Lumped Parameter Model for Computing the Minimum Pressure During Mechanical Heart Valve Closure

Simulation of the Frank-Starling Law of the Heart

We developed a lumped parameter, computer-based model of an equivalent electronic circuit for a one-atrium one-ventricle (frog) heart attached to a vascular circuit, to simulate a basic concept of cardiovascular physiology, the Frank-Starling Law of the Heart. A series of simulations was performed, to observe changes in cardiovascular variables (e.g., arterial pressure, ventricular volume, and valve flows) if either preload or afterload was increased. The simulated data agreed qualitatively, and quantitatively when experimental data are available, with data obtained on amphibian or on mammalian myocardium. In addition, the data obtained in these simulations improve our understanding of the mechanism(s) whereby the heart muscle adapts itself to increased distension (increased preload) or to impeded systolic contraction (increased afterload). The analysis of the measured valve flows suggests that the ventricle is a highly input sensitive pump because the input pressure determines the diastolic distension and, consequently, the force of ventricular systolic contraction. On the other hand, the ventricle is a relatively output insensitive pump. Therefore, not only atrium contraction, but also predominantly the preceding ventricular systolic contraction is the main mechanism of the subsequent diastolic ventricular filling. We conclude that the presented model enables the study of basic concepts of cardiovascular physiology.

A robust and efficient valve model based on resistive immersed surfaces

A procedure for modeling the heart valves is presented. Instead of modeling complete leaflet motion, leaflets are modeled in open and closed configurations. The geometry of each configuration can be defined, for example, from in vivo image data. This method enables significant computational savings compared with complete fluid-structure interaction and contact modeling, while maintaining realistic three-dimensional velocity and pressure distributions near the valve, which is not possible from lumped parameter modeling. Leaflets are modeled as immersed, fixed surfaces over which a resistance to flow is assigned. On the basis of local flow conditions, the resistance values assigned for each configuration are changed to switch the valve between open and closed states. This formulation allows for the pressure to be discontinuous across the valve. To illustrate the versatility of the model, realistic and patient-specific simulations are presented, as well as comparison with complete fluid-structure interaction simulation.