A modified Holzapfel-Ogden law for a residually stressed finite strain model of the human left ventricle in diastole

Wang, H.M., Luo, X.Y. , Gao, H. , Ogden, R.W. , Griffith, B.E., Berry, C. and Wang, T.J. (2014) A modified Holzapfel-Ogden law for a residually stressed finite strain model of the human left ventricle in diastole. Biomechanics and Modeling in Mechanobiology, 13(1), pp. 99-113. (doi: 10.1007/s10237-013-0488-x) (PMID:23609894) (PMCID:PMC3880672)

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Publisher's URL: http://dx.doi.org/10.1007/s10237-013-0488-x


In this work, we introduce a modified Holzapfel-Ogden hyperelastic constitutive model for ventricular myocardium that accounts for residual stresses, and we investigate the effects of residual stresses in diastole using a magnetic resonance imaging–derived model of the human left ventricle (LV). We adopt an invariant-based constitutive modelling approach and treat the left ventricular myocardium as a non-homogeneous, fibre-reinforced, incompressible material. Because in vivo images provide the configuration of the LV in a loaded state even in diastole, an inverse analysis is used to determine the corresponding unloaded reference configuration. The residual stress in this unloaded state is estimated by two different methods. One is based on three-dimensional strain measurements in a local region of the canine LV, and the other uses the opening angle method for a cylindrical tube. We find that including residual stress in the model changes the stress distributions across the myocardium and that whereas both methods yield qualitatively similar changes, there are quantitative differences between the two approaches. Although the effects of residual stresses are relatively small in diastole, the model can be extended to explore the full impact of residual stress on LV mechanical behaviour for the whole cardiac cycle as more experimental data become available. In addition, although not considered here, residual stresses may also play a larger role in models that account for tissue growth and remodelling.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Luo, Professor Xiaoyu and Ogden, Professor Raymond and Gao, Dr Hao and Berry, Professor Colin
Authors: Wang, H.M., Luo, X.Y., Gao, H., Ogden, R.W., Griffith, B.E., Berry, C., and Wang, T.J.
College/School:College of Medical Veterinary and Life Sciences > School of Cardiovascular & Metabolic Health
College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Biomechanics and Modeling in Mechanobiology
ISSN (Online):1617-7940
Copyright Holders:Copyright © 2013 The Authors
First Published:First published in Biomechanics and Modeling in Mechanobiology 13(1):99-113
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
560111Finite element-immersed boundary method and its application to mitral valvesXiaoyu LuoEngineering & Physical Sciences Research Council (EPSRC)EP/I029990/1M&S - MATHEMATICS