肌肉组织力电耦合及主-被动非线性力学行为S-FEM模拟研究

The muscle tissue is an extremely complex system due to the differences in structural functions, anisotropic hyperelasticity, incompressibility and motility of living tissue. The numerical simulation has become a powerful approach for the study of mechanics properties of this complex system. This project aims to build a coupled electro-mechanical model based on smoothed finite element method (S-FEM), which can improve the efficiency of the pro-process, enhance the computational accuracy, provide systematic estimates of the active-passive behavior of muscle tissues and further reveal the deformation mechanism of muscle tissues. The main contents of this project are: (1) To construct the individualized and precise finite element model based on the CT scan and unstructured meshes and to achieve automatic creation of smoothing domains; (2) A linear smoothed finite element method (LS-FEM) is developed for solving the volumetric locking, pressure oscillation and low convergence within the incompressible problems; (3) An anisotropic incompressible hyperelastic constitutive is introduced into LS-FEM and the coupled electro-mechanical model is established with the consideration of the spatiotemporal evolution of the action potential field. (4) A dynamic explicit program and nonlinear simulation platform based on LS-FEM are developed for the simulation of excitation-contraction coupling in muscle tissues, and to investigate how the arrangement of muscle fibers, damage, etc. influence the active-passive nonlinear mechanical behavior of muscle tissues under the state of non-uniform activation.

肌肉组织因其结构功能差异性，材料各向异性超弹性、不可压缩性及活性组织的能动性而成为一个极其复杂的系统，数值模拟已成为研究这一复杂系统力学特性的重要手段。项目拟建立肌肉组织S-FEM力电耦合数值模型，实现高效的前处理和高精度的求解，对肌肉主-被动力学行为进行更为精准的预测，并进一步揭示其收缩变形机理。项目主要开展以下研究：（1）基于CT图像数据和非结构化网格，对肌肉组织进行个体化、精确化有限元建模，实现光滑积分域的自动生成；（2）发展线性光滑有限元算法（LS-FEM），解决模拟不可压缩问题过程中体积锁定、压力振荡、收敛性低等难点；（3）引入各向异性不可压超弹性本构，并考虑肌肉内部动作电位场时空演化过程，建立肌肉组织力电耦合数值模型；（4）开发模拟肌肉组织兴奋-收缩偶联的LS-FEM显式算法，搭建非线性仿真平台，并研究非均匀激活状态下肌纤维排列方式、损伤等对肌肉主-被动非线性力学行为的影响。

肌肉组织因其结构功能差异性，材料各向异性超弹性、不可压缩性及活性组织的能动性而成为一个极其复杂的系统，数值模拟已成为研究这一复杂系统力学特性的重要手段。项目主要利用梯度光滑技术和弱-弱形式建模，并考虑多种单元类型、时间依赖、肌肉内部动作电位场时空演化过程的非线性粘-超弹性材料及几何非线性大变形，建立非线性固体力学求解程序。依据项目申请书主要开展了以下方面的研究：1）实现了复杂生物组织的个体化、精确化有限元建模，实现光滑积分域的自动生成；2）建立基于多边形单元的光滑有限元方法，并将其拓展至三维问题，建立基于四面体单元的完全拉格朗日选择性光滑有限元显式算法，用以求解三维生物组织粘-超弹性动态大变形问题。实现卷积积分的广义的Maxwell粘-超弹性固体模型和选择性光滑有限元法耦合，使剪切松弛与体积松弛相互独立，使得粘-超弹性本构模型更加灵活；3）发展基于四面体单元的统一实现的光滑有限元算法，用以模拟生物组织的粘超弹性的固体力学问题，并从理论上讨论了其方法的稳定性；4）建立基于统一实现的光滑有限元方法（UI-SFEM），用以求解动脉壁、牙齿矫正和人体脊椎的复杂生物组织的力学行为；5）建立了模拟肌肉组织兴奋-收缩偶联的光滑有限元显示算法。综上，项目通过系列多材料、多组件的生物组织数值算例，对本项目所提算法的计算精度、效率及网格依赖性等进行验证分析。