Rapid estimation of cortical neuron activation thresholds by transcranial magnetic stimulation using convolutional neural networks

Abstract

Background: Transcranial magnetic stimulation (TMS) can modulate neural activity by evoking action potentials in cortical neurons. TMS neural activation can be predicted by coupling subject-specific head models of the TMS-induced electric field (E-field) to populations of biophysically realistic neuron models; however, the significant computational cost associated with these models limits their utility and eventual translation to clinically relevant applications.

Objective: To develop computationally efficient estimators of the activation thresholds of multi-compartmental cortical neuron models in response to TMS-induced E-field distributions.

Methods: Multi-scale models combining anatomically accurate finite element method (FEM) simulations of the TMS E-field with layer-specific representations of cortical neurons were used to generate a large dataset of activation thresholds. 3D convolutional neural networks (CNNs) were trained on these data to predict thresholds of model neurons given their local E-field distribution. The CNN estimator was compared to an approach using the uniform E-field approximation to estimate thresholds in the non-uniform TMS-induced E-field.

Results: The 3D CNNs estimated thresholds with mean absolute percent error (MAPE) on the test dataset below 2.5% and strong correlation between the CNN predicted and actual thresholds for all cell types (R² > 0.96). The CNNs estimated thresholds with a 2-4 orders of magnitude reduction in the computational cost of the multi-compartmental neuron models. The CNNs were also trained to predict the median threshold of populations of neurons, speeding up computation further.

Conclusion: 3D CNNs can estimate rapidly and accurately the TMS activation thresholds of biophysically realistic neuron models using sparse samples of the local E-field, enabling simulating responses of large neuron populations or parameter space exploration on a personal computer.

Keywords: Convolutional neural network; Finite element method; Machine learning; Neuron models; Threshold; Transcranial magnetic stimulation.