Análise de sensibilidade de alternâncias cardíacas em modelos celulares de eletrofisiologia

Abstract

Cardiac arrhythmias are a serious health problem that can lead to sudden cardiac arrest, heart failure, and ultimately death. Alternans is frequently observed in patients with cardiac arrhythmias, particularly those affecting the ventricles. It consists of a beat-to-beat variation in the duration or amplitude of the cardiac action potential, which may also be reflected in changes in the electrocardiogram. Understanding the mechanisms that lead to its occurrence is therefore clinically relevant. In this effort, mathematical models of cellular electrophysiology are fundamental tools, as they allow the controlled investigation of the conditions that favor the onset of alternans. The ability of a model to reproduce alternans depends on its formulation and its parameters, and studies that systematically identify which parameters govern the occurrence of this phenomenon are still scarce. Determining these parameters is essential both to understand the mechanisms of alternans and to assess the consistency of the models themselves. The main objective of this work was to identify the parameters that most influence the occurrence of alternans, employing sensitivity analysis techniques, with emphasis on Monte Carlo Filtering (MCF), in addition to Sobol indices. To accelerate these analyses, which would otherwise require a prohibitive number of full-model simulations, surrogate models (emulators) were used, with the classical Monte Carlo method serving as reference. In addition to Polynomial Chaos Expansion (PCE), two other surrogate modeling techniques were investigated: Gaussian Processes (GP) and Random Forests (RF), employed both in the regression of the quantities of interest and in the direct classification of alternans occurrence, with a systematic comparison between the two strategies in terms of accuracy and computational cost. The approach was applied to three cell models of increasing complexity: the simplified modified Mitchell-Schaeffer model, the detailed ten Tusscher-Panfilov model, and the Mahajan-Shiferaw model. The results identified the determining parameters for alternans in each model. For the biophysically detailed models, the conductance of the L-type calcium current stood out as the most influential parameter, demonstrating the ability of the approach to recover physiologically relevant relationships from the internal structure of the models, as well as to identify interactions between parameters that are not evident a priori.