A 1D model for the pulmonary and coronary circulation accounting for time-varying external pressure

Pulmonary and coronary hæmodynamics are strongly influenced by the rhythmic motion of heart and lungs – studies show that coronary arterial flow drops to near 0 during systole and pulmonary flow increases during normal respiration. Several previous studies have attempted to capture this motion, and the effect it has on arterial and venous blood flow. However, the method of inclusion of “external pressure” is often ad hoc or requires tuning parameters that lack a physical meaning. For the first time, we present a 1D model for blood flow in the pulmonary and the coronary arteries and veins that is implemented using only physiological measured data. To achieve this, we develop an existing 1D model for viscous blood flow in thin, elastic walled arteries and veins to include an explicit dependence on a prescribed timevarying external pressure. The arterial and venous sides are matched using a pair of grand admittance matrices of a structured tree that were derived using the 1D theory; one of the matrices encodes the effect of fluid pressure on venous flow and the other the impact of external pressure. We extend the boundary condition used to join arterial or venous segments to directly model vessel stenoses or trifurcations. We use the model to simulate pulmonary blood flow during quiet respiration, pneumothorax, and mechanical ventilation of adults. We find good agreement between our model results and reports from the literature. We develop a framework for building realistic coronary arterial and venous networks from a number of sources. We build several networks that have different branching patterns and levels of detail, and quantify the impact on arterial flow and pressure these have. The volume of the large vessel network in the reference configuration is an important determinant of coronary flow. Further, we compare networks with a simplified venous structure against a branching venous network in which the right and left coronary arteries ultimately drain into the right atrium via the coronary sinus, finding that the morphometry of the venous network is an important determinant of arterial flow. We show that the model can be used to model vascular rarefaction and microvascular stiffening, showing good agreement with reports from the literature