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

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.

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 neuro-modulation 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.

The evolution of Big Data in neuroscience and neurology

Neurological diseases are on the rise worldwide, leading to increased healthcare costs and diminished quality of life in patients. In recent years, Big Data has started to transform the fields of Neuroscience and Neurology. Scientists and clinicians are collaborating in global alliances, combining diverse datasets on a massive scale, and solving complex computational problems that demand the utilization of increasingly powerful computational resources. This Big Data revolution is opening new avenues for developing innovative treatments for neurological diseases. Our paper surveys Big Data's impact on neurological patient care, as exemplified through work done in a comprehensive selection of areas, including Connectomics, Alzheimer's Disease, Stroke, Depression, Parkinson's Disease, Pain, and Addiction (e.g., Opioid Use Disorder). We present an overview of research and the methodologies utilizing Big Data in each area, as well as their current limitations and technical challenges. Despite the potential benefits, the full potential of Big Data in these fields currently remains unrealized. We close with recommendations for future research aimed at optimizing the use of Big Data in Neuroscience and Neurology for improved patient outcomes.

Supplementary Information

The online version contains supplementary material available at 10.1186/s40537-023-00751-2.

Delayed closed-loop neurostimulation for the treatment of pathological brain rhythms in mental disorders: a computational study

Mental disorders are among the top most demanding challenges in world-wide health. A large number of mental disorders exhibit pathological rhythms, which serve as the disorders characteristic biomarkers. These rhythms are the targets for neurostimulation techniques. Open-loop neurostimulation employs stimulation protocols, which are rather independent of the patients health and brain state in the moment of treatment. Most alternative closed-loop stimulation protocols consider real-time brain activity observations but appear as adaptive open-loop protocols, where e.g., pre-defined stimulation sets in if observations fulfil pre-defined criteria. The present theoretical work proposes a fully-adaptive closed-loop neurostimulation setup, that tunes the brain activities power spectral density (PSD) according to a user-defined PSD. The utilized brain model is non-parametric and estimated from the observations via magnitude fitting in a pre-stimulus setup phase. Moreover, the algorithm takes into account possible conduction delays in the feedback connection between observation and stimulation electrode. All involved features are illustrated on pathological α- and γ-rhythms known from psychosis. To this end, we simulate numerically a linear neural population brain model and a non-linear cortico-thalamic feedback loop model recently derived to explain brain activity in psychosis.

Quasi-static approximation error of electric field analysis for transcranial current stimulation

Objective.Numerical modeling of electric fields induced by transcranial alternating current stimulation (tACS) is currently a part of the standard procedure to predict and understand neural response. Quasi-static approximation (QSA) for electric field calculations is generally applied to reduce the computational cost. Here, we aimed to analyze and quantify the validity of the approximation over a broad frequency range.Approach.We performed electromagnetic modeling studies using an anatomical head model and considered approximations assuming either a purely ohmic medium (i.e. static formulation) or a lossy dielectric medium (QS formulation). The results were compared with the solution of Maxwell's equations in the cases of harmonic and pulsed signals. Finally, we analyzed the effect of electrode positioning on these errors.Main results.Our findings demonstrate that the QSA is valid and produces a relative error below 1% up to 1.43 MHz. The largest error is introduced in the static case, where the error is over 1% across the entire considered spectrum and as high as 20% in the brain at 10 Hz. We also highlight the special importance of considering the capacitive effect of tissues for pulsed waveforms, which prevents signal distortion induced by the purely ohmic approximation. At the neuron level, the results point a difference of sense electric field as high as 22% at focusing point, impacting pyramidal cells firing times.Significance.QSA remains valid in the frequency range currently used for tACS. However, neglecting permittivity (static formulation) introduces significant error for both harmonic and non-harmonic signals. It points out that reliable low frequency dielectric data are needed for accurate transcranial current stimulation numerical modeling.

Extracellular and intracellular components of the impedance of neural tissue

Electric phenomena in brain tissue can be measured using extracellular potentials, such as the local field potential, or the electro-encephalogram. The interpretation of these signals depends on the electric structure and properties of extracellular media, but the measurements of these electric properties are still debated. Some measurements point to a model in which the extracellular medium is purely resistive, and thus parameters such as electric conductivity and permittivity should be independent of frequency. Other measurements point to a pronounced frequency dependence of these parameters, with scaling laws that are consistent with capacitive or diffusive effects. However, these experiments correspond to different preparations, and it is unclear how to correctly compare them. Here, we provide for the first time, impedance measurements (in the 1-10 kHz frequency range) using the same setup in various preparations, from primary cell cultures to acute brain slices, and a comparison with similar measurements performed in artificial cerebrospinal fluid with no biological material. The measurements show that when the current flows across a cell membrane, the frequency dependence of the macroscopic impedance between intracellular and extracellular electrodes is significant, and cannot be captured by a model with resistive media. Fitting a mean-field model to the data shows that this frequency dependence could be explained by the ionic diffusion mainly associated with Debye layers surrounding the membranes. We conclude that neuronal membranes and their ionic environment induce strong deviations to resistivity that should be taken into account to correctly interpret extracellular potentials generated by neurons.

Multi-scale modeling toolbox for single neuron and subcellular activity under Transcranial Magnetic Stimulation

BACKGROUND

Transcranial Magnetic Stimulation (TMS) is a widely used non-invasive brain stimulation method. However, its mechanism of action and the neural response to TMS are still poorly understood. Multi-scale modeling can complement experimental research to study the subcellular neural effects of TMS. At the macroscopic level, sophisticated numerical models exist to estimate the induced electric fields. However, multi-scale computational modeling approaches to predict TMS cellular and subcellular responses, crucial to understanding TMS plasticity inducing protocols, are not available so far.

OBJECTIVE

We develop an open-source multi-scale toolbox Neuron Modeling for TMS (NeMo-TMS) to address this problem.

METHODS

NeMo-TMS generates accurate neuron models from morphological reconstructions, couples them to the external electric fields induced by TMS, and simulates the cellular and subcellular responses of single-pulse and repetitive TMS.

RESULTS

We provide examples showing some of the capabilities of the toolbox.

CONCLUSION

NeMo-TMS toolbox allows researchers a previously not available level of detail and precision in realistically modeling the physical and physiological effects of TMS.

An insight into electrical resistivity of white matter and brain tumors

BACKGROUND

There is a lack of information regarding electrical properties of white matter and brain tumors.

OBJECTIVE

To investigate the feasibility of in-vivo measurement of electrical resistivity during brain surgery and establish a better understanding of the resistivity patterns of brain tumors in correlation to the white matter.

METHODS

A bipolar probe was used to measure electrical resistivity during surgery in a prospective cohort of patients with brain tumors. For impedance measurement, the probe applied a constant current of 0.7 μA with a frequency of 140 Hz. The measurement was performed in the white matter within and outside peritumoral edema as well as in non-enhancing, enhancing and necrotic tumor areas. Resistivity values expressed in ohmmeter (Ω∗m) were compared between different intracranial tissues and brain tumors.

RESULTS

Ninety-two patients (gliomas WHO II:16, WHO III:10, WHO IV:33, metastasis:33) were included. White matter outside peritumoral edema had higher resistivity values (13.3 ± 1.7 Ω∗m) than within peritumoral edema (8.5 ± 1.6 Ω∗m), and both had higher values than brain tumors including non-enhancing (WHO II:6.4 ± 1.3 Ω∗m, WHO III:6.3 ± 0.9 Ω∗m), enhancing (WHO IV:5 ± 1 Ω∗m, metastasis:5.4 ± 1.3 Ω∗m) and necrotic tumor areas (WHO IV:3.9 ± 1.1 Ω∗m, metastasis:4.3 ± 1.3 Ω∗m), p=<0.001. No difference was found between low-grade and anaplastic gliomas, p = 0.808, while resistivity values in both were higher than the highest values found in glioblastomas, p = 0.003 and p = 0.004, respectively.

CONCLUSIONS

The technique we applied enabled us to measure electrical resistivity of white matter and brain tumors in-vivo presumably with a significant effect with regard to dielectric polarization. Our results suggest that there are significant differences within different areas and subtypes of brain tumors and that white matter exhibits higher electrical resistivity than brain tumors.

Ambiguity in the interpretation of the low-frequency dielectric properties of biological tissues

The frequency-dependent behaviour of the dielectric properties of biological tissues in the frequency range below 1 kHz has been under debate since the past century. Here, we reanalyse the raw data of the main resource of the dielectric properties of biological tissues in impedance representation. Employing a Kramers-Kronig validity test and parameter estimation techniques, we can describe the data by two physical parametric models that correspond to opposing biophysical interpretations: on the one hand the data can be explained only by intrinsic tissue properties, but on the other hand evidence for electrode-specific effects can be found for all tissues under investigation. The first interpretation would justify the continued use of a parametric model comprising four Cole-Cole dispersions, which describe the dielectric properties from extremely low to very high frequencies. As an alternative that is in accordance with the second interpretation, we suggest to omit the slowest of the four dispersions in the model and increase the static conductivity to account for a frequency-independent conductivity below 1 kHz.

Development, validation, and pilot MRI safety study of a high-resolution, open source, whole body pediatric numerical simulation model

Numerical body models of children are used for designing medical devices, including but not limited to optical imaging, ultrasound, CT, EEG/MEG, and MRI. These models are used in many clinical and neuroscience research applications, such as radiation safety dosimetric studies and source localization. Although several such adult models have been reported, there are few reports of full-body pediatric models, and those described have several limitations. Some, for example, are either morphed from older children or do not have detailed segmentations. Here, we introduce a 29-month-old male whole-body native numerical model, "MARTIN", that includes 28 head and 86 body tissue compartments, segmented directly from the high spatial resolution MRI and CT images. An advanced auto-segmentation tool was used for the deep-brain structures, whereas 3D Slicer was used to segment the non-brain structures and to refine the segmentation for all of the tissue compartments. Our MARTIN model was developed and validated using three separate approaches, through an iterative process, as follows. First, the calculated volumes, weights, and dimensions of selected structures were adjusted and confirmed to be within 6% of the literature values for the 2-3-year-old age-range. Second, all structural segmentations were adjusted and confirmed by two experienced, sub-specialty certified neuro-radiologists, also through an interactive process. Third, an additional validation was performed with a Bloch simulator to create synthetic MR image from our MARTIN model and compare the image contrast of the resulting synthetic image with that of the original MRI data; this resulted in a "structural resemblance" index of 0.97. Finally, we used our model to perform pilot MRI safety simulations of an Active Implantable Medical Device (AIMD) using a commercially available software platform (Sim4Life), incorporating the latest International Standards Organization guidelines. This model will be made available on the Athinoula A. Martinos Center for Biomedical Imaging website.

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.

Realistic modeling of mesoscopic ephaptic coupling in the human brain

Several decades of research suggest that weak electric fields may influence neural processing, including those induced by neuronal activity and proposed as a substrate for a potential new cellular communication system, i.e., ephaptic transmission. Here we aim to model mesoscopic ephaptic activity in the human brain and explore its trajectory during aging by characterizing the electric field generated by cortical dipoles using realistic finite element modeling. Extrapolating from electrophysiological measurements, we first observe that modeled endogenous field magnitudes are comparable to those in measurements of weak but functionally relevant self-generated fields and to those produced by noninvasive transcranial brain stimulation, and therefore possibly able to modulate neuronal activity. Then, to evaluate the role of these fields in the human cortex in large MRI databases, we adapt an interaction approximation that considers the relative orientation of neuron and field to estimate the membrane potential perturbation in pyramidal cells. We use this approximation to define a simplified metric (EMOD1) that weights dipole coupling as a function of distance and relative orientation between emitter and receiver and evaluate it in a sample of 401 realistic human brain models from healthy subjects aged 16-83. Results reveal that ephaptic coupling, in the simplified mesoscopic modeling approach used here, significantly decreases with age, with higher involvement of sensorimotor regions and medial brain structures. This study suggests that by providing the means for fast and direct interaction between neurons, ephaptic modulation may contribute to the complexity of human function for cognition and behavior, and its modification across the lifespan and in response to pathology.

Determination of the electrical impedance of neural tissue from its microscopic cellular constituents

The electrical properties of neural tissue are important in a range of different applications in biomedical engineering and basic science. These properties are characterized by the electrical admittivity of the tissue, which is the inverse of the specific tissue impedance.

OBJECTIVE

Here we derived analytical expressions for the admittivity of various models of neural tissue from the underlying electrical and morphological properties of the constituent cells.

APPROACH

Three models are considered: parallel bundles of fibers, fibers contained in stacked laminae and fibers crossing each other randomly in all three-dimensional directions.

MAIN RESULTS

An important and novel aspect that emerges from considering the underlying cellular composition of the tissue is that the resulting admittivity has both spatial and temporal frequency dependence, a property not shared with conventional conductivity-based descriptions. The frequency dependence of the admittivity results in non-trivial spatiotemporal filtering of electrical signals in the tissue models. These effects are illustrated by considering the example of pulsatile stimulation with a point source electrode. It is shown how changing temporal parameters of a current pulse, such as pulse duration, alters the spatial profile of the extracellular potential. In a second example, it is shown how the degree of electrical anisotropy can change as a function of the distance from the electrode, despite the underlying structurally homogeneity of the tissue. These effects are discussed in terms of different current pathways through the intra- and extra-cellular spaces, and how these relate to near- and far-field limits for the admittivity (which reduce to descriptions in terms of a simple conductivity).

SIGNIFICANCE

The results highlight the complexity of the electrical properties of neural tissue and provide mathematical methods to model this complexity.

Simulation of transcranial magnetic stimulation in head model with morphologically-realistic cortical neurons

BACKGROUND

Transcranial magnetic stimulation (TMS) enables non-invasive modulation of brain activity with both clinical and research applications, but fundamental questions remain about the neural types and elements TMS activates and how stimulation parameters affect the neural response.

OBJECTIVE

To develop a multi-scale computational model to quantify the effect of TMS parameters on the direct response of individual neurons.

METHODS

We integrated morphologically-realistic neuronal models with TMS-induced electric fields computed in a finite element model of a human head to quantify the cortical response to TMS with several combinations of pulse waveforms and current directions.

RESULTS

TMS activated with lowest intensity intracortical axonal terminations in the superficial gyral crown and lip regions. Layer 5 pyramidal cells had the lowest thresholds, but layer 2/3 pyramidal cells and inhibitory basket cells were also activated at most intensities. Direct activation of layers 1 and 6 was unlikely. Neural activation was largely driven by the field magnitude, rather than the field component normal to the cortical surface. Varying the induced current direction caused a waveform-dependent shift in the activation site and provided a potential mechanism for experimentally observed differences in thresholds and latencies of muscle responses.

CONCLUSIONS

This biophysically-based simulation provides a novel method to elucidate mechanisms and inform parameter selection of TMS and other cortical stimulation modalities. It also serves as a foundation for more detailed network models of the response to TMS, which may include endogenous activity, synaptic connectivity, inputs from intrinsic and extrinsic axonal projections, and corticofugal axons in white matter.

Is the Extracellular Impedance High and Non-resistive in Cerebral Cortex?

A recent commentary to Biophysical Journal criticized a previous study published in the same journal by Gomes et al. in 2016, and an alternative interpretation of the measurements was proposed. We reply here to these criticisms and provide some additional clarification, in particular, about a possible misinterpretation of the electrical circuit corresponding to these experiments. We suggest that, indeed, the extracellular impedance in cerebral cortex could be high and non-resistive, and we propose further experiments to settle this issue.

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.

Investigating large-scale brain dynamics using field potential recordings: analysis and interpretation

New technologies to record electrical activity from the brain on a massive scale offer tremendous opportunities for discovery. Electrical measurements of large-scale brain dynamics, termed field potentials, are especially important to understanding and treating the human brain. Here, our goal is to provide best practices on how field potential recordings (electroencephalograms, magnetoencephalograms, electrocorticograms and local field potentials) can be analyzed to identify large-scale brain dynamics, and to highlight critical issues and limitations of interpretation in current work. We focus our discussion of analyses around the broad themes of activation, correlation, communication and coding. We provide recommendations for interpreting the data using forward and inverse models. The forward model describes how field potentials are generated by the activity of populations of neurons. The inverse model describes how to infer the activity of populations of neurons from field potential recordings. A recurring theme is the challenge of understanding how field potentials reflect neuronal population activity given the complexity of the underlying brain systems.

Low intensity transcranial electric stimulation: Safety, ethical, legal regulatory and application guidelines

Low intensity transcranial electrical stimulation (TES) in humans, encompassing transcranial direct current (tDCS), transcutaneous spinal Direct Current Stimulation (tsDCS), transcranial alternating current (tACS), and transcranial random noise (tRNS) stimulation or their combinations, appears to be safe. No serious adverse events (SAEs) have been reported so far in over 18,000 sessions administered to healthy subjects, neurological and psychiatric patients, as summarized here. Moderate adverse events (AEs), as defined by the necessity to intervene, are rare, and include skin burns with tDCS due to suboptimal electrode-skin contact. Very rarely mania or hypomania was induced in patients with depression (11 documented cases), yet a causal relationship is difficult to prove because of the low incidence rate and limited numbers of subjects in controlled trials. Mild AEs (MAEs) include headache and fatigue following stimulation as well as prickling and burning sensations occurring during tDCS at peak-to-baseline intensities of 1-2mA and during tACS at higher peak-to-peak intensities above 2mA. The prevalence of published AEs is different in studies specifically assessing AEs vs. those not assessing them, being higher in the former. AEs are frequently reported by individuals receiving placebo stimulation. The profile of AEs in terms of frequency, magnitude and type is comparable in healthy and clinical populations, and this is also the case for more vulnerable populations, such as children, elderly persons, or pregnant women. Combined interventions (e.g., co-application of drugs, electrophysiological measurements, neuroimaging) were not associated with further safety issues. Safety is established for low-intensity 'conventional' TES defined as <4mA, up to 60min duration per day. Animal studies and modeling evidence indicate that brain injury could occur at predicted current densities in the brain of 6.3-13A/m2 that are over an order of magnitude above those produced by tDCS in humans. Using AC stimulation fewer AEs were reported compared to DC. In specific paradigms with amplitudes of up to 10mA, frequencies in the kHz range appear to be safe. In this paper we provide structured interviews and recommend their use in future controlled studies, in particular when trying to extend the parameters applied. We also discuss recent regulatory issues, reporting practices and ethical issues. These recommendations achieved consensus in a meeting, which took place in Göttingen, Germany, on September 6-7, 2016 and were refined thereafter by email correspondence.

Estimates of peak electric fields induced by Transcranial magnetic stimulation in pregnant women as patients using an FEM full-body model

Transcranial magnetic stimulation (TMS) for treatment of depression during pregnancy is an appealing alternative to fetus-threatening drugs. However, no studies to date have been performed that evaluate the safety of TMS for a pregnant mother patient and her fetus. A full-body FEM model of a pregnant woman with about 100 tissue parts has been developed specifically for the present study. This model allows accurate computations of induced electric field in every tissue given different locations of a shape-eight coil, a biphasic pulse, common TMS pulse durations, and using different values of the TMS intensity measured in SMT (Standard Motor Threshold) units. Our simulation results estimate the maximum peak values of the electric field in the fetal area for every fetal tissue separately and for the TMS intensity of one SMT unit.

Virtual Human Models for Electromagnetic Studies and Their Applications

Numerical simulation of electromagnetic, thermal, and mechanical responses of the human body to different stimuli in magnetic resonance imaging safety, antenna research, electromagnetic tomography, and electromagnetic stimulation is currently limited by the availability of anatomically adequate and numerically efficient cross-platform computational models or "virtual humans." The objective of this study is to provide a comprehensive review of modern human models and body region models available in the field and their important features.

Focal Local Field Potential Signature of the Single-Axon Monosynaptic Thalamocortical Connection

A resurgence has taken place in recent years in the use of the extracellularly recorded local field potential (LFP) to investigate neural network activity. To probe monosynaptic thalamic activation of cortical postsynaptic target cells, so called spike-trigger-averaged LFP (stLFP) signatures have been measured. In these experiments, the cortical LFP is measured by multielectrodes covering several cortical lamina and averaged on spontaneous spikes of thalamocortical (TC) cells. Using a well established forward-modeling scheme, we investigated the biophysical origin of this stLFP signature with simultaneous synaptic activation of cortical layer-4 neurons, mimicking the effect of a single afferent spike from a single TC neuron. Constrained by previously measured intracellular responses of the main postsynaptic target cell types and with biologically plausible assumptions regarding the spatial distribution of thalamic synaptic inputs into layer 4, the model predicted characteristic contributions to monosynaptic stLFP signatures both for the regular-spiking (RS) excitatory neurons and the fast-spiking (FS) inhibitory interneurons. In particular, the FS cells generated stLFP signatures of shorter temporal duration than the RS cells. Added together, a sum of the stLFP signatures of these two principal synaptic targets of TC cells were observed to resemble experimentally measured stLFP signatures. Outside the volume targeted by TC afferents, the resulting postsynaptic LFP signals were found to be sharply attenuated. This implies that such stLFP signatures provide a very local measure of TC synaptic activation, and that newly developed inverse current-source density (CSD)-estimation methods are needed for precise assessment of the underlying spatiotemporal CSD profiles.SIGNIFICANCE STATEMENT Despite its long history and prevalent use, the proper interpretation of the extracellularly recorded local field potential (LFP) is still not fully established. Here we investigate by biophysical modeling the origin of the focal LFP signature of the single-axon monosynaptic thalamocortical connection as measured by spike-trigger-averaging of cortical LFPs on spontaneous spikes of thalamocortical neurons. We find that this LFP signature is well accounted for by a model assuming thalamic projections to two cortical layer-4 cell populations: one excitatory (putatively regular-spiking cells) and one inhibitory (putatively fast-spiking cells). The LFP signature is observed to decay sharply outside the cortical region receiving the thalamocortical projection, implying that it indeed provides a very local measure of thalamocortical synaptic activation.

The development and modelling of devices and paradigms for transcranial magnetic stimulation

Magnetic stimulation is a non-invasive neurostimulation technique that can evoke action potentials and modulate neural circuits through induced electric fields. Biophysical models of magnetic stimulation have become a major driver for technological developments and the understanding of the mechanisms of magnetic neurostimulation and neuromodulation. Major technological developments involve stimulation coils with different spatial characteristics and pulse sources to control the pulse waveform. While early technological developments were the result of manual design and invention processes, there is a trend in both stimulation coil and pulse source design to mathematically optimize parameters with the help of computational models. To date, macroscopically highly realistic spatial models of the brain, as well as peripheral targets, and user-friendly software packages enable researchers and practitioners to simulate the treatment-specific and induced electric field distribution in the brains of individual subjects and patients. Neuron models further introduce the microscopic level of neural activation to understand the influence of activation dynamics in response to different pulse shapes. A number of models that were designed for online calibration to extract otherwise covert information and biomarkers from the neural system recently form a third branch of modelling.

From Maxwell's equations to the theory of current-source density analysis

Despite the widespread use of current‐source density (CSD) analysis of extracellular potential recordings in the brain, the physical mechanisms responsible for the generation of the signal are still debated. While the extracellular potential is thought to be exclusively generated by the transmembrane currents, recent studies suggest that extracellular diffusive, advective and displacement currents—traditionally neglected—may also contribute considerably toward extracellular potential recordings. Here, we first justify the application of the electro‐quasistatic approximation of Maxwell's equations to describe the electromagnetic field of physiological origin. Subsequently, we perform spatial averaging of currents in neural tissue to arrive at the notion of the CSD and derive an equation relating it to the extracellular potential. We show that, in general, the extracellular potential is determined by the CSD of membrane currents as well as the gradients of the putative extracellular diffusion current. The diffusion current can contribute significantly to the extracellular potential at frequencies less than a few Hertz; in which case it must be subtracted to obtain correct CSD estimates. We also show that the advective and displacement currents in the extracellular space are negligible for physiological frequencies while, within cellular membrane, displacement current contributes toward the CSD as a capacitive current. Taken together, these findings elucidate the relationship between electric currents and the extracellular potential in brain tissue and form the necessary foundation for the analysis of extracellular recordings.

Impedance Spectrum in Cortical Tissue: Implications for Propagation of LFP Signals on the Microscopic Level

Brain research investigating electrical activity within neural tissue is producing an increasing amount of physiological data including local field potentials (LFPs) obtained via extracellular in vivo and in vitro recordings. In order to correctly interpret such electrophysiological data, it is vital to adequately understand the electrical properties of neural tissue itself. An ongoing controversy in the field of neuroscience is whether such frequency-dependent effects bias LFP recordings and affect the proper interpretation of the signal. On macroscopic scales and with large injected currents, previous studies have found various grades of frequency dependence of cortical tissue, ranging from negligible to strong, within the frequency band typically considered relevant for neuroscience (less than a few thousand hertz). Here, we performed a detailed investigation of the frequency dependence of the conductivity within cortical tissue at microscopic distances using small current amplitudes within the typical (neuro)physiological micrometer and sub-nanoampere range. We investigated the propagation of LFPs, induced by extracellular electrical current injections via patch-pipettes, in acute rat brain slice preparations containing the somatosensory cortex in vitro using multielectrode arrays. Based on our data, we determined the cortical tissue conductivity over a 100-fold increase in signal frequency (5-500 Hz). Our results imply at most very weak frequency-dependent effects within the frequency range of physiological LFPs. Using biophysical modeling, we estimated the impact of different putative impedance spectra. Our results indicate that frequency dependencies of the order measured here and in most other studies have negligible impact on the typical analysis and modeling of LFP signals from extracellular brain recordings.

Assessing human brain impedance using simultaneous surface and intracerebral recordings

Most of the literature on the brain impedance proposes a frequency-independent resistive model. Recently, this conclusion was tackled by a series of papers (Bédard et al., 2006; Bédard and Destexhe, 2009; Gomes et al., 2016), based on microscopic sale modeling and measurements. Our paper aims to investigate the impedance issue using simultaneous in vivo depth and surface signals recorded during intracerebral electrical stimulation of epileptic patients, involving a priori different tissues with different impedances. Our results confirm the conclusions from Logothethis et al. (2007): there is no evidence of frequency dependence of the brain tissue impedance (more precisely, there is no difference, in terms of frequency filtering, between the brain and the skull bone), at least at a macroscopic scale. In order to conciliate findings from both microscopic and macroscopic scales, we recall different neural/synaptic current generators' models from the literature and we propose an original computational model, based on fractional dynamics.

Motor Cortex Neurostimulation Technologies for Chronic Post-stroke Pain: Implications of Tissue Damage on Stimulation Currents

Background: Central post stroke pain (CPSP) is a highly refractory syndrome that can occur after stroke. Primary motor cortex (M1) brain stimulation using epidural brain stimulation (EBS), transcranial magnetic stimulation (TMS), and transcranial direct current stimulation (tDCS) have been explored as potential therapies for CPSP. These techniques have demonstrated variable clinical efficacy. It is hypothesized that changes in the stimulating currents that are caused by stroke-induced changes in brain tissue conductivity limit the efficacy of these techniques. Methods: We generated MRI-guided finite element models of the current density distributions in the human head and brain with and without chronic focal cortical infarctions during EBS, TMS, and tDCS. We studied the change in the stimulating current density distributions' magnitude, orientation, and maxima locations between the different models. Results: Changes in electrical properties at stroke boundaries altered the distribution of stimulation currents in magnitude, location, and orientation. Current density magnitude alterations were larger for the non-invasive techniques (i.e., tDCS and TMS) than for EBS. Nonetheless, the lesion also altered currents during EBS. The spatial shift of peak current density, relative to the size of the stimulation source, was largest for EBS. Conclusion: In order to maximize therapeutic efficiency, neurostimulation trials need to account for the impact of anatomically disrupted neural tissues on the location, orientation, and magnitude of exogenously applied currents. The relative current-neuronal structure should be considered when planning stimulation treatment, especially across techniques (e.g., using TMS to predict EBS response). We postulate that the effects of altered tissue properties in stroke regions may impact stimulation induced analgesic effects and/or lead to highly variable outcomes during brain stimulation treatments in CPSP.

In vitro Magnetic Stimulation: A Simple Stimulation Device to Deliver Defined Low Intensity Electromagnetic Fields

Non-invasive brain stimulation (NIBS) by electromagnetic fields appears to benefit human neurological and psychiatric conditions, although the optimal stimulation parameters and underlying mechanisms remain unclear. Although, in vitro studies have begun to elucidate cellular mechanisms, stimulation is delivered by a range of coils (from commercially available human stimulation coils to laboratory-built circuits) so that the electromagnetic fields induced within the tissue to produce the reported effects are ill-defined. Here, we develop a simple in vitro stimulation device with plug-and-play features that allow delivery of a range of stimulation parameters. We chose to test low intensity repetitive magnetic stimulation (LI-rMS) delivered at three frequencies to hindbrain explant cultures containing the olivocerebellar pathway. We used computational modeling to define the parameters of a stimulation circuit and coil that deliver a unidirectional homogeneous magnetic field of known intensity and direction, and therefore a predictable electric field, to the target. We built the coil to be compatible with culture requirements: stimulation within an incubator; a flat surface allowing consistent position and magnetic field direction; location outside the culture plate to maintain sterility and no heating or vibration. Measurements at the explant confirmed the induced magnetic field was homogenous and matched the simulation results. To validate our system we investigated biological effects following LI-rMS at 1 Hz, 10 Hz and biomimetic high frequency, which we have previously shown induces neural circuit reorganization. We found that gene expression was modified by LI-rMS in a frequency-related manner. Four hours after a single 10-min stimulation session, the number of c-fos positive cells increased, indicating that our stimulation activated the tissue. Also, after 14 days of LI-rMS, the expression of genes normally present in the tissue was differentially modified according to the stimulation delivered. Thus we describe a simple magnetic stimulation device that delivers defined stimulation parameters to different neural systems in vitro. Such devices are essential to further understanding of the fundamental effects of magnetic stimulation on biological tissue and optimize therapeutic application of human NIBS.

Hybrid Scheme for Modeling Local Field Potentials from Point-Neuron Networks

With rapidly advancing multi-electrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both research and clinical applications. Proper understanding of the LFP requires detailed mathematical modeling incorporating the anatomical and electrophysiological features of neurons near the recording electrode, as well as synaptic inputs from the entire network. Here we propose a hybrid modeling scheme combining efficient point-neuron network models with biophysical principles underlying LFP generation by real neurons. The LFP predictions rely on populations of network-equivalent multicompartment neuron models with layer-specific synaptic connectivity, can be used with an arbitrary number of point-neuron network populations, and allows for a full separation of simulated network dynamics and LFPs. We apply the scheme to a full-scale cortical network model for a ∼1 mm² patch of primary visual cortex, predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate effects of input correlations and neuron density on the LFP. The generic nature of the hybrid scheme and its public implementation in hybridLFPy form the basis for LFP predictions from other and larger point-neuron network models, as well as extensions of the current application with additional biological detail.

Intracellular Impedance Measurements Reveal Non-ohmic Properties of the Extracellular Medium around Neurons

Determining the electrical properties of the extracellular space around neurons is important for understanding the genesis of extracellular potentials, as well as for localizing neuronal activity from extracellular recordings. However, the exact nature of these extracellular properties is still uncertain. Here, we introduce a method to measure the impedance of the tissue, one that preserves the intact cell-medium interface using whole-cell patch-clamp recordings in vivo and in vitro. We find that neural tissue has marked non-ohmic and frequency-filtering properties, which are not consistent with a resistive (ohmic) medium, as often assumed. The amplitude and phase profiles of the measured impedance are consistent with the contribution of ionic diffusion. We also show that the impact of such frequency-filtering properties is possibly important on the genesis of local field potentials, as well as on the cable properties of neurons. These results show non-ohmic properties of the extracellular medium around neurons, and suggest that source estimation methods, as well as the cable properties of neurons, which all assume ohmic extracellular medium, may need to be reevaluated.

R, Milham MP, Mehta AD, Schroeder CE. Spatiotemporal structure of intracranial electric fields induced by transcranial electric stimulation in humans and nonhuman primates

Transcranial electric stimulation (TES) is an emerging technique, developed to non-invasively modulate brain function. However, the spatiotemporal distribution of the intracranial electric fields induced by TES remains poorly understood. In particular, it is unclear how much current actually reaches the brain, and how it distributes across the brain. Lack of this basic information precludes a firm mechanistic understanding of TES effects. In this study we directly measure the spatial and temporal characteristics of the electric field generated by TES using stereotactic EEG (s-EEG) electrode arrays implanted in cebus monkeys and surgical epilepsy patients. We found a small frequency dependent decrease (10%) in magnitudes of TES induced potentials and negligible phase shifts over space. Electric field strengths were strongest in superficial brain regions with maximum values of about 0.5 mV/mm. Our results provide crucial information of the underlying biophysics in TES applications in humans and the optimization and design of TES stimulation protocols. In addition, our findings have broad implications concerning electric field propagation in non-invasive recording techniques such as EEG/MEG.

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.

1D Current Source Density (CSD) Estimation in Inverse Theory: A Unified Framework for Higher-Order Spectral Regularization of Quadrature and Expansion-Type CSD Methods

Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested conditions. The unified framework we propose expands the set of available estimation methods, provides increased flexibility for 1D CSD estimation in noisy experimental conditions, and allows for a meaningful comparison between estimation schemes.

Detectability of the somatosensory evoked high frequency oscillation (HFO) co-recorded by scalp EEG and ECoG under propofol

Objective

The somatosensory evoked potential (SEP) elicited by median nerve stimulation consists of the N20 peak together with the concurrent high frequency oscillation (HFO, > 500 Hz). We describe the conditions for HFO detection in ECoG and scalp EEG in intraoperative recordings.

Methods

During neurosurgical interventions in six patients under propofol anesthesia, the SEP was recorded from subdural electrode strips (15 recordings) and from scalp electrodes (10/15 recordings). We quantified the spatial attenuation of the Signal-to-Noise Ratio (SNR) of N20 and HFO along the contacts of the electrode strip. We then compared the SNR of ECoG and simultaneous scalp EEG in a biophysical framework.

Results

HFO detection under propofol anesthesia was demonstrated. Visual inspection of strip cortical recordings revealed phase reversal for N20 in 14/15 recordings and for HFO in 10/15 recordings. N20 had higher maximal SNR (median 33.5 dB) than HFO (median 23 dB). The SNR of N20 attenuated with a larger spatial extent (median 7.2 dB/cm) than the SNR of HFO (median 12.3 dB/cm). We found significant correlations between the maximum SNR (rho = 0.58, p = 0.025) and the spatial attenuation (rho = 0.86, p < 0.001) of N20 and HFO. In 3/10 recordings we found HFO in scalp EEG. Based on the spatial attenuation and SNR in the ECoG, we estimated the scalp EEG amplitude ratio N20/HFO and found significant correlation with recorded values (rho = 0.65, p = 0.049).

Conclusions

We proved possible the intraoperative SEP HFO detection under propofol anesthesia. The spatial attenuation along ECoG contacts represents a good estimator of the area contributing to scalp EEG. The SNR and the spatial attenuation in ECoG recordings provide further insights for the prediction of HFO detectability in scalp EEG. The results obtained in this context may not be limited to SEP HFO, but could be generalized to biological signatures lying in the same SNR and frequency range.

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Somatosensory evoked HFOs can be recorded in ECoG and scalp EEG intraoperatively under propofol anesthesia.

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The HFO amplitude in ECoG attenuated to noise level over a smaller spatial scale than the N20 amplitude.

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The spatial attenuation of the cortical SNR directly relates to the noise level and to the scalp EEG amplitude.

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Parameters extracted from ECoG allowed estimating the ratio of N20/HFO amplitude in scalp EEG.

Modeling sequence and quasi-uniform assumption in computational neurostimulation

Computational neurostimulation aims to develop mathematical constructs that link the application of neuromodulation with changes in behavior and cognition. This process is critical but daunting for technical challenges and scientific unknowns. The overarching goal of this review is to address how this complex task can be made tractable. We describe a framework of sequential modeling steps to achieve this: (1) current flow models, (2) cell polarization models, (3) network and information processing models, and (4) models of the neuroscientific correlates of behavior. Each step is explained with a specific emphasis on the assumptions underpinning underlying sequential implementation. We explain the further implementation of the quasi-uniform assumption to overcome technical limitations and unknowns. We specifically focus on examples in electrical stimulation, such as transcranial direct current stimulation. Our approach and conclusions are broadly applied to immediate and ongoing efforts to deploy computational neurostimulation.

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.

Hypothesis-driven methods to augment human cognition by optimizing cortical oscillations

Cortical oscillations have been shown to represent fundamental functions of a working brain, e.g., communication, stimulus binding, error monitoring, and inhibition, and are directly linked to behavior. Recent studies intervening with these oscillations have demonstrated effective modulation of both the oscillations and behavior. In this review, we collect evidence in favor of how hypothesis-driven methods can be used to augment cognition by optimizing cortical oscillations. We elaborate their potential usefulness for three target groups: healthy elderly, patients with attention deficit/hyperactivity disorder, and healthy young adults. We discuss the relevance of neuronal oscillations in each group and show how each of them can benefit from the manipulation of functionally-related oscillations. Further, we describe methods for manipulation of neuronal oscillations including direct brain stimulation as well as indirect task alterations. We also discuss practical considerations about the proposed techniques. In conclusion, we propose that insights from neuroscience should guide techniques to augment human cognition, which in turn can provide a better understanding of how the human brain works.

Neuroenhancement: enhancing brain and mind in health and in disease

Humans have long used cognitive enhancement methods to expand the proficiency and range of the various mental activities that they engage in, including writing to store and retrieve information, and computers that allow them to perform myriad activities that are now commonplace in the internet age. Neuroenhancement describes the use of neuroscience-based techniques for enhancing cognitive function by acting directly on the human brain and nervous system, altering its properties to increase performance. Cognitive neuroscience has now reached the point where it may begin to put theory derived from years of experimentation into practice. This special issue includes 16 articles that employ or examine a variety of neuroenhancement methods currently being developed to increase cognition in healthy people and in patients with neurological or psychiatric illness. This includes transcranial electromagnetic stimulation methods, such as transcranial direct current stimulation (tDCS) and transcranial magnetic stimulation (TMS), along with deep brain stimulation, neurofeedback, behavioral training techniques, and these and other techniques in conjunction with neuroimaging. These methods can be used to improve attention, perception, memory and other forms of cognition in healthy individuals, leading to better performance in many aspects of everyday life. They may also reduce the cost, duration and overall impact of brain and mental illness in patients with neurological and psychiatric illness. Potential disadvantages of these techniques are also discussed. Given that the benefits of neuroenhancement outweigh the potential costs, these methods could potentially reduce suffering and improve quality of life for everyone, while further increasing our knowledge about the mechanisms of human cognition.