.00079 0.00153 0.00471 0.00241 -0.00097  _  .  .  ......  cont'd  • APPENDIX D  ONE WAY  CLASSIFICATION METHOD  96.  G e n e r a l model f o r one way c l a s s i f i c a t i o n i s as f o l l o w s : A n a l y s i s of Variance Table Sum o f Squares  Source o f Estimate Between class  S  Within class  S.(i)  = n2 (x  ±  i  =7.  ±  Degree o f Freedom  - x)  p - 1  2  .(x. . - x . )  S  =S. . (x. . - x) 13  Where: x  I /p-1  N - p  2  -s2  Total  Mean Square  S  x.  ( i )  <x  + n  /N-P  2  cr  N - l  13  = o b s e r v a t i o n s which r e p r e s e n t n r e p l i c a t e j =1  a  Average Mean Square  results,  ... n, i n each o f p c l a s s e s i = 1 ... p.  = mean v a l u e w i t h i n the c l a s s  I  x  = mean v a l u e o f t o t a l o b s e r v a t i o n s .  The  e s t i m a t e o f the b a s i c v a r i a n c e cy , the " w i t h i n c l a s s "  e s t i m a t e i n t h i s case, i s ' f r e q u e n t l y spoken o f as the e r r o r , o r the e r r o r variance estimate.  2  Under the h y p o t h e s i s  =  2  o, both e s t i m a t e s have an  *  average v a l u e Q- , and the h y p o t h e s i s can be t e s t e d by computing the r a t i o o f the between c l a s s e s e s t i m a t e t o the w i t h i n c l a s s e s , o r e r r o r e s t i m a t e ,  2 and by c o n c l u d i n g C £ > ° g r e a t e r than  a  t  t  n  e  significant  l '  F , 1  -L  i f this ratio i s  F^.  For the p r e s e n t a n a l y s i s Q i g F  level a  Q  7' 0.05  =  , o  = 5.317  _  c  U•U J  5  ,  5  05  9  from F d i s t r i b u t i o n .  97.  i)  Tyrode and IN.CH^COOH Total  N. l  Means  T. /N. l l  Tyrode  0.55708  4  0.139  0.0776  IN.CH COOH  0.83158  5  0.166  0.0776  3  T o t a l T = 1.38866 2 T /N Zx . 2  N=9  = 0.214 -  13  =0.216  Analysis  of Variance  Table  S.E..  S. .  D.F.  Between c l a s s  0.00163  1  0.00163  Within  0.00054  7  0.0000773  0.00217  8  class  Total  F  l '  2  7' 0 05  =  5  ,  5  9  T h e r e f o r e 0£- > 6  X  Means  F ratio 21.07.  F = 21.07 i s g r e a t e r than  05  Q  t h i s means t h e r e i s a d i f f e r e n c e between  classes,  i . e . , t h e r e i s a d i f f e r e n c e between s l o p e s i n tyrode and i n IN.CH^ COOH.  ii)  Tyrode and 0.IN.HC1 Total  N.  Means  T. /N.  Tyrode  0.5174  4  0,1294  0.0669  0.IN.HC1  0.6804  5  0.1361  0.0926  T = 1.198  N == 9  T /N = 0.1594 2  T, T. /N. = 0.1595 1 X T x .. = 0.1609 2  ^  13  2  X  X  ANALYSIS OF VARIANCE TABLE S.0-  S.E.  D.F.  Means  F 0.5  Between c l a s s  0.0001  1  0.0001  Within class  0.0014  7  0.0002  F = 0.5 <  F^  r  %  0  - 5.59  5  There i s no d i f f e r e n c e between  iii]  classes.  Tyrode and C o l l a g e n a s e 2 Total  Ni  Means  Ti_' /N1  Tyrode  0.4943  4  0.1236  0.06109  Collagenase  0.8019  5  0.1604  0.1286  T = 1.296  5.Tj /N^ = 0.1897  N = 9  2  ^ ± 2  T /N = 0.1867 2  °-  =  1899  ANALYSIS OF VARIANCE TABLE Between  S.E.  class  class Within class  S:Q>  D.F.  Means  F  0.003  1  0.003  98.46  0.00027  7  0.000038  F = 78.46 >  F  r  ?  ,  o  ;  b  5  T h e r e f o r e t h i s i s a d e f i n i t e d i f f e r e n c e between  classes.  l y ] Tyrode and H y a l u r o n i d a s e Total  N:..  Means  2 T l i /N-: l  Tyrode  0.5986  4  0.1492  0.089  Hyaluronidase  0.7369  . 5  0.1474  0.1086  T = 1.334  l  N = 9  £T:- /N:; = 0.1977 2  I  T /N = 0.1977 2  ^  X  :  i j  2  =  l  0.1988  ANALYSIS OF VARIANCE TABLE  Between  D.F.  Means  F  0.00001  1  0.00001  0.064  0.001094  7  0.000156  S.£-  S.E. class  Within Class F-  0.064 <  F  r  ?  ,  o  ;  q  5  T h e r e f o r e t h e r e i s no d i f f e r e n c e between c l a s s e s .  v] Tyrode and P a p a i n N:; x  Total  Means  Tyrode  0.6006  0.12012  Papain  0.7928  0.1585  2  1  x  0.07215 0.1257  ,.2 I T ; /N; = 0.1978 x x  N = 10  T = 1.393  T: /N;  .2  T /N = 0.1941  ExJ.J .= 0.1983  ANALYSIS OF VARIANCE TABLE S.S-  S.E.  D.F.  Means  F 59.52  Between C l a s s  0.00369  1  0.00369  Within  0.000496  8  0.000062  class F - 59.52  >  F  r  g  ,  0  .  Q 5  T h e r e f o r e t h e r e i s a d e f i n i t e d i f f e r e n c e between c l a s s e s .  v i ] Tyrode and T r y p s i n Total  x  Means  T:;/N:; x x 2  Tyrode  0.6538  5  0.1307  0.0855  Trypsin  0.7419  5  0.1484  0.1101  T = 1.396 T /N = 0.1948  N = 10 Ex.; •  •LT: /SI = 0.1956 x x =0.1958  100.  ANALYSIS OF VARIANCE TABLE S. 9*  S.E. Between Within  class class F = 28.08  Means  F 28.08  0.000775  1  0.000775  0.000221  8  0.0000276  > F  r  8  ,  0  i  Q  5  Therefore there i s a d e f i n i t e d i f f e r e n c e  between  classes.  APPENDIX E  FIGURES  FIGURE E - l  Load Compression Curves i n 0.1N.HC1  0  '  FIGURE E-2  X  BOO  Weight \g )  200  Load Compression Curves i n P a p a i n  500  FIGURE E-4  •  F a t i g u e Curves i n Tyrode  Solution  0  Time  FIGURE E-5  (sec)  '  5  0  -•  F a t i g u e Curves i n Tyrode S o l u t i o n  90  Time  Weight  (sec)  30 g  Thickness  L82mm  100 FIGURE E-6  F a t i g u e Curves i n Tyrode S o l u t i o n  0  Time  FIGURE E-7  (seb)  50  F a t i g u e Curves i n Tyrode  90  Solution  •601 .  Time i—  (sec )  r  :  O  u CO 5 0  o O  eight  80 g  Thickness  !00  J  1.82 mm  M• O  L FIGURE E-9  Fatigue  Curves i n Tyrode S o l u t i o n  Time  0  1  J  '  I  !  T  (sec ) "— —5 !  50 1  1  !  '  S—  1  Weight  FIGURE E-10  F a t i g u e Curves I n Tyrode S o l u t i o n  !  '  lOOg  "  1  Time  FIGURE 12  (sec)  F a t i g u e Curves i n IN.CH COOH  Time  0  (sec)  50  o o  co 5 0 o  eight  O  lOg  h i c k n e s s 3.1  00 FIGURE E-13  F a t i g u e C u r v e s • i n 0.1N.HC1  Time  FIGURE E-15  (sec)  F a t i g u e Curves i n C o l l a g e n a s e  Time  Weight  (sec)  30 g  Thickness 2 . 4 7 mm  100^  —  s  :  —  8  »—— FIGURE  E-16  1  1 Fatigue  Curves i n  &— Hyaluronidase  -JL  Time  FIGURE E-17  (set)  F a t i g u e Curves i n  Hyaluronidase  FIGURE  E-18  F a t i g u e Curves  i n Papain  •031  Time  (sec)  0  50  Thickness  [QO^  :  :—a»_  90  2.56mm  1 FIGURE E-20  .  6 Fatigue  , I  a  Curves i n T r y p s i n  •  »  «  Time  \ Q Q l  ;  5  1;  '  ,«  FIGURE E-21  (sec)  8  •  Fatigue  i  »  Curves i n T r y p s i n  /  »  i  to  u>  FIGURE E-22-a  S i m u l a t i o n of the Model i n Tyrode S o l u t i o n  FIGURE E-22-b  S i m u l a t i o n o f the Model i n Tyrode S o l u t i o n  S i m u l a t i o n of the Model i n Tyrode  Solution  ho cr.  FIGURE E-23-b  S i m u l a t i o n o f the Model i n Tyrode  Solution  N5  FIGURE E-24-a  S i m u l a t i o n o f the Model i n Tyrode S o l u t i o n  00  FIGURE E-24-b  S i m u l a t i o n o f the Model i n Tyrode S o l u t i o n  FIGURE E-25-a  S i m u l a t i o n o f the Model i n P a p a i n  FIGURE E-25-b  Simulation of the Model i n Papain  APPENDIX F  POTENTIOMETER VALUES FOR SIMULATION  132.  Potentiometer's Name  21  23  24  25  E- 22  E- 23  E- 24  E- 25  Q03  0 .1  0 .1  0. 1  0. 1  0. 1  0. 1  0. 1  0. 1  Q.13  0 .9  0 .9  0. 9  0. 9  0. 9  0. 9  0. 9  0. 9  Q04  0 .2  0 .2  0. 2  0. 2  0. 2  0. 2  0. 2  0. 2  Oil  0 .01  0 .01  0. 01  0. 01  0. 01  0 . 01  0. 01  0. 01  Q.15  0 .5  0 .5  0. 4  0. 5  0. 4  0. 4  0. 5  0. 4  Q05  0 .8  0 .6  0. 9  0. 2  0. 7  0. 8  1, 000  0. 6  Q09  0 .5  0 .5  0. 4  0. 5  0. 4  0. 4  0. 5  0. 4  Q.08  0 .8  0 .6  0. 8  0. 8  0. 6  0. 7  0. 9  0. 6  Q18  0 .45  0 .6  0. 6  0. 5  0. 6  0. 6  0. 6  0. 5  Q17  0 .4  0 .5  0. 5  0. 6  0. 3  0. 4  . 0. 6  0. 6  Q19  0 .18  0 .05  0 . 14  0. 25  0 . 075  0 . 12  0 . 20  0. 25  Q33  0 .2  0 .35  0 . 15  0. 2  0. 3  0 . 25  0 . 15  0. 2  Q.31  0 .1  0 .1  0. 1  0. 1  0. 1  0. 1  0. 1  0. 1  Q32  0 .05  0 .05  0. 05  0 . 05  0. 05  0 . 05  0. 05  0. 05  Q.44-  0 .1  0 .1  0. 1  0. 1  0. 1  0. 1  0. 1  0. 1  Q;42  0 .45  0 .1  0. 4  0. 4  0. 2  0. 3  0. 6  0. 4  

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