A robust multi-objective optimization framework to capture both cellular and intercellular properties in cardiac cellular model tuning: Analyzing different regions of membrane resistance profile in parameter fitting

Abstract

Mathematical models of cardiac cells have been established to broaden understanding of cardiac function. In the process of developing electrophysiological models for cardiac myocytes, precise parameter tuning is a crucial step. The membrane resistance (Rm) is an essential feature obtained from cardiac myocytes. This feature reflects intercellular coupling and affects important phenomena, such as conduction velocity, and early after-depolarizations, but it is often overlooked during the phase of parameter fitting. Thus, the traditional parameter fitting that only includes action potential (AP) waveform may yield incorrect values for Rm. In this paper, a novel multi-objective parameter fitting formulation is proposed and tested that includes different regions of the Rm profile as additional objective functions for optimization. As Rm depends on the transmembrane voltage (Vm) and exhibits singularities for some specific values of Vm, analyses are conducted to carefully select the regions of interest for the proper characterization of Rm. Non-dominated sorting genetic algorithm II is utilized to solve the proposed multi-objective optimization problem. To verify the efficacy of the proposed problem formulation, case studies and comparisons are carried out using multiple models of human cardiac ventricular cells. Results demonstrate Rm is correctly reproduced by the tuned cell models after considering the curve of Rm obtained from the late phase of repolarization and Rm value calculated in the rest phase as additional objectives. However, relative deterioration of the AP fit is observed, demonstrating trade-off among the objectives. This framework can be useful for a wide range of applications, including the parameters fitting phase of the cardiac cell model development and investigation of normal and pathological scenarios in which reproducing both cellular and intercellular properties are of great importance.

Considering discrepancy when calibrating a mechanistic electrophysiology model

“…Gaussian noise ∼ N (0, σ 2 ) to the resulting voltage traces (model outputs), with σ chosen to be 1 mV. We use the calibration data (1 Hz pacing) to estimate eight maximal conductance/current density parameters for I Na , I CaL , I Kr , I Ks , I to , I NaCa , I K1 and I NaK using Model F. We will investigate whether the calibrated Model F makes accurate predictions in the validation and CoU situations (using the parameter estimates from the calibration data, as is commonly done in electrophysiology modelling [30][31][32][33][34]). The code to reproduce all of the results in this paper are available at https://github.com/ CardiacModelling/fickleheart-method-tutorials.…”

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

“…The procedure to calculate the in different phases of the and justification for the selection of specific regions of profile are described in detail in [6]. Briefly, to obtain the in a specific voltage ( ) value, is clamped to 10 higher and lower of the original value in the separate simulations, and the corresponding currents are recorded after 5…”

“…These objectives are utilized with different combinations in various scenarios (Section III-A). Information about selected parameters and their boundaries can be found in [6].…”

“…The tuned models successfully reproduce cellular electrophysiological behavior; however, many of them fail in reproducing the properties that determine inter-cellular electrical interactions accurately. To address this problem, in our previous study [6], which was built on the work done by Kaur et al [7], we proposed a robust optimization approach for cellular models that specifically accounts for inter-cellular behavior. In the E. Pouranbarani and A. Nygren are with the Department of Electrical and Computer Engineering, University of Calgary, Alberta, Canada T2N 1N4 (email: elnaz.pouranbarani@ucalgary.ca; nygren@ucalgary.ca).…”

“…Membrane resistance ( ) is a cellular characteristic that reflects the inter-cellular interaction (electrotonic effects) [17]. Although was taken into consideration in cellular model tuning in our previous work [6], to the best of our knowledge, the performance of the proposed framework at the tissue level has not been properly examined so far. Following from our previous work, in this paper, the parameters of the cellular model are first tuned.…”