Brain strain rate response: addressing computational ambiguity and experimental data for model validation

Traumatic brain injury (TBI) is an alarming global public health issue with high morbidity and mortality rates. Although the causal link between external insults and consequent brain injury remains largely elusive, both strain and strain rate are generally recognized as crucial factors for brain injury development. With respect to the flourishment of strain-based exploration, concerning ambiguity and inconsistency are noted in the scheme for strain rate calculation within the TBI research community. Furthermore, there is no experimental data that can be used to validate the strain rate responses of finite element (FE) models of the human brain. Thus, the current work presented a theoretical clarification of two commonly used strain rate computational schemes: the strain rate was either calculated as the time derivative of strain or derived from the rate of deformation tensor. To further substantiate this theoretical disparity, these two schemes were respectively implemented to estimate the strain rate responses from a previous-published cadaveric experiment and an FE brain model secondary to a concussive impact. The results clearly showed scheme-dependent responses, both in the experimentally determined principal strain rate and FE-derived principal and tract-oriented strain rates. The results suggest that cross-scheme comparison of strain rate responses is inappropriate, and the utilized strain rate computational scheme needs to be reported in future studies. The newly calculated experimental strain rate curves can be used for strain rate validation of FE head models. Highlights A theoretical clarification of two strain rate computational schemes was presented, in which the strain rate was respectively calculated as the time derivative of strain or derived from the rate of deformation tensor. Discordant cross-scheme responses were substantiated by experimental principal strain rate and computational principal and tract-oriented strain rates. Cross-scheme comparison of strain rate responses is inappropriate. The newly calculated experimental strain rate curves can be used for strain rate validation of FE head model Graphic abstract