On the AIC based model reduction for the general Holzapfel-Ogden myocardial constitutive law

Guan, D., Ahmad, F., Theobald, P., Soe, S., Luo, X. and Gao, H. (2019) On the AIC based model reduction for the general Holzapfel-Ogden myocardial constitutive law. Biomechanics and Modeling in Mechanobiology, 18, pp. 1213-1232. (doi:10.1007/s10237-019-01140-6) (PMID:30945052) (PMCID:PMC6647490)

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Abstract

Constitutive laws that describe the mechanical responses of cardiac tissue under loading hold the key to accurately model the biomechanical behaviour of the heart. There have been ample choices of phenomenological constitutive laws derived from experiments, some of which are quite sophisticated and include effects of microscopic fibre structures of the myocardium. A typical example is the strain-invariant-based Holzapfel–Ogden 2009 model that is excellently fitted to simple shear tests. It has been widely used and regarded as the state-of-the-art constitutive law for myocardium. However, there has been no analysis to show if it has both adequate descriptive and predictive capabilities for other tissue tests of myocardium. Indeed, such an analysis is important for any constitutive laws for clinically useful computational simulations. In this work, we perform such an analysis using combinations of tissue tests, uniaxial tension, biaxial tension and simple shear from three different sets of myocardial tissue studies. Starting from the general 14-parameter myocardial constitutive law developed by Holzapfel and Ogden, denoted as the general HO model, we show that this model has good descriptive and predictive capabilities for all the experimental tests. However, to reliably determine all 14 parameters of the model from experiments remains a great challenge. Our aim is to reduce the constitutive law using Akaike information criterion, to maintain its mechanical integrity whilst achieving minimal computational cost. A competent constitutive law should have descriptive and predictive capabilities for different tissue tests. By competent, we mean the model has least terms but is still able to describe and predict experimental data. We also investigate the optimal combinations of tissue tests for a given constitutive model. For example, our results show that using one of the reduced HO models, one may need just one shear response (along normal-fibre direction) and one biaxial stretch (ratio of 1 mean fibre : 1 cross-fibre) to satisfactorily describe Sommer et al. human myocardial mechanical properties. Our study suggests that single-state tests (i.e. simple shear or stretching only) are insufficient to determine the myocardium responses. We also found it is important to consider transmural fibre rotations within each myocardial sample of tests during the fitting process. This is done by excluding un-stretched fibres using an “effective fibre ratio”, which depends on the sample size, shape, local myofibre architecture and loading conditions. We conclude that a competent myocardium material model can be obtained from the general HO model using AIC analysis and a suitable combination of tissue tests.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Luo, Professor Xiaoyu and Guan, Mr Debao and Gao, Dr Hao
Authors: Guan, D., Ahmad, F., Theobald, P., Soe, S., Luo, X., and Gao, H.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Biomechanics and Modeling in Mechanobiology
Publisher:Springer
ISSN:1617-7959
ISSN (Online):1617-7940
Published Online:03 April 2019
Copyright Holders:Copyright © The Authors 2019
First Published:First published in Biomechanics and Modeling in Mechanobiology 18:1213-1232
Publisher Policy:Reproduced under a Creative Commons license

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
694461EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - MATHEMATICS