Regional myocardial flow heterogeneity explained with fractal networks

Abstract

There is marked heterogeneity in regional myocardial blood flow. To explain how the distribution of flow broadens with an increase in the spatial resolution of the measurement, we developed fractal models for vascular networks. A dichotomous branching network of vessels represents the arterial tree and connects to a similar venous network. A small difference in vessel lengths and radii between the two daughter vessels, with the same degree of asymmetry at each branch generation, predicts the dependence of the relative dispersion (mean +/- SD) on spatial resolution of the perfusion measurement reasonably well. When the degree of asymmetry increases with successive branching, a better fit to data on sheep and baboons results. When the asymmetry is random, a satisfactory fit is found. These models show that a difference in flow of 20% between the daughter vessels at a branch point gives a relative dispersion of flow of approximately 30% when the heart is divided into 100-200 pieces. Although these simple models do not represent anatomic features accurately, they provide valuable insight on the heterogeneity of flow within the heart.