Modeling calcium-dependent passive cardiac mechanics in the mouse

While previous studies have characterized the impact of nonlinearity, anisotropy, and viscoelasticity on myocardial mechanics, calcium itself has been thought to primarily affect the active, not passive, mechanics. Recent experimental studies, however, have demonstrated that calcium has a tremendous effect on the passive viscoelasticity of myocardial tissues. This has significant implications for the mechanics of the beating heart, as calcium cycling would imply dynamic changes in the passive function of the heart and could contribute to elevated stiffening in conditions such as diastolic heart failure. In this study, we aim to extend recently developed fractional viscoelastic constitutive models to incorporate this calcium-sensitive response. We show that the effect of calcium on the passive mechanical response requires additional Maxwell arms in the viscoelastic form. The effect of calcium appears to induce a pure viscoelastic response with a first-order exponential decay, characterized by a fast time constant of ∼2.17s. We find that this form captured the passive mechanical response at all calcium levels. This calcium dependence appears as a pure scaling factor in the form of a Hill curve and can elevate passive mechanics by 6-fold in mouse trabeculae. This model will enable more accurate computational models of the heart that incorporate the effects of calcium on passive mechanics. Statement of Significance: Previous studies on the passive mechanics of myocardium have often ignored the effects of calcium, assuming it primarily affects the active response. However, recent experiments have demonstrated a tremendous effect on passive viscoelasticity. This has significant implications, as calcium cycling would imply a dynamic change in passive function and could contribute to elevated stiffness in conditions such as diastolic heart failure. In this study, we show that the effect of calcium can be modeled with an additional Maxwell arm in a fractional viscoelastic model. Calcium induces a pure viscoelastic response with a first-order exponential decay (2̃.17s). The dependence on concentration appears as a scaling factor in the form of a Hill curve and can elevate passive mechanics by sixfold.