Model combining hydrodynamics and fractal theory for analysis of in vivo peripheral pulmonary and systemic resistance of shunt cardiac defects

Abstract

The fractal state of the arterial vascular tree is considered to have a universal dimension related to the principle of minimum work rate, but can demonstrate the capacity to adapt to other dimensions in disease states such as congenital high-flow pulmonary hypertension (PH) by a process that is incompletely understood. To document and interpret fractal adaptation in patients with different degrees of PH, pulmonary and systemic vascular resistance was analyzed by a model that evaluated the fractal dimension, x, of the Poiseuille resistance contribution of the arterial vessel radius between 10 and 100 μm, via the proportionality Q∝( R peri/ BL) − x/4 , with Q, R peri, and BL clinically observed variables representing total pulmonary or systemic blood flow, its peripheral arterial resistance, and body length, respectively. Identification of x in the pulmonary (P) and systemic (S) beds was evaluated from hemodynamic data of 213 patients, categorized into 7 groups by PH grade. In controls without PH, x P=2.2 while the dimension increased to 3.0, with the systemic dimension constant at x S=3.1. Our model predicts that severe grades of PH are associated with: a more elongated and hindered vessel in the periphery, and reductions in vessel numbers, as unit pulmonary resistive arterial trees ( N 1) and their component intra-acinar arteries ( N W). These model network changes suggest a complex adaptive process of arterial network reorganization in the pulmonary circulation to minimize the work rate of high-flow congenital heart defects.