A stochastic model for the self-similar heterogeneity of regional organ blood flow

The theory of exponential dispersion models was applied to construct a stoc hastic model for heterogeneities in regional organ blood flow as inferred f rom the deposition of labeled microspheres, The requirements that the dispe rsion model be additive (or reproductive), scale invariant, and represent a compound Poisson distribution, implied that the relative dispersion (RD = standard deviation/mean) of brood flow should exhibit self-similar scaling in macroscopic tissue samples of masses m and m(ref) such that RD(m) = RD(m (ref)). (m/m(ref))(1-D), where D was a constant. Under these circumstances this empirical relationship was a consequence of a compound Poisson-gamma d istribution that represented macroscopic blood flow. The model also predict ed that blood flow, at the microcirculatory level, should also be heterogen eous but obey a gamma distribution-a prediction supported by observation.