Electric field distribution in a finite-volume head model of deep brain stimulation

Modeling the volume of tissue activated in deep brain stimulation and its clinical influence: a review

Deep brain stimulation (DBS) is a neuromodulatory therapy that has been FDA approved for the treatment of various disorders, including but not limited to, movement disorders (e.g., Parkinson's disease and essential tremor), epilepsy, and obsessive-compulsive disorder. Computational methods for estimating the volume of tissue activated (VTA), coupled with brain imaging techniques, form the basis of models that are being generated from retrospective clinical studies for predicting DBS patient outcomes. For instance, VTA models are used to generate target-and network-based probabilistic stimulation maps that play a crucial role in predicting DBS treatment outcomes. This review defines the methods for calculation of tissue activation (or modulation) including ones that use heuristic and clinically derived estimates and more computationally involved ones that rely on finite-element methods and biophysical axon models. We define model parameters and provide a comparison of commercial, open-source, and academic simulation platforms available for integrated neuroimaging and neural activation prediction. In addition, we review clinical studies that use these modeling methods as a function of disease. By describing the tissue-activation modeling methods and highlighting their application in clinical studies, we provide the neural engineering and clinical neuromodulation communities with perspectives that may influence the adoption of modeling methods for future DBS studies.

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.

Automatic Quality Control of the numerical accuracy of EEG Lead fields

Precise individualized EEG source localization is predicated on having accurate subject-specific Lead Fields (LFs) obtained from their Magnetic Resonance Images (MRI). LF calculation is a complex process involving several error-prone steps that start with obtaining a realistic head model from the MRI and finalizing with computationally expensive solvers such as the Boundary Element Method (BEM) or Finite Element Method (FEM). Current Big-Data applications require the calculation of batches of hundreds or thousands of LFs. LF. Quality Control is conventionally checked subjectively by experts, a procedure not feasible in practice for larger batches. To facilitate this step, we introduce the Lead Field Automatic-Quality Control Index (LF-AQI) that flags LF with potential errors. We base our LF-AQI on the assumption that LFs obtained from simpler head models, i.e., the homogeneous head model LF (HHM-LF) or spherical head model LF (SHM-LF), deviate only moderately from a "good" realistic test LF. Since these simpler LFs are easier to compute and check for errors, they may serve as "reference LF" to detect anomalous realistic test LF. We investigated this assumption by comparing correlation-based channel ρ_min(ref,test)and source τ_min(ref,test) similarity indices (SI) between "gold standards," i.e., very accurate FEM and BEM LFs, and the proposed references (HHM-LF and SHM-LF). Surprisingly we found that the most uncomplicated possible reference, HHM-LF had high SI values with the gold standards-leading us to explore further use of the channel ρ_min(HHM-LF,test)and source τ_min(HHM-LF,test)_{SI as a basis for} our LF-AQI. Indeed, these SI successfully detected five simulated scenarios of LFs artifacts. This result encouraged us to evaluate the SI on a large dataset and thus define our LF-AQI. We thus computed the SI of 1251 LFs obtained from the Child Mind Institute (CMI) MRI dataset. When ρ_min(HHM-LF,test)and source τ_min(HHM-LF,test) were plotted for all test subjects on a 2D space, most were tightly clustered around the median of a high similarity centroid (HSC), except for a smaller proportion of outliers. We define the LF-AQI for a given LF as the log Euclidean distance between its SI and the HSC median. To automatically detect outliers, the threshold is at the 90^th percentile of the CMI LF-AQIs (-0.9755). LF-AQI greater than this threshold flag individual LF to be checked. The robustness of this LF-AQI screening was checked by repeated out-of-sample validation. Strikingly, minor corrections in re-processing the flagged cases eliminated their status as outliers. Furthermore, the "doubtful" labels assigned by LF-AQI were validated by neuroscience students using a Likert scale questionnaire designed to manually check the LF's quality. Item Response Theory (IRT) analysis was applied to the questionnaire results to compute an optimized model and a latent variable θ for that model. A linear mixed model (LMM) between the θ and LF-AQI resulted in an effect with a Cohen's d value of 1.3 and a p-value <0.001, thus validating the correspondence of LF-AQI with the visual quality control. We provide an open-source pipeline to implement both LF calculation and its quality control to allow further evaluation of our index.

Conductive Scaffolds for Bone Tissue Engineering: Current State and Future Outlook

Bone tissue engineering strategies attempt to regenerate bone tissue lost due to injury or disease. Three-dimensional (3D) scaffolds maintain structural integrity and provide support, while improving tissue regeneration through amplified cellular responses between implanted materials and native tissues. Through this, scaffolds that show great osteoinductive abilities as well as desirable mechanical properties have been studied. Recently, scaffolding for engineered bone-like tissues have evolved with the use of conductive materials for increased scaffold bioactivity. These materials make use of several characteristics that have been shown to be useful in tissue engineering applications and combine them in the hope of improved cellular responses through stimulation (i.e., mechanical or electrical). With the addition of conductive materials, these bioactive synthetic bone substitutes could result in improved regeneration outcomes by reducing current factors limiting the effectiveness of existing scaffolding materials. This review seeks to overview the challenges associated with the current state of bone tissue engineering, the need to produce new grafting substitutes, and the promising future that conductive materials present towards alleviating the issues associated with bone repair and regeneration.

Optimization of Electrical Stimulation for Safe and Effective Guidance of Human Cells

Direct current (DC) electrical stimulation has been shown to have remarkable effects on regulating cell behaviors. Translation of this technology to clinical uses, however, has to overcome several obstacles, including Joule heat production, changes in pH and ion concentration, and electrode products that are detrimental to cells. Application of DC voltages in thick tissues where their thickness is >0.8 mm caused significant changes in temperature, pH, and ion concentrations. In this study, we developed a multifield and -chamber electrotaxis chip, and various stimulation schemes to determine effective and safe stimulation strategies to guide the migration of human vascular endothelial cells. The electrotaxis chip with a chamber thickness of 1 mm allows 10 voltages applied in one experiment. DC electric fields caused detrimental effects on cells in a 1 mm chamber that mimicking 3D tissue with a decrease in cell migration speed and an increase in necrosis and apoptosis. Using the chip, we were able to select optimal stimulation schemes that were effective in guiding cells with minimal detrimental effects. This experimental system can be used to determine optimal electrical stimulation schemes for cell migration, survival with minimal detrimental effects on cells, which will facilitate to bring electrical stimulation for in vivo use.

Bio-Heat Model of Kilohertz-Frequency Deep Brain Stimulation Increases Brain Tissue Temperature

OBJECTIVES

Early clinical trials suggest that deep brain stimulation at kilohertz frequencies (10 kHz-DBS) may be effective in improving motor symptoms in patients with movement disorders. The 10 kHz-DBS can deliver significantly more power in tissue compared to conventional frequency DBS, reflecting increased pulse compression (duty cycle). We hypothesize that 10 kHz-DBS modulates neuronal function through moderate local tissue heating, analogous to kilohertz spinal cord stimulation (10 kHz-SCS). To establish the role of tissue heating in 10 kHz-DBS (30 μs, 10 kHz, at intensities of 3-7 mA_peak ), a decisive first step is to characterize the range of temperature changes during clinical kHz-DBS protocols.

MATERIALS AND METHODS

We developed a high-resolution magnetic resonance imaging-derived DBS model incorporating joule-heat coupled bio-heat multi-physics to establish the role of tissue heating. Volume of tissue activated (VTA) under assumptions of activating function (for 130 Hz) or heating (for 10 kHz) based neuromodulation are contrasted.

RESULTS

DBS waveform power (waveform RMS) determined joule heating at the deep brain tissues. Peak heating was supralinearly dependent on stimulation RMS. The 10 kHz-DBS stimulation with 2.3 to 5.4 mA_RMS (corresponding to 3 to 7 mA_peak ) produced 0.10 to 1.38°C heating at the subthalamic nucleus (STN) target under standard tissue parameters. Maximum temperature increases were predicted inside the electrode encapsulation layer (enCAP) with 2.3 to 5.4 mA_RMS producing 0.13 to 1.87°C under standard tissue parameters. Tissue parameter analysis predicted STN heating was especially sensitive (ranging from 0.44 to 1.35°C at 3.8 mA_RMS ) to decreasing enCAP electrical conductivity and decreasing STN thermal conductivity.

CONCLUSIONS

Subject to validation with in vivo measurements, neuromodulation through a heating mechanism of action by 10 kHz-DBS can indicate novel therapeutic pathways and strategies for dose optimization.

Input-Output Functions in Human Heads Obtained With Cochlear Implant and Transcranial Electric Stimulation

OBJECTIVES

Electric stimulation is used to treat a number of neurologic disorders such as epilepsy and depression. However, delivering the required current to far-field neural targets is often ineffective because of current spread through low-impedance pathways. Here, the specific aims are to develop an empirical measure for current passing through the human head and to optimize stimulation strategies for targeting deeper structures, including the auditory nerve, by utilizing the cochlear implant (CI).

MATERIALS AND METHODS

Outward input/output (I/O) functions were obtained by CI stimulation and recording scalp potentials in five CI subjects. Conversely, inward I/O functions were obtained by noninvasive transcranial electric stimulation (tES) and recording intracochlear potentials using the onboard recording capability of the CI.

RESULTS

I/O measures indicate substantial current spread, with a maximum of 2.2% gain recorded at the inner ear target during tES (mastoid-to-mastoid electrode configuration). Similarly, CI stimulation produced a maximum of 1.1% gain at the scalp electrode nearest the CI return electrode. Gain varied with electrode montage according to a point source model that accounted for distances between the stimulating and recording electrodes. Within the same electrode montages, current gain patterns varied across subjects suggesting the importance of tissue properties, geometry, and electrode positioning.

CONCLUSION

These results provide a novel objective measure of electric stimulation in the human head, which can help to optimize stimulation parameters that improve neural excitation of deep structures by reducing the influence of current spread.

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.

A Study on the Feasibility of the Deep Brain Stimulation (DBS) Electrode Localization Based on Scalp Electric Potential Recordings

Deep Brain Stimulation (DBS) is an effective therapy for patients disabling motor symptoms from Parkinson's disease, essential tremor, and other motor disorders. Precise, individualized placement of DBS electrodes is a key contributor to clinical outcomes following surgery. Electroencephalography (EEG) is widely used to identify the sources of intracerebral signals from the potential on the scalp. EEG is portable, non-invasive, low-cost, and it could be easily integrated into the intraoperative or ambulatory environment for localization of either the DBS electrode or evoked potentials triggered by stimulation itself. In this work, we studied with numerical simulations the principle of extracting the DBS electrical pulse from the patient's EEG - which normally constitutes an artifact - and localizing the source of the artifact (i.e., the DBS electrodes) using EEG localization methods. A high-resolution electromagnetic head model was used to simulate the EEG potential at the scalp generated by the DBS pulse artifact. The potential distribution on the scalp was then sampled at the 256 electrode locations of a high-density EEG Net. The electric potential was modeled by a dipole source created by a given pair of active DBS electrodes. The dynamic Statistical Parametric Maps (dSPM) algorithm was used to solve the EEG inverse problem, and it allowed localization of the position of the stimulus dipole in three DBS electrode bipolar configurations with a maximum error of 1.5 cm. To assess the accuracy of the computational model, the results of the simulation were compared with the electric artifact amplitudes over 16 EEG electrodes measured in five patients. EEG artifacts measured in patients confirmed that simulated data are commensurate to patients' data (0 ± 6.6 μV). While we acknowledge that further work is necessary to achieve a higher accuracy needed for surgical navigation, the results presented in this study are proposed as the first step toward a validated computational framework that could be used for non-invasive localization not only of the DBS system but also brain rhythms triggered by stimulation at both proximal and distal sites in the human central nervous system.

A multi-scale computational model of the effects of TMS on motor cortex

The detailed biophysical mechanisms through which transcranial magnetic stimulation (TMS) activates cortical circuits are still not fully understood. Here we present a multi-scale computational model to describe and explain the activation of different pyramidal cell types in motor cortex due to TMS. Our model determines precise electric fields based on an individual head model derived from magnetic resonance imaging and calculates how these electric fields activate morphologically detailed models of different neuron types. We predict neural activation patterns for different coil orientations consistent with experimental findings. Beyond this, our model allows us to calculate activation thresholds for individual neurons and precise initiation sites of individual action potentials on the neurons’ complex morphologies. Specifically, our model predicts that cortical layer 3 pyramidal neurons are generally easier to stimulate than layer 5 pyramidal neurons, thereby explaining the lower stimulation thresholds observed for I-waves compared to D-waves. It also shows differences in the regions of activated cortical layer 5 and layer 3 pyramidal cells depending on coil orientation. Finally, it predicts that under standard stimulation conditions, action potentials are mostly generated at the axon initial segment of cortical pyramidal cells, with a much less important activation site being the part of a layer 5 pyramidal cell axon where it crosses the boundary between grey matter and white matter. In conclusion, our computational model offers a detailed account of the mechanisms through which TMS activates different cortical pyramidal cell types, paving the way for more targeted application of TMS based on individual brain morphology in clinical and basic research settings.

Effect of Anatomically Realistic Full-Head Model on Activation of Cortical Neurons in Subdural Cortical Stimulation-A Computational Study

Electrical brain stimulation (EBS) is an emerging therapy for the treatment of neurological disorders, and computational modeling studies of EBS have been used to determine the optimal parameters for highly cost-effective electrotherapy. Recent notable growth in computing capability has enabled researchers to consider an anatomically realistic head model that represents the full head and complex geometry of the brain rather than the previous simplified partial head model (extruded slab) that represents only the precentral gyrus. In this work, subdural cortical stimulation (SuCS) was found to offer a better understanding of the differential activation of cortical neurons in the anatomically realistic full-head model than in the simplified partial-head models. We observed that layer 3 pyramidal neurons had comparable stimulation thresholds in both head models, while layer 5 pyramidal neurons showed a notable discrepancy between the models; in particular, layer 5 pyramidal neurons demonstrated asymmetry in the thresholds and action potential initiation sites in the anatomically realistic full-head model. Overall, the anatomically realistic full-head model may offer a better understanding of layer 5 pyramidal neuronal responses. Accordingly, the effects of using the realistic full-head model in SuCS are compelling in computational modeling studies, even though this modeling requires substantially more effort.

Simulation and experimental study of DC electric field distribution characteristics of rat hippocampal slices in vitro

Direct current (DC) electric field is a noninvasive neuromodulation tool that can inhibit or facilitate excitability of neurons. Despite its efficacy, the dielectric constant of artificial cerebrospinal fluid and the position and direction of brain slices and other factors can affect the field intensity and distribution acting on the surface of rat hippocampus slices, thus causing errors. In this study, we describe a new analytical method optimized for DC electric fields acting on brain slices, and the design of an external DC electric field stimulator to allow scientific evaluation of brain slices. We investigated parameters regarding the uniformity of electric field distribution and identified the maximal parameters using the finite element method. Then, we selected and simplified slice images using magnetic resonance imaging data and calculated the electric field intensity of the original and simplified models. The electric field simulator induced action potential and excitatory postsynaptic current with intensities of 1, 5, and 10 V/m. This study describes the development of a new electric field stimulator and successfully demonstrates its practicability for scientific evaluation of tissue slices.

Technical aspects of neurostimulation: Focus on equipment, electric field modeling, and stimulation protocols

Neuromodulation is a field of science, medicine, and bioengineering that encompasses implantable and non-implantable technologies for the purpose of improving quality of life and functioning of humans. Brain neuromodulation involves different neurostimulation techniques: transcranial magnetic stimulation (TMS), transcranial direct current stimulation (tDCS), vagus nerve stimulation (VNS), and deep brain stimulation (DBS), which are being used both to study their effects on cognitive brain functions and to treat neuropsychiatric disorders. The mechanisms of action of neurostimulation remain incompletely understood. Insight into the technical basis of neurostimulation might be a first step towards a more profound understanding of these mechanisms, which might lead to improved clinical outcome and therapeutic potential. This review provides an overview of the technical basis of neurostimulation focusing on the equipment, the present understanding of induced electric fields, and the stimulation protocols. The review is written from a technical perspective aimed at supporting the use of neurostimulation in clinical practice.

Recovery of Dynamics and Function in Spiking Neural Networks with Closed-Loop Control

There is a growing interest in developing novel brain stimulation methods to control disease-related aberrant neural activity and to address basic neuroscience questions. Conventional methods for manipulating brain activity rely on open-loop approaches that usually lead to excessive stimulation and, crucially, do not restore the original computations performed by the network. Thus, they are often accompanied by undesired side-effects. Here, we introduce delayed feedback control (DFC), a conceptually simple but effective method, to control pathological oscillations in spiking neural networks (SNNs). Using mathematical analysis and numerical simulations we show that DFC can restore a wide range of aberrant network dynamics either by suppressing or enhancing synchronous irregular activity. Importantly, DFC, besides steering the system back to a healthy state, also recovers the computations performed by the underlying network. Finally, using our theory we identify the role of single neuron and synapse properties in determining the stability of the closed-loop system.

Brain stimulation is being used to ease symptoms in several neurological disorders in cases where pharmacological treatment is not effective (anymore). The most common way for stimulation so far has been to apply a fixed, predetermined stimulus irrespective of the actual state of the brain or the condition of the patient. Recently, alternative strategies such as event-triggered stimulation protocols have attracted the interest of researchers. In these protocols the state of the affected brain area is continuously monitored, but the stimulus is only applied if certain criteria are met. Here we go one step further and present a truly closed-loop stimulation protocol. That is, a stimulus is being continuously provided and the magnitude of the stimulus depends, at any point in time, on the ongoing neural activity dynamics of the affected brain area. This results not only in suppression of the pathological activity, but also in a partial recovery of the transfer function of the activity dynamics. Thus, the ability of the lesioned brain area to carry out relevant computations is restored up to a point as well.

A latent force model for describing electric propagation in deep brain stimulation: a simulation study

Deep brain stimulation (DBS) is a neurosurgical method used to treat symptoms of movement disorders by implanting electrodes in deep brain areas. Often, the DBS modeling approaches found in the literature assume a quasi-static approximation, and discard any dynamic behavior. Nevertheless, in a real DBS system the stimulus corresponds to a wave that changes as a function of time. It is clear that DBS demands an approach that takes into account the time-varying behavior of the input stimulus. In this work, we present a novel latent force model for describing the dynamic electric propagation occurred during DBS. The performance of the proposed model was studied by simulations under different conditions. The results show that our approach is able to take into account the time variations of the source and the produced field. Moreover, by restricting our model it is possible to obtain solutions for electrostatic formulations, here experimental results were compared with the finite element method. Additionally, our approach allows a solution to the inverse problem, which is a valuable clinical application allowing the appropriate tuning of the DBS device by the expert physician.

Computational modeling of neurostimulation in brain diseases

Neurostimulation as a therapeutic tool has been developed and used for a range of different diseases such as Parkinson's disease, epilepsy, and migraine. However, it is not known why the efficacy of the stimulation varies dramatically across patients or why some patients suffer from severe side effects. This is largely due to the lack of mechanistic understanding of neurostimulation. Hence, theoretical computational approaches to address this issue are in demand. This chapter provides a review of mechanistic computational modeling of brain stimulation. In particular, we will focus on brain diseases, where mechanistic models (e.g., neural population models or detailed neuronal models) have been used to bridge the gap between cellular-level processes of affected neural circuits and the symptomatic expression of disease dynamics. We show how such models have been, and can be, used to investigate the effects of neurostimulation in the diseased brain. We argue that these models are crucial for the mechanistic understanding of the effect of stimulation, allowing for a rational design of stimulation protocols. Based on mechanistic models, we argue that the development of closed-loop stimulation is essential in order to avoid inference with healthy ongoing brain activity. Furthermore, patient-specific data, such as neuroanatomic information and connectivity profiles obtainable from neuroimaging, can be readily incorporated to address the clinical issue of variability in efficacy between subjects. We conclude that mechanistic computational models can and should play a key role in the rational design of effective, fully integrated, patient-specific therapeutic brain stimulation.

Relationship between neural activation and electric field distribution during deep brain stimulation

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 future studies to approximate the VTA during model-based investigations of DBS without the need of computational axon models.

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.

MRI-based multiscale model for electromagnetic analysis in the human head with implanted DBS

Deep brain stimulation (DBS) is an established procedure for the treatment of movement and affective disorders. Patients with DBS may benefit from magnetic resonance imaging (MRI) to evaluate injuries or comorbidities. However, the MRI radio-frequency (RF) energy may cause excessive tissue heating particularly near the electrode. This paper studies how the accuracy of numerical modeling of the RF field inside a DBS patient varies with spatial resolution and corresponding anatomical detail of the volume surrounding the electrodes. A multiscale model (MS) was created by an atlas-based segmentation using a 1 mm³ head model (mRes) refined in the basal ganglia by a 200 μm² ex-vivo dataset. Four DBS electrodes targeting the left globus pallidus internus were modeled. Electromagnetic simulations at 128 MHz showed that the peak of the electric field of the MS doubled (18.7 kV/m versus 9.33 kV/m) and shifted 6.4 mm compared to the mRes model. Additionally, the MS had a sixfold increase over the mRes model in peak-specific absorption rate (SAR of 43.9 kW/kg versus 7 kW/kg). The results suggest that submillimetric resolution and improved anatomical detail in the model may increase the accuracy of computed electric field and local SAR around the tip of the implant.

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.

Methods for high-resolution anisotropic finite element modeling of the human head: automatic MR white matter anisotropy-adaptive mesh generation

This study proposes an advanced finite element (FE) head modeling technique through which high-resolution FE meshes adaptive to the degree of tissue anisotropy can be generated. Our adaptive meshing scheme (called wMesh) uses MRI structural information and fractional anisotropy maps derived from diffusion tensors in the FE mesh generation process, optimally reflecting electrical properties of the human brain. We examined the characteristics of the wMeshes through various qualitative and quantitative comparisons to the conventional FE regular-sized meshes that are non-adaptive to the degree of white matter anisotropy. We investigated numerical differences in the FE forward solutions that include the electrical potential and current density generated by current sources in the brain. The quantitative difference was calculated by two statistical measures of relative difference measure (RDM) and magnification factor (MAG). The results show that the wMeshes are adaptive to the anisotropic density of the WM anisotropy, and they better reflect the density and directionality of tissue conductivity anisotropy. Our comparison results between various anisotropic regular mesh and wMesh models show that there are substantial differences in the EEG forward solutions in the brain (up to RDM=0.48 and MAG=0.63 in the electrical potential, and RDM=0.65 and MAG=0.52 in the current density). Our analysis results indicate that the wMeshes produce different forward solutions that are different from the conventional regular meshes. We present some results that the wMesh head modeling approach enhances the sensitivity and accuracy of the FE solutions at the interfaces or in the regions where the anisotropic conductivities change sharply or their directional changes are complex. The fully automatic wMesh generation technique should be useful for modeling an individual-specific and high-resolution anisotropic FE head model incorporating realistic anisotropic conductivity distributions towards more accurate analysis of bioelectromagnetic problems.

Deep brain stimulation mechanisms: beyond the concept of local functional inhibition

Deep brain electrical stimulation has become a recognized therapy in the treatment of a variety of motor disorders and has potentially promising applications in a wide range of neurological diseases including neuropsychiatry. Behavioural observation that electrical high-frequency stimulation of a given brain area induces an effect similar to a lesion suggested a mechanism of functional inhibition. In vitro and in vivo experiments as well as per operative recordings in patients have revealed a variety of effects involving local changes of neuronal excitability as well as widespread effects throughout the connected network resulting from activation of axons, including antidromic activation. Here we review current data regarding the local and network activity changes induced by high-frequency stimulation of the subthalamic nucleus and discuss this in the context of motor restoration in Parkinson's disease. Stressing the important functional consequences of axonal activation in deep brain stimulation mechanisms, we highlight the importance of developing anatomical knowledge concerning the fibre connections of the putative therapeutic targets.

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

The aim of this study was to examine the effect of dispersive tissue properties on the volume-conducted voltage waveforms and volume of tissue activated during deep brain stimulation. Inhomogeneous finite-element models were developed, incorporating a distributed dispersive electrode-tissue interface and encapsulation tissue of high and low conductivity, under both current-controlled and voltage-controlled stimulation. The models were used to assess the accuracy of capacitive models, where material properties were estimated at a single frequency, with respect to the full dispersive models. The effect of incorporating dispersion in the electrical conductivity and relative permittivity was found to depend on both the applied stimulus and the encapsulation tissue surrounding the electrode. Under current-controlled stimulation, and during voltage-controlled stimulation when the electrode was surrounded by high-resistivity encapsulation tissue, the dispersive material properties of the tissue were found to influence the voltage waveform in the tissue, indicated by RMS errors between the capacitive and dispersive models of 20%-38% at short pulse durations. When the dispersive model was approximated by a capacitive model, the accuracy of estimates of the volume of tissue activated was very sensitive to the frequency at which material properties were estimated. When material properties at 1 kHz were used, the error in the volume of tissue activated by capacitive approximations was reduced to -4.33% and 11.10%, respectively, for current-controlled and voltage-controlled stimulations, with higher errors observed when higher or lower frequencies were used.