Parameterizing Cardiac Models for Medical Cyber-physical Systems

This project is a component of a larger effort is to develop the foundations of modeling, synthesis and development of verified medical device software and systems from verified closed-loop models of the device and organ(s). This research spans both implantable medical devices such as cardiac pacemakers and physiological control systems such as drug infusion pumps which have multiple networked medical systems. Here we focus on advancing two aspects of this work: (1) development of patient-specific models and therapies and (2) multi-scale modeling of complex physiological phenomena.

Mathematical models, generally posed as a system of differential equations, are an important tool for studying phenomena in cardiac electrophysiology ranging from cellular and subcellular mechanisms to tissue-level properties of arrhythmias and defibrillation. However, finding parameters for these models that fit experimental data is challenging because of the large number of parameters, biological variability, and the highly nonlinear nature of the problem. Because it may be necessary to perform multiple parameterizations for a single experiment, computational efficiency is also important. Here, we examine parameter fitting by two methods, a genetic algorithm and data assimilation, and consider finding parameterizations to fit the models to surrogate data generated from models, including model recovery cases, as well as to experimental data from microelectrode recordings. We use flexible phenomenological reaction-diffusion models that can reproduce a broad range of cardiac dynamics. We find that the genetic algorithm works well in many cases, including for experimental data, even when fitting large numbers of parameters, provided that the bounds on parameters are not excessively large. Estimating parameters as part of data assimilation can be convenient when state estimation is also required, but the algorithm can fit only some parameters robustly; in many cases, the assimilation of data can account for the small differences evident in wave properties over the assimilation interval, thereby making it unnecessary to adjust the parameter value. Overall, both approaches show promise for finding model parameterizations, but the genetic algorithm appears better positioned for determining model parameterizations, whereas data assimilation shows promise for estimating certain parameters as part of state estimation. Our results will be useful in developing individualized models as well as model populations calibrated to achieve population-level diversity, both of which can lead to more accurate and robust results in simulating interactions between organs and devices.