A stochastic model of the electrically stimulated auditory nerve:single-pulse response

Most models of neural response to electrical stimulation, such as the Hodgkin-Huxley equations, are deterministic, despite significant physiological evidence for the existence of stochastic activity. For instance, the range of discharge probabilities measured in response to single electrical pulses cannot be explained at all by deterministic models. Furthermore, there is growing evidence that the stochastic component of auditory nerve response to electrical stimulation may be fundamental to functionally significant physiological and psychophysical phenomena. In this paper we present a simple and computationally efficient stochastic model of single-fiber response to single biphasic electrical pulses, based on a deterministic threshold model of action potential generation. Comparisons with physiological data from cat auditory nerve fibers are made, and it is shown that the stochastic model predicts discharge probabilities measured in response to single biphasic pulses more accurately than does the equivalent deterministic model. In addition, physiological data show an increase in stochastic activity with increasing pulse width of anodic/cathodic biphasic pulses, a phenomenon not present for monophasic stimuli. These and other data from the auditory nerve are then used to develop a population model of the total auditory nerve, where each fiber is described by the single-fiber model.     

利用单电极不对称双向脉冲刺激实现哺乳动物有髓神经纤维选择性兴奋的仿真研究

本研究的目的是要从理论上探讨利用单电极双向脉冲刺激实现哺乳动物神经纤维选择性刺激,(即当刺激一束神经时,不兴奋粗神经而兴奋细神经)的可能性.双向脉冲刺激可以降低刺激脉冲对神经纤维产生的电化学损伤.为研究哺乳动物有髓神经纤维的电特性,建立了一个基于简单的无穷大、各向同性的容积导体模型的仿真系统.利用该仿真系统,采用"不对称但电荷平衡"的双向脉冲刺激,计算了神经纤维的兴奋和阻断阈值与纤维直径、纤维-电极间距离的关系.结果表明:在距电极一定距离内采用该双向脉冲刺激模式确实可以实现哺乳动物有髓神经纤维的选择性兴奋.     

Selective activation of small motor axons by quasitrapezoidalcurrent pulses

We have found a method to activate electrically smaller nerve fibers without activating larger fibers in the same nerve trunk. The method takes advantage of the fact that action potentials are blocked with less membrane hyperpolarization in larger fibers than in smaller fibers. In our nerve stimulation system, quasitrapezoidal-shaped current pulses were delivered through a tripolar cuff electrode to effect differential block by membrane hyperpolarization. The quasitrapezoidal-shaped pulses with a square leading edge, a 350 microsecond(s) plateau, and an exponential trailing phase ensured the block of propagating action potentials and prevented the occurrence of anodal break excitation. The tripolar cuff electrode design restricted current flow inside the cuff and thus eliminated the undesired nerve stimulation due to a "virtual cathode." Experiments were performed on 13 cats. The cuff electrode was placed on the medial gastrocnemius nerve. Both compound and single fiber action potentials were recorded from L7 ventral root filaments. The results demonstrated that larger alpha motor axons could be blocked at lower current levels than smaller alpha motor axons, and that all alpha fibers could be blocked at lower current levels than gamma fibers. A statistical analysis indicated that the blocking threshold was correlated with the axonal conduction velocity or fiber diameter. This method could be used in physiological experiments and neural prostheses to achieve a small-to-large recruitment order in motor or sensory systems.     

Inversion of the current-distance relationship by transientdepolarization

The objective of this research was to develop a technique to excite selectively nerve fibers distant from an electrode without exciting nerve fibers close to the electrode. The shape of the stimulus current waveform was designed based on the nonlinear conductance properties of neuronal sodium channels. Models of mammalian peripheral myelinated axons and experimental measurements on cat sciatic nerve were used to determine the effects of subthreshold polarization on neural excitability and recruitment. Subthreshold membrane depolarization generated a transient decrease in neural excitability and thus an increase in the threshold for stimulation by a subsequent stimulus pulse. The decrease in excitability increased as the duration and amplitude of the subthreshold depolarization were increased, and the increase in threshold was greater for fibers close to the electrode. When a depolarizing stimulus pulse was applied immediately after the subthreshold depolarization, nerve fibers far from the electrode could be stimulated without stimulating fibers close to the electrode. Subthreshold depolarizing prepulses inverted the current-distance relationship and allowed selective stimulation of nerve fibers far from the electrode     

A novel electrode array for diameter-dependent control of axonal excitability: a simulation study

Electrical extracellular stimulation of peripheral nerve activates the large-diameter motor fibers before the small ones, a recruitment order opposite the physiological recruitment of myelinated motor fibers during voluntary muscle contraction. Current methods to solve this problem require a long-duration stimulus pulse which could lead to electrode corrosion and nerve damage. The hypothesis that the excitability of specific diameter fibers can be suppressed by reshaping the profile of extracellular potential along the axon using multiple electrodes is tested using computer simulations in two different volume conductors. Simulations in a homogenous medium with a nine-contact electrode array show that the current excitation threshold (Ith) of large diameter axons (13-17 microm) (0.6-3.0 mA) is higher than that of small-diameter axons (2-7 microm) (0.4-0.7 mA) with 200-microm axon-electrode distance and 10-micros stimulus pulse. The electrode array is also tested in a three-dimensional finite-element model of the sacral root model of dog (ventral root of S3). A single cathode activates large-diameter axons before activating small axons. However, a nine-electrode array activates 50% of small axons while recruiting only 10% of large ones and activates 90% of small axons while recruiting only 50% of large ones. The simulations suggest that the near-physiological recruitment order can be achieved with an electrode array. The diameter selectivity of the electrode array can be controlled by the electrode separation and the method is independent of pulse width.     

Sensory Effects of Transient Electrical Stimulation?Evaluation with a Neuroelectric Model

A model of myelinated nerve axon was used to study the initiation and propagation of action potentials for a variety of extracellular electrical stimuli. Frankenhaeuser-Huxley nonlinearities were incorporated at each of several nodes in a longitudinal array, and the extracellular current pulse was modeled as a spatial distribution of voltage disturbance along the membrane. Results from the model were compared to data from human sensory experiments and from animal electrophysiological experiments. Effects of polarity, electrode position, pulse duration, and biphasic oscillation frequency were examined. Biphasic pulses have higher excitation thresholds than monophasic pulses, provided the duration of a single phase is short relative to the time constant of the membrane depolarization process. The shapes of strength/duration curves from sensory experiments conform well to model predictions for monophasic stimuli. Strength/frequency curves derived from the model are similar to those from sensory stimulation with sinusoidal currents. The shapes of strength/frequency curves can be explained by membrane integration effects at high frequencies and membrane leakage effects at low frequencies. The model predicts lower thresholds for cathodal than for anodal stimulation: the predicted degree of polarity selectivity is confirmed by direct stimulation of axons in animal experiments, but is at variance with the selectivity found in human transcutaneous stimulation.     

Analysis of monophasic and biphasic electrical stimulation of nerve

In an earlier study, biphasic and monphasic electrical stimulation of the auditory nerve was performed in cats with a cochlear implant. Single-unit recordings demonstrated that spikes resulting from monophasic and biphasic stimuli have different thresholds and latencies. Monophasic thresholds are lower and latencies are shorter under cathodic stimulation. Results from stochastic simulations of a biophysical model of electrical stimulation are similar. A simple analysis of a linear, "integrate to threshold" membrane model accounts for the threshold and latency differences observed experimentally and computationally. Since biphasic stimuli are used extensively in functional electrical stimulation, this analysis greatly simplifies the biophysical interpretation of responses to clinically relevant stimuli by relating them to the responses obtained with monophasic stimuli.     

Optimization of Neural Stimuli Based Upon a Variable Threshold Potential

The commonly used assumption of a constant transmembrance potential threshold for nerve has yielded many useful threshold related results. These results include the strength-duration curve for monophasic constant current stimuli and the minimum power waveform of Offner. This paper shows that the constant threshold assumption is not adequate for ranges of pulsewidths where it has seen frequent previous application, and that it is not applicable for the case of biphasic stimulation. Based upon results from the Frankenhaeuser-Huxley model of myelinated nerve, a more accurate form of potential threshold for monophasic stimuli is developed which is shown to extend to ranges of stimulus parameters inadequately modeled by the constant threshold assumption. An extrapolation of this threshold condition to the case of biphasic stimulation is also considered, along with minimum power and damage waveforms derived with use of a nonconstant threshold potential function. A procedure for clinically determining the parameters necessary to evaluate optimal pulsewidths-is also presented.     

Analysis of a Model for Excitation of Myelinated Nerve

Excellent models have been presented in the literature which relate membrane potential to transverse membrane current and which describe the propagation of action potentials along the axon, for both myelinated and nonmyelinated fibers. There is not, however, an adequate model for nerve excitation which allows one to compute the threshold of a nerve fiber for pulses of finite duration using electrodes that are not in direct contact with the fiber. This paper considers this problem and presents a model of the electrical properties of myelinated nerve which describes the time course of events following stimulus application up to the initiation of the action potential. The time-varying current and potential at all nodes can be computed from the model, and the strength-duration curve can be determined for arbitrary electrode geometries, although only the case of a monopolar electrode is considered in this paper. It is shown that even when the stimulus is a constant-current pulse, the membrane current at the nodes varies considerably with time. The strength-duration curve calculated from the model is consistent with previously published experimental data, and the model provides a quantitative relationship between threshold and fiber diameter which shows there is less selectivity among fibers of large diameter than those of small diameter.     

Selective stimulation of smaller fibers in a compound nerve trunkwith single cathode by rectangular current pulses

Electrical stimulation of unmyelinated nerve fibers is analyzed, using point sources in a simple volume conductor model and a dynamic Hodgkin-Huxley model of nerve fiber. The excitation and blocking threshold of single cathode stimulation with an indifference anode at infinity are calculated by solving difference equations with axons of different diameters. The relation between the blocking threshold and the pulsewidth of single cathode stimulation is also calculated. The results suggest a method of selectively stimulating the smaller fibers in a compound nerve trunk. Two kinds of stimulation electrodes are designed to test this method. Both of them are proven to yield results in accordance with the authors' model by the animal experiments on a toad's sciatic nerve trunk. It is possible to excite the smaller fibers without exciting the larger ones in a compound nerve trunk by properly controlling the stimulus intensity. The method is likely to be used in both physiological experiments and neural prostheses     

Effects of regional stimulation using a miniature stimulatorimplanted in feline posterior biceps femoris

The effects of placement of a miniature implantable stimulator on motor unit recruitment were examined in the posterior head of cat biceps femoris. The implantable stimulator (13-mm long×2-mm diameter) was injected either proximally near the main nerve branch, or distally near the muscle insertion, through a 12-gauge hypodermic needle. Glycogen-depletion methods were used to map the distribution of fibers activated by electrical stimulation. Muscle fibers were found to be depleted at most or all proximodistal levels of the muscle, but the density of depleted fibers varied transversely according to the stimulus strength and proximity of the device to the nerve-entry site. Thus, muscle cross sections often had a “patchy” appearance produced because different proportions of depleted fibers intermingled with undepleted fibers in different parts of the cross section. In other preparations, the force of muscle contraction was measured when stimuli of varying strengths were delivered by the stimulator positioned at the same proximal or distal sites within the muscle. Devices placed close to the nerve-entry site produced the greatest forces. Those placed more distally produced less force. As stimulus current and/or pulse width increased, muscle force increased, often in steps, until a maximum was reached, which was usually limited by the compliance voltage of the device to less than the force produced by whole nerve stimulation     

Long-term intramuscular electrical activation of the phrenic nerve:efficacy as a ventilatory prosthesis

The efficacy of a system for long-term intramuscular activation of the phrenic nerve as a ventilatory prosthesis was evaluated in seven dogs. Five dogs underwent chronic bilateral intramuscular diaphragm stimulation (IDS) for 61 to 183 days at stimulus parameters selected to evoke at least 120% of the animal's basal ventilation. Two dogs maintained as controls did not undergo chronic stimulation. The ability of IDS to provide long-term ventilation without diaphragm fatigue was evaluated in terms of the ventilatory capacity of IDS, the effects of chronic IDS on diaphragm contractile properties, and the phrenic nerve recruitment properties of chronic IDS electrodes. Hemi-diaphragms with electrodes placed within 2 cm of the phrenic nerve trunk could be completely activated by 25 mA pulses having a 100 μs pulse width. The tidal volume evoked by IDS in this study was 167% (±48 s.d.) of that required for full-time basal ventilation without diaphragm fatigue. Evoked tidal volume increased after 8 to 9 weeks of chronic IDS for stimulus pulse intervals longer than 50 ms. Electrode recruitment properties were stable for both active and passive implanted electrodes. It is concluded from these studies that with properly placed electrodes IDS is capable of providing reliable full-time ventilatory support without fatiguing the diaphragm     

The effect of stimulus pulse duration on selectivity of neuralstimulation

Choice of stimulus parameters is an important consideration in the design of neural prosthetic systems. The objective of this study was to determine the effect of rectangular stimulus pulsewidth (PW) on the selectivity of peripheral nerve stimulation. Computer simulations using a cable model of a mammalian myelinated nerve fiber indicated that shorter PW's increased the difference between the threshold currents of fibers lying at different distances from an electrode. Experimental measurements of joint torque generated by peripheral nerve stimulation demonstrated that shorter PW's generated larger torques before spillover and created a larger dynamic range of currents between threshold and spillover. Thus, shorter PW's allowed more spatially selective stimulation of nerve fibers. Analysis of the response of a passive cable model to different duration stimuli indicated that PW dependent contributions of distributed sources to membrane polarization accounted for the observed differences in selectivity     

A Technique for Collision Block of Peripheral Nerve: Frequency Dependence

A previously reported stimulation technique which elicits a unidirectionally propagated nerve action potential has been evaluated with repetition rates from 10 to 100 Hiz. Block of propagation in one direction from the stimulus site was sustained up to 50 Hz with monophasic stimulation and 30 Hz with biphasic stimulation. The use of long stimulating pulses produces pronounced degradation of the block at high frequencies.     

Tissue damage by pulsed electrical stimulation

Repeated pulsed electrical stimulation is used in a multitude of neural interfaces; damage resulting from such stimulation was studied as a function of pulse duration, electrode size, and number of pulses using a fluorescent assay on chick chorioallontoic membrane (CAM) in vivo and chick retina in vitro. Data from the chick model were verified by repeating some measurements on porcine retina in-vitro. The electrode size varied from 100 microm to 1 mm, pulse duration from 6 micros to 6 ms, and the number of pulses from 1 to 7500. The threshold current density for damage was independent of electrode size for diameters greater than 300 microm, and scaled as 1/r2 for electrodes smaller than 200 microm. Damage threshold decreased with the number of pulses, dropping by a factor of 14 on the CAM and 7 on the retina as the number of pulses increased from 1 to 50, and remained constant for a higher numbers of pulses. The damage threshold current density on large electrodes scaled with pulse duration as approximately 1/t0.5, characteristic of electroporation. The threshold current density for repeated exposure on the retina varied between 0.061 A/cm2 at 6 ms to 1.3 A/cm2 at 6 micros. The highest ratio of the damage threshold to the stimulation threshold in retinal ganglion cells occurred at pulse durations near chronaxie-around 1.3 ms.     

Modeling the effects of electric fields on nerve fibers: influenceof tissue electrical properties

The effects of anisotropy and inhomogeneity of the electrical conductivity of extracellular tissue on excitation of nerve fibers by an extracellular point source electrode were determined by computer simulation. Analytical solutions to Poison's equation were used to calculate potentials in anisotropic infinite homogeneous media and isotropic semi-infinite inhomogeneous media, and the net driving function was used to calculate excitation thresholds for nerve fibers. The slope and intercept of the current-distance curve in anisotropic media were power functions of the ratio and product of the orthogonal conductivities, respectively. Excitation thresholds in anisotropic media were also dependent on the orientation of the fibers, and in strongly anisotropic media (sigma z/sigma xy > 4) there were reversals in the recruitment order between different diameter fibers and between fibers at different distances from the electrode. In source-free regions of inhomogeneous media (two regions of differing conductivity separated by a plane boundary), the current-distance relationship of fibers parallel to the interface was dependent only on the average conductivity, whereas in regions containing the source the current-distance relationship was dependent on the individual values of conductivity. Reversals in recruitment order between fibers at different distances from the electrode and between fibers of differing diameter were found in inhomogeneous media. The results of this simulation study demonstrate that the electrical properties of the extracellular medium can have a strong influence on the pattern of neuronal excitation generated by extracellular electric fields, and indicate the importance of tissue electrical properties in interpreting results of studies employing electrical stimulation applied in complex biological volume conductors.     

Proposal of a new method for narrowing and moving the stimulated region of cochlear implants: animal experiment and numerical analysis

We have proposed the tripolar electrode stimulation method (TESM) for narrowing the stimulation region and continuously moving the stimulation site for cochlear implants. The TESM stimulates the auditory nerve array using three adjacent electrodes which are selected among the electrodes of an electrode array within the lymphatic fluid. Current is emitted from each of the two lateral electrodes and received by the central electrode. The current received by the central electrode is made equal to the sum of the currents emitted from the lateral electrodes. In this paper, we evaluate whether or not TESM works according to a theory which is based on numerical analysis using an electrical equivalent circuit model of the auditory nerve fibers. In this simulation, the sums of the excited model fibers are compared to the compound action potentials (CAP's) which we obtained through animal experiments. To identify the main parameter while maintaining the amplitude of the CAP (the sum of the fired fibers), we assumed the presence of some parameters from the radial current density profile. In the case of the width value among the parameters being kept constant, the amplitude of the CAP was almost constant; thus, the number of the fired fibers was also almost constant. The width value equals the distance between the points at which the profile of the radial current density of the electrode array and the line of the radial threshold current density of the electrode array intersect. It is possible to determine the measure of the stimulation region or site by controlling the width value and the ratios of the currents emitted from the lateral electrodes. As a result, we succeeded in narrowing the stimulation region by controlling the sum of the currents emitted from the two lateral electrodes. Also we succeeded in continuously moving the stimulation site by modifying the currents emitted from the two lateral electrodes.     

A four-channel IBM PC/AT compatible biphasic pulse generator fornerve stimulation

An IBM PC/AT compatible four-channel biphasic pulse generator has been developed to assist in functional electrical stimulation (FES) related research. Each channel uses a bipolar 12-bit digital-to-analog converter (DAC) to generate biphasic voltage pulses between +/- 5 VDC and three 16-bit timers to control first, second, and interphase durations. Two vectored interrupt generators are available for precise pulse timing control. Potential uses of this device include FES research, the characterization of the recruitment properties of percutaneous electrodes in multichannel stimulation systems, or as a subassembly in commercial medical devices requiring electrical simulation in an IBM PC/AT platform.     

Different pulse shapes to obtain small fiber selective activation by anodal blocking--a simulation study

The aim of this study was to investigate whether it is possible to reduce a charge per pulse, which is needed for selective nerve stimulation. Simulation is performed using a two-part simulation model: a volume conductor model to calculate the electrical potential distribution inside a tripolar cuff electrode and a human fiber model to simulate the fiber response to simulation. Selective stimulation is obtained by anodal block. To obtain anodal block of large fibers, long square pulses (> 350 micros) with a relatively high currents (1-2.5 mA) are usually required. These pulses might not be safe for a long-term application because of a high charge per pulse. In this study, several pulse shapes are proposed that have less charge per pulse compared with the conventional square pulse and would therefore be safer in a chronic application. Compared with the conventional square pulse, it was possible to reduce the charge with all proposed pulse shapes, but the best results are obtained with a combination of a square depolarizing pulse and a blocking pulse. The charge per pulse was up to 32% less with that pulse shape than with a square pulse. Using a hyperpolarizing anodal prepulse preceding a square pulse, it was not possible to block nerve fibers in a whole nerve bundle and to obtain reduction of a charge per phase. Reduction of the charge could be achieved only with spatially selective blocking. The charge per phase was larger for the combination of a hyperpolarizing anodal prepulse and a two-step pulse than for the two-step pulse alone.