Biophysical Aspects of Radiation Quality

MICRODOSIMETRY..AND THE THEORY OF STRAGGLING. Theoretical developments in microdosimetry (the determination of the spatial distribution of energy deposition on a microscopic scale) are described. It is pointed out that microdosimetric theory is equivalent to LET theory plus straggling theory. The influence of each of the different random factors (varying LET, varying track length, varying number of primary collisions and varying energy transferred in primary events) can be expressed as a relative variance and these relative variances can be summed to give the relative "variance" of the single-event spectrum. The track-length variation and the variation in the number of primary events will often not be important. Although the LET variation may be quite important, it appears that the energy spectrum of primary collisions will usually make the decisive contribution. T h i s p a p e r d e s c r i b e s s t u d i e s f o l l o w i n g t h o s e c o n c e r n e d w i t h t h e b i o l o g i c a l a p p l i c a t i o n o f m i c r o d o s i m e t r y , w i t h t h e m a t h e m a t i c a l s c h e m e o f f u n c t i o n s n e e d e d f o r t h i s p u r p o s e , a n d w i t h a f i r s t t h e o r e t i c a l d e t e r m i n a t i o n o f s o m e o f t h e s e f u n c t i o n s [ 1 ] . T h e p r e v i o u s t h e o r e t i c a l c a l c u l a t i o n s , b a s e d o n M o n t e C a r l o m e t h o d s , w e r e i n g o o d a g r e e m e n t w i t h t h e e x p e r i m e n t a l d a t a . H o w e v e r , n e w i m p r o v e m e n t s i n t h e e x p e r i m e n t a l t e c h n i q u e m a d e i t d e s i r a b l e t o d e v e l o p a c c u r a t e t h e o r e t i c a l m e t h o d s . W h i l e m o r e r e f i n e d a n d , n e c e s s a r i l y , m o r e a b s t r a c t c o m p u t a t i o n s a r e a p p l i e d , one s h o u l d a l s o a t t e m p t a c l e a r e r u n d e r s t a n d i n g o f t h e d i f f e r e n t f a c t o r s i n v o l v e d . T h i s p a p e r t h e r e f o r e , o u t l i n e s a g e n e r a l t h e o r e t i c a l i n v e s t i g a t i o n i n t o t h e s p e c t r a o f l o c a l e n e r g y d e n s i t y . T h e b a s i s i s R o s s i ' s c o n c e p t o f l o c a l e n e r g y d i s t r i b u t i o n [ 2 ] ; t h e w o r k r e p o r t e d w a s done p a r t l y i n h i s l a b o r a t o r i e s a t C o l u m b i a U n i v e r s i t y . T h i s w o r k i s d i v i d e d i n t o t w o s e c t i o n s : F i r s t , t h e d i f f e r e n t r a n d o m f a c t o r s w h i c h m a k e up t h e d i s t r i b u t i o n o f l o c a l e n e r g y d e n s i t y a r e b r i e f l y d i s c u s s e d . A f o r m u l a i s t h e n g i v e n w h i c h c o m p r i s e s a l l t h e s e f a c t o r s . T h i s f o r m u l a i s t h e b a s i s f o r t h e n u m e r i c a l c a l c u l a t i o n s a n d h a s b e e n u s e d s u c c e s s f u l l y i n t h e p a s t . I t i s , h o w e v e r , r a t h e r c o m p l i c a t e d a n d does n o t g i v e a s i m p l e i d e a as t o t h e r e l a t i v e c o n t r i b u t i o n s o f t h e d i f f e r e n t f a c t o r s t o t h e s h a p e o f t h e l o c a l e n e r g y s p e c t r a . B e c a u s e o f t h i s d i f f i c u l t y , a r e l a t i o n o f r e m a r k a b l e s i m p l i c i t y i s p r e s e n t e d w h i c h c o n n e c t s t h e v a r i a n c e o f t h e m i c r o d o s i m e t r y s p e c t r a w i t h t h e v a r i a n c e o f t h e i n d i v i d u a l r a n d o m f a c t o r s . T h i s r e l a t i o n l e a d s t o t h e s e c o n d p a r t a n d t o a p o i n t w h i c h i s c e n t r a l t o t h i s p a p e r . I t t u r n s o u t t h a t , e x c e p t f o r l a r g e v o l u m e s