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

Figures

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  FIGURE 1. Schematic representation of the two-compartment modeling approach used for simulation of ischemic myocardial dysfunction. A myocardial patch with volume Vpatch was subdivided into a hypothetical contractile and noncontractile patch (i.e., compartment) with volumes VC and VNC , respectively, being serially coupled (A). Myocardial volume VC generated active stress, while VNC was passive (C). Myocardial stiffness was determined by passive constitutive behavior of VNC , determined by the zero-passive stress sarcomere length ( Ls0,pas ) and nonlinearity parameter ( kECM ) (B). The resulting strain pattern of Vpatch (D) and its stress–strain loop (C) were calculated from the volume-weighted average sarcomere length and stress of VC and VNC . AVO, aortic valve opening; AVC, aortic valve closure.

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  FIGURE 2. Patient-specific parameter estimation protocol. The input of the optimization algorithm (INPUT) consisted of 1) 18-segment longitudinal strain, 2) 18-segment longitudinal strain rate (calculated as the first-order time derivative of strain), 3) LV end-diastolic volume (EDV), and 4) LV ejection fraction (EF). Strain and strain rate signals were analyzed until early diastole, as indicated by the gray-enhanced parts of the strain and strain rate signals. For numerical optimization (OPTIMIZATION), a multi-swarm particle swarm optimization (MSPSO) algorithm similar to the one previously described in the study by Van Osta et al. (2021) was run, which estimated (OUTPUT): global LV wall area, global stroke volume, global ventricular contraction duration, regional contractile dysfunction, and regional compliance.

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  FIGURE 3. Simulated left ventricular (LV) end-systolic pressure-volume relations (ESPVRs) for a baseline healthy LV (black loops and line) and for an ischemic LV affecting 20% of the LV wall mass modeled by a two-compartment approach (blue loops and line) and a one-compartment approach (red loops and line). ESPVRs were constructed by afterload manipulations through reducing and increasing arterial resistance by 20% compared to the reference resistance. The two-compartment simulation of ischemia demonstrated a rightward shift of the ESPVR with a moderate reduction in the slope, while the one-compartment simulation demonstrated a severe reduction in both the slope and zero-pressure volume.

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  FIGURE 4. Comparison between measured LV pressure-segment length loops in a representative dog after 15 min of left anterior descending (LAD) coronary artery occlusion, followed by 15 min and 3 h of reperfusion [(A), resketched from Lyseggen et al. (2005)] and simulated LV pressure-segment length loops (B) for varying regional contractile dysfunction ( NCVF ). ed, end-diastole; es, end-systole.

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  FIGURE 5. Comparison between the temporal behavior of the measured segment length, strain, and LV pressure in the same representative dog as in Figure 4 after 15 min of left anterior descending (LAD) coronary artery occlusion followed by 15 min and 3 h of reperfusion (dark red tracings, resketched from Lyseggen et al. (2005)) and the simulated segment length, strain, and LV pressure (blue and green tracings) for the best matching severities of regional contractile dysfunction ( NCVF ). ed, end-diastole; es, end-systole.

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  FIGURE 6. Comparison between measured LV pressure-segment length loops in a representative dog after 15 min and 4 h of left anterior descending (LAD) coronary artery occlusion, followed by 15 min of reperfusion [(A), resketched from Lyseggen et al. (2005)] and simulated LV pressure-segment length loops (B) for no contractile dysfunction ( NCVF = 0, blue loop) and complete contractile dysfunction ( NCVF = 1, all three green loops), where nonlinearity parameter ( kECM ) and zero-stress sarcomere length ( Ls0,pas ) were calibrated for the green loops to mimic the experimental measurements (values can be found in Table 3). ed, end-diastole; es, end-systole.

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  FIGURE 7. Comparison between the temporal behavior of the measured segment length, strain, and LV pressure in the same representative dog as in Figure 6 after 15 min and 4 h of left anterior descending (LAD) coronary artery occlusion, followed by 15 min of reperfusion (dark red tracings, resketched from Lyseggen et al. (2005)) and the simulated segment length, strain, and LV pressure (blue and green tracings) for no contractile dysfunction ( NCVF = 0) and for three simulations of complete contractile dysfunction ( NCVF = 1), with calibrated values of the nonlinearity parameter ( kECM ) and zero-stress sarcomere length ( Ls0,pas ). ed, end-diastole; es, end-systole.

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  FIGURE 8. Echocardiographic strain measurements (black panels) and simulated strain patterns obtained using an optimization algorithm (white panels) at the baseline and 6-month follow-up in one patient from the DEFI-MI subcohort (patient 1, a 47-year-old male). Estimated NCVF values at the baseline were higher in the anterior (A), anteroseptal (AS), and inferoseptal (IS) wall segments than in the rest of the heart. After 6 months, the scar tissue was found in the same area using late gadolinium enhancement (LGE). Although contractile dysfunction remained at 6-month follow-up, NCVF values in the A, AS, and IS segments were lower. I, inferior; P, posterior; L, lateral; b, base; m, mid-ventricle; a, apex.

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  FIGURE 9. Echocardiographic strain measurements (black panels) and simulated strain patterns obtained using an optimization algorithm (white panels) at the baseline and 6-month follow-up in one patient from the DEFI-MI subcohort (patient 2, a 51-year-old female). Estimated NCVF values at the baseline were higher in the anterior (A), anteroseptal (AS), and inferoseptal (IS) wall segments and in the apical (a) inferior (I), posterior (P), and lateral (L) wall segments than in the rest of the heart. After 6 months, the scar tissue was found using late gadolinium enhancement (LGE) in a part of this dysfunctional area, extending from the apex into the mid-ventricular (m) anteroseptal segment. Increased values of the NCVF were remained in these scarred segments. b, base.

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  FIGURE 10. Estimated NCVF values at the baseline and 6-month follow-up in all 22 segments with LGE>25% at 6-month follow-up. Different symbol–color combinations indicate different patients, as shown in the legend. The majority of segments (68%) demonstrated a reduction of the NCVF at 6-month follow-up with respect to the baseline. Results for patient 1 and patient 2 are also shown in Figures 8, 9, respectively. Results for patients 3–6 are shown in Supplementary Section 11.3.