A Lumped Two-Compartment Model for Simulation of Ventricular Pump and Tissue Mechanics in Ischemic Heart Disease

Introduction: Computational modeling of cardiac mechanics and hemodynamics in ischemic heart disease (IHD) is important for a better understanding of the complex relations between ischemia-induced heterogeneity of myocardial tissue properties, regional tissue mechanics, and hemodynamic pump function. We validated and applied a lumped two-compartment modeling approach for IHD integrated into the CircAdapt model of the human heart and circulation. Methods: Ischemic contractile dysfunction was simulated by subdividing a left ventricular (LV) wall segment into a hypothetical contractile and noncontractile compartment, and dysfunction severity was determined by the noncontractile volume fraction ( $NCVF$ ). Myocardial stiffness was determined by the zero-passive stress length ( $L_{s0,pas})$ and nonlinearity ( $k_{ECM}$ ) of the passive stress-sarcomere length relation of the noncontractile compartment. Simulated end-systolic pressure volume relations (ESPVRs) for 20% acute ischemia were qualitatively compared between a two- and one-compartment simulation, and parameters of the two-compartment model were tuned to previously published canine data of regional myocardial deformation during acute and prolonged ischemia and reperfusion. In six patients with myocardial infarction (MI), the $NCVF$ was automatically estimated using the echocardiographic LV strain and volume measurements obtained acutely and 6 months after MI. Estimated segmental $NCVF$ values at the baseline and 6-month follow-up were compared with percentage late gadolinium enhancement (LGE) at 6-month follow-up. Results: Simulation of 20% of $NCVF$ shifted the ESPVR rightward while moderately reducing the slope, while a one-compartment simulation caused a leftward shift with severe reduction in the slope. Through tuning of the $NCVF$ , $L_{s0,pas}$ , and $k_{ECM}$ , it was found that manipulation of the $NCVF$ alone reproduced the deformation during acute ischemia and reperfusion, while additional manipulations of $L_{s0,pas}$ and $k_{ECM}$ were required to reproduce deformation during prolonged ischemia and reperfusion. Out of all segments with LGE>25% at the follow-up, the majority (68%) had higher estimated $NCVF$ at the baseline than at the follow-up. Furthermore, the baseline $NCVF$ correlated better with percentage LGE than $NCVF$ did at the follow-up. Conclusion: We successfully used a two-compartment model for simulation of the ventricular pump and tissue mechanics in IHD. Patient-specific optimizations using regional myocardial deformation estimated the $NCVF$ in a small cohort of MI patients in the acute and chronic phase after MI, while estimated $NCVF$ values closely approximated the extent of the myocardial scar at the follow-up. In future studies, this approach can facilitate deformation imaging-based estimation of myocardial tissue properties in patients with cardiovascular diseases.