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Article: An efficient numerical method for uncertainty quantification in cardiology models

TitleAn efficient numerical method for uncertainty quantification in cardiology models
Authors
Keywordscomputational cardiology
uncertainty quantification
generalized polynomial chaos
Hodgkin-Huxley model
Fitz-Hugh Nagumo model
Issue Date2019
PublisherBegell House, Inc.. The Journal's web site is located at http://uncertainty-quantification.com/
Citation
International Journal for Uncertainty Quantification, 2019, v. 9 n. 3, p. 275-294 How to Cite?
AbstractMathematical 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 because 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 deviation of the stochastic solution can be controlled by the parameter uncertainty. More precisely, the standard deviation of the stochastic solution is positively linear to the standard deviation of the random parameter. We utilized monodomain equations, which are representative mathematical models to demonstrate the results with the most widely used ionic models, the Hodgkin-Huxley model and Fitz-Hugh Nagumo model.
Persistent Identifierhttp://hdl.handle.net/10722/272213
ISSN
2019 Impact Factor: 4.911
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorZhang, Z-
dc.contributor.authorGao, X-
dc.contributor.authorYing, W-
dc.date.accessioned2019-07-20T10:37:53Z-
dc.date.available2019-07-20T10:37:53Z-
dc.date.issued2019-
dc.identifier.citationInternational Journal for Uncertainty Quantification, 2019, v. 9 n. 3, p. 275-294-
dc.identifier.issn2152-5080-
dc.identifier.urihttp://hdl.handle.net/10722/272213-
dc.description.abstractMathematical 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 because 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 deviation of the stochastic solution can be controlled by the parameter uncertainty. More precisely, the standard deviation of the stochastic solution is positively linear to the standard deviation of the random parameter. We utilized monodomain equations, which are representative mathematical models to demonstrate the results with the most widely used ionic models, the Hodgkin-Huxley model and Fitz-Hugh Nagumo model.-
dc.languageeng-
dc.publisherBegell House, Inc.. The Journal's web site is located at http://uncertainty-quantification.com/-
dc.relation.ispartofInternational Journal for Uncertainty Quantification-
dc.subjectcomputational cardiology-
dc.subjectuncertainty quantification-
dc.subjectgeneralized polynomial chaos-
dc.subjectHodgkin-Huxley model-
dc.subjectFitz-Hugh Nagumo model-
dc.titleAn efficient numerical method for uncertainty quantification in cardiology models-
dc.typeArticle-
dc.identifier.emailZhang, Z: zhangzw@hku.hk-
dc.identifier.authorityZhang, Z=rp02087-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1615/Int.J.UncertaintyQuantification.2019027857-
dc.identifier.scopuseid_2-s2.0-85068919882-
dc.identifier.hkuros298664-
dc.identifier.volume9-
dc.identifier.issue3-
dc.identifier.spage275-
dc.identifier.epage294-
dc.identifier.isiWOS:000478800200005-
dc.publisher.placeUnited States-
dc.identifier.issnl2152-5080-

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