Mesh convergence depends on the element formulation of finite element brain models

Finite element (FE) head models are virtual tools to study brain biomechanics and their predictions must be numerically convergent. Previous convergence studies focused on the influence of mesh size, but the potential effect of element formulation on model convergence was often ignored. To address this, one original model with brain mesh size as 6.4 ± 1.9 mm was modified to generate three derivatives with the same mesh topology but different element sizes, i.e., a coarse model (mesh size: 12.2 ± 3.9 mm), a medium model (mesh size: 3.2 ± 1.0 mm), and a fine model (mesh size: 1.6 ± 0.5 mm). Three commonly used element formulations, i.e., reduced integration, selectively reduced (S/R) integration, and full integration, were implemented to the brain elements. These models were subjected to rotational loadings along the axial, coronal, and sagittal axes, respectively. The maximum relative displacement at representative sites and 95 ^th percentile maximum principal strain at the whole brain level were used to evaluate mesh convergency. The results showed that the S/R integration yielded a 5% difference between the original and medium meshes, while the reduced and full integration revealed a difference over 5% even between the medium and fine meshes. This study verified that the mesh convergence of FE brain models is affected by the choice of element formulation and the S/R integration contributes to the fastest convergence behavior than the reduced and full integrations. It provided practical information on how to develop numerically convergent and computationally efficient FE brain models.