Modeling Current Sources for Neural Stimulation in COMSOL

Simulation-Informed Power Budget Estimate of a Fully-Implantable Brain-Computer Interface

This study aims to estimate the maximum power consumption that guarantees a thermally safe operation for a titanium-enclosed chest wall unit (CWU) subcutaneously implanted in the pre-pectoral area. This unit is a central piece of an envisioned fully-implantable bi-directional brain-computer interface (BD-BCI). To this end, we created a thermal simulation model using the finite element method implemented in COMSOL. We also performed a sensitivity analysis to ensure that our predictions were robust against the natural variation of physiological and environmental parameters. Based on this analysis, we predict that the CWU can consume between 378 and 538 mW of power without raising the surrounding tissue's temperature above the thermal safety threshold of 2 ∘ C. This power budget should be sufficient to power all of the CWU's basic functionalities, which include training the decoder, online decoding, wireless data transmission, and cortical stimulation. This power budget assessment provides an important specification for the design of a CWU-an integral part of a fully-implantable BD-BCI system.

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.

A full-head model to investigate intra and extracochlear electric fields in cochlear implant stimulation

Objective.Despite the widespread use and technical improvement of cochlear implant (CI) devices over past decades, further research into the bioelectric bases of CI stimulation is still needed. Various stimulation modes implemented by different CI manufacturers coexist, but their true clinical benefit remains unclear, probably due to the high inter-subject variability reported, which makes the prediction of CI outcomes and the optimal fitting of stimulation parameters challenging. A highly detailed full-head model that includes a cochlea and an electrode array is developed in this study to emulate intracochlear voltages and extracochlear current pathways through the head in CI stimulation.Approach.Simulations based on the finite element method were conducted under monopolar, bipolar, tripolar (TP), and partial TP modes, as well as for apical, medial, and basal electrodes. Variables simulated included: intracochlear voltages, electric field (EF) decay, electric potentials at the scalp and extracochlear currents through the head. To better understand CI side effects such as facial nerve stimulation, caused by spurious current leakage out from the cochlea, special emphasis is given to the analysis of the EF over the facial nerve.Main results.The model reasonably predicts EF magnitudes and trends previously reported in CI users. New relevant extracochlear current pathways through the head and brain tissues have been identified. Simulated results also show differences in the magnitude and distribution of the EF through different segments of the facial nerve upon different stimulation modes and electrodes, dependent on nerve and bone tissue conductivities.Significance.Full-head models prove useful tools to model intra and extracochlear EFs in CI stimulation. Our findings could prove useful in the design of future experimental studies to contrast FNS mechanisms upon stimulation of different electrodes and CI modes. The full-head model developed is freely available for the CI community for further research and use.

Neural Tissue-Like, not Supraphysiological, Electrical Conductivity Stimulates Neuronal Lineage Specification through Calcium Signaling and Epigenetic Modification

Electrical conductivity is a pivotal biophysical factor for neural interfaces, though optimal values remain controversial due to challenges isolating this cue. To address this issue, conductive substrates made of carbon nanotubes and graphene oxide nanoribbons, exhibiting a spectrum of conductivities from 0.02 to 3.2 S m-1, while controlling other surface properties is designed. The focus is to ascertain whether varying conductivity in isolation has any discernable impact on neural lineage specification. Remarkably, neural-tissue-like low conductivity (0.02-0.1 S m-1) prompted neural stem/progenitor cells to exhibit a greater propensity toward neuronal lineage specification (neurons and oligodendrocytes, not astrocytes) compared to high supraphysiological conductivity (3.2 S m-1). High conductivity instigated the apoptotic process, characterized by increased apoptotic fraction and decreased neurogenic morphological features, primarily due to calcium overload. Conversely, cells exposed to physiological conductivity displayed epigenetic changes, specifically increased chromatin openness with H3acetylation (H3ac) and neurogenic-transcription-factor activation, along with a more balanced intracellular calcium response. The pharmacological inhibition of H3ac further supported the idea that such epigenetic changes might play a key role in driving neuronal specification in response to neural-tissue-like, not supraphysiological, conductive cues. These findings underscore the necessity of optimal conductivity when designing neural interfaces and scaffolds to stimulate neuronal differentiation and facilitate the repair process.

Shedding Light on Cardiac Excitation: In Vitro and In Silico Analysis of Native Ca2+ Channel Activation in Guinea Pig Cardiomyocytes Using Organic Photovoltaic Devices

OBJECTIVE

This study aims to explore the potential of organic electrolytic photocapacitors (OEPCs), an innovative photovoltaic device, in mediating the activation of native voltage-gated Cav1.2 channels (ICa,L) in Guinea pig ventricular cardiomyocytes.

METHODS

Whole-cell patch-clamp recordings were employed to examine light-triggered OEPC mediated ICa,L activation, integrating the channel's kinetic properties into a multicompartment cell model to take intracellular ion concentrations into account. A multidomain model was additionally incorporated to evaluate effects of OEPC-mediated stimulation. The final model combines external stimulation, multicompartmental cell simulation, and a patch-clamp amplifier equivalent circuit to assess the impact on achievable intracellular voltage changes.

RESULTS

Light pulses activated ICa,L, with amplitudes similar to voltage-clamp activation and high sensitivity to the L-type Ca2+ channel blocker, nifedipine. Light-triggered ICa,L inactivation exhibited kinetic parameters comparable to voltage-induced inactivation.

CONCLUSION

OEPC-mediated activation of ICa,L demonstrates their potential for nongenetic optical modulation of cellular physiology potentially paving the way for the development of innovative therapies in cardiovascular health. The integrated model proves the light-mediated activation of ICa,L and advances the understanding of the interplay between the patch-clamp amplifier and external stimulation devices.

SIGNIFICANCE

Treating cardiac conduction disorders by minimal-invasive means without genetic modifications could advance therapeutic approaches increasing patients' quality of life compared with conventional methods employing electronic devices.

Flexible circumferential bioelectronics to enable 360-degree recording and stimulation of the spinal cord

The spinal cord is crucial for transmitting motor and sensory information between the brain and peripheral systems. Spinal cord injuries can lead to severe consequences, including paralysis and autonomic dysfunction. We introduce thin-film, flexible electronics for circumferential interfacing with the spinal cord. This method enables simultaneous recording and stimulation of dorsal, lateral, and ventral tracts with a single device. Our findings include successful motor and sensory signal capture and elicitation in anesthetized rats, a proof-of-concept closed-loop system for bridging complete spinal cord injuries, and device safety verification in freely moving rodents. Moreover, we demonstrate potential for human application through a cadaver model. This method sees a clear route to the clinic by using materials and surgical practices that mitigate risk during implantation and preserve cord integrity.

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.

Computational models of compound nerve action potentials: Efficient filter-based methods to quantify effects of tissue conductivities, conduction distance, and nerve fiber parameters

BACKGROUND

Peripheral nerve recordings can enhance the efficacy of neurostimulation therapies by providing a feedback signal to adjust stimulation settings for greater efficacy or reduced side effects. Computational models can accelerate the development of interfaces with high signal-to-noise ratio and selective recording. However, validation and tuning of model outputs against in vivo recordings remains computationally prohibitive due to the large number of fibers in a nerve.

METHODS

We designed and implemented highly efficient modeling methods for simulating electrically evoked compound nerve action potential (CNAP) signals. The method simulated a subset of fiber diameters present in the nerve using NEURON, interpolated action potential templates across fiber diameters, and filtered the templates with a weighting function derived from fiber-specific conduction velocity and electromagnetic reciprocity outputs of a volume conductor model. We applied the methods to simulate CNAPs from rat cervical vagus nerve.

RESULTS

Brute force simulation of a rat vagal CNAP with all 1,759 myelinated and 13,283 unmyelinated fibers in NEURON required 286 and 15,860 CPU hours, respectively, while filtering interpolated templates required 30 and 38 seconds on a desktop computer while maintaining accuracy. Modeled CNAP amplitude could vary by over two orders of magnitude depending on tissue conductivities and cuff opening within experimentally relevant ranges. Conduction distance and fiber diameter distribution also strongly influenced the modeled CNAP amplitude, shape, and latency. Modeled and in vivo signals had comparable shape, amplitude, and latency for myelinated fibers but not for unmyelinated fibers.

CONCLUSIONS

Highly efficient methods of modeling neural recordings quantified the large impact that tissue properties, conduction distance, and nerve fiber parameters have on CNAPs. These methods expand the computational accessibility of neural recording models, enable efficient model tuning for validation, and facilitate the design of novel recording interfaces for neurostimulation feedback and understanding physiological systems.

Patient-specific computational models of retinal prostheses

Retinal prostheses stimulate inner retinal neurons to create visual perception for blind patients. Implanted arrays have many small electrodes. Not all electrodes induce perception at the same stimulus amplitude, requiring clinicians to manually establish a visual perception threshold for each one. Phosphenes created by single-electrode stimuli can also vary in shape, size, and brightness. Computational models provide a tool to predict inter-electrode variability and automate device programming. In this study, we created statistical and patient-specific field-cable models to investigate inter-electrode variability across seven epiretinal prosthesis users. Our statistical analysis revealed that retinal thickness beneath the electrode correlated with perceptual threshold, with a significant fixed effect across participants. Electrode-retina distance and electrode impedance also correlated with perceptual threshold for some participants, but these effects varied by individual. We developed a novel method to construct patient-specific field-cable models from optical coherence tomography images. Predictions with these models significantly correlated with perceptual threshold for 80% of participants. Additionally, we demonstrated that patient-specific field-cable models could predict retinal activity and phosphene size. These computational models could be beneficial for determining optimal stimulation settings in silico, circumventing the trial-and-error testing of a large parameter space in clinic.

Adaptive octree meshes for simulation of extracellular electrophysiology

Objective.The interaction between neural tissues and artificial electrodes is crucial for understanding and advancing neuroscientific research and therapeutic applications. However, accurately modeling this space around the neurons rapidly increases the computational complexity of neural simulations.Approach.This study demonstrates a dynamically adaptive simulation method that greatly accelerates computation by adjusting spatial resolution of the simulation as needed. Use of an octree structure for the mesh, in combination with the admittance method for discretizing conductivity, provides both accurate approximation and ease of modification on-the-fly.Main results.In tests of both local field potential estimation and multi-electrode stimulation, dynamically adapted meshes achieve accuracy comparable to high-resolution static meshes in an order of magnitude less time.Significance.The proposed simulation pipeline improves model scalability, allowing greater detail with fewer computational resources. The implementation is available as an open-source Python module, providing flexibility and ease of reuse for the broader research community.

How far does electrical stimulation activate white matter tracts? A computational modeling study

OBJECTIVE

The aim of this study was to model how the different parameters of electrical stimulation (intensity, pulse shape, probe geometry) influence the extent of white matter activation.

METHODS

The electrical potentials generated by the stimulating electrodes were determined by solving Laplace equation. The temporal evolution of membrane potentials at each nodes of Ranvier of an axon was then computed by solving the coupled system of differential equations describing membrane dynamics and cable propagation.

RESULTS

Regions of unilateral propagation were observed for monophasic pulses delivered with a bipolar probe aligned along the tract. For biphasic pulses, the largest activation areas and depths were found with a high inter-electrode-distance (IED) bipolar probe, oriented orthogonally to the tract. The smallest activation areas and depths were found for bipolar stimulations with the probe aligned parallel to the tract and low IED. For isotropic white matter regions, the activation area and depth were three times larger than for anisotropic white matter tracts.

CONCLUSIONS

Bipolar probes with biphasic pulses offer the greatest versatility: an orthogonal orientation acts as two monopolars (increased sensitivity when searching for a tract), whereas a parallel orientation corresponds to a single monopolar (increased specificity). Activation is more superficial when stimulating highly anisotropic tracts.

SIGNIFICANCE

This knowledge is essential for interpreting the behavorial effects of stimulation and the recordings of axono-cortical evoked potentials.

Patient-specific computational models of retinal prostheses

Retinal prostheses stimulate inner retinal neurons to create visual perception for blind patients. Implanted arrays have many small electrodes, which act as pixels. Not all electrodes induce perception at the same stimulus amplitude, requiring clinicians to manually establish a visual perception threshold for each one. Phosphenes created by single-electrode stimuli can also vary in shape, size, and brightness. Computational models provide a tool to predict inter-electrode variability and automate device programming. In this study, we created statistical and patient-specific field-cable models to investigate inter-electrode variability across seven epiretinal prosthesis users. Our statistical analysis revealed that retinal thickness beneath the electrode correlated with perceptual threshold, with a significant fixed effect across participants. Electrode-retina distance and electrode impedance also correlated with perceptual threshold for some participants, but these effects varied by individual. We developed a novel method to construct patient-specific field-cable models from optical coherence tomography images. Predictions with these models significantly correlated with perceptual threshold for 80% of participants. Additionally, we demonstrated that patient-specific field-cable models could predict retinal activity and phosphene size. These computational models could be beneficial for determining optimal stimulation settings in silico, circumventing the trial-and-error testing of a large parameter space in clinic.

MXene functionalized collagen biomaterials for cardiac tissue engineering driving iPSC-derived cardiomyocyte maturation

Electroconductive biomaterials are gaining significant consideration for regeneration in tissues where electrical functionality is of crucial importance, such as myocardium, neural, musculoskeletal, and bone tissue. In this work, conductive biohybrid platforms were engineered by blending collagen type I and 2D MXene (Ti3C2Tx) and afterwards covalently crosslinking; to harness the biofunctionality of the protein component and the increased stiffness and enhanced electrical conductivity (matching and even surpassing native tissues) that two-dimensional titanium carbide provides. These MXene platforms were highly biocompatible and resulted in increased proliferation and cell spreading when seeded with fibroblasts. Conversely, they limited bacterial attachment (Staphylococcus aureus) and proliferation. When neonatal rat cardiomyocytes (nrCMs) were cultured on the substrates increased spreading and viability up to day 7 were studied when compared to control collagen substrates. Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) were seeded and stimulated using electric-field generation in a custom-made bioreactor. The combination of an electroconductive substrate with an external electrical field enhanced cell growth, and significantly increased cx43 expression. This in vitro study convincingly demonstrates the potential of this engineered conductive biohybrid platform for cardiac tissue regeneration.

Validated computational models predict vagus nerve stimulation thresholds in preclinical animals and humans

Objective.We demonstrated how automated simulations to characterize electrical nerve thresholds, a recently published open-source software for modeling stimulation of peripheral nerves, can be applied to simulate accurately nerve responses to electrical stimulation.Approach.We simulated vagus nerve stimulation (VNS) for humans, pigs, and rats. We informed our models using histology from sample-specific or representative nerves, device design features (i.e. cuff, waveform), published material and tissue conductivities, and realistic fiber models.Main results.Despite large differences in nerve size, cuff geometry, and stimulation waveform, the models predicted accurate activation thresholds across species and myelinated fiber types. However, our C fiber model thresholds overestimated thresholds across pulse widths, suggesting that improved models of unmyelinated nerve fibers are needed. Our models of human VNS yielded accurate thresholds to activate laryngeal motor fibers and captured the inter-individual variability for both acute and chronic implants. For B fibers, our small-diameter fiber model underestimated threshold and saturation for pulse widths >0.25 ms. Our models of pig VNS consistently captured the range ofin vivothresholds across all measured nerve and physiological responses (i.e. heart rate, Aδ/B fibers, Aγfibers, electromyography, and Aαfibers). In rats, our smallest diameter myelinated fibers accurately predicted fast fiber thresholds across short and intermediate pulse widths; slow unmyelinated fiber thresholds overestimated thresholds across shorter pulse widths, but there was overlap for pulse widths >0.3 ms.Significance.We elevated standards for models of peripheral nerve stimulation in populations of models across species, which enabled us to model accurately nerve responses, demonstrate that individual-specific differences in nerve morphology produce variability in neural and physiological responses, and predict mechanisms of VNS therapeutic and side effects.

Modeling the Impact of Electrode/Tissue Geometry on Electrical Stimulation in Stereo-EEG

PURPOSE

Electrical stimulation through depth electrodes is used to map function and seizure onset during stereoelectroencephalography in patients undergoing evaluation for epilepsy surgery. Factors such as electrode design, location, and orientation are expected to impact effects of electrical stimulation.

METHODS

We developed a steady-state finite element model of brain tissue including five layers (skull through white matter) and an implanted electrode to explore the impact of electrode design and placement on the activation of brain tissue by electrical stimulation. We calculated electric potentials, current densities, and volume of tissue activated ( Volact ) in response to constant current bipolar stimulation. We modeled two depth electrode designs (3.5- and 4.43-mm intercontact spacing) and varied electrode location and orientation.

RESULTS

The electrode with greater intercontact spacing produced 8% to 23% larger Volact (1% to 16% considering only gray matter). Vertical displacement of the electrodes by half intercontact space increased Volact for upward displacement (6% to 83% for all brain tissue or -5% to 96% gray matter only) and decreased Volact (1% to 16% or 24% to 49% gray matter only) for downward displacement. Rotating the electrode in the tissue by 30° to 60° with respect to the vertical axis increased Volact by 30% to 90% (20%-48% gray matter only).

CONCLUSIONS

Location and orientation of depth electrodes with respect to surrounding brain tissue have a large impact on the amount of tissue activated during electrical stimulation mapping in stereoelectroencephalography. Electrode design has an impact, although modest for commonly used designs. Individualization of stimulation intensity at each location remains critical, especially for avoiding false-negative results.

Fibers in smaller fascicles have lower activation thresholds with cuff electrodes due to thinner perineurium and smaller cross-sectional area

Objective. In nerve stimulation therapies, fibers in larger fascicles generally have higher activation thresholds, but the mechanisms are not well understood. We implemented and analyzed computational models to uncover the effects of morphological parameters on activation thresholds.Approach. We implemented finite element models of human vagus nerve stimulation to quantify the effects of morphological parameters on thresholds in realistic nerves. We also implemented simplified models to isolate effects of perineurium thickness, endoneurium diameter, fiber diameter, and fascicle location on current density, potential distributions (Ve), and activation thresholds across cuff geometries and stimulation waveforms. UsingVefrom each finite element model, we simulated activation thresholds in biophysical cable models of mammalian axons.Main results. Perineurium thickness increases with fascicle diameter, and both thicker perineurium and larger endoneurial diameter contributed to higher activation thresholds via lower peak and broader longitudinal potentials. Thicker perineurium caused less current to enter the fascicle transversely, decreasing peakVe. Thicker perineurium also inhibited current from leaving the fascicle, causing more constant longitudinal current density, broadeningVe. With increasing endoneurial diameter, intrafascicular volume increased faster than surface area, thereby decreasing intrafascicular current density and peakVe. Additionally, larger fascicles have greater cross-sectional area, thereby facilitating longitudinal intrafascicular current flow and broadeningVe. A large neighboring fascicle could increase activation thresholds, and for a given fascicle, fiber diameter had the greatest effect on thresholds, followed by fascicle diameter, and lastly, fascicle location within the epineurium. The circumneural cuff elicited robust activation across the nerve, whereas a bipolar transverse cuff with small contacts delivering a pseudo-monophasic waveform enabled more selective activation across fiber diameters and locations.Significance. Our computational studies provide mechanistic understanding of neural responses across relevant morphological parameters of peripheral nerves, thereby informing rational design of effective therapies.

Measuring and modeling the effects of vagus nerve stimulation on heart rate and laryngeal muscles

BACKGROUND

Reduced heart rate (HR) during vagus nerve stimulation (VNS) is associated with therapy for heart failure, but stimulation frequency and amplitude are limited by patient tolerance. An understanding of physiological responses to parameter adjustments would allow differential control of therapeutic and side effects. To investigate selective modulation of the physiological responses to VNS, we quantified the effects and interactions of parameter selection on two physiological outcomes: one related to therapy (reduced HR) and one related to side effects (laryngeal muscle EMG).

METHODS

We applied a broad range of stimulation parameters (mean pulse rates (MPR), intra-burst frequencies, and amplitudes) to the vagus nerve of anesthetized mice. We leveraged the in vivo recordings to parameterize and validate computational models of HR and laryngeal muscle activity across amplitudes and temporal patterns of VNS. We constructed a finite element model of excitation of fibers within the mouse cervical vagus nerve.

RESULTS

HR decreased with increased amplitude, increased MPR, and decreased intra-burst frequency. EMG increased with increased MPR. Preferential HR effects over laryngeal EMG effects required combined adjustments of amplitude and MPR. The model of HR responses highlighted contributions of ganglionic filtering to VNS-evoked changes in HR at high stimulation frequencies. Overlap in activation thresholds between small and large modeled fibers was consistent with the overlap in dynamic ranges of related physiological measures (HR and EMG).

CONCLUSION

The present study provides insights into physiological responses to VNS required for informed parameter adjustment to modulate selectively therapeutic effects and side effects.

Ear-EEG sensitivity modeling for neural sources and ocular artifacts

The ear-EEG has emerged as a promising candidate for real-world wearable brain monitoring. While experimental studies have validated several applications of ear-EEG, the source-sensor relationship for neural sources from across the brain surface has not yet been established. In addition, modeling of the ear-EEG sensitivity to sources of artifacts is still missing. Through volume conductor modeling, the sensitivity of various configurations of ear-EEG is established for a range of neural sources, in addition to ocular artifact sources for the blink, vertical saccade, and horizontal saccade eye movements. Results conclusively support the introduction of ear-EEG into conventional EEG paradigms for monitoring neural activity that originates from within the temporal lobes, while also revealing the extent to which ear-EEG can be used for sources further away from these regions. The use of ear-EEG in scenarios prone to ocular artifacts is also supported, through the demonstration of proportional scaling of artifacts and neural signals in various configurations of ear-EEG. The results from this study can be used to support both existing and prospective experimental ear-EEG studies and applications in the context of sensitivity to both neural sources and ocular artifacts.

Surround Inhibition Mediates Pain Relief by Low Amplitude Spinal Cord Stimulation: Modeling and Measurement

Low-frequency (<200 Hz), subperception spinal cord stimulation (SCS) is a novel modality demonstrating therapeutic efficacy for treating chronic neuropathic pain. When stimulation parameters were carefully titrated, patients experienced rapid onset (seconds-minutes) pain relief without paresthesia, but the mechanisms of action are unknown. Using an integrated computational model and in vivo measurements in urethane-anesthetized rats, we quantified how stimulation parameters (placement, pulse width, frequency, and amplitude) influenced dorsal column (DC) axon activation and neural responses in the dorsal horn (DH). Both modeled and recorded DC axons responded with irregular spiking patterns in response to low-amplitude SCS. Maximum inhibition of DH neurons occurred at ∼80% of the predicted sensory threshold in both modeled and recorded neurons, and responses were strongly dependent on spatially targeting of stimulation, i.e., the complement of DC axons activated, and on stimulation parameters. Intrathecal administration of bicuculline shifted neural responses to low-amplitude stimulation in both the model and experiment, suggesting that analgesia is dependent on segmental GABAergic mechanisms. Our results support the hypothesis that low-frequency subperception SCS generates rapid analgesia by activating a small number of DC axons which inhibit DH neuron activity via surround inhibition.

An in-silico analysis of electrically-evoked responses of midget and parasol retinal ganglion cells in different retinal regions

BACKGROUND

Visual outcomes provided by present retinal prostheses that primarily target retinal ganglion cells (RGCs) through epiretinal stimulation remain rudimentary, partly due to the limited knowledge of retinal responses under electrical stimulation. Better understanding of how different retinal regions can be quantitatively controlled with high spatial accuracy, will be beneficial to the design of micro-electrode arrays (MEAs) and stimulation strategies for next-generation wide-view, high-resolution epiretinal implants.

METHODS

A computational model was developed to assess neural activity at different eccentricities (2 mm and 5 mm) within the human retina. This model included midget and parasol RGCs with anatomically accurate cell distribution and cell-specific morphological information. We then performed in silico investigations of region-specific RGC responses to epiretinal electrical stimulation using varied electrode sizes (5 µm - 210 µm diameter), emulating both commercialized retinal implants and recently-developed prototype devices.

RESULTS

Our model of epiretinal stimulation predicted RGC population excitation analogous to the complex percepts reported in human subjects. Following this, our simulations suggest that midget and parasol RGCs have characteristic regional differences in excitation under preferred electrode sizes. Relatively central (2 mm) regions demonstrated higher number of excited RGCs but lower overall activated receptive field (RF) areas under the same stimulus amplitudes (two-way ANOVA, p < 0.05). Furthermore, the activated RGC numbers per unit active RF area (number-RF ratio) were significantly higher in central than in peripheral regions, and higher in the midget than in the parasol population under all tested electrode sizes (two-way ANOVA, p < 0.05). Our simulations also suggested that smaller electrodes exhibit a higher range of controllable stimulation parameters to achieve pre-defined performance of RGC excitation. ..

Modeling implanted metals in electrical stimulation applications

OBJECTIVE

Metal implants impact the dosimetry assessment in electrical stimulation techniques. Therefore, they need to be included in numerical models. While currents in the body are ionic, metals only allow electron transport. In fact, charge transfer between tissues and metals requires electric fields to drive electrochemical reactions at the interface. Thus, metal implants may act as insulators or as conductors depending on the scenario. The aim of this paper is to provide a theoretical argument that guides the choice of the correct representation of metal implants in electrical models while considering the electrochemical nature of the problem Approach: We built a simple model of a metal implant exposed to a homogeneous electric field of various magnitudes. The same geometry was solved using two different models: a purely electric one (with different conductivities for the implant), and an electrochemical one. As an example of application, we also modeled a transcranial electrical stimulation (tES) treatment in a realistic head model with a skull plate using a high and low conductivity value for the plate.

MAIN RESULTS

Metal implants generally act as electric insulators when exposed to electric fields up to around 100 V/m and they only resemble a perfect conductor for fields in the order of 1000 V/m and above. The results are independent of the implant's metal, but they depend on its geometry. tES modeling with implants incorrectly treated as conductors can lead to errors of 50% or more in the estimation of the induced fields Significance: Metal implants can be accurately represented by a simple electrical model of constant conductivity, but an incorrect model choice can lead to large errors in the dosimetry assessment. Our results can be used to guide the selection of the most appropriate model in each scenario.

Comparison of methodologies for modeling directional deep brain stimulation electrodes

Deep brain stimulation (DBS) is an established clinical therapy, and directional DBS electrode designs are now commonly used in clinical practice. Directional DBS leads have the ability to increase the therapeutic window of stimulation, but they also increase the complexity of clinical programming. Therefore, computational models of DBS have become available in clinical software tools that are designed to assist in the identification of therapeutic settings. However, the details of how the DBS model is implemented can influence the predictions of the software. The goal of this study was to compare different methods for representing directional DBS electrodes within finite element volume conductor (VC) models. We evaluated 15 different DBS VC model variants and quantified how their differences influenced estimates on the spatial extent of axonal activation from DBS. Each DBS VC model included the same representation of the brain and head, but the details of the current source and electrode contact were different for each model variant. The more complex VC models explicitly represented the DBS electrode contacts, while the more simple VC models used boundary condition approximations. The more complex VC models required 2-3 times longer to mesh, build, and solve for the DBS voltage distribution than the more simple VC models. Differences in individual axonal activation thresholds across the VC model variants were substantial (-24% to +47%). However, when comparing total activation of an axon population, or estimates of an activation volume, the differences between model variants decreased (-7% to +8%). Nonetheless, the technical details of how the electrode contact and current source are represented in the DBS VC model can directly affect estimates of the voltage distribution and electric field in the brain tissue.

Translating node of Ranvier currents to extraneural electrical fields: a flexible FEM modeling approach

Simulations of electroneurogram recording could help find the optimal set of electrodes and algorithms for selective neural recording. However, no flexible methods are established for selective neural recording as for neural stimulation. This paper proposes a method to couple a compartmental and a FEM nerve model, implemented in NEURON and COMSOL, respectively, to translate Node of Ranvier currents into extraneural electric fields. The study simulate ex-vivo experimental conditions, and the method allows flexibility in electrode geometries and nerve topologies. This model has been made available in a public repository⁴. So far, the model behavior complies with available experimental results and expectations from literature. There is good agreement in terms of signal amplitude and waveform, and computational times are acceptable, leaving room for flexible simulation studies complementary to animal tests.

ASCENT (Automated Simulations to Characterize Electrical Nerve Thresholds): A pipeline for sample-specific computational modeling of electrical stimulation of peripheral nerves

Electrical stimulation and block of peripheral nerves hold great promise for treatment of a range of disease and disorders, but promising results from preclinical studies often fail to translate to successful clinical therapies. Differences in neural anatomy across species require different electrodes and stimulation parameters to achieve equivalent nerve responses, and accounting for the consequences of these factors is difficult. We describe the implementation, validation, and application of a standardized, modular, and scalable computational modeling pipeline for biophysical simulations of electrical activation and block of nerve fibers within peripheral nerves. The ASCENT (Automated Simulations to Characterize Electrical Nerve Thresholds) pipeline provides a suite of built-in capabilities for user control over the entire workflow, including libraries for parts to assemble electrodes, electrical properties of biological materials, previously published fiber models, and common stimulation waveforms. We validated the accuracy of ASCENT calculations, verified usability in beta release, and provide several compelling examples of ASCENT-implemented models. ASCENT will enable the reproducibility of simulation data, and it will be used as a component of integrated simulations with other models (e.g., organ system models), to interpret experimental results, and to design experimental and clinical interventions for the advancement of peripheral nerve stimulation therapies.

Despite promising results from preclinical studies, novel therapies using electrical stimulation of peripheral nerves often fail to produce successful clinical outcomes due to differences in neural anatomy across species. These differences often require different electrodes to interface with the nerves and/or different stimulation parameters to achieve equivalent nerve responses. Further, differences in nerve anatomy across a population contribute to differences in nerve responses to stimulation. These inter-species and inter-individual differences can be studied using computational modeling of individual-specific peripheral nerve morphology and biophysical properties. To accelerate the process of computational modeling of individual nerve anatomy, we developed ASCENT, a software platform for simulating the responses of sample-specific nerves to electrical stimulation with custom electrodes and stimulation parameters. ASCENT automates the complex, multi-step process required to build computational models of preclinical and clinical studies and to design novel stimulation protocols using biophysically realistic simulations. The ASCENT pipeline will be used to develop technologies that increase the selectivity and efficiency of stimulation and to accelerate the translation of novel peripheral nerve stimulation therapies to the clinic.

Validation of a parameterized, open-source model of nerve stimulation

Peripheral nerve stimulation is an effective treatment for various neurological disorders. The method of activation and stimulation parameters used impact the efficacy of the therapy, which emphasizes the need for tools to model this behavior. Computational modeling of nerve stimulation has proven to be a useful tool for estimating stimulation thresholds, optimizing electrode design, and exploring previously untested stimulation methods. Despite their utility, these tools require access to and familiarity with several pieces of specialized software. A simpler, streamlined process would increase accessibility significantly. We developed an open-source, parameterized model with a simple online user interface that allows user to adjust up to 36 different parameters (https://nervestimlab.utdallas.edu). The model accurately predicts fiber activation thresholds for nerve and electrode combinations reported in literature. Additionally, it replicates characteristic differences between stimulation methods, such as lower thresholds with monopolar stimulation as compared to tripolar stimulation. The model predicted that the difference in threshold between monophasic and biphasic waveforms, a well-characterized phenomenon, is not present during stimulation with bipolar electrodes.In vivotesting on the rat sciatic nerve validated this prediction, which has not been previously reported. The accuracy of the model when compared to previous experiments, as well as the ease of use and accessibility to generate testable hypotheses, indicate that this software may represent a useful tool for a variety of nerve stimulation applications.

Digital Health Integration With Neuromodulation Therapies: The Future of Patient-Centric Innovation in Neuromodulation

Digital health can drive patient-centric innovation in neuromodulation by leveraging current tools to identify response predictors and digital biomarkers. Iterative technological evolution has led us to an ideal point to integrate digital health with neuromodulation. Here, we provide an overview of the digital health building-blocks, the status of advanced neuromodulation technologies, and future applications for neuromodulation with digital health integration.

The effect of axon trajectory on retinal ganglion cell activation with epiretinal stimulation

For epiretinal prostheses, disc electrodes stimulate retinal ganglion cells (RGCs) with electric current to create visual percepts. Prior studies have determined that the sodium channel band (SOCB), located on the RGC axon (30-50 μm from the soma) is the most sensitive site to extracellular stimulation because of its high sodium channel density. Biophysical cable models used to study RGC activation in silico often rely on simplified axon trajectories, disregarding the non-uniform paths that axons follow to the optic disc. However, since axonal activation is a critical mechanism in epiretinal stimulation, it is important to investigate variable RGC axon trajectories. In this study, we use a computational model to perform a sensitivity analysis examining how the morphology of an RGC axon affects predictions of retinal activation. We determine that RGC cable models are sensitive to changes in the ascending axon trajectory between the soma and nerve fiber layer. On the other hand, RGC cable models are relatively robust to trajectory deviations in the plane parallel to the disc electrode's surface. Overall, our results suggest that incorporating natural variations of soma depth and nerve fiber layer entry angle could result in a more realistic model of the retina's response to epiretinal stimulation and a better understanding of elicited visual percepts.

Non-monotonic kilohertz frequency neural block thresholds arise from amplitude- and frequency-dependent charge imbalance

Reversible block of nerve conduction using kilohertz frequency electrical signals has substantial potential for treatment of disease. However, the ability to block nerve fibers selectively is limited by poor understanding of the relationship between waveform parameters and the nerve fibers that are blocked. Previous in vivo studies reported non-monotonic relationships between block signal frequency and block threshold, suggesting the potential for fiber-selective block. However, the mechanisms of non-monotonic block thresholds were unclear, and these findings were not replicated in a subsequent in vivo study. We used high-fidelity computational models and in vivo experiments in anesthetized rats to show that non-monotonic threshold-frequency relationships do occur, that they result from amplitude- and frequency-dependent charge imbalances that cause a shift between kilohertz frequency and direct current block regimes, and that these relationships can differ across fiber diameters such that smaller fibers can be blocked at lower thresholds than larger fibers. These results reconcile previous contradictory studies, clarify the mechanisms of interaction between kilohertz frequency and direct current block, and demonstrate the potential for selective block of small fiber diameters.

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

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

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

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

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Individual VTAs deviate from optimal stimulation sites to varying degrees.

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

Background

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

Methods

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

Results

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

Conclusion

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

Novel Electrode Designs for Neurostimulation in Regenerative Medicine: Activation of Stem Cells

Neural stem and progenitor cells (i.e., neural precursors) are found within specific regions in the central nervous system and have great regenerative capacity. These cells are electrosensitive and their behavior can be regulated by the presence of electric fields (EFs). Electrical stimulation is currently used to treat neurological disorders in a clinical setting. Herein we propose that electrical stimulation can be used to enhance neural repair by regulating neural precursor cell (NPC) kinetics and promoting their migration to sites of injury or disease. We discuss how intrinsic and extrinsic factors can affect NPC migration in the presence of an EF and how this impacts electrode design with the goal of enhancing tissue regeneration. We conclude with an outlook on future clinical applications of electrical stimulation and highlight technological advances that would greatly support these applications.

Biophysics of Temporal Interference Stimulation

Temporal interference (TI) is a non-invasive neurostimulation technique that utilizes high-frequency external electric fields to stimulate deep neuronal structures without affecting superficial, off-target structures. TI represents a potential breakthrough for treating conditions, such as Parkinson's disease and chronic pain. However, early clinical work on TI stimulation was met with mixed outcomes challenging its fundamental mechanisms and applications. Here, we apply established physics to study the mechanisms of TI with the goal of optimizing it for clinical use. We argue that TI stimulation cannot work via passive membrane filtering, as previously hypothesized. Instead, TI stimulation requires an ion-channel mediated signal rectification process. Unfortunately, this mechanism is also responsible for high-frequency conduction block in off-target tissues, thus challenging clinical applications of TI. In consequence, we propose a set of experimental controls that should be performed in future experiments to refine our understanding and practice of TI stimulation. A record of this paper's transparent peer review process is included in the Supplemental Information.

Creation of virtual channels in the retina using synchronous and asynchronous stimulation - a modelling study

OBJECTIVE

Implantable retinal prostheses aim to provide artificial vision to those suffering from retinal degenerative diseases by electrically stimulating the remaining retinal neurons using a multi-electrode array. The spatial resolution of these devices can be improved by creation of so-called virtual channels (VCs) that are commonly achieved through synchronized stimulation of multiple electrodes. It is largely unclear though if VCs can be created using asynchronous stimulation, which was the primary aim of this study.

APPROACH

A computational model of multi-layered retina and epi-retinal dual-electrode stimulation was developed to simulate the neural activity of populations of retinal ganglion cells (RGCs) using the VC strategy under both synchronous and asynchronous stimulation conditions.

MAIN RESULTS

Our simulation suggests that VCs can be created using asynchronous stimulation. VC performance under both synchronous and asynchronous stimulation conditions can be improved by optimizing stimulation parameters such as current intensity, current ratio (α) between two electrodes, electrode spacing and the stimulation waveform. In particular, two VC performance measures; (1) linear displacement of the centroid of RGC activation, and (2) the RGC activation size consistency as a function of different current ratios α, have comparable performance under asynchronous and synchronous stimulation with appropriately selected stimulation parameters.

SIGNIFICANCE

Our findings support the possibility of creating VCs in the retina under both synchronous and asynchronous stimulation conditions. The results provide theoretical evidence for future retinal prosthesis designs with higher spatial resolution and power efficiency whilst reducing the number of current sources required to achieve these outcomes.

Quantitative comparisons of block thresholds and onset responses for charge-balanced kilohertz frequency waveforms

OBJECTIVE

There is growing interest in delivering kilohertz frequency (KHF) electrical signals to block conduction in peripheral nerves for treatment of various diseases. Previous studies used different KHF waveforms to achieve block, and it remains unclear how waveform affects nerve block parameters.

APPROACH

We quantified the effects of waveform on KHF block of the rat tibial nerve in vivo and in computational models. We compared block thresholds and onset responses across current-controlled sinusoids and charge-balanced rectangular waveforms with different asymmetries and duty cycles.

MAIN RESULTS

Sine waves had higher block thresholds than square waves, but used less power at block threshold. Block threshold had an inverse relationship with duty cycle of rectangular waveforms irrespective of waveform asymmetry. Computational model results were consistent with relationships measured in vivo, although the models underestimated the effect of duty cycle on increasing thresholds. The axonal membrane substantially filtered waveforms, the filter transfer function was strikingly similar across waveforms, and filtering resulted in post-filtered rms block thresholds that were approximately constant across waveforms in silico and in vivo. Onset response was not consistently affected by waveform shape, but onset response was smaller at amplitudes well above block threshold. Therefore, waveforms with lower block thresholds (e.g. sine waves or square waves) could be more readily increased to higher amplitudes relative to block threshold to reduce onset response. We also observed a reduction in onset responses across consecutive trials after initial application of supra-block threshold amplitudes.

SIGNIFICANCE

Waveform had substantial effects on block thresholds, and the amplitude relative to block threshold had substantial effects on onset response. These data inform choice of waveform in subsequent studies and clinical applications, enhance effective use of block in therapeutic applications, and facilitate the design of parameters that achieve block with minimal onset responses.

Automatic three-dimensional reconstruction of fascicles in peripheral nerves from histological images

Computational studies can be used to support the development of peripheral nerve interfaces, but currently use simplified models of nerve anatomy, which may impact the applicability of simulation results. To better quantify and model neural anatomy across the population, we have developed an algorithm to automatically reconstruct accurate peripheral nerve models from histological cross-sections. We acquired serial median nerve cross-sections from human cadaveric samples, staining one set with hematoxylin and eosin (H&E) and the other using immunohistochemistry (IHC) with anti-neurofilament antibody. We developed a four-step processing pipeline involving registration, fascicle detection, segmentation, and reconstruction. We compared the output of each step to manual ground truths, and additionally compared the final models to commonly used extrusions, via intersection-over-union (IOU). Fascicle detection and segmentation required the use of a neural network and active contours in H&E-stained images, but only simple image processing methods for IHC-stained images. Reconstruction achieved an IOU of 0.42±0.07 for H&E and 0.37±0.16 for IHC images, with errors partially attributable to global misalignment at the registration step, rather than poor reconstruction. This work provides a quantitative baseline for fully automatic construction of peripheral nerve models. Our models provided fascicular shape and branching information that would be lost via extrusion.

A Patient-Specific Computational Framework for the Argus II Implant

Goal

Retinal prosthesis performance is limited by the variability of elicited phosphenes. The stimulating electrode's position with respect to retinal ganglion cells (RGCs) affects both perceptual threshold and phosphene shape. We created a modeling framework incorporating patient-specific anatomy and electrode location to investigate RGC activation and predict inter-electrode differences for one Argus II user.

Methods

We used ocular imaging to build a three-dimensional finite element model characterizing retinal morphology and implant placement. To predict the neural response to stimulation, we coupled electric fields with multi-compartment cable models of RGCs. We evaluated our model predictions by comparing them to patient-reported perceptual threshold measurements.

Results

Our model was validated by the ability to replicate clinical impedance and threshold values, along with known neurophysiological trends. Inter-electrode threshold differences in silico correlated with in vivo results.

Conclusions

We developed a patient-specific retinal stimulation framework to quantitatively predict RGC activation and better explain phosphene variations.

Multimodal characterization of the human nucleus accumbens

Dysregulation of the nucleus accumbens (NAc) is implicated in numerous neuropsychiatric disorders. Treatments targeting this area directly (e.g. deep brain stimulation) demonstrate variable efficacy, perhaps owing to non-specific targeting of a functionally heterogeneous nucleus. Here we provide support for this notion, first observing disparate behavioral effects in response to direct simulation of different locations within the NAc in a human patient. These observations motivate a segmentation of the NAc into subregions, which we produce from a diffusion-tractography based analysis of 245 young, unrelated healthy subjects. We further explore the mechanism of these stimulation-induced behavioral responses by identifying the most probable subset of axons activated using a patient-specific computational model. We validate our diffusion-based segmentation using evidence from several modalities, including MRI-based measures of function and microstructure, human post-mortem immunohistochemical staining, and cross-species comparison of cortical-NAc projections that are known to be conserved. Finally, we visualize the passage of individual axon bundles through one NAc subregion in a post-mortem human sample using CLARITY 3D histology corroborated by 7T tractography. Collectively, these findings extensively characterize human NAc subregions and provide insight into their structural and functional distinctions with implications for stereotactic treatments targeting this region.

Assessment of axonal recruitment using model-guided preclinical spinal cord stimulation in the ex vivo adult mouse spinal cord

Spinal cord stimulation (SCS) is used clinically to limit chronic pain, but fundamental questions remain on the identity of axonal populations recruited. We developed an ex vivo adult mouse spinal cord preparation to assess recruitment following delivery of clinically analogous stimuli determined by downscaling a finite element model of clinical SCS. Analogous electric field distributions were generated with 300-µm × 300-µm electrodes positioned 200 µm above the dorsal column (DC) with stimulation between 50 and 200 µA. We compared axonal recruitment using electrodes of comparable size and stimulus amplitudes when contacting the caudal thoracic DC and at 200 or 600 μm above. Antidromic responses recorded distally from the DC, the adjacent Lissauer tract (LT), and in dorsal roots (DRs) were found to be amplitude and site dependent. Responses in the DC included a unique component not seen in DRs, having the lowest SCS recruitment amplitude and fastest conduction velocity. At 200 μm above, mean cathodic SCS recruitment threshold for axons in DRs and LT were 2.6 and 4.4 times higher, respectively, than DC threshold. SCS recruited primary afferents in all (up to 8) caudal segments sampled. Whereas A and C fibers could be recruited at nearby segments, only A fiber recruitment and synaptically mediated dorsal root reflexes were observed in more distant (lumbar) segments. In sum, clinically analogous SCS led to multisegmental recruitment of several somatosensory-encoding axonal populations. Most striking is the possibility that the lowest threshold recruitment of a nonprimary afferent population in the DC are postsynaptic dorsal column tract cells (PSDCs) projecting to gracile nuclei.NEW & NOTEWORTHY Spinal cord stimulation (SCS) is used clinically to control pain. To identify axonal populations recruited, finite element modeling identified scaling parameters to deliver clinically analogous SCS in an ex vivo adult mouse spinal cord preparation. Results showed that SCS first recruited an axonal population in the dorsal column at a threshold severalfold lower than primary afferents. These putative postsynaptic dorsal column tract cells may represent a previously unconsidered population responsible for SCS-induced paresthesias necessary for analgesia.

ELFENN: A Generalized Platform for Modeling Ephaptic Coupling in Spiking Neuron Models

The transmembrane ionic currents that underlie changes in a cell's membrane potential give rise to electric fields in the extracellular space. In the context of brain activity, these electric fields form the basis for extracellularly recorded signals, such as multiunit activity, local field potentials and electroencephalograms. Understanding the underlying neuronal dynamics and localizing current sources using these signals is often challenging, and therefore effective computational modeling approaches are critical. Typically, the electric fields from neural activity are modeled in a post-hoc form, i.e., a traditional neuronal model is used to first generate the membrane currents, which in turn are then used to calculate the electric fields. When the conductivity of the extracellular space is high, the electric fields are weak, and therefore treating membrane currents and electric fields separately is justified. However, in brain regions of lower conductivity, extracellular fields can feed back and significantly influence the underlying transmembrane currents and dynamics of nearby neurons—this is often referred to as ephaptic coupling. The closed-loop nature of ephaptic coupling cannot be modeled using the post-hoc approaches implemented by existing software tools; instead, electric fields and neuronal dynamics must be solved simultaneously. To this end, we have developed a generalized modeling toolbox for studying ephaptic coupling in compartmental neuron models: E_LFENN (E_Lectric Field Effects in Neural Networks). In open loop conditions, we validate the separate components of E_LFENN for modeling membrane dynamics and associated field potentials against standard approaches (NEURON and LFPy). Unlike standard approaches however, E_LFENN enables the closed-loop condition to be modeled as well, in that the field potentials can feed back and influence membrane dynamics. As an example closed-loop case, we use E_LFENN to study phase-locking of action potentials generated by a population of axons running parallel in a bundle. Being able to efficiently explore ephaptic coupling from a computational perspective using tools, such as E_LFENN will allow us to better understand the physical basis of electric fields in the brain, as well as the conditions in which these fields may influence neuronal dynamics in general.

On the parameters used in finite element modeling of compound peripheral nerves

OBJECTIVE

Computational modeling is an important tool for developing and optimizing implantable neural stimulation devices, but requires accurate electrical and geometrical parameter values to improve predictive value. We quantified the effects of perineurial (resistive sheath around each fascicle) and endoneurial (within each fascicle) parameter values for modeling peripheral nerve stimulation.

APPROACH

We implemented 3D finite element models of compound peripheral nerves and cuff electrodes to quantify activation and block thresholds of model axons. We also implemented a 2D finite element model of a bundle of axons to estimate the bulk transverse endoneurial resistivity; we compared numerical estimates to an analytical solution.

MAIN RESULTS

Since the perineurium is highly resistive, potentials were approximately constant over the cross section of a fascicle, and the perineurium resistivity, longitudinal endoneurial resistivity, and fascicle diameter had important effects on thresholds. Activation thresholds increased up to ~130% for higher perineurium resistivity (~400 versus 2200 Ω m) and by ~35%-250% for lower longitudinal endoneurial resistivity (3.5 versus 0.75 Ω m), with larger increases for smaller diameter axons and for axons in larger fascicles. Further, thresholds increased by ~30%-180% for larger fascicle radii, yielding a larger increase with higher perineurium resistivity. Thresholds were largely insensitive to the transverse endoneurial resistivity, but estimates of the bulk resistivity increased with extracellular resistivity and axonal area fraction; the numerical and analytical estimates were in strong agreement except at high axonal area fractions, where structured axon placements that achieved tighter packing produced electric field inhomogeneities.

SIGNIFICANCE

We performed a systematic investigation of the effects of values and methods for modeling the perineurium and endoneurium on thresholds for neural stimulation and block. These results provide guidance for future modeling studies, including parameter selection, data interpretation, and comparison to experimental results.