Estimation of the Distribution of Blood Vessel Diameters from the Arteriovenous Passage of Microspheres

Abstract

We present an estimator of the probability density of capillary diameters based on a simple probabilistic model of microsphere passage through a microvascular bed. With this model, an estimate of the density is obtained as the solution of an integral equation. The density is approximated by a linear combination of B-splines with the coefficients restricted to be nonnegative. Equations for maximum likelihood estimates of the coefficients are obtained. The proposed method is applied to data from the dog intestinal circulation.