Metamodelling of a computational model of cardiac physiology using multivariate regression and deep learning

Abstract

The primary goal of this thesis is to model the heart function. This thesis investigates how data-driven modelling might help with this. Mechanistic models, which are theory-driven and guided by a system of differential equations that describe a well known mechanical, biological and chemical phenomenon or processes, are used to model a majority of complex biological processes. These models exhibit a complex high-dimensional system and a high computational cost. However, metamodels are data-driven, and are calibrated using the input-output data obtained by running a large number of simulations using the mechanistic model. Metamodels are known to reduce computational demand, aid in sensitivity analysis, model comparison, and assist in model parameterization with reference to measured data. This thesis explores two metamodelling approaches, HC-PLSR, and Deep Learning to emulate the Pandit-Hinch-Niederer model that couples cellular functions for rat cardiac excitation-contraction. The input parameters for simulating the mechanistic model were varied using Latin hypercube sampling and the generated action potentials were recorded for 250ms. Additionally, both the classical and inverse metamodelling techniques were used to map input-output relationships. The results reveal that metamodelling using deep learning is a powerful emulator, while the HC-PLSR metamodelling enables a more comprehensive inference of the model behavior. The results also highlight the importance of subspace analysis in explaining the broad spectrum of behavior that complex models display.