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Passive material parameter estimation can facilitate the in vivo assessment of myocardial stiffness, an important biomarker for heart failure stratification and screening. Parameter estimation strategies employing biomechanical models of various degrees of complexity have been proposed, usually involving a significant number of cardiac mechanics simulations. The clinical translation of these strategies however is limited by the associated computational cost and the model simplifications. A simpler and arguably more robust alternative is the use of data-based approaches, which do not involve mechanical simulations and can be based for example on the formulation of the energy balance in the myocardium from imaging and pressure data. This approach however requires the estimation of the mechanical work at the myocardial boundaries and the strain energy stored, tasks that are challenging when external loads are unknown - especially at the base which deforms extensively within the cardiac cycle. In this work we employ the principle of virtual work in a strictly data-based approach to uniquely identify myocardial material parameters by eliminating the effect of the unknown boundary tractions at the base. The feasibility of the method is demonstrated on a synthetic data set using a popular transversely isotropic material model followed by a sensitivity analysis to modelling assumptions and data noise.

Myocardial stiffness is a useful diagnostic and prognostic biomarker, but only accessible through indirect surrogates. Computational 3D cardiac models, through the process of personalization, can estimate the material parameters of the ventricles, allowing the estimation of stiffness and potentially improving clinical decisions. The availability of detailed 3D cardiac imaging data, which are not routinely available for the conventional cardiologist, is nevertheless required to constrain these models and extract a unique set of parameters. In this work we propose a strategy to provide the same ability to identify the material parameters, but from 2D observations that are obtainable in the clinic (echocardiography). The solution combines the adaptation of an energy-based cost function, and the estimation of the out of plane deformation based on an incompressibility assumption. In-silico results, with an analysis of the sensitivity to errors in the deformation, fibre orientation, and pressure data, demonstrate the feasibility of the approach.

Myocardial stiffness is a clinical biomarker used to diagnose and stratify diseases such as heart failure. This biomechanical property can be inferred from the personalisation of computational cardiac models to clinical measures. Nevertheless, previous attempts have been unable to determine a unique set of material constitutive parameters. In this study we address this shortcoming by proposing a new cost function that allows us to uncouple key parameters and uniquely describe passive material properties in patients from available clinical data.

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_1=3000\pm 1700\,\hbox {Pa}$$\end{document}C1=3000±1700Pa and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =45\pm 25$$\end{document}α=45±25 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f=25\pm 14$$\end{document}bf=25±14, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{ft}=11\pm 6$$\end{document}bft=11±6, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{t}=9\pm 5$$\end{document}bt=9±5) for the HF cases and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_1=1700\,\hbox {Pa}$$\end{document}C1=1700Pa and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =15$$\end{document}α=15 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f=8$$\end{document}bf=8, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{ft}=4$$\end{document}bft=4, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{t}=3$$\end{document}bt=3) for the healthy case.