Heart-on-a-chip devices can be used to control and monitor the cellular microenvironment of human cardiac microtissue, showing great potential as powerful cardiotoxicity screening platforms. Human induced pluripotent stem cell derived cardiomyocytes are combined with microfluidic technology to derive a tissue mimicking adult human ventricular dimensions, physiology and uniaxial beating properties, which can be used for pharmalogical studies and disease modeling [3]. Within such microphysiological systems, indicators of cardiac function, such as electrophysiology (action potential, calcium transient) and beating physiology (beat rate, contraction velocity) can be readily measured using image analysis techniques [2]. However, important mechanical properties such as myocyte contractility, tissue stress and tissue stiffness, cannot easily be revealed using current techniques. We thus
propose a numerical model simulating the dynamic mechanics of the microtissue.

For our model we combined previously published models for cardiac electrochemical and mechanical properties, embedded with a geometrical representation of the tissue chamber, to quantify the passive and active properties of the system. We used a zero-dimensional point model of cardiac myofilaments developed by Rice et. al. [4] to calculate the force generated by single myocytes. This was coupled with a three-dimensional continuum model for myocardial mechanics given by Guccione et. al [1]. Together this gave a set of non-linear partial differential equations describing the stress and deformation, which we set up to find an equilibrium solution and calculate the resulting Cauchy stress. We imposed appropriate boundary conditions and solve the system using FEniCS – both the framework for spatially dependent nonlinear boundary value problems, and for time-dependent initial value problems – and evaluated the system using data provided from experimental pharmacology studies.

Our results provide a quantification of the Cauchy stress developed through active myocardial contraction through the domain, and relative changes under differing simulated conditions. We compared these results with experimental measurements of contraction forces, using the same points for measurements. In this dual analysis we observed a comparable relative increase in Cauchy stress and microscopic measurements of contraction force, respectively, correlated with increasing drug doses. This combined in silico / in vitro system give us a platform for the quantification of internal mechanical properties, providing a framework for understanding the physiology complexity of microorgan tissues. Such a system can give new insight in cardiac mechanics in itself, and might also be important for further development of appropriate mathematical models.