E x p e r i m e n t s w e r e p e r f o r m e d wi t h a CL1SO4 s o l u t i o n p h a n t o m ( T| = 2 sec, To = 0 . 9 3 sec) o n t h e 2 . 3 5 T s y s t e m . I m a g e s w e r e a c q u i r e d u s i n g a v o l u m e t r a n s m i t t e r coi l o f a sl o t t e d - t u b e d e s i g n a n d a s e p a r a t e s u r fa ce coil as the r e c e i v e r . T h e 2 - e x p e r i m e n t s i n g l e - s h o t s e q u e n c e w a s i m p l e m e n t e d wi t h the o p t i m i s e d a n d s t a n d a r d sequence p a r a m e t e r s d e s c r i b e d in t h e p r e v i o u s s ect i on a n d the t r a c e ( D ) c a l c u l a t e d u s i n g Eq . [6.5]. T h e v a r i a n c e o f t he t r a c e ( D ) m a p s w as e s t i m a t e d b y r e p e t i t i o n o f t he e x p e r i m e n t (n=350) a n d s u b s e q u e n t r e g i o n a l a na l y s i s ( 2 82 pi xe l s ) . T h e t h e o r e t i c a l a n d e x p e r i m e n t a l r e s u l t s ar e s h o w n in T a b l e 6. 3. A g o o d a g r e e m e n t b e t w e e n t h e o r y a n d e x p e r i m e n t w a s t h e r e b y f o u n d . 196
C h ap ter 7 Study o f R ep eated Ischaem ia b [sec/mm^] 448 552 111 / no 3 / 3 6 / 2 TR [sec] T33 150 Trace(D) [x l0 ‘^ mmVsec] 2.265 2.286 Gd“ (calculated) 2 7 3 206
(5^
(experimental) 268 2 1 0 lower at 95% 2 2 7 177 higher Gd" at 95% 31 3 245 T a b l e 6 . 3 E x p e r i m e n t a l v a l i d a t i o n w i th a c o p p e r s ul p h a t e p h a n t o m . C o m p a r i s o n o f o p t i m i s e d a n d s t a n d a r d e x p e r i m e n t s ( n = 3 5 0 ) . T h e S N R ( To / o in E q. [6. 7]) w a s d e t e r m i n e d f r o m a p ai r o f b a s e l i n e i m a g e s . T | a n d To m e a s u r e m e n t s w e r e p e r f o r m e d w i t h E P I - b a s e d i n v e r s i o n r e c o v e r y a n d s p i n - e c h o 2 D - F T m e a s u r e m e n t s at m u l t i p l e e c h o t i m e s r e s p e c t i v e l y . U n i t s o f are m n / / s e c “. T h e s e resul t s w e r e r e p o r t e d in (Pell,1995). 6.3.3 Discussion T h i s s t u d y h a s p r e s e n t e d a m e a n s to o p t i m i s e t he s e t - u p p a r a m e t e r s o f r a p i d d i f f u s i o n c o e f f i c i e n t q u a n t i f i c a t i o n . T h i s m e t h o d is e a s y to i m p l e m e n t a n d t he r es u l t s o f this s t u d y d e m o n s t r a t e t he b e n e f i t s o f o p t i m a l e x p e r i m e n t a l p a r a m e t e r s f o r t he 2 - e x p e r i m e n t s c h e m e o f t r a c e ( D ) m e a s u r e m e n t . T h e p r e c i s i o n in t h e v a lu e o f t h e d i f f u s i o n c o e f f i c i e n t w a s d e s c r i b e d in t e r m s o f the v a r i a n c e in the r e s u l t a n t m a p s a n d a m i n i m i s a t i o n w a s p e r f o r m e d w i t h r e s p e c t to t he b - v a l u e , the n u m b e r o f w e i g h t e d i m a g e s a n d t he r e pe t i t i o n t i me . T h e a c c u r a c y as we l l as t he p r e c i s i o n is a f f e c t ed b y the i m a g i n g s c h e m e . T h e u n d e r e s t i m a t i o n o f A D C s h a s b e e n s h o w n to be i m p r o v e d in s i m u l a t e d d a t a b y a r e d u c t i o n in t h e n u m b e r o f d i f f e r e n t d i f f u s i o n - w e i g h t e d i m a g e s ( Ei s , 1995). T h e p r e c i s i o n c a n b e i n c r e a s e d b y s i gna l a v e r a g i n g . A r e d u c t i o n in t he r e p e t i t i o n t i m e a l l o w s thi s b u t t he i n c r e a s e d S N R as a r es u l t o f si gna l a v e r a g i n g m u s t b e b a l a n c e d a g a i n s t the r e d u c t i o n in S N R d u e to t he a dd i t i o n a l T i - w e i g h t i n g . T h e o p t i m i s a t i o n o f t he b - v a l u e is e q u i v a l e n t to s a m p l i n g in a h i g h l y s e n s i t i v e a r e a o f t he b - v a l u e d o m a i n . In t he a b s e n c e o f n o i s e , t he o p t i m a l b - v a l u e w o u l d be t he h i g h e s t a c h i e v a b l e w i t h the a v a i l a b l e g r a d i e n t
C h a p te r 7 S tu d y o f R e p e a te d Isch aem ia
Strength. However, noise is a significant factor in M RI and an appropriate value must, therefore, be chosen that balances the diffusion sensitivity in the image with the resultant SNR.
T he results o f this study dem onstrate the time efficient use of m ultiple averaging o f the diffusion-w eighted im age at the expense of the baseline image (bo=0) which possesses a
larger inherent SNR. The optimal theoretical b-value schem e for the CUSO4 phantom
provides a single-averaged diffusion-w eighted im age with a SNR that is approxim ately 30% of the baseline im age (exp(-biD )) (i.e. in the case of no=ni = l). The SN R in the resultant trace(D ) im age, SN R d , can be calculated by m anipulation of Eq. [6.9] (S N R d =
D/Od) and is approxim ately 33% of the baseline image. The acquisition o f a diffusion- w eighted m ap instead of the interpretation o f the diffusion-w eighted im age, does not, therefore, im pair the available SNR.
T he optim isation schem e that is described here has been perform ed for a sam ple w ith a know n, single, hom ogeneous value of the ADC. A 2-experim ent schem e and a baseline im age w ith bo=0 are, therefore, natural choices. By extension of Eq. [6.8] to n=3
experim ents, it can be shown that m ultiple experim ents will never im prove the reproducibility in this situation. This assertion presupposes a linear relationship betw een
InSi and the b-values; if m ultiexponential behaviour is expected, accurate quantification o f the A D C will necessitates multiple experim ent and m ultiexponential fitting. A nother study has, how ever, suggested that 3-experim ent schemes are advisable in spite o f the resultant reduction in the precision on account o f possible random, non-stochastic errors such as those due to m otion or hardware im perfections (Eis, 1995).
In the m ore realistic situation of a sample with a range o f unknow n diffusion coefficients, the analysis of Eq. [6.8] becom es very com plex. A m ore sophisticated
treatm ent involving the Cram ér-Rao theory of low er bounds (van den Bos, 1982) can be used to determ ine the optimal set-up param eters in this situation, and this theory has been applied to quantitative T2 relaxometry (Jones, 1996). The graphs in Fig. 6.9 and
6 . 1 0 dem onstrate that the sensitivity of the optim al response is relatively flat over a range close to turning point of the profiles. In a recent report, it has been proposed that a b-value should be chosen that sensitises the error response of the 2-experim ent schem e
to the range of ADC values to be m easured (Xing, 1997). An interval can be constructed that is related to the com bination of b and D values over which a sensitivity response is
C h a p te r 7 S tu d y o f R ep e a te d Isc h ae m ia
achieved that is within specified bounds of the turning point. In this m anner, X ing et al.
describe an optim al 2-experim ent scheme for quantitative ADC m easurem ents in the hum an brain in which the baseline image is slightly diffusion-w eighted (b=300 sec/mm^) in order to reduce contam ination from C SF due to the effects o f partial volum e.