Modelling the effects of electric fields on nerve fibres: influence of the myelin sheath

Experimental validation of a PNS-optimized whole-body gradient coil

PURPOSE

Peripheral nerve stimulation (PNS) limits the usability of state-of-the-art whole-body and head-only MRI gradient coils. We used detailed electromagnetic and neurodynamic modeling to set an explicit PNS constraint during the design of a whole-body gradient coil and constructed it to compare the predicted and experimentally measured PNS thresholds to those of a matched design without PNS constraints.

METHODS

We designed, constructed, and tested two actively shielded whole-body Y-axis gradient coil winding patterns: YG1 is a conventional symmetric design without PNS-optimization, whereas YG2's design used an additional constraint on the allowable PNS threshold in the head-imaging landmark, yielding an asymmetric winding pattern. We measured PNS thresholds in 18 healthy subjects at five landmark positions (head, cardiac, abdominal, pelvic, and knee).

RESULTS

The PNS-optimized design YG2 achieved 46% higher average experimental thresholds for a head-imaging landmark than YG1 while incurring a 15% inductance penalty. For cardiac, pelvic, and knee imaging landmarks, the PNS thresholds increased between +22% and +35%. For abdominal imaging, PNS thresholds did not change significantly between YG1 and YG2 (-3.6%). The agreement between predicted and experimental PNS thresholds was within 11.4% normalized root mean square error for both coils and all landmarks. The PNS model also produced plausible predictions of the stimulation sites when compared to the sites of perception reported by the subjects.

CONCLUSION

The PNS-optimization improved the PNS thresholds for the target scan landmark as well as most other studied landmarks, potentially yielding a significant improvement in image encoding performance that can be safely used in humans.

Myelin dystrophy impairs signal transmission and working memory in a multiscale model of the aging prefrontal cortex

Normal aging leads to myelin alterations in the rhesus monkey dorsolateral prefrontal cortex (dlPFC), which are positively correlated with degree of cognitive impairment. It is hypothesized that remyelination with shorter and thinner myelin sheaths partially compensates for myelin degradation, but computational modeling has not yet explored these two phenomena together systematically. Here, we used a two-pronged modeling approach to determine how age-related myelin changes affect a core cognitive function: spatial working memory. First, we built a multicompartment pyramidal neuron model fit to monkey dlPFC empirical data, with an axon including myelinated segments having paranodes, juxtaparanodes, internodes, and tight junctions. This model was used to quantify conduction velocity (CV) changes and action potential (AP) failures after demyelination and subsequent remyelination. Next, we incorporated the single neuron results into a spiking neural network model of working memory. While complete remyelination nearly recovered axonal transmission and network function to unperturbed levels, our models predict that biologically plausible levels of myelin dystrophy, if uncompensated by other factors, can account for substantial working memory impairment with aging. The present computational study unites empirical data from ultrastructure up to behavior during normal aging, and has broader implications for many demyelinating conditions, such as multiple sclerosis or schizophrenia.

NRV: An open framework for in silico evaluation of peripheral nerve electrical stimulation strategies

Electrical stimulation of peripheral nerves has been used in various pathological contexts for rehabilitation purposes or to alleviate the symptoms of neuropathologies, thus improving the overall quality of life of patients. However, the development of novel therapeutic strategies is still a challenging issue requiring extensive in vivo experimental campaigns and technical development. To facilitate the design of new stimulation strategies, we provide a fully open source and self-contained software framework for the in silico evaluation of peripheral nerve electrical stimulation. Our modeling approach, developed in the popular and well-established Python language, uses an object-oriented paradigm to map the physiological and electrical context. The framework is designed to facilitate multi-scale analysis, from single fiber stimulation to whole multifascicular nerves. It also allows the simulation of complex strategies such as multiple electrode combinations and waveforms ranging from conventional biphasic pulses to more complex modulated kHz stimuli. In addition, we provide automated support for stimulation strategy optimization and handle the computational backend transparently to the user. Our framework has been extensively tested and validated with several existing results in the literature.

A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields

Objective.Commonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or 'whole' finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.Approach.Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.Main Results.Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh.Significance.Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

Modeling and simulation for prediction of multiple sclerosis progression

In light of extensive work that has created a wide range of techniques for predicting the course of multiple sclerosis (MS) disease, this paper attempts to provide an overview of these approaches and put forth an alternative way to predict the disease progression. For this purpose, the existing methods for estimating and predicting the course of the disease have been categorized into clinical, radiological, biological, and computational or artificial intelligence-based markers. Weighing the weaknesses and strengths of these prognostic groups is a profound method that is yet in need and works directly at the level of diseased connectivity. Therefore, we propose using the computational models in combination with established connectomes as a predictive tool for MS disease trajectories. The fundamental conduction-based Hodgkin-Huxley model emerged as promising from examining these studies. The advantage of the Hodgkin-Huxley model is that certain properties of connectomes, such as neuronal connection weights, spatial distances, and adjustments of signal transmission rates, can be taken into account. It is precisely these properties that are particularly altered in MS and that have strong implications for processing, transmission, and interactions of neuronal signaling patterns. The Hodgkin-Huxley (HH) equations as a point-neuron model are used for signal propagation inside a small network. The objective is to change the conduction parameter of the neuron model, replicate the changes in myelin properties in MS and observe the dynamics of the signal propagation across the network. The model is initially validated for different lengths, conduction values, and connection weights through three nodal connections. Later, these individual factors are incorporated into a small network and simulated to mimic the condition of MS. The signal propagation pattern is observed after inducing changes in conduction parameters at certain nodes in the network and compared against a control model pattern obtained before the changes are applied to the network. The signal propagation pattern varies as expected by adapting to the input conditions. Similarly, when the model is applied to a connectome, the pattern changes could give an insight into disease progression. This approach has opened up a new path to explore the progression of the disease in MS. The work is in its preliminary state, but with a future vision to apply this method in a connectome, providing a better clinical tool.

AxoDetect: an automated nerve image segmentation and quantification workflow for computational nerve modeling

Objective.Bioelectronic treatments targeting near-organ innervation have unprecedented clinical applications. Particularly in the spleen, the inhibition of the cholinergic inflammatory response by near-organ nerve stimulation has potential to replace pharmacological treatments in chronic and autoimmune diseases. A caveat is that the optimization of therapeutic stimulation parameters relies onin vivoexperimentation, which becomes challenging due to the small nerve diameters (2 μm), complex anatomy, and mixed axon type composition of the autonomic nerves. Effective development ofin silicomodels requires tools which allow for fast and efficient quantification of axonal composition of specific nerves. Current approaches to generate such information rely on manual image segmentation and quantification.Approach.We developed a combined image-segmentation and model-generation software called AxoDetect: a target- and format-agnostic computer vision algorithm which can segment myelin, endo/epineurium, and both myelinated and unmyelinated fibers from a nerve image without training.Main results.AxoDetect is over 10 times faster on average when compared with current automatic methods while maintaining flexibility through the use of tunable pixel threshold filters to detect different types of tissue. When compared to a distribution-based and a manually segmented model of the splenic nerve terminal branch 1, the model generated with AxoDetect had comparable threshold prediction and was able to accurately detect an increase in activation threshold caused by the addition of surrounding fat tissue to the modeled nerve.Significance.AxoDetect contributes to the acceleration of neuromodulation treatment development through faster model design and iteration without requiring training. Furthermore, the computer vision approach and tunable nature of the filters in our method allow for its use in a variety of histological applications. Our approach will impact not only the study of nerves but also the design of implantable neural interfaces to enhance bioelectronic therapeutic options.

Modelling and analysis of cAMP-induced mixed-mode oscillations in cortical neurons: Critical roles of HCN and M-type potassium channels

Cyclic AMP controls neuronal ion channel activity. For example hyperpolarization-activated cyclic nucleotide-gated (HCN) and M-type K+ channels are activated by cAMP. These effects have been suggested to be involved in astrocyte control of neuronal activity, for example, by controlling the action potential firing frequency. In cortical neurons, cAMP can induce mixed-mode oscillations (MMOs) consisting of small-amplitude, subthreshold oscillations separating complete action potentials, which lowers the firing frequency greatly. We extend a model of neuronal activity by including HCN and M channels, and show that it can reproduce a series of experimental results under various conditions involving and inferring with cAMP-induced activation of HCN and M channels. In particular, we find that the model can exhibit MMOs as found experimentally, and argue that both HCN and M channels are crucial for reproducing these patterns. To understand how M and HCN channels contribute to produce MMOs, we exploit the fact that the model is a three-time scale dynamical system with one fast, two slow, and two super-slow variables. We show that the MMO mechanism does not rely on the super-slow dynamics of HCN and M channel gating variables, since the model is able to produce MMOs even when HCN and M channel activity is kept constant. In other words, the cAMP-induced increase in the average activity of HCN and M channels allows MMOs to be produced by the slow-fast subsystem alone. We show that the slow-fast subsystem MMOs are due to a folded node singularity, a geometrical structure well known to be involved in the generation of MMOs in slow-fast systems. Besides raising new mathematical questions for multiple-timescale systems, our work is a starting point for future research on how cAMP signalling, for example resulting from interactions between neurons and glial cells, affects neuronal activity via HCN and M channels.

Ionic plasmon-polariton in application to neurosignaling

The diffusive ion current is insufficient to explain the fast saltatory conduction observed in myelinated axons and in pain-sensing C fibers in the human nervous system, where the stimulus signal exhibits a velocity two orders of magnitude greater than the upper limit of ion diffusion velocity, even when the diffusion is accelerated by myelin, as in the discrete cable model including the Hodgkin-Huxley mechanism. The agreement with observations has been achieved in a wave-type model of stimulus signal kinetics via synchronized ion local density oscillations propagating as a wave in axons periodically corrugated by myelin segments in myelinated axons, or by periodically distributed rafts with clusters of Na^{+} channels in C fibers. The resulting so-called plasmon-polariton model for saltatory conduction reveals also the specific role of myelin, which is different from what was previously thought. This can be important for identifying a new target for the future treatment of demyelination diseases.

A physiological model of phrenic nerve excitation by electrical stimulation

Mechanical ventilation is essential in intensive care treatment but leads to diaphragmatic atrophy, which in turn contributes to prolonged weaning and increased mortality. One approach to prevent diaphragmatic atrophy while achieving pulmonary ventilation is electrical stimulation of the phrenic nerve. To automize phrenic nerve stimulation resulting in lung protective tidal volumes with lowest possible currents, mathematical models are required. Nerve stimulation models are often complex, so many parameters have to be identified prior to implementation. This paper presents a novel, simplified approach to model phrenic nerve excitation to obtain an individualized patient model using a few data points. The latter is based on the idea that nerve fibers are excited when the electric field exceeds a threshold. The effect of the geometry parameter on the model output was analyzed, and the model was validated with measurement data from a pig trial (RMSE in between 0.44 × 10-2and 1.64 × 10-2for parameterized models). The modeled phrenic nerve excitation behaved similarly to the measured tidal volumes, and thus could be used to develop automated phrenic nerve stimulation systems for lung protective ventilation.

A Boundary Element Method of Bidomain Modeling for Predicting Cellular Responses to Electromagnetic Fields

Objective

Commonly used cable equation-based approaches for determining the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or "whole" finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.

Methods

Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.

Main Results

Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is made computationally tractable, and the relative placement of devices and cells can be varied without the need to generate a new mesh.

Significance

Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

Myelin dystrophy in the aging prefrontal cortex leads to impaired signal transmission and working memory decline: a multiscale computational study

Normal aging leads to myelin alternations in the rhesus monkey dorsolateral prefrontal cortex (dlPFC), which are often correlated with cognitive impairment. It is hypothesized that remyelination with shorter and thinner myelin sheaths partially compensates for myelin degradation, but computational modeling has not yet explored these two phenomena together systematically. Here, we used a two-pronged modeling approach to determine how age-related myelin changes affect a core cognitive function: spatial working memory. First we built a multicompartment pyramidal neuron model fit to monkey dlPFC data, with axon including myelinated segments having paranodes, juxtaparanodes, internodes, and tight junctions, to quantify conduction velocity (CV) changes and action potential (AP) failures after demyelination and subsequent remyelination in a population of neurons. Lasso regression identified distinctive parameter sets likely to modulate an axon's susceptibility to CV changes following demyelination versus remyelination. Next we incorporated the single neuron results into a spiking neural network model of working memory. While complete remyelination nearly recovered axonal transmission and network function to unperturbed levels, our models predict that biologically plausible levels of myelin dystrophy, if uncompensated by other factors, can account for substantial working memory impairment with aging. The present computational study unites empirical data from electron microscopy up to behavior on aging, and has broader implications for many demyelinating conditions, such as multiple sclerosis or schizophrenia.

A systematic review of computational models for the design of spinal cord stimulation therapies: from neural circuits to patient-specific simulations

Seventy years ago, Hodgkin and Huxley published the first mathematical model to describe action potential generation, laying the foundation for modern computational neuroscience. Since then, the field has evolved enormously, with studies spanning from basic neuroscience to clinical applications for neuromodulation. Computer models of neuromodulation have evolved in complexity and personalization, advancing clinical practice and novel neurostimulation therapies, such as spinal cord stimulation. Spinal cord stimulation is a therapy widely used to treat chronic pain, with rapidly expanding indications, such as restoring motor function. In general, simulations contributed dramatically to improve lead designs, stimulation configurations, waveform parameters and programming procedures and provided insight into potential mechanisms of action of electrical stimulation. Although the implementation of neural models are relentlessly increasing in number and complexity, it is reasonable to ask whether this observed increase in complexity is necessary for improved accuracy and, ultimately, for clinical efficacy. With this aim, we performed a systematic literature review and a qualitative meta-synthesis of the evolution of computational models, with a focus on complexity, personalization and the use of medical imaging to capture realistic anatomy. Our review showed that increased model complexity and personalization improved both mechanistic and translational studies. More specifically, the use of medical imaging enabled the development of patient-specific models that can help to transform clinical practice in spinal cord stimulation. Finally, we combined our results to provide clear guidelines for standardization and expansion of computational models for spinal cord stimulation.

Peripheral nerve stimulation informed design of a high-performance asymmetric head gradient coil

PURPOSE

Peripheral nerve stimulation (PNS) limits the image encoding performance of both body gradient coils and the latest generation of head gradients. We analyze a variety of head gradient design aspects using a detailed PNS model to guide the design process of a new high-performance asymmetric head gradient to raise PNS thresholds and maximize the usable image-encoding performance.

METHODS

A novel three-layer coil design underwent PNS optimization involving PNS predictions of a series of candidate designs. The PNS-informed design process sought to maximize the usable parameter space of a coil with <10% nonlinearity in a 22 cm region of linearity, a relatively large inner diameter (44 cm), maximum gradient amplitude of 200 mT/m, and a high slew rate of 900 T/m/s. PNS modeling allowed identification and iterative adjustment of coil features with beneficial impact on PNS such as the number of winding layers, shoulder accommodation strategy, and level of asymmetry. PNS predictions for the final design were compared to measured thresholds in a constructed prototype.

RESULTS

The final head gradient achieved up to 2-fold higher PNS thresholds than the initial design without PNS optimization and compared to existing head gradients with similar design characteristics. The inclusion of a third intermediate winding layer provided the additional degrees of freedom necessary to improve PNS thresholds without significant sacrifices to the other design metrics.

CONCLUSION

Augmenting the design phase of a new high-performance head gradient coil by PNS modeling dramatically improved the usable image-encoding performance by raising PNS thresholds.

All-optical observation on activity-dependent nanoscale dynamics of myelinated axons

SIGNIFICANCE

In the mammalian brain, rapid conduction of neural information is supported by the myelin, the functional efficacy of which shows steep dependence on its nanoscale cytoarchitecture. Although previous in vitro studies have suggested that neural activity accompanies nanometer-scale cellular deformations, whether neural activity can dynamically remodel the myelinated axon has remained unexplored due to the technical challenge in observing its nanostructural dynamics in living tissues.

AIM

We aim to observe activity-dependent nanostructural dynamics of myelinated axons in a living brain tissue.

APPROACH

We introduced a novel all-optical approach combining a nanoscale dynamic readout based on spectral interferometry and optogenetic control of neural excitation in an acute brain slice preparation.

RESULTS

In response to optogenetically evoked neuronal burst firing, the myelinated axons exhibited progressive and reversible spectral redshifts, corresponding to the transient swelling at a subnanometer scale. We further revealed that the activity-dependent nanostructural dynamics was localized to the paranode.

CONCLUSIONS

Our all-optical studies substantiate that myelinated axon exhibits activity-dependent nanoscale swelling, which potentially serves to dynamically tune the transmission speed of neural information.

Heterogeneity and regulation of oligodendrocyte morphology

Oligodendrocytes form multiple myelin sheaths in the central nervous system (CNS), which increase nerve conduction velocity and are necessary for basic and higher brain functions such as sensory function, motor control, and learning. Structures of the myelin sheath such as myelin internodal length and myelin thickness regulate nerve conduction. Various parts of the central nervous system exhibit different myelin structures and oligodendrocyte morphologies. Recent studies supported that oligodendrocytes are a heterogenous population of cells and myelin sheaths formed by some oligodendrocytes can be biased to particular groups of axons, and myelin structures are dynamically modulated in certain classes of neurons by specific experiences. Structures of oligodendrocyte/myelin are also affected in pathological conditions such as demyelinating and neuropsychiatric disorders. This review summarizes our understanding of heterogeneity and regulation of oligodendrocyte morphology concerning central nervous system regions, neuronal classes, experiences, diseases, and how oligodendrocytes are optimized to execute central nervous system functions.

Dark Rearing in the Visual Critical Period Causes Structural Changes in Myelinated Axons in the Adult Mouse Visual Pathway

An appropriate sensory experience during the early developmental period is important for brain maturation. Dark rearing during the visual critical period delays the maturation of neuronal circuits in the visual cortex. Although the formation and structural plasticity of the myelin sheaths on retinal ganglion cell axons modulate the visual function, the effects of dark rearing during the visual critical period on the structure of the retinal ganglion cell axons and their myelin sheaths are still unclear. To address this question, mice were reared in a dark box during the visual critical period and then normally reared to adulthood. We found that myelin sheaths on the retinal ganglion cell axons of dark-reared mice were thicker than those of normally reared mice in both the optic chiasm and optic nerve. Furthermore, whole-mount immunostaining with fluorescent axonal labeling and tissue clearing revealed that the myelin internodal length in dark-reared mice was shorter than that in normally reared mice in both the optic chiasm and optic nerve. These findings demonstrate that dark rearing during the visual critical period affects the morphology of myelin sheaths, shortens and thickens myelin sheaths in the visual pathway, despite the mice being reared in normal light/dark conditions after the dark rearing.

Optimizing sensory fiber activation during cervical transcutaneous spinal stimulation using different electrode configurations: A computational analysis

BACKGROUND

Cervical transcutaneous spinal cord stimulation (tSCS) is a rehabilitation tool which has been used to promote upper-limb motor recovery after spinal cord injury. Importantly, optimizing sensory fiber activation at specific spinal segments could enable activity-dependent neuromodulation during rehabilitation.

METHODS

An anatomically realistic cervical tSCS computational model was used to analyze the activation of α-motor and Aα-sensory fibers at C7 and C8 spinal segments using nine cathode electrode configurations. Specifically, the cathode was simulated at three vertebral level positions: C6, C7, and T1; and in three sizes: 5.0 x 5.0, 3.5 x 3.5; and 2.5 x 2.5 cm² , while the anode was on the anterior neck. Finite element method was used to estimate the electric potential distribution along α-motor and Aα-sensory fibers, and computational models were applied to simulate the fiber membrane dynamics during tSCS. The minimum stimulation intensity necessary to activate the fibers (activation threshold) was estimated and compared across cathode configurations in an effort to optimize sensory fiber activation.

RESULTS

Our results showed that nerve fibers at both C7 and C8 spinal segments were recruited at lower stimulation intensities when the cathode was positioned over the C7 or T1 vertebra compared with the C6 position. Sensory fibers were activated at lower stimulation intensities using smaller electrodes, which could also affect the degree of nerve fiber activation across different positions. Importantly, Aα-sensory fibers were consistently recruited before α-motor fibers.

CONCLUSIONS

These results imply that cathode positioning could help optimize preferential activation of hand muscles during cervical tSCS.

Preferential activation of proprioceptive and cutaneous sensory fibers compared to motor fibers during cervical transcutaneous spinal cord stimulation: A computational study

OBJECTIVE

Cervical transcutaneous spinal cord stimulation (tSCS) is a promising technology that can support motor function recovery of upper-limbs after spinal cord injury. Its efficacy may depend on the ability to recruit sensory afferents, conveying excitatory inputs onto motoneurons. Therefore, understanding its physiological mechanisms is critical to accelerate its development towards clinical applications. In this study, we used an anatomically realistic cervical tSCS computational model to compare α-motor, Aα-sensory, and Aβ-sensory fiber activation thresholds and activation sites.

APPROACH

We developed a 3D geometry of the cervical body and tSCS electrodes with a cathode centred at the C7 spinous process and an anode placed over the anterior neck. The geometrical model was used to estimate the electric potential distributions along motor and sensory fiber trajectories at the C7 spinal level using a finite element method. We implemented dedicated motor and sensory fiber models to simulate the α-motor and Aα-sensory fibers using 12, 16, and 20 µm diameter fibers, and Aβ-sensory fibers using 6, 9, and 12 µm diameter fibers. We estimated nerve fiber activation thresholds and sites for a 2 ms monophasic stimulating pulse and compared them across the fiber groups.

MAIN RESULTS

Our results showed lower activation thresholds of Aα- and Aβ-sensory fibers compared with α-motor fibers, suggesting preferential sensory fiber activation. We also found no differences between activation thresholds of Aα-sensory and large Aβ-sensory fibers, implying their co-activation. The activation sites were located at the dorsal and ventral root levels.

SIGNIFICANCE

Using a realistic computational model, we demonstrated preferential activation of dorsal root Aα- and Aβ-sensory fibers compared with ventral root α-motor fibers during cervical tSCS. These findings suggest high proprioceptive and cutaneous contributions to neural activations during cervical tSCS, which inform the underlying mechanisms of upper-limb functional motor recovery.

White matter tract conductivity is resistant to wide variations in paranodal structure and myelin thickness accompanying the loss of Tyro3: an experimental and simulated analysis

Myelination within the central nervous system (CNS) is crucial for the conduction of action potentials by neurons. Variation in compact myelin morphology and the structure of the paranode are hypothesised to have significant impact on the speed of action potentials. There are, however, limited experimental data investigating the impact of changes in myelin structure upon conductivity in the central nervous system. We have used a genetic model in which myelin thickness is reduced to investigate the effect of myelin alterations upon action potential velocity. A detailed examination of the myelin ultrastructure of mice in which the receptor tyrosine kinase Tyro3 has been deleted showed that, in addition to thinner myelin, these mice have significantly disrupted paranodes. Despite these alterations to myelin and paranodal structure, we did not identify a reduction in conductivity in either the corpus callosum or the optic nerve. Exploration of these results using a mathematical model of neuronal conductivity predicts that the absence of Tyro3 would lead to reduced conductivity in single fibres, but would not affect the compound action potential of multiple myelinated neurons as seen in neuronal tracts. Our data highlight the importance of experimental assessment of conductivity and suggests that simple assessment of structural changes to myelin is a poor predictor of neural functional outcomes.

Recording Saltatory Conduction Along Sensory Axons Using a High-Density Microelectrode Array

Myelinated fibers are specialized neurological structures used for conducting action potentials quickly and reliably, thus assisting neural functions. Although demyelination leads to serious functional impairments, little is known the relationship between myelin structural change and increase in conduction velocity during myelination and demyelination processes. There are no appropriate methods for the long-term evaluation of spatial characteristics of saltatory conduction along myelinated axons. Herein, we aimed to detect saltatory conduction from the peripheral nervous system neurons using a high-density microelectrode array. Rat sensory neurons and intrinsic Schwann cells were cultured. Immunofluorescence and ultrastructure examination showed that the myelinating Schwann cells appeared at 1 month, and compact myelin was formed by 10 weeks in vitro. Activity of rat sensory neurons was evoked with optogenetic stimulation, and axon conduction was detected with high-density microelectrode arrays. Some conductions included high-speed segments with low signal amplitude. The same segment could be detected with electrical recording and immunofluorescent imaging for a myelin-related protein. The spatiotemporal analysis showed that some segments show a velocity of more than 2 m/s and that ends of the segments show a higher electrical sink, suggesting that saltatory conduction occurred in myelinated axons. Moreover, mathematical modeling supported that the recorded signal was in the appropriate range for axon and electrode sizes. Overall, our method could be a feasible tool for evaluating spatial characteristics of axon conduction including saltatory conduction, which is applicable for studying demyelination and remyelination.

Refinement of axonal conduction and myelination in the mouse optic nerve indicate an extended period of postnatal developmental plasticity

Retinal ganglion cells generate a pattern of action potentials to communicate visual information from the retina to cortical areas. Myelin, an insulating sheath, wraps axonal segments to facilitate signal propagation and when deficient, can impair visual function. Optic nerve development and initial myelination has largely been considered complete by the fifth postnatal week. However, the relationship between the extent of myelination and axonal signaling in the maturing optic nerve is not well characterized. Here, we examine the relationship between axon conduction and elements of myelination using extracellular nerve recordings, immunohistochemistry, western blot analysis, scanning electron microscopy, and simulations of nerve responses. Comparing compound action potentials from mice aged 4-12 weeks revealed five functional distinct axonal populations, an increase in the number of functional axons, and shifts toward fast-conducting axon populations at 5 and 8 weeks postnatal. At these ages, our analysis revealed increased myelin thickness, lower g-ratios and changes in the 14 kDa MBP isoform, while the density of axons and nodes of Ranvier remained constant. At 5 postnatal weeks, axon diameter increased, while at 8 weeks, increased expression of a mature sodium ion channel subtype, Na_v 1.6, was observed at nodes of Ranvier. A simulation model of nerve conduction suggests that ion channel subtype, axon diameter, and myelin thickness are more likely to be key regulators of nerve function than g-ratio. Such refinement of axonal function and myelin rearrangement identified an extended period of maturation in the normal optic nerve that may facilitate the development of visual signaling patterns. This article is protected by copyright. All rights reserved.

Frequency Shapes the Quality of Tactile Percepts Evoked through Electrical Stimulation of the Nerves

Electrical stimulation of the peripheral nerves of human participants provides a unique opportunity to study the neural determinants of perceptual quality using a causal manipulation. A major challenge in the study of neural coding of touch has been to isolate the role of spike timing-at the scale of milliseconds or tens of milliseconds-in shaping the sensory experience. In the present study, we address this question by systematically varying the pulse frequency (PF) of electrical stimulation pulse trains delivered to the peripheral nerves of seven participants with upper and lower extremity limb loss via chronically implanted neural interfaces. We find that increases in PF lead to systematic increases in perceived frequency, up to ∼50 Hz, at which point further changes in PF have little to no impact on sensory quality. Above this transition frequency, ratings of perceived frequency level off, the ability to discriminate changes in PF is abolished, and verbal descriptors selected to characterize the sensation change abruptly. We conclude that sensation quality is shaped by temporal patterns of neural activation, even if these patterns are imposed on a fixed neural population, but this temporal patterning can only be resolved up to ∼50 Hz. These findings highlight the importance of spike timing in shaping the quality of a sensation and will contribute to the development of encoding strategies for conveying touch feedback through bionic hands and feet.SIGNIFICANCE STATEMENT A major challenge in the study of neural coding of touch has been to understand how temporal patterns in neuronal responses shape the sensory experience. We address this question by varying the pulse frequency (PF) of electrical pulse trains delivered through implanted nerve interfaces in seven amputees. We concomitantly vary pulse width to separate the effect of changing PF on sensory quality from its effect on perceived magnitude. We find that increases in PF lead to increases in perceived frequency, a qualitative dimension, up to ∼50 Hz, beyond which changes in PF have little impact on quality. We conclude that temporal patterning in the neuronal response can shape quality and discuss the implications for restoring touch via neural interfaces.

Optimal pulse configuration for peripheral inductive nerve stimulation

Peripheral magnetic stimulation is a promising technique for several applications like rehabilitation or diagnose of neuronal pathways. However, most available magnetic stimulation devices are designed for transcranial stimulation and require high-power, expensive hardware. Modern technology such as rectangular pulses allows to adapt parameters like pulse shape and duration in order to reduce the required energy. Nevertheless, the effect of different temporal electromagnetic field shapes on neuronal structures is not yet fully understood. We created a simulation environment to find out how peripheral nerves are affected by induced magnetic fields and what pulse shapes have the lowest energy requirements. Using the electric field distribution of a Figure-of-8 coil together with an axon model in saline solution, we calculated the potential along the axon and determined the required threshold current to elicit an action potential. Further, for the purpose of selective stimulation, we investigated different axon diameters. Our results show that rectangular pulses have the lowest thresholds at a pulse duration of 20 μs. For sinusoidal coil currents, the optimal pulse duration was found to be 40 μs. Most importantly, with an asymmetric rectangular pulse, the coil current could be reduced from 2.3 kA (cosine shaped pulse) to 600 A. In summary, our results indicate that for magnetic nerve stimulation the use of rectangular pulse shapes holds the potential to reduce the required coil current by a factor of 4, which would be a massive improvement.

A Huygens' surface approach to rapid characterization of peripheral nerve stimulation

PURPOSE

Peripheral nerve stimulation (PNS) modeling has a potential role in designing and operating MRI gradient coils but requires computationally demanding simulations of electromagnetic fields and neural responses. We demonstrate compression of an electromagnetic and neurodynamic model into a single versatile PNS matrix (P-matrix) defined on an intermediary Huygens' surface to allow fast PNS characterization of arbitrary coil geometries and body positions.

METHODS

The Huygens' surface approach divides PNS prediction into an extensive pre-computation phase of the electromagnetic and neurodynamic responses, which is independent of coil geometry and patient position, and a fast coil-specific linear projection step connecting this information to a specific coil geometry. We validate the Huygens' approach by performing PNS characterizations for 21 body and head gradients and comparing them with full electromagnetic-neurodynamic modeling. We demonstrate the value of Huygens' surface-based PNS modeling by characterizing PNS-optimized coil windings for a wide range of patient positions and poses in two body models.

RESULTS

The PNS prediction using the Huygens' P-matrix takes less than a minute (instead of hours to days) without compromising numerical accuracy (error ≤ 0.1%) compared to the full simulation. Using this tool, we demonstrate that coils optimized for PNS at the brain landmark using a male model can also improve PNS for other imaging applications (cardiac, abdominal, pelvic, and knee imaging) in both male and female models.

CONCLUSION

Representing PNS information on a Huygens' surface extended the approach's ability to assess PNS across body positions and models and test the robustness of PNS optimization in gradient design.

Selective myelinated nerve fiber stimulation via temporal interfering electric fields

We have investigated selective electrical stimulation of myelinated nerve fibers using a computational model of temporal interfering (TI) fields. The model consists of two groups of electrodes placed on the outer bundle surface, each group stimulated at a different frequency. We manipulated the stimulus waveform, magnitude and frequency of short-duration stimuli (70ms), and investigated fiber-specific stimulus-elicited compound action potentials. Results show that under 100Hz & 200Hz TI stimulation with 0.6mA total current shared by the electrodes, continuous action potentials were generated in deeper nerve fibers, and that the firing region was steerable by changing individual electrode currents. This study provides a promising platform for non-invasive nerve bundle stimulation by TI fields.

Astrocyte Ca2+-evoked ATP release regulates myelinated axon excitability and conduction speed

In the brain’s gray matter, astrocytes regulate synapse properties, but their role is unclear for the white matter, where myelinated axons rapidly transmit information between gray matter areas. We found that in rodents, neuronal activity raised the intracellular calcium concentration ([Ca2+]i) in astrocyte processes located near action potential–generating sites in the axon initial segment (AIS) and nodes of Ranvier of myelinated axons. This released adenosine triphosphate, which was converted extracellularly to adenosine and thus, through A2a receptors, activated HCN2-containing cation channels that regulate two aspects of myelinated axon function: excitability of the AIS and speed of action potential propagation. Variations in astrocyte-derived adenosine level between wake and sleep states or during energy deprivation could thus control white matter information flow and neural circuit function.

Dissecting whole-brain conduction delays through MRI microstructural measures

Network models based on structural connectivity have been increasingly used as the blueprint for large-scale simulations of the human brain. As the nodes of this network are distributed through the cortex and interconnected by white matter pathways with different characteristics, modeling the associated conduction delays becomes important. The goal of this study is to estimate and characterize these delays directly from the brain structure. To achieve this, we leveraged microstructural measures from a combination of advanced magnetic resonance imaging acquisitions and computed the main determinants of conduction velocity, namely axonal diameter and myelin content. Using the model proposed by Rushton, we used these measures to calculate the conduction velocity and estimated the associated delays using tractography. We observed that both the axonal diameter and conduction velocity distributions presented a rather constant trend across different connection lengths, with resulting delays that scale linearly with the connection length. Relying on insights from graph theory and Kuramoto simulations, our results support the approximation of constant conduction velocity but also show path- and region-specific differences.

In-vitro Recordings of Neural Magnetic Activity From the Auditory Brainstem Using Color Centers in Diamond: A Simulation Study

Magnetometry based on nitrogen-vacancy (NV) centers in diamond is a novel technique capable of measuring magnetic fields with high sensitivity and high spatial resolution. With the further advancements of these sensors, they may open up novel approaches for the 2D imaging of neural signals in vitro. In the present study, we investigate the feasibility of NV-based imaging by numerically simulating the magnetic signal from the auditory pathway of a rodent brainstem slice (ventral cochlear nucleus, VCN, to the medial trapezoid body, MNTB) as stimulated by both electric and optic stimulation. The resulting signal from these two stimulation methods are evaluated and compared. A realistic pathway model was created based on published data of the neural morphologies and channel dynamics of the globular bushy cells in the VCN and their axonal projections to the principal cells in the MNTB. The pathway dynamics in response to optic and electric stimulation and the emitted magnetic fields were estimated using the cable equation. For simulating the optic stimulation, the light distribution in brain tissue was numerically estimated and used to model the optogenetic neural excitation based on a four state channelrhodopsin-2 (ChR2) model. The corresponding heating was also estimated, using the bio-heat equation and was found to be low (<2°C) even at excessively strong optic signals. A peak magnetic field strength of ∼0.5 and ∼0.1 nT was calculated from the auditory brainstem pathway after electrical and optical stimulation, respectively. By increasing the stimulating light intensity four-fold (far exceeding commonly used intensities) the peak magnetic signal strength only increased to 0.2 nT. Thus, while optogenetic stimulation would be favorable to avoid artefacts in the recordings, electric stimulation achieves higher peak fields. The present simulation study predicts that high-resolution magnetic imaging of the action potentials traveling along the auditory brainstem pathway will only be possible for next generation NV sensors. However, the existing sensors already have sufficient sensitivity to support the magnetic sensing of cumulated neural signals sampled from larger parts of the pathway, which might be a promising intermediate step toward further maturing this novel technology.

Effects of temperature and ion channel blocks on propagation of action potential in myelinated axons

Potassium ion and sodium ion channels play important roles in the propagation of action potentials along a myelinated axon. The random opening and closing of ion channels can cause the fluctuation of action potentials. In this paper, an improved Hodgkin-Huxley chain network model is proposed to study the effects of ion channel blocks, temperature, and ion channel noise on the propagation of action potentials along the myelinated axon. It is found that the chain network has minimum coupling intensity threshold and maximum tolerance temperature threshold that allow the action potentials to pass along the whole axon, and the blockage of ion channels can change these two thresholds. A striking result is that the simulated value of the optimum membrane size (inversely proportional to noise intensity) coincides with the area range of feline thalamocortical relay cells in biological experiments.

Combining direct current and kilohertz frequency alternating current to mitigate onset activity during electrical nerve block

Objective.

Electrical nerve block offers the ability to immediately and reversibly block peripheral nerve conduction and would have applications in the emerging field of bioelectronics. Two modalities of electrical nerve block have been investigated—kilohertz frequency alternating current (KHFAC) and direct current (DC). KHFAC can be safely delivered with conventional electrodes, but has the disadvantage of having an onset response, which is a period of increased neural activation before block is established and currently limits clinical translation. DC has long been known to block neural conduction without an onset response but creates damaging reactive species. Typical electrodes can safely deliver DC for less than one second, but advances in high capacitance electrodes allow DC delivery up to 10 s without damage. The present work aimed to combine DC and KHFAC into a single waveform, named the combined reduced onset waveform (CROW), which can initiate block without an onset response while also maintaining safe block for long durations. This waveform consists of a short, DC pre-pulse before initiating KHFAC.

Approach.

Simulations of this novel waveform were carried out in the axonal simulation environment NEURON to test feasibility and gain insight into the mechanisms of action. Two sets of acute experiments were then conducted in adult Sprague–Dawley rats to determine the effectiveness of the waveform in mitigating the onset response.

Main results.

The CROW reduced the onset response both in silico and in vivo. The onset area was reduced by over 90% with the tested parameters in the acute experiments. The amplitude of the DC pulse was shown to be particularly important for effective onset mitigation, requiring amplitudes 6–8 times the DC block threshold.

Significance.

This waveform can reliably reduce the onset response due to KHFAC and could allow for wider clinical implementation of electrical nerve block.

3D patient-specific spinal cord computational model for SCS management: potential clinical applications

BACKGROUND AND OBJECTIVE

Although Spinal Cord Stimulation (SCS) is an established therapy for treating neuropathic chronic pain, in tonic stimulation, postural changes, electrode migration or badly-positioned electrodes can produce annoying stimulation (intercostal neuralgia) in about 35% of the patients. SCS models are used to study the effect of electrical stimulation to better manage the stimulation parameters and electrode position. The goal of this work was to develop a realistic 3D patient-specific spinal cord model from a real patient and develop a future clinical application that would help physicians to optimize paresthesia coverage in SCS therapy.

METHODS

We developed two 3D patient-specific models from a high-resolution MRI of two patients undergoing SCS treatment. The model consisted of a finite element model of the spinal cord and a sensory myelinated nerve fiber model. The same simulations were performed with a generalized spinal cord model and we compared the results with the clinical data to evaluate the advantages of a patient-specific model. To identify the geometrical parameters that most influence the stimulation predictions, a sensitivity analysis was conducted. We used the patient-specific model to perform a clinical application involving the pre-implantation selection of electrode polarity and study the effect of electrode offset.

RESULTS

The patient-specific model correlated better with clinical data than the generalized model. Electrode-dura mater distance, dorsal CSF thickness, and CSF diameter are the geometrical parameters that caused significant changes in the stimulation predictions. Electrode polarity could be planned and optimized to stimulate the patient's painful dermatomes. The addition of offset in parallel electrodes would not have been beneficial for one of the patients of this study because they reduce neural activation displacement.

CONCLUSIONS

This is the first study to relate the activation area model prediction in dorsal columns with the clinical effect on paresthesia coverage. The outcomes show that 3D patient-specific models would help physicians to choose the best stimulation parameters to optimize neural activation and SCS therapy in tonic stimulation.

A Multiscale Approach to Axon and Nerve Stimulation Modeling: A Review

Electrical nerve fiber stimulation is a technique widely used in prosthetics and rehabilitation, and its study from a computational point of view can be a useful instrument to support experimental tests. In the last years, there was an increasing interest in computational modeling of neural cells and numerical simulations on nerve fibers stimulation because of its usefulness in forecasting the effect of electrical current stimuli delivered to tissues through implanted electrodes, in the design of optimal stimulus waveforms based on the specific application (i.e., inducing limb movements, sensory feedback or physiological function restoring), and in the evaluation of the current stimuli properties according to the characteristics of the nerves surrounding tissue. Therefore, a review study on the main modeling and computational frameworks adopted to investigate peripheral nerve stimulation is an important instrument to support and drive future research works. To this aim, this paper deals with mathematical models of neural cells with a detailed description of ion channels and numerical simulations using finite element methods to describe the dynamics of electrical stimulation by implanted electrodes in peripheral nerve fibers. In particular, we evaluate different nerve cell models considering different ion channels present in neurons and provide a guideline on multiscale numerical simulations of electrical nerve fibers stimulation.

Statistical field theory of the transmission of nerve impulses

Background

Stochastic processes leading voltage-gated ion channel dynamics on the nerve cell membrane are a sufficient condition to describe membrane conductance through statistical mechanics of disordered and complex systems.

Results

Voltage-gated ion channels in the nerve cell membrane are described by the Ising model. Stochastic circuit elements called “Ising Neural Machines” are introduced. Action potentials are described as quasi-particles of a statistical field theory for the Ising system.

Conclusions

The particle description of action potentials is a new point of view and a powerful tool to describe the generation and propagation of nerve impulses, especially when classical electrophysiological models break down.

The particle description of action potentials allows us to develop a new generation of devices to study neurodegenerative and demyelinating diseases as Multiple Sclerosis and Alzheimer’s disease, even integrated by connectomes. It is also suitable for the study of complex networks, quantum computing, artificial intelligence, machine and deep learning, cryptography, ultra-fast lines for entanglement experiments and many other applications of medical, physical and engineering interest.

Optimization of MRI Gradient Coils With Explicit Peripheral Nerve Stimulation Constraints

Peripheral Nerve Stimulation (PNS) limits the acquisition rate of Magnetic Resonance Imaging data for fast sequences employing powerful gradient systems. The PNS characteristics are currently assessed after the coil design phase in experimental stimulation studies using constructed coil prototypes. This makes it difficult to find design modifications that can reduce PNS. Here, we demonstrate a direct approach for incorporation of PNS effects into the coil optimization process. Knowledge about the interactions between the applied magnetic fields and peripheral nerves allows the optimizer to identify coil solutions that minimize PNS while satisfying the traditional engineering constraints. We compare the simulated thresholds of PNS-optimized body and head gradients to conventional designs, and find an up to 2-fold reduction in PNS propensity with moderate penalties in coil inductance and field linearity, potentially doubling the image encoding performance that can be safely used in humans. The same framework may be useful in designing and operating magneto- and electro-stimulation devices.

Periaxonal and nodal plasticities modulate action potential conduction in the adult mouse brain

Central nervous system myelination increases action potential conduction velocity. However, it is unclear how myelination is coordinated to ensure the temporally precise arrival of action potentials and facilitate information processing within cortical and associative circuits. Here, we show that myelin sheaths, supported by mature oligodendrocytes, remain plastic in the adult mouse brain and undergo subtle structural modifications to influence action potential conduction velocity. Repetitive transcranial magnetic stimulation and spatial learning, two stimuli that modify neuronal activity, alter the length of the nodes of Ranvier and the size of the periaxonal space within active brain regions. This change in the axon-glial configuration is independent of oligodendrogenesis and robustly alters action potential conduction velocity. Because aptitude in the spatial learning task was found to correlate with action potential conduction velocity in the fimbria-fornix pathway, modifying the axon-glial configuration may be a mechanism that facilitates learning in the adult mouse brain.

Neuroinflammation in the normal-appearing white matter (NAWM) of the multiple sclerosis brain causes abnormalities at the nodes of Ranvier

Changes to the structure of nodes of Ranvier in the normal-appearing white matter (NAWM) of multiple sclerosis (MS) brains are associated with chronic inflammation. We show that the paranodal domains in MS NAWM are longer on average than control, with Kv1.2 channels dislocated into the paranode. These pathological features are reproduced in a model of chronic meningeal inflammation generated by the injection of lentiviral vectors for the lymphotoxin-α (LTα) and interferon-γ (IFNγ) genes. We show that tumour necrosis factor (TNF), IFNγ, and glutamate can provoke paranodal elongation in cerebellar slice cultures, which could be reversed by an N-methyl-D-aspartate (NMDA) receptor blocker. When these changes were inserted into a computational model to simulate axonal conduction, a rapid decrease in velocity was observed, reaching conduction failure in small diameter axons. We suggest that glial cells activated by pro-inflammatory cytokines can produce high levels of glutamate, which triggers paranodal pathology, contributing to axonal damage and conduction deficits.

Current thinking on the mechanisms by which multiple sclerosis gives rise to cumulative neurological disability revolves largely around focal lesions of inflammation and demyelination. However, some of the debilitating symptoms, such as severe fatigue, might be better explained by a more diffuse pathology. This study shows that paranodes in the white matter become abnormal as a result of neuroinflammation, which may be the result of the action of cytokines that cause glia to release glutamate.

Myelination of parvalbumin interneurons shapes the function of cortical sensory inhibitory circuits

Myelination of projection neurons by oligodendrocytes is key to optimize action potential conduction over long distances. However, a large fraction of myelin enwraps the axons of parvalbumin-positive fast-spiking interneurons (FSI), exclusively involved in local cortical circuits. Whether FSI myelination contributes to the fine‐tuning of intracortical networks is unknown. Here we demonstrate that FSI myelination is required for the establishment and maintenance of the powerful FSI-mediated feedforward inhibition of cortical sensory circuits. The disruption of GABAergic synaptic signaling of oligodendrocyte precursor cells prior to myelination onset resulted in severe FSI myelination defects characterized by longer internodes and nodes, aberrant myelination of branch points and proximal axon malformation. Consequently, high-frequency FSI discharges as well as FSI-dependent postsynaptic latencies and strengths of excitatory neurons were reduced. These dysfunctions generated a strong excitation-inhibition imbalance that correlated with whisker-dependent texture discrimination impairments. FSI myelination is therefore critical for the function of mature cortical inhibitory circuits.

Myelination optimizes conduction speed of excitatory neurons. However, whether myelination of interneurons (INs) refines cortical networks is unclear. Here, the authors show that INs myelination shapes feedforward inhibition of mouse cortical sensory circuits and impacts whisker-mediated behaviour.

Mediating different-diameter Aβ nerve fibers using a biomimetic 3D TENS computational model

BACKGROUND

Significant progress has been made over the last 50 years in the design, development and testing of transcutaneous electrical nerve stimulation (TENS) in mediating different levels of tactile sensations. However, without knowing how best to stimulate the nerve fibers, the elicited sensation quality will always remain poor and unnatural.

NEW METHOD

A new biomimetic 3D TENS computational model is developed to quantify the neural activation mechanism with varied surface electrodes. This model includes seven-layered anatomical structure of the forearm and biophysically-detailed myelinated Aβ fibers. The Aβ-fiber diameters from 1.5 - 7.5 μm were randomly distributed beneath the skin to mimic the physiologically-realistic fiber population. The arithmetic averaging algorithm and Gaussian filter were adopted to identify the sensation center and to quantify sensation intensities under different stimulation conditions.

RESULTS

Fibers larger than 4.5 μm can usually be activated producing tactile sensations such as light touch, pressure, buzz, and vibration. While, fibers with diameters of 3.5 and 3 μm can only be excited at uncomfortable numb and pain sensations. The resulted modelling predictions match the recent psychophysical experimental data.

COMPARISON WITH EXISTING METHOD(S)

The new TENS model is more physiologically-realistic by introducing a detailed morphological information and key ionic mechanisms in nerve fibers.

CONCLUSIONS

Our results indicate that TENS may be a promising method to target functionally-distinct neural pathways in an effort to improve the elicited tactile sensations quality with electrical stimulation. This work provides a promising platform of discovering neural mechanisms under TENS.

Advances in Astrocyte Computational Models: From Metabolic Reconstructions to Multi-omic Approaches

The growing importance of astrocytes in the field of neuroscience has led to a greater number of computational models devoted to the study of astrocytic functions and their metabolic interactions with neurons. The modeling of these interactions demands a combined understanding of brain physiology and the development of computational frameworks based on genomic-scale reconstructions, system biology, and dynamic models. These computational approaches have helped to highlight the neuroprotective mechanisms triggered by astrocytes and other glial cells, both under normal conditions and during neurodegenerative processes. In the present review, we evaluate some of the most relevant models of astrocyte metabolism, including genome-scale reconstructions and astrocyte-neuron interactions developed in the last few years. Additionally, we discuss novel strategies from the multi-omics perspective and computational models of other glial cell types that will increase our knowledge in brain metabolism and its association with neurodegenerative diseases.

New wave-type mechanism of saltatory conduction in myelinated axons and micro-saltatory conduction in C fibres

We present a new wave-type model of saltatory conduction in myelinated axons. Poor conductivity in the neuron cytosol limits electrical current signal velocity according to cable theory, to 1–3 m/s, whereas saltatory conduction occurs with a velocity of 100–300 m/s. We propose a wave-type mechanism for saltatory conduction in the form of the kinetics of an ionic plasmon-polariton being the hybrid of the electro-magnetic wave and of the synchronized ionic plasma oscillations in myelinated segments along an axon. The model agrees with observations and allows for description of the regulatory role of myelin. It explains also the mechanism of conduction deficiency in demyelination syndromes such as multiple sclerosis. The recently observed micro-saltatory conduction in ultrathin unmyelinated C fibers with periodic ion gate clusters is also explained.

Saltatory Conduction along Myelinated Axons Involves a Periaxonal Nanocircuit

The propagation of electrical impulses along axons is highly accelerated by the myelin sheath and produces saltating or "jumping" action potentials across internodes, from one node of Ranvier to the next. The underlying electrical circuit, as well as the existence and role of submyelin conduction in saltatory conduction remain, however, elusive. Here, we made patch-clamp and high-speed voltage-calibrated optical recordings of potentials across the nodal and internodal axolemma of myelinated neocortical pyramidal axons combined with electron microscopy and experimentally constrained cable modeling. Our results reveal a nanoscale yet conductive periaxonal space, incompletely sealed at the paranodes, which separates the potentials across the low-capacitance myelin sheath and internodal axolemma. The emerging double-cable model reproduces the recorded evolution of voltage waveforms across nodes and internodes, including rapid nodal potentials traveling in advance of attenuated waves in the internodal axolemma, revealing a mechanism for saltation across time and space.

Optimizing selective stimulation of peripheral nerves with arrays of coils or surface electrodes using a linear peripheral nerve stimulation metric

OBJECTIVE

We present a PNS oracle, which solves these computation time and linearity problems and is, therefore, well-suited for fast optimization of voltage distributions in contact electrode arrays and current drive patterns in non-contact magnetic coil arrays.

APPROACH

The PNS oracle metric for a nerve fiber is computed from an electric field map using only linear operations (projection, differentiation, convolution, scaling). Due to its linearity, this PNS metric can be precomputed for a set of coil or electrode segments, allowing rapid PNS prediction and comparison of any possible coil or electrode stimulation configuration constructed from this set. The PNS oracle is closely related to the classical activating function and modified driving functions but is adjusted to better correlate with full neurodynamic modeling of myelinated mammalian nerves.

MAIN RESULTS

We validated the PNS oracle in three MRI gradient coils and two body models and found good correlation between the PNS oracle and the full neurodynamic modeling approach (R ²  >  0.995). Finally, we demonstrated its potential utility by optimizing the driving currents and voltages of arrays of 108 magnetic coils or 108 contact electrodes to selectively stimulate target nerves in the lower leg.

SIGNIFICANCE

Peripheral nerve stimulation (PNS) by electromagnetic fields can be accurately simulated using coupled electromagnetic and neurodynamic modeling. Such simulations are slow and non-linear in the electric field, which makes it difficult to iteratively optimize coil and electrode configurations or drive patterns aiming to avoid PNS or to initiate it for therapeutic purposes.

Computational analysis of non-invasive deep brain stimulation based on interfering electric fields

Neuromodulation modalities are used as effective treatments for some brain disorders. Non-invasive deep brain stimulation (NDBS) via temporally interfering electric fields has emerged recently as a non-invasive strategy for electrically stimulating deep regions in the brain. The objective of this study is to provide insight into the fundamental mechanisms of this strategy and assess the potential uses of this method through computational analysis. Analytical and numerical methods are used to compute the electric potential and field distributions generated during NDBS in homogeneous and inhomogeneous models of the brain. The computational results are used for specifying the activated area in the brain (macroscopic approach), and quantifying its relationships to the stimulation parameters. Two automatic algorithms, using artificial neural network (ANN), are developed for the homogeneous model with two and four electrode pairs to estimate stimulation parameters. Additionally, the extracellular potentials are coupled to the compartmental axon cable model to determine the responses of the neurons to the modulated electric field in two developed models and to evaluate the precise activated area location (microscopic approach). Our results show that although the shape of the activated area was different in macroscopic and microscopic approaches, it located only at depth. Our optimization algorithms showed significant accuracy in estimating stimulation parameters. Moreover, it demonstrated that the more the electrode pairs, the more controllable the activated area. Finally, compartmental axon cable modeling results verified that neurons can demodulate and follow the electric field modulation envelope amplitude (MEA) in our models. The results of this study help develop the NDBS method and eliminate some limitations associated with the nonautomated optimization algorithm.

Estimating axon conduction velocity in vivo from microstructural MRI

The conduction velocity (CV) of action potentials along axons is a key neurophysiological property central to neural communication. The ability to estimate CV in humans in vivo from non-invasive MRI methods would therefore represent a significant advance in neuroscience. However, there are two major challenges that this paper aims to address: (1) Much of the complexity of the neurophysiology of action potentials cannot be captured with currently available MRI techniques. Therefore, we seek to establish the variability in CV that can be captured when predicting CV purely from parameters that have been reported to be estimatable from MRI: inner axon diameter (AD) and g-ratio. (2) errors inherent in existing MRI-based biophysical models of tissue will propagate through to estimates of CV, the extent to which is currently unknown. Issue (1) is investigated by performing a sensitivity analysis on a comprehensive model of axon electrophysiology and determining the relative sensitivity to various morphological and electrical parameters. The investigations suggest that 85% of the variance in CV is accounted for by variation in AD and g-ratio. The observed dependency of CV on AD and g-ratio is well characterised by the previously reported model by Rushton. Issue (2) is investigated through simulation of diffusion and relaxometry MRI data for a range of axon morphologies, applying models of restricted diffusion and relaxation processes to derive estimates of axon volume fraction (AVF), AD and g-ratio and estimating CV from the derived parameters. The results show that errors in the AVF have the biggest detrimental impact on estimates of CV, particularly for sparse fibre populations (AVF<0.3). For our equipment set-up and acquisition protocol, CV estimates are most accurate (below 5% error) where AVF is above 0.3, g-ratio is between 0.6 and 0.85 and AD is high (above 4μm). CV estimates are robust to errors in g-ratio estimation but are highly sensitive to errors in AD estimation, particularly where ADs are small. We additionally show CV estimates in human corpus callosum in a small number of subjects. In conclusion, we demonstrate accurate CV estimates are possible in regions of the brain where AD is sufficiently large. Problems with estimating ADs for smaller axons presents a problem for estimating CV across the whole CNS and should be the focus of further study.

Action potential propagation and synchronisation in myelinated axons

With the advent of advanced MRI techniques it has become possible to study axonal white matter non-invasively and in great detail. Measuring the various parameters of the long-range connections of the brain opens up the possibility to build and refine detailed models of large-scale neuronal activity. One particular challenge is to find a mathematical description of action potential propagation that is sufficiently simple, yet still biologically plausible to model signal transmission across entire axonal fibre bundles. We develop a mathematical framework in which we replace the Hodgkin-Huxley dynamics by a spike-diffuse-spike model with passive sub-threshold dynamics and explicit, threshold-activated ion channel currents. This allows us to study in detail the influence of the various model parameters on the action potential velocity and on the entrainment of action potentials between ephaptically coupled fibres without having to recur to numerical simulations. Specifically, we recover known results regarding the influence of axon diameter, node of Ranvier length and internode length on the velocity of action potentials. Additionally, we find that the velocity depends more strongly on the thickness of the myelin sheath than was suggested by previous theoretical studies. We further explain the slowing down and synchronisation of action potentials in ephaptically coupled fibres by their dynamic interaction. In summary, this study presents a solution to incorporate detailed axonal parameters into a whole-brain modelling framework.

With more and more data becoming available on white-matter tracts, the need arises to develop modelling frameworks that incorporate these data at the whole-brain level. This requires the development of efficient mathematical schemes to study parameter dependencies that can then be matched with data, in particular the speed of action potentials that cause delays between brain regions. Here, we develop a method that describes the formation of action potentials by threshold activated currents, often referred to as spike-diffuse-spike modelling. A particular focus of our study is the dependence of the speed of action potentials on structural parameters. We find that the diameter of axons and the thickness of the myelin sheath have a strong influence on the speed, whereas the length of myelinated segments and node of Ranvier length have a lesser effect. In addition to examining single axons, we demonstrate that action potentials between nearby axons can synchronise and slow down their propagation speed.