Uncertainty and variability in computational and mathematical models of cardiac physiology.

Gary R Mirams,Richard H Clayton,Pras Pathmanathan,Richard A Gray,Peter Challenor

doi:10.1113/jp271671

Abstract

Key points Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome.We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge.The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools.We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome.We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient‐specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety‐critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for predictive model outputs. We propose that the future of the Cardiac Physiome should include a probabilistic approach to quantify the relationship of variability and uncertainty of model inputs and outputs.

Highlights

The Cardiac Physiome project is an international effort to integrate different types of data across a range of time and space scales into models that encode quantitatively our understanding of cardiac physiology (Bassingthwaighte et al 2009)
uncertainty quantification (UQ) can be used, for example, to determine a probability distribution for an output such as action potential duration (APD) predicted by a cardiac action potential model, based on uncertainty in selected model inputs
The focus is often on membrane voltage and intracellular Ca2+ concentration since these outputs directly influence electrical propagation and tension generation and may be measurable. Specific features such as APD have been used to characterise the action potential (Britton et al 2013; Chang et al 2015), and so these can be treated as model outputs that correspond to inputs such as model parameters and initial conditions

Summary

Introduction

The Cardiac Physiome project is an international effort to integrate different types of data across a range of time and space scales into models that encode quantitatively our understanding of cardiac physiology (Bassingthwaighte et al 2009). UQ can be used, for example, to determine a probability distribution for an output such as APD predicted by a cardiac action potential model, based on uncertainty in selected model inputs.

Results

Conclusion