Estimation of Active Tension in Cardiac Microtissues by Solving a PDE-Constrained Optimization Problem

Microphysiological systems (MPS) provide a highly controlled environment for the development and testing of human-induced pluripotent stem cell-based cardiac microtissues, with promising applications in disease modeling and drug development. Through optical measurements in such systems, we can quantify mechanical features such as motion and velocity during contraction. While these are useful for evaluating relative changes in muscle twitch, it remains challenging to quantify and characterize the actual active tension driving the contraction. Here, we aimed to quantify the active tension over time and space by solving an inverse problem in cardiac mechanics expressed by partial differential equations (PDEs). We formulated this as a PDE-constrained optimization problem based on a mechanical model defined for two-dimensional representations of the microtissues. Our optimization predicts active tension generated by the tissue as well as the fiber direction angle distribution. We used synthetic as well as experimental data to investigate the performance of our inversion protocol. Next, we employed the procedure to evaluate active tension changes in drug escalation studies of the inotropes omecamtiv mecarbil and Bay K8644. For both drug compounds, we observed a comparable increase in displacement, strain, and model-predicted active strain values upon higher drug doses. The estimated active tension was observed to be highest in the middle part of the tissue, and the fiber direction was mostly aligned with the longitudinal direction of the tissue. The computational framework presented here allows for spatiotemporal estimation of active tension in cardiac microtissues based on optical measurements. In the future, such methodologies might develop into valuable tools in drug development protocols.