P089 Incorporating initial polarization in neural simulations for accurate modeling of brain stimulation

Abstract

Introduction Accurate modeling of neural activation provides mechanistic understanding of non-invasive brain stimulation and means for optimization of stimulus parameters. The cable equation is commonly used to couple extracellular electric fields to neuronal models. However, its conventional form does not account for some aspects of the neuronal membranes’ response, such as polarization of soma or fibers by transverse electric fields, and has limitations in the theoretical foundation for coupling inductive magnetic stimulation. Until now, the membranes’ detailed interactions with the electric fields could only be modeled by computationally expensive finite element simulation of fine neural structures. Objectives This modeling study incorporates initial polarization into the cable equation to improve the accuracy of estimating neural activation of both electrical and magnetic stimulation. Materials and methods The initial polarization of axon segments and somas was derived analytically and incorporated into the cable equation. Test cases were simulated for neuron models with either linear or nonlinear membrane to evaluate the influence of initial polarization on polarization rate and action potential thresholds. Results Initial polarization can reduce the neural firing threshold by 5–50% for typical axon radii, electrode distances, and pulse widths. Short pulse widths and large electrode distance, such as those in non-invasive stimulation, result in larger decreases in threshold. The depolarization rates of nonlinear membrane models showed that the initial polarization mechanism has activation strength similar to the spatial gradient of the applied field, and contributes significantly to activating the soma and axon initial segment. Initial polarization reduces stimulation thresholds and may potentially shift the spike initiation site from axon terminals to the initial segments. This could be an important effect in transcranial stimulation due to the low spatial gradients of the applied fields. Conclusion Initial polarization may contribute significantly to neural activation. It is captured by the proposed modified cable equation, which could give more accurate estimation of the site and threshold for neural activation with exogenous electric fields. Download : Download high-res image (190KB) Download : Download full-size image