A central problem in biomechanical studies of personalized human left ventricular (LV) modelling is to estimate material properties from in vivo clinical measurements. In this work we evaluate the passive myocardial mechanical properties inversely from the in vivo LV chamber pressure–volume and strain data. The LV myocardium is described using a structure-based orthotropic Holzapfel–Ogden constitutive law with eight parameters. In the first part of the paper we demonstrate how to use a multi-step non-linear least-squares optimization procedure to inversely estimate the parameters from the pressure–volume and strain data obtained from a synthetic LV model in diastole. In the second part, we show that to apply this procedure to clinical situations with limited in vivo data, additional constraints are required in the optimization procedure. Our study, based on three different healthy volunteers, demonstrates that the parameters of the Holzapfel–Ogden law could be extracted from pressure–volume and strain data with a suitable multi-step optimization procedure. Although the uniqueness of the solution cannot be addressed using our approaches, the material response is shown to be robustly determined.

H. Gao

W. G. Li

L. Cai

C. Berry

X. Y. Luo

Journal of Engineering Mathematics

该杂志的目的是促进数学在工程和应用科学问题中的应用。它还旨在通过数学强调应用科学和工程科学的基本问题的内在统一性。该杂志的范围包括以下内容：• 数学：常微分方程和偏微分方程、积分方程、渐近学、变分和泛函分析方法、数值分析、计算方法。• 应用领域：连续介质力学、稳定性理论、波传播、扩散, 传热传质, 自由边界问题;流体力学：航空和流体动力学、边界层、冲击波、流体机械、流体结构相互作用、对流、燃烧、声学、多相流、过渡和湍流、蠕动流、流变学、多孔介质流、海洋工程、大气工程、非牛顿流动、船舶流体动力学；固体力学：弹性、经典力学、非线性力学、振动、板壳、断裂力学；生物医学工程、地球物理工程、反应扩散问题；和相关领域。该杂志还偶尔发表由杰出研究人员撰写的受邀“观点”文章，审查他们的权威性概述，并对其专业领域当前感兴趣的主题的最新发展进行回顾。希望为此类文章提出主题的作者应直接与主编联系。鼓励潜在作者查阅该期刊的最新期刊，以判断他们的手稿是否与已发表论文的风格和内容一致。

The Journal of Engineering Mathematics aims to promote the application of mathematics in engineering and applied sciences, while emphasizing the inherent unity between applied sciences and engineering sciences. The scope of the journal includes: • Mathematics: ordinary differential equations, partial differential equations, integral equations, asymptotic analysis, variational methods and functional analysis, numerical analysis, and computational methods; • Application areas: continuum mechanics, stability theory, wave propagation, diffusion, heat and mass transfer, free boundary problems; fluid mechanics: aerodynamics and fluid dynamics, boundary layers, shock waves, fluid machinery, fluid-structure interactions, convection, combustion, acoustics, multiphase flows, transition and turbulence, creeping flows, rheology, porous media flows, ocean engineering, atmospheric engineering, non-Newtonian flows, and ship hydrodynamics; solid mechanics: elasticity, classical mechanics, nonlinear mechanics, vibrations, plates and shells, fracture mechanics; biomedical engineering, geophysical engineering, reaction-diffusion problems, and related fields. The journal also occasionally publishes invited 'perspective' articles written by distinguished researchers, reviewing their authority and the latest developments on topics of current interest in their fields. Authors wishing to propose topics for such articles should contact the editor directly. Potential authors are encouraged to consult recent issues of the journal to determine whether their manuscripts align with the style and content of previously published papers.

《Journal of Engineering Mathematics》旨在促进数学在工程和应用科学中的应用，同时强调应用科学与工程科学之间的内在统一性。该期刊的范围包括：• 数学：常微分方程、偏微分方程、积分方程、渐近分析、变分法和泛函分析、数值分析及计算方法；• 应用领域：连续介质力学、稳定性理论、波传播、扩散、传热与质传、自由边界问题；流体力学：航空与流体动力学、边界层、冲击波、流体机械、流体结构相互作用、对流、燃烧、声学、多相流、过渡与湍流、蠕动流、流变学、多孔介质流、海洋工程、大气工程、非牛顿流动、船舶流体动力学；固体力学：弹性、经典力学、非线性力学、振动、板壳、断裂力学；生物医学工程、地球物理工程、反应扩散问题及相关领域。该期刊还偶尔发表由杰出研究人员撰写的受邀“观点”文章，审查其权威性，并回顾其专业领域当前感兴趣的主题的最新发展。希望为此类文章提出主题的作者应直接与主编联系。鼓励潜在作者查阅该期刊的最新期刊，以判断他们的手稿是否与已发表论文的风格和内容一致。

Parameter estimation in a Holzapfel–Ogden law for healthy myocardium

This study, based on three different healthy volunteers, demonstrates that the parameters of the Holzapfel–Ogden law could be extracted from pressure–volume and strain data with a suitable multi-step optimization procedure.

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工程技术, 数学跨学科应用	4

Parameter estimation in a Holzapfel–Ogden law for healthy myocardium

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