Residual stress estimates from multi-cut opening angles of the left ventricle

Zhuan, X. and Luo, X. (2020) Residual stress estimates from multi-cut opening angles of the left ventricle. Cardiovascular Engineering and Technology, 11(4), pp. 381-393. (doi: 10.1007/s13239-020-00467-x) (PMID:32557186)

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Purpose: Residual stress tensor has an essential influence on the mechanical behaviour of soft tissues and can be particularly useful in evaluating growth and remodelling of the heart and arteries. It is currently unclear if one single radial cut using the opening angle method can accurately estimate the residual stress. In many previous models, it has been assumed that a single radial cut can release the residual stress in a ring of the artery or left ventricle. However, experiments by Omens et al. (Biomech Model Mechanobiol 1:267–277, 2003) on mouse hearts, have shown that this is not the case. The aim of this paper is to answer this question using a multiple-cut mathematical model. Methods: In this work, we have developed models of multiple cuts to estimate the residual stress in the left ventricle and compared with the one-cut model. Both two and four-cut models are considered. Given that the collagen fibres are normally coiled in the absence of loading, we use the isotropic part of the Holzapfel-Ogden strain energy function to model the unloaded myocardium. Results: The estimated residual hoop stress from our multiple-cut model is around 8 to 9 times greater than that of a single-cut model. Although in principle infinite cuts are required to release the residual stress, we find four cuts seem to be sufficient as the model agrees well with experimental measurements of the myocardial thickness. Indeed, even the two-cut model already gives a reasonable estimate of the maximum residual hoop stress. We show that the results are not significantly different using homogeneous or heterogeneous material models. Finally, we explain that the multiple cuts approach also applies to arteries. Conclusion: We conclude that both radial and circumferential cuts are required to release the residual stress in the left ventricle; using multiple radial cuts alone is not sufficient. A multiple-cut model gives a marked increase of residual stress in a left ventricle ring compared to that of the commonly used single-cut model.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Luo, Professor Xiaoyu and Zhuan, Mr Xin
Authors: Zhuan, X., and Luo, X.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Cardiovascular Engineering and Technology
ISSN (Online):1869-4098
Published Online:15 June 2020
Copyright Holders:Copyright © 2020 The Author(s)
First Published:First published in Cardiovascular Engineering and Technology 11(4): 381-393
Publisher Policy:Reproduced under a Creative Commons licence

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
303231A whole-heart model of multiscale soft tissue mechanics and fluid structureinteraction for clinical applications (Whole-Heart-FSI)Xiaoyu LuoEngineering and Physical Sciences Research Council (EPSRC)EP/S020950/1M&S - Mathematics
303798Growth and Remodelling in Neoanatal Porcine Heart-- Pushing Mathematics through ExperimentsXiaoyu LuoEngineering and Physical Sciences Research Council (EPSRC)EP/S014284/1M&S - Mathematics
172141EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - Mathematics