Longitudinal position matrix of the pig coronary vasculature and its hemodynamic implications

Hemodynamic analysis of coronary blood flow must be based on a statistically valid geometric model of the coronary vasculature. We have previously developed a diameter-defined Strahler model for the arterial and venous trees and a network model for the capillaries. A full set of data describing the geometric properties of the porcine coronary vasculature was given. The order number, diameter, length, connectivity matrix [m,n] (CM), and parallel-series features were measured for all orders of vessels of the right coronary artery (RCA), left anterior descending artery (LAD), left circumflex artery (LCX), and coronary venous system. The purpose of the present study is to present another feature of the branching pattern of the coronary vasculature: the longitudinal position matrix [m,n] (LPM), whose component in row m and column n is the fractional longitudinal position of the branch point on vessels of order n at which vessels of order m branch off (m less than or equal to n). The LPM of the pig RCA, LAD and LCX arterial trees, as well as the coronary sinusal and thebesian venous trees, are presented. The hemodynamic implications of the LPM are illustrated by comparing two kinds of circuits: one, the CM + LPM model, simulates the mean data on the morphology (diameters, lengths, and numbers), CM, and LPM of vessels, whereas the other, the CM model, simulates the mean data on the morphology and CM without considering the LPM. We found that the LPM affects the hemodynamics of corollary blood flow especially with regard to the nonuniformity or dispersion of flow distribution.