Abstract 15470: Mathematical Modeling of the Determinants and Consequences of Mitral Regurgitation: Jacobian Sensitivity Analysis of a Lumped Parameter Model of the Cardiovascular System

Abstract

Background: Mitral regurgitation (MR) results in complex changes to hemodynamics, which lumped parameter (LP) models of the cardiovascular (CV) system can model. A previously validated LP model using time varying elastance of the atria and ventricles models pressure, volume, and flow in the four chambers and valves of the heart and arterial and venous compartments. Here we model moderate MR and perform a Jacobian matrix sensitivity analysis to explore impact of CV parameters on MR variables. Methods: Using MATLAB app designer, we made an app to give input parameter and output variable specification for the LP model, displaying pressure, volume, and flow curves and specified output variables at equilibrium. Sensitivity analysis was done with a Jacobian matrix, showing the proportional change (Δ) in output variables ( y i ) to change in each input parameter ( x j ), [(Δy i /y i )/(Δx j /x j )]. We assessed the change in these output variables: LA peak pressure (LAP), Forward Stroke Volume (FSV), and MR Volume (MRVol); in response to changes in these input parameters: LV End Systolic Elastance (LVESE), MR Orifice Area (MROA), and peripheral vascular resistance (PVR) in the setting of moderate MR (MROA=0.3 cm 2 ). Results: Pressure curves for the left atrium and ventricle and aorta with and without moderate MR are shown, with the Jacobian sensitivity matrix in Figure 1. To use the Jacobian matrix, multiply a small proportional change in the input parameter (rows) with the value under the output variable (columns). For example, a 10% increase in MROA will cause a 3.7% increase in LAP, 0.8% fall in FSV, and 8.3% increase in MRVol. Conclusion: This analysis shows how small changes in many parameters impact multiple output variables. MRVol is most sensitive to changes in MROA, while the impact of LVESE (contractility) and PVR (afterload) are appropriately discordant. This model warrants further study to predict instantaneous hemodynamic changes in MR and a host of other entities.