Efficient Computation of the Neural Activation During Deep Brain Stimulation for Dispersive Electrical Properties of Brain Tissue

Adaptive Estimation of the Neural Activation Extent in Computational Volume Conductor Models of Deep Brain Stimulation

“…The field model is able to compute stationary current fields (purely resistive material properties) as well as electro-quasistatic fields (complex material properties including conductivity and relative permittivity) for heterogeneous and rotationally asymmetric tissue distributions. The support for incorporating complex material properties further allows for computing the time-dependent field solution dependent on the dispersive electrical properties of biological tissue for any applied voltage-or current-controlled DBS signal using the Fourier Finite element method [8]. The implementation of the field and neuron parts in one Python package made it possible to adaptively estimate the neural activation extent based on the computed field solution and stimulation signal.…”

“…Different values for the dielectric properties of the volume conductor model compartments are employed to investigate the approximation quality for different cases of tissue heterogeneity in the target area. The dielectric properties are obtained from equation (3) using the parameters for white matter, grey matter, and cerebrospinal fluid from [17] at a frequency of 2 kHz, which constitutes a good approximation of the dispersive nature of the tissue properties for common DBS signals [8]. The corresponding conductivity values are approximately 0.064 Sm −1 for white matter, 0.103 Sm −1 for grey matter, and 2.000 Sm −1 for cerebrospinal fluid.…”

“…Computational models provide a possibility to estimate the stimulation impact by determining activated areas in the deep brain based on the given patient-specific parameters. The extent of neural activation, or the volume of tissue activated (VTA), is a common computational modeling approach to estimate the size of the activated tissue during DBS and has been applied in various computational studies in this area including homogeneous [5], rotationally symmetric [6], heterogeneous [7], [8], and anisotropic volume conductor models [9] of the human brain and deep brain target areas. In general, the approach is based on positioning a number of models of mammalian nerve fibers (axon models) in a grid located in a plane perpendicular to the electrode lead.…”

“…The field solution in the target area is commonly computed by creating a volume conductor model of the DBS electrode and the surrounding tissue. For solving the governing equations, which are typically the stationary current field or electro-quasistatic equation for DBS applications [7], [10], often commercial software solutions, such as COMSOL Multiphysics R (http://www.comsol.com) are used [5], [7], [8], [11], [12], [13], while, to our knowledge, no studies employing open-source solutions on the field model have been published in scientific journals yet. Regarding the coupling of the neuronal activation in axon models and the extracellular field distribution, a Python package with the purpose to compute the local field potentials for a given axon distribution of defined activation was presented in [14].…”

The Physical Axon : Modeling, Simulation and Electrode Evaluation

“…Martens' model, Model I, is described in Åström et al [10] with the specific intent of studying the maximum distance from a stimulation source that will trigger an AP. Model II is an established model created by McIntyre et al [6] and implemented by Schmidt [67] with a python scripts for data interfacing, and a bisecting test approach for activation distance to improve the processing efficiency. For this comparison, model inputs were set.…”