Data Driven Modeling of Cardiac Dynamics and Model Evaluation

Data Driven Modeling of Cardiac Dynamics and Model Evaluation

The development of detailed physiological models of the heart, the availability of large quantities of high-quality structural and functional experimental data, and ever-increasing computational power have significantly enhanced the understanding of cardiac dynamics and hold the promise of new clinical applications for diagnosis and treatment of heart disease. However, the systematic integration of experimental data into high-dimensional, multi-scale models and their subsequent evaluation, validation and analysis remains a major challenge. Therefore, we are developing a data driven, integrative strategy that combines high-resolution imaging techniques with state of the art numerical modeling through innovative state estimation methods.

High-resolution Cardiac Imaging

Physiological cardiac modeling requires detailed structural, functional, and dynamical characterization of the heart. The MPRG Biomedical Physics develops high-resolution fluorescence imaging techniques (optical mapping) for intact, Langendorff-perfused hearts (see Fig. 1). Techniques from computer vision research are applied to reconstruct the three-dimensional shape of the heart from multiple silhouettes. We combine optical mapping with motion tracking, which permits, for the first time, fluorescence imaging of contractile, moving cardiac tissue. This unique experimental technique enables the simultaneous measurement of membrane voltage, intracellular calcium, and surface strain.

Mathematical Modeling of the Heart

We are using mathematical models of cardiac tissue with various levels of complexity, ranging from generic to detailed physiological descriptions. The choice of the model depends on the specific problem at hand. Generic models play an important role for the understanding of fundamental principles of excitable media. For example, we have used generic models to explore the nonlinear dynamics underlying the interaction of rotating waves with heterogeneities. However, generic models do not permit to elucidate the molecular basis of cardiac function.

State and Parameter Estimation

While physical models often can be derived from first principles, they may contain parameters whose values are not or only partially known and may depend on the physical context. To identify these parameters, the model may be adapted to experimental data. Here both (unknown) parameters and model variables have to be adjusted, including hidden (i.e. not observed) state variables determining the temporal evolution of the model. For some applications this adaption has to be continuously updated to “track” some process by continously incorporating measured data into the model (a procedure called data assimilation in geosciences and meteorology).