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A Viscoelastic Model for Human Myocardium

14 Pages Posted: 13 May 2021 Publication Status: Under Review

See all articles by David Nordsletten

David Nordsletten

University of Michigan at Ann Arbor - Departments of Biomedical Engineering and Cardiac Surgery

Adela Capilnasiu

King's College London - Division of Biomedical Engineering and Imaging Sciences

Will Zhang

University of Michigan at Ann Arbor - Department of Biomedical Engineering

Anna Wittgenstein

King's College London - Division of Biomedical Engineering and Imaging Sciences

Myrianthi Hadjicharalambous

University of Cyprus - Department of Mechanical & Manufacturing Engineering

Gerhard Sommer

Graz University of Technology - Institute of Biomechanics

Ralph Sinkus

King's College London - Division of Biomedical Engineering and Imaging Sciences

Gerhard A. Holzapfel

Graz University of Technology - Institute of Biomechanics

Abstract

Understanding the biomechanics of the heart in health and disease plays an important role in the diagnosis and treatment of heart failure. The use of computational biomechanical models for therapy assessment is paving the way for personalized treatment, and relies on accurate constitutive equations mapping strain to stress. Current state-of-the art constitutive equations account for the nonlinear anisotropic stress-strain response of cardiac muscle using hyperelasticity theory. While providing a solid foundation for understanding the biomechanics of heart tissue, most current laws neglect viscoelastic phenomena observed experimentally. Utilizing experimental data from human myocardium and knowledge of the hierarchical structure of heart muscle, we present a fractional nonlinear anisotropic viscoelastic constitutive model. The model is shown to replicate biaxial stretch, triaxial cyclic shear and triaxial stress relaxation experiments (mean error ~7.5%), comparing well with its hyperelastic (mean error ~25%) counterparts. Model sensitivity, fidelity and parameter uniqueness are demonstrated. The model is also compared to rate-dependent biaxial stretch as well as different modes of biaxial stretch, illustrating extensibility of the model to a range of loading phenomena.

Keywords: human ventricular myocardium; viscoelasticity; passive mechanical behavior; cardiac mechanics; tissue mechanics; large deformation

Suggested Citation

Nordsletten, David and Capilnasiu, Adela and Zhang, Will and Wittgenstein, Anna and Hadjicharalambous, Myrianthi and Sommer, Gerhard and Sinkus, Ralph and Holzapfel, Gerhard A., A Viscoelastic Model for Human Myocardium. Available at SSRN: https://ssrn.com/abstract=3845711 or http://dx.doi.org/10.2139/ssrn.3845711

David Nordsletten (Contact Author)

University of Michigan at Ann Arbor - Departments of Biomedical Engineering and Cardiac Surgery ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

Adela Capilnasiu

King's College London - Division of Biomedical Engineering and Imaging Sciences ( email )

London
United Kingdom

Will Zhang

University of Michigan at Ann Arbor - Department of Biomedical Engineering

500 S. State Street
Ann Arbor, MI 48109
United States

Anna Wittgenstein

King's College London - Division of Biomedical Engineering and Imaging Sciences ( email )

London
United Kingdom

Myrianthi Hadjicharalambous

University of Cyprus - Department of Mechanical & Manufacturing Engineering ( email )

75 Kallipoleos Street
Nicosia CY 1678, Nicosia P.O. Box 2
Cyprus

Gerhard Sommer

Graz University of Technology - Institute of Biomechanics ( email )

Kopernikusgasse 24/IV
Graz, Styria A-8010
Austria

Ralph Sinkus

King's College London - Division of Biomedical Engineering and Imaging Sciences ( email )

London
United Kingdom

Gerhard A. Holzapfel

Graz University of Technology - Institute of Biomechanics ( email )

Kopernikusgasse 24/IV
Graz, Styria A-8010
Austria

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