Single pointwise samples of electric field on a neuron model cannot predict activation threshold by brain stimulation

Some computational models of neural activation by transcranial magnetic stimulation overestimate the electric field (E-field) threshold compared to in vivo measurements. A recent study proposed a statistical method to account for the influence of microscopic perturbations to the E-field. The method, however, relies on the unsubstantiated assumption that thresholds can be predicted by single pointwise samples of the E-field strength along neural cables.

We analyzed neural responses to E-field with microscopic perturbations and demonstrate via theoretical derivation and simulations that neural activation is not determined by pointwise E-field amplitude but rather by spatial integration of the E-field along the neural cable. Therefore, the influence of microscopic E-field perturbations is negligible due to the spatiotemporal filtering by the neural membrane and axoplasm.

We derive the axial and transmembrane currents in a neural cable for an imposed E-field with microscopic perturbations. We simulate neural activation thresholds of unmyelinated and myelinated axons in two stimulation scenarios and compare thresholds for E-field activation with and without perturbations.

In the theoretical derivation, the perturbation terms average out to zero on larger spatial scales indicating that they do not influence neural activation thresholds. Simulated thresholds with the E-field spatial perturbations present had negligible differences (< 3.4%) compared to those without.

Single point samples of the microscopic E-field on a neural cable cannot predict neural activation thresholds. Neural simulations should be used to determine any influence of the E-field spatial perturbations. The latter, however, are unlikely to account for the difference between experimental and simulated E-field thresholds.