Differences between two maximal principal strain rate calculation schemes in traumatic brain analysis with in-vivo and in-silico datasets

Brain deformation caused by a head impact leads to traumatic brain injury (TBI). The maximum principal strain (MPS) was used to measure the extent of brain deformation and predict injury, and the recent evidence has indicated that incorporating the maximum principal strain rate (MPSR) and the product of MPS and MPSR, denoted as MPS × SR, enhances the accuracy of TBI prediction. However, ambiguities have arisen about the calculation of MPSR. Two schemes have been utilized: one is to use the time derivative of MPS (MPSR₁), and another is to use the first eigenvalue of the strain rate tensor (MPSR₂). Both MPSR₁ and MPSR₂ have been applied in previous studies to predict TBI. To quantify the discrepancies between these two methodologies, we compared them across eight in-vivo and one in-silico head impact datasets and found that 95MPSR₁ was slightly larger than 95MPSR₂ and 95MPS × SR₁ was 4.85 % larger than 95MPS × SR₂ in average. Across every element in all head impacts, the average MPSR₁ was 12.73 % smaller than MPSR₂, and MPS × SR₁ was 11.95 % smaller than MPS × SR₂. Furthermore, logistic regression models were trained to predict TBI using MPSR (or MPS × SR), and no significant difference was observed in the predictability. The consequence of misuse of MPSR and MPS × SR thresholds (i.e. compare threshold of 95MPSR₁ with value from 95MPSR₂ to determine if the impact is injurious) was investigated, and the resulting false rates were found to be around 1 %. The evidence suggested that these two methodologies were not significantly different in detecting TBI.