Computation of Activating Fields for Approximation of the Orientation-Specific Neural Response to Electrical Stimulation (original) (raw)
Related papers
IEEE Transactions on Biomedical Engineering, 2000
Deep brain stimulation (DBS) is an established therapy for movement disorders, but the fundamental mechanisms by which DBS has its effects remain unknown. Computational models can provide insights into the mechanisms of DBS, but to be useful, the models must have sufficient detail to predict accurately the electric fields produced by DBS. We used a finite element method model of the Medtronic 3387 electrode array, coupled to cable models of myelinated axons, to quantify how interpolation errors, electrode geometry, and the electrodetissue interface affect calculation of electrical potentials and stimulation thresholds for populations of model nerve fibers. Convergence of the potentials was not a sufficient criterion for ensuring the same degree of accuracy in subsequent determination of stimulation thresholds, because the accuracy of the stimulation thresholds depended on the order of the elements. Simplifying the 3387 electrode array by ignoring the inactive contacts and extending the terminated end of the shaft had position dependent effects on the potentials and excitation thresholds, and these simplifications may impact correlations between DBS parameters and clinical outcomes. When the current density in the bulk tissue is uniform, the effect of the electrode-tissue interface impedance could be approximated by filtering the potentials calculated with a static lumped electrical equivalent circuit. Further, for typical DBS parameters during voltage-regulated stimulation, it was valid to approximate the electrode as an ideal polarized electrode with a nonlinear capacitance. Validation of these computational considerations enables accurate modeling of the electric field produced by DBS.
Brain Stimulation, 2013
Transcranial stimulation encompasses all non-invasive brain stimulation techniques where electrical current is generated or induced in the brain for experimental or therapeutic purposes using scalp electrodes or magnetic coils. Each modality (e.g. transcranial current stimulation, cranial electrotherapy stimulation, transcranial magnetic stimulation, electroconvulsive therapy) produces a spatiotemporal pattern of electric current flow in the brain that then determines neurophysiological response. Due to the relatively large separation between electrode/coil and stimulated tissue, the target region is often in the "farfield" of the electric field. Thus, unlike stimulation with implanted electrodes, the gradient of the electric field is limited in the vicinity of the brain target. Computational models of transcranial stimulation predict brain current flow patterns for dose optimization. Translational animal models aim at elucidating the cellular mechanisms of neuromodulation. Here we identify and define a ubiquitous assumption underlying both computational and animal models, referred to herein as the "quasi-uniform assumption". Though we attempt to rationalize the biophysical plausibility for the quasi-uniform assumption based on the limited electric field gradients generated during stimulation, our goal is neither to justify nor repudiate it, but rather emphasize its implicit use in a majority of modeling and animal studies. The quasi-uniform assumption states that local polarization in a target region is proportional to the local electric field magnitude (EF): Polarization(target)∝EF(target). This assumption is not trivial because membrane polarization has long been linked to the change in electric field, via the so-called "activating function". However, it is well known that in a uniform electric field, where by definition the electric field gradient is zero, membrane compartments may polarize linearly with electric field (see below). The term "quasi-uniform" implies that the spatial gradient of electric field is locally negligible (within a brain region) to bring about changes in membrane polarization, and thus local membrane polarization is determined by electric field. The electric field may vary globally across brain regions, thus determining which targets are preferentially polarized. The general quasi-uniform assumption is that polarization is linear with electric field magnitude for each target with comparable sensitivity: Polarization(target)=αEF(target), where a is fixed across targets and EF is the local electric field at each target. The general assumption ignores regional differences in morphology, biophysics, and function, but may be a reasonable first approximation when considering cortex. Because any neuromodulation, and resulting cognitive/behavioral changes, are assumed to follow from membrane polarization, the extent of polarization indicates the probability of a region to be influenced by the stimulation. Certainly, "neuromodulation" encompasses a broad swath of potential acute and plastic changes, and is dependent not only on polarization but also endogenous factors such as ongoing (patho)physiological neuronal activity. Changes may even be non-monotonic with polarization level. Nonetheless, membrane polarization remains the only known biophysical mechanism of action for transcranial stimulation modalities.
Relationship between neural activation and electric field distribution during deep brain stimulation
IEEE transactions on bio-medical engineering, 2015
Models and simulations are commonly used to study deep brain stimulation (DBS). Simulated stimulation fields are often defined and visualized by electric field isolevels or volumes of tissue activated (VTA). The aim of the present study was to evaluate the relationship between stimulation field strength as defined by the electric potential V, the electric field E, and the divergence of the electric field ∇(2) V, and neural activation. Axon cable models were developed and coupled to finite-element DBS models in three-dimensional (3-D). Field thresholds ( VT , ET, and ∇(2) VT ) were derived at the location of activation for various stimulation amplitudes (1 to 5 V), pulse widths (30 to 120 μs), and axon diameters (2.0 to 7.5 μm). Results showed that thresholds for VT and ∇(2) VT were highly dependent on the stimulation amplitude while ET were approximately independent of the amplitude for large axons. The activation field strength thresholds presented in this study may be used in futu...
Fast simulation and optimization tool to explore selective neural stimulation
European Journal of Translational Myology, 2016
In functional electrical stimulation, selective stimulation of axons is desirable to activate a specific target, in particular muscular function. This implies to simulate a fascicule without activating neighboring ones i.e. to be spatially selective. Spatial selectivity is achieved by the use of multicontact cuff electrodes over which the stimulation current is distributed. Because of the large number of parameters involved, numerical simulations provide a way to find and optimize electrode configuration. The present work offers a computation effective scheme and associated tool chain capable of simulating electrode-nerve interface and find the best spread of current to achieve spatial selectivity.
Neural stimulation with magnetic fields: analysis of induced electric fields
IEEE Transactions on Biomedical Engineering, 1992
Spatial distributions of the derivative of the electric field induced in a planar semi-infinite tissue model by various current-carrying coils and their utility in neural stimulation are evaluated. Analytical expressions are obtained for the electric field and its spatial derivatives produced by an infinitely short current element. Fields and their derivatives for an arbitrarily shaped coil are then obtained by numerical summation of contributions from all the elements forming the coil. The simplicity of the solution and a very short computation time make this method particularly attractive for gaining a physical insight into the spatial behavior of the stimulating parameter and for the optimization of coils. Such analysis is useful as the first step before undertaking a more complex numerical analysis of a model more closely representing the tissue geometry and heterogeneity.
Progress In Electromagnetics Research, 2012
Deep brain stimulation (DBS) is a well-established treatment for Parkinson's disease, essential tremor and dystonia. It has also been successfully applied to treat various other neurological and psychiatric conditions including depression and obsessive-compulsive disorder. Numerous computational models, mostly based on the Finite Element Method (FEM) approach have been suggested to investigate the biophysical mechanisms of electromagnetic wave-tissue interaction during DBS. These models, although emphasizing the importance of various electrical and geometrical parameters, mostly have used simplified geometries over a tightly restricted tissue volume in the case of monopolar stimulation. In the present work we show that topological arrangements and geometrical properties of the model have a significant effect on the distribution of voltages in the concerned tissues. The results support reconsidering the current approach for modeling monopolar DBS which uses a restricted cubic area extended a few centimeters around the active electrode to predict the volume of activated tissue. We propose a new technique called multi-resolution FEM modeling, which may improve the accuracy of the prediction of volume of activated tissue and yet be computationally tractable on personal computers.
Journal of Neuroscience Methods, 2010
Please cite this article in press as: Yousif N, et al. Evaluating the impact of the deep brain stimulation induced electric field on subthalamic neurons: A computational modelling study. a b s t r a c t Deep brain stimulation (DBS) is an effective surgical treatment used to alleviate the symptoms of neurological disorders, most commonly movement disorders. However, the mechanism of how the applied stimulus pulses interact with the surrounding neuronal elements is not yet clearly understood, slowing progress and development of this promising therapeutic technology. To extend previous approaches of using isolated, myelinated axon models used to estimate the effect of DBS, we propose that taking into account entire neurons will reveal stimulation induced effects overlooked by previous studies. We compared the DBS induced volume of tissue activated (VTA) using arrays of whole cell models of subthalamic nucleus (STN) excitatory neurons consisting of a cell body and an anatomically accurate dendritic tree, to the common models of axon arrays. Our results demonstrate that STN neurons have a higher excitation threshold than axons, as stimulus amplitudes 10 times as large elicit a VTA range a fifth of the distance from the electrode surface. However, the STN neurons do show a change in background firing rate in response to stimulation, even when they are classified as sub-threshold by the VTA definition. Furthermore the whole neuron models are sensitive to regions of high current density, as the distribution of firing is centred on the electrode contact edges These results demonstrate the importance of accurate neuron models for fully appreciating the spatial effects of DBS on the immediate surrounding brain volume within small distances of the electrode, which are overlooked by previous models of isolated axons and individual neurons.
Journal of Neural Engineering, 2019
Objective.-We present a PNS oracle, which solves these computation time and linearity problems and is, therefore, well-suited for fast optimization of voltage distributions in contact electrode arrays and current drive patterns in non-contact magnetic coil arrays. Approach.-The PNS oracle metric for a nerve fiber is computed from an electric field map using only linear operations (projection, differentiation, convolution, scaling). Due to its linearity, this PNS metric can be precomputed for a set of coil or electrode segments, allowing rapid PNS prediction and comparison of any possible coil or electrode stimulation configuration constructed from this set. The PNS oracle is closely related to the classical activating function and modified driving functions but is adjusted to better correlate with full neurodynamic modeling of myelinated mammalian nerves. Main results.-We validated the PNS oracle in three MRI gradient coils and two body models and found good correlation between the PNS oracle and the full neurodynamic modeling approach (R 2 > 0.995). Finally, we demonstrated its potential utility by optimizing the driving currents and voltages of arrays of 108 magnetic coils or 108 contact electrodes to selectively stimulate target nerves in the lower leg. Significance.-Peripheral nerve stimulation (PNS) by electromagnetic fields can be accurately simulated using coupled electromagnetic and neurodynamic modeling. Such simulations are slow and non-linear in the electric field, which makes it difficult to iteratively optimize coil and 6
Tissue heterogeneity as a mechanism for localized neural stimulation by applied electric fields
Physics in Medicine and Biology, 2007
We investigate the heterogeneity of electrical conductivity as a new mechanism to stimulate excitable tissues via applied electric fields. In particular, we show that stimulation of axons crossing internal boundaries can occur at boundaries where the electric conductivity of the volume conductor changes abruptly. The effectiveness of this and other stimulation mechanisms was compared by means of models and computer simulations in the context of transcranial magnetic stimulation. While, for a given stimulation intensity, the largest membrane depolarization occurred where an axon terminates or bends sharply in a high electric field region, a slightly smaller membrane depolarization, still sufficient to generate action potentials, also occurred at an internal boundary where the conductivity jumped from 0.143 S m −1 to 0.333 S m −1 , simulating a whitematter-grey-matter interface. Tissue heterogeneity can also give rise to local electric field gradients that are considerably stronger and more focal than those impressed by the stimulation coil and that can affect the membrane potential, albeit to a lesser extent than the two mechanisms mentioned above. Tissue heterogeneity may play an important role in electric and magnetic 'far-field' stimulation.
A Novel Electrode Array for Diameter-Dependent Control of Axonal Excitability: A Simulation Study
IEEE Transactions on Biomedical Engineering, 2004
Electrical extracellular stimulation of peripheral nerve activates the large-diameter motor fibers before the small ones, a recruitment order opposite the physiological recruitment of myelinated motor fibers during voluntary muscle contraction. Current methods to solve this problem require a long-duration stimulus pulse which could lead to electrode corrosion and nerve damage. The hypothesis that the excitability of specific diameter fibers can be suppressed by reshaping the profile of extracellular potential along the axon using multiple electrodes is tested using computer simulations in two different volume conductors. Simulations in a homogenous medium with a nine-contact electrode array show that the current excitation threshold (th) of large diameter axons (13-17 m) (0.6-3.0 mA) is higher than that of small-diameter axons (2-7 m) (0.4-0.7 mA) with 200-m axon-electrode distance and 10-s stimulus pulse. The electrode array is also tested in a three-dimensional finite-element model of the sacral root model of dog (ventral root of S3). A single cathode activates large-diameter axons before activating small axons. However, a nine-electrode array activates 50% of small axons while recruiting only 10% of large ones and activates 90% of small axons while recruiting only 50% of large ones. The simulations suggest that the near-physiological recruitment order can be achieved with an electrode array. The diameter selectivity of the electrode array can be controlled by the electrode separation and the method is independent of pulse width. Index Terms-Neural prostheses, recruitment order, selective neural stimulation. I. INTRODUCTION T HE goal of functional electrical stimulation (FES) research is to develop systems capable of restoring function in patients with neurological deficits by stimulating nerve and muscles. Several types of electrodes have been developed for this purpose, e.g., intramuscular [1], epimysial [2], intraneural [3], and epineural electrodes [4]. Each has its own advantages and disadvantages depending on the specific application. The ideal neural stimulation should have the following features: 1) axon-diameter selectivity; 2) spatial selectivity; 3) minimal charge injection; and 4) biocompatibility. Conventional neural stimulation methods activate larger motor units before smaller ones [5], a recruitment order opposite the Manuscript