The research of the mechanical properties of skeletal muscle has never stopped, whether in experimental tests or simulations of passive mechanical properties. To investigate the effect of biomechanical properties of micro-components and geometric structure of muscle fibers on macroscopic mechanical behavior, in this manuscript, we establish a multiscale model where constitutive models are proposed for fibers and the extracellular matrix, respectively. Besides, based on the assumption that the fiber cross-section can be expressed by Voronoi polygons, we optimize the Voronoi polygons as curved-edge Voronoi polygons to compare the effects of the two cross-sections on macroscopic mechanical properties. Finally, the macroscopic stress response is obtained through the numerical homogenization method. To verify the effectiveness of the multi-scale model, we measure the mechanical response of skeletal muscles in the in-plane shear, longitudinal shear, and tensions, including along the fiber direction and perpendicular to the fiber direction. Compared with experimental data, the simulation results show that this multiscale framework predicts both the tension response and the shear response of skeletal muscle accurately. The root mean squared error (RMSE) is 0.0035 MPa in the tension along the fiber direction; The RMSE is 0.011254 MPa in the tension perpendicular to the fiber direction; The RMSE is 0.000602 MPa in the in-plane shear; The RMSE was 0.00085 MPa in the longitudinal shear. Finally, we obtained the influence of the component constitutive model and muscle fiber cross-section on the macroscopic mechanical behavior of skeletal muscle. In terms of the tension perpendicular to the fiber direction, the curved-edge Voronoi polygons achieve the result closer to the experimental data than the Voronoi polygons. Skeletal muscle mechanics experiments verify the effectiveness of our multiscale model. The comparison results of experiments and simulations prove that our model can accurately capture the tension and shear behavior of skeletal muscle.
Citation: Fengjie Liu, Monan Wang, Yuzheng Ma. Multiscale modeling of skeletal muscle to explore its passive mechanical properties and experiments verification[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1251-1279. doi: 10.3934/mbe.2022058
The research of the mechanical properties of skeletal muscle has never stopped, whether in experimental tests or simulations of passive mechanical properties. To investigate the effect of biomechanical properties of micro-components and geometric structure of muscle fibers on macroscopic mechanical behavior, in this manuscript, we establish a multiscale model where constitutive models are proposed for fibers and the extracellular matrix, respectively. Besides, based on the assumption that the fiber cross-section can be expressed by Voronoi polygons, we optimize the Voronoi polygons as curved-edge Voronoi polygons to compare the effects of the two cross-sections on macroscopic mechanical properties. Finally, the macroscopic stress response is obtained through the numerical homogenization method. To verify the effectiveness of the multi-scale model, we measure the mechanical response of skeletal muscles in the in-plane shear, longitudinal shear, and tensions, including along the fiber direction and perpendicular to the fiber direction. Compared with experimental data, the simulation results show that this multiscale framework predicts both the tension response and the shear response of skeletal muscle accurately. The root mean squared error (RMSE) is 0.0035 MPa in the tension along the fiber direction; The RMSE is 0.011254 MPa in the tension perpendicular to the fiber direction; The RMSE is 0.000602 MPa in the in-plane shear; The RMSE was 0.00085 MPa in the longitudinal shear. Finally, we obtained the influence of the component constitutive model and muscle fiber cross-section on the macroscopic mechanical behavior of skeletal muscle. In terms of the tension perpendicular to the fiber direction, the curved-edge Voronoi polygons achieve the result closer to the experimental data than the Voronoi polygons. Skeletal muscle mechanics experiments verify the effectiveness of our multiscale model. The comparison results of experiments and simulations prove that our model can accurately capture the tension and shear behavior of skeletal muscle.
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Fengjie Liu, Monan Wang, Yuzheng Ma. Multiscale modeling of skeletal muscle to explore its passive mechanical properties and experiments verification[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1251-1279. doi: 10.3934/mbe.2022058
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