Effect of dispersive conductivity and permittivity in volume conductor models of deep brain stimulation

Quasistatic approximation in neuromodulation

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuromodulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g. Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

Nonlinear effects at the electrode-tissue interface of deep brain stimulation electrodes

Objective.The electrode-tissue interface provides the critical path for charge transfer in neurostimulation therapies and exhibits well-established nonlinear properties at high applied currents or voltages. These nonlinear properties may influence the efficacy and safety of applied stimulation but are typically neglected in computational models. In this study, nonlinear behavior of the electrode-tissue interface impedance was incorporated in a computational model of deep brain stimulation (DBS) to simulate the impact on neural activation and safety considerations.Approach.Nonlinear electrode-tissue interface properties were incorporated in a finite element model of DBS electrodesin vitroandin vivo,in the rat subthalamic nucleus, using an iterative approach. The transition point from linear to nonlinear behavior was determined for voltage and current-controlled stimulation. Predicted levels of neural activation during DBS were examined and the region of linear operation of the electrode was compared with the Shannon safety limit.Main results.A clear transition of the electrode-tissue interface impedance to nonlinear behavior was observed for both current and voltage-controlled stimulation. The transition occurred at lower values of activation overpotential for simulatedin vivothanin vitroconditions (91 mV and 165 mV respectively for current-controlled stimulation; 110 mV and 275 mV for voltage-controlled stimulation), corresponding to an applied current of 30μA and 45μA, or voltage of 330 mV at 1 kHz. The onset of nonlinearity occurred at lower values of the overpotential as frequency was increased. Incorporation of nonlinear properties resulted in activation of a higher proportion of neurons under voltage-controlled stimulation. Under current-controlled stimulation, the predicted transition to nonlinear behavior and Faradaic charge transfer at stimulation amplitudes of 30μA, corresponds to a charge density of 2.29μC cm-2and charge of 1.8 nC, well-below the Shannon safety limit.Significance.The results indicate that DBS electrodes may operate within the nonlinear region at clinically relevant stimulation amplitudes. This affects the extent of neural activation under voltage-controlled stimulation and the transition to Faradaic charge transfer for both voltage- and current-controlled stimulation with important implications for targeting of neural populations and the design of safe stimulation protocols.

Towards a more accurate quasi-static approximation of the electric potential for neurostimulation with kilohertz-frequency sources. J Neural Eng 2023;20:10.1088/1741-2552/ad1612. [PMID: 38100821 PMCID: PMC10822676 DOI: 10.1088/1741-2552/ad1612]

Objective.Our goal was to determine the conditions for which a more precise calculation of the electric potential than the quasi-static approximation may be needed in models of electrical neurostimulation, particularly for signals with kilohertz-frequency components.Approach.We conducted a comprehensive quantitative study of the differences in nerve fiber activation and conduction block when using the quasi-static and Helmholtz approximations for the electric potential in a model of electrical neurostimulation.Main results.We first show that the potentials generated by sources of unbalanced pulses exhibit different transients as compared to those of charge-balanced pulses, and this is disregarded by the quasi-static assumption. Secondly, relative errors for current-distance curves were below 3%, while for strength-duration curves these ranged between 1%-17%, but could be improved to less than 3% across the range of pulse duration by providing a corrected quasi-static conductivity. Third, we extended our analysis to trains of pulses and reported a 'congruence area' below 700 Hz, where the fidelity of fiber responses is maximal for supra-threshold stimulation. Further examination of waveforms and polarities revealed similar fidelities in the congruence area, but significant differences were observed beyond this area. However, the spike-train distance revealed differences in activation patterns when comparing the response generated by each model. Finally, in simulations of conduction-block, we found that block thresholds exhibited errors above 20% for repetition rates above 10 kHz. Yet, employing a corrected value of the conductivity improved the agreement between models, with errors no greater than 8%.Significance.Our results emphasize that the quasi-static approximation cannot be naively extended to electrical stimulation with high-frequency components, and notable differences can be observed in activation patterns. As well, we introduce a methodology to obtain more precise model responses using the quasi-static approach, retaining its simplicity, which can be a valuable resource in computational neuroengineering.

Organic Neuroelectronics: From Neural Interfaces to Neuroprosthetics

Requirements and recent advances in research on organic neuroelectronics are outlined herein. Neuroelectronics such as neural interfaces and neuroprosthetics provide a promising approach to diagnose and treat neurological diseases. However, the current neural interfaces are rigid and not biocompatible, so they induce an immune response and deterioration of neural signal transmission. Organic materials are promising candidates for neural interfaces, due to their mechanical softness, excellent electrochemical properties, and biocompatibility. Also, organic nervetronics, which mimics functional properties of the biological nerve system, is being developed to overcome the limitations of the complex and energy-consuming conventional neuroprosthetics that limit long-term implantation and daily-life usage. Examples of organic materials for neural interfaces and neural signal recordings are reviewed, recent advances of organic nervetronics that use organic artificial synapses are highlighted, and then further requirements for neuroprosthetics are discussed. Finally, the future challenges that must be overcome to achieve ideal organic neuroelectronics for next-generation neuroprosthetics are discussed.

Linking profiles of pathway activation with clinical motor improvements - A retrospective computational study

BACKGROUND

Deep brain stimulation (DBS) is an established therapy for patients with Parkinson's disease. In silico computer models for DBS hold the potential to inform a selection of stimulation parameters. In recent years, the focus has shifted towards DBS-induced firing in myelinated axons, deemed particularly relevant for the external modulation of neural activity.

OBJECTIVE

The aim of this project was to investigate correlations between patient-specific pathway activation profiles and clinical motor improvement.

METHODS

We used the concept of pathway activation modeling, which incorporates advanced volume conductor models and anatomically authentic fiber trajectories to estimate DBS-induced action potential initiation in anatomically plausible pathways that traverse in close proximity to targeted nuclei. We applied the method on two retrospective datasets of DBS patients, whose clinical improvement had been evaluated according to the motor part of the Unified Parkinson's Disease Rating Scale. Based on differences in outcome and activation levels for intrapatient DBS protocols in a training cohort, we derived a pathway activation profile that theoretically induces a complete alleviation of symptoms described by UPDRS-III. The profile was further enhanced by analyzing the importance of matching activation levels for individual pathways.

RESULTS

The obtained profile emphasized the importance of activation in pathways descending from the motor-relevant cortical regions as well as the pallidothalamic pathways. The degree of similarity of patient-specific profiles to the optimal profile significantly correlated with clinical motor improvement in a test cohort.

CONCLUSION

Pathway activation modeling has a translational utility in the context of motor symptom alleviation in Parkinson's patients treated with DBS.

Stimulation-induced changes at the electrode-tissue interface and their influence on deep brain stimulation

OBJECTIVE

During deep brain stimulation (DBS) the electrode-tissue interface forms a critical path between device and brain tissue. Although changes in the electrical double layer and glial scar can impact stimulation efficacy, the effects of chronic DBS on the electrode-tissue interface have not yet been established.

APPROACH

In this study, we characterised the electrode-tissue interface surrounding chronically implanted DBS electrodes in rats and compared the impedance and histological properties at the electrode interface in animals that received daily stimulation and in those where no stimulation was applied, up to eight weeks post-surgery. A computational model was developed based on the experimental data, which allowed the dispersive electrical properties of the surrounding encapsulation tissue to be estimated. The model was then used to study the effect of stimulation-induced changes in the electrode-tissue interface on the electric field and neural activation during voltage- and current-controlled stimulation.

MAIN RESULTS

Incorporating the observed changes in simulations in silico, we estimated the frequency-dependent dielectric properties of the electrical double layer and surrounding encapsulation tissue. Through simulations we show how stimulation-induced changes in the properties of the electrode-tissue interface influence the electric field and alter neural activation during voltage-controlled stimulation. A substantial increase in the number of stimulated collaterals, and their distance from the electrode, was observed during voltage-controlled stimulation with stimulated ETI properties. In vitro examination of stimulated electrodes confirmed that high frequency stimulation leads to desorption of proteins at the electrode interface, with a concomitant reduction in impedance.

SIGNIFICANCE

The demonstration of stimulation-induced changes in the electrode-tissue interface has important implications for future DBS systems including closed-loop systems where the applied stimulation may change over time. Understanding these changes is particularly important for systems incorporating simultaneous stimulation and sensing, which interact dynamically with brain networks.

A finite element method framework to model extracellular neural stimulation

OBJECTIVE

Increasing complexity in extracellular stimulation experiments and neural implant design also requires realistic computer simulations capable of modeling the neural activity of nerve cells under the influence of an electrical stimulus. Classical model approaches are often based on simplifications, are not able to correctly calculate the electric field generated by complex electrode designs, and do not consider electrical effects of the cell on its surrounding. A more accurate approach is the finite element method (FEM), which provides necessary techniques to solve the Poisson equation for complex geometries under consideration of electrical tissue properties. Especially in situations where neurons experience large and non-symmetric extracellular potential gradients, a FEM solution that implements the cell membrane model can improve the computer simulation results. To investigate the response of neurons in an electric field generated by complex electrode designs, a FEM framework for extracellular stimulation was developed in COMSOL.

APPROACH

Methods to implement morphologically- and biophysically-detailed neurons including active Hodgkin-Huxley (HH) cell membrane dynamics as well as the stimulation setup are described in detail. Covered methods are (i) development of cell and electrode geometries including meshing strategies, (ii) assignment of physics for the conducting spaces and the realization of active electrodes, (iii) implementation of the HH model, and (iv) coupling of the physics to get a fully described model.

MAIN RESULTS

Several implementation examples are briefly presented: (i) a full FEM implementation of a HH model cell stimulated with a honeycomb electrode, (ii) the electric field of a cochlear electrode placed inside the cochlea, and (iii) a proof of concept implementation of a detailed double-cable cell membrane model for myelinated nerve fibers.

SIGNIFICANCE

The presented concepts and methods provide basic and advanced techniques to realize a full FEM framework for innovative studies of neural excitation in response to extracellular stimulation.

Deep brain stimulation electrode modeling in rats

Deep Brain Stimulation (DBS) is an efficacious treatment option for an increasing range of brain disorders. To enhance our knowledge about the mechanisms of action of DBS and to probe novel targets, basic research in animal models with DBS is an essential research base. Beyond nonhuman primate, pig, and mouse models, the rat is a widely used animal model for probing DBS effects in basic research. Reconstructing DBS electrode placement after surgery is crucial to associate observed effects with modulating a specific target structure. Post-mortem histology is a commonly used method for reconstructing the electrode location. In humans, however, neuroimaging-based electrode localizations have become established. For this reason, we adapt the open-source software pipeline Lead-DBS for DBS electrode localizations from humans to the rat model. We validate our localization results by inter-rater concordance and a comparison with the conventional histological method. Finally, using the open-source software pipeline OSS-DBS, we demonstrate the subject-specific simulation of the VTA and the activation of axon models aligned to pathways representing neuronal fibers, also known as the pathway activation model. Both activation models yield a characterization of the impact of DBS on the target area. Our results suggest that the proposed neuroimaging-based method can precisely localize DBS electrode placements that are essentially rater-independent and yield results comparable to the histological gold standard. The advantages of neuroimaging-based electrode localizations are the possibility of acquiring them in vivo and combining electrode reconstructions with advanced imaging metrics, such as those obtained from diffusion or functional magnetic resonance imaging (MRI). This paper introduces a freely available open-source pipeline for DBS electrode reconstructions in rats. The presented initial validation results are promising.

Atlas-independent, N-of-1 tissue activation modeling to map optimal regions of subthalamic deep brain stimulation for Parkinson disease

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Neuroanatomical variations among patients are obscured in atlas-based VTA modeling.

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N-of-1 neuroanatomical and VTA modeling enables patient-level precision.

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Mean optimal stimulation is dorsomedial to the STN, near its posterior half.

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Individual VTAs deviate from optimal stimulation sites to varying degrees.

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Optimal stimulation sites for rigidity, bradykinesia, and tremor partially overlap.

Background

Motor outcomes after subthalamic deep brain stimulation (STN DBS) for Parkinson disease (PD) vary considerably among patients and strongly depend on stimulation location. The objective of this retrospective study was to map the regions of optimal STN DBS for PD using an atlas-independent, fully individualized (N-of-1) tissue activation modeling approach and to assess the relationship between patient-level therapeutic volumes of tissue activation (VTAs) and motor improvement.

Methods

The stimulation-induced electric field for 40 PD patients treated with bilateral STN DBS was modeled using finite element analysis. Neurostimulation models were generated for each patient, incorporating their individual STN anatomy, DBS lead position and orientation, anisotropic tissue conductivity, and clinical stimulation settings. A voxel-based analysis of the VTAs was then used to map the optimal location of stimulation. The amount of stimulation in specific regions relative to the STN was measured and compared between STNs with more and less optimal stimulation, as determined by their motor improvement scores and VTA. The relationship between VTA location and motor outcome was then assessed using correlation analysis. Patient variability in terms of STN anatomy, active contact position, and VTA location were also evaluated. Results from the N-of-1 model were compared to those from a simplified VTA model.

Results

Tissue activation modeling mapped the optimal location of stimulation to regions medial, posterior, and dorsal to the STN centroid. These regions extended beyond the STN boundary towards the caudal zona incerta (cZI). The location of the VTA and active contact position differed significantly between STNs with more and less optimal stimulation in the dorsal-ventral and anterior-posterior directions. Therapeutic stimulation spread noticeably more in the dorsal and posterior directions, providing additional evidence for cZI as an important DBS target. There were significant linear relationships between the amount of dorsal and posterior stimulation, as measured by the VTA, and motor improvement. These relationships were more robust than those between active contact position and motor improvement. There was high variability in STN anatomy, active contact position, and VTA location among patients. Spherical VTA modeling was unable to reproduce these results and tended to overestimate the size of the VTA.

Conclusion

Accurate characterization of the spread of stimulation is needed to optimize STN DBS for PD. High variability in neuroanatomy, stimulation location, and motor improvement among patients highlights the need for individualized modeling techniques. The atlas-independent, N-of-1 tissue activation modeling approach presented in this study can be used to develop and evaluate stimulation strategies to improve clinical outcomes on an individual basis.

FEMfuns: A Volume Conduction Modeling Pipeline that Includes Resistive, Capacitive or Dispersive Tissue and Electrodes

Applications such as brain computer interfaces require recordings of relevant neuronal population activity with high precision, for example, with electrocorticography (ECoG) grids. In order to achieve this, both the placement of the electrode grid on the cortex and the electrode properties, such as the electrode size and material, need to be optimized. For this purpose, it is essential to have a reliable tool that is able to simulate the extracellular potential, i.e., to solve the so-called ECoG forward problem, and to incorporate the properties of the electrodes explicitly in the model. In this study, this need is addressed by introducing the first open-source pipeline, FEMfuns (finite element method for useful neuroscience simulations), that allows neuroscientists to solve the forward problem in a variety of different geometrical domains, including different types of source models and electrode properties, such as resistive and capacitive materials. FEMfuns is based on the finite element method (FEM) implemented in FEniCS and includes the geometry tessellation, several electrode-electrolyte implementations and adaptive refinement options. The Python code of the pipeline is available under the GNU General Public License version 3 at https://github.com/meronvermaas/FEMfuns . We tested our pipeline with several geometries and source configurations such as a dipolar source in a multi-layer sphere model and a five-compartment realistically-shaped head model. Furthermore, we describe the main scripts in the pipeline, illustrating its flexible and versatile use. Provided with a sufficiently fine tessellation, the numerical solution of the forward problem approximates the analytical solution. Furthermore, we show dispersive material and interface effects in line with previous literature. Our results indicate substantial capacitive and dispersive effects due to the electrode-electrolyte interface when using stimulating electrodes. The results demonstrate that the pipeline presented in this paper is an accurate and flexible tool to simulate signals generated on electrode grids by the spatiotemporal electrical activity patterns produced by sources and thereby allows the user to optimize grids for brain computer interfaces including exploration of alternative electrode materials/properties.

OSS-DBS: Open-source simulation platform for deep brain stimulation with a comprehensive automated modeling

In this study, we propose a new open-source simulation platform that comprises computer-aided design and computer-aided engineering tools for highly automated evaluation of electric field distribution and neural activation during Deep Brain Stimulation (DBS). It will be shown how a Volume Conductor Model (VCM) is constructed and examined using Python-controlled algorithms for generation, discretization and adaptive mesh refinement of the computational domain, as well as for incorporation of heterogeneous and anisotropic properties of the tissue and allocation of neuron models. The utilization of the platform is facilitated by a collection of predefined input setups and quick visualization routines. The accuracy of a VCM, created and optimized by the platform, was estimated by comparison with a commercial software. The results demonstrate no significant deviation between the models in the electric potential distribution. A qualitative estimation of different physics for the VCM shows an agreement with previous computational studies. The proposed computational platform is suitable for an accurate estimation of electric fields during DBS in scientific modeling studies. In future, we intend to acquire SDA and EMA approval. Successful incorporation of open-source software, controlled by in-house developed algorithms, provides a highly automated solution. The platform allows for optimization and uncertainty quantification (UQ) studies, while employment of the open-source software facilitates accessibility and reproducibility of simulations.

Influence of Patient-Specific Head Modeling on EEG Source Imaging

Electromagnetic source imaging (ESI) techniques have become one of the most common alternatives for understanding cognitive processes in the human brain and for guiding possible therapies for neurological diseases. However, ESI accuracy strongly depends on the forward model capabilities to accurately describe the subject's head anatomy from the available structural data. Attempting to improve the ESI performance, we enhance the brain structure model within the individual-defined forward problem formulation, combining the head geometry complexity of the modeled tissue compartments and the prior knowledge of the brain tissue morphology. We validate the proposed methodology using 25 subjects, from which a set of magnetic-resonance imaging scans is acquired, extracting the anatomical priors and an electroencephalography signal set needed for validating the ESI scenarios. Obtained results confirm that incorporating patient-specific head models enhances the performed accuracy and improves the localization of focal and deep sources.

Simulation of Closed-Loop Deep Brain Stimulation Control Schemes for Suppression of Pathological Beta Oscillations in Parkinson's Disease

This study presents a computational model of closed-loop control of deep brain stimulation (DBS) for Parkinson's disease (PD) to investigate clinically viable control schemes for suppressing pathological beta-band activity. Closed-loop DBS for PD has shown promising results in preliminary clinical studies and offers the potential to achieve better control of patient symptoms and side effects with lower power consumption than conventional open-loop DBS. However, extensive testing of algorithms in patients is difficult. The model presented provides a means to explore a range of control algorithms in silico and optimize control parameters before preclinical testing. The model incorporates (i) the extracellular DBS electric field, (ii) antidromic and orthodromic activation of STN afferent fibers, (iii) the LFP detected at non-stimulating contacts on the DBS electrode and (iv) temporal variation of network beta-band activity within the thalamo-cortico-basal ganglia loop. The performance of on-off and dual-threshold controllers for suppressing beta-band activity by modulating the DBS amplitude were first verified, showing levels of beta suppression and reductions in power consumption comparable with previous clinical studies. Proportional (P) and proportional-integral (PI) closed-loop controllers for amplitude and frequency modulation were then investigated. A simple tuning rule was derived for selecting effective PI controller parameters to target long duration beta bursts while respecting clinical constraints that limit the rate of change of stimulation parameters. Of the controllers tested, PI controllers displayed superior performance for regulating network beta-band activity whilst accounting for clinical considerations. Proportional controllers resulted in undesirable rapid fluctuations of the DBS parameters which may exceed clinically tolerable rate limits. Overall, the PI controller for modulating DBS frequency performed best, reducing the mean error by 83% compared to DBS off and the mean power consumed to 25% of that utilized by open-loop DBS. The network model presented captures sufficient physiological detail to act as a surrogate for preclinical testing of closed-loop DBS algorithms using a clinically accessible biomarker, providing a first step for deriving and testing novel, clinically suitable closed-loop DBS controllers.

Estimation of dispersive properties of encapsulation tissue surrounding deep brain stimulation electrodes in the rat

The aim of this study was to estimate the electrical properties of the encapsulation tissue surrounding chronically implanted electrodes for deep brain stimulation in the rat. The impedance spectrum of a concentric bipolar microelectrode implanted in the rat brain was measured immediately following surgery and after 8 weeks of implantation. The experimental impedance data were used in combination with a finite element model of the rat brain using a parametric sweep method to estimate the electrical properties of the tissue surrounding the electrode in acute and chronic conditions. In the acute case, the conductivity and relative permittivity of the peri-electrode space were frequency independent with an estimated conductivity of 0.38 S/m and relative permittivity of 123. The electrical properties of the encapsulation tissue in the chronic condition were fitted to a dispersive Cole-Cole model. The estimated conductivity and relative permittivity in the chronic condition at 1 kHz were 0.028 S/m and 2×10⁵, respectively. The estimated tissue properties can be used in combination with computational modeling as a basis for optimization of chronically implanted electrodes to increase the efficacy of long-term neural recording and stimulation.

Deep Brain Stimulation Programming for Movement Disorders: Current Concepts and Evidence-Based Strategies

Deep brain stimulation (DBS) has become the treatment of choice for advanced stages of Parkinson's disease, medically intractable essential tremor, and complicated segmental and generalized dystonia. In addition to accurate electrode placement in the target area, effective programming of DBS devices is considered the most important factor for the individual outcome after DBS. Programming of the implanted pulse generator (IPG) is the only modifiable factor once DBS leads have been implanted and it becomes even more relevant in cases in which the electrodes are located at the border of the intended target structure and when side effects become challenging. At present, adjusting stimulation parameters depends to a large extent on personal experience. Based on a comprehensive literature search, we here summarize previous studies that examined the significance of distinct stimulation strategies for ameliorating disease signs and symptoms. We assess the effect of adjusting the stimulus amplitude (A), frequency (f), and pulse width (pw) on clinical symptoms and examine more recent techniques for modulating neuronal elements by electrical stimulation, such as interleaving (Medtronic®) or directional current steering (Boston Scientific®, Abbott®). We thus provide an evidence-based strategy for achieving the best clinical effect with different disorders and avoiding adverse effects in DBS of the subthalamic nucleus (STN), the ventro-intermedius nucleus (VIM), and the globus pallidus internus (GPi).

Implantable Direct Current Neural Modulation: Theory, Feasibility, and Efficacy

Implantable neuroprostheses such as cochlear implants, deep brain stimulators, spinal cord stimulators, and retinal implants use charge-balanced alternating current (AC) pulses to recover delivered charge and thus mitigate toxicity from electrochemical reactions occurring at the metal-tissue interface. At low pulse rates, these short duration pulses have the effect of evoking spikes in neural tissue in a phase-locked fashion. When the therapeutic goal is to suppress neural activity, implants typically work indirectly by delivering excitation to populations of neurons that then inhibit the target neurons, or by delivering very high pulse rates that suffer from a number of undesirable side effects. Direct current (DC) neural modulation is an alternative methodology that can directly modulate extracellular membrane potential. This neuromodulation paradigm can excite or inhibit neurons in a graded fashion while maintaining their stochastic firing patterns. DC can also sensitize or desensitize neurons to input. When applied to a population of neurons, DC can modulate synaptic connectivity. Because DC delivered to metal electrodes inherently violates safe charge injection criteria, its use has not been explored for practical applicability of DC-based neural implants. Recently, several new technologies and strategies have been proposed that address this safety criteria and deliver ionic-based direct current (iDC). This, along with the increased understanding of the mechanisms behind the transcutaneous DC-based modulation of neural targets, has caused a resurgence of interest in the interaction between iDC and neural tissue both in the central and the peripheral nervous system. In this review we assess the feasibility of in-vivo iDC delivery as a form of neural modulation. We present the current understanding of DC/neural interaction. We explore the different design methodologies and technologies that attempt to safely deliver iDC to neural tissue and assess the scope of application for direct current modulation as a form of neuroprosthetic treatment in disease. Finally, we examine the safety implications of long duration iDC delivery. We conclude that DC-based neural implants are a promising new modulation technology that could benefit from further chronic safety assessments and a better understanding of the basic biological and biophysical mechanisms that underpin DC-mediated neural modulation.

Optimization-Based Contact Fault Alleviation in Deep Brain Stimulation Leads

Deep brain stimulation (DBS) is a neurosurgical treatment in, e.g., Parkinson's Disease. Electrical stimulation in DBS is delivered to a certain target through electrodes implanted into the brain. Recent developments aiming at better stimulation target coverage and lesser side effects have led to an increase in the number of contacts in a DBS lead as well as higher hardware complexity. This paper proposes an optimization-based approach to alleviation of the fault impact on the resulting therapeutical effect in field steering DBS. Faulty contacts could be an issue given recent trends of increasing number of contacts in DBS leads. Hence, a fault detection/alleviation scheme, such as the one proposed in this paper, is necessary ensure resilience in the chronic stimulation. Two alternatives are considered and compared with the stimulation prior to the fault: one using higher amplitudes on the remaining contacts and another with alleviating contacts in the neighborhood of the faulty one. Satisfactory compensation for a faulty contact can be achieved in both ways. However, to designate alleviating contacts, a model-based optimization procedure is necessary. Results suggest that stimulating with more contacts yields configurations that are more robust to contact faults, though with reduced selectivity.

Simplified parametric models of the dielectric properties of brain and muscle tissue during electrical stimulation

Parametric models are commonly used to describe the dispersive dielectric properties of biological tissues. While distinct regions of dispersion have been identified, the relative contribution of each during electrical stimulation is unknown. This study quantified the contribution of individual poles in parametric models of brain and muscle dielectric properties during electrical stimulation. The effect on the extracellular voltage waveform and threshold current for nerve stimulation of selectively removing subsets of poles from Cole-Cole and Debye models was examined. Errors were introduced when dispersions below 100 kHz were removed in both brain and muscle tissue. Poles below 1 kHz influenced the amplitude of the extracellular voltage waveform and the predicted minimum stimulation current. Poles between 1 kHz and 100 kHz influenced the waveform shape, with a minor effect on stimulus amplitude. The results confirm that low frequency dispersion in conductivity and permittivity can fundamentally influence the electric field and neural response during stimulation and provide insight into the relative contribution of the different dispersive regimes. Furthermore, they provide justification for for simplifying parametric models of dielectric properties through the removal of high frequency poles above 100 kHz which could improve the efficiency of time-domain solvers for simulations involving time-varying or aperiodic stimuli as may be required for certain closed-loop stimulation paradigms.

Hydrogel bioelectronics

Hydrogels have emerged as a promising bioelectronic interfacing material. This review discusses the fundamentals and recent advances in hydrogel bioelectronics.

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

OBJECTIVE

The aim of this study is to propose an adaptive scheme embedded into an open-source environment for the estimation of the neural activation extent during deep brain stimulation and to investigate the feasibility of approximating the neural activation extent by thresholds of the field solution.

METHODS

Open-source solutions for solving the field equation in volume conductor models of deep brain stimulation and computing the neural activation are embedded into a Python package to estimate the neural activation dependent on the dielectric tissue properties and axon parameters by employing a spatially adaptive scheme. Feasibility of the approximation of the neural activation extent by field thresholds is investigated to further reduce the computational expense.

RESULTS

The varying extents of neural activation for different patient-specific dielectric properties were estimated with the adaptive scheme. The results revealed the strong influence of the dielectric properties of the encapsulation layer in the acute and chronic phase after surgery. The computational time required to determine the neural activation extent in each studied model case was substantially reduced.

CONCLUSION

The neural activation extent is altered by patient-specific parameters. Threshold values of the electric potential and electric field norm facilitate a computationally efficient method to estimate the neural activation extent.

SIGNIFICANCE

The presented adaptive scheme is able to robustly determine neural activation extents and field threshold estimates for varying dielectric tissue properties and axon diameters while substantially reducing the computational expense.

Uncertainty Quantification of Oscillation Suppression During DBS in a Coupled Finite Element and Network Model

Models of the cortico-basal ganglia network and volume conductor models of the brain can provide insight into the mechanisms of action of deep brain stimulation (DBS). In this study, the coupling of a network model, under parkinsonian conditions, to the extracellular field distribution obtained from a three dimensional finite element model of a rodent's brain during DBS is presented. This coupled model is used to investigate the influence of uncertainty in the electrical properties of brain tissue and encapsulation tissue, formed around the electrode after implantation, on the suppression of oscillatory neural activity during DBS. The resulting uncertainty in this effect of DBS on the network activity is quantified using a computationally efficient and non-intrusive stochastic approach based on the generalized Polynomial Chaos. The results suggest that variations in the electrical properties of brain tissue may have a substantial influence on the level of suppression of oscillatory activity during DBS. Applying a global sensitivity analysis on the suppression of the simulated oscillatory activity showed that the influence of uncertainty in the electrical properties of the encapsulation tissue had only a minor influence, in agreement with previous experimental and computational studies investigating the mechanisms of current-controlled DBS in the literature.

Time resolved dosimetry of human brain exposed to low frequency pulsed magnetic fields

An accurate dosimetry is a key issue to understanding brain stimulation and related interaction mechanisms with neuronal tissues at the basis of the increasing amount of literature revealing the effects on human brain induced by low-level, low frequency pulsed magnetic fields (PMFs). Most literature on brain dosimetry estimates the maximum E field value reached inside the tissue without considering its time pattern or tissue dispersivity. Nevertheless a time-resolved dosimetry, accounting for dispersive tissues behavior, becomes necessary considering that the threshold for an effect onset may vary depending on the pulse waveform and that tissues may filter the applied stimulatory fields altering the predicted stimulatory waveform's size and shape. In this paper a time-resolved dosimetry has been applied on a realistic brain model exposed to the signal presented in Capone et al (2009 J. Neural Transm. 116 257-65), accounting for the broadband dispersivity of brain tissues up to several kHz, to accurately reconstruct electric field and current density waveforms inside different brain tissues. The results obtained by exposing the Duke's brain model to this PMF signal show that the E peak in the brain is considerably underestimated if a simple monochromatic dosimetry is carried out at the pulse repetition frequency of 75 Hz.

Analyzing the tradeoff between electrical complexity and accuracy in patient-specific computational models of deep brain stimulation

OBJECTIVE

Deep brain stimulation (DBS) is an adjunctive therapy that is effective in treating movement disorders and shows promise for treating psychiatric disorders. Computational models of DBS have begun to be utilized as tools to optimize the therapy. Despite advancements in the anatomical accuracy of these models, there is still uncertainty as to what level of electrical complexity is adequate for modeling the electric field in the brain and the subsequent neural response to the stimulation.

APPROACH

We used magnetic resonance images to create an image-based computational model of subthalamic DBS. The complexity of the volume conductor model was increased by incrementally including heterogeneity, anisotropy, and dielectric dispersion in the electrical properties of the brain. We quantified changes in the load of the electrode, the electric potential distribution, and stimulation thresholds of descending corticofugal (DCF) axon models.

MAIN RESULTS

Incorporation of heterogeneity altered the electric potentials and subsequent stimulation thresholds, but to a lesser degree than incorporation of anisotropy. Additionally, the results were sensitive to the choice of method for defining anisotropy, with stimulation thresholds of DCF axons changing by as much as 190%. Typical approaches for defining anisotropy underestimate the expected load of the stimulation electrode, which led to underestimation of the extent of stimulation. More accurate predictions of the electrode load were achieved with alternative approaches for defining anisotropy. The effects of dielectric dispersion were small compared to the effects of heterogeneity and anisotropy.

SIGNIFICANCE

The results of this study help delineate the level of detail that is required to accurately model electric fields generated by DBS electrodes.

Numerical characterization of intraoperative and chronic electrodes in deep brain stimulation

An intraoperative electrode (microelectrode) is used in the deep brain stimulation (DBS) technique to pinpoint the brain target and to choose the best parameters for the electrical stimulus. However, when the intraoperative electrode is replaced with the chronic one (macroelectrode), the observed effects do not always coincide with predictions. To investigate the causes of such discrepancies, a 3D model of the basal ganglia has been considered and realistic models of both intraoperative and chronic electrodes have been developed and numerically solved. Results of simulations of the electric potential (V) and the activating function (AF) along neuronal fibers show that the different geometries and sizes of the two electrodes do not change the distributions and polarities of these functions, but rather the amplitudes. This effect is similar to the one produced by the presence of different tissue layers (edema or glial tissue) in the peri-electrode space. Conversely, an inaccurate positioning of the chronic electrode with respect to the intraoperative one (electric centers not coincident) may induce a completely different electric stimulation in some groups of fibers.

Volume conductor model of transcutaneous electrical stimulation with kilohertz signals

OBJECTIVE

Incorporating high-frequency components in transcutaneous electrical stimulation (TES) waveforms may make it possible to stimulate deeper nerve fibers since the impedance of tissue declines with increasing frequency. However, the mechanisms of high-frequency TES remain largely unexplored. We investigated the properties of TES with frequencies beyond those typically used in neural stimulation.

APPROACH

We implemented a multilayer volume conductor model including dispersion and capacitive effects, coupled to a cable model of a nerve fiber. We simulated voltage- and current-controlled transcutaneous stimulation, and quantified the effects of frequency on the distribution of potentials and fiber excitation. We also quantified the effects of a novel transdermal amplitude modulated signal (TAMS) consisting of a non-zero offset sinusoidal carrier modulated by a square-pulse train.

MAIN RESULTS

The model revealed that high-frequency signals generated larger potentials at depth than did low frequencies, but this did not translate into lower stimulation thresholds. Both TAMS and conventional rectangular pulses activated more superficial fibers in addition to the deeper, target fibers, and at no frequency did we observe an inversion of the strength-distance relationship. Current regulated stimulation was more strongly influenced by fiber depth, whereas voltage regulated stimulation was more strongly influenced by skin thickness. Finally, our model reproduced the threshold-frequency relationship of experimentally measured motor thresholds.

SIGNIFICANCE

The model may be used for prediction of motor thresholds in TES, and contributes to the understanding of high-frequency TES.

Measurement of evoked potentials during thalamic deep brain stimulation

BACKGROUND

Deep brain stimulation (DBS) treats the symptoms of several movement disorders, but optimal selection of stimulation parameters remains a challenge. The evoked compound action potential (ECAP) reflects synchronized neural activation near the DBS lead, and may be useful for feedback control and automatic adjustment of stimulation parameters in closed-loop DBS systems.

OBJECTIVES

Determine the feasibility of recording ECAPs in the clinical setting, understand the neural origin of the ECAP and sources of any stimulus artifact, and correlate ECAP characteristics with motor symptoms.

METHODS

The ECAP and tremor response were measured simultaneously during intraoperative studies of thalamic DBS, conducted in patients who were either undergoing surgery for initial lead implantation or replacement of their internal pulse generator.

RESULTS

There was large subject-to-subject variation in stimulus artifact amplitude, which model-based analysis suggested may have been caused by glial encapsulation of the lead, resulting in imbalances in the tissue impedance between the contacts. ECAP recordings obtained from both acute and chronically implanted electrodes revealed that specific phase characteristics of the signal varied systematically with stimulation parameters. Further, a trend was observed in some patients between the energy of the initial negative and positive ECAP phases, as well as secondary phases, and changes in tremor from baseline. A computational model of thalamic DBS indicated that direct cerebellothalamic fiber activation dominated the clinically measured ECAP, suggesting that excitation of these fibers is critical in DBS therapy.

CONCLUSIONS

This work demonstrated that ECAPs can be recorded in the clinical setting and may provide a surrogate feedback control signal for automatic adjustment of stimulation parameters to reduce tremor amplitude.

Influences of interpolation error, electrode geometry, and the electrode-tissue interface on models of electric fields produced by deep brain stimulation

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 electrode-tissue 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.

Analysis of deep brain stimulation electrode characteristics for neural recording

OBJECTIVE

Closed-loop deep brain stimulation (DBS) systems have the potential to optimize treatment of movement disorders by enabling automatic adjustment of stimulation parameters based on a feedback signal. Evoked compound action potentials (ECAPs) and local field potentials (LFPs) recorded from the DBS electrode may serve as suitable closed-loop control signals. The objective of this study was to understand better the factors that influence ECAP and LFP recording, including the physical presence of the electrode, the geometrical dimensions of the electrode, and changes in the composition of the peri-electrode space across recording conditions.

APPROACH

Coupled volume conductor-neuron models were used to calculate single-unit activity as well as ECAP responses and LFP activity from a population of model thalamic neurons.

MAIN RESULTS

Comparing ECAPs and LFPs measured with and without the presence of the highly conductive recording contacts, we found that the presence of these contacts had a negligible effect on the magnitude of single-unit recordings, ECAPs (7% RMS difference between waveforms), and LFPs (5% change in signal magnitude). Spatial averaging across the contact surface decreased the ECAP magnitude in a phase-dependent manner (74% RMS difference), resulting from a differential effect of the contact on the contribution from nearby or distant elements, and decreased the LFP magnitude (25% change). Reductions in the electrode diameter or recording contact length increased signal energy and increased spatial sensitivity of single neuron recordings. Moreover, smaller diameter electrodes (500 µm) were more selective for recording from local cells over passing axons, with the opposite true for larger diameters (1500 µm). Changes in electrode dimensions had phase-dependent effects on ECAP characteristics, and generally had small effects on the LFP magnitude. ECAP signal energy and LFP magnitude decreased with tighter contact spacing (100 µm), compared to the original dimensions (1500 µm), with the opposite effect on the ECAP at longer contact-to-contact distances (2000 µm). Finally, acute edema reduced the single neuron and population ECAP signal energy, as well as LFP magnitude, and glial encapsulation had the opposite effect, after accounting for loss of cells in the peri-electrode space.

SIGNIFICANCE

This study determined recording conditions and electrode designs that influence ECAP and LFP recording fidelity.

Effects of antidromic and orthodromic activation of STN afferent axons during DBS in Parkinson's disease: a simulation study

Recent studies suggest that subthalamic nucleus (STN)-Deep Brain Stimulation (DBS) may exert at least part of its therapeutic effect through the antidromic suppression of pathological oscillations in the cortex in 6-OHDA treated rats and in parkinsonian patients. STN-DBS may also activate STN neurons by initiating action potential propagation in the orthodromic direction, similarly resulting in suppression of pathological oscillations in the STN. While experimental studies have provided strong evidence in support of antidromic stimulation of cortical neurons, it is difficult to separate relative contributions of antidromic and orthodromic effects of STN-DBS. The aim of this computational study was to examine the effects of antidromic and orthodromic activation on neural firing patterns and beta-band (13-30 Hz) oscillations in the STN and cortex during DBS of STN afferent axons projecting from the cortex. High frequency antidromic stimulation alone effectively suppressed simulated beta activity in both the cortex and STN-globus pallidus externa (GPe) network. High frequency orthodromic stimulation similarly suppressed beta activity within the STN and GPe through the direct stimulation of STN neurons driven by DBS at the same frequency as the stimulus. The combined effect of both antidromic and orthodromic stimulation modulated cortical activity antidromically while simultaneously orthodromically driving STN neurons. While high frequency DBS reduced STN beta-band power, low frequency stimulation resulted in resonant effects, increasing beta-band activity, consistent with previous experimental observations. The simulation results indicate effective suppression of simulated oscillatory activity through both antidromic stimulation of cortical neurons and direct orthodromic stimulation of STN neurons. The results of the study agree with experimental recordings of STN and cortical neurons in rats and support the therapeutic potential of stimulation of cortical neurons.

Current approaches to model extracellular electrical neural microstimulation

Nowadays, high-density microelectrode arrays provide unprecedented possibilities to precisely activate spatially well-controlled central nervous system (CNS) areas. However, this requires optimizing stimulating devices, which in turn requires a good understanding of the effects of microstimulation on cells and tissues. In this context, modeling approaches provide flexible ways to predict the outcome of electrical stimulation in terms of CNS activation. In this paper, we present state-of-the-art modeling methods with sufficient details to allow the reader to rapidly build numerical models of neuronal extracellular microstimulation. These include (1) the computation of the electrical potential field created by the stimulation in the tissue, and (2) the response of a target neuron to this field. Two main approaches are described: First we describe the classical hybrid approach that combines the finite element modeling of the potential field with the calculation of the neuron's response in a cable equation framework (compartmentalized neuron models). Then, we present a “whole finite element” approach allowing the simultaneous calculation of the extracellular and intracellular potentials, by representing the neuronal membrane with a thin-film approximation. This approach was previously introduced in the frame of neural recording, but has never been implemented to determine the effect of extracellular stimulation on the neural response at a sub-compartment level. Here, we show on an example that the latter modeling scheme can reveal important sub-compartment behavior of the neural membrane that cannot be resolved using the hybrid approach. The goal of this paper is also to describe in detail the practical implementation of these methods to allow the reader to easily build new models using standard software packages. These modeling paradigms, depending on the situation, should help build more efficient high-density neural prostheses for CNS rehabilitation.

Quantification of uncertainties in brain tissue conductivity in a heterogeneous model of deep brain stimulation using a non-intrusive projection approach

The aim of this study was to examine the effects of uncertainty of the conductivity values on the resulting field distribution in a heterogeneous finite element model of deep brain stimulation (DBS). A non-intrusive projection method was used by expanding the input random variables and the resulting potential on a multidimensional basis called the Polynomial Chaos (PC). The finite element model incorporates an accurate model of a DBS electrode used in clinical treatment extended by an encapsulation layer around the electrode body. Areas of grey matter, white matter and cerebrospinal fluid were derived from averaged magnetic resonance imaging (MRI). The uncertainties of the conductivity values of these tissue types were modelled as uniform random variables using data from literature to obtain their upper and lower boundaries.

Impact of brain tissue filtering on neurostimulation fields: a modeling study

Electrical neurostimulation techniques, such as deep brain stimulation (DBS) and transcranial magnetic stimulation (TMS), are increasingly used in the neurosciences, e.g., for studying brain function, and for neurotherapeutics, e.g., for treating depression, epilepsy, and Parkinson's disease. The characterization of electrical properties of brain tissue has guided our fundamental understanding and application of these methods, from electrophysiologic theory to clinical dosing-metrics. Nonetheless, prior computational models have primarily relied on ex-vivo impedance measurements. We recorded the in-vivo impedances of brain tissues during neurosurgical procedures and used these results to construct MRI guided computational models of TMS and DBS neurostimulatory fields and conductance-based models of neurons exposed to stimulation. We demonstrated that tissues carry neurostimulation currents through frequency dependent resistive and capacitive properties not typically accounted for by past neurostimulation modeling work. We show that these fundamental brain tissue properties can have significant effects on the neurostimulatory-fields (capacitive and resistive current composition and spatial/temporal dynamics) and neural responses (stimulation threshold, ionic currents, and membrane dynamics). These findings highlight the importance of tissue impedance properties on neurostimulation and impact our understanding of the biological mechanisms and technological potential of neurostimulatory methods.

Neural origin of evoked potentials during thalamic deep brain stimulation

Closed-loop deep brain stimulation (DBS) systems could provide automatic adjustment of stimulation parameters and improve outcomes in the treatment of Parkinson's disease and essential tremor. The evoked compound action potential (ECAP), generated by activated neurons near the DBS electrode, may provide a suitable feedback control signal for closed-loop DBS. The objectives of this work were to characterize the ECAP across stimulation parameters and determine the neural elements contributing to the signal. We recorded ECAPs during thalamic DBS in anesthetized cats and conducted computer simulations to calculate the ECAP of a population of thalamic neurons. The experimental and computational ECAPs were similar in shape and had characteristics that were correlated across stimulation parameters (R(2) = 0.80-0.95, P < 0.002). The ECAP signal energy increased with larger DBS amplitudes (P < 0.0001) and pulse widths (P < 0.002), and the signal energy of secondary ECAP phases was larger at 10-Hz than at 100-Hz DBS (P < 0.002). The computational model indicated that these changes resulted from a greater extent of neural activation and an increased synchronization of postsynaptic thalamocortical activity, respectively. Administration of tetrodotoxin, lidocaine, or isoflurane abolished or reduced the magnitude of the experimental and computational ECAPs, glutamate receptor antagonists 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) and D(-)-2-amino-5-phosphonopentanoic acid (APV) reduced secondary ECAP phases by decreasing postsynaptic excitation, and the GABAA receptor agonist muscimol increased the latency of the secondary phases by augmenting postsynaptic hyperpolarization. This study demonstrates that the ECAP provides information about the type and extent of neural activation generated during DBS, and the ECAP may serve as a feedback control signal for closed-loop DBS.

Simulation of cortico-basal ganglia oscillations and their suppression by closed loop deep brain stimulation

A new model of deep brain stimulation (DBS) is presented that integrates volume conduction effects with a neural model of pathological beta-band oscillations in the cortico-basal ganglia network. The model is used to test the clinical hypothesis that closed-loop control of the amplitude of DBS may be possible, based on the average rectified value of beta-band oscillations in the local field potential. Simulation of closed-loop high-frequency DBS was shown to yield energy savings, with the magnitude of the energy saved dependent on the strength of coupling between the subthalamic nucleus and the remainder of the cortico-basal ganglia network. When closed-loop DBS was applied to a strongly coupled cortico-basal ganglia network, the stimulation energy delivered over a 480 s period was reduced by up to 42%. Greater energy reductions were observed for weakly coupled networks, as the stimulation amplitude reduced to zero once the initial desynchronization had occurred. The results provide support for the application of closed-loop high-frequency DBS based on electrophysiological biomarkers.

Recording evoked potentials during deep brain stimulation: development and validation of instrumentation to suppress the stimulus artefact

The clinical efficacy of deep brain stimulation (DBS) for the treatment of movement disorders depends on the identification of appropriate stimulation parameters. Since the mechanisms of action of DBS remain unclear, programming sessions can be time consuming, costly and result in sub-optimal outcomes. Measurement of electrically evoked compound action potentials (ECAPs) during DBS, generated by activated neurons in the vicinity of the stimulating electrode, could offer insight into the type and spatial extent of neural element activation and provide a potential feedback signal for the rational selection of stimulation parameters and closed-loop DBS. However, recording ECAPs presents a significant technical challenge due to the large stimulus artefact, which can saturate recording amplifiers and distort short latency ECAP signals. We developed DBS-ECAP recording instrumentation combining commercial amplifiers and circuit elements in a serial configuration to reduce the stimulus artefact and enable high fidelity recording. We used an electrical circuit equivalent model of the instrumentation to understand better the sources of the stimulus artefact and the mechanisms of artefact reduction by the circuit elements. In vitro testing validated the capability of the instrumentation to suppress the stimulus artefact and increase gain by a factor of 1000 to 5000 compared to a conventional biopotential amplifier. The distortion of mock ECAP (mECAP) signals was measured across stimulation parameters, and the instrumentation enabled high fidelity recording of mECAPs with latencies of only 0.5 ms for DBS pulse widths of 50 to 100 µs/phase. Subsequently, the instrumentation was used to record in vivo ECAPs, without contamination by the stimulus artefact, during thalamic DBS in an anesthetized cat. The characteristics of the physiological ECAP were dependent on stimulation parameters. The novel instrumentation enables high fidelity ECAP recording and advances the potential use of the ECAP as a feedback signal for the tuning of DBS parameters.

Contribution of dielectric dispersions to voltage waveforms arising from electrical stimulation

This study presents an analysis of the effect of incorporating a subset of the complete set of dielectric dispersions in electric field models of implanted electrical stimulation. An analytic volume conductor model was used to determine the voltage waveform at a distance of 5mm from a point current stimulus for 17 different biological tissues. The RMS error of the voltage waveform resulting from the incorporation of a subset of all poles with respect to the voltage waveform resulting from the incorporation of the complete set of dispersive poles was calculated. The stimulus amplitude necessary to elicit action potential propagation in a myelinated mammalian nerve fibre in each of the dispersive models was also determined using a multi-compartment cable axon model. It was found that, for all tissues, removal of dispersions with pole frequencies greater than 1 MHz had a negligible effect on the threshold stimulation amplitude, suggesting that they may be neglected when constructing volume conductor models of electrical stimulation. However, removal of low-frequency dispersions below 1 MHz resulted in greater reductions in the threshold stimulus amplitudes necessary for activation of axons, with errors of up to 86% observed.

Modeling extracellular electrical neural stimulation: from basic understanding to MEA-based applications

Extracellular electrical stimulation of neural networks has been widely used empirically for decades with individual electrodes. Since recently, microtechnology provides advanced systems with high-density microelectrode arrays (MEAs). Taking the most of these devices for fundamental goals or developing neural prosthesis requires a good knowledge of the mechanisms underlying electrical stimulation. Here, we review modeling approaches used to determine (1) the electric potential field created by a stimulation and (2) the response of an excitable cell to an applied field. Computation of the potential field requires solving the Poisson equation. While this can be performed analytically in simple electrode-neuron configurations, numerical models are required for realistic geometries. In these models, special care must be taken to model the potential drop at the electrode/tissue interface using appropriate boundary conditions. The neural response to the field can then be calculated using compartmentalized cell models, by solving a cable equation, the source term of which (called activating function) is proportional to the second derivative of the extracellular field along the neural arborization. Analytical and numerical solutions to this equation are first presented. Then, we discuss the use of approximated solutions to intuitively predict the neuronal response: Either the "activating function" or the "mirror estimate", depending on the pulse duration and the cell space constant. Finally, we address the design of optimal electrode configurations allowing the selective activation of neurons near each stimulation site. This can be achieved using either multipolar configurations, or the "ground surface" configuration, which can be easily integrated in high-density MEAs. Overall, models highlighting the mechanisms of electrical microstimulation and improving stimulating devices should help understanding the influence of extracellular fields on neural elements and developing optimized neural prostheses for rehabilitation.