Real-time dynamic simulation for highly accurate spatiotemporal brain deformation from impact.

Real-time dynamic simulation remains a significant challenge for spatiotemporal data of high dimension and resolution. In this study, we establish a transformer neural network (TNN) originally developed for natural language processing and a separate convolutional neural network (CNN) to estimate five-dimensional (5D) spatiotemporal brain-skull relative displacement resulting from impact (isotropic spatial resolution of 4 mm with temporal resolution of 1 ms). Sequential training is applied to train (N = 5184 samples) the two neural networks for estimating the complete 5D displacement across a temporal duration of 60 ms. We find that TNN slightly but consistently outperforms CNN in accuracy for both displacement and the resulting voxel-wise four-dimensional (4D) maximum principal strain (e.g., root mean squared error (RMSE) of ~1.0% vs. ~1.6%, with coefficient of determination, >0.99 vs. >0.98, respectively, and normalized RMSE (NRMSE) at peak displacement of 2%-3%, based on an independent testing dataset; N = 314). Their accuracies are similar for a range of real-world impacts drawn from various published sources (dummy, helmet, football, soccer, and car crash; average RMSE/NRMSE of ~0.3 mm/~4%-5% and average of ~0.98 at peak displacement). Sequential training is effective for allowing instantaneous estimation of 5D displacement with high accuracy, although TNN poses a heavier computational burden in training. This work enables efficient characterization of the intrinsically dynamic brain strain in impact critical for downstream multiscale axonal injury model simulation. This is also the first application of TNN in biomechanics, which offers important insight into how real-time dynamic simulations can be achieved across diverse engineering fields.