Stereological characterization of plates and platelet growth
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p e r i m e t e r and c r o s s - s e c t i o n a l a r e a by applying the r e l a t i o n analogous to Eq. [5] that holds for a c o l l e c t i o n of a r e a s in the plane :3
: 7rAA/LA
where A A is the a r e a f r a c t i o n of t h e s e two d i m e n s i o n a l f e a t u r e s and L A is t h e i r p e r i m e t e r length p e r unit a r e a of s t r u c t u r e . If these a r e a s a r e a s s u m e d to be d i s p e r s e d t h r o u g h the v o l u m e of a t h r e e d i m e n s i o n a l s t r u c t u r e , as the c r o s s - s e c t i o n a l a r e a s of p l a t e l e t s , then the m e a n i n t e r c e p t in the p l a t e l e t p l a n e s is given, by analogy with Eq. [6]:
1. R. T. DeHoffand F. N. Rhines:QuantitativeMieroscopy,McGraw-Hill,New York, 1968. 2. R. T. DeHoff:Met. Trans., 1971,vol. 2, pp. 521-23.
Stereological Characterization of Plates and Platelet Growth
AV ~ Sy 7~p = -~2 = ~r -ff~ V - 4 MV
R. T . D e H O F F M i c r o s t r u c t u r e s which c o n s i s t of a d i s p e r s i o n of p l a t e l e t s may be s t e r e o l o g i c a l l y c h a r a c t e r i z e d by m e a s u r i n g t h e i r v o l u m e f r a c t i o n V V and s u r f a c e a r e a S V . It is shown that a t h i r d p a r a m e t e r , r e p r e s e n t e d in the i n t e g r a l m e a n c u r v a t u r e M V , 1 which is e s t i m a t e d f r o m the a r e a t a n g e n t count, a mode a v a i l a b l e on n e a r l y a l l image a n a l y z i n g c o m p u t e r s , a l s o p r o v i d e s useful i n f o r m a t i o n about such s t r u c t u r e s . I n t e g r a l m e a n c u r v a t u r e is useful in this context b e c a u s e it is s i m p l y r e l a t e d to the total length of the p e r i m e t e r of the p l a t e s , in unit v o l u m e , L V .2 2 L V = -~ M V
[1]
Model the p l a t e s in the s t r u c t u r e as c o m p o s e d of p a r a l l e l s u r f a c e s a d i s t a n c e r apart, where r is s m a l l in c o m p a r i s o n to the l a t e r a l d i m e n s i o n s of the plate. The p e r i m e t e r c o n t o u r may be a r b i t r a r y in shape. Let A be the a r e a of an i n d i v i d u a l plate in the plane of the plate. Then, b e c a u s e the a r e a of the edges of the plate may be n e g l e c t e d , the total c r o s s - s e c t i o n a l a r e a of p l a t e s in unit v o l u m e : 1 A V = -~ SV
[2]
The v o l u m e f r a c t i o n of p l a t e s in the s t r u c t u r e may be written:
VV = - r A v
[3]
where u is the a v e r a g e plate t h i c k n e s s defined by:
-i ~ f f TdA/f f dA AV
[4]
AV
It is c o m m o n to c h a r a c t e r i z e the s c a l e of m i c r o s t r u e t u r e s with the mean l i n e a l i n t e r c e p t : s
~ 4V V _ 4 T A V _ Sv 2Av
27
[6]
[5]
T h u s , this s t a n d a r d d e s c r i p t o r of s c a l e r e p o r t s plate t h i c k n e s s , and c o n t a i n s no i n f o r m a t i o n about the l a t e r a l d i m e n s i o n s of the p l a t e s . The m e a n l i n e a l i n t e r c e p t in the plane of the plate, Xp, may be obtai
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