Viscoelastic Eshelby Analysis of Cardiomyocyte Contraction in the Cell-in-Gel System

We present a mathematical model to guide and interpret ongoing Cell-in-Gel experiments, where isolated cardiac myocytes are embedded in a constraining viscoelastic hydrogel, to study mechano-chemo-transduction mechanisms at the single cell level. A recently developed mathematical model, based on the elastic Eshelby inclusion problem, is here extended to account for viscoelasticity of the inclusion (cell) and the matrix (gel). This provides a tool to calculate time-dependent 3D stress and strain fields of a single myocyte contracting periodically inside a viscoelastic matrix, which is used to explore the sensitivity of the cell’s mechanical response to constitutive properties and geometry. A parametric study indicates that increased gel crosslink concentration significantly alters the strain and stress fields inside the cell and creates an increased time-lag in the mechanical response of the cell during contraction. It is also found that autoregulation at the cellular level in response to afterload, potentially in the form of increased cell stiffness, has a strong influence on cell contraction.