A selective smoothed finite element method with visco‐hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

Abstract

Brain tissues are known for exhibiting complex nonlinear and time-dependent properties, which require visco-hyperelastic constitutive models for proper simulation. In this paper, a Total Lagrangian Explicit Selective Smoothed Finite Element Method (Selective S-FEM) is formulated to analyze the dynamic behavior of incompressible brain tissues undergoing extremely large deformation. The proposed Selective S-FEM deals with three-dimensional problems using four-node tetrahedron elements that can be automatically generated for geometrically complex soft tissues. It consists of the three key ingredients. (i) A visco-hyperelastic constitutive model is developed within the framework of S-FEM in the first time, allowing adequate modeling of the dynamic brain tissue behavior. (ii) Selective S-FEM strategy is used for overcome the mesh distortion and the volumetric locking that often occurs in soft tissues. (iii) Total Lagrangian formulation is used in an explicit algorithm allowing rigorous simulation of extreme large deformation. (iv) A combined implementation of Selective S-FEM with the visco-hyperelastic constitutive model for dynamic simulations. The shear deformation is calculated by Face/Edge-based S-FEM, and the volume deformation is calculated by NS-FEM. Numerical experiments show that Selective S-FEM is a robust solver with good accuracy, and excellent ability to reduce element distortion effects in simulate time-dependence behavior of bio-tissues.

A novel approach for tetrahedral-element-based finite element simulations of anisotropic hyperelastic intervertebral disc behavior

“…One order of magnitude smaller than inGraff (2012),Freed et al (2005),Wu et al (2020).Frontiers in Bioengineering and Biotechnology frontiersin.org…”

“…Yet, an optimal choice of the time step is paramount to ensure the desired accuracy of numerical solutions while maintaining computational efficiency. While this time step is deformation-dependent ( Ogden, 1997 ), it is traditionally prescribed as a suitably small constant (dependent on the material parameters) in typical explicit FE solvers such as Ansys LS-DYNA and Radioss for ease of implementation in a range of problems in mechanics ( Freed et al, 2005 ; Wu et al, 2020 ). However, in highly non-linear anisotropic hyperelastic materials like IVD tissue, this time step can be noticeably influenced by the state of deformation and local material symmetry, suggesting a re-evaluation of the traditional approach.…”

Effective Viscoplastic-Softening Model Suitable for Brain Impact Modelling

“…However, the wet specimen revealed a concave inflexion typical for polymers. Some of the extended models introduce hyperelastic and hyper-viscoelastic behaviour, or the combined features of basic models [ 8 , 17 , 26 , 27 , 28 , 29 ]. In [ 30 ], the authors modelled a brain’s material properties using both hyperelastic and viscoelastic constitutive laws.…”

A direct Jacobian total Lagrangian explicit dynamics finite element algorithm for real‐time simulation of hyperelastic materials

“…5 The real-time and accurate simulation of nonlinear deformations is also essential to many biomedical applications such as patient-specific whole-body image registration, 6 intraoperative brain-shift compensation, 7 virtual training for electrocardiology procedures, 8 and real-time surgical simulation of cataract surgery, laparoscopic surgery, and tumor removal. 9 Currently, many of the reported numerical algorithms are mainly focused on the improvement of numerical accuracy 10,11 and convergence, 12 with fewer considerations on computational efficiency. These algorithms utilize sophisticated constitutive formulations and computing procedures to achieve a very high order of accuracy, but the solutions are often computationally expensive to obtain.…”

“…Currently, many of the reported numerical algorithms are mainly focused on the improvement of numerical accuracy 10,11 and convergence 12 , with fewer considerations on computational efficiency. These algorithms utilise sophisticated constitutive formulations and computing procedures to achieve a very high order of accuracy, but the solutions are often computationally expensive to obtain.…”