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Application of surface coils to in-vivo studies using ³¹P-NMR spectroscopy Schachter, Joyce 1985

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APPLICATION OF SURFACE COILS TO IN-VIVO STUDIES USING 31P-NMR SPECTROSCOPY by JOYCE SCHACHTER B.Sc.(Hons.), Simon F r a s e r U n i v e r s i t y , 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Chemistry) We accept t h i s t h e s i s as conforming *:o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA August 1985 e Joyce Schachter, 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 (3/81) i i A B S T R A C T T h e w o r k d e s c r i b e d i n t h i s t h e s i s i s d i v i d e d i n t o t w o p a r t s : t e s t i n g a n d e v a l u a t i o n o f s o m e s u r f a c e c o i l s , a n d a p p l i c a t i o n o f t h e s u r f a c e c o i l s t o in-vivo s t u d i e s . I n p a r t i c u l a r , t h e l o c a l i z a t i o n p r o p e r t i e s o f s u r f a c e c o i l s w e r e e x a m i n e d a n d o p t i m i z e d u s i n g t h e h i g h e s t p e r f o r m a n c e c o i l g e o m e t r y a n d w i r e . A p p l i c a t i o n o f t h e s u r f a c e c o i l t e c h n i q u e t o in-vivo s t u d i e s i n v o l v e d m e a s u r i n g c h a n g e s i n m e t a b o l i c s t a t u s o f m u s c l e a n d b r a i n t i s s u e i n r a t s u s i n g 3 1 P s p e c t r o s c o p y . T h e p r o p e r t i e s o f s u r f a c e c o i l s h a v e b e e n s t u d i e d b y e v a l u a t i n g t h e i r e x c i t a t i o n p a t t e r n s w i t h ' H a n d 3 1 P NMR s p e c t r o s c o p y . S u r f a c e c o i l s , m a n u f a c t u r e d i n d i f f e r e n t s i z e s , g e o m e t r i e s , a n d m a t e r i a l s w e r e t e s t e d f o r Q f a c t o r s , s i g n a l - t o - n o i s e r a t i o s , a n d p u l s e w i d t h s r e q u i r e d f o r e x c i t a t i o n o f t h e s a m p l e . A s i l v e r p l a t i n g o n t h e c o p p e r w i r e u s e d t o f a b r i c a t e t h e s u r f a c e c o i l s w a s f o u n d t o i n c r e a s e t h e Q a n d s i g n a l - t o - n o i s e o f t h e c o i l . E x a m i n a t i o n o f t h e e x c i t a t i o n p a t t e r n s o f t h e s u r f a c e c o i l s w i t h p o i n t s a m p l e s c h a r a c t e r i z e d t h e B , f i e l d o f t h e c o i l s a s d e c r e a s i n g a x i a l l y a n d r a d i a l l y f r o m t h e c o i l . C a l c u l a t i o n s o f t h e m a g n i t u d e o f t h e B , f i e l d r e v e a l t h a t i t s d o m e - l i k e s h a p e e x t e n d s t o a p p r o x i m a t e l y o n e c o i l r a d i u s a b o v e t h e s u r f a c e c o i l . I t w a s f o u n d t h a t s a m p l e s l y i n g o u t s i d e t h e d o m a i n o f t h i s i i i " s e n s i t i v e volume" d i d not c o n t r i b u t e t o a s p e c t r u m . These d a t a were a l l c o r r e l a t e d and t h e "0.9" s i l v e r p l a t e d c o i l was deemed t o be t h e most e f f i c i e n t c o i l w i t h w h i c h t o p u r s u e f u r t h e r in-vivo s t u d i e s . In-vivo 3 1 P s t u d i e s of r a t t i s s u e s were p r e c e d e d by in-vitro s p e c t r a l measurements of v a r i o u s m e t a b o l i t e s a t p h y s i o l o g i c a l c o n c e n t r a t i o n s . T h e s e s t a n d a r d s were u s e d t o a i d i n t h e i d e n t i f i c a t i o n of r e s o n a n c e s i n t h e in-vivo s p e c t r a . M e t a b o l i c c h a n g e s s u c h as a r t i f i c i a l l y i n d u c e d i s c h e m i a i n m u s c l e , d e c e a s e d b r a i n , and a r t i f i c i a l l y i n d u c e d b r a i n d e m e n t i a were compared w i t h " n o r m a l " 3 1 P s p e c t r a of a n a e s t h e t i z e d r a t t i s s u e s . I t was f o u n d t h a t oxygen d e p r i v a t i o n i s r e a d i l y o b s e r v e d w i t h t h i s t e c h n i q u e whereas t h e p r e p a r a t i o n of b r a i n d e m e n t i a c a n n o t be d i a g n o s e d w i t h 3 1 P NMR s p e c t r o s c o p y . i v TABLE OF CONTENTS CHAPTER I - INTRODUCTION 1 CHAPTER II - PROPERTIES OF SURFACE COILS 9 2.1 - I n t r o d u c t i o n 10 2.2 - Theory 11 2.3 - Surface C o i l s and Q Fa c t o r 21 2.4 - S i g n a l - t o - N o i s e and the 90 Degree Pulse 2 4 2.5 - Two and Three "Point" Experiments 30 2.6 - C a p i l l a r y Tube Experiments 36 2.7 - Depth and Pulse Width i n Surface C o i l s 44 2.8 - Summary 49 2.9 - Experimental 5 0 CHAPTER III - IN-VIVO STUDIES USING 3 1 P NMR SPECTROSCOPY 51 3.1 - I n t r o d u c t i o n 52 3.2 - Surface C o i l f o r In-vivo Experiments 56 3.3 - In-vivo Experiments 57 (a) Background Information 57 (b) I n - v i t r o References 61 (c) In-vivo Muscle Spectra 66 (d) In-vivo B r a i n Spectra 70 3.4 - Experimental 81 CHAPTER IV - CONCLUSION 8 3 REFERENCES 8 8 APPENDIX 93 L I S T OF TABLES T a b l e I Q F a c t o r s f o r some s u r f a c e c o i l s T a b l e II M o l e c u l a r s t r u c t u r e and 3 1 P NMR s p e c t r a of s e l e c t e d p h o s p h o r u s - c o n t a i n i n g m e t a b o l i t e s . v i L I S T O F F I G U R E S Chap te r 11 F i g . 1 S c h e m a t i c r e p r e s e n t a t i o n o f a s i n g l e t u r n 13 s u r f a c e c o i l s h o wing r f m a g n e t i c f i e l d component v e c t o r s . F i g . 2 C o n t o u r p l o t of B , ( x y ) f i e l d of a s i n g l e t u r n 15 s u r f a c e c o i l . F i g . 3 C o n t o u r p l o t s f o r t h e B , ( x y ) f i e l d o f s u r f a c e 17 c o i l s . F i g . 4 S c h e m a t i c r e p r e s e n t a t i o n of s u r f a c e c o i l s 19 t e s t e d . F i g . 5 Peak h e i g h t v s p u l s e w i d t h f o r 90 d e g r e e a n g l e 25 d e t e r m i n a t i o n . F i g . 6 S i g n a l - t o - n o i s e r a t i o s f o r v a r i o u s c o i l s . 28 F i g . 7 (a) S c h e m a t i c r e p r e s e n t a t i o n of c o n f i g u r a t i o n 32 of t h r e e " p o i n t " s o u r c e s above s u r f a c e c o i l ; (b) p u l s e s e q u e n c e employed i n two and t h r e e " p o i n t " e x p e r i m e n t s ; ( c ) s p e c t r a f o r t h r e e " p o i n t " s o u r c e s of H 2 0 . F i g . 8 (A) Peak h e i g h t v s p u l s e w i d t h f o r two " p o i n t " 33 s o u r c e s o f H 20; (B) peak h e i g h t v s p u l s e w i d t h f o r t h r e e " p o i n t " s o u r c e s of H 2 0 . F i g . 9 S c h e m a t i c c r o s s - s e c t i o n of c a p i l l a r y tube 37 phantom. F i g . 1 0 S p e c t r a f r o m H 20 c a p i l l a r y t u b e phantom 38 e x c i t e d w i t h p u l s e w i d t h s from 5 - 7 0 Msec i n 5 usee i n c r e m e n t s . F i g . 1 1 Peak h e i g h t v s p u l s e w i d t h f o r rows of H 20 i n 40 c a p i l l a r y t u b e phantom. F i g . 1 2 Peak h e i g h t v s p u l s e w i d t h f o r rows of H 3 P 0 2 42 i n c a p i l l a r y t u b e phantom. F i g . 1 3 (A) Peak h e i g h t v s p u l s e w i d t h f o r 1H and 4 3 3 1 P ; (B) peak h e i g h t v s p u l s e w i d t h f o r rows of H 3 P 0 2 i n c a p i l l a r y t u b e phantom. F i g . 1 4 A x i a l d i s t a n c e and 90 d e g r e e p u l s e w i d t h 45 v i i r e l a t i o n s h i p f o r a v a r i e t y o f s u r f a c e c o i l s . F i g . 1 5 E n l a r g e d v e r s i o n of F i g . 1 4 B . 47 F i g . 1 6 80.3 MHz 1H s p e c t r a f r o m phantom c o m p r i s e d of 48 two a d j a c e n t v i a l s . C h a p t e r I I I F i g . 1 7 S e l e c t e d s t e p s o f t h e g l y c o l y t i c pathway. 54 F i g . 1 8 E n e r g e t i c s o f p h o s p h a t e exchange r e a c t i o n s of 59 m e t a b o l i sm. F i g . 1 9 In-vitro 3 1 P NMR s p e c t r a of v a r i o u s m i x t u r e s 65 of m e t a b o l i t e s a t pH=7. F i g . 2 0 3 1 P NMR in-vivo s p e c t r a of (a) human arm; (b) 67' r a t l e g . F i g . 2 1 3 1 P NMR in-vivo s p e c t r a of a r t i f i c i a l l y 69 i n d u c e d i s c h e m i a i n a r a t l e g . F i g . 2 2 3 1 P NMR in-vivo s p e c t r u m o f r a t b r a i n . 72 F i g . 2 3 3 1 P NMR in-vivo s p e c t r u m of r a t b r a i n . 74 F i g . 2 4 S c h e m a t i c d r a w i n g o f a b r a i n n e u r o n . 78 F i g . 2 5 3 1 P NMR in-vivo s p e c t r u m of l e s i o n e d r a t 79 b r a i n . v i i i Acknowledgement I would l i k e t o thank L a u r i e H a l l f o r h i s e n c o u r a g e m e n t and g u i d a n c e , E d i e McGeer and P e t e r R e i n e r f o r t h e i r c o o p e r a t i o n and s u p p o r t , and L a l i t h T a l a g a l a f o r many i l l u m i n a t i n g d i s c u s s i o n s and h i s i n v a l u a b l e h e l p . I would a l s o l i k e t o a c k n o w l e d g e t h e a s s i s t a n c e o f S a r a t h A byakoon. 1 CHAPTER I INTRODUCTION 2 The l a s t t w e n t y y e a r s has w i t n e s s e d many c h a n g e s and a d v a n c e s i n t h e a p p l i c a t i o n o f NMR t o c h e m i c a l and b i o c h e m i c a l s y s t e m s . From t h e i n i t i a l use of narrow b o r e magnets and l i q u i d u s s a m p l e s , t o whole-body tomographs and in-vivo i m a g i n g , t h e r e have emerged many new t e c h n i q u e s , new i n s t r u m e n t s , and a new v o c a b u l a r y t o match. L a u t e r b u r ' s i n t r o d u c t i o n o f NMR i m a g i n g 1 and t h e s u b s e q u e n t f u r o r c r e a t e d a f l u r r y o f r e s e a r c h a c t i v i t y i n t h i s a r e a . W i t h i n a few y e a r s , t h e b a s i c t e n e t s of i m a g i n g and t h e s c o p e o f e x p e r i m e n t a l t e c h n i q u e s were c o n s i d e r e d s u f f i c i e n t l y d e v e l o p e d t h a t NMR has a g a i n t u r n e d i t s f o c u s . However, a l o n g w i t h t h e i m p r e s s i v e t e c h n o l o g i c a l a d v a n c e s of t h e 60's and 70's i n F o u r i e r t r a n s f o r m a t i o n and NMR i m a g i n g , t h e r e has been p r o g r e s s i n t h e s c i e n c e a s w e l l . A f t e r t h e i n i t i a l i n t r o d u c t i o n of NMR i m a g i n g i n 1973, 1 many p h y s i c o - c h e m i c a l methods were d e s i g n e d t o e x p l o r e t h e c a p a c i t i e s and s c o p e of t h e t e c h n i q u e . Known as t h e b a c k - p r o j e c t i o n method, t h e f i r s t i m a g i n g e x p e r i m e n t d i f f e r e d f r o m c o n v e n t i o n a l NMR s i m p l y by t h e employment o f a m a g n e t i c f i e l d g r a d i e n t r a t h e r t h a n a homogeneous f i e l d . In e s s e n c e , t h e q u a n t i t y measured was t h e d e n s i t y of n u c l e i ( p r o t o n s ) i n t h e sample. Imaging soon became p o p u l a r w h i l e s p e c t r o s c o p y was somewhat o v e r l o o k e d by c o m p a r i s o n . The p o t e n t i a l a p p l i c a t i o n s o f i m a g i n g i n m e d i c i n e were q u i c k l y r e a l i z e d and r e s e a r c h was a d v a n c e d r a p i d l y i n t h i s d i r e c t i o n . In a d d i t i o n t o 3 new i m a g i n g t e c h n i q u e s b e i n g d e v e l o p e d , 2 ' 3 whole-body m a c h i n e s f o r human in-vivo i m a g i n g were p r o d u c e d , o p e r a t i n g a t low f i e l d s and u s i n g t h e e s t a b l i s h e d b a c k - p r o j e c t i o n method. The n o n - i n v a s i v e n a t u r e of t h i s i m a g i n g t e c h n i q u e c o n t r a s t e d w i t h o t h e r methods s u c h as CT, X - r a y s , PET, e t c . u s e d f o r t h e p o s s i b l e i d e n t i f i c a t i o n of tumours, m u l t i p l e s c l e r o s i s l e s i o n s and o t h e r c h r o n i c c o n d i t i o n s soon made NMR v e r y p o p u l a r as a m e d i c a l d i a g n o s t i c d e v i c e . A l t h o u g h In-vivo s p e c t r o s c o p y made some p r o g r e s s d u r i n g t h e p e r i o d when NMR i m a g i n g was b e i n g r a p i d l y e x p l o i t e d , i t was l e f t i n r e l a t i v e s e c l u s i o n u n t i l t h e p a s t few y e a r s . In a d d i t i o n t o p r o t o n s p e c t r a , o t h e r N M R - s e n s i t i v e n u c l e i c an be u s e d t o s t u d y t h e p r o c e s s e s of l i v i n g s y s t e m s . The most i m p o r t a n t and p r o m i s i n g n u c l e u s i s p h o s p h o r u s w h i c h i s c o n t a i n e d i n many of t h e i n t e r m e d i a t e s i n v o l v e d i n b i o - e n e r g y m e t a b o l i s m , e g . ATP, g l u c o s e - 6 - p h o s p h a t e , p h o s p h o c r e a t i n e . I n d e e d , t h e f i r s t p u b l i s h e d work of in-vivo h i g h - r e s o l u t i o n s p e c t r o s c o p y w h i c h a p p e a r e d i n 1980, was a 3 1 P s p e c t r u m of a r a t ' s l e g . " The k i n e t i c s and t h e r m o d y n a m i c s of i m p o r t a n t e n z y m e - r e g u l a t e d b i o c h e m i c a l r e a c t i o n s c a n be s t u d i e d w i t h t h i s n u c l e u s as w e l l . S i n c e numerous d i s e a s e s a f f e c t body ( i n c l u d i n g b r a i n ) m e t a b o l i s m , t h e p r o s p e c t o f u s i n g t h e 3 1 P n u c l e u s as a marker f o r d i s e a s e c o n t i n u e s t o be e x p l o r e d . A t t e m p t s t o a c h i e v e c l e a r l y r e s o l v e d p r o t o n s p e c t r a o f b i o l o g i c a l t i s s u e s h a v e , however, met w i t h 4 d i f f i c u l t i e s . The most n o t a b l e o f t h e s e , t h e dominance of t h e w a t e r peak, c h a l l e n g e d r e s e a r c h e r s t o c r e a t e new p u l s e s e q u e n c e s t o e l i m i n a t e o r a t l e a s t r e d u c e t h i s o b s t r u c t i o n . T h e r e now e x i s t s a c o l l e c t i o n o f s o - c a l l e d " w a t e r - s u p p r e s s i o n " t e c h n i q u e s 5 ' 6 w h i c h a r e d e s i g n e d s o l e l y f o r t h i s p u r p o s e . O t h e r n u c l e i b e i n g u s e d f o r in-vivo s p e c t r o s c o p y i n c l u d e 1 3 C , 2 3 N a , and 3 9 K . 7 " 1 3 U n t i l t h e l a s t few y e a r s , i m a g i n g and s p e c t r o s c o p y seemed t o be d e v e l o p i n g a l o n g d i f f e r e n t p a t h s . The two s u p p o s e d l y d i v e r g e n t d i s c i p l i n e s s t a r t e d t o merge a f t e r an i n t e r e s t was e x p r e s s e d i n o b t a i n i n g NMR-type d a t a from a l o c a l i z e d r e g i o n i n a s a m p l e . Thus, m e d i c a l u s e r s of NMR w i s h e d t o be a b l e t o image s p e c i f i c o r g a n s o r body p a r t s w i t h o u t i n t e r f e r e n c e e f f e c t s from s u r r o u n d i n g t i s s u e s ; t h i s d e s i r e grew o u t o f t h e i n t r i n s i c i n s e n s i t i v i t y of NMR, t h e c l u m s i n e s s o f t h e f i r s t i m a g i n g d e v i c e s and t h e r e s u l t i n g p o o r r e s o l u t i o n of t h e images. T h e r e was a l s o r e c o g n i z e d t o be a need f o r h i g h - r e s o l u t i o n s p e c t r o s c o p i c d a t a from l o c a l i z e d r e g i o n s . T hus t h e two "hands" of t h e same body f o u n d t h a t t h e y were g r a p p l i n g w i t h t h e same p r o b l e m . Magnet s y s t e m s w i t h i n t e r m e d i a t e s i z e d b o r e s , and u s u a l l y h i g h e r f i e l d s , were t h e n d e v e l o p e d a s t h e b a s i s f o r e q u i p m e n t u s e d t o improve e x p e r i m e n t a l methods. Though much o f t h e e a r l y work i n " l o c a l i z a t i o n " i n v o l v e d s t u d i e s o f p e r f u s e d o r g a n s and e x c i s e d t i s s u e , t h i s 5 a p p r o a c h was c l e a r l y u n s u i t a b l e f o r human p a t i e n t s ; hence t h e q u e s t f o r new methods of l o c a l i z i n g NMR was soon underway. The i d e a was t o o b t a i n a s much i n f o r m a t i o n as p o s s i b l e f r o m a d e s i g n a t e d volume o f t h e s a m p l e ; t h i s w o u l d not o n l y i n c l u d e s p i n d e n s i t y measurements by i m a g i n g , but a l s o t h e v e r y d e s i r a b l e c h e m i c a l s h i f t d a t a f o r a l l p e r t i n e n t n u c l e i . I d e a l l y t h e o b j e c t i v e was t o be a b l e t o c h o o s e any a r b i t r a r y volume e l e m e n t i n t h e sample f r o m w h i c h h i g h r e s o l u t i o n s p e c t r a would be o b t a i n e d . T h i s would be a l i m i t i n g c a s e f o r l o c a l i z e d s p e c t r o s c o p y , and v a r i o u s methods were d e m o n s t r a b l y s u c c e s s f u l i n a p p r o a c h i n g t h i s o b j e c t i v e u s i n g s o p h i s t i c a t e d h a r d w a r e and s o f t w a r e c o m b i n a t i o n s . 1 " ' 1 5 T h u s , t h e d i g r e s s i o n w i t h w h i c h NMR i m a g i n g had e n t i c e d p h y s i c a l c h e m i s t s r e t u r n e d back t o t h e main s c i e n c e of s p e c t r o s c o p y , but now w i t h a new e m p h a s i s : r e g i o n a l l o c a l i z a t i o n . The i n t r o d u c t i o n of s u r f a c e c o i l s " t o NMR s p e c t r o s c o p y s i g n i f i e d a c o n s i d e r a b l e a d v a n c e i n e n d e a v o u r s t o a c h i e v e t h i s s p a t i a l l o c a l i z a t i o n . A s u r f a c e c o i l , w h i c h i s a s m a l l l o o p o f w i r e , s e r v e s as t h e p r o b e u s e d w i t h i n a c o n v e n t i o n a l s u p e r - c o n d u c t i n g w i d e - b o r e magnet. The s i m p l i c i t y and e f f e c t i v e n e s s of a s u r f a c e c o i l , c o n t r a s t e d w i t h o t h e r more s o p h i s t i c a t e d t e c h n i q u e s s u c h as t h e s e n s i t i v e p o i n t m e t h o d 1 5 and T o p i c a l M a g n e t i c Resonance ( T M R ) 1 6 made t h e f o r m e r a p p e a r a s a v e r y a t t r a c t i v e p r a c t i c a l t o o l . S u r f a c e c o i l s of v a r i o u s s i z e s , m a t e r i a l s and g e o m e t r i e s , a c t i v a t e d by a 6 v a r i e t y of p u l s e s e q u e n c e s , have y i e l d e d a new and i n n o v a t i v e r e g i m e of NMR e x p e r i m e n t s . The key t o t h e l o c a l i z a t i o n p r o p e r t y of s u r f a c e c o i l s l i e s i n t h e i r e x c e l l e n t f i l l i n g f a c t o r , and t h e i r f l e x i b i l i t y i n b o t h shape and p o s i t i o n i n g w i t h r e s p e c t t o t h e e x p e r i m e n t a l r e g i o n o f i n t e r e s t . The c u r r e n t e m p h a s i s on in-vivo s p e c t r o s c o p y u s i n g n o n - i n v a s i v e t e c h n i q u e s has g e n e r a t e d f u r t h e r i n c e n t i v e s i n t o r e s e a r c h w i t h s u r f a c e c o i l s . The r a d i o - f r e q u e n c y ( r f ) m a g n e t i c f i e l d , o r s e n s i t i v e volume, c r e a t e d by p a s s i n g c u r r e n t t h r o u g h a s u r f a c e c o i l i s a h e m i s p h e r i c a l l y shaped r e g i o n w h i c h e x t e n d s t o one c o i l r a d i u s from t h e c o i l p l a n e a t i t s f u r t h e s t p o i n t . O u t s i d e t h e s e n s i t i v e volume, t h e B, f i e l d i s t o o weak t o i n d u c e any NMR s i g n a l s . T h e r e a r e c u r r e n t l y many g r o u p s u s i n g s u r f a c e c o i l s f o r in-vivo e x p e r i m e n t s , s i n c e t h e t e c h n i q u e i s q u i t e new, o p e r a t i o n a l l y s i m p l e , and e a s y t o implement. New e x p e r i m e n t a l methods a r e s t i l l b e i n g d e v e l o p e d even w h i l e t h e t h e o r e t i c a l u n d e r s t a n d i n g of t h e c o i l s i s b r o a d e n e d and p r e v i o u s l y u n r e c o g n i z e d f a c t o r s a c c o u n t e d f o r . T h u s , t h e r e i s now a need t o e v a l u a t e t h e c u r r e n t use of s u r f a c e c o i l s as a means f o r l o c a l i z i n g s p e c t r o s c o p y , and t h e i r p o t e n t i a l l y i m p o r t a n t r o l e i n t h e f u t u r e . At t h e moment t h e r e a r e many u s e r s o f s u r f a c e c o i l s but few i n n o v a t o r s o f s u r f a c e c o i l s c i e n c e . One r e a s o n f o r t h i s i s t h a t s u r f a c e c o i l s became v e r y p o p u l a r , v e r y q u i c k l y , p r e c i s e l y b e c a u s e of t h e i r s i m p l i c i t y , and w i d e s p r e a d use 7 of t h e c o i l s by and l a r g e p r e c e d e d a t h o r o u g h u n d e r s t a n d i n g o f t h e i r p r o p e r t i e s . I t i s e s s e n t i a l t o f i l l t h i s gap i n NMR s p e c t r o s c o p y and t o p r o v i d e r e a s o n a b l e j u s t i f i c a t i o n f o r c h o o s i n g t o use s u r f a c e c o i l s as t h e p r e f e r r e d method; t h i s r e q u i r e s t h a t t h e i r p e r f o r m a n c e be p l a c e d i n p e r s p e c t i v e w i t h o t h e r l o c a l i z a t i o n t e c h n i q u e s . In o r d e r t o do t h i s , i t i s i m p e r a t i v e t o f i r s t e l u c i d a t e f u l l y t h e p r o p e r t i e s and l i m i t a t i o n s of s u r f a c e c o i l s t h e m s e l v e s . T h i s t h e s i s i s an e x a m i n a t i o n o f t h e c u r r e n t s t a t u s of s u r f a c e c o i l s i n NMR s p e c t r o s c o p y , and t h e e x t e n t of t h e i r a p p l i c a t i o n t o in-vivo b i o l o g i c a l s y s t e m s . The e x i s t i n g t e c h n o l o g y r e g a r d i n g s u r f a c e c o i l s has been e v a l u a t e d and summarized i n C h a p t e r I I . R e s u l t s o f t h i s k i n d have been p r e v i o u s l y r e p o r t e d i n s e p a r a t e a c c o u n t s , but a g e n e r a l s u r v e y and commentary s u c h as t h i s has n o t p r e v i o u s l y a p p e a r e d . In a d d i t i o n , improvements t o t h e d e s i g n o f t h e c o i l s were made t o o p t i m i z e t h e i r p e r f o r m a n c e . V a r i o u s e x p e r i m e n t a l t e s t s , u s i n g c h e m i c a l phantoms, were p e r f o r m e d on t h e c o i l s t o i n t e r - c o m p a r e t h e i r e f f i c i e n c y . In view of t h e a p p l i c a t i o n of t h e c o i l s t o o t h e r s y s t e m s , a c o i l w i t h a p p r o p r i a t e o p t i m a l f e a t u r e s was c h o s e n f o r f u r t h e r e x p e r i m e n t a t i o n . C h a p t e r I I I p r e s e n t s a d i s c u s s i o n o f t h e a p p l i c a t i o n o f s u r f a c e c o i l t e c h n o l o g y t o in-vivo s y s t e m s . S p e c i f i c a l l y , t h e 3 1 P n u c l e u s was u s e d t o p r o b e t h e 8 m e t a b o l i c s t a t u s o f b r a i n and m u s c l e t i s s u e i n r a t s . P r e l i m i n a r y in-vitro s t u d i e s c o n s i s t e d of p r e p a r i n g phantoms c o n t a i n i n g p h o s p h o r u s m e t a b o l i t e s a t p h y s i o l o g i c a l c o n d i t i o n s and o b t a i n i n g t h e i r 3 1 P . NMR s p e c t r a t o be u s e d a s s t a n d a r d s f o r peak i d e n t i f i c a t i o n . The in-vivo e x p e r i m e n t s i n v o l v e d a p p l i c a t i o n of a p h y s i o l o g i c a l i n s u l t t o t h e sample p r i o r t o s p e c t r o s c o p i c measurement. G i v e n t h a t t h e d e p t h and b r e a d t h of knowledge about l i v i n g s y s t e m s r e t r i e v a b l e v i a NMR s p e c t r o s c o p y has n o t y e t r e a c h e d i t s l i m i t s , t h e r e r e m a i n many u n e x p l o r e d a r e a s , and p o s s i b l e i m p l i c a t i o n s and f u t u r e d i r e c t i o n s o f in-vivo 3 1 P e x p e r i m e n t a t i o n a r e d i s c u s s e d a t t h e end o f t h e t h e s i s . 9 CHAPTER II PROPERTIES OF SURFACE COILS 10 ( 2 . 1 ) I n t r o d u c t i o n The f l e x i b i l i t y i n d e s i g n o f s u r f a c e c o i l s has r e s u l t e d i n a s u n d r y c o l l e c t i o n of v a r i o u s s i z e s , s h a p e s , and m a t e r i a l s . The p a r t i c u l a r c o i l u s e d w i l l be d e t e r m i n e d by t h e t y p e of e x p e r i m e n t b e i n g p e r f o r m e d as w e l l a s t h e geometry of t h e s a m p l e . In t h i s c h a p t e r , c h o i c e of t h e most a p p r o p r i a t e c o i l was b a s e d on c o n s i d e r a t i o n s o f t h e s i z e and shape of a r a t ' s head, as w e l l a s t h e l o s s o f e f f i c i e n c y of t h e c o i l i n c o n t a c t w i t h a m i l d l y c o n d u c t i n g ( i . e . l i v i n g ) s p e c i m e n . The most a d v a n t a g e o u s p r o p e r t y o f s u r f a c e c o i l s i s t h e i r a b i l i t y t o o b t a i n s p e c t r a f r o m t h e r e g i o n o v e r w h i c h t h e y a r e p l a c e d . They l o c a l i z e s i g n a l s by v i r t u e o f t h e i r s i z e and r f d i s t r i b u t i o n . What was o r i g i n a l l y c o n s i d e r e d a d i s a d v a n t a g e of s u r f a c e c o i l s , namely t h e i r i n h e r e n t p r o d u c t i o n of a n o n u n i f o r m r a d i o - f r e q u e n c y m a g n e t i c f i e l d has a c t u a l l y been c o n v e n i e n t i n t h e a p p l i c a t i o n of r o t a t i n g frame z e u g m a t o g r a p h y 1 7 , d e p t h p u l s e s 1 8 " 2 1 , and DRESS 2 2 s p e c t r o s c o p y . D e p t h p u l s e s , i n p a r t i c u l a r , a r e w e l l s u i t e d t o o b t a i n i n g s p e c t r a f r o m r e g i o n s d e e p e r i n t h e sample w h i c h a r e s e p a r a t e d from t h e s u r f a c e c o i l by o t h e r l a y e r s l y i n g c l o s e r t o t h e s u r f a c e o f t h e s p e c i m e n . R o t a t i n g frame z e u g m a t o g r a p h y i s most u s e f u l f o r c o m p a r t m e n t a l i z e d o r g a n s s u c h as t h e eye o r h e a r t where membranes p r o v i d e t h e b o u n d a r i e s d e f i n i n g c o n c e n t r a t i o n g r a d i e n t s of m e t a b o l i t e s . The p a r t i c u l a r 11 sample and e x p e r i m e n t a l o b j e c t i v e w i l l d e t e r m i n e t h e d e g r e e of l o c a l i z a t i o n and hence t h e method r e q u i r e d . In t h i s c h a p t e r , c h a n g e s i n t h e e x c i t a t i o n p a t t e r n i n t h e s e n s i t i v e volume o f some s u r f a c e c o i l s have been e x a m i n e d e x p e r i m e n t a l l y . T h i s knowledge h e l p e d t o d e t e r m i n e t h e e x p e r i m e n t a l p a r a m e t e r s and methods r e q u i r e d f o r f u r t h e r in-vivo a p p l i c a t i o n s . T h e o r e t i c a l s t u d i e s of t h e e x c i t a t i o n p a t t e r n s o f s u r f a c e c o i l s have been p r e s e n t e d i n t h e l i t e r a t u r e . 2 3 ' 2 " (2.2) Theory S t u d i e s e m p l o y i n g s u r f a c e c o i l s have c r e a t e d t h e need t o d e v e l o p a t h e o r e t i c a l u n d e r s t a n d i n g o f t h e i r m a g n e t i c and e l e c t r i c a l p r o p e r t i e s a s t h e y i n f l u e n c e NMR e x p e r i m e n t s . V a r i o u s c a l c u l a t i o n s of t h e i n d u c e d inhomogeneous m a g n e t i c f i e l d have p r e s e n t e d g r a p h i c a l d i s p l a y s " ' 2 3 ' 2 " w h i c h a i d i n u n d e r s t a n d i n g t h e p r o p e r t i e s o f t h e s e s u r f a c e c o i l s , t h e i r a d v a n t a g e s and l i m i t a t i o n s . The m a g n e t i c f i e l d i n d u c e d by a c u r r e n t p a s s i n g t h r o u g h a s u r f a c e c o i l c an be c a l c u l a t e d a c c o r d i n g t o Smythe's e q u a t i o n s 2 5 , w h i c h a r e m o d i f i e d v e r s i o n s o f t h e B i o t - S a v a r t law. When a u n i t c u r r e n t f l o w s t h r o u g h t h e c o i l w i r e , t h e t o t a l r f m a g n e t i c f i e l d p r o d u c e d , B,, c a n be d i v i d e d i n t o an a x i a l component, B , and a r a d i a l component, B r , w h i c h c a n r o t a t e t h r o u g h 360 d e g r e e s i n t h e xz p l a n e . I n t h i s c a s e , t h e s u r f a c e c o i l l i e s i n t h e 1 2 xz p l a n e ( s e e F i g . 1 ( a ) ) . The component of B 1 w h i c h r o t a t e s o v e r t h e xy p l a n e , B , ( x y ) , i s of i n t e r e s t s i n c e i t i s o r t h o g o n a l t o t h e d i r e c t i o n o f t h e s t a t i c m a g n e t i c f i e l d , B 0 , i s r e s p o n s i b l e f o r c h a n g e s i n m a g n e t i z a t i o n i n t h e s ample, and i s d i r e c t l y r e l a t e d t o r e c e i v e r c o i l s e n s i t i v i t y . 2 6 S u r f a c e c o i l s , b e i n g b o t h t r a n s m i t t e r s and r e c e i v e r s a r e a p p r o p r i a t e l y s t u d i e d as s u c h . The r a d i a l component, B r , o f B, can a l s o be s p l i t i n t o two components: B r ( z ) , p a r a l l e l t o B 0 , and B r ( x ) , p e r p e n d i c u l a r t o b o t h B 0 and B = ( F i g . 1 ( b ) ) . The B ^ x y ) v e c t o r i s composed o f an a x i a l component, B . and a 3. p e r p e n d i c u l a r component, B ( x ) , d i r e c t e d a l o n g t h e x - a x i s whose m a g n i t u d e i s d e t e r m i n e d by t h e r a d i a l v e c t o r , B r . The component o f B r a l o n g t h e x - a x i s , B r ( x ) , i s g i v e n by B r ( x ) = B r s i n 0 (1) where 6 i s t h e a n g l e between B r and B 0 . B r ( x ) c a n now be v e c t o r i a l l y a dded t o B t o o b t a i n t h e t o t a l B , ( x y ) p r o d u c e d by t h e c o i l ( F i g . 1 ( c ) ) : B, ( x y ) = B a + B r (x) (2) To c a l c u l a t e B , ( x y ) , t h e Smythe e q u a t i o n s 2 5 t a k e t h e f o r m : 2ir [(b+x) 2 + y 2 ] , / 2 K + b : (b-x) 2 + y : ( 3 a ) F i g . 1 S c h e m a t i c r e p r e s e n t a t i o n of a s i n g l e t u r n s u r f a c e c o i l s howing r f m a g n e t i c f i e l d component v e c t o r s . 14 1 4 2ir x [ ( b + x ) 2 + y 2 ] 1 / 2 -K + b 2 + x 2 + y 2 ( b - x ) 2 + y 2 (3b) where u i s t h e p e r m e a b i l i t y o f t h e medium a b o u t t h e c o i l , b i s t h e c o i l r a d i u s , x and y a r e r e d u c e d c o o r d i n a t e s (s e e F i g . 1 ) , and K and E a r e t h e c o m p l e t e e l l i p t i c a l i n t e g r a l s o f t h e f i r s t and s e c o n d k i n d . 8 " 9 A B ^ x y ) c o n t o u r p l o t i s shown i n F i g . 2 f o r a s i n g l e t u r n c o i l w i t h a d i a m e t e r of 2.0 cm. Computer programs u s e d f o r c a l c u l a t i n g t h i s and o t h e r c o n t o u r p l o t s c an be f o u n d i n t h e A p p e n d i x . F u r t h e r c o n t o u r p l o t s and d i s c u s s i o n o f c o i l s w i t h d i f f e r e n t g e o m e t r y f o l l o w s l a t e r . The m a g n e t i c f i e l d i n d u c e d by a c u r r e n t p a s s i n g t h r o u g h a s u r f a c e c o i l c a n t h e r e f o r e be seen t o d i m i n i s h i n m a g n i t u d e w i t h i n c r e a s i n g d i s t a n c e from t h e c o i l p l a n e , and i s e f f e c t i v e l y a r a d i o f r e q u e n c y m a g n e t i c f i e l d g r a d i e n t . The r e g i o n above t h e c o i l o v e r w h i c h t h e B , ( x y ) f i e l d e x t e n d s , c a l l e d t h e " s e n s i t i v e volume", i s dome-shaped i n t h r e e d i m e n s i o n s , and. s u b t e n d s a h e m i s p h e r i c a l e x c i t a t i o n r e g i o n w i t h a p p r o x i m a t e l y t h e same r a d i u s as t h e c o i l ( F i g . 2 ( a ) ) . 2 0 The shape of t h e s e n s i t i v e volume depends upon t h e geometry of t h e c o i l . W i t h i n t h e s e n s i t i v e volume, a s e r i e s of f i n i t e s p i n p l a n e s c a n be i m a g i n e d t o e x i s t w h i c h a r e c o p l a n a r w i t h t h e s u r f a c e c o i l w h i c h c o r r e s p o n d t o t h e s p a t i a l d i s t r i b u t i o n of e x c i t a t i o n . T h e s e p l a n e s o f u n i f o r m e x c i t a t i o n e x t e n d r a d i a l l y a t l e a s t r/2 o f f - a x i s and 15 o I N X o e g -w -2.0 -1.0 0.0 1.0 2.0 X F i g . 2 C o n t o u r p l o t o f B , ( x y ) f i e l d o f a s i n g l e t u r n s u r f a c e c o i l w i t h same o r i e n t a t i o n as p e r F i g . 1 ; (a) z=0.0; (b) z=0.5 ( r e d u c e d c o o r d i n a t e s ) . Numbered c o n t o u r s show r e l a t i v e B, m a g n i t u d e s a s p e r c e n t a g e s o f B, a t t h e c o i l c e n t e r . 16 a x i a l l y a t l e a s t r/2 away from t h e c o i l p l a n e 2 0 ( d o t t e d l i n e i n F i g . 2 ) . F o r any p u l s e l e n g t h a p p l i e d , t h e n u c l e i i n a sample a d j a c e n t t o t h e c o i l w i l l e x p e r i e n c e a r a n g e of t i p a n g l e s d e p e n d i n g on t h e i r r e s p e c t i v e p o s i t i o n s w i t h r e s p e c t t o t h e c o i l . G e n e r a l l y , f o r a p u l s e w i d t h , t , a p p l i e d t h r o u g h t h e c o i l , t h e t i p a n g l e , a o f n u c l e i i n t h e sample w o u l d be a = 7 l t [B, (xy) ] (4) where 7 i s t h e g y r o m a g n e t i c r a t i o o f t h e n u c l e u s o f i n t e r e s t , I i s t h e c u r r e n t p a s s i n g t h r o u g h t h e c o i l , and B , ( x y ) i s t h e xy component of B,, t h e f i e l d i n d u c e d by a u n i t c u r r e n t p a s s i n g t h r o u g h t h e c o i l . S i n c e B ^ x y ) i s a s p a t i a l l y d e p e n d e n t q u a n t i t y , w h i c h d e c r e a s e s w i t h i n c r e a s i n g a x i a l d i s t a n c e f r o m t h e c o i l p l a n e , i t c a n n o t be c o n s i d e r e d as a c o n s t a n t . T h e r e f o r e , f o r a p r e d e t e r m i n e d p u l s e w i d t h , t h e t i p a n g l e s i n d u c e d w i l l assume a range of v a l u e s d e p e n d e n t on t h e m a g n i t u d e o f B , ( x y ) a t e a c h p a r t i c u l a r p o i n t . Thus, a i s a l s o a s p a t i a l l y d e p e n d e n t q u a n t i t y . T h i s f e a t u r e i s one o f t h e most i m p o r t a n t d i s t i n c t i o n s of s u r f a c e c o i l s a s o p p o s e d t o c o n v e n t i o n a l NMR p r o b e s ( s o l e n o i d , s a d d l e c o i l s ) where a i s c o n s t a n t o v e r a l a r g e volume of t h e sample. The d i a g r a m s i n F i g . 3 w h i c h a r e c o n t o u r s o f t h e B , ( x y ) of t h e c o i l s , a r e a l s o c o n t o u r s of c o n s t a n t t i p a n g l e p r o d u c e d by u n i t c u r r e n t p a s s i n g t h r o u g h t h e c o i l s . F o r example, a p u l s e p r o d u c i n g a 90 d e g r e e t i p a n g l e a t r away f r o m t h e 1 7 II F i g . 3 Contour p l o t s f o r B , ( x y ) f i e l d of s u r f a c e c o i l s with same o r i e n t a t i o n as per F i g . 1 : (a) f l a t ; (b) double t u r n ; (c) 0.9 c o i l ; column I: z=0.5; column I I : z=0.0. 18 c o i l c e n t e r would c a u s e a 30% i n c r e a s e i n s e n s i t i v e volume o f t h e c o i l compared t o a 90 d e g r e e t i p a n g l e a t r/2 f o r a s i n g l e t u r n c o i l . 2 4 G e n e r a l l y , l o n g e r p u l s e w i d t h s not o n l y i n c r e a s e t i p a n g l e s c l o s e t o t h e c o i l but a l s o e x t e n d t h e s e n s i t i v e volume o f t h e c o i l d e e p e r i n t o t h e sample. D e s p i t e t h i s e l e c t r o n i c t r i c k , e a c h o f t h e c o i l s i n F i g . 4 has a u n i q u e p a t t e r n of c o n t o u r s w h i c h i m p l i e s t h e p o t e n t i a l d e p t h o f i t s s e n s i t i v e v olume. The g e n e r a l t r e n d o f B, i s t o d e c r e a s e i n m a g n i t u d e as d i s t a n c e f r o m t h e c o i l p l a n e i n c r e a s e s . S i g n a l s coming from r e g i o n s f u r t h e r t h a n c a . r c o n t r i b u t e o n l y m a r g i n a l l y t o a s p e c t r u m and, i n f a c t , e x p e r i m e n t a l l y w i l l n ot a p p e a r f o r sam p l e s o f u n i f o r m shape and homogeneous c o n c e n t r a t i o n . T h i s a p p l i e s t o a l l c o i l s i n F i g . 4 . P r i o r t o r f e x c i t a t i o n , t h e e q u i l i b r i u m m a g n e t i z a t i o n of t h e sample, M 0, i s a l i g n e d w i t h t h e main m a g n e t i c f i e l d , B 0 . T h i s m a g n e t i z a t i o n i n t e r a c t s w i t h a p p l i e d r a d i o - f r e q u e n c y waves by r o t a t i n g away from B 0 t o some a n g l e a ( E q n . 4 ) . The component of m a g n e t i z a t i o n i n t h e xy p l a n e , M x y , i s t h e s o u r c e of t h e NMR s i g n a l r e c e i v e d : M x y = M ° s i n a C5) Sample r e g i o n s l y i n g c l o s e r t o t h e c o i l p l a n e e x p e r i e n c e a s t r o n g e r B ^ x y ) f i e l d t h a n r e g i o n s f u r t h e r away. 19 F i g . 4 S c h e m a t i c r e p r e s e n t a t i o n o f s u r f a c e c o i l s t e s t e d : (a) s i n g l e t u r n ; (b) d o u b l e t u r n ; ( c ) f l a t ; (d) e l l i p t i c a l ; (e) 0.9 c o i l . 20 S i m i l a r l y , m a g n e t i z a t i o n M l y i n g c l o s e t o t h e c o i l p l a n e i n d u c e s a s t r o n g e r s i g n a l i n t h e c o i l t h a n M x y , o f t h e same m a g n i t u d e , s i t u a t e d f u r t h e r away. T h i s b e h a v i o r , known as t h e p r i n c i p l e o f r e c i p r o c i t y , 2 7 i s an e x p r e s s i o n of t h e d u a l d e pendence o f t h e NMR s i g n a l , S, on B , ( x y ) i n e x p e r i m e n t s where a s i n g l e c o i l i s u s e d f o r t r a n s m i s s i o n and r e c e p t i o n 2 3 ( s e e Eqn.4 and 5 ) . S <* B, (xy) M x y ( 6 ) The s i g n a l - t o - n o i s e v a l u e i s a f f e c t e d n o t o n l y by t h e m a g n i t u d e o f t h e s i g n a l i t s e l f , but a l s o by t h e e f f e c t s of d i f f e r e n t t y p e s of n o i s e . N o i s e i s a c o m p o s i t e q u a n t i t y w h i c h a r i s e s from two s o u r c e s : r e s i s t i v i t y o f t h e c o i l i t s e l f , and n o i s e g e n e r a t e d by t h e s a m p l e . The l a t t e r of t h e s e i s a c o m b i n a t i o n of m a g n e t i c and d i e l e c t r i c l o s s e s w h i c h a r e i m p o r t a n t t o c o n s i d e r f o r " l o s s y " o r c o n d u c t i v e s a m p l e s . S i g n a l - t o - n o i s e a l s o d e p e n d s on t h e f r a c t i o n of t h e s e n s i t i v e volume w h i c h i s o c c u p i e d , c a l l e d t h e f i l l i n g f a c t o r . S u r f a c e c o i l s , b e i n g f l e x i b l e i n s i z e and shape have c h a r a c t e r i s t i c a l l y e x c e l l e n t f i l l i n g f a c t o r s . A h i g h q u a l i t y f a c t o r , Q, w i l l i m p r o v e a c o i l ' s s i g n a l - t o - n o i s e as w i l l o t h e r f a c t o r s p e r t a i n i n g t o t h e e l e c t r i c a l p r o p e r t i e s o f t h e c o i l a s w e l l a s t h e e n t i r e c i r c u i t . F o r a d e t a i l e d d i s c u s s i o n o f s i g n a l - t o - n o i s e r a t i o s , t h e r e a d e r s h o u l d r e a d r e f e r e n c e 28. 21 (2.3) S u r f a c e C o i l s and Q F a c t o r The q u a l i t y f a c t o r , Q, o f a r e c e i v e r c o i l , s u c h as a s u r f a c e c o i l , i s a f u n c t i o n of t h e c o i l ' s i n d u c t a n c e , L, and r e s i s t a n c e , R: Q = Lw/R (7) where u> i s t h e r e s o n a n t f r e q u e n c y o f t h e c i r c u i t . The Q of t h e r e s o n a n t c i r c u i t c a n be r e g a r d e d as a m a g n i f i c a t i o n f a c t o r t h a t d e t e r m i n e s how much t h e v o l t a g e a c r o s s L o r t h e c a p a c i t a n c e , C, i s i n c r e a s e d by t h e r e s o n a n t r i s e o f c u r r e n t i n a s e r i e s c i r c u i t . 2 9 The Q f a c t o r i s i m p o r t a n t s i n c e b o t h B, and s i g n a l - t o - n o i s e a r e p r o p o r t i o n a l t o i t s s q u a r e r o o t . A h i g h Q f a c t o r w i l l i n c r e a s e b o t h t h e s e q u a n t i t i e s w h i c h a r e d e s i r a b l y o p t i m i z e d a t h i g h e r v a l u e s . D u r i n g t h e t u n i n g p r o c e s s , t h e c a p a c i t a n c e of t h e r e c e i v e r c o i l c i r c u i t i s a d j u s t e d so t h a t LCo) 2 = 1 (8) w h i c h i s t h e r e s o n a n c e c o n d i t i o n f o r a s e r i e s c i r c u i t . The i n d u c t a n c e of t h e c o i l , w h i c h i s s l i g h t l y s e n s i t i v e t o t h e t y p e of sample p r e s e n t , t h e r e f o r e i n f l u e n c e s t h e s h a r p n e s s of t h e c i r c u i t ' s t u n i n g . Eddy c u r r e n t s p r o d u c e d i n " l o s s y " o r c o n d u c t i v e samples by t h e B, f i e l d c a u s e a d e c r e a s e i n t h e c o i l ' s i n d u c t a n c e and hence a l o w e r i n g o f t h e Q f a c t o r . 22 The Q f a c t o r s of v a r i o u s c o i l s were measured and a r e l i s t e d i n T a b l e I . V a l u e s f o r l o a d e d and u n l o a d e d c o i l s a r e shown. The c o i l s were l o a d e d by r e s t i n g a human arm on them. In t h i s way, t h e e f f i c i e n c y of t h e c o i l , w h i l e p e r f o r m i n g i n an a c t u a l e x p e r i m e n t was c l a r i f i e d . An a v e r a g e l o s s of 40% e f f i c i e n c y was n o t e d upon l o a d i n g t h e c o i l s c o n n e c t e d w i t h a d o u b l e - t u n e d c i r c u i t ( 3 1 P and 1 H ) . S i n g l e - t u n e d c i r c u i t s s u f f e r an even l a r g e r r e d u c t i o n i n e f f i c i e n c y when t h e y a r e l o a d e d ; t h e s e p r o b e s have h i g h e r i n i t i a l v a l u e s and c o n s e q u e n t l y show h i g h e r o v e r a l l e f f i c i e n c y . Most of t h e s t u d i e s of phantoms were p e r f o r m e d w i t h a d o u b l e - t u n e d c i r c u i t p r o b e , but t h e r a t s p e c t r a were t a k e n w i t h a s i n g l e - t u n e d p r o b e . I n i t i a l l y , t h e s u r f a c e c o i l s m a n u f a c t u r e d f o r t h e s e e x p e r i m e n t s were c o n s t r u c t e d f r o m h o l l o w c o p p e r t u b i n g . T h i s p r o d u c e d s u r f a c e c o i l s of r e a s o n a b l e e f f i c i e n c y : a 4.5 cm d i a m e t e r s i n g l e t u r n c o i l w i t h a Q o f 150 i s t y p i c a l f o r t h i s s i z e , shape and m a t e r i a l . S m a l l e r c o i l s were more d e s i r a b l e f o r t h e p l a n n e d in-vivo s p e c t r a ; t h e g e o m e t r i e s shown i n F i g . 4 were a d o p t e d by n e c e s s i t y o r s u g g e s t i o n s from t h e l i t e r a t u r e . 2 ' 3 0 ' 3 1 G e n e r a l l y , t h e c o i l s w i t h two t u r n s , w h e t h e r f l a t , or a d j a c e n t , p r o d u c e l a r g e r s e n s i t i v e volumes t h a n s i n g l e t u r n c o i l s , a s shown i n F i g s . 2 and 3. In a d d i t i o n , b o t h d o u b l e t u r n c o i l s , i n w h i c h t h e two l o o p s a r e not c o p l a n a r , p r o d u c e l a r g e r s e n s i t i v e volumes t h a n t h e d o u b l e t u r n f l a t c o i l . T h i s s u b t l e t y i n f l u e n c e s t h e e f f i c i e n c y of t h e c o i l s and t h e 23 T a b l e I Q F a c t o r s f o r some s u r f a c e c o i l s ( 3 , P ) (1H> O l-i •o C D 4-> <U o »-i u CO -rt C o -l-l c 3 u n l o a d e d 1 54 245 155 250 l o a d e d 140 52 88 164 u n l o a d e d 200 360 250 100 l o a d e d 95 155 180 100 24 d i v e r s i t y o f t h e i r a p p l i c a t i o n s t o v a r i o u s e x p e r i m e n t s . T h i n c o p p e r w i r e was u s e d f o r c o n s t r u c t i o n o f s m a l l e r c o i l s , u n t i l i t was f o u n d t h a t a s i l v e r c o a t i n g on t h e c o p p e r w i r e i n c r e a s e d c o i l e f f i c i e n c y . T h i s f o l l o w s f r o m t h e b e t t e r c o n d u c t i n g p r o p e r t i e s of s i l v e r and t h e we l l - k n o w n f l o w o f c u r r e n t a l o n g t h e s u r f a c e o f a w i r e . P e r u s a l of T a b l e I r e v e a l s t h a t t h e f l a t c o i l has t h e h i g h e s t l o a d e d Q f a c t o r and t h e 0.9 c o i l t h e l o w e s t . However, f u r t h e r c o n s i d e r a t i o n s of t h e s i g n a l - t o - n o i s e r a t i o , w h i c h w i l l be d i s c u s s e d l a t e r , p r o v i d e d s t r o n g a r g u m e n t s t o show t h a t t h i s c o i l was n o t t h e most a p p r o p r i a t e f o r f u t u r e in-vivo e x p e r i m e n t s . (2.4) S i g n a l - t o - N o i s e and t h e 90 Degree P u l s e A good i n d i c a t i o n of t h e e f f i c i e n c y of a s u r f a c e c o i l and i t s p o t e n t i a l f o r y i e l d i n g good s i g n a l - t o - n o i s e i s t h e w i d t h o f t h e 90 d e g r e e p u l s e a t t h e c o i l c e n t e r . A number of e x p e r i m e n t s were p e r f o r m e d t o d e t e r m i n e t h e p r o p e r p u l s e w i d t h f o r some o f t h e c o i l s i n F i g . 4 . F i r s t , a s m a l l b e a k e r , w i t h t h e d i a m e t e r of t h e s u r f a c e c o i l , was f i l l e d w i t h water and p l a c e d on t h e c o i l . A number o f one p u l s e e x p e r i m e n t s were p e r f o r m e d w i t h t h e p u l s e w i d t h v a r i e d s y s t e m a t i c a l l y i n r e g u l a r i n c r e m e n t s . The r e s u l t i n g d a t a i n F i g . 5 shows a s y m m e t r i c c u r v e s w h i c h i n c r e a s e t o a maximum and t h e n d e c r e a s e w i t h a s l o p e u n i q u e t o e a c h c o i l . In view of t h e r f m a g n e t i c f i e l d g r a d i e n t c r e a t e d by t h e s u r f a c e c o i l , t h e g r a p h s must be 25 0 j ! ! [ 0 25 50 75 P u l s e W i d t h ( » s e c ) F i g . 5 Peak h e i g h t v s p u l s e w i d t h f o r 90 d e g r e e a n g l e d e t e r m i n a t i o n ; t o p : 4.5 cm s i n g l e t u r n Cu c o i l ; m i d d l e : 2 cm d o u b l e t u r n Ag/Cu c o i l ; b o t t o m : 2 cm f l a t Ag/Cu c o i l . 26 i n t e r p r e t e d c a r e f u l l y s i n c e t h e sample i s n o t e x p e r i e n c i n g a u n i f o r m B, f i e l d . Even t h o u g h t h e sample has a u n i f o r m s p i n d e n s i t y , i . e . a b e a k e r of w a t e r , s i g n a l i n t e n s i t y c h a n g e s i n moving from t h e p l a n e o f t h e c o i l t o r e g i o n s a x i a l l y f u r t h e r away due t o t h e change i n t h e r f f i e l d . S i n c e t h e c u r v e r e p r e s e n t s t h e s i g n a l a c c u m u l a t e d f o r t h e sample o c c u p y i n g t h e e n t i r e s e n s i t i v e volume o f t h e c o i l , t h e maxima i n t h e s e g r a p h s must c o r r e s p o n d t o t h e p u l s e w i d t h w h i c h i n d u c e s t h e l a r g e s t s p a t i a l l y a v e r a g e d t i p a n g l e i n t h e sample. Once p u l s e w i d t h s become l o n g e r t h a n t h i s optimum v a l u e , c o n t r i b u t i o n f r o m s i g n a l s w i t h t i p a n g l e s g r e a t e r t h a n 180 d e g r e e s a r i s i n g f r o m some r e g i o n s w i t h i n t h e s e n s i t i v e v o l u m e , a r e i n c r e a s e d and w i l l be s u b t r a c t e d f r o m t h e t o t a l s i g n a l , c a u s i n g a d e c r e a s e i n t o t a l peak h e i g h t . In a d d i t i o n , t h e r e g i o n of t h e sample e x p e r i e n c i n g a 90 d e g r e e p u l s e i s f u r t h e r away from t h e c o i l where t h e B, f i e l d i s weaker. In c o n s i d e r a t i o n o f t h e p r i n c i p l e o f r e c i p r o c i t y , t h i s n u c l e a r i n d u c t i o n s i g n a l w i l l be weaker as w e l l . The shape o f t h e c u r v e f o r t h e f l a t c o i l ( F i g . 5 ( c ) ) d i f f e r s f r o m t h e r e s t . The s e c o n d r i s e o f t h e c u r v e r e s u l t s f r o m t h e i n t e r a c t i o n of t h e f i e l d s o f t h e s m a l l and l a r g e l o o p s w h i c h c r e a t e s a r e g i o n c l o s e t o t h e c o i l t h a t y i e l d s a s m a l l p o s i t i v e s i g n a l when most o f t h e s a m p l e ' s n u c l e i a r e s u b j e c t e d t o a c a . 180 d e g r e e p u l s e . 27 U s i n g t h e p u l s e w i d t h measured f r o m t h e maxima of t h e c u r v e s i n F i g . 5 , t h e f i r s t s e r i e s o f t e s t s f o r s i g n a l - t o - n o i s e were done. F i g . 6 shows t h e r e s u l t s of t h e s e t e s t s . H e r e , t h e e f f e c t s o f c o i l g eometry and m a t e r i a l a r e most a p p a r e n t . The two d o u b l e t u r n c o i l s had t h e same geo m e t r y and d i m e n s i o n s , o n l y d i f f e r i n g by t h e f a c t t h a t one was s i l v e r p l a t e d . A c o m p a r i s o n of c o i l g e o metry was made between two s i l v e r p l a t e d c o p p e r c o i l s e a c h o f d i a m e t e r 2.0 cm ( F i g . 4 b - 4 c ) . In e a c h of t h e s e c a s e s , an i n c r e a s e of 35-40% i n s i g n a l - t o - n o i s e was n o t e d w i t h t h e c o i l w h i c h y i e l d e d t h e h i g h e r s i g n a l - t o - n o i s e r a t i o . The s i l v e r p l a t i n g i n c r e a s e d s i g n a l - t o - n o i s e by 40% and t h e g e o m e t r y f a c t o r c a u s e d an improvement of 35%. T h e s e c h a n g e s a r e s i g n i f i c a n t and s h o u l d be c o n s i d e r e d when d e s i g n i n g c o i l s . I t s h o u l d be n o t e d t h a t t h e e x p e r i m e n t s u s e d t o t e s t s i g n a l - t o - n o i s e w i l l a l s o be a r e f l e c t i o n o f t h e e x t e n t of t h e s e n s i t i v e volume of t h e c o i l s , e x c e p t i n c a s e s where c o i l g e o m e t r y was c o n s t a n t and o n l y c o i l m a t e r i a l v a r i e d . In c o n s i d e r a t i o n of t h i s f a c t , m e a s u r i n g s i g n a l - t o - n o i s e p e r u n i t volume r a t h e r t h a n t h e e n t i r e s e n s i t i v e volume w o u l d p r o v i d e more i l l u m i n a t i n g d a t a . E s t i m a t e s o f s e n s i t i v e volumes were made by a p p r o x i m a t i n g t h e r a d i u s of t h e l o w e s t v a l u e d c o n t o u r i n F i g s . 2 and 3 and c a l c u l a t i n g t h e volume of a h e m i s p h e r e . T h i s r e v e a l e d t h a t t h e s i g n a l - t o - n o i s e v a l u e s r e p o r t e d i n F i g . 6 m a g n i f y t h e d i f f e r e n c e s between t h e t e s t e d c o i l s b u t show t h e same t r e n d as s i g n a l - t o - n o i s e 28 f l a t 15.3 4 6 2 double tu rn i 11.8 double turn ii 9.4 single turn 3 9 1 .9 coil 8 4 6 F i g . 6 S i g n a l - t o - n o i s e r a t i o s f o r v a r i o u s c o i l s ; t h i n l i n e : 5 ml b e a k e r o f 1 0 0 mM N a 2 H P 0 i , ; t h i c k l i n e : 1 0 0 ml b e a k e r of H 3 P O a ( 8 5 % ) ; ( i ) Ag/Cu c o i l ; ( i i ) Cu c o i l . 29 p e r u n i t volume v a l u e s . The o n l y e x c e p t i o n t o t h i s was t h e 2 cm s i n g l e t u r n c o i l w h i c h showed a l o w e r s i g n a l - t o - n o i s e t h a n t h e f l a t c o i l but h i g h e r s i g n a l - t o - n o i s e p e r u n i t volume. S i g n a l - t o - n o i s e v a l u e s were a l l e n h a n c e d w i t h th e u s e o f c o p p e r r f s h i e l d s f i t t e d a c r o s s t h e ends o f t h e magnet b o r e . T h i s i s a good p r a c t i c e i n any c a s e where t h e magnet and s p e c t r o m e t e r a r e not w e l l i s o l a t e d f r o m e x t e r n a l r f i n t e r f e r e n c e s . A r e c e n t a d v a n c e 3 2 i n s u r f a c e c o i l d e s i g n i n c o r p o r a t e s a F a r a d a y s h i e l d as a m a t r i x f o r t h e c o i l w i r e ; t h e e n t i r e ensemble r e s e m b l i n g a t h i c k c o i n . T h i s t y p e o f s h i e l d i n g i s a p p a r e n t l y more e f f e c t i v e t h a n a t e f l o n c o a t i n g f o r t h e w i r e a n d t h e c o i l i s s t i l l l i g h t w e i g h t and p o r t a b l e ; t h u s t h e s h i e l d i n g d e t r a c t s l i t t l e f r o m t h e c o i l ' s m o b i l i t y o v e r t h e sample. A n o t h e r example of t h e i n f l u e n c e of . g e o m e t r y and m a t e r i a l was c l e a r l y shown w i t h t h e 0.9 t y p e c o i l . The d i a m e t e r of t h i s c o i l was c a . 2.0 cm w i t h t h e e x a c t g eometry o u t l i n e d i n r e f e r e n c e ( 3 1 ) . In a d d i t i o n , a s l i g h t l y t h i c k e r w i r e was u s e d w h i c h was a l s o p l a t e d w i t h s i l v e r . The 0.9 c o i l r e g i s t e r e d much h i g h e r s i g n a l - t o - n o i s e t h a n any of t h e o t h e r c o i l s . The g e o m e t r y of t h i s c o i l c h a r a c t e r i z e s a B, m a g n e t i c f i e l d w h i c h e x t e n d s a x i a l l y f u r t h e r i n t o t h e s a m ple t h a n any o f t h e o t h e r c o i l s ( s e e F i g . 3 ( c ) ) . The l i n e a r l y d e c r e a s i n g m a g n e t i c f i e l d g r a d i e n t of t h i s c o i l i s a f e a t u r e w h i c h 30 s i m p l i f i e s t h e e x c i t a t i o n p a t t e r n w i t h i n t h e s e n s i t i v e volume and would e n s u r e a more u n i f o r m s i g n a l i n d u c t i o n t h a n would a n o n l i n e a r B, f i e l d . The d e p t h i n t o t h e sample o f t h e r e g i o n o f i n t e r e s t w i l l d e t e r m i n e t h e t y p e of c o i l u s e d . F o r e x p e r i m e n t s w h i c h r e q u i r e s h a l l o w s u r f a c e s p e c t r a , t h e f l a t c o i l w o u l d be more a p p r o p r i a t e . The 0.9 c o i l i s more u s e f u l f o r o b t a i n i n g i n f o r m a t i o n from a s e n s i t i v e volume up t o a d e p t h of a t l e a s t one r a d i u s , and p r e s e n t l y works b e s t w i t h s p e c i m e n s of u n i f o r m c o m p o s i t i o n a l t h o u g h e f f o r t s a r e underway t o a c h i e v e f u r t h e r l o c a l i s a t i o n w i t h i n t h e s e n s i t i v e volume. (2.5) Two and T h r e e P o i n t E x p e r i m e n t s The two and t h r e e " p o i n t " e x p e r i m e n t s were d e v e l o p e d t o t e s t t h e e f f e c t of t h e B, g r a d i e n t on t h e sample r e g i o n of i n t e r e s t . The " p o i n t s " were made f r o m t h e b o t t o m s o f 5 mm NMR t u b e s , f i l l e d w i t h water so t h a t t h e y a p p r o x i m a t e d a s p h e r e , or d r o p , o f w a t e r . In t h e t h r e e " p o i n t " e x p e r i m e n t , t h e 4.5 cm s i n g l e t u r n Cu c o i l was u s e d and t h e " p o i n t s " were p l a c e d a l o n g t h e c o i l a x i s a t 0, r / 2 , and r away from t h e c o i l center,. T h e s e " p o i n t s " of w a t e r were u s e d t o a p p r o x i m a t e s m a l l volume e l e m e n t s w i t h i n t h e s e n s i t i v e volume o f t h e c o i l o v e r w h i c h B , ( x y ) c o u l d be c o n s i d e r e d t o be c o n s t a n t . By e l i m i n a t i n g t h e v a r i a b i l i t y of B , ( x y ) o v e r t h e sample volume, i t would be p o s s i b l e t o o b s e r v e d i f f e r e n c e s i n t i p a n g l e , and f r e q u e n c y o f s i g n a l a m p l i t u d e m o d u l a t i o n w i t h p u l s e w i d t h 31 w i t h i n t h e s e n s i t i v e v olume. Two and t h r e e " p o i n t " e x p e r i m e n t s were done t o compare t h e s e e f f e c t s w i t h two s u r f a c e c o i l s of d i f f e r i n g s i z e , geometry and m a t e r i a l . A s t a t i c m a g n e t i c f i e l d g r a d i e n t was a p p l i e d c o a x i a l l y t o t h e c o i l t o i n d u c e a r e s o n a n c e f r e q u e n c y s h i f t between t h e " p o i n t " phantoms. G r a d i e n t s i n t h e B, f i e l d w i l l n ot i n t e r f e r e w i t h t h e r e s o l u t i o n o f d e t a i l s of c h e m i c a l s h i f t , u n l i k e B 0 g r a d i e n t s , w h i c h a c t s i m i l a r l y t o e l e c t r o n i c s h i e l d i n g . 3 3 The B 0 f i e l d was shimmed t o o b s e r v e a s i n g l e w a ter peak t o e n s u r e t h a t b o t h " p o i n t s " e x p e r i e n c e d t h e same m a g n i t u d e of t h e l i n e a r a p p l i e d g r a d i e n t . The p u l s e s e q u e n c e and r e s u l t i n g s p e c t r a a r e shown i n F i g . 7 . The p u l s e w i d t h was s y s t e m a t i c a l l y i n c r e a s e d f r o m 10 t o 75 usee i n i n c r e m e n t s of 5 Msec w i t h a d e l a y of 10 sec between e x p e r i m e n t s . I n i t i a l l y t h e s i g n a l i n t e n s i t y f r o m a l l " p o i n t s " i n c r e a s e s w i t h t h e p u l s e w i d t h but b e c a u s e t h e " p o i n t " i n t h e c o i l p l a n e i s s u b j e c t t o h i g h e r B , ( x y ) f i e l d t h a n t h e " p o i n t s " a t r / 2 , and r , i t s m a g n e t i z a t i o n e x p e r i e n c e s a g r e a t e r t i p a n g l e f o r a g i v e n p u l s e w i d t h , e.g. 180 d e g r e e s , w h i l e t h e " p o i n t " a t r/2 i s t i p p e d o n l y s l i g h t l y more t h a n 90 d e g r e e s . F i g . 8 i s a m a n i f e s t a t i o n of t h e d i f f e r e n c e i n a m p l i t u d e m o d u l a t i o n of t h e " p o i n t s " as a f u n c t i o n of t h e i r r e s p e c t i v e p o s i t i o n s w i t h r e s p e c t t o t h e c o i l p l a n e . S i n c e t h e t i p a n g l e (Eqn.4) i n d u c e d a t t h e two " p o i n t s " i s d i f f e r e n t , t h e s i g n a l , S, r e c e i v e d from t h e 32 F i g . 7 (a) Schematic r e p r e s e n t a t i o n of c o n f i g u r a t i o n of three " p o i n t " sources above s u r f a c e c o i l ; (b) pul s e sequence employed i n two and three " p o i n t " experiments; (c.) s p e c t r a f o r three " p o i n t " sources of H 20. Roman numerals correspond t o sample " p o i n t s " . ( s p e c t r a l width=±1000 Hz; scans=1; block size=1024 p o i n t s ; p u l s e width=25-500 usee (8=25 ttsec); r e l a x n delay=0.5 sec; y gradient=0.04 G/cm; l i n e broadening=10 Hz) 33 , , , , , , 1 , , , 0 1 2 3 4 5 (X10 2) P i i l se W i d t h (ysec) Fig.8 (A) Peak he i g h t vs pulse width f o r two " p o i n t " sources of H 20 u s i n g 2 cm f l a t Ag/Cu s u r f a c e c o i l ; (B) peak height vs pu l s e width f o r three " p o i n t " sources of H 20 u s i n g 4.5 s i n g l e t u r n s u r f a c e c o i l . Roman numerals correspond to sample " p o i n t s " shown i n F i g . 7 ( a ) . 3 4 two " p o i n t s " w i l l a l s o be d i f f e r e n t : S = M 0 s i n a (9) where s u b s t i t u t i n g f o r a y i e l d s S = M 0 s i n { 7 l t [ B , ( x y ) ] } (10) The f r e q u e n c y of a m p l i t u d e m o d u l a t i o n w i t h p u l s e w i d t h , ( t ) f o r e a c h " p o i n t " i s t h e n w h i c h w i l l be u n e q u a l f o r t h e two " p o i n t s " b e c a u s e B , ( x y ) a t t h e " p o i n t s " i s d i f f e r e n t . The r a t e of a m p l i t u d e m o d u l a t i o n o f t h e s i g n a l d e c r e a s e s w i t h i n c r e a s i n g a x i a l d i s t a n c e f r o m t h e c o i l . A n o t h e r " p o i n t " e x p e r i m e n t was done u s i n g two " p o i n t s " p l a c e d a l o n g t h e c o i l a x i s a t 0 and r / 2 away from t h e c o i l c e n t e r u s i n g t h e 4 . 5 cm s i n g l e t u r n c o p p e r c o i l . F i g . 8 shows t h e e f f e c t o f t h e B, g r a d i e n t on peak h e i g h t and a m p l i t u d e m o d u l a t i o n f o r t h e two and t h r e e " p o i n t " e x p e r i m e n t s . D e s p i t e t h e use of two d i f f e r e n t s u r f a c e c o i l s , t h e p a t t e r n of a m p l i t u d e m o d u l a t i o n of t h e " p o i n t s " i s s i m i l a r . I t i s e x p e c t e d t h a t t h e " p o i n t " l o c a t e d i n t h e c o i l p l a n e would p r o d u c e t h e h i g h e s t r e s o n a n c e peak h e i g h t s and have t h e h i g h e s t f r e q u e n c y o f a m p l i t u d e m o d u l a t i o n s i n c e B , ( x y ) i s a t a maximum t h e r e P f = 7 I [ B , ( x y ) ] 2 T T (11) 35 (Eqns.8 and 9 ) . The " p o i n t " a t r away f r o m t h e c o i l p l a n e w o u l d p r o d u c e a s i g n a l w i t h l o w e r peak h e i g h t and a m p l i t u d e m o d u l a t i o n f r e q u e n c y s i n c e i t i s s i t u a t e d i n a r e g i o n o f r e l a t i v e l y weaker B ^ x y ) f i e l d . F i g . 8 shows t h e s e e f f e c t s c l e a r l y f o r t h e two and t h r e e " p o i n t " e x p e r i m e n t s . A s e l e c t e d , though b r o a d , r e g i o n of sample volume c a n p o t e n t i a l l y be i s o l a t e d d e p e n d i n g on t h e p u l s e w i d t h u s e d . The most n o t a b l e d i f f e r e n c e between t h e g r a p h s f o r t h e two c o i l s i s i n t h e p u l s e w i d t h r e q u i r e d t o p r o d u c e a 90 d e g r e e t i p a n g l e i n e a c h " p o i n t " . However, t h i s has no b e a r i n g on t h e o b j e c t i v e o f t h i s e x p e r i m e n t . S e l e c t i v e s a m p l i n g by c h o o s i n g a p p r o p r i a t e p u l s e w i d t h s works r e a s o n a b l y w e l l f o r d i s c r e t e phantoms; f o r example, a t a p u l s e w i d t h o f c a . 100 //sec, t h e " p o i n t " i n t h e c o i l p l a n e u n d e r g o e s a 180 d e g r e e f l i p but t h e m a g n e t i z a t i o n a t r/2 i s a t c a . 100 d e g r e e s , hence a h i g h - r e s o l u t i o n s p e c t r u m c o u l d be o b t a i n e d w i t h m i n i m a l c o n t r i b u t i o n s from t h e f o r m e r " p o i n t " . However, i n a c o n t i n u o u s s p e c i m e n , some i n t e r f e r e n c e c o u l d a r i s e f r o m r e g i o n s w h i c h have m a g n e t i z a t i o n f l i p p e d t o a n g l e s i n t e r m e d i a t e between 90 and 180 d e g r e e s ; l o c a l i z a t i o n of s i g n a l s w i t h i n t h e s e n s i t i v e volume of a s u r f a c e c o i l by v a r y i n g t h e p u l s e w i d t h can be a c h i e v e d w i t h phantoms but i s n o t r e l i a b l e f o r p r e c i s e in-vivo a p p l i c a t i o n s . 36 (2.6) C a p i l l a r y Tube E x p e r i m e n t s The two and t h r e e " p o i n t " e x p e r i m e n t s gave e v i d e n c e f o r t h e p o t e n t i a l t o s e p a r a t e s i g n a l s b a s e d on t h e i r s p a t i a l c o o r d i n a t e s . The n e x t s t e p was t o d e t e r m i n e how t h i n and wide t h e i s o l a t e d r e g i o n c o u l d be. T h i s would show more c l e a r l y how t h e r a t e o f a m p l i t u d e m o d u l a t i o n d e c r e a s e d c h a r a c t e r i s t i c a l l y f o r e a c h s u r f a c e c o i l . T w e n t y - f o u r c a p i l l a r y t u b e s ( I . D . 1.5 mm, O.D. 3.0 mm, l e n g t h 5 cm) were a r r a n g e d i n t o s i x rows of f o u r t u b e s e a c h . E a c h row d e f i n e d a p l a n e of water 1.5 mm t h i c k s e p a r a t e d f r o m t h e a d j a c e n t p l a n e by a d i s t a n c e o f 1.5 mm. F i g . 9 shows t h e i d e a l and e x p e r i m e n t a l d i m e n s i o n s o f t h e phantom. T h i s phantom was u s e d w i t h b o t h w a t e r ( 1H) and p h o s p h o r u s a c i d ( 3 1 P ) . The p u l s e s e q u e n c e d e p i c t e d i n F i g . 7 was u s e d w i t h a s t a t i c m a g n e t i c f i e l d g r a d i e n t w h i c h was t h r e e t i m e s t h e m a g n i t u d e of t h a t u s e d i n t h e " p o i n t " e x p e r i m e n t s . T h i s was r e q u i r e d t o c l e a r l y s e p a r a t e t h e r e s o n a n c e f r e q u e n c y s h i f t s o f t h e sample p l a n e s . P u l s e w i d t h s were v a r i e d as b e f o r e and t h e r e s u l t i n g s p e c t r a a r e shown i n F i g . 1 0 . C l e a r l y , t h e use of s h o r t p u l s e w i d t h s a l l o w s o n l y t h e r e g i o n c l o s e s t t o t h e c o i l t o c o n t r i b u t e t o a s p e c t r u m ; t h a t i s , t h e s e n s i t i v e volume o f t h e c o i l e x t e n d i n g t o c a . r from t h e c o i l p l a n e ( F i g . 2 ) . S a m p l e l y i n g n e a r t h e c o i l w i r e e x p e r i e n c e s a g r e a t e r a m p l i t u d e m o d u l a t i o n t h a n t h a t f u r t h e r away, and t h e r e i s a " p o i n t " when t h e r e g i o n c l o s e s t t o t h e c o i l , i . e . 2.5 mm from t h e c o i l p l a n e , F i g . 9 S c h e m a t i c c r o s s - s e c t i o n o f c a p i l l a r y t u b e phantom. Murobers below a r r o w s a r e i d e a l d i m e n s i o n s (mm); numbers a b o v e a r r o w s a r e a c t u a l a v e r a g e d d i m e n s i o n s o f t h e h e i g h t o f e a c h row o f t u b e s from t h e b a s e . Roman n u m e r a l s c o r r e s p o n d t o phantom p l a n e s . 38 (*) W F i g . 1 0 S p e c t r a f r o m H 2 0 c a p i l l a r y t ube phantom e x c i t e d w i t h p u l s e w i d t h s f r o m 5 - 7 0 usee i n 5 usee i n c r e m e n t s ; (a) 2 cm f l a t Ag/Cu c o i l ; (b) 2 cm d o u b l e t u r n Ag/Cu c o i l . Roman n u m e r a l s c o r r e s p o n d t o phantom p l a n e s i n F i g . 9 . ( s p e c t r a l w i d t h = ± l 0 0 0 Hz; scans=1; b l o c k s i z e = 2 0 4 8 p o i n t s ; p u l s e d e l a y = 0 . 5 s e c ; y g r a d i e n t = 0 . 1 3 G/cm; l i n e b r o a d e n i n g = 1 0 Hz) 39 w i l l undergo a 180 degree f l i p while the spi n s 5.5 mm from the c o i l plane are being t i p p e d by some angle which l e a v e s a r e s u l t a n t magnetization i n the xy plane. In p a r t i c u l a r , the s i g n a l from n u c l e i c l o s e to the c o i l can be minimized (180 degrees) when s i g n a l s f u r t h e r away from the c o i l are maximized (90 degrees). T h i s can be seen f o r both f l a t , and double looped c o n f i g u r a t i o n s where the d i s p e r s i o n - l i k e s i g n a l i n d i c a t e s a f l i p angle of 180 degrees. I t should a l s o be noted that at c a . 40 usee f o r the f l a t c o i l , both planes nearest the c o i l , i . e . the e n t i r e area up to r/2 away w i l l not c o n t r i b u t e to the spectrum thus a l l o w i n g s p e c t r a l viewing of the region between 8 and 11 mm i n t o the sample. Peak amplitude modulation vs p u l s e width p l o t s are shown i n Fig.11 f o r a v a r i e t y of c o i l s . Features of note in these graphs are the " p o i n t s " where s i g n a l i n t e n s i t y of one plane vanishes while another plane i s maximized. T h i s occurs at 23 Msec and 40 jusec i n F i g . 10(b) where the s i g n a l s from the f i r s t plane and then from the e n t i r e r e g i o n up to ca. r are minimized. The double turn s i l v e r p l a t e d c o i l has a d i f f e r e n t p a t t e r n of r i s i n g s i g n a l i n t e n s i t i e s and indeed these p a t t e r n s are unique and c h a r a c t e r i s t i c to each c o i l . Longer p u l s e widths must be a p p l i e d to achieve the same f l i p angle due to t h i s c o i l ' s lower Q. In t h i s case, the only volume which c o u l d p o t e n t i a l l y be i s o l a t e d with a s p e c i f i c p ulse width i s the r e g i o n between r/2 and r , however, t h i s i s a f a i r l y 4 0 25 SO 75 WO False Width (vt*c> F i g . 1 1 Peak h e i g h t v s p u l s e w i d t h f o r rows o f H 2 0 i n c a p i l l a r y t u b e phantom; t o p : 2 cm f l a t Ag/Cu c o i l ; m i d d l e : 2 cm d o u b l e t u r n Ag/Cu c o i l ; b o t t o m : 2 cm d o u b l e t u r n Cu c o i l . Roman n u m e r a l s c o r r e s p o n d t o phantom p l a n e s i n F i g . 9 . 41 t h i c k s l i c e : 5 mm f o r a s u r f a c e c o i l o f 2 cm d i a m e t e r . T h e s e same e x p e r i m e n t s were r e p e a t e d w i t h p h o s p h o r u s a c i d , H 3 P 0 2 , t o t e s t t h e r e s p o n s e of 3 1 P n u c l e i ( s e e F i g . 1 2 ) . The o n l y d i f f e r e n c e i n t h e s e g r a p h s s h o u l d be an i n c r e a s e i n p u l s e w i d t h by a f a c t o r o f t h e r a t i o of t h e n u c l e a r g y r o m a g n e t i c r a t i o s of 3 1 P t o 1H. In p r a c t i c e , t h e g e n e r a l p a t t e r n o f s i g n a l i n t e n s i t y and a m p l i t u d e m o d u l a t i o n f o r a l l t h e p l a n e s was f o u n d t o be t h e same, whether 'H o r 3 1 P was measured. The e l l i p t i c a l c o i l was t e s t e d f o r i t s 90 d e g r e e p u l s e l e n g t h , ( 1 H and 3 1 P ) and f o r i t s a b i l i t y t o s e p a r a t e s i g n a l s u s i n g t h e c a p i l l a r y t u b e phantom ( 3 1 P o n l y , F i g . 1 3 ) . The p u l s e w i d t h s p r o d u c i n g t h e l a r g e s t peak h e i g h t d i f f e r by a f a c t o r o f c a . 1.5 w h i c h i s 60% o f t h e g y r o m a g n e t i c r a t i o s . The shape of t h e c u r v e s f o r t h e e l l i p t i c a l c o i l b e a r s s i m i l a r i t i e s t o b o t h c o a x i a l and f l a t s i l v e r p l a t e d c o i l s . I t i s s i m i l a r t o t h e c o a x i a l c o i l i n t h a t a t b o t h r/6 and r / 2 , t h e sample i s e x c i t e d w i t h p u l s e w i d t h s o f s i m i l a r v a l u e s whereas w i t h t h e f l a t c o i l , t h e s e two r e g i o n s r e q u i r e v e r y d i f f e r e n t p u l s e w i d t h s t o a c h i e v e a 90 d e g r e e t i p a n g l e . The s i m i l a r i t y t o t h e f l a t c o i l e x i s t s i n t h e p a t t e r n of a m p l i t u d e m o d u l a t i o n o f t h e f i r s t two p l a n e s o f t h e phantom. When th e f i r s t p l a n e u n d e r g o e s a 180 d e g r e e s p i n f l i p , t h e s p i n s i n t h e s e c o n d p l a n e a r e a t c a . 90 d e g r e e s , whereas f o r t h e c o a x i a l c o i l , t h e m a g n e t i z a t i o n i s c l o s e r t o 120 42 -6- _____ i • 1 1 f 0 25 50 75 100 P u l s e W i d t h (*sec) F i g . 12 Peak h e i g h t v s p u l s e w i d t h f o r rows o f H 3 P 0 2 i n c a p i l l a r y t u b e phantom; t o p : 2 cm f l a t Ag/Cu c o i l ; m i d d l e : 2 cm d o u b l e t u r n Ag/Cu c o i l ; b o t t o m : o b l a t e e l i p t i c a l Ag/Cu c o i l . Roman n u m e r a l s c o r r e s p o n d t o phantom p l a n e s i n F i g . 9 . 4 3 _4-| T 1 I I 0 2 5 5 0 7 5 100 P u l s e W i d t h ( v s e c ) Fig.13 (A) Peak height vs p u l s e width f o r rH and 3 1 P usi n g p r o l a t e e l l i p t i c a l c o i l ; (B) peak h e i g h t vs pulse width f o r rows of H 3 P 0 2 i n c a p i l l a r y tube phantom using p r o l a t e e l l i p t i c a l c o i l . Roman numerals correspond to c o i l p l a n e s i n F i g . 9 . 44 d e g r e e s . In a d d i t i o n , t h e p l a n e s f u r t h e r away have r e a c h e d a t most h a l f o f t h e i r maximum h e i g h t and w i l l n ot c o n t r i b u t e a s much t o t h e r e s u l t i n g s p e c t r u m a s i f t h e c o a x i a l c o i l were u s e d . T h i s c o i l was d e s i g n e d w i t h t h e s p e c i f i c p u r p o s e o f r a t b r a i n s p e c t r a i n mind but o t h e r c o i l s were f o u n d t o have h i g h e r Q and b e t t e r s i g n a l - t o - n o i s e . (2.7) D e p t h and P u l s e W i d t h i n S u r f a c e C o i l s F i g . 1 4 shows t h e r e l a t i o n s h i p between 90 d e g r e e p u l s e w i d t h and p e n e t r a t i o n d e p t h i n t o t h e sample t a k e n f r o m d a t a from t h e c a p i l l a r y t u b e and t h r e e " p o i n t " e x p e r i m e n t s . Most c o i l s f o l l o w t h e t r e n d w h i c h d i c t a t e s t h a t l o n g e r p u l s e w i d t h s a r e r e q u i r e d f o r e x c i t a t i o n of d i s t a n t r e g i o n s . The d o t s r e p r e s e n t t h e p u l s e w i d t h o f t h e maximum peak h e i g h t shown i n F i g . 5 f o r t h e 90 d e g r e e t i p a n g l e d e t e r m i n a t i o n e x p e r i m e n t . By i n t e r p o l a t i o n of t h e " p o i n t s " i n F i g . 1 4 , i t can be seen t h a t i n most c a s e s , t h i s p u l s e w i d t h c o r r e s p o n d s t o a r e g i o n of t h e sample l o c a t e d a b o u t r/4 a x i a l l y away from t h e c o i l ' s p l a n e . The d i m e n s i o n s o f t h e volume o f t h i s r e g i o n may be a p p r o x i m a t e d by t h e e x t e n t of B , ( x y ) u n i f o r m i t y shown i n F i g . 2 ( d o t t e d l i n e ) and t h e o u t e r d i a m e t e r of one c a p i l l a r y t u b e t o g i v e a volume of c a . 10 mm x 10 mm x 3 mm. P e r u s a l of F i g . 1 0 r e v e a l s t h a t a c a . 25 usee p u l s e w i d t h f o r t h e f l a t c o i l m i n i m i z e s t h e s i g n a l f r o m t h e p l a n e of s p i n s c l o s e s t t o t h e c o i l b u t y i e l d s an cn Axial Distance from Coi l F i g . 1 4 A x i a l d i s t a n c e and 90 d e g r e e p u l s e w i d t h r e l a t i o n s h i p f o r a v a r i e t y of s u r f a c e c o i l s . (A) 'H; (B) 3 , P ; (a) 4.5 cm s i n g l e t u r n Cu c o i l ; (b) 2 cm d o u b l e t u r n Cu c o i l ; (c) 2 cm f l a t Ag/Cu c o i l ; (d) 2 cm d o u b l e t u r n Ag/Cu c o i l ; (e) p r o l a t e e l l i p s e Ag/Cu; ( f ) o b l a t e e l l i p s e Ag/Cu. 46 a p p r e c i a b l e s i g n a l from t h e n e x t a d j a c e n t p l a n e o f s p i n s . T h i s p u l s e w i d t h i n F i g . 1 4 c o r r e s p o n d s t o t h e sample r e g i o n l o c a t e d c a . r/2 from t h e c o i l p l a n e , and i s n o t e d i n F i g . 5 on t h e c u r v e . In t h e 90 d e g r e e t i p a n g l e d e t e r m i n a t i o n , t h e r e f o r e , t h e maximum peak h e i g h t g e n e r a l l y c o r r e s p o n d s t o t h e sample r e g i o n c a . r/4 from t h e c o i l p l a n e w h i l e t h e p u l s e w i d t h r e q u i r e d t o e x c i t e t h e sample a t r/2 i s d e t e r m i n e d by t h e e f f i c i e n c y and geome t r y of t h e c o i l , t h e l a r g e (4.5 cm) s i n g l e t u r n c o i l d e v i a t e d f r o m t h i s t r e n d s h owing t h e maximum s i g n a l c o ming from r/2 away. F i g . 1 5 i s an expanded view of F i g . 1 4 b w i t h d a t a from t h e 2 cm s i n g l e t u r n Ag/Cu and 2 cm Ag/Cu 0.9 s u r f a c e c o i l s a d d e d . The 3 1 P d a t a shows t h a t t h e s l o p e of t h e 0.9 c o i l was t h e l e a s t p o s i t i v e ; t h i s c o i l was t h e b e s t i n s e p a r a t i n g t h e g r e a t e s t i n t e n s i t y s i g n a l f r o m e a c h p l a n e of s p i n s i n t h e c a p i l l a r y t u b e e x p e r i m e n t u s i n g t h e s m a l l e s t p u l s e w i d t h s o f a l l t h e c o i l s . The e x p e r i m e n t d e p i c t e d i n F i g . 1 6 was done u s i n g s m a l l v i a l s ( I . D . 1.3 cm, O.D. 1.4 cm, l e n g t h 5 cm). Two v i a l s were t a p e d t o g e t h e r and p l a c e d on t h e c o i l , v e r t i c a l l y ; one c o n t a i n e d e t h a n o l and t h e o t h e r e t h y l a c e t a t e , b o t h n e a t . The v i a l c o n t a i n i n g e t h a n o l was p l a c e d n e a r e s t t h e c o i l and t h e s p e c t r u m i s shown i n F i g . 1 6 ( a ) . A p u l s e w i d t h o f 24 Msec was u s e d so t h a t s i g n a l s f r o m t h e r e g i o n r/2 away would be m a x i m i z e d w h i l e m i n i m i z i n g t h o s e from t h e r e g i o n c l o s e r t o t h e c o i l . The 47 0 r / 4 r/2 3r/4 r Axial Distance from Coil Plane Fig.15 Enlarged version of Fig.14B; (a) prolate e l l i p s e Ag/Cu; (b) 2 cm double turn Ag/Cu; (c) 2 cm single turn Ag/Cu; (d) 2 cm f l a t Ag/Cu; (e) oblate e l l i p s e Ag/Cu; (f) 0.9 c o i l Ag/Cu. 48 (a) F i g . 1 6 80 MHz *H s p e c t r a f r o m phantom c o m p r i s e d o f two a d j a c e n t v i a l s (O.D. 1 cm); ( a ) e t h a n o l ( E t ) a d j a c e n t t o t h e c o i l ( c ) ; (b) e t h y l a c e t a t e (EA) a d j a c e n t t o t h e c o i l ; ( c ) v i a l s l a i d f l a t o v e r t h e c o i l . ( s p e c t r a l w i d t h = ± 7 0 0 . 2 8 Hz; scans=24; b l o c k s i z e = 2 0 4 8 p o i n t s ; p u l s e d e l a y = 0 . 5 s e c ) 4 9 s a m p l e w a s t u r n e d o v e r a n d t h e e x p e r i m e n t r e p e a t e d . N o i n t e r f e r e n c e f r o m t h e u p p e r v i a l w a s r e g i s t e r e d w i t h e i t h e r s p e c t r u m . T h e s a m p l e w a s t h e n t u r n e d f l a t s o t h a t b o t h l i q u i d s w e r e w i t h i n t h e s e n s i t i v e v o l u m e o f t h e c o i l . I n t h i s c a s e , c o n t r i b u t i o n s f r o m b o t h l i q u i d s w e r e o b s e r v e d i n t h e r e s u l t i n g s p e c t r u m . A t 24 Msec , h o w e v e r , t h e f l a t c o i l c a n e x p e r i m e n t a l l y " s e e " f r o m a b o u t 5 t o 15 mm a x i a l l y a w a y , b u t t h e r e w a s n o i n t e f e r e n c e f r o m t h e l i q u i d i n t h e u p p e r v i a l . E v e n a f t e r 1 0 0 s c a n s , t h e r e w a s n o d e t e c t a b l e c h a n g e i n t h e e t h a n o l s p e c t r u m , n o r w a s t h e r e a n y i n t e r f e r e n c e w h e n u s i n g h i g h e r p u l s e w i d t h s . T h i s i s t o b e e x p e c t e d s i n c e t h e l i q u i d s a r e o f c o m p a r a b l e p r o t o n c o n c e n t r a t i o n . I n t h e c a s e w h e r e t h e l o w e r v i a l c o n t a i n e d a m u c h l e s s c o n c e n t r a t e d s o l u t i o n t h a n t h e u p p e r , i n t e r f e r e n c e f r o m t h e m o r e c o n c e n t r a t e d s o l u t i o n w o u l d l i k e l y b e o b s e r v e d i n s p e c t r a w h e r e t h e l o w e r v i a l w a s a d j a c e n t t o t h e c o i l . (2.8) Summary T h e f l e x i b i l i t y i n d e s i g n o f s u r f a c e c o i l s i s a n a d v a n t a g e t o t h e i r u s e i n l o c a l i z a t i o n s p e c t r o s c o p y . T h e s i z e o f t h e s e n s i t i v e v o l u m e o f a s u r f a c e c o i l i s g e n e r a l l y d e t e r m i n e d b y t h e c o i l ' s r a d i u s b u t c a n b e s l i g h t l y i n f l u e n c e d i n p r a c t i c e b y g e o m e t r y a n d m a t e r i a l u s e d f o r t h e c o i l w i r e . I t i s d e s i r a b l e f o r a c o i l t o h a v e a h i g h Q f a c t o r t o o b t a i n g o o d s i g n a l - t o - n o i s e r a t i o s a n d B , f i e l d s o f h i g h e r m a g n i t u d e s . T h e t i p a n g l e s 50 i n d u c e d by c u r r e n t p a s s i n g t h r o u g h s u r f a c e c o i l s a r e s p a t i a l l y d e p e n d e n t and v a r y p r o p o r t i o n a t e l y w i t h t h e B, f i e l d . G e n e r a l l y , s h o r t p u l s e w i d t h s e x c i t e sample r e g i o n s l y i n g c l o s e t o t h e c o i l w h i l e l o n g e r p u l s e w i d t h s i n d u c e s i g n a l s from more d i s t a n t r e g i o n s i n t h e s e n s i t i v e v olume. The maximum peak h e i g h t o b t a i n e d by e x c i t i n g a homogeneous sample u s u a l l y a r i s e s from t h e l a r g e c o n c e n t r a t i o n of p o s i t i v e t i p a n g l e s l e s s t h a n 180 d e g r e e s i n t h e r e g i o n r/4 f r o m t h e c o i l p l a n e . S p e c i f i c p u l s e w i d t h s can t h e r e f o r e be u s e d as a c r u d e means of f u r t h e r i m p r o v i n g t h e l o c a l i z i n g p r o p e r t i e s of s u r f a c e c o i l s . T h e s e r e s u l t s a r e i n a greement w i t h t h e o r e t i c a l s t u d i e s p r e v i o u s l y r e p o r t e d i n t h e l i t e r a t u r e . 4 ' 2 3 ' 2 ' 1 2.9 E x p e r i m e n t a l A l l s p e c t r a were r e c o r d e d a t room t e m p e r a t u r e u s i n g a s p e c t r o m e t e r e q u i p p e d w i t h an O x f o r d R e s e a r c h Systems (1.89 T ) , 30 cm h o r i z o n t a l b o r e magnet and a N i c o l e t NT-300 c o n s o l e c o n t r o l l e d by a N i c o l e t 1280 computer and 239C p u l s e programmer o p e r a t i n g a t 80.3 MHz f o r 1H and 32.5 MHz f o r 3 1 P. Samples f o r NMR s p e c t r a were u s e d as n e a t l i q u i d s o r s o l u t i o n s p r e p a r e d a n a l y t i c a l l y by a c c u r a t e l y w e i g h i n g and d i s s o l v i n g i n d e i o n i z e d d i s t i l l e d w a t e r . The m a g n e t i c f i e l d g r a d i e n t s were p r o d u c e d by t h e s h im c o i l s u s i n g d r i v i n g v o l t a g e s g e n e r a t e d by d i g i t a l - t o - a n a l o g u e c o n v e r t e r s i n t h e 293C u n i t . 51 CHAPTER III IN-VIVO STUDIES USING 3 1 P NMR SPECTROSCOPY 52 (3.1) Introduction In-vivo s p e c t r o s c o p y i s r a p i d l y a p p r o a c h i n g t h e s t a g e where i t can be u s e d a s a c l i n i c a l d i a g n o s t i c t o o l . In t h e l a s t two y e a r s , t h e r e has been a s t e a d i l y i n c r e a s i n g number of p a p e r s p u b l i s h e d on b i o l o g i c a l a p p l i c a t i o n s of s p e c t r o s c o p y , most o f t e n u s i n g t h e 3 1 P n u c l e u s . A l t h o u g h t h e 3 1 P n u c l e u s has o n l y 1/15 t h e s e n s i t i v i t y of p r o t o n s , t h i s i s o t o p e o c c u r s n a t u r a l l y w i t h 100% abundance, t h e r e f o r e no e n r i c h m e n t i s n e c e s s a r y f o r sample p r e p a r a t i o n . The c u r r e n t o b j e c t i v e i s t o c h a r a c t e r i z e m e t a b o l i s m as a c c u r a t e l y as p o s s i b l e . M e t a b o l i s m , c o n s i d e r e d an i m p o r t a n t key t o u n d e r s t a n d i n g d i s e a s e d s t a t e s , i s a u n i v e r s a l p r o c e s s t h a t i s c h e m i c a l l y i d e n t i c a l f o r a l l e n e r g y p r o c e s s e s i n humans, and c h e m i c a l l y s i m i l a r between s p e c i e s and even t h e p l a n t and a n i m a l k ingdoms. The t e n , o r so, c l e a r l y r e s o l v e d p e a k s i n a 3 1 P h i g h r e s o l u t i o n s p e c t r u m c o m p r i s e a f a i r l y s i m p l e m a n i f e s t a t i o n of t h e m e t a b o l i c s t a t e of an i n d i v i d u a l . T r a n s i t o r y a i l m e n t s s u c h as i s c h e m i a and c h r o n i c c o n d i t i o n s s u c h as M c A r d l e ' s syndrome have a l r e a d y been i d e n t i f i e d w i t h 3 1 P NMR s p e c t r o s c o p y , 3 " and work i s c u r r e n t l y p r o g r e s s i n g t o l e n g t h e n t h e l i s t o f o b s e r v a b l e d i s o r d e r s . A p h o s p h o r u s - 3 1 s p e c t r u m o f l i v i n g t i s s u e i s a r e f l e c t i o n o f t h e f e r m e n t a t i o n s t a g e o f c a t a b o l i s m , t h e 53 a n a e r o b i c breakdown o f b i o c h e m i c a l " f u e l s " . The c h a i n o f r e a c t i o n s i n v o l v i n g t r a n s f o r m a t i o n o f g l u c o s e and e l e c t r o n - t r a n s f e r p r o c e s s e s r e s u l t s i n t h e f o r m a t i o n o f a d e n o s i n e t r i p h o s p h a t e ( A T P ) , t h e p r i m e e n e r g y s o u r c e f o r a l l c h e m i c a l r e a c t i o n s w i t h i n t h e body ( s e e F i g . 1 7 ) . The major p a r t i c i p a n t s of t h e m o l e c u l a r b i o - e n e r g y c y c l e a r e p h o s p h o r u s c o n t a i n i n g compounds: ATP, a d e n o s i n e d i p h o s p h a t e (ADP), p h o s p h o c r e a t i n e ( P C r ) , i n o r g a n i c p h o s p h a t e ( P i ) , p h o s p h o e s t e r s ( P E ) , and su g a r p h o s p h a t e s ( S P ) , a l l o f w h i c h show narrow r e s o n a n c e s , d i s p e r s e d o v e r a b a n d w i d t h of c a . 40 ppm i n t h e r e l a t i v e l y s i m p l e 3 1 P NMR s p e c t r u m . In l i v i n g t i s s u e s , ATP, PCr, and P i a r e p r e s e n t a t c o n c e n t r a t i o n s o f a t l e a s t 0.2mM, s u f f i c i e n t l y c o n c e n t r a t e d f o r d e t e c t i o n by NMR. Many o t h e r m e t a b o l i t e s and enzyme r e g u l a t o r s s u c h a s a d e n o s i n e monophosphate (AMP), p h o s p h o e t h a n o l a m i n e (PE A ) , and 2 , 3 - d i p h o s p h o g l y c e r a t e (2,3-DPG), e t c . a r e p r e s e n t i n c o n c e n t r a t i o n s o f o n l y a few m i c r o m o l a r , o r a r e f l o w i n g i n b l o o d and a r e not v i s i b l e i n t h e s p e c t r a , or a r e h i d d e n u n d e r a n o t h e r p r o m i n e n t peak. Changes e i t h e r i n peak h e i g h t o r c h e m i c a l s h i f t , a r e r e g a r d e d a s i n d i c a t i v e of a l t e r e d m e t a b o l i c s t a t u s . A p a r t i c u l a r l y u s e f u l m e t a b o l i c p o i n t e r i s t h e c h e m i c a l s h i f t of P i w h i c h has been shown t o be pH s e n s i t i v e . 3 5 T h u s , c o n d i t i o n s a s m i l d as m u s c l e f a t i g u e and l a c t i c a c i d b u i l d - u p have been d e t e c t e d by 3 1 P NMR.3" P r e v i o u s t o t h e a v a i l a b i l i t y o f NMR s p e c t r o s c o p y f o r in-vivo a n a l y s i s , m e t a b o l i c s t u d i e s 54 Stage I Conversion of sugars to glyceraldehyde phosphate; input of ATP glucose ATP c e l l membrane glycogen, starch glucose 1-rphosphate _ ADP glucose 6-phosphate fructose 6-phosphate ^ > ADP fructose 1,6-diphosphate I 2-glyceraIdehyde phosphate Stage II Oxidoreduction and coupled formation of ATP; output of lactate ATP* 1,3-diphosphoglycerate ADP ^ > 3-pho sphoglyc erat e I 2-phosphoglycerate phosphoenolpyruvate ADP ATP« pyruvate lactate F i g . 1 7 S e l e c t e d s t e p s o f t h e g l y c o l y t i c pathway. 55 of t h e b r a i n were f o r m i d a b l y d i f f i c u l t b e c a u s e of t h e p r o b l e m s a s s o c i a t e d w i t h t e c h n i q u e s s u c h as p e r f u s i o n and f r e e z e - e x t r a c t i o n . 3 6 C l e a r l y o b s e r v a b l e NMR p a r a m e t e r s , s u c h as t h o s e m e n t i o n e d above, have e n c o u r a g e d much r e s e a r c h i n t h e a r e a o f d i a g n o s t i c s p e c t r o s c o p y . So f a r , most NMR s p e c t r o s c o p i c s t u d i e s of in-vivo s y s t e m s have r e q u i r e d t h e s u b j e c t t o be s m a l l ( t o f i t i n t o t h e b o r e of t h e m a g n e t ) , mammalian ( f o r c o m p a r i s o n w i t h humans), and e a s i l y a n a e s t h e t i z e d . F o r t h e s e r e a s o n s r a t s have been t h e most commonly u s e d a n i m a l s , but g e r b i l s , g u i n e a p i g s , c a t s and dogs have a l s o p l a y e d r o l e s i n NMR e x p e r i m e n t s . The u n d e r l y i n g o b j e c t i v e o f s u c h s t u d i e s has been t o l e a r n more a b o u t human p h y s i o l o g i c a l p r o c e s s e s , p a r t i c u l a r l y o f t h e b r a i n ; s i m i l a r i t i e s between human and o t h e r mammalian b r a i n s , and e t h i c a l c o n s i d e r a t i o n s , make a n i m a l m o d e l s a v a l i d and c o n v e n i e n t c h o i c e f o r e x p e r i m e n t a l s p e c i m e n s . T h i s c h a p t e r p r e s e n t s t h e r e s u l t s o f e x p e r i m e n t s i n t e n d e d t o e l u c i d a t e and c h a r a c t e r i z e m e t a b o l i c c h a n g e s i n r a t t i s s u e s . P r e l i m i n a r y t e s t s in-vitro on phantoms w h i c h mimic p h y s i o l o g i c a l s y s t e m s were p e r f o r m e d t o i d e n t i f y v a r i o u s m e t a b o l i t e s by t h e i r c h e m i c a l s h i f t . T h e s e d a t a a r e p r e s e n t e d f i r s t ; t h e in-vivo r e s u l t s and d i s c u s s i o n t h e r e o f f o l l o w a f t e r w a r d s . 56 (3.2) S u r f a c e C o i l f o r In-vivo E x p e r i m e n t s The o b j e c t i v e of t h e work d e t a i l e d i n C h a p t e r II was t o e l u c i d a t e t h e p r o p e r t i e s o f some s u r f a c e c o i l s and f i n d t h e b e s t one s u i t e d f o r in-vivo s p e c t r o s c o p y . The e a s e w i t h w h i c h s u r f a c e c o i l s c a n be s h a p e d t o t h e geome t r y and s i z e o f t h e sample i s an a d v a n t a g e . However, t h e e l l i p t i c a l c o i l , w h i c h was b e t t e r s u i t e d t o t h e shape of a r a t ' s head, had l o w e r Q and s i g n a l - t o - n o i s e measurements t h a n t h e 0 . 9 c o i l . T h i s l a t t e r c o i l was made w i t h t h i c k e r w i r e w h i c h e n h a n c e s c o i l s e n s i t i v i t y , a l b e i t t h a t i t d o e s n o t p e r f o r m a s w e l l a s t h i n n e r w i r e i n terms of a c h i e v i n g h i g h r e s o l u t i o n . 3 6 In t h e p r e s e n t s t u d y , i n w h i c h i t was more i m p o r t a n t t o o b s e r v e g r o s s c h a n g e s i n t h e s p e c t r a r a t h e r t h a n v e r y h i g h l y r e s o l v e d p e a k s , t h e c o m b i n a t i o n o f t h e t h i c k w i r e and l i n e a r B, g r a d i e n t was j u d g e d t o be t h e most s u i t a b l e f o r t h e e n v i s a g e d e x p e r i m e n t s . A l l t h e in-vivo e x p e r i m e n t s were made u s i n g t h e s i n g l e t u n e d p r o b e . The v i a l e x p e r i m e n t d e p i c t e d i n F i g . 1 2 showed t h a t t h e major c o n t r i b u t i o n t o s p e c t r a emanated f r o m t h e r e g i o n o f sample w h i c h o c c u p i e d t h e s e n s i t i v e volume of t h e c o i l . The s e n s i t i v e volume f o r most c i r c u l a r s u r f a c e c o i l s i s t h e h e m i s p h e r e s u b t e n d e d by a l i n e w h i c h o r i g i n a t e s a t t h e c o i l c e n t e r , t h e l e n g t h o f w h i c h i s t h e c o i l ' s r a d i u s . The 0 . 9 c o i l had a d i a m e t e r o f 2 . 3 cm, mak i n g i t s s e n s i t i v e volume e x t e n d t o a p p r o x i m a t e l y 1 . 1 57 cm f r o m t h e c o i l p l a n e . On a v e r a g e , t h e head o f a. 300 g r a t i s c a . 2.0 cm wid e , but t h e b r a i n i t s e l f i s o n l y c a . 1.2 cm wide i n c l u d i n g l e f t and r i g h t l o b e s . The jaw and s k u l l of a r a t a r e c o n n e c t e d w i t h l i g a m e n t s , and a n i m a t e d by t h e m a s s e t t e r m u s c l e w h i c h i s c a . 4 mm t h i c k and l o c a t e d j u s t below t h e e a r and w h i c h e f f e c t i v e l y s h i e l d s t h e b r a i n from t h e s i d e . W i t h t h e measurement mode u s e d h e r e , t h e s e n s i t i v e volume e x t e n d s i n t o t h e b r a i n by c a . 7 mm, meaning t h a t o n l y one s i d e of t h e b r a i n i s s a m p l e d . T h i s i s i d e a l l y s u i t e d t o t h e o b j e c t i v e of t h e p l a n n e d e x p e r i m e n t s i n c e d i f f e r e n c e s between t h e r e s p e c t i v e s i d e s o f t h e b r a i n were o f i n t e r e s t . (3.3) In-Vivo E x p e r i m e n t s (a) B a c k g r o u n d I n f o r m a t i o n In t h i s s e c t i o n , some in-vivo 3 1 P NMR e x p e r i m e n t s w i l l be d i s c u s s e d . The c h o i c e of phosphorus-31 as t h e n u c l e u s o f i n t e r e s t i s s u i t e d t o t h e s t u d y o f m e t a b o l i s m s i n c e most of t h e m o l e c u l e s c o n t a i n i n g p h o s p h o r u s i n mammals a r e i n v o l v e d i n e n e r g y e x c h a n g e . B e f o r e e m b a r k i n g on t h e a c t u a l e x p e r i m e n t a l r e s u l t s , i t i s i n s t r u c t i v e f i r s t t o d i s c u s s some o f t h e b i o c h e m i c a l r e a c t i o n s w h i c h a r e b e i n g o b s e r v e d v i a NMR. A n i m a l s b u i l d up and br e a k down e n e r g y - s t o r e s by p r o c e s s e s c a l l e d a n a b o l i s m and c a t a b o l i s m , w h i c h a r e a k i n t o p h o t o s y n t h e s i s and r e s p i r a t i o n i n p l a n t s . S t o r a g e o f 58 e n e r g y i n mammals i s a c c o m p l i s h e d v i a d i g e s t i o n and a b s o r p t i o n o f f o o d s . E n e r g y needed t o do b i o c h e m i c a l work i s o b t a i n e d t h r o u g h t h e g l y c o l y t i c p a t h w a y , w h i c h i s t h e p r o c e s s by wh i c h g l u c o s e i s u t i l i z e d a s an e n e r g y s o u r c e w i t h l a c t a t e p r o d u c e d a s a b y - p r o d u c t . The major c o n s t i t u e n t s of t h e g l y c o l y t i c pathway a r e shown i n F i g . 1 7 3 7 . The s u b s t r a t e s e n c l o s e d i n t h e i n s e t p a r t a k e i n r e a c t i o n s w i t h i n t h e c e l l whereas t h e o t h e r s a r e p r e s e n t i n t h e i n t e r c e l l u l a r s p a c e s . F i g . 1 8 3 7 i s a s c h e m a t i c r e p r e s e n t a t i o n of t h e mechanism o f t h e ATP-ADP s y s t e m . B i o c h e m i c a l e n e r g y p r o c e s s e s of mammals a r e e c o n o m i c a l l y d e s i g n e d t o o b t a i n t h e maximum o u t p u t w i t h t h e mimimum i n p u t . Hence h i g h e n e r g y compounds a r e u s u a l l y c o u p l e d indirectly t o low e n e r g y compounds t o e f f e c t a t r a n s f e r of a l a r g e amount of e n e r g y w i t h l i t t l e l o s t t o t h e s y s t e m . The u n i v e r s a l c u r r e n c y f o r a l l in-vivo b i o c h e m i s t r y i s ATP; i t i s u s e d t o b u i l d e n e r g y - r e s e r v e compounds and i s e x p e n d e d i n e n e r g y r e q u i r i n g r e a c t i o n s . T h e r e a r e v e r y few b i o c h e m i c a l s w h i c h have g r e a t e r p h o s p h a t e l e a v i n g p o t e n t i a l t h a n ATP. P h o s p h o e n o l p y r u v a t e (PEP) i s one o f t h e s e compounds and i s l i s t e d i n F i g . 1 8 3 7 . In o r d e r t o p r o d u c e g l u c o s e - 6 - p h o s p h a t e , PEP l o s e s one p h o s p h a t e g r o u p t o become p y r u v a t e and ATP: PEP + ADP ;==^  p y r u v a t e + ATP The ATP t h e n c o m b i n e s w i t h g l u c o s e t o y i e l d g l u c o s e - 6 - p h o s p h a t e : 59 16 r !4 -4 h 2 0 phosphoenol pyruvate 1,3-diphospho-glycerate t High-energy P donors phosphocreatine reservoir PCr + ADP- *Cr + ATP Low-energy P acceptors V , glucose 6-phosphate glycerol 3-phosphate Reaction Coordinate F i g . 18 E n e r g e t i c s of. p h o s p h a t e e x c h a n g e r e a c t i o n s of m e t a b o l i s m . 60 g l u c o s e + ATP g l u c o s e - 6 - p h o s p h a t e + ADP In t h i s way a h i g h e n e r g y p h o s p h a t e d o n o r , ( P E P ) , i s c o u p l e d t o a low e n e r g y p h o s p h a t e a c c e p t o r , (G6P), w i t h o u t l a r g e amounts of e n e r g y b e i n g e x p e n d e d and a b s o r b e d i n one s t e p and t h e s y s t e m d o e s not s t r a y f a r f rom t h e r m a l e q u i l i b r i u m . In f a c t , e v i d e n c e s u g g e s t s 3 7 t h a t a l l b i o c h e m i c a l p r o c e s s e s a c t i n t h i s way w i t h ATP and ADP as t h e m e d i a t o r s i n t h e e n e r g y c y c l e . In t h e b a c k g r o u n d of a l l t h i s b i o c h e m i c a l a c t i v i t y , l i e s an e n e r g y r e s e r v o i r where h i g h e n e r g y p h o s p h a t e s a r e s t o r e d i n compounds c a l l e d p h o s p h a g e n s . The major phosphagen i n v e r t e b r a t e s i s p h o s p h o c r e a t i n e ; t h i s i s u s e d f o r s t o r i n g m e t a b o l i c p o t e n t i a l i n t h e form of p h o s p h a t e bond e n e r g y . PCr i s a n o t h e r m o l e c u l e w i t h a h i g h e r p h o s p h a t e l e a v i n g p o t e n t i a l t h a n ATP and i s formed by t h e a d d i t i o n o f a p h o s p h a t e g r o u p t o c r e a t i n e : PCr + ADP 5 = = ^ c r e a t i n e + ATP where t h e e q u i l i b r i u m l i e s t o t h e r i g h t . The r e a c t i o n above i s o f p r i m e i m p o r t a n c e i n m u s c u l a r c o n t r a c t i o n when PCr i s u s e d t o c r e a t e l a r g e amounts o f ATP. The amount of ATP i n m u s c l e a c t u a l l y r e m a i n s f a i r l y c o n s t a n t d u r i n g m u s c l e - c o n t r a c t i o n u n t i l t h e PCr l e v e l i s d e p l e t e d . I t has sometimes been f o u n d , t h a t more ATP was u s e d by t h e m u s c l e t h a n was p r e s e n t i n t h e c e l l b e f o r e t h e 61 c o n t r a c t i o n . 3 8 In t h e p r e s e n t s t u d i e s , two d i f f e r e n t b a r b i t u r a t e s were u s e d t o a n a e s t h e t i z e t h e r a t s : P e n t a b a r b i t o l , w h i c h i s w i d e l y u s e d f o r s h o r t - t e r m s t u d i e s , and i n a c t i n , f o r l o n g - t e r m measurements; b o t h i n j e c t e d i n t e r p e r i t o n e a l l y by s y r i n g e . The s h o r t - t e r m a n a e s t h e t i c was s u i t a b l e f o r c a . 45 m i n u t e s whereas t h e l o n g - t e r m one l a s t e d c a . 48 h o u r s . The o n l y v i s i b l e e f f e c t s on t h e r a t were s l o w e r b r e a t h i n g and g e n e r a l m u s c u l a r r e l a x a t i o n w h i c h would be e x p e c t e d i n an u n c o n s c i o u s ( s l e e p i n g ) s t a t e . (b) In-vitro R e f e r e n c e s In s p i t e o f ample s t u d i e s i n t h e l i t e r a t u r e , p r i o r t o any in-vivo s p e c t r o s c o p i c measurements, i t was deemed n e c e s s a r y t o i d e n t i f y t h e e x p e c t e d r e s o n a n c e s by t h e i r c h e m i c a l s h i f t s . S o l u t i o n s of v a r i o u s p h y s i o l o g i c a l m e t a b o l i t e s were p r e p a r e d a n a l y t i c a l l y in-vitro, and t i t r a t e d t o n e u t r a l pH. 3 1 P s p e c t r a were o b t a i n e d from m i x t u r e s o f t h e s e s o l u t i o n s u s i n g t h e same s u r f a c e c o i l a s f o r t h e in-vivo work. I t i s i m p o r t a n t t o n o t e t h a t an i n t e r n a l s t a n d a r d , PCr, was u s e d as t h e z e r o o f t h e a b c i s s a of t h e s p e c t r a and a l l c h e m i c a l s h i f t s were measured r e l a t i v e t o i t . T h i s c o r r e c t s d r i f t i n g o f t h e p e a k s due t o s m a l l d i f f e r e n c e s of t h e s h i m s e t t i n g s i n t h e magnet. R e c o r d i n g t h e s e s p e c t r a f a c i l i t a t e d f u r t h e r i d e n t i f i c a t i o n o f p e a k s i n in-vivo s p e c t r a by c o m p a r i s o n 62 o f c h e m i c a l s h i f t s . T a b l e I I l i s t s t h e m e t a b o l i t e s w h i c h a p p e a r c l e a r l y i n a 3 1 P s p e c t r u m o f l i v i n g t i s s u e , a l o n g w i t h t h e i r m o l e c u l a r s t r u c t u r e and NMR s p e c t r u m . S p e c t r a o f v a r i o u s m i x t u r e s f o l l o w i n F i g . 1 9 . In t h e c o u r s e of t h e breakdown o f g l u c o s e , p h o s p h o r u s c o n t a i n i n g m o i e t i e s a r e c r e a t e d , e a c h of w h i c h c a n t h e o r e t i c a l l y be f o u n d i n a 3 1 P NMR s p e c t r u m . However, s i n c e c h e m i c a l s h i f t s a r e d e p e n d e n t on m o l e c u l a r s t r u c t u r e and e l e c t r o n i c s h i e l d i n g , some o f t h e compounds shown i n T a b l e I and F i g . 19 d i f f e r o n l y s l i g h t l y i n c h e m i c a l s h i f t and may be d i f f i c u l t t o d i s t i n g u i s h i n a s p e c t r u m . P e r u s a l o f t h e s e l e c t i o n of compounds i n T a b l e I I i n d i c a t e s t h a t some r e s o n a n c e s may be h i d d e n by o t h e r s t r o n g e r s i g n a l s . I n f o r m a t i o n a b o u t t h e s e s u b s t a n c e s , s u c h a s c-AMP and o - p h o s p h o e t h a n o l a m i n e , f o r example, w i l l be more d i f f i c u l t t o e x t r a c t f o r t h i s r e a s o n . The l i m i t a t i o n s of 3 1 P s p e c t r o s c o p y i n v i e w o f t h i s f a c t w i l l be d i s c u s s e d l a t e r . G e n e r a l l y i t s h o u l d be n o t e d t h a t e s t e r p h o s p h a t e s a n d i n o r g a n i c p h o s p h a t e a p p e a r d o w n f i e l d from p h o s p h o c r e a t i n e and n u c l e o s i d e p h o s p h a t e s a p p e a r u p f i e l d . P h o s p h o r i c a c i d would a p p e a r d o w n f i e l d from PCr were i t p r e s e n t as w e l l . E x a c t c h e m i c a l s h i f t s r e c o r d e d f o r v a r i o u s p h o s p h o r u s c o n t a i n i n g m e t a b o l i t e s 3 6 have been o b t a i n e d in-vitro and c a n a c t a s a g u i d e f o r peak a s s i g n m e n t s . PC Pi o-I o—p=o 1 o I o—p=o ? r O — P = 0 N .a I / ^ N I \ ^ C H C H . N N H ^ j ^ H OH OH O - H C H . I I I /« 0 = P ~ N — C — N — C H , — c f NH O II O—P—o 20 0 -20 pptn T a b l e I I M o l e c u l a r s t r u c t u r e and 3 1 P NMR s p e c t r a of s e l e c t e d p h o s p h o r u s - c o n t a i n i n g m e t a b o l i t e s . AMP PEA o —C H . y°\ A d e n i n e H H i H \ | " j / H 0 = P O O H I O H C H . C H . N H . I O I 0=P—o I H H O I I I H — C C C H . I I ? ? c=o c=o I I CH 2 CH 2 • i i C H . C H . "I ^ ' I 2 0 0 - 2 0 ppm PEP C H 2 = C — c o -o—p—o-o Table II Molecular structure and 3 1 P NMR spectra of selected phosphorus-containing metabolites.(cont'd) 1.2 F i g . 1 9 I n - v i t r o 3 , P s p e c t r a o f v a r i o u s m i x t u r e s o f m e t a b o l i t e s a t pH=7; (A) ATP + ADP; (B) ATP + PCr; (C) ATP + PCr + P i ; (D) ATP + PCr + c-AMP; (E) ATP + PCr + c-AMP + P i ; (F) ATP + PCr + o-PEA + P i ; (1) 30 mM ATP; (2) 25 mM ADP; (3) 41 mM P C r ; (4) 25 mM P i ; (5) 0.5 M c-AMP; (6) 0.5 M o-PEA; u s i n g 2 cm 0.9 Ag/Cu c o i l . ( s p e c t r a l w i d t h = ± l 0 0 0 Hz; scans=200; b l o c k s i z e = 2 0 4 8 p o i n t s ; p u l s e d e lay=2 s e c ; l i n e b r o a d e n i n g = 1 0 Hz) 66 ( c ) In-Vivo M u s c l e S p e c t r a M u s c l e t i s s u e i s u n d e r s t a n d a b l y o f i n t e r e s t i n a p p l i c a t i o n s o f 3 1 P NMR s i n c e l a r g e amounts of e n e r g y a r e u s e d i n a n i m a t i n g a s k e l e t o n . The b i o c h e m i c a l e n e r g y pathway c a n e a s i l y be t a p p e d w i t h m u s c l e as w e l l . Human s u b j e c t s may be a s k e d t o e x e r c i s e an arm or l e g p r i o r t o o b t a i n i n g s p e c t r a o r r a t m u s c l e c a n a r t i f i c i a l l y be made i s c h e m i c . F i g . 2 0 ( b ) shows a 3 1 P s p e c t r u m o f a l e g of an a n a e ' s t h e t i z e d ( i n a c t i n ) r a t . M e t a b o l i t e s c l e a r l y v i s i b l e i n t h e s p e c t r u m a r e PCr, ATP, P i , and s u g a r p h o s p h a t e s . PCr and ATP a r e p r e s e n t i n c a . 20 mM and 5-10 mM c o n c e n t r a t i o n s r e s p e c t i v e l y . The ATP pe a k s a r e a l l o f s i m i l a r h e i g h t and l i n e w i d t h ; ADP i s p r e s u m a b l y b u r i e d under t h e s e r e s o n a n c e s . The l a c k of a s i g n a l f r o m 2 , 3 - d i p h o s p h o g l y c e r a t e i n m u s c l e i n d i c a t e s t h a t b l o o d and s k i n p h o s p h a t e s do n o t c o n t r i b u t e s i g n i f i c a n t l y t o t h e s p e c t r u m . 3 6 F i g . 2 0 ( a ) i s a 3 1 P s p e c t r u m o f a human arm shown t o i l l u s t r a t e t h e u n i v e r s a l c h a r a c t e r i s t i c s o f v e r t e b r a t e m u s c l e m e t a b o l i s m . D i f f e r e n c e s i n s i g n a l - t o - n o i s e and number o f a c q u i s i t i o n s between t h e two s p e c t r a a r e due t o improvements i n c o i l and p r o b e d e s i g n w h i c h o c c u r r e d i n b e t w e e n r e c o r d i n g t h e s e s p e c t r a . The method a d o p t e d f o r c h a r a c t e r i z i n g s p e c t r a a s m u s c l e o r b r a i n t i s s u e was t o measure t h e PCr//3ATP peak h e i g h t r a t i o . " T h e s e two p e a k s have been c h o s e n s i n c e F i g . 2 0 3 1 P NMR in-vivo s p e c t r a o f (a) human arm; (b) r a t l e g ; u s i n g 2 cm 0.9 Ag/Cu c o i l . [Human a r m ( u s i n g 2 cm d o u b l e t u r n Cu c o i l ) : p u l s e width=38 Msec; scans=400; b l o c k s i z e = l 0 2 4 p o i n t s ; l i n e b r o a d e n i n g = 8 Hz; Rat l e g ( u s i n g 2 cm 0.9 Ag/Cu c o i l ) : p u l s e width=12 usee; scans=200; b l o c k s i z e = 2 0 4 8 p o i n t s ; l i n e b r o a d e n i n g = 1 0 Hz; b o t h s p e c t r a : s p e c t r a l w i d t h = ± 1 0 0 0 ' H z ; p u l s e delay=2 s e c ] 68 t h e y a r i s e as r e s o n a n c e s from a s i n g l e s o u r c e r a t h e r t h a n a c o m b i n a t i o n of s i g n a l s . M u s c l e s p e c t r a g e n e r a l l y have a PCr/|3ATP r a t i o of c a . 4:1. In o r d e r t o o b s e r v e a d i f f e r e n t s t a t e of m e t a b o l i s m , an e l a s t i c was p l a c e d a r o u n d t h e r a t ' s l e g j u s t below t h e h i p j o i n t t o r e s t r i c t t h e f l o w of b l o o d t o and f r o m t h e l e g . E x p e r i m e n t s s u c h as t h i s have p r e v i o u s l y been r e p o r t e d i n t h e l i t e r a t u r e " ' 3 6 but were u n d e r t a k e n h e r e as a v e r i f i c a t i o n of t h e method and equipment u s e d . S p e c t r a were a c q u i r e d e v e r y c a . 4 m i n u t e s f o r a b o u t 1.5 h o u r s a f t e r w h i c h t h e e l a s t i c was removed, w i t h s p e c t r a c o n t i n u i n g t o be r e c o r d e d f o r a n o t h e r 40 m i n u t e s . R e s u l t s a r e shown i n F i g . 2 1 . D u r i n g t h e i n t e r v a l when t h e r a t ' s l e g became i n c r e a s i n g l y i s c h e m i c , i t c a n be c l e a r l y s een t h a t t h e p h o s p h o c r e a t i n e i s b e i n g d e p e l e t e d w i t h t h e concommitant i n c r e a s e o f i n o r g a n i c p h o s p h a t e . The s t e a d y s t a t e l e v e l s of ATP i n t h e s e s p e c t r a s u g g e s t t h a t PCr p l a y e d a m a j o r r o l e as a s o u r c e o f p h o s p h a t e e n e r g y , c o n t r a r y t o what would n o r m a l l y be e x p e c t e d . T h i s e x p e r i m e n t , however, i s a m a n i f e s t a t i o n of t h e e f f e c t s o f a b n o r m a l s t r e s s on m u s c l e t i s s u e , as o p p o s e d t o t h e e f f e c t s o f moderate e x e r c i s e . A c l o s e r l o o k a t F i g . 2 1 ( d ) - ( e ) s u g g e s t s t h a t t h e r e may be a l i m i t below w h i c h t h e e n e r g y s t o r e s o f PCr w i l l n o t f a l l . D u r i n g t h i s p e r i o d o f t h e e x p e r i m e n t , t h e l e v e l of PCr r e m a i n e d v i r t u a l l y c o n s t a n t . A s t r i k i n g f e a t u r e of t h i s s e t o f s p e c t r a i s t h e r a p i d i t y w i t h w h i c h PCr i s r e s t o r e d a f t e r 6 9 F i g . 2 A 3 1 P NMR in-vivo s p e c t r a o f a r t i f i c i a l l y i n d u c e d i s c h e m i a i n a r a t l e g u s i n g 2 c m 0 . 9 c o i l ; ( 1 ) S P ? ( 2 ) P i ; ( 3 ) P C r ; ( 4 ) A T P / A D P ; ( 5 ) A T P ; ( A ) p r i o r t o i n s u l t ; ( B ) a f t e r 2 0 m i n ; ( C ) a f t e r 4 4 m i n ; ( D ) a f t e r 6 4 m i n ; ( E ) a f t e r 8 4 m i n ; ( F ) 5 m i n a f t e r c i r c u l a t i o n r e s t o r e d ; ( G ) 3 0 m i n u t e s a f t e r c i r c u l a t i o n r e s t o r e d ; u s i n g 2 c m 0 . 9 A g / C u c o i l , ( s p e c t r a l w i d t h = ± l 0 0 0 H z ; s c a n s = 2 0 0 ; b l o c k s i z e = 2 0 4 8 p o i n t s ; p u l s e w i d t h = l 2 M s e c ; p u l s e d e l a y = 1 s e c ; l i n e b r o a d e n i n g = 1 0 H z ) 70 r e m o v a l o f t h e e l a s t i c o b s t r u c t i o n . W i t h i n 5 m i n u t e s o f t h e r e t u r n o f b l o o d c i r c u l a t i o n t o t h e r a t ' s l e g , PCr had been v i r t u a l l y r e s t o r e d t o i t ' s o r i g i n a l h e i g h t . E x e r c i s i n g a human f o r e a r m y i e l d s s i m i l a r r e s u l t s t o t h e above e x p e r i m e n t , t h o u g h n o t as d r a m a t i c . An i n c r e a s e o f i n o r g a n i c p h o s p h a t e w i t h o u t any e f f e c t on PCr i s t h e u s u a l o b s e r v a t i o n when t h e m u s c l e r e m a i n s o x y g e n a t e d . Under a n a e r o b i c c o n d i t i o n s , a d e c r e a s e i n m u s c l e pH, and b o r r o w i n g f rom PCr e n e r g y r e s e r v e s p r e v a i l s . (d) In-Vivo B r a i n S p e c t r a S k e l e t a l m u s c l e i s a c h o i c e s u b j e c t f o r 3 1 P NMR s p e c t r a b e c a u s e i t i s e a s i l y a c c e s s e d and shows d e t e c t a b l e c o n c e n t r a t i o n s o f p h o s p h o r u s c o n t a i n i n g m e t a b o l i t e s . However, b r a i n m e t a b o l i s m , b e i n g o f p r i m a r y i n t e r e s t h e r e was t h e o b j e c t o f f u r t h e r e x p e r i m e n t a t i o n . The f i r s t 3 1 P in-vivo r a t b r a i n s p e c t r u m was p u b l i s h e d i n 4 9 80 1 and s i n c e t h e n , a h a n d f u l o f f r u i t f u l e x p e r i m e n t s have a p p e a r e d i n t h e l i t e r a t u r e . 3 9 " " 2 The c h o i c e of r a t s f o l l o w s s t a n d a r d p h y s i o l o g i c a l p r a c t i c e s s i n c e t h e y can be u s e d as models f o r human b r a i n p r o c e s s e s , a r e v e r y r e s i s t a n t t o d i s e a s e and a r e e a s i l y b r e d under c o n t r o l l e d c o n d i t i o n s . P h y s i o l o g i c a l i n s u l t s a p p l i e d t o r a t b r a i n t i s s u e s c a n a c t as m o d e l s f o r human d i s e a s e s , t h e c a u s e s and p o t e n t i a l c u r e s o f w h i c h r e m a i n unknown. 71 A t y p i c a l 3 1 P in-vivo s p e c t r u m of r a t b r a i n i s shown i n F i g . 2 2 . D e s p i t e s m a l l v a r i a t i o n s i n peak h e i g h t and shape between a n i m a l s , t h i s s p e c t r u m c a n be c o n s i d e r e d a s a g e n e r i c r a t b r a i n s p e c t r u m . F e a t u r e s a p p e a r i n g h e r e w h i c h a r e common t o m u s c l e t i s s u e a r e t h e ATP, PCr, P i and s u g a r p h o s p h a t e p e a k s , t h e l a t t e r b e i n g more p r o m i n e n t h e r e . T h e r e i s a l s o t h e a p p e a r a n c e o f a r e s o n a n c e a t c a . 2.5 ppm w h i c h i s l i k e l y p h o s p h o e n o l p y r u v a t e . The i n o r g a n i c p h o s p h a t e r e s o n a n c e a t c a . 5 ppm i s p a r t i a l l y o b s c u r e d by t h e 2- p h o s p h a t e of 2,3-DPG i n b l o o d . 3 6 T h i s i n t e r f e r e n c e does n o t o c c u r i n m u s c l e s p e c t r a . E l e v a t i o n s i n b r a i n p h o s p h o d i e s t e r l e v e l s may be a s s o c i a t e d w i t h t h i s f a i r l y m o b i l e s u b s t i t u e n t o f m y e l i n , t h e p r o t e i n c o a t i n g on n e u r a l a x o n s . E l e v a t i o n s i n b r a i n s u g a r p h o s p h a t e s may be due t o g r e a t e r b r a i n e n e r g y demands s u p p l i e d v i a g l y c o l y s i s . 2 2 - A s u b t l e but u s e f u l c h a r a c t e r i s t i c of b r a i n s p e c t r a s u c h a s t h i s i s t h e r e d u c e d PCr/|3ATP r a t i o a s compared w i t h m u s c l e s p e c t r a . In b r a i n t h i s q u a n t i t y i s r e d u c e d t o 5:2 ( c f . m u s c l e s p e c t r a : 4:1) as a c o n s e q u e n c e of t h e i n t r i n s i c a l l y , l o n g e r T, of PCr i n b r a i n compared t o m u s c l e . 2 2 In a d d i t i o n , t h e r e i s a b r o a d r e s o n a n c e s u p e r i m p o s e d on t h e s p e c t r u m w h i c h a r i s e s from t h e immo b i l e p h o s p h a t e s i n t h e bone o f t h e s k u l l . P r i o r t o o b t a i n i n g t h i s and o t h e r s p e c t r a , r a t b r a i n s p e c t r a were o b t a i n e d by l a y i n g t h e r a t s u p i n e l y o v e r t h e s u r f a c e c o i l . T h i s r e s u l t e d i n a much l a r g e r hump w h i c h c o u l d be 7 2 PCr A T P -J 1 1 1 1 1 1 1 1 1 1 T 20 0 -20 ppm F i g . 2 2 3 1 P NMR in-vivo s p e c t r u m o f r a t b r a i n ; u s i n g 2 cm f l a t Ag/Cu c o i l . ( s p e c t r a l w i d t h = ± l 0 0 0 Hz; scans=600; b l o c k s i z e = 2 0 4 8 p o i n t s ; p u l s e width=24 Msec; p u l s e d e l a y = 2 . 5 s e c ; l i n e b r o a d e n i n g - 1 0 Hz) 73 p a r t i a l l y removed by c o n v o l u t i o n d i f f e r e n c e . * ' 4 3 ' * 4 T h i s p r o b l e m was somewhat a l l e v i a t e d b o t h by r e m o v i n g t h e f i r s t p o i n t o f t h e FID d u r i n g d a t a p r o c e s s i n g , o r p l a c i n g t h e s u r f a c e c o i l on t h e s i d e of t h e r a t ' s head and t h u s a v o i d i n g a " s h i e l d " of bone. I n s t e a d t h e o b s t r u c t i o n e n c o u n t e r e d h e r e was t h e m a s s e t t e r m u s c l e , t h e m u s c l e c o n n e c t i n g t h e jaw t o t h e s k u l l . Though i n t e r f e r e n c e would be t h e same on b o t h s i d e s o f t h e h e a d , r e m o v a l o f t h e m a s s e t t e r m u s c l e i n d i c a t e d t h a t i t s c o n t r i b u t i o n t o t h e s p e c t r a was n e g l i g i b l e . In an e f f o r t t o o b s e r v e d i f f e r e n c e s i n b r a i n m e t a b o l i s m , a p r e l i m i n a r y t e s t was u s e d t o e s t a b l i s h t h e s e n s i t i v i t y o f NMR t o b r a i n t i s s u e . A f t e r a c q u i r i n g " a s p e c t r u m o f a n o r m a l r a t ' s b r a i n , t h e r a t was s u b s e q u e n t l y s a c r i f i c e d w i t h an o v e r d o s e o f b a r b i t u r a t e . A n o t h e r s p e c t r u m was t h e n a c q u i r e d of t h e d e c e a s e d r a t ' s b r a i n . S p e c t r a a r e shown i n F i g . 23. The o b j e c t i v e h e r e was t o d e t e r m i n e whether a s t u d y of b r a i n d i s e a s e would be f e a s i b l e v i a NMR. I f 3 1 P NMR was n o t s e n s i t i v e enough t o show a d i f f e r e n c e f o r t h e most d r a m a t i c m e t a b o l i c change o f a l l , i t c e r t a i n l y c o u l d n o t be u s e d t o d e t e c t more s u b t l e d e v i a t i o n s f r o m n o r m a l m e t a b o l i s m . The d e c e a s e d r a t b r a i n s p e c t r u m has some c h a r a c t e r i s t i c f e a t u r e s w h i c h c o r r e s p o n d t o t h e b i o c h e m i c a l u n d e r s t a n d i n g o f d e a t h . In. t h i s c a s e , " d e a t h " r e f e r s t o t h e f i f t e e n m i n u t e p e r i o d f o l l o w i n g t h e —1 i 1 1 1 1 1 1 1 1 r 20 0 -20 ppm F i g . 2 3 3 1 P NMR in-vivo s p e c t r u m o f r a t b r a i n ; (A) l i v e r a t ; (B) d e c e a s e d r a t ; (1) monosugar p h o s p h a t e s ; (2) P i ; (3) PCr; (4) ATP/ADP; (5) ATP; u s i n g 2 cm 0.9 Ag/Cu c o i l , ( s p e c t r a l w i d t h = ± l 0 0 0 Hz; scans=200; b l o c k s i z e = 2 0 4 8 p o i n t s ; p u l s e width=12 usee; p u l s e delay=1 s e c ; l i n e b r o a d e n i n g = 1 0 Hz) 75 c e s s a t i o n of t h e h e a r t b e a t . The l a r g e i n o r g a n i c p h o s p h a t e peak and s m a l l PCr peak i n d i c a t e t h a t c a t a b o l i s m i s p r o c e e d i n g t o c o m p l e t i o n . The r e s i d u a l s i g n a l f r o m PCr g i v e s f u r t h e r e v i d e n c e t h a t much p h o s p h a t e bond e n e r g y has been expended w i t h t h e r e s u l t i n g b u i l d - u p o f P i a t t h e e x p e n s e o f a l l o t h e r p h o s p h a t e donor m o l e c u l e s . The f a c t t h a t PCr y i e l d s a s i g n a l a t a l l i n t h e s p e c t r u m i n d i c a t e s t h a t a s m a l l r e m a i n d e r of t h e phosphagen i s l e f t o v e r , s i m i l a r t o t h e c a s e o f t h e i s c h e m i c r a t l e g ( F i g . 2 1 ) . Peak s h a p e s f o r ATP/ADP e v e n t u a l l y b r o a d e n and l o s e r e s o l u t i o n w i t h t i m e , s u g g e s t i n g some i n s t a b i l i t y o r d e c o m p o s i t i o n o f t h e s e m e t a b o l i t e s . W i t h s p e c t r a l i d e n t i f i c a t i o n o f l i v e v s d e c e a s e d m e t a b o l i c s t a t e s , i t was p o s s i b l e t o p r o c e e d t o an e x a m i n a t i o n of a r a t model f o r human b r a i n d i s e a s e . In an e f f o r t t o o b s e r v e t h e e f f e c t s o f m i l d l y a l t e r e d m e t a b o l i s m i n t h e b r a i n , a p h y s i o l o g i c a l i n s u l t was a r t i f i c i a l l y a p p l i e d t o a c h i e v e t h i s . The p r o c e d u r e i n v o l v e d t h e i n j e c t i o n of k a i n i c a c i d ( I ) i n t o one s i d e of a r a t ' s b r a i n . K a i n i c a c i d , an e x t r e m e l y p o t e n t n e u r o t o x i n , was u s e d f o r i t s d e l e t e r i o u s e f f e c t s on t h e b r a i n w h i c h a r e s i m i l a r t o t h o s e c a u s e d by A l z h e i m e r ' s d i s e a s e i n humans. Many e f f o r t s t o e l u c i d a t e t h e c h a r a c t e r i s t i c s and c a u s e s o f A l z h e i m e r ' s d i s e a s e , o r H u n t i n g t o n ' s C h o r e a , u t i l i z e k a i n i c a c i d t r e a t m e n t s as m o d e l s f o r t h e s e c o n d i t i o n s . I n j e c t i n g one s i d e o f t h e b r a i n a l l o w e d t h e o t h e r l o b e t o be u s e d as a c o n t r o l ; 7 6 b i o l o g i c a l l y , t h i s p r o c e d u r e i s more r e l i a b l e t h a n c o m p a r i n g one a n i m a l t o a n o t h e r s i n c e t h e r e i s a l a r g e s t a n d a r d d e v i a t i o n f o r " n o r m a l " c h a r a c t e r i s t i c s and e v e r y r a t b r a i n i s s i m u l t a n e o u s l y s i m i l a r y e t u n i q u e . K a i n i c a c i d (KA) i s an i n g r e d i e n t of t h e seaweed Digenea Simplex w h i c h grows o f f t h e c o a s t of J a p a n . F i r s t i s o l a t e d i n 1953 by Takemoto and h i s c o l l e a g u e s , " 5 i t was shown t o have a n t h e l m i n t i c and i n some c a s e s e m e t i c p r o p e r t i e s but i t s e f f e c t on mammalian n e u r o n s was unknown u n t i l l a t e r . However, i t was known t h a t L - g l u t a m a t e ( I I ) was a s t r o n g e x c i t a n t of n e u r o n s i n v a r i o u s p a r t s o f t h e c e n t r a l n e r v o u s s y s t e m , hence KA ( I ) w h i c h i s a d i s u b s t i t u t e d d e r i v a t i v e o f g l u t a m a t e , was s u s p e c t e d o f showing s i m i l a r o r o p p o s i t e b e h a v i o r . U n l i k e g l u t a m a t e , however, k a i n i c a c i d i s a h e t e r o c y c l i c m o l e c u l e . e e e J. — CH — CHr-CH g l u t a m a t e ka ina te 77 K a i n i c a c i d i s h i g h l y n e u r o t o x i c due t o i t s a b i l i t y t o c a u s e s u s t a i n e d c e l l d e p o l a r i z a t i o n , and c o n c o m m i t a n t i n c r e a s e i n n e u r a l membrane p e r m e a b i l i t y . 4 5 E s s e n t i a l l y , KA k i l l s n e u r o n s by e x c i t i n g them t o d e a t h . Of t h e s u b s t i t u t e d g l u t a m a t e s r e c o g n i z e d as e x c i t o t o x i c , KA i s t h e most p o t e n t and l o n g a c t i n g i n t h e mammalian c e n t r a l n e r v o u s s y s t e m . The e x a c t mechanism by w h i c h t h e a c i d o p e r a t e s i s s t i l l unknown, a l t h o u g h some t h e o r i e s have been a d v a n c e d . What i s known, however, i s t h a t k a i n i c a c i d , l i k e g l u t a m a t e , i s s e l e c t i v e l y t o x i c . I t c a n k i l l o n l y n e u r o n s whose c e l l b o d i e s l i e i n t h e v i c i n i t y of t h e i n j e c t i o n b u t c a n n o t p e n e t r a t e a x o ns o r d e n d r i t e s o f o t h e r n e r v e c e l l s t e r m i n a t i n g o r p a s s i n g t h r o u g h t h i s r e g i o n ( s e e F i g . 2 4 ) . In t h i s way, KA has been u s e d as a h i g h l y s p e c i f i c l e s i o n i n g a g e n t s i n c e t h e damage i t does i s l o c a l i z e d t o a g i v e n b r a i n volume. However, some n e u r o n s a r e r e l a t i v e l y r e s i s t a n t t o KA and a few a r e even c o m p l e t e l y u n a f f e c t e d . The u s u a l d o s e g i v e n t o a r a t was f r o m 2 t o 10 n anomoles i n a volume o f up t o a few m i c r o l i t r e s . L a r g e d o s e s o f KA a r e s u p e r f l u o u s s i n c e t h e a c t i v i t y o f t h e n e r v e s y n a p s e s i s v i r t u a l l y a r r e s t e d a f t e r a d o s e of 15 n a n o m o l e s . 4 5 The e x p e r i m e n t a l r a t was i n j e c t e d w i t h 5 nmoles and l e f t t o r e s t f o r one week w h i l e t h e a c i d a c t e d on t h e b r a i n t i s s u e . 3 1 P NMR s p e c t r a were t h e n a c q u i r e d f r o m b o t h s i d e s o f t h e r a t ' s head a f t e r a n a e s t h e t i z i n g t h e r a t w i t h i n a c t i n . The s p e c t r a a r e shown i n F i g . 25. 78 dendrite F i g . 2 4 S c h e m a t i c d r a w i n g o f a b r a i n n e u r o n . D e n d r i t e f i b r e s a r e u s u a l l y p r o f u s e d l y b r a n c h e d t o b r i n g much i n f o r m a t i o n t o t h e c e l l body. The l o n g t h i n axon c a r r i e s i n f o r m a t i o n away from t h e c e l l body; K a i n i c a c i d c an d i f f u s e a c r o s s o n l y t h e c e l l body membrane, b u t c a n n o t p e n e t r a t e axons o r d e n d r i t e s . 20 0 -20 20 0 -20 ppm F i g . 2 5 3 1 P NMR in-vivo s p e c t r u m o f l e s i o n e d r a t b r a i n ; (A) r i g h t b r a i n ; (B) l e f t b r a i n ; u s i n g 2 cm 0.9 Ag/Cu c o i l , ( s p e c t r a l w i d t h = ± l 0 0 0 Hz; scans=200; b l o c k size=2048 p o i n t s ; p u l s e width=12 /usee; p u l s e delay=1 s e c ; l i n e b r oadening=10 Hz) 8 0 W i t h i n t h e r a n g e of s t a n d a r d d e v i a t i o n e x p e c t e d f o r a s p e c t r u m o f l i v i n g t i s s u e , i t i s n o t p o s s i b l e t o d i f f e r e n t i a t e t h e s e s p e c t r a by any d i s t i n g u i s h i n g f e a t u r e s . The many s p e c t r a a c q u i r e d f r o m any one s i d e o f t h e head show a s much v a r i a t i o n i n peak h e i g h t and r e s o l u t i o n a s do t h e s e two. The s i g n i f i c a n c e o f t h i s i s m a n i f o l d . I t may s u g g e s t t h a t t h e d o s a g e a p p l i e d t o t h e b r a i n was n o t enough t o g e n e r a t e a d e t e c t a b l e change v i a NMR. A c o n c e n t r a t i o n of 5 nanomoles i n a few m i c r o l i t r e s may be s i g n i f i c a n t and m e a s u r a b l e w i t h f i n e n e u r o c h e m i c a l d e v i c e s b u t w o u l d n o t e x c e e d t h e minimum l i m i t o f s e n s i t i v i t y of NMR. Thus a l a r g e r o r more p e r v a s i v e i n s u l t may be r e q u i r e d . A n o t h e r p o s s i b i l i t y i s t h a t t h e a c t i o n of KA d o e s n o t h i n g t o a l t e r t h e p h o s p h o r u s c o n t a i n i n g m e t a b o l i t e s w i t h i n t h e c e l l . S i n c e KA i n t e r a c t s a t s y n a p s e s , i t may o n l y be i n v o l v e d i n d e b i l i t a t i n g n e u r o t r a n s m i t t e r s o r c h a n g i n g t h e p h y s i c a l s t r u c t u r e o f t h e r e c e p t o r s i t e s of n e u r o n s . In t h i s c a s e no change i n t h e 3 1 P s p e c t r u m w o u l d be e x p e c t e d , t h o u g h i n t e r m s o f c o n c e n t r a t i o n , t h i s c o n c l u s i o n c o u l d n o t be assumed b a s e d on t h e d o s a g e g i v e n , s i n c e t h e o v e r w h e l m i n g c o n c e n t r a t i o n o f p h o s p h o r u s m e t a b o l i t e s i n t h e r e s t o f t h e b r a i n (same s i d e ) would o b l i t e r a t e t h e a p p e a r a n c e o f t h i s e f f e c t i n t h e s p e c t r u m . F u r t h e r a t t e m p t s t o " s a t u r a t e " t h e r a t b r a i n w i t h KA or t o make m u l t i p l e l e s i o n s s i m p l y l e d t o t h e d e a t h of t h e a n i m a l . A p o t e n t i a l a d j u n c t t o t h i s e x p e r i m e n t m i g h t be t o f u r t h e r 81 i n j e c t t h e r a t w i t h an enzyme o r p h o s p h o r u s - c o n t a i n i n g m e t a b o l i t e t o o b s e r v e whether a s p e c i f i c s t e p i n t h e g l y c o l y t i c pathway has been b l o c k e d . In a d d i t i o n t o t h i s , o nce r e l i a b l e w a t e r s u p p r e s s i o n t e c h n i q u e s a r e e s t a b l i s h e d , s p e c t r a of e a c h s i d e o f a l e s i o n e d r a t b r a i n may y i e l d more f r u i t f u l r e s u l t s s i n c e p r o t o n r e s o n a n c e s from n e u r o t r a n s m i t t e r s can be t r a c e d . In c o n s i d e r a t i o n o f t h e v a r i o u s e x p l a n a t i o n s f o r o b s e r v i n g s t a t i s t i c a l l y s i m i l a r s p e c t r a f o r a d i s e a s e d and n o r m a l b r a i n , f u r t h e r a t t e m p t s a t c h a r a c t e r i z i n g t h i s c o n d i t i o n v i a NMR may n o t y i e l d more i l l u m i n a t i n g r e s u l t s . In a d d i t i o n , t h e e f f e c t o f t h e a n a e s t h e t i c s has n o t been c o n s i d e r e d a s a s e p a r a t e e n t i t y i n i t s e l f . By t h e i r v e r y n a t u r e , a n a e s t h e t i c s o p e r a t e by a f f e c t i n g m e t a b o l i s m and a s t u d y on t h e i r p r e c i s e e f f e c t s i s d e s i r a b l e . U n f o r t u n a t e l y , p r o b l e m s a s s o c i a t e d w i t h o b t a i n i n g NMR s p e c t r a f r o m s t a t i o n a r y s a m p l e s p r e c l u d e d a c q u i s i t i o n o f s p e c t r a f r o m u n a n a e s t h e t i z e d r a t s . I t i s n o t known t h e n , w h ether t h e e f f e c t o f t h e a n a e s t h e t i c on m e t a b o l i s m would a l s o mask t h e a c t i o n o f k a i n i c a c i d on b r a i n t i s s u e . T h e s e q u e s t i o n s beg f o r a t t e n t i o n f r o m f u r t h e r e x p e r i m e n t a t i o n w i t h NMR and a n i m a l m o d e l s . 3.4 Experimental The s p e c t r o m e t e r and magnet u s e d f o r t h e s e e x p e r i m e n t s were d e s c r i b e d i n s e c t i o n 2.9. S o l u t i o n s were made a n a l y t i c a l l y by w e i g h i n g a c c u r a t e l y and d i s s o l v i n g 82 i n d e i o n i z e d d i s t i l l e d w a t e r ; pH was a d j u s t e d by t i t r a t i n g w i t h d i l u t e HC1 and NaOH; t h e a p p r o p r i a t e a l i q u o t s were p i p e t t e d i n t o t h e sample c o n t a i n e r . M a l e W i s t a r r a t s (250-350 gm) were u s e d f o r a l l in-vivo e x p e r i m e n t s e x c e p t t h e human arm e x p e r i m e n t f o r w h i c h a v o l u n t e e r was employed. A n a e s t h e t i c s were p r e p a r e d i n c o n c e n t r a t i o n s o f 5 gm % ( p e n t a b a r b i t o l ) , and 10 gm % ( i n a c t i n ) and d o s a g e s f o r b o t h were g i v e n a t 0.1 ml/100 gm body w e i g h t . I n j e c t i o n s were made i n t e r p e r i t o n e a l l y by s y r i n g e . Shimming on r a t heads was a c c o m p l i s h e d by c h a n g i n g t h e t r a n s m i t t e r f r e q u e n c y and p r e a m p l i f i e r t o 1H w h i l e t h e p r o b e was ke p t t u n e d t o 3 1 P." 6 83 C O N C L U S I O N 84 The work p r e s e n t e d i n t h i s t h e s i s was u n d e r t a k e n i n an e f f o r t t o b r i d g e t h e chasm w h i c h s e p a r a t e d t h e o b j e c t i v e s o f l o c a l i z a t i o n s p e c t r o s c o p y from i t s p r e s e n t s u n d r y a p p l i c a t i o n s . To t h i s end, t h e p r o p e r t i e s of s u r f a c e c o i l s have been s t u d i e d t o p r o v i d e j u s t i f i c a t i o n f o r t h e i r u s e . A f t e r e l u c i d a t i n g some of t h e a d v a n t a g e s and d i s a d v a n t a g e s of s u r f a c e c o i l s , a c o i l was c h o s e n w i t h o p t i m a l geometry and t h e most s u i t a b l e w i r e f o r t h e a p p l i c a t i o n i n t e n d e d . In-vivo e x a m i n a t i o n s o f t h e m e t a b o l i c s t a t u s o f r a t m u s c l e and b r a i n were p e r f o r m e d w i t h a s u r f a c e c o i l u s i n g t h e p h o s p h o r u s - 3 1 n u c l e u s as a p r o b e . Some c o n c l u s i o n s and d i r e c t i v e s w i l l now be p r e s e n t e d i n view of t h e s e and o t h e r r e s u l t s i n t h e 1 i t e r a t u r e . I t has been o b s e r v e d t h a t t h e most n o t a b l e c h a r a c t e r i s t i c o f s u r f a c e c o i l s , namely t h e n o n u n i f o r m B, f i e l d , i s what makes f u r t h e r l o c a l i z e d s p e c t r o s c o p y p o s s i b l e . D i f f e r e n c e s i n peak a m p l i t u d e m o d u l a t i o n f r e q u e n c y w i t h i n t h e s e n s i t i v e volume of t h e s u r f a c e c o i l a l l o w t h e e x p e r i m e n t o r t o use p r e d e t e r m i n e d p u l s e w i d t h s a s a form of c r u d e s p a t i a l l o c a l i z a t i o n t o a c h i e v e a 90 d e g r e e p u l s e a t t h e c h o s e n r e g i o n . Sample m a t e r i a l l o c a t e d more t h a n one c o i l r a d i u s away from t h e s u r f a c e c o i l g e n e r a l l y d o e s n o t c o n t r i b u t e t o t h e s p e c t r u m . The s i g n a l - t o - n o i s e a c h i e v e d w i t h s u r f a c e c o i l s i s v e r y good due t o t h e i r e x c e l l e n t f i l l i n g f a c t o r , and c a n be 85 i n f l u e n c e d by t h e g e o m e t r y o f t h e c o i l a s w e l l as t h e m a t e r i a l u s e d f o r t h e c o i l w i r e . A s i l v e r p l a t e d c o p p e r w i r e y i e l d s s u r f a c e c o i l s o f h i g h e r Q and s i g n a l - t o - n o i s e t h a n p u r e c o p p e r c o i l s . In view o f t h e s c i e n c e o f s u r f a c e c o i l s t h e m s e l v e s , i t seems i m p e r a t i v e a t t h i s p o i n t t o use s u r f a c e c o i l s w h i c h have been d e s i g n e d s t r i c t l y t o t h e r e q u i r e m e n t s of t h e sample and e x p e r i m e n t . C o i l g e o m e t r i e s a s w e l l as t h e use of two o r more c o i l s i n v a r i o u s c o n f i g u r a t i o n s s h o u l d be e x p l o r e d a s p o s s i b l e means t o a c h i e v e t h e t y p e o f B, f i e l d d e s i r e d . The B, f i e l d shape s h o u l d d e t e r m i n e t h e c o i l d e s i g n . However, r e l a t i v e s i m p l i c i t y i n c o i l d e s i g n a p p e a r s t o be t h e c u r r e n t and a p p r o p r i a t e g o a l w i t h more e m p h a s i s p l a c e d on u s i n g s u i t a b l e p u l s e s e q u e n c e s f o r o b t a i n i n g l o c a l i z e d s i g n a l s f r o m t h e s e n s i t i v e v olume. The f a c t t h a t m e t a b o l i c d e v i a t i o n s can be d e t e c t e d by NMR i s e n c o u r a g i n g enough t o p u r s u e i t s p o t e n t i a l a p p l i c a t i o n s . I t has been shown t h a t 3 1 P NMR i s s e n s i t i v e t o c h a n g e s i n oxygen u p t a k e o f m u s c l e s and d r a s t i c m e t a b o l i c d e v i a t i o n s o f t h e b r a i n . However, t h e e f f e c t s of k a i n i c a c i d were n o t o b s e r v e d w i t h t h i s t e c h n i q u e . L a c k of any s p e c t r a l e v i d e n c e f o r t h e a l t e r e d t i s s u e i m p l i e s t h a t t h e i n s u l t was n o t s e v e r e enough t o be m a n i f e s t as a p o s i t i v e i n d i c a t o r ; o r t h a t t h e i n s u l t does n o t a f f e c t t h e m e t a b o l i c c h e m i s t r y of t h e b r a i n . The l a t t e r h y p o t h e s i s may be e x p l o r e d f u r t h e r by 1H o r o t h e r NMR s e n s i t i v e n u c l e i b e f o r e a h y p o t h e s i s on t h e a c t i o n o f 86 KA c a n be a d v a n c e d . Most o f t h e NMR r e s u l t s p u b l i s h e d t o d a t e on a b e r r a n t m e t a b o l i c s t a t e s show t h e same s p e c t r a l i n d i c a t o r . T h a t i s , t h e i n c r e a s e of t h e i n o r g a n i c p h o s p h a t e peak w i t h a c o n c o m m i t a n t d e c r e a s e o f t h e p h o s p h o c r e a t i n e peak. W i t h o u t f o r e k n o w l e d g e of t h e p a r t i c u l a r d i s e a s e , or sample p r e p a r a t i o n i t would be i m p o s s i b l e t o use t h e s e 3 1 P s p e c t r a d i a g n o s t i c a l l y ; r a t h e r o n l y as a c o n f i r m a t i o n t h a t some a b n o r m a l s t a t e e x i s t e d . U n t i l 3 1 P NMR c a n be d e v e l o p e d as a r e l i a b l e q u a n t i t a t i v e t o o l , where c o n c e n t r a t i o n s of e n e r g y m e t a b o l i t e s c an be a c c u r a t e l y c a l c u l a t e d , many u n r e l a t e d d i s e a s e d t i s s u e s w i l l a p p e a r u n d i f f e r e n t i a t e d by a 3 1 P NMR s p e c t r u m . The use o f o t h e r n u c l e i a s p r o b e s i n t h i s c a s e would h e l p t o c l a r i f y t h e s i t u a t i o n . F u r t h e r s t u d i e s o f in-vivo s y s t e m s w i t h 3 1 P NMR s p e c t r o s c o p y u s i n g s u r f a c e c o i l s w i l l c o n t i n u e t o map t h e 3 1 P p r o f i l e o f v a r i o u s body p a r t s and o r g a n s . The n e x t s t e p may be t o p e r f o r m s l i g h t l y more i n v a s i v e e x p e r i m e n t s , s u c h as i n j e c t i n g a m e t a b o l i t e i n t o t h e body of a d i s e a s e d a n i m a l t o show how t h e d i s e a s e a f f e c t s m e t a b o l i s m i n more d e t a i l . T h i s c o u l d be a t e m p o r a r y t a n g e n t w h i c h i s l i k e l y t o f o l l o w i f f i n e r r e s o l u t i o n o f t h e 3 1 P s p e c t r u m i s n o t a t t a i n e d , e s p e c i a l l y i n t h e r e g i o n d o w n f i e l d f r o m t h e PCr p e a k s . More d a t a a n a l y s i s o f t h e s p e c t r u m i t s e l f may y i e l d i l l u m i n a t i n g i n d i c a t o r s 87 a b o u t t h e m e c h a n i c s of m e t a b o l i s m . F a c t o r s s u c h as peak h e i g h t r a t i o s and r e l a t i v e peak i n t e n s i t i e s may be examined i n more d e t a i l t o r e v e a l u s e f u l i n f o r m a t i o n p r e v i o u s l y o v e r l o o k e d or u n a v a i l a b l e . B e f o r e 3 1 P NMR can be u s e d as a c l i n i c a l d i a g n o s t i c t o o l , s t a n d a r d s of s p e c t r a must be t a b u l a t e d a s s t a t i s t i c a l a v e r a g e s o f many s a m p l e s . The n a t u r a l b i o l o g i c a l v a r i a t i o n w i t h i n a s p e c i e s s h o u l d be r e c o r d e d a s a " n o r m a l " s p e c t r u m b e f o r e an a b n o r m a l m e t a b o l i c s t a t e c a n be i d e n t i f i e d . 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H o r i k a w a , C, T a n a k a , K. H i r a k a w a , H. N i s h i k a w a and H. W a t a r i , Brain Research, 296, 370, 1984. 77. D.T. D e l p y , R.E. G o r d o n , P.L. Hope , P e d i at ri cs 70,310, 1982. 78. R.K. D e u e l , G.M. Yue, W.R. Sherman, D.J. S c h i c k n e r , and J . J . H . Ackerman, Science 228, 1329, 1985. 79. M.A. F o s t e r , " M a g n e t i c Resonance i n M e d i c i n e and B i o l o g y " , Pergamon P r e s s , London, 1984. 80. R.S. B a l a b a n , D.G. G a d i a n , and G.K. Radda, Kidney Int. 20, 575, 1981. 81. P. S t y l e s , M.B. S m i t h , R.W. B r i g g s , and G.K. Radda, / . Mag. Reson. 62, 397, 1985. 93 A P P E N D I X The d e r i v a t i o n of t h e v e c t o r p o t e n t i a l and f i e l d of a c i r c u l a r l o o p o f w i r e was o u t l i n e d by S m y t h e 2 5 and u s e d by o t h e r s * 3 1 t o c a l c u l a t e t h e f i e l d of s u r f a c e c o i l s . F o r a p o i n t , P, l o c a t e d i n t h e yz p l a n e above t h e c o i l i n t h e f i g u r e below, a t a r a d i a l d i s t a n c e , p, f r o m t h e c o i l c e n t e r , Smythe f i n d s t h e a x i a l , B a , and r a d i a l , Bp, f i e l d s t o be: B, 2v K [ ( r + p ) 2 + y 2 ] 1 / 2 <r-p) .2 -( i i ) where n i s t h e p e r m e a b i l i t y o f t h e medium s u r r o u n d i n g t h e c o i l , I i s t h e c u r r e n t f l o w i n g t h r o u g h t h e c o i l , r , t h e c o i l r a d i u s , and K and I , t h e c o m p l e t e e l l i p t i c a l i n t e g r a l s o f t h e f i r s t and s e c o n d k i n d , r e s p e c t i v e l y . 94 In t h e c a l c u l a t i o n of B, c o n t o u r s f o r t h i s t h e s i s , t h e f o l l o w i n g a s s u m p t i o n s and s u b s t i t u t i o n s were made: (1) u n i t c u r r e n t was assumed t o be f l o w i n g t h r o u g h t h e c o i l w i r e , hence 1=1; (2) c o i l r a d i u s , r=1; (3) t h e d i s t a n c e , p, w h i c h was a v a r i a b l e i n t h i s c a s e , was s e t t o (4) t h e d i s t a n c e f r o m t h e c o i l c e n t e r t o t h e p o i n t , P, was t h e n To s i m p l i f y t h e c a l c u l a t i o n i n t h e FORTRAN programs u s e d , t h e a r b i t r a r y v a r i a b l e s , A, B, C, and D were s e t t o p o r t i o n s o f t h e e q u a t i o n : A = (1 + x 2 + y 2 + z 2 ) [1 - ( x 2 + z 2 ) 1 / 2 ] 2 + y 2 B * 1 {[1 + ( x 2 + z 2 ) 1 / 2 ] 2 + y 2 } ! / 2 (x 2+y 2)1/2 (1 - x 2 - y 2 - z 2 ) t i - ( x 2 + z 2 ) 1 / 2 ] 2 + y2 The f o l l o w i n g p r o g r a m s l i s t e q u a t i o n s ( i ) and ( i i ) a s : B a = (E x D + K) x B ( i ) * B r = ( E x A - K ) x B x C ( i i ) * 95 2 C THIS PROGRAM CALCULATES THE COMPONENTS OF A MAGNETIC I 3 C INDUCED BY A UNIT CURRENT RUNNING IN A CIRCULAR LOOP 4 DIMENSION XP(201),YP(101).ZP(201,101) S PI-4.*ATAN(1.0) 6 C 7 C e c 9 c 10 CC 11 C 12 C 13 Z-0.5 14 DO 400 J-1,201 15 X-(FL0AT(J)-101.)/50. 16 c 17 DO 300 K-1,101 18 Y-(FL0AT(K)-1.)/50.0 19 C 20 IR-1 21 C 22 XZ«SQRT(X«»2+Z«*2) 23 c 24 C 25 C chock f o r p o i n t s on the r i n g 26 C 27 C 28 IF((ABS(XZ-1.0).LE.10E-6).AND.(K.E0.1)) GO TO 300 29 A-( 1 .+X«»2+Y"2+Z*»2)/( ( 1 .-XZ)*«2+Y"2) 30 C 31 B-1 ./SORT(( 1 .+XZ)"2+Y*«2) 32 c 33 D«<1.-X»»2-Y»«2-Z»*2)/((1.-XZ)«»2+Y*«2) 34 C 35 IF(K.NE.1) GO TO 140 36 C-0.0 37 c 38 GO TO 180 39 c 40 C check f o r p o i n t s on the a x i s 41 C 42 140 IF((XZ-0.).GT.10E-6) GO TO 170 43 IR-0 44 GO TO 180 45 170 C-Y/XZ 46 180 XISQ-4.«XZ/((1.+XZ)*«2+Y««2) 47 XI-SORT(XISO) 48 EF1-ELIK1(XI,IND1) 49 ES1-ELIEKXI.IND2) " 50 IF(IR.EQ.I) GO TO 190 51 BRAD-0.0 52 GO TO 195 53 190 BRAD-(ES1*A-EF1)»B*C 54 195 BAX-(ES1»D+EF1)*B 54.5 THETA«ATAN(-X/Z) 55 C IF(d.NE.21) THETA-PI/2. 56 c IF(d.E0.21) THETA-0.0 57 BX"BRAD*SIN(THETA) 58 BY-BAX 59 B1»SQRT(BX«»2*BY«»2) 60 ZP(d,K)-B1 61 RA-BX/BY 62 ALPHA-ATAN(RA ) • 180.0/PI 63 C 64 c 65 c 66 c 67 C 68 GO TO 300 69 c 70 c 71 300 CONTINUE 72 400 CONTINUE 73 DO BOO M-1,101 74 ' BOO YP(M)-(FL0AT(M)-1.)/50.0 75 DO 850 L-1,201 76 850 XP(L>-(FL0AT(L)-101.)/50. 77 C 78 CALL AXIS(-2.0,0.0.1HX.-1,4.0.0.0,-2.0,1.0) 79 CALL AXISIO.0.0.0,1HY,1,2.0,90.0.0.0,1.0) 80 DO 950 1-1.500 81 CN-FLOAT(I) 82 CALL CNT0UR(XP,201,YP,101,ZP.201,CN.0.O.CN) 83 950 CONTINUE 84 CALL PLOTND 85 C 86 STOP 87 END 2 C THIS PROGRAM CALCULATES THE COMPONENTS OF A MAGNETIC FIELD 3 C INDUCED BV A UNIT CURRENT RUNNING IN A DOUBLE LOOP. 4 DIMENSION XP(201),YP(101).ZP(201.101) 5 PI«4.*ATAN(1.0) 6 R'0.6 7 C WITE(6, 100) 8 C100 F0RMAT(/3X,'XI',6X,'Yl',6X,'Z1',6X.'X2'.6X,'Y2' ,6X.'Z2 9 C • 'BX1•,5X.'BY1',5X,'B11',5X, 10 C • 'B1'.6X,'ALPHA' , 3X,'BETA',4X.'GAMMA'/) 1 1 C DO 600 1-1.3 12 Zl'0.5 13 22-21/R 14 DO 500 J-1.201 15 X1»(FL0AT(J)-1O1.)/50. 16 X2'X1/R 17 DO 400 K»1, 101 IS Y1-(FL0AT(K)-1.0)/50. 19 Y2-Y1/R 20 1R1«1 21 IR2«1 22 X*1-SORT(X1*«2*Z1»*2) 23 X?2-SQRT(X2««2+Z2*»2) 24 C 25 C check for points on the ring 26 C 27 IF(<ABS(XZ1-0.6).LE.10E-3).AND.(K.E0.1)) GO TO 400 28 IF((ABS(XZ1-1.0).LE.10E-3).AN0.<K.EQ.1)) GO TO 400 29 IF((ABS(XZ2-1.0).LE.10E-3).ANO.(K.EO.1)) GO TO 400 30 IF((ABS(XZ2-1.6).LE.1OE-3).AN0.(K.EQ.1)) GO TO 400 31 AIMi.+xi*«a*Yi««a*zi»«2)/<< 1 -xzi)*»2*Yi««2) 32 A2M1.*X2**2»Y2**2»Z2«*2)/<(1.-XZ2)**2+Y2««2) 33 81*1 ./SQRTM 1 .*XZ1)'«2*Y1*«Z> 34 B2-1./SQRT<(1.»XZ2)**2*Y2«»2) 35 D1"(1.-X1»»2-YI*»2-Z1«*2)/((1.-XZ1)»«2*Y1«»2) 36 D2-(1.-X2*»2-Y2**2-Z2«»2)/((1.-XZ2)*»2+Y2**2) 37 IF(K.NE.1) GO TO 140 38 C1-0.0 • 39 C2-0.0 40 GO TO 180 41 C 42 C check for points on the axis 43 C 44 140 IF((XZ1-0.0).QT.10E-6) GO TO 170 45 IR1-0 46 GO TO 180 47 170 C1«Y1/XZ1 48 180 XIS01-4.*XZ1/((1.*XZ1)**2+Y1««2) 49 XI1-SORT(XIS01) 50 EFI-ELIKI(XII.INDI) 51 ES1'ELIE1(XI1.IND2) 52 IF(IR1.E0.1) GO TO 190 S3 BRAD 1-0.0 54 GO TO 195 55 190 BRAD1«(ES1*A1-EF1)«B1«C1 56 195 BAX1-(ES1*D1*EF1)«B1 57 THETA'ATAN(-X1/Z1) 56 C IFtJ.NE.1) THETA-PI/2. 59 C IF(d.EO.1) THETA-0.0 60 BX1>BRA01*SIN(THETA) 61 BYl-BAX1 62 81l'SORT(BX1<«2*BY1«»2) 63 RAt'BXI/BYl 64 ALPHA-ATAN(RA1)•180.0/PI 6X. 65 C 66 IF((XZ2-0.0).GT.10E-6) GO TO 270 67 IR2-0 68 GO TO 280 69 270 C2-Y2/XZ2 70 280 XIS02-4.«XZ2/((1 .+XZ2)»»2+Y2*»2) 71 XI2«S0RT(XIS02) 72 EF2-EL1K1(XI2,IND1) 73 ES2-ELIEKXI2. IND2) 74 IF(IR2.E0.1) GO TO 290 75 BRAD2<=0.0 76 GO TO 295 77 290 BRAD2»(ES2»A2-EF2)«B2»C2 78 295 BAX2»(ES2*D2+EF2)«B2 79 PHI-ATAN(-X2/Z2) 80 C IF(J.NE.1) PHI-PI/2. 81 C IF(d.EO.1) PHI-0.0 82 BX2»BRAD2*SIN(PHI) 83 BY2-BAX2 84 B12-=S0RT(BX2,«2+BY2*«2) 85 RA2-BX2/BY2 86 BETA**ATAN(RA2)*180.0/PI 87 C 88 C sum of smalt and large fields 89 C 90 BX-BXUBX2 91 BV-BYt«BY2 92 B1'SORT(BX»»2+BY»«2) 93 ZP(J.K)«B1 94 RATIO-BX/BY 95 GAMMA =ATAN(RAT 10)•180.0/PI 96 C WRITE(6.30O) X 1. Y'l. Z1. X2.Y2.Z2.BX1. BY 1,B 11.81. 97 C •ALPHA.BETA,GAMMA 98 C3O0 FORMAT(10F8.4,3FB.2) 99 GO TO 400 100 C490 WRITE(6.495) X1.Y1.Z1 101 C495 F0RMAT(/'(X1.Y1.Z1)" '.3F5.2.' . point Is on the 102 C •ring'/) 103 C GO TO 400 104 C590 WRITE(6.595) X2.Y2.Z2 105 C595 FORMAT(/'(X2,Y2.Z2)- '.3F5.2.' . point Is on the 106 C •ring'/) 107 400 CONTINUE 108 500 CONTINUE 1 10 DO 800 M-1,101 111 800 YP(M)-(FL0AT(M)-1.)/50.0 112 DO 850 L-1.201 113 850 XP(L)-(FL0AT(L)-I01.)/50. 114 CALL AXIS(-2.0.0.0.1HX.-1.4.0.0.0.-2.0.1.0) 115 CALL AXIS(0.O,0.0.IHY,1,2.0.90.0.0.0,1.0) 116 00 950 I•1,500 117 CN-FLDAT(I) 118 CALL CNTOURIXP.201.YP.101,ZP.201.CN.0.0.CN) 1 19 950 CONTINUE 120 CALL PLOTND 121 STOP 122 END L O 2 C THIS PROGRAM CALCULATES THE COMPONENTS OF A MAGNETIC FIELD 3 C INDUCED BV A UNIT CURRENT RUNNING IN A 0.9 COIL DIAM-2.0 4' DIMENSION XP(201).YP(101).ZP<201.101) S PI-4.«ATAN(1.0) 6 R-0.9 7 C WRITE(6.100) 8 C1CO F0RMAT(/3X.'X1'.6X,'Y1'.6X.'Z1'.6X.'X2'.6X,'Y2',6X.'Z2 9 C • 'BX1',5X.'BY1•,5X.'B11',5X, 10 C « 'BI',6X.'ALPHA',3X.'BETA',4X,'GAMMA',3X.'B1REL'/) 1 1 12 C Z1-0.0 13 Z2-0.0 14 DO 500 J"1.201 15 X1-(FL0AT(J)-101.)/50. 16 X2-XI/R 17 00 400 K-1.101 18 Y1-(FLOAT(K)-1.0)/50. 19 Y2-Y1/R 20 IR1-1 21 IR2-1 22 XZ1-SORT(X1**2*Z1**2> 23 XZ2-SORT(X2*«2+Z2«»2) 24 g-SQRT(X1'«2*Yt««2*Z1««2) 25 01-SQRT(XI••2*0.0625) 26 C 27 C check f o r p o i n t s on the r i n g 28 C IF((ABS(XZ2-1.O).LE.10E-3).AND.(K.EQ .O) GO TO 400 29 30 IF(ABS(Of-1.0307764).LE.IOE-3) GO TO 400 31 AIM 1 .*X1"2*Y1«*2+Z1««2)/<( 1.-XZ1)*«2*Y1*«2) 32 A2M 1 • +X2"2*Y2 ,*2*Z2**2)/((1. -XZ2)**2+Y2 , ,2) 33 B1-1./SQRT((1 •XZ1)*«2+Y1«»2) 34 B2-1./S0RT<( 1 +XZ2)«*2*Y2**2) 35 DIM 1.-X1»«2-Y1««2-Z1**2)/((1.-XZ1)»*2+Y1*»2) 36 D2M1.-X2**2-V2**2-Z2**2)/((1.-XZ2)**2*Y2**2) 37 IF(K.NE.1) GO TO 140 38 C1-0.0 39 C2-0.0 40 GO TO 180 41 C 42 C check f o r p o i n t s on the a x i s 43 C 44 140 IF((XZ1-0.0).GT.10E-6) GO TO 170 45 IR1-0 46 GO TO 180 47 170 C1-Y1/XZ1 48 180 XISQ1-4.«XZ1/((1.*XZ1)»*2+Y1«*2) 49 XI1-SQRT(XISQ1) 50 EF1-ELIK1(XI1,IND1) 51 ES1-ELlE1(Xt1,IND2) 52 IFCIR1 EQ.1) GO TO 190 53 BRAD 1-0.0 54 GO TO 195 55 190 BRAD1MES1*A1-EF1)*B1»C1 56 195 BAX1-(ES1*D1+EF1)»B1 57 C 58 IF(J.NE.I) THETA-PI/2. 59 IFId.EQ.1) THETA-0.0 60 BX1-BRAD1*SIN(THETA) 61 BY 1-BAX1 62 B11-SORT(BX1**2+BY1**2) 63 RAI-BX1/BYI 64 ALPHA-ATAN(RA1)•180.0/PI 65 C 66 IF((XZ2-0.0).GT.10E-6) GO TO 270 67 IR2-0 68 GO TO 280 69 270 C2-Y2/XZ2 70 280 XIS02-4.«XZ2/((1.+XZ2)»»2*Y2*«2) 71 XI2»SORT(XIS02) ,6X. 72 EF2-ELIK1(XI2.IND1) 73 ES2-ELIEKXI2.IND2) 74 IF(IR2.E0.1) GO TO 290 75 BRAD2-0.0 76 GO TO 295 77 290 BRAD2-(ES2*A2-EF2)*B2»C2 78 295 BAX2-(ES2»D2*EF2)»B2 79 C 80 IFfd.NE.1) PHI-PI/2. 81 IF(d.EO.1) PHI-O.O 82 BX2-BRAD2*SIN(PH!) 83 BY2-BAX2 84 B12-SQRT(BX2»«2*BY2«*2) 85 RA2-BX2/BY2 86 BETA-ATAN(RA2)*180.0/PI B7 C 88 C sum of small and large f i e l d s 89 C 90 BX-BX1+BX2 91 BY-BY1+BY2 92 B1-SORT(BX»»2+BY»»2) 93 ZP(d,K)-B1 94 RATIO-BX/BY 95 GAMMA-ATAN(RATIO)*180.0/PI 96 C WRITE(6.300) X1.YI,Z1.X2.Y2.Z2,BX1.BY1.B11.B1. 97 C •ALPHA.BETA,GAMMA 98 C300 FORMAT(10F8.4.3F8.3 99 C GO TO 400 100 C490 WRITE(6.495) X1.Y1.Z1 101 C495 F0RMAT(/'(X1.Y1.Z1)« '.3F5.2.' , po i n t Is on the 102 C • r i n g ' / ) 103 C GO TO 400 104 C590 WRITE(6,S95) X2.Y2.Z2 FORMAT(/'(X2.Y2.Z2)- '.3F5.2.' . po i n t 1s on the 105 C595 106 C • r i n g ' / ) 107 400 CONTINUE 108 500 CONTINUE 109 DO 800 M-1,101 110 800 YP(M)-(FL0AT(M)-1./50.) 111 DO 850 L-1.201 112 850 XP(L)-(FLOAT!L)-101./50.) 113 CALL AX ISC-2.0,0.0.1HX.1.100.0.0.0.-2.0.1.0) 114 CALL AX IS(-2.0.0.0.1HY.-1,36.0.90.0,0.0.1.0) 115 DO 900 1-1,500 116 CN-FL0AT(I) 117 CALL CNT0UR(XP,2O1,YP,101.ZP.201.CN,1.0.CN) 118 900 CONTINUE 119 CALL PLOTND 120 C 121 STOP 122 END 2 C THIS PROGRAM CALCULATES THE COMPONENTS OF A MAGNETIC FIELD 61 RA1*BX1/BY 1 3 C INOUCED BY A UNIT CURRENT RUNNING IN A 0.9 COIL DIAM-2.0 62 ALPHA-ATAN(RAI)*180.0/PI 4 DIMENSION XP(161),YP(85).ZP(161.85) 63 C S PI»4.*ATAN(1.0) 64 IF((XZ2-0.0).GT.10E-6) GO TO 270 6 R-1.0 65 IR2-0 7 C WRITE(6,100) 66 GO TO 280 8 C100 FORMAT(/3X.'XI',6X.'Yl',6X.'Z1',GX.'X2',6X.'Y2',6X.'Z2',6X. 67 270 C2-Y2/XZ2 9 C • 'BX1',5X.'BY1',5X,'B11'.5X, 68 280 XISQ2-4.*XZ2/((1.+XZ2)**2*Y2**2) 10 c • 'BI',6X,'ALPHA',3X,'BETA',4X.'GAMMA',3X.'B1REL'/) 69 XI2*S0RT(XIS02) 11 c 70 EF2-ELIKKXI2, IND1) 12 Zl'0.5 71 ES2-ELIE1(XI2,IND2) 13 Z2-Z1/R 72 IFIIR2.E0.1) GO TO 290 14 DO 500 J-1,161 73 BRAD2-0.0 IS X1-((FL0AT(J)*25.)-2025.)/1000. 74 GO TO 295 16 X2-X1/R 75 290 BRAD2-(ES2*A2-EF2)*B2*C2 17 DO 400 K-1.85 76 295 BAX2»(ES2*D2+EF2)*B2 IB Yt-((FL0AT(K)*25.)-125.)/1000. 77 PHI-ATAN(-X2/Z2) 19 V2*(((FL0AT(K)*2S.)-25.J/1000.)/R 78 C IF(J.NE.1) PHI-PI/2. 20 IR1«1 79 C IFIJ.EO 1) PHI-0.0 21 I R2» 1 80 BX2"BRAD2*SIN(PHI) 22 XZ1"SQRT(X1**2+Z1«*2) 81 BY2-BAX2 23 XZ2-SQRT(X2**2+Z2**2) 82 B12-S0RT(BX2**2*BY2**2) 23. 5 0*SQRT(XI»*2+Y1«»2+Z1**2) 83 RA2»BX2/BY2 23. 7 Q1»SORT(X1**2*V1**2) 84 BETA'ATAN(RA2)*180.0/PI 24 c 85 C 25 c check f o r point s on the r i n g 86 C sum of small and lar g e f i e l d s 26 c 87 C 27 IF((ABS(XZ2-1.0).LE.10E-6).AND.(K.EQ.U) GO TO 400 88 BX«BX1+BX2 28 IF((ABS(Q1-0.871779).LE.10E-6).AND.(K.EO.1))G0 TO 400 89 BY*BY1+BY2 28. . 1 IF((ABS(1.-XZ1).LE.10E-6).AND.(K.EO.5)) GO TO 400 90 B1*SORT(BX*«2+BY**2) 28. .5 IF((ABS(XZ1-0.8660254).LE.10E-6).AND.<K.EQ.5))G0 TO 400 91 ZP(J.K)«B1 28. 6 IF( (ABS(01-0.8660254).LE.10E-6).AND.(K.E0.5))G0 TO 400 92 RATIO-BX/BY 29 A1-( 1.+X1**2*Y1«*2*Z1**2)/((1.-XZ1 )**2*Y1«*2) 93 GAMMA3ATAN(RATIO)*180.0/PI 30 A2*( 1 .+X2**2+Y2**2*Z2**2)/(< 1.-XZ2)«»2*Y2**2) 94 C WRITE(6.300) XI,Y1,Z1.X2.Y2.Z2.BX1,BY1.BI1,B1, 31 B1«1./SQRT(<1.*XZ1)**2+Y1**2) 95 C •ALPHA.BETA,GAMMA 32 B2-1./SQRT(<l.*XZ2)**2*Y2**2) 96 C300 FORMAT(10F8.4.3F8.2 33 D1-(1.-X1**2-Y1**2-Z1**2)/(<1.-XZ1)*»2*Y1«*2) 97 C GO TO 400 34 D2*(1.-X2**2-Y2**2-Z2»*2)/((1.-XZ2)**2*Y2**2) 98 C490 WRITE(6.495) X1.Y1.Z1 35 IF(K.NE.1) GO TO 140 99 C495 F0RMAT(/'(X1.Y1,ZD- '.3F5.2.' , point Is on the lar g e r 36 C1-O.0. 100 C • r i n g ' / ) 37 C2-0.0 101 C GO TO 400 38 GO TO 180 102 C590 WRITE(6.595) X2.Y2.Z2 39 c 103 C595 F0RMAT(/'(X2.Y2.Z2)« '.3F3.2.' , po i n t Is on the sma11er 40 c check For point s on the a x i s 104 C • r i n g ' / ) 41 c 105 400 CONTINUE 42 140 IF((XZ1-0.0).GT.10E-6) GO TO 170 106 500 CONTINUE 43 IR1-0 106. 1 DO 800 M"1,85 44 GO TO 180 106. 16 800 YP(M)-((FLOAT(M)*25.)-125.)/1000. 45 170 C1-Y1/XZ1 106. 22 DO 850 L*1,161 46 180 XISQ1"4.*XZ1/((1.*XZ1)**2+Y1**2) 106. 28 850 XP(L)-((FL0AT(L)*25.)-2025.)/1000. 47 Xll-SORT(XISOI) 106 . 34 CALL AXIS(-2.0.-0.10.1HX,-1.4.0.0.0.-2.0.1.0) 48 EFI-ELIKI(XII.INDI) 106. .4 CALL AX I S(0.0,-0. 10. 1HY, 1,2.0.90.0.0.0, 1 .0) 49 ES1-ELIEKXI1.IND2) 106. 46 DO 900 1-1,500 50 IF(IR1 .EO.1) GO TO 190 106. 52 CN=FLOAT(I) 51 BRAOI'O.O 106. 58 CALL CNTOUR(XP.161.VP.8S.ZP.161.CN.O.O.CN) 52 GO TO 195 106. 64 900 CONTINUE 53 190 BRAD1«(ES1*A1-EF1)*B1*C1 106. 7 CALL PLOTND 54 195 BAX1-(ES1«D1+EF1)*B1 107 C 55 THETA»ATAN(-X1/Z1) 108 STOP 56 c IF(J.NE.1) THETA.PI/2. 109 END 57 c IF(J.EQ.1) THETA-0.0 58 BX1"BRAD1*SIN(THETA) 59 BY1-BAX1 60 B11-S0RT(BX1**2+BY1**2) CO 

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