Dominique M. Durand

Modeling the effects of electric fields on nerve fibers: Determination of excitation thresholds

A method for predicting excitation of axons based on the response of passive models is proposed. An expression describing the transmembrane potential induced in passive models to an applied electric field is presented. Two terms drive the polarization of each node: a source term described by the activating function at the node, and an ohmic term resulting from redistribution of current from sources at other nodes. It is shown that a total equivalent driving function including both terms can be used to provide predictions of excitation thresholds for any applied field. The method requires only knowledge of the intracellular strength-duration relationship of the axon, the passive step response of the axon to an intracellular current, and the values of the extracellular potentials. Excitation thresholds for any given applied field can then be calculated using a simple algebraic expression. This method eliminates the errors associated with use of the activating function alone, and greatly reduces the computation required.<<ETX>>

Functionally selective peripheral nerve stimulation with a flat interface nerve electrode

One of the important goals of peripheral nerve electrode development is to design an electrode for selective recruitment of the different functions of a common nerve trunk. A challenging task is gaining selective access to central axon populations. In this paper, a simple electrode that takes advantage of the neural plasticity to reshape the nerve is presented. The flat interface nerve electrode (FINE) reshapes the nerve into a flat geometry to increase the surface area and move central axon populations close to the surface. The electrode was implanted acutely on the sciatic nerve of eight cats. The FINE can significantly reshape the nerve and fascicles (p<0.0001) while maintaining the same total nerve cross-sectional area. The stimulation thresholds were 2.89 nC for pulse amplitude modulation and 10.2 nC for pulsewidth modulation. Monopolar, square-pulse stimulation with single contacts on the FINE selectively recruited each of the four main branches of the sciatic nerve. Simultaneous stimulation with two contacts produced moments about the ankle joint that were a combination of the moments produced by the individual contacts when stimulated separately.

Effects of induced electric fields on finite neuronal structures: a simulation study

An analysis is presented of magnetic stimulation of finite length neuronal structures using computer simulations. Models of finite neuronal structures in the presence of extrinsically applied electric fields indicate that excitation can be characterized by two driving functions: one due to field gradients and the other due to fields at the boundaries of neuronal structures. It is found that boundary field driving functions play an important role in governing excitation characteristics during magnetic stimulation. Simulations indicate that axons whose lengths are short compared to the spatial extent of the induced field are easier to excite than longer axons of the same diameter. Simulations also indicate that independent cellular dendritic processes are probably not excited during magnetic stimulation. Analysis of the temporal distribution of induced fields indicates that the temporal shape of the stimulus waveform modulates excitation thresholds and propagation of action potentials.<<ETX>>

Suppression of epileptiform activity by high frequency sinusoidal fields in rat hippocampal slices

1 Sinusoidal high frequency (20‐50 Hz) electric fields induced across rat hippocampal slices were found to suppress zero‐Ca2+, low‐Ca2+, picrotoxin, and high‐K+ epileptiform activity for the duration of the stimulus and for up to several minutes following the stimulus. 2 Suppression of spontaneous activity by high frequency stimulation was found to be frequency (< 500 Hz) but not orientation or waveform dependent. 3 Potassium‐sensitive microelectrodes showed that block of epileptiform activity was always coincident with a stimulus‐induced rise in extracellular potassium concentration during stimulation. Post‐stimulus inhibition was always associated with a decrease in extracellular potassium activity below baseline levels. 4 Intracellular recordings and optical imaging with voltage‐sensitive dyes showed that during suppression neurons were depolarized yet did not fire action potentials. 5 Direct injection of sinusoidal current into individual pyramidal cells did not result in a tonic depolarization. Injection of large direct current (DC) depolarized neurons and suppressed action potential generation. 6 These findings suggest that high frequency stimulation suppresses epileptiform activity by inducing potassium efflux and depolarization block.

Suppression and control of epileptiform activity by electrical stimulation: a review

Epilepsy is a devastating disease affecting /spl sim/1% of the worlds population. Although drug therapy is effective in many patients, 25% are not responsive to anticonvulsants. In addition, up to 50% of those receiving regular mediation suffer major side effects. Surgical resection is another treatment also associated with serious complications. An alternative method to control seizure activity is electrical stimulation. Several electrical stimulation protocols have been developed in animal models of epilepsy that can reduce or completely suppress seizures. Moreover, in over 5000 patients worldwide, electrical stimulation has been used to control seizures. The mechanisms underlying some of the techniques of seizure control are not understood. Some stimulation protocols, such as DC stimulation, rely on the effects of fields and currents on the membrane polarization. Other methods using single pulses, such as phase-resetting, desynchronization, and chaos control rely on the modulation of the dynamic properties of the neuronal networks. Both low- and high-frequency periodic stimulation can suppress seizures not only during stimulation, but also by inducing long-term changes in brain function. The purpose of this review is to present these approaches and to discuss their underlying mechanisms and potential for clinical implementation.

Local suppression of epileptiform activity by electrical stimulation in rat hippocampus in vitro

High frequency electrical stimulation of deep brain structures (DBS) has been effective at controlling abnormal neuronal activity in Parkinsons patients and is now being applied for the treatment of pharmacologically intractable epilepsy. The mechanisms underlying the therapeutic effects of DBS are unknown. In particular, the effect of the electrical stimulation on neuronal firing remains poorly understood. Previous reports have showed that uniform electric fields with both AC (continuous sinusoidal) or DC waveforms could suppress epileptiform activity in vitro. In the present study, we tested the effects of monopolar electrode stimulation and low‐duty cycle AC stimulation protocols, which more closely approximate those used clinically, on three in vitro epilepsy models. Continuous sinusoidal stimulation, 50 % duty‐cycle sinusoidal stimulation, and low (1.68 %) duty‐cycle pulsed stimulation (120 μs, 140 Hz) could completely suppress spontaneous low‐Ca2+ epileptiform activity with average thresholds of 71.11 ± 26.16 μA, 93.33 ± 12.58 μA and 300 ± 100 μA, respectively. Continuous sinusoidal stimulation could also completely suppress picrotoxin‐ and high‐K+‐induced epileptiform activity with either uniform or localized fields. The suppression generated by the monopolar electrode was localized to a region surrounding the stimulation electrode. Potassium concentration and transmembrane potential recordings showed that AC stimulation was associated with an increase in extracellular potassium concentration and neuronal depolarization block; AC stimulation efficacy was not orientation‐selective. In contrast, DC stimulation blocked activity by membrane hyperpolarization and was orientation‐selective, but had a lower threshold for suppression.

Phase synchronization in two coupled chaotic neurons

Abstract Chaotically-spiking dynamics of Hindmarsh–Rose neurons are discussed based on a flexible definition of phase for chaotic flow. The phase synchronization of two coupled chaotic neurons is in fact the spike synchronization. As a multiple time-scale model, the coupled HR neurons have quite different behaviors from the Rossler oscillators only having single time-scale mechanism. Using such a multiple time-scale model, the phase function can detect synchronization dynamics that cannot be distinguished by cross-correlation. Moreover, simulation results show that the Lyapunov exponents cannot be used as a definite criterion for the occurrence of chaotic phase synchronization for such a system. Evaluation of the phase function shows its utility in analyzing nonlinear neural systems.

Chronic Response of the Rat Sciatic Nerve to the Flat Interface Nerve Electrode

AbstractThe chronic effects of a reshaping nerve electrode, the flat interface nerve electrode (FINE), on sciatic nerve physiology, histology, and blood–nerve barrier (BNB) are presented. The FINE electrode applies a small force to a nerve to reshape the nerve and fascicles into elongated ovals. This increases the interface between the nerve and electrode for selective stimulation and recording of peripheral nerve activity. The hypothesis of this study is that a small force applied noncircumferentially to a nerve can chronically reshape the nerve without effecting nerve physiology, histology, or the blood–nerve barrier permeability. Three FINE electrode designs were implanted on rat sciatic nerves to examine the nerves response to small, moderate, and high reshaping forces. The chronic reshaping, physiology, and histology of the nerve were examined at 1, 7, and 28 days postimplant. All FINEs significantly reshape both the nerve and the fascicles compared to controls. FINEs that applied high forces caused a neurapraxia type injury characterized by changes in the animals footprint, nerve histology, and the BNB permeability. The physiological changes were greatest at 7 days and fully recover to normal by 14 days postimplant. The moderate force FINE did not result in changes in the footprint or BNB permeability. Only a minor decrease in axon density without accompanying evidence of axon demyelination or regeneration was observe for the moderate force. The small force FINE does not cause any change in nerve physiology, histology, or BNB permeability compared to the sham treatment. An electrode that applies a small force that results in an estimated intrafascicular pressure of less than 30 mm Hg can reshape the nerve without significant changes in the nerve physiology or histology. These results support the conclusion that a small force chronically applied to the nerve reshapes the nerve without injury.

Influence of pulse sequence, polarity and amplitude on magnetic stimulation of human and porcine peripheral nerve

1 Mammalian phrenic nerve, in a trough filled with saline, was excited by magnetic coil (MC)‐induced stimuli at defined stimulation sites, including the negative‐going first spatial derivative of the induced electric field along a straight nerve, at a bend in the nerve, and at a cut nerve ending. At all such sites, the largest amplitude response for a given stimulator output setting was elicited by an induced damped polyphasic pulse consisting of an initial quarter‐cycle hyperpolarization followed by a half‐cycle depolarization compared with a predominantly ‘monophasic’ quarter‐cycle depolarization. 2 Simulation studies demonstrated that the increased efficacy of the induced quarter‐cycle hyperpolarizing‐half‐cycle depolarizing polyphasic pulse was mainly attributed to the greater duration of the outward membrane current phase, resulting in a greater outward charge transfer afforded by the half‐cycle (i.e. quarter‐cycles 2 and 3). The advantage of a fast rising initial quarter‐cycle depolarization was more than offset by the slower rising, but longer duration depolarizing half‐cycle. 3 Simulation further revealed that the quarter‐cycle hyperpolarization‐half‐cycle depolarization showed only a 2.6 % lowering of peak outward current and a 3.5 % lowering of outward charge transfer at threshold, compared with a half‐cycle depolarization alone. Presumably, this slight increase in efficacy reflects modest reversal of Na+ inactivation by the very brief initial hyperpolarization. 4 In vitro, at low bath temperature, the nerve response to an initial quarter‐cycle depolarization declined in amplitude as the second hyperpolarizing phase progressively increased in amplitude and duration. This ‘pull‐down’ phenomenon nearly disappeared as the bath temperature approached 37 °C. Possibly, at the reduced temperature, delay in generation of the action potential permitted the hyperpolarization phase to reduce excitation. 5 Pull‐down was not observed in the thenar muscle responses to median nerve stimulation in a normal human at normal temperature. However, pull‐down emerged when the median nerve was cooled by placing ice over the forearm. 6 In a nerve at subnormal temperature straddled with non‐conducting inhomogeneities, polyphasic pulses of either polarity elicited the largest responses. This was also seen when stimulating distal median nerve at normal temperature. These results imply excitation by hyperpolarizing‐depolarizing pulse sequences at two separate sites. Similarly, polyphasic pulses elicited the largest responses from nerve roots and motor cortex. 7 The pull‐down phenomenon has a possible clinical application in detecting pathologically slowed activation of Na+ channels. The current direction of the polyphasic waveform may become a significant factor with the increasing use of repetitive magnetic stimulators which, for technical reasons, induce a cosine‐shaped half‐cycle, preceded and followed by quarter‐cycles of opposite polarity.

The somatic shunt cable model for neurons

The derivation of the equations for an electrical model of nerve cells is presented. The model consists of an equivalent cylinder, a lumped somatic impedance, and a variable shunt at the soma. This shunt was introduced to take into account the fast voltage decays observed following the injections of current pulses in some motoneurons and hippocampal granule cells that could not be explained by existing models. The shunt can be interpreted either by penetration damage with the electrode or by a lower membrane specific resistance at the soma than in the dendrites. A solution of the model equations is presented that allows the estimation of the electrotonic length L, the membrane time constant tau m, the dendritic dominance ratio rho, and the shunt parameter epsilon, based only on the measurement of the first two coefficients and time constants in the multiexponential voltage response to injected current pulses.