$53 ON THE F R A C T A L
DIMENSION
OF THE PURKINJE
CELL D E N D R I T I C
TREE
T O S H I A K I T A K E D A I , K A T S U H I K O O H T O M O .2# a n d T A K A H I D E M A T S U O K A .2 I L a b o r a t o r y of P h y s i o l o g i c a l S~ience, Jichi School of Nursing, M i n a m i k a w a c h i - m a c h i , Tochigi-ken, 329-04 Japan, ~ D e p a r t m e n t of Electrical Engineering, U t s u n o m i y a University, 2753, Ishii-machi, U t s u n o m i y a - s i , 321 Japan, #Present address: R and B division, Sony M a g n e t i c Products INC., Tagajo-si, 985 Japan. F o l l o w i n g Mandelbrot's proposal of "Fractal geometry", some natural structures, e.g., c l o u d s , c o a s t line, c o r a l reefs, t r e e s , b r o n c h i a l t r e e s etc., h a v e b e e n found to be fractal. The cerebellar Purkinje cell has a highly branched d e n d r i t i c t r e e e x t e n d i n g in a t r a n s v e r s e p l a n e to the f o l i u m . S u c h a t w o - d i m e n s i o n a l tree pattern was subjected to f r a c t a l a n a l y s i s to e v a l u a t e the i n t r i c a c y of t h e d e n d r i t i c tree and it was revealed that this fractal d i m e n s i o n w a s useful to study postnatal d e v e l o p m e n t of d e n d r i t i c trees. Rats of ages of 7 - 100 postnatal days were deeply anesthetized with nembutal and perfused transcardially w i t h 5% g l u t a r a l d e h y d e and 2.4% p o t a s s i u m dichromate. After fixation for 6 days, blocks were impregnated w i t h 0.5% s i l v e r n i t r a t e s o l u t i o n for 3 days. Golgi-stained P u r k i n j e c e l l s in f o l i u m at the p r i m a r y f i s s u r e , w h i c h is o n e of t h e e a r l i e s t m a t u r i n g region in the cerebellum, were selected and their d e n d r i t i c tree patterns w e r e t r a c e d w i t h c a m e r a lucida. T h e p a t t e r n s w e r e p r o j e c t e d o n t o a grid, a n d r e g i s t e r e d w i t h a d i g i t i z e r into c o m p u t e r disc files. The n u m b e r of squares w h i c h traverse the patterns w e r e counted as the grid size changed. A log-log plot of the n u m b e r versus grid size s h o w e d a linear r e l a t i o n s h i p indicating that the Purkinje cell d e n d r i t i c tree has a statistical self-similarity. The fit of the data to the line was e v a l u a t e d by c o n t r i b u t i o n ratios w h i c h were in the range of 0.985 - 0.999 in the present data. The i n c l i n a t i o n of the line by least-square fitting gave the dimension (D) of t h e d e n d r i t i c tree. D w a s 1.34 at 5 d a y s old, w h i c h i n c r e a s e d sigmoidally to 1.77 at 50 d a y s old. T h e w i d t h of t h e d e n d r i t i c f i e l d d e v e l o p e d with approximately t h e s a m e t i m e c o u r s e as d i m e n s i o n . The developmental time c o u r s e of an a r e a of the d e n d r i t i c f i e l d l a g g e d by s e v e r a l d a y s to t h a t of the width, w h i c h is due to l i m i t a t i o n of lateral g r o w t h because the g r o w i n g dendrite reaches the boundary to the n e i g h b o r i n g Purkinje cells at first.
EFFECT
OF F I B R O N E C T I N
ON R E G E N E R A T I O N
OF THE C E R E B E L L O F U G A L
PROJECTION
SABURO KAWAGUCHI, H I R O F U M I MIYATA*, N O B U O KATO* and BUNGO OKUDA*, Brain Research, Faculty of Medicine, Kyoto University, Kyoto 606,
IN THE CAT
Institute Japan
for
In c o n t r a s t to t h e c u r r e n t c o n c e p t of a b o r t i v e r e g e n e r a t i o n of m a m m a l i a n CNS axons, marked regeneration of t h e c e r e b e l l o f u g a l projection infrequently occurs after t r a n s e c t i o n of the d e c u s s a t i o n of the superior cerebellar peduncle in kittens a n d a d u l t c a t s (J P h y s i o l S o c J p n 45, 443, "83; J C o m p N e u r o l 245, 258, "86). Prior reports have been unable to d e t e r m i n e the reasons behind successful or abortive r e g e n e r a t i o n f o l l o w i n g a lesion. Thus, the a i m of the present e x p e r i m e n t s w a s to f i n d f a c t o r s or c o n d i t i o n s w h i c h a r e f a v o r a b l e f o r a x o n a l r e g e n e r a t i o n . In adult cats the d e c u s s a t i o n of the b r a c h i u m c o n j u n c t i v u m w a s t r a n s e c t e d sagittally by i m p l a n t a t i o n of an edged U-shaped w i r e into the brain s t e m base at the midline. Various substances (5-fluorodeoxyuridine + arabinosylcytosine, norepinephrine, s u b s t a n c e P, l a m i n i n , f i b r o n e c t i n ) w e r e a p p l i e d i n t o t h e l e s i o n b y an o s m o t i c minipump for 2 weeks after transection (n=5 to ii for e a c h s u b s t a n c e ) . After being raised for 25-93 days postoperatively, the a n i m a l s w e r e subjected to an HRPi n j e c t i o n into the c e r e b e l l a r lateral and i n t e r p o s i t u s nuclei to label a n t e r o g r a d e ly the c e r e b e l l o f u g a l p r o j e c t i o n a r i s i n g f r o m these nuclei. In five of ii cats in w h i c h f i b r o n e c t i n h a d b e e n a p p l i e d , l a b e l e d f i b e r s p a s s i n g t h r o u g h t h e l e s i o n or around the lesion by m a k i n g detours w e r e observed. These fibers, t e r m i n a t i n g m a i n l y in the c o n t r a l a t e r a l red nucleus and t h a l a m i c V A - V L nuclear c o m p l e x and partly in the ipsilateral homologous s t r u c t u r e s , a r e c o n s i d e r e d to h a v e b e e n r e g e n e r a t e d . They w e r e small in n u m b e r in t w o cats but c o n s i d e r a b l y n u m e r o u s in the other three in w h i c h c e r e b e l l o c e r e b r a l responses w e r e evoked. This indicates the o c c u r r e n c e of successful regeneration in t h e l a t t e r a n i m a l s . In t h e a n i m a l s in w h i c h o t h e r substances had been applied, labeled fibers w e r e m o s t l y c o n c e n t r a t e d at the m a r g i n of the lesion facing glial scars w i t h no further extension, a l t h o u g h o c c a s i o n a l l y a trace a m o u n t of labeled fibers ascended the brain s t e m ipsilaterally. The occurrence of successful r e g e n e r a t i o n in the a n i m a l s t r e a t e d w i t h fibronectin, higher than that in the c h e m i c a l l y u n t r e a t e d a n i m a l s of the previous e x p e r i m e n t s (3/19), appears to indicate that f i b r o n e c t i n facilitates axonal r e g e n e r a t i o n in the CNS.