Influence of cellular mechano-calcium feedback in numerical models of cardiac electromechanics

TL;DR

This paper addresses how mechano-calcium feedback ($MCF$) influences cardiac electromechanics and whether efficient, reduced-cost frameworks can capture its organ-level effects. It develops a fully coupled cellular EM model that includes $MCF$ and compares it against non-$MCF$ baselines, then couples this at the tissue scale in both monodomain and eikonal-driven multiscale formulations. Calibrations ensure consistent baseline Ca transients and force kinetics; results show that $MCF$ has modest impact under baseline conditions but becomes more pronounced with altered force generation, while the eikonal-driven framework replicates $MCF$ effects with orders-of-magnitude faster simulations. The work demonstrates that an $E$ikonal-based approach incorporating $MCF$ provides a viable, computationally efficient tool for computational cardiology, enabling organ-scale analyses without sacrificing key biophysical fidelity.

Abstract

Multiphysics and multiscale mathematical models enable the non-invasive study of cardiac function. These models often rely on simplifying assumptions that neglect certain biophysical processes to balance fidelity and computational cost. In this work, we propose an eikonal-based framework that incorporates mechano-calcium feedback -- the effect of mechanical deformation on calcium-troponin buffering -- while introducing only negligible computational overhead. To assess the impact of mechano-calcium feedback at the organ level, we develop a bidirectionally coupled cellular electromechanical model and integrate it into two cardiac multiscale frameworks: a monodomain-driven model that accounts for geometric feedback on electrophysiology and the proposed eikonal-based approach, which instead neglects geometric feedback. By ensuring consistent cellular model calibration across all scenarios, we isolate the role of mechano-calcium feedback and systematically compare its effects against models without it. Our results indicate that, under baseline conditions, mechano-calcium feedback has minimal influence on overall cardiac function. However, its effects become more pronounced in altered force generation scenarios, such as inotropic modulation. Furthermore, we demonstrate that the eikonal-based framework, despite omitting other types of mechano-electric feedback, effectively captures the role of mechano-calcium feedback at significantly lower computational costs than the monodomain-driven model, reinforcing its utility in computational cardiology.

Figures (14)

• Figure 1: Representation of the time advancement and coupling scheme of the fully coupled multiscale problem, as in fedele_comprehensive_2023. Dashed arrows indicate the time advancement of a single model, while full arrows indicate coupling between models. The thick arrow represents the new coupling \ref{['eq:catn_dt_active_force']}.
• Figure 2: Value of the discrepancy metric $\varphi_\mathrm{ion}$ depending on the choice of the parameter $\theta_\mathrm{ion}$. (a): Discrepancy metric $\varphi_\mathrm{ion}$ depending of the maximal calcium-troponin buffer concentration $\mathrm{Tn}_\mathrm{c,max}$. (b): Discrepancy metric $\varphi_\mathrm{ion}$ depending of the total cytosolic buffer concentration $\mathrm{Buf}_\mathrm{c}$.
• Figure 3: Discrepancy metric $\varphi_\mathrm{af,kin}$ depending of the kinetic parameters $k_\mathrm{off},k_\mathrm{basic}$ in $\boldsymbol{R}_{2,\mathrm{kin}}$. The red dot represents the parameters at which the minimum is attained.
• Figure 4: Free intracellular calcium $[\mathrm{Ca}^{2+}]_\mathrm{i}$ for each step of the calibration process.
• Figure 5: Buffer-bound calcium concentration amplitudes for each step of the calibration process. (a): Troponin-bound calcium concentration $[\mathrm{Ca}^{2+}]_\mathrm{Tn}$ amplitude. (b): Total buffer-bound (troponin and other) calcium concentration $[\mathrm{Ca}^{2+}]_{\overline{\mathrm{Buf}}}$ amplitude.