Exclusion of protein from high polymer media. I. Derivation of probability distribution for the number of fiber centers within any sphere of radius r.

Ogston's (1958) fiber model based on Poisson's distribution function gives the average number of fibers making contact and no contact inside a sphere of radius r. The probability of penetration of spherical particles within a fibrous network was derived from the moment generating function [Formula: see text] A is the number of particles that intrude into a sphere of radious r. alpha(mu) is the probability that a particle, whose center is mu units away from the origin, intrudes into a sphere of radius r. A has a Poisson distribution with a mean value E(A) = 4pinualpha(mu)mu(2)dmu. The theoretical derivation of the distribution function of A gives Ogston's fiber model.