Improved Accuracy of Cardiac Tissue-Level Simulations by Considering Membrane Resistance as a Cellular-Level Optimization Objective.

Cardiac cellular models are utilized as the building blocks for tissue simulation. One of the imprecisions of conventional cellular modeling, especially when the models are used in tissue-level modeling, stems from the mere consideration of cellular properties (e.g., action potential shape) in parameter tuning of the model. In our previous work, we put forward an accurate framework in which membrane resistance (Rm) reflecting inter-cellular characteristics, i.e., electrotonic effects, was considered alongside cellular features in cellular model fitting. This paper, for the first time, examines the hypothesis that considering Rm as an additional optimization objective improves the accuracy of tissue-level modeling. To study this hypothesis, after cellular-level optimization of a well-known model, source-sink mismatch configurations in a 2-dimensional model are investigated. The results demonstrate that including Rm in the optimization protocol yields a substantial improvement in the relative error of the critical transition border which is defined as the minimum window size between source and sink that wave propagates. Model developers can utilize the proposed concept during parameter tuning to increase the accuracy of models.

A Novel Bi-Level Framework for Fitting the Parameters in Cardiac Cellular Models.

Cardiac models constructed from sets of differential equations provide invaluable information about heart mechanism and disorder of both human and animals. As tuning the parameters is a profoundly important step of modeling, this paper presents a novel parametrization technique based on a bilevel framework that benefits from two solution approaches, namely mixed integer genetic algorithm (MIGA) and linear least squares (LLS). In the upper-level optimization step, the action potential (AP) of the model is fitted to the reference AP using MIGA. In the lower-level optimization step, the mismatch between the total current of the model and reference is minimized via a clamp concept-based linearization and LLS solution approach. Notably, the clamp concept can diminish the nonlinearity of the parameter fitting problem. The issue of dependency on initial parameters in the lower-level problem, as well as the sensitivity of model parameters to linearization, are circumvented by MIGA in the upper-level optimization. For evaluation of MIGA-LLS performance, two complex human ventricular models are employed. The results demonstrate that in comparison to the genetic algorithm (GA)-based approach, the proposed framework significantly reduces the average and variation of normalized root-mean-squared error (NRMSE) in terms of the AP and total current in different trials. Variability in the resulting parameter values is considerably decreased as well.