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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019027857
Forthcoming Article

An efficient numerical method for uncertainty quantification in cardiology models

Xindan Gao
School of Mathematical sciences, Shanghai Jiao Tong University
Wenjun Ying
School of Mathematical sciences, Shanghai Jiao Tong University
Zhiwen Zhang
The University of Hong Kong

ABSTRACT

Mathematical models of cardiology involve conductivity and massive parameters describing the dynamics of ionic channels. The conductivity is space dependent and cannot be measured directly. The dynamics of ionic channels are highly nonlinear and the parameters have unavoidable uncertainties since they are estimated using repeated experimental data. Such uncertainties can impact model dependability and credibility since they spread to model parameters during model calibration. It is necessary to study how the uncertainties influence the solution compared to the deterministic solution and to quantify the difference resulting from uncertainty. In this paper, the generalized polynomial chaos method and stochastic collocation method are used to solve the corresponding stochastic partial differential equations. Numerical results are shown to demonstrate that each parameter has different effects on the model responses. More importantly, a quadratic convergence of the expectation is exhibited in the numerical results. The amplitude of standard variance of the stochastic solution can be controlled by the parameter uncertainty. More precisely, the standard variance of the stochastic solution is positively linear to the standard variance of the random parameter. We utilized mono-domain equations which are representative mathematical models to demonstrate the results with the most widely used ionic models Hodgkin-Huxley model and Fitz-Hugh Nagumo model.