TY - JOUR
T1 - A stochastic model for the self-similar heterogeneity of regional organ blood flow
JF - Proceedings of the National Academy of Sciences
JO - Proc Natl Acad Sci USA
SP - 837
LP - 841
M3 - 10.1073/pnas.98.3.837
VL - 98
IS - 3
AU - Kendal, Wayne S.
Y1 - 2001/01/30
UR - http://www.pnas.org/content/98/3/837.abstract
N2 - The theory of exponential dispersion models was applied to construct a stochastic model for heterogeneities in regional organ blood flow as inferred from the deposition of labeled microspheres. The requirements that the dispersion model be additive (or reproductive), scale invariant, and represent a compound Poisson distribution, implied that the relative dispersion (RD = standard deviation/mean) of blood flow should exhibit self-similar scaling in macroscopic tissue samples of masses m and mref such that RD(m) = RD(mref). (m/mref)1−D, where D was a constant. Under these circumstances this empirical relationship was a consequence of a compound Poisson-gamma distribution that represented macroscopic blood flow. The model also predicted that blood flow, at the microcirculatory level, should also be heterogeneous but obey a gamma distribution—a prediction supported by observation.
ER -