Mesh Convergence Behavior and the Effect of Element Integration of a Human Head Injury Model

Abstract

Numerous head injury models exist that vary in mesh density by orders of magnitude. A careful study of the mesh convergence behavior is necessary, especially in terms of strain most relevant to brain injury. To this end, as well as to investigate the effect of element integration scheme on simulated strains, we re-meshed the Worcester Head Injury Model at five mesh densities (~ 7.2–1000 k high-quality hexahedral elements of the brain). Results from explicit dynamic simulations of three cadaveric impacts and an in vivo head rotation were compared. First, scalar metrics of the whole brain only considering magnitude were used, including peak maximum principal strain and population-based median strain. They were further extended to deep white matter regions and the entire brain elements, respectively, to form two “response vectors” to account for both magnitude and distribution. Using benchmark enhanced full-integration elements (C3D8I), a minimum of 202.8 k brain elements were necessary to converge for response vectors of the deep white matter regions. This model was further used to simulate with reduced integration (C3D8R). We found that hourglass energy higher than the common rule of thumb (e.g., up to 44.38% vs. < 10% of internal energy) was necessary to maintain comparable strain relative to C3D8I. Based on these results, it is recommended that a human head injury model should have a minimum number of 202.8 k elements, or an average element size of no larger than 1.8 mm, for the brain. C3D8R formulation with relax stiffness hourglass control using a high scaling factor is also recommended to achieve sufficient accuracy without substantial computational cost.