<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${R}^{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>>0.90. Under the “worst case scenario” for independent validation (N = 75 testing samples identified), the CNN achieves an <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${R}^{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> 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.</p>

Large-scale modeling of axonal dynamic responses via deep learning

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发表日期：

2025年12月12日

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Chaokai Zhang,
Adam Clansey,
Lara Bartels,
Daniel Bondi,
Julian Kloiber,
Alexander Jaffray,
Paul van Donkelaar,
Alexander Rauscher,
Lyndia Wu,
Songbai Ji

摘要

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 ${R}^{2}$ $R^{2}$ >0.90. Under the “worst case scenario” for independent validation (N = 75 testing samples identified), the CNN achieves an ${R}^{2}$ $R^{2}$ 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.