A viscoelastic Eshelby inclusion model and analysis of the Cell-in-Gel system.

We develop a viscoelastic generalization of the elastic Eshelby inclusion solution, where the inclusion and surrounding matrix are two different viscoelastic solids and the inclusion's eigenstrain is a time-periodic oscillatory input. The solution exploits the Correspondence Principle of Linear Viscoelasticity and a Discrete Fourier Transform to efficiently capture the steady-state oscillatory behavior of the 3-D mechanical fields. The approach is illustrated here in the context of the recently-developed in vitro Cell-in-Gel system, where an isolated live cardiomyocyte (the inclusion) is paced to contract periodically within a soft hydrogel (the matrix), for the purpose of studying the effect of mechanical load on biochemical signals that regulate contractility. The addition of viscoelasticity improves the fidelity of our previous elastic Eshelby inclusion analysis of the Cell-in-Gel system by accounting for the time-varying fields and the resulting hysteresis and dissipated mechanical energy. This mathematical model is used to study the parametric sensitivities of the relative stiffness of the inclusion, the inclusion's aspect ratio (slenderness), and the cross-link density of the hydrogel matrix.

Modeling cardiomyocyte mechanics and autoregulation of contractility by mechano-chemo-transduction feedback.

The heart pumps blood into circulation against vascular resistance and actively regulates the contractile force to compensate for mechanical load changes. Our experimental data show that cardiomyocytes have a mechano-chemo-transduction (MCT) mechanism that increases intracellular Ca 2 + transient to enhance contractility in response to increased mechanical load. This study advances the cardiac excitation- Ca 2 + signaling-contraction (E-C) coupling model on conceptual and technical fronts. First, we developed analytical and computational models to perform 3-dimensional mechanical analysis of cardiomyocytes contracting in a viscoelastic medium under mechanical load. Next, we proposed an MCT feedback loop in the E-C coupling dynamic system to shift the feedforward paradigm of cardiac E-C coupling to an autoregulation model. Our combined modeling and experimental studies reveal that MCT enables autoregulation of E-C coupling and contractility in single cardiomyocytes, which underlies the heart's intrinsic autoregulation in compensatory response to load changes in order to maintain the stroke volume and cardiac output.

Erratum: Modeling cardiomyocyte mechanics and autoregulation of contractility by mechano-chemo-transduction feedback.

[This corrects the article DOI: 10.1016/j.isci.2022.104667.].