A model of the vascular resistance and compliance distribution in a lung lobe

Abstract

The arterial and venous pressure curves obtained after occluding the venous outflow from a dog lung lobe perfused with constant flow contain information about the intralobar longitudinal distribution of vascular resistance ( R) and compliance ( C). To utilize this information, a lumped model consisting of four parallel C's separated by three serial R's was used. Solutions of the governing differential equations yield a nonlinear system of four algebraic equations in the seven unknowns and the measured data. Three of the equations form a linear subsystem in which the unknowns are the three R's and the coefficients are functions of the four C's. This is an underdetermined system, but when nonnegativity and boundedness constraints are adjoined, the solution set falls within a narrow band of distributions of cumulative R relative to cumulative C. The shape of this band changes when data are obtained from lobes influenced by various vasoactive stimuli revealing the changes in the longitudinal distribution of the vascular resistance relative to the vascular compliance.