Large-scale modeling of axonal dynamic responses via deep learning

Large-scale axonal dynamic simulation is critical to study white matter injury but is prohibitive in computational cost. We solve this challenge by training a convolutional neural network (CNN) that takes fiber strain profiles as inputs to instantly estimate multimodal axonal injury parameters. First, tractography-based fiber strains are derived based on subject-specific simulations of N = 46 head impacts from a male ice hockey player. To generate the minimum training dataset, the brain is subdivided into coarse cubes (isotropic resolution of 6 mm; N = 4979 voxels). A stratified (one sample per cube) and adaptive (by controlling a similarity threshold) sampling strategy is devised to iteratively identify the most distinct profiles from N = 45 head impacts used for training (with the remaining one reserved for independent validation). They serve as the input to a male axonal injury model for simulation. A CNN is then trained to estimate the peak strains in microtubule and axolemma as well as the failure percentages of tau proteins and neurofilaments. The CNN is cross-validated to determine the minimum training samples of N = 2000 to reach $R^2$ >0.90. Under the "worst case scenario" for independent validation (N = 75 testing samples identified), the CNN achieves an $R^2$ of 0.91-0.98 and a normalized root mean-squared error (NRMSE) of 2.7-5.0%. Finally, we showcase the CNN by generating high-resolution multimodal axonal responses for the entire white matter within 12 s (isotropic resolution of 2 mm with ~ 92,500 voxels), vs. an estimated ~ 12 years using conventional direct simulations (~ 31.5-million-fold efficiency gain). This study demonstrates the potential of deep learning to enable large-scale mechanistic investigations of white matter injury in the future.