A Lumped Two-Compartment Model for Simulation of Ventricular Pump and Tissue Mechanics in Ischemic Heart Disease
Tijmen Koopsen, Nick van Osta, Tim van Loon, Frans A. van Nieuwenhoven, Frits W. Prinzen, Bas R van Klarenbosch, Feddo P. Kirkels, Arco J. Teske, Kevin Vernooy, Tammo Delhaas, Joost Lumens
Abstract
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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> ). Myocardial stiffness was determined by the zero-passive stress length ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math> and nonlinearity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>E</mml:mi><mml:mi>C</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> ) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> was automatically estimated using the echocardiographic LV strain and volume measurements obtained acutely and 6 months after MI. Estimated segmental <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m6"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m7"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m8"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m9"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>E</mml:mi><mml:mi>C</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> , it was found that manipulation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m10"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> alone reproduced the deformation during acute ischemia and reperfusion, while additional manipulations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m11"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m12"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>E</mml:mi><mml:mi>C</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> were required to reproduce deformation during prolonged ischemia and reperfusion. Out of all segments with LGE&gt;25% at the follow-up, the majority (68%) had higher estimated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m13"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> at the baseline than at the follow-up. Furthermore, the baseline <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m14"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> correlated better with percentage LGE than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m15"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m16"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> in a small cohort of MI patients in the acute and chronic phase after MI, while estimated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m17"><mml:mrow><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:math> 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.