Evaluation of a Novel Finite Element Model of Active Contraction in the Heart

Figures

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  Figure 1. Representative animal-specific FE model of a rat LV. (A) Full view of the LV model with the four segments labeled, (B) Short axis view of a mid-ventricular slice, and (C) Long axis view of a longitudinal slice. Stars represent the points in the model where strain was compared to experimental measurements during the optimization.

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  Figure 2. Representative examples from a single rat of (A) the volumetric flowrate into and out of the LV used to drive the cardiac cycle in the FE model, (B) the LV volume (LVV) generated by the FE model, and (C) the calcium transient in the LV model. (D) The LV pressure-volume relationship generated by all of the FE models and experiments. LV pressure (LVP) data are mean ± standard error (SE); n = 5. LVV data shown in (D) were normalized to end diastolic volume (EDV).

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  Figure 3. Schematic of the 2-state contraction model based on MyoSim. x1 to xn are different lengths of cross-bridges (n = 21 in the proposed FE model); xps is the cross-bridge length when the myosin head is bound to a directly opposed binding site; k1 (xi) and k−1 (xi) are the strain-dependent rate constants for the attachment and detachment transitions, respectively.

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  Figure 4. End systolic axial strain components (A: Ecc, B: Err, and C: Ell) averaged at the mid-LV in the mid-myocardial layer. Data are mean ± SE; n = 5; *p < 0.05 for comparisons between model-predicted and experiment-derived strains using paired two-tailed t-test.

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  Figure 5. End systolic shear strain components (A: Ecr, B: Ecl, and C: Erl) averaged at the mid-LV in the mid-myocardial layer. Data are mean ± SE; n = 5; *p < 0.05 for comparisons between model-predicted and experiment-derived strains using paired two-tailed t-test.

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  Figure 6. End systolic circumferential-longitudinal (CL) shear angles averaged at the mid-LV in the mid-myocardial layer. Data are mean ± SE; n = 5. No significant differences between model-predicted and experiment-derived results using paired two-tailed t-test.

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  Figure 7. Profiles of sarcomere length (SL) over 2 cardiac cycles obtained from 3 representative elements located at the base, mid-LV, and apex in the lateral epicardium. Data are mean (thick solid lines) ± SE (shaded area); n = 5. Note that the simulations start from the unloaded state. Arrows indicate the beginning of re-lengthening.

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  Figure 8. Profiles of sarcomere length (SL) over 2 cardiac cycles obtained from 3 representative elements located in the lateral epicardium (epi), mid-myocardium (mid), and endocardium (endo) at the mid-LV. Data are mean (thick solid lines) ± SE (shaded area); n = 5. Note that the simulations start from the unloaded state. Arrows indicate the beginning of re-lengthening.

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  Figure 9. Force-pCa curve for Case 1. The square markers represent the values from the single element simulations, while the curve fit is the Hill equation with a value of pCa50 = 6.53 and a Hill coefficient = 2.51.