Key result
Novel fractional viscoelastic model cuts myocardial biomechanical modeling error by ~68% versus hyperelastic models.
Why the study?
Most current constitutive equations for cardiac muscle neglect viscoelastic phenomena observed experimentally, limiting computational biomechanical models used for personalized therapy assessment in heart failure.
Absolute Event Rate: 7.65% vs 24.17%
A novel fractional viscoelastic constitutive model for human myocardium significantly improves the accuracy of replicating passive biomechanical responses compared to standard hyperelastic models.
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 SIGNIFICANCE: The 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.
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Nordsletten et al. (2021) studied Myocardial biomechanics. Fractional nonlinear anisotropic viscoelastic model vs. Hyperelastic models (Holzapfel-Ogden and Costa) was evaluated on Mean error in replicating experimental data (biaxial stretch, triaxial cyclic shear, and triaxial stress relaxation). A novel fractional nonlinear anisotropic viscoelastic model replicated human myocardial biomechanical experiments with a mean error of 7.65%, improving upon hyperelastic models which had errors around 25%.
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