Blockage of pain by electrical spinal cord stimulation.

BACKGROUND: Electrical spinal cord stimulation (SCS) is an alternative to conventional medication for chronic pain relief. Several hypotheses exist concerning the neurophysiological, vascular, and neurochemical mechanism behind SCS. METHODS: The excitation and blockade effects of the three common SCS waveforms (tonic, burst, and high-frequency stimulation) on the nerve fibers bypassing the region of the electrodes are analyzed in a computational study. The simulations are based on the model of Hodgkin and Huxley which is fitted to spike durations of 1 ms. RESULTS: SCS is a FDA approved technique for pain relief, but the mechanisms of action are still under investigation. The first element in the chain of mechanisms is the generation and the block of spikes in nerve fibers close to the stimulating electrode. For these "primary fibers" computer simulations showed that conventional SCS generates sharply synchronized spikes whereas the spread of the spiking times by burst stimulation is expected to cause the suppression of paresthesia. This rather uniform spread of spiking times (in comparison to tonic stimulation) is a consequence of more pulses (5 vs. 1), longer pulses, and increasing intensities within each train of 5 pulses. CONCLUSIONS: High-frequency stimulation can block the conduction of spikes but the distance of the fiber to the lead is a critical factor.

A simple model considering spiking probability during extracellular axon stimulation.

The spiking probability of an electrically stimulated axon as a function of stimulus amplitude increases in a sigmoidal dependency from 0 to 1. However, most computer simulation studies for neuroprosthetic applications calculate thresholds for neural targets with a deterministic model and by reducing the sigmoid curve to a step function, they miss an important information about the control signal, namely how the spiking efficiency increases with stimulus intensity. Here, this spiking efficiency is taken into account in a compartment model of the Hodgkin Huxley type where a noise current is added in every compartment with an active membrane. A key parameter of the model is a common factor knoise which defines the ion current fluctuations across the cell membrane for every compartment by its maximum sodium ion conductance. In the standard model Gaussian signals are changed every 2.5 µs as a compromise of accuracy and computational costs. Additionally, a formula for other noise transmission times is presented and numerically tested. Spiking probability as a function of stimulus intensity can be approximated by the cumulative distribution function of the normal distribution with RS = σ/µ. Relative spread RS, introduced by Verveen, is a measure for the spread (normalized by the threshold intensity µ), that decreases inversely with axon diameter. Dynamic range, a related measure used in neuroprosthetic studies, defines the intensity range between 10% and 90% spiking probability. We show that (i) the dynamic range normalized by threshold is 2.56 times RS, (ii) RS increases with electrode-axon distance and (iii) we present knoise values for myelinated and unmyelinated axon models in agreement with recoded RS data. The presented method is applicable for other membrane models and can be extended to whole neurons that are described by multi-compartment models.

A finite element method framework to model extracellular neural stimulation.

Objective.Increasing complexity in extracellular stimulation experiments and neural implant design also requires realistic computer simulations capable of modeling the neural activity of nerve cells under the influence of an electrical stimulus. Classical model approaches are often based on simplifications, are not able to correctly calculate the electric field generated by complex electrode designs, and do not consider electrical effects of the cell on its surrounding. A more accurate approach is the finite element method (FEM), which provides necessary techniques to solve the Poisson equation for complex geometries under consideration of electrical tissue properties. Especially in situations where neurons experience large and non-symmetric extracellular potential gradients, a FEM solution that implements the cell membrane model can improve the computer simulation results. To investigate the response of neurons in an electric field generated by complex electrode designs, a FEM framework for extracellular stimulation was developed in COMSOL.Approach.Methods to implement morphologically- and biophysically-detailed neurons including active Hodgkin-Huxley (HH) cell membrane dynamics as well as the stimulation setup are described in detail. Covered methods are (a) development of cell and electrode geometries including meshing strategies, (b) assignment of physics for the conducting spaces and the realization of active electrodes, (c) implementation of the HH model, and (d) coupling of the physics to get a fully described model.Main results.Several implementation examples are briefly presented: (a) a full FEM implementation of a HH model cell stimulated with a honeycomb electrode, (b) the electric field of a cochlear electrode placed inside the cochlea, and (c) a proof of concept implementation of a detailed double-cable cell membrane model for myelinated nerve fibers.Significance.The presented concepts and methods provide basic and advanced techniques to realize a full FEM framework for innovative studies of neural excitation in response to extracellular stimulation.

Impact of electrode position on the dynamic range of a human auditory nerve fiber.

Objective. Electrodes of a cochlear implant generate spikes in auditory nerve fibers (ANFs). While the insertion depth of each of the electrodes is linked to a frequency section of the acoustic signal, the amplitude of the stimulating pulses controls the loudness of the related frequency band. However, in comparison to acoustic stimulation the dynamic range (DR) of an electrically stimulated ANF is quite small.Approach. The DR of an electrically stimulated ANF is defined as the interval of stimulus amplitudes that causes firing probabilities between 10% and 90%. A compartment model that includes sodium ion current fluctuations as the stochastic key component for spiking was evaluated for different electrode placements and fiber diameters.Main results. The DR is reversely related to ANF diameter. An increased DR is expected to improve the quality of auditory perception for CI users. Electrodes are often placed as close to the center axis of the cochlea as possible. The analysis of the simulated auditory nerve firing showed that this placement is disadvantageous for the DR of a selected ANF.Significance. Five times larger DRs are expected for electrodes close to the terminal of the dendrite or at mid-dendritic placement as opposed to electrodes close to the modiolus.

Block Phenomena During Electric Micro-Stimulation of Pyramidal Cells and Retinal Ganglion Cells.

Electric micro-stimulation of the nervous system is a means to restore various body functions. The stimulus amplitude necessary to generate action potentials, the lower threshold (LT), is well characterized for many neuronal populations. However, electric overstimulation above an upper threshold (UT) prevents action potential generation and therefore hinders optimal neuro-rehabilitation. Previous studies demonstrated the impact of the UT in micro-stimulation of retinal ganglion cells (RGCs). The observed phenomenon is mostly explained by (i) reversed sodium ion flow in the soma membrane, and (ii) anodal surround block that hinders spike conduction in strongly hyperpolarized regions of the axon at high stimulus intensities. However, up to now, no detailed study of the nature of these phenomena has been presented, particularly for different cell types. Here, we present computational analyses of LT and UT for layer 5 pyramidal cells (PCs) as well as alpha RGCs. Model neurons were stimulated in close vicinity to the cell body and LTs and UTs as well as the ratio UT/LT were compared. Aside from a simple point source electrode and monophasic stimuli also realistic electrode and pulse configurations were examined. The analysis showed: (i) in RGCs, the soma contributed to action potential initiation and block for small electrode distances, whereas in PCs the soma played no role in LTs or UTs. (ii) In both cell types, action potential always initiated within the axon initial segment at LT. (iii) In contrast to a complete block of spike conductance at UT that occurred in RGCs, an incomplete block of spiking appeared in PC axon collaterals. (iv) PC axon collateral arrangement influenced UTs but had small impact on LTs. (v) Population responses of RGCs change from circular regions of activation to ring-shaped patterns for increasing stimulus amplitude. A better understanding of the stimulation window that can reliably activate target neurons will benefit the future development of neuroprostheses.

Polarity Sensitivity of Human Auditory Nerve Fibers Based on Pulse Shape, Cochlear Implant Stimulation Strategy and Array.

Neural health is of great interest to determine individual degeneration patterns for improving speech perception in cochlear implant (CI) users. Therefore, in recent years, several studies tried to identify and quantify neural survival in CI users. Among all proposed techniques, polarity sensitivity is a promising way to evaluate the neural status of auditory nerve fibers (ANFs) in CI users. Nevertheless, investigating neural health based on polarity sensitivity is a challenging and complicated task that involves various parameters, and the outcomes of many studies show contradictory results of polarity sensitivity behavior. Our computational study benefits from an accurate three-dimensional finite element model of a human cochlea with realistic human ANFs and determined ANF degeneration pattern of peripheral part with a diminishing of axon diameter and myelination thickness based on degeneration levels. In order to see how different parameters may impact the polarity sensitivity behavior of ANFs, we investigated polarity behavior under the application of symmetric and asymmetric pulse shapes, monopolar and multipolar CI stimulation strategies, and a perimodiolar and lateral CI array system. Our main findings are as follows: (1) action potential (AP) initiation sites occurred mainly in the peripheral site in the lateral system regardless of stimulation strategies, pulse polarities, pulse shapes, cochlear turns, and ANF degeneration levels. However, in the perimodiolar system, AP initiation sites varied between peripheral and central processes, depending on stimulation strategies, pulse shapes, and pulse polarities. (2) In perimodiolar array, clusters formed in threshold values based on cochlear turns and degeneration levels for multipolar strategies only when asymmetric pulses were applied. (3) In the perimodiolar array, a declining trend in polarity (anodic threshold/cathodic threshold) with multipolar strategies was observed between intact or slight degenerated cases and more severe degenerated cases, whereas in the lateral array, cathodic sensitivity was noticed for intact and less degenerated cases and anodic sensitivity for cases with high degrees of degeneration. Our results suggest that a combination of asymmetric pulse shapes, focusing more on multipolar stimulation strategies, as well as considering the distances to the modiolus wall, allows us to distinguish the degeneration patterns of ANFs across the cochlea.

Dendritic Degeneration of Human Auditory Nerve Fibers and Its Impact on the Spiking Pattern Under Regular Conditions and During Cochlear Implant Stimulation.

Due to limitations of human in vivo studies, detailed computational models enable understanding the neural signaling in the degenerated auditory system and cochlear implants (CIs). Four human cochleae were used to quantify hearing levels depending on dendritic changes in diameter and myelination thickness from type I of the auditory nerve fibers (ANFs). Type I neurons transmit the auditory information as spiking pattern from the inner hair cells (IHCs) to the cochlear nucleus. The impact of dendrite diameter and degree of myelination on neural signal transmission was simulated for (1) synaptic excitation via IHCs and (2) stimulation from CI electrodes. An accurate three-dimensional human cochlear geometry, along with 30 auditory pathways, mimicked the CI environment. The excitation properties of electrical potential distribution induced by two CI were analyzed. Main findings: (1) The unimodal distribution of control dendrite diameters becomes multimodal for hearing loss cases; a group of thin dendrites with diameters between 0.3 and 1 µm with a peak at 0.5 µm appeared. (2) Postsynaptic currents from IHCs excite such thin dendrites easier and earlier than under control conditions. However, this advantage is lost as their conduction velocity decreases proportionally with the diameter and causes increased spike latency and jitter in soma and axon. Firing probability reduces through the soma passage due to the low intracellular current flow in thin dendrites during spiking. (3) Compared with dendrite diameter, variations in myelin thickness have a small impact on spiking performance. (4) Contrary to synaptic excitation, CIs cause several spike initiation sites in dendrite, soma region, and axon; moreover, fiber excitability reduces with fiber diameter. In a few cases, where weak stimuli elicit spikes of a target neuron (TN) in the axon, dendrite diameter reduction has no effect. However, in many cases, a spike in a TN is first initiated in the dendrite, and consequently, dendrite degeneration demands an increase in threshold currents. (5) Threshold currents of a TN and co-stimulation of degenerated ANFs in other frequency regions depend on the electrode position, including its distance to the outer wall, the cochlear turn, and the three-dimensional pathway of the TN.

Finite element analysis and three-dimensional reconstruction of tonotopically aligned human auditory fiber pathways: A computational environment for modeling electrical stimulation by a cochlear implant based on micro-CT.

The application of cochlear implants can be studied with computational models. The electrical potential distribution induced by an implanted device is evaluated with a volume conductor model, which is used as input for neuron models to simulate the reaction of cochlear neurons to micro-stimulation. In order to reliably predict the complex excitation profiles it is vital to consider an accurate representation of the human cochlea geometry including detailed three-dimensional pathways of auditory neurons reaching from the organ of Corti through the cochlea-volume. In this study, high-resolution micro-CT imaging (Δx = Δy = Δz = 3 µm) was used to reconstruct the pathways of 30 tonotopically organized nerve fiber bundles, distributed over eight octaves (11500-40 Hz). Results of the computational framework predict: (i) the peripheral process is most sensitive to cathodic stimulation (CAT), (ii) in many cases CAT elicits spikes in the peripheral terminal at threshold but with larger stimuli there is a second spike initiation site within the peripheral process, (iii) anodic stimuli (ANO) can excite the central process even at threshold, (iv) the recruitment of fibers by electrodes located in the narrowing middle- and apical turn is complex and impedes focal excitation of low frequency fibers, (v) degenerated cells which lost the peripheral process are more sensitive to CAT when their somata are totally covered with 2 membranes of a glial cell but they become ANO sensitive when the myelin covering is reduced.

Functional Magnetic Resonance Imaging in the Final Stage of Creutzfeldt-Jakob Disease.

Sporadic Creutzfeldt-Jakob disease (sCJD) is a rare fatal degenerative disease of the central nervous system. The clinical course is characterized by rapid progression of neurological and neuromuscular symptoms. The late stage with loss of consciousness is not well characterized. We report a 62-year-old male patient with sCJD with the clinical picture of a vegetative state/apallic syndrome, in whom we studied cortical responses using a vibration paradigm. The functional magnetic resonance imaging (fMRI) investigation demonstrated a clear response within the sensorimotor cortex, the cerebellum, the parietal cortex, the insular, and frontal inferior region. The finding of persistent cortical activity on fMRI in a patient with CJD in a state of unconsciousness has implications for the clinical management and for ethical considerations.

Genetic algorithms for feature selection when classifying severe chronic disorders of consciousness.

The diagnosis and prognosis of patients with severe chronic disorders of consciousness are still challenging issues and a high rate of misdiagnosis is evident. Hence, new tools are needed for an accurate diagnosis, which will also have an impact on the prognosis. In recent years, functional Magnetic Resonance Imaging (fMRI) has been gaining more and more importance when diagnosing this patient group. Especially resting state scans, i.e., an examination when the patient does not perform any task in particular, seems to be promising for these patient groups. After preprocessing the resting state fMRI data with a standard pipeline, we extracted the correlation matrices of 132 regions of interest. The aim was to find the regions of interest which contributed most to the distinction between the different patient groups and healthy controls. We performed feature selection using a genetic algorithm and a support vector machine. Moreover, we show by using only those regions of interest for classification that are most often selected by our algorithm, we get a much better performance of the classifier.

Analysis of upper threshold mechanisms of spherical neurons during extracellular stimulation.

Exceeding a certain stimulation strength can prevent the generation of somatic action potentials, as has been demonstrated in vitro with extracellularly stimulated dorsal root ganglion cells as well as retinal ganglion cells. This phenomenon, termed upper threshold, is currently thought to be a consequence of sodium current reversal in strongly depolarized regions. Here we analyze the contribution of membrane kinetics, using spherical model neurons that are stimulated externally with a microelectrode, in more detail. During extracellular pulse application, the electric field depolarizes one part and hyperpolarizes the other part of the cell. Strong transmembrane currents are generated only in the active depolarized region, changing the overall polarization level. The asymmetric membrane voltage distribution caused by the stimulus strongly influences the cell's behavior during and even after the stimulus. Effects on membrane voltage and transmembrane currents during and after the stimulus are shown and discussed in detail. Aside from the sodium current reversal, two more key mechanisms were identified in causing the upper threshold: strong potassium currents and inactivation of sodium channels. The contributions of the mechanisms involved strongly depend on cell properties, stimulus parameters, and other factors such as temperature. The conclusions presented here are based on several retinal ganglion cell models of the Fohlmeister group, a model with original Hodgkin-Huxley membrane, and a pyramidal cell model. NEW & NOTEWORTHY The upper threshold phenomenon in extracellular stimulation is analyzed in detail for spherical cells. Three main mechanisms were identified that prevent the generation of action potentials at high stimulation strengths: 1) strong potassium currents, 2) inactivating sodium ion channels, and 3) sodium current reversal. Ion channel kinetics in retinal ganglion cells, pyramidal cells, and the original Hodgkin-Huxley model were investigated under the influence of an extracellular stimulus.

Compartment models for the electrical stimulation of retinal bipolar cells.

Bipolar cells of the retina are among the smallest neurons of the nervous system. For this reason, compared to other neurons, their delay in signaling is minimal. Additionally, the small bipolar cell surface combined with the low membrane conductance causes very little attenuation in the signal from synaptic input to the terminal. The existence of spiking bipolar cells was proven over the last two decades, but until now no complete model including all important ion channel types was published. The present study amends this and analyzes the impact of the number of model compartments on simulation accuracy. Characteristic features like membrane voltages and spike generation were tested and compared for one-, two-, four- and 117-compartment models of a macaque bipolar cell. Although results were independent of the compartment number for low membrane conductances (passive membranes), nonlinear regimes such as spiking required at least a separate axon compartment. At least a four compartment model containing the functionally different segments dendrite, soma, axon and terminal was needed for understanding signaling in spiking bipolar cells. Whereas for intracellular current application models with small numbers of compartments showed quantitatively correct results in many cases, the cell response to extracellular stimulation is sensitive to spatial variation of the electric field and accurate modeling therefore demands for a large number of short compartments even for passive membranes.

Functional magnetic resonance imaging under anaesthesia of a patient with severe chronic disorders of consciousness.

CLINICAL CASE: We report on a 19-year old male patient who is recovering from near-drowning. The patient was admitted for re-evaluation in a Minimally Conscious State. METHOD: A regular functional Magnetic Resonance Imaging was not possible due to complex motor tics of the patient with sudden flexion and extension movements of arms and legs as well as opisthotonic retroflexion of the head and trunk. Thus, the patient was anaesthetised and functional Magnetic Resonance Imaging was performed under general anaesthesia which was introduced and maintained with Sevoflorane and Fentanyl provided analgesia. Four functional runs were performed and the patient's responses were recorded. During each one of these runs one extremity (dorsum manus or pedis) was stimulated with a brush with an operator-paced frequency of about 2 Hz. RESULTS AND CONCLUSION: Clear responses were found in the somatosensory cortex contra lateral within the post central gyrus during stimulation of the left hand. Considering the other three extremities no significant responses were found. Nevertheless, we conclude that a functional Magnetic Resonance Imaging under anaesthesia is possible for patients with severe chronic disorders of consciousness and brain areas responding to stimuli can be detected.

Upper stimulation threshold for retinal ganglion cell activation.

OBJECTIVE: The existence of an upper threshold in electrically stimulated retinal ganglion cells (RGCs) is of interest because of its relevance to the development of visual prosthetic devices, which are designed to restore partial sight to blind patients. The upper threshold is defined as the stimulation level above which no action potentials (direct spikes) can be elicited in electrically stimulated retina. APPROACH: We collected and analyzed in vitro recordings from rat RGCs in response to extracellular biphasic (anodic-cathodic) pulse stimulation of varying amplitudes and pulse durations. Such responses were also simulated using a multicompartment model. MAIN RESULTS: We identified the individual cell variability in response to stimulation and the phenomenon known as upper threshold in all but one of the recorded cells (n = 20/21). We found that the latencies of spike responses relative to stimulus amplitude had a characteristic U-shape. In silico, we showed that the upper threshold phenomenon was observed only in the soma. For all tested biphasic pulse durations, electrode positions, and pulse amplitudes above lower threshold, a propagating action potential was observed in the distal axon. For amplitudes above the somatic upper threshold, the axonal action potential back-propagated in the direction of the soma, but the soma's low level of hyperpolarization prevented action potential generation in the soma itself. SIGNIFICANCE: An upper threshold observed in the soma does not prevent spike conductance in the axon.

Peripheral Nervous System Reconstruction Reroutes Cortical Motor Output-Brain Reorganization Uncovered by Effective Connectivity.

Cortical reorganization in response to peripheral nervous system damage is only poorly understood. In patients with complete brachial plexus avulsion and subsequent reconnection of the end of the musculocutaneous nerve to the side of a phrenic nerve, reorganization leads to a doubled arm representation in the primary motor cortex. Despite, homuncular organization being one of the most fundamental principles of the human brain, movements of the affected arm now activate 2 loci: the completely denervated arm representation and the diaphragm representation. Here, we investigate the details behind this peripherally triggered reorganization, which happens in healthy brains. fMRI effective connectivity changes within the motor network were compared between a group of patients and age matched healthy controls at 7 Tesla (6 patients and 12 healthy controls). Results show the establishment of a driving input of the denervated arm area to the diaphragm area which is now responsible for arm movements. The findings extend current knowledge about neuroplasticity in primary motor cortex: a denervated motor area may drive an auxilliary area to reroute its motor output.

Impact of Electrode Position on the Elicitation of Sodium Spikes in Retinal Bipolar Cells.

Bipolar cells of the magnocellular pathway in the primate retina can generate action potentials because they have an axonal segment with high sodium channel density, comparable to the sodium channel band in retinal ganglion cells or pyramidal cells. The similarity between the non-human primate and the human retina is of interest for the research on retinal implants for the blind, and especially, the conditions to elicit sodium spikes in bipolar cells using extracellular stimulation. A comparison of excitation characteristics of three model neurons, a bipolar cell, a retinal ganglion cell, and a cortical pyramidal cell, demonstrates the similarities and differences regarding stimulation with microelectrodes. Moving a microelectrode parallel to the axon of a neuron commonly allows to generate spikes for every position - and this rule holds both for cathodic and anodic pulses. However, for the simulated bipolar cell anodic pulses cannot generate sodium spikes directly. Further, there is only a small region for electrode placing where extracellular cathodic stimulation causes direct spike initiation in the sodium channel band. For all other positions, a sodium spike can only be generated by antidromic current flow originating from strongly depolarized terminals.

Mobile gait analysis via eSHOEs instrumented shoe insoles: a pilot study for validation against the gold standard GAITRite®.

Clinical gait analysis contributes massively to rehabilitation support and improvement of in-patient care. The research project eSHOE aspires to be a useful addition to the rich variety of gait analysis systems. It was designed to fill the gap of affordable, reasonably accurate and highly mobile measurement devices. With the overall goal of enabling individual home-based monitoring and training for people suffering from chronic diseases, affecting the locomotor system. Motion and pressure sensors gather movement data directly on the (users) feet, store them locally and/or transmit them wirelessly to a PC. A combination of pattern recognition and feature extraction algorithms translates the motion data into standard gait parameters. Accuracy of eSHOE were evaluated against the reference system GAITRite in a clinical pilot study. Eleven hip fracture patients (78.4 ± 7.7 years) and twelve healthy subjects (40.8 ± 9.1 years) were included in these trials. All subjects performed three measurements at a comfortable walking speed over 8 m, including the 6-m long GAITRite mat. Six standard gait parameters were extracted from a total of 347 gait cycles. Agreement was analysed via scatterplots, histograms and Bland-Altman plots. In the patient group, the average differences between eSHOE and GAITRite range from -0.046 to 0.045 s and in the healthy group from -0.029 to 0.029 s. Therefore, it can be concluded that eSHOE delivers adequately accurate results. Especially with the prospect as an at home supplement or follow-up to clinical gait analysis and compared to other state of the art wearable motion analysis systems.

The impact of calcium current reversal on neurotransmitter release in the electrically stimulated retina.

OBJECTIVE: In spite of intense theoretical and experimental investigations on electrical nerve stimulation, the influence of reversed ion currents on network activity during extracellular stimulation has not been investigated so far. APPROACH: Here, the impact of calcium current reversal on neurotransmitter release during subretinal stimulation was analyzed with a computational multi-compartment model of a retinal bipolar cell (BC) that was coupled with a four-pool model for the exocytosis from its ribbon synapses. Emphasis was laid on calcium channel dynamics and how these channels influence synaptic release. MAIN RESULTS: Stronger stimulation with anodic pulses caused transmembrane voltages above the Nernst potential of calcium in the terminals and, by this means, forced calcium ions to flow in the reversed direction from inside to the outside of the cell. Consequently, intracellular calcium concentration decreased resulting in a reduced vesicle release or preventing release at all. This mechanism is expected to lead to a pronounced ring-shaped pattern of exocytosis within a group of neighbored BCs when the stronger stimulated cells close to the electrode fail in releasing vesicles. SIGNIFICANCE: Stronger subretinal stimulation causes failure of synaptic exocytosis due to reversal of calcium flow into the extracellular space in cells close to the electrode.

Gamma-Band Modulation and Coherence in the EEG by Involuntary Eye Movements in Patients in Unresponsive Wakefulness Syndrome.

Gamma power and coherence in the electroencephalogram increase in healthy individuals in association with voluntary eye movements, saccades. Patients with unresponsive wakefulness syndrome show repetitive involuntary eye movements that are similar to saccades but progress at a much lower speed. In the present study, we explored the changes in gamma power and coherence related to these eye movements and investigated whether any relationship to the patients' clinical status could be found that would indicate first neurophysiological signs of recovery. To this end, we assessed the clinical status and registered classical scalp electroencephalography with 19 surface electrodes and electro-oculogram of 45 consecutive patients at admission and at 4 weekly intervals. Slow gamma activity (in the frequency range of 37-40 Hz) was analyzed before, during, and after eye movements (pre, -intra and post-eye movement) by means of "continuous wavelet transform." We graded recovery using clinical behavioral scales, taking into account the variables, age, gender, recovery (yes or no), as well as the patients diagnoses (traumatic brain injury, hypoxia, hemorrhage, infection). Statistical evaluation was performed using DataLab, R, and Kruskal-Wallis methods. Based on the clinical status, we distinguished between recovering and chronic groups of patients. In comparison with the chronic group, the recovering group showed significantly higher gamma power over the posterior electrodes and significant higher values of coherence in the gamma-band activity during the presaccadic period of eye movements. We suggest that our findings on the onset of involuntary eye movements in the recovering group of patients with unresponsive wakefulness syndrome indicates a first neurophysiological sign of favorable prognosis.

From Squid to Mammals with the HH Model through the Nav Channels' Half-Activation-Voltage Parameter.

The model family analyzed in this work stems from the classical Hodgkin-Huxley model (HHM). for a single-compartment (space-clamp) and continuous variation of the voltage-gated sodium channels (Nav) half-activation-voltage parameter ΔV1/2, which controls the window of sodium-influx currents. Unlike the baseline HHM, its parametric extension exhibits a richer multitude of dynamic regimes, such as multiple fixed points (FP's), bi- and multi-stability (coexistence of FP's and/or periodic orbits). Such diversity correlates with a number of functional properties of excitable neural tissue, such as the capacity or not to evoke an action potential (AP) from the resting state, by applying a minimal absolute rheobase current amplitude. The utility of the HHM rooted in the giant squid for the descriptions of the mammalian nervous system is of topical interest. We conclude that the model's fundamental principles are still valid (up to using appropriate parameter values) for warmer-blooded species, without a pressing need for a substantial revision of the mathematical formulation. We demonstrate clearly that the continuous variation of the ΔV1/2 parameter comes close to being equivalent with recent HHM 'optimizations'. The neural dynamics phenomena described here are nontrivial. The model family analyzed in this work contains the classical HHM as a special case. The validity and applicability of the HHM to mammalian neurons can be achieved by picking the appropriate ΔV1/2 parameter in a significantly broad range of values. For such large variations, in contrast to the classical HHM, the h and n gates' dynamics may be uncoupled--i.e. the n gates may no longer be considered in mere linear correspondence to the h gates. ΔV1/2 variation leads to a multitude of dynamic regimes--e.g. models with either 1 fixed point (FP) or with 3 FP's. These may also coexist with stable and/or unstable periodic orbits. Hence, depending on the initial conditions, the system may behave as either purely excitable or as an oscillator. ΔV1/2 variation leads to significant changes in the metabolic efficiency of an action potential (AP). Lower ΔV1/2 values yield a larger range of AP response frequencies, and hence provide for more flexible neural coding. Such lower values also contribute to faster AP conduction velocities along neural fibers of otherwise comparable-diameter. The 3 FP case brings about an absolute rheobase current. In comparison in the classical HHM the rheobase current is only relative--i.e. excitability is lost after a finite amount of elapsed stimulation time. Lower ΔV1/2 values translate in lower threshold currents from the resting state.