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 ∼7.68%), showing improvements compared to its hyperelastic (mean error ∼24%) 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. Statement of SignificanceThe viscoelastic response of human heart tissues has yet to be integrated into common constitutive models describing cardiac mechanics. In this work, a fractional viscoelastic modeling approach is introduced based on the hierarchical structure of heart tissue. From these foundations, the current state-of-the-art biomechanical models of the heart muscle are transformed using fractional viscoelasticity, replicating passive muscle function across multiple experimental tests. Comparisons are drawn with current models to highlight the improvements of this approach and predictive responses show strong qualitative agreement with experimental data. The proposed model presents the first constitutive model aimed at capturing viscoelastic nonlinear response across multiple testing regimes, providing a platform for better understanding the biomechanics of myocardial tissue in health and disease.
Highlights
MethodsThe complex structure of myocardial tissue has led to discussion over the origins of viscoelasticity
The proposed model presents the first constitutive model aimed at capturing viscoelastic nonlinear response across multiple testing regimes, providing a platform for better understanding the biomechanics of myocardial tissue in health and disease
Many constituent components of the myocardium have been implicated as the source of viscoelasticity, including tissue perfusion, extracellular fluid, myocytes, the extracellular matrix (ECM) and others
Summary
The complex structure of myocardial tissue has led to discussion over the origins of viscoelasticity. Many constituent components of the myocardium have been implicated as the source of viscoelasticity, including tissue perfusion, extracellular fluid, myocytes, the extracellular matrix (ECM) and others. Studies have shown that the main constituents of the ECM exhibit viscoelasticity [57], suggesting molecular friction as a source of viscoelastic response. While these factors are often considered and advocated for individually, it is highly likely that all factors can contribute to the viscoelastic response of the myocardium with varying degrees of importance depending on the spatiotemporal scales and loading conditions considered. We review the evidence for these different factors contributing to the viscoelastic response of myocardial tissue
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