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

Guan, Debao; Ahmad, Faizan; Theobald, Peter; Soe, Shwe; Luo, Xiaoyu; Gao, Hao

Abstract

© 2019, The Author(s). 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 testsfor a given constitutive model. For example, our results show thatusing one of the reduced HO models, one mayneed just one shear response (along normal-fibredirection) and one biaxial stretch (ratio of 1 mean fibre : 1 cross-fibre) to satisfactorily describe Sommer et al. human myocardial mechanical properties. Our studysuggests that single-state tests (i.e. simple shear or stretching only) are insufficient to determine the myocardium responses. We also foundit is important to consider transmural fibre rotations within eachmyocardial sampleof tests during the fitting process.This is done byexcluding un-stretched fibres usingan “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.

Citation

Guan, D., Ahmad, F., Theobald, P., Soe, S., Luo, X., & Gao, H. (2019). On the AIC-based model reduction for the general Holzapfel–Ogden myocardial constitutive law. Biomechanics and Modeling in Mechanobiology, 18(4), 1213-1232. https://doi.org/10.1007/s10237-019-01140-6

• Journal Article Type: Article
• Acceptance Date: Mar 19, 2019
• Online Publication Date: Apr 3, 2019
• Publication Date: Aug 1, 2019
• Deposit Date: Aug 22, 2019
• Publicly Available Date: Aug 28, 2019
• Journal: Biomechanics and Modeling in Mechanobiology
• Print ISSN: 1617-7959
• Electronic ISSN: 1617-7940
• Publisher: Springer (part of Springer Nature)
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Issue: 4
• Pages: 1213-1232
• DOI: https://doi.org/10.1007/s10237-019-01140-6
• Keywords: Akaike information criterion (AIC); Holzapfel–Ogden (HO) constitutive law; Reduced HO models; Simple shear tests; Uniaxial tests; Biaxial tests; Myocardial mechanical tests
• Public URL: https://uwe-repository.worktribe.com/output/2368026
• Publisher URL: https://doi.org/10.1007/s10237-019-01140-6
• Related Public URLs: http://orca.cf.ac.uk/120926/