Modeling of the Pulmonary Vasculature

Mathematical models in physiology aim to describe an observable structure or function (or how they relate) using mathematical equations. A computational model solves a system of equations to predict an output, usually as some controlling parameters are varied over a physiological range. The motivation for this is not simply to duplicate the real process, but rather to provide insight that could not be obtained solely through observation and measurement. Integrative computational models provide a means to relate reductionist measurements to integrated organ function and clinical measurements. They are complementary to experimental studies, and can be used to study integrated function while controlling complexity and interactions that would normally occur during experimentation and therefore potentially obscure some important function. Perfusion of the pulmonary vasculature is a multiscale phenomenon that involves scale-dependent structure and function, therefore requiring different model assumptions for the microcirculation and the arterial or venous flows. The pulmonary vasculature interacts with the surrounding lung tissue, and vessel dimensions (and therefore resistance to flow) are further dependent on hydrostatic pressure gradients, vasoconstriction and vasodilation, and the topology and material composition of the vascular trees. The regional distribution of blood in the lung is determined by the effect of gravity on hydrostatic pressure gradients and regional tissue expansion (and therefore stretch or compression of capillaries), by pulmonary vascular resistance, and by the physical properties of blood. These factors interact in a dynamically expanding and recoiling organ, with time-varying boundary conditions for blood pressure, and subject to the effect of changes in posture. In this chapter, we focus specifically on models of the pulmonary vasculature that have been used to study structure–function relationships in pulmonary perfusion.