Research On Multiscale Modeling And Simulation Of Biomechanics Properties Of Skeletal Muscle

The modeling and simulation of passive biomechanical properties of skeletal muscle has always been a research hotspot.The passive biomechanical models of skeletal muscle are widely used in the definition of skeletal muscle material properties in the fields of virtual surgery systems,impact mechanics research,rehabilitation engineering,etc.Therefore,it is of great significance to establish an accurate biomechanical model of skeletal muscle.The establishment of a skeletal muscle biomechanical model based on a multiscale method is useful for exploring the influence of skeletal muscle microscopic factors on macroscopic mechanical properties,studying the force transmission process in the skeletal muscle and skeleton system,and exploring the microstructural changes caused by large strain injury and disease of skeletal muscle.In this thesis,the mechanical properties of skeletal muscle are studied from the perspectives of experiment,multiscale modeling and simulation.To determine model parameters of the multiscale model and verify the validity of the multiscale model the multiscale model,the quasi-static biomechanical experiment of skeletal muscle is designed and performed.Taking pig hind leg skeletal muscle as the experimental object,four experimental categories are set up respectively,including longitudinal tension,transverse tension,out-of-plane longitudinal shear and in-plane shear.With the help of the electronic universal material testing machine,the force-displacement data of each experimental categories are measured separately,and the average value of the measured data are obtained.Then,the nominal stress-nominal strain curves of skeletal muscle under four deformations are obtained by calculation.The experimental results show that skeletal muscle has different shear mechanical behaviors in out-of-plane longitudinal shear and in-plane shear.Researching the biomechanical properties of skeletal muscle by multiscale methods has been a hotspot in recent years.However,there are still many problems need to be solved,such as:there is a certain difference between the microstructural model of muscle fibers and the structural observed under a microscope;The biomechanical models of micro-components cannot effectively simulate the mechanical behavior of skeletal muscle during shear deformation;The computational cost of multiscale numerical models is relatively high.In order to solve the above problems,the research contents of this thesis are as follows:（1）In view of the difference between the muscle fiber microstructure model and the image observed under the microscope,curved-edge Voronoi polygons are proposed as the cross-section of muscle fibers,and the corresponding representative volume element（RVE）is established at the microscale.In the process of establishing the RVE model,two schemes are used for the geometric structure of the muscle fiber.Scheme1:Using Voronoi polygon as the cross-section of muscle fibers;Scheme 2:Optimize the straight boundary of the Voronoi polygon,use curve lines instead of straight lines,so that the cross-section of the muscle fiber is oval,that is,curved-edge Voronoi polygons,using curved-edge Voronoi polygons as the cross-section of the muscle fiber.The two schemes provide finite element models for the subsequent simulation of the multiscale numerical model to study the influence of the muscle fiber structure on the macroscopic mechanical properties of skeletal muscle.It is proposed to use the Voronoi polygon as the cross-section of the muscle fiber to provide a new solution for the design of the muscle fiber structure,and to make a significant contribution to making the muscle fiber structure design model closer to the real structure.In addition to the cross-section shape of muscle fibers,the volume fraction of muscle fibers is also a key factor need to be considered in establishing the RVE model.In this thesis,RVE models with volume fractions of 0.7,0.8,and 0.9 are established to study the effect of muscle fiber volume fraction on the macroscopic mechanical properties of skeletal muscle.This study provides a reference for the establishment of skeletal muscle microstructure models at different ages and pathological conditions.Finally,mesh generated RVE models and add periodic boundary conditions.（2）A new biomechanical model（MMA model）is proposed to solve the problem that the microscopic component biomechanical model cannot effectively capture the mechanical behavior of skeletal muscle during shear deformation.The MMA model is used as the biomechanical model of muscle fibers and connective tissue.The MMA model established in this thesis adopts complete strain invariantsI₄,I₅,I₆,I₇ so that the shear behavior of skeletal muscle is reflected at the level of material properties.The established MMA model is applied to the finite element simulation with the help of the secondary development of the user material subprogram（UMAT）.The finite element simulation results verify that the proposed MMA model can simulate compressibility,anisotropy and hyperelasticity,and obtain unequal shear moduli in different planes during shear deformation.Since the transmission of force in skeletal muscle is realized by shear deformation,the biomechanical model of skeletal muscle established in this paper is of great significance to study the mechanism of internal force transmission in skeletal muscle.（3）Combine the experimental results of skeletal muscle,the RVE models,the biomechanical models of muscle fibers and connective tissue to establish a multiscale numerical model of skeletal muscle.According to the experimental results,the parameters of the biomechanical model are determined,the multiscale homogenization method are used to realize the connection between the microscale and the macro-scale,and the macroscopic mechanical behavior of skeletal muscle is finally obtained.Four deformation forms of longitudinal tension,transverse tension,out-of-plane longitudinal shear and in-plane shear are performed to verify the convergence of the model.This thesis research the effects of model parameters,muscle fiber volume fraction and muscle fiber structure on skeletal muscle on macroscopic mechanical behavior.Combined with experimental data,the effectiveness of the multiscale numerical model is verified.The multiscale numerical model of skeletal muscle can not only study the influence of microscopic factors of skeletal muscle on macroscopic mechanical behavior,but also study the influence of diseases on the biomechanical properties of skeletal muscle,and it can be used to simulate the remodeling and regeneration of skeletal muscle.In addition,it can also be used to verify the ability of multiscale analytical model to capture the effects of micro-geometric factors on skeletal muscle’s macro-mechanical behavior.（4）In order to solve the problem of the high computational cost of the multiscale numerical model of skeletal muscle,a multiscale analytical model of skeletal muscle is established based on the Voigt approximation method.The finite element simulation proves that the effect of muscle fiber volume fraction on the trend of simulation results of multiscale analytical model is exactly the same as that of multiscale numerical model simulation under four deformation conditions of longitudinal tension,transverse tension,out-of-plane longitudinal shear and in-plane shear.Combined with experimental data,the validity of the multiscale analytical model is verified.Comparing the computing time of the multiscale numerical model and multiscale analytical model,it is verified that the multiscale analytical model of skeletal muscle has advantages in computing speed.A new solution is provided for the application of multiscale models of skeletal muscle in fields where require computational efficiency.