Determination of the Distribution of Conduction Velocities in Human Nerve Trunks

A technique is described which enables the distribution of conduction velocities within the alpha fiber group of an in situ human peripheral nerve trunk to be determined. The technique is based on the analysis of the shape of compound nerve action potentials recorded from surface electrodes and is non-invasive. Velocity distributions calculated for a group of normal adults are presented and represent the first known measurements of this parameter.     

Improved nerve cuff electrode recordings with subthreshold anodiccurrents

A method has been developed for improving the signal amplitudes of the recordings obtained with nerve cuff electrodes. The amplitude of the electroneurogram (ENG) has been shown to increase with increasing distance between the contacts when cuff electrodes are used to record peripheral nerve activity. The effect is directly related to the propagation speed of the action potentials. Computer simulations have shown that the propagation velocity of action potentials in a length of a nerve axon can be decreased by subthreshold extracellular anodic currents. Slowing the action potentials is analogous to increasing the cuff length in that both result in longer intercontact delays, thus, larger signal outputs. This phenomenon is used to increase the amplitudes of whole nerve recordings obtained with a short cuff electrode. Computer simulations predicting the slowing effect of anodic currents as well as the experimental verification of this effect are presented. The increase in the amplitude of compound action potentials (CAPs) is demonstrated experimentally in an in vitro preparation. This method can be used to improve the signal-to-noise ratios when recording from short nerve segments where the cuff length is limited     

The Forward Problem in Electroneurography I: A Generalized Volume Conductor Model

We describe a generalized volume conductor model for the compound action potential (CAP) of a peripheral nerve in situ. The extracellular single fiber action potentials (SFAP's), the constituting elements of the CAP, are expressed in terms of the intracellular action potentials and of the effect of volume conduction using a convolution formulation. The model incorporates variations in the intracellular action potential duration over the fiber population. Volume conduction is described in a generalized formalism for a class of cylinder symmetrical configurations. The CAP is finally formulated as a linear sumation of the SFAP's, with incorporation of the distribution of propagaytion velocities over the fiber population. We show that the final expressions for SFAP's and CAP can be given in a mathematically transparent form, which gives a clear insight into the mechanisms involved in the genesis of different potential waveshapes.     

The single nerve fiber action potential and the filter bank--a modeling approach

Single fiber action potentials (SFAPs) from peripheral nerves, such as recorded with cuff electrodes, can be modelled as the convolution of a source current and a weight function that describes the recording electrodes and the surrounding medium. It is shown that for cuff electrodes, the weight function is linearly scaled with the action potential (AP) velocity and that it is, therefore, possible to implement a model of the recorded SFAPs based on a wavelet multiresolution technique (filterbank), where the wavelet scale is proportional to the AP velocity. The model resulted in single fiber action potentials matching the results from other models with a goodness of fit exceeding 0.99. This formulation of the SFAP may serve as a basis for model-based wavelet analysis and for advanced cuff design.     

Median Nerve Afferent Action Potential Recorded at the Wrist

Median nerve afferent action potentials can be recorded at the wrist in response to a current pulse applied to the index and middle fingers. Latencies of such action potentials have diagnostic value; however, because of difficulties in recording techniques, such latency measurements have not been used widely in clinical environments. A recording technique with very little stimulus artifact is presented.     

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.     

The inverse problem in electroneurography. I. Conceptual basis andmathematical formulation

A mathematical technique for the analysis of the compound action potential (CAP) of a peripheral nerve is presented. The procedure deals with the estimation of the number of active fibers contributing to the CAP and the distribution of their conduction velocities. The CAP is described as a filtered Poisson process, the (time-varying) filter representing the single-fiber action potential waveshapes. The estimation procedure consists of two parts. The first part, related to the fast conducting fibers contributing to the CAP main complex, uses least-squares optimization techniques for the reconstruction of the CAP waveshape. The second part, applying to the small late components of the CAP due to slowly conducting fibres, explicitly uses the Poisson process formulism and is based on reconstructing the energy for variance in the CAP     

Mechanoelectrical feedback in cardiac myocytes fromstretch-activated ion channels

Stretch-activated ion channels (SACS) in cardiac myocytes from neonatal rats were studied in cell-attached patches. Stretch of membrane patches by suction in the recording pipette caused the triggering of action potentials that were recorded as action currents (ACs). The significance of a temporal correlation between SAC open probability and ACs was tested using the Kolmogorov-Smirnov and Poisson distributions. It was shown that the 50-ms epoch immediately preceding the action current has unique kinetics and represented a peak in SAC open probability (p<0.001). Thus it appears that current from a small number of SAC's injects sufficient charge (0.2 pC during 50 ms) to trigger action potentials in myocytes. These data strengthen the hypothesis that passive mechanical stretch of myocardium can be arrhythmogenic     

An Analyzer for Autonomic Nerve Activities in Acute and Chronic Animals

A real-time analyzer for autonomic nerve activity in acute and chronic animals has been developed. This device, using a finite difference method, can separate individual neural spikes from compound nerve action potentials consisting of base-line drift due to bodily movement, 60 Hz power-line interference, and bioelectrical signals such as electromyogram and electrocardiogram, and with poor signal-to-noise ratio recorded in multifiber preparations or whole nerves. Because there is no phase distortion of neural spikes, the precise time interval between the individual neural spikes can be measured and is converted to analog voltage with a rate meter. This device can perform quantitative analyses of compound nerve action potentials in real time, independent of 60 Hz power-line interference, ECG, and base-line drift.     

A method for evaluating the selectivity of electrodes implanted fornerve simulation

The scale of stimulating electrodes possible for use in functional electrical stimulation to restore motor and sensory function is rapidly approaching that of individual neurons. Although the electrodes may approach the dimensions of single nerve cells, it is unclear if the region of excitation elicited by each electrode will be correspondingly small. Previous techniques for evaluating this have either been tedious or have lacked the resolution necessary. This paper describes a method that uses the refractory interaction of the compound action potentials elicited by a stimulus pulse pair, along with high-resolution recording of those potentials, to achieve measurements of the selectivity of stimulation down to the scale of a few axon diameters. The feasibility of this technique is demonstrated in sciatic nerves of frogs (Rana Catesbiana) acutely implanted with a sapphire electrode array.     

Tail Extrapolation in MLSE Receivers Using Nonparametric Channel Model Estimation

This paper presents a method for determining the probability of rare events, in particular for probability density function (pdf) and bit error rate (BER) estimation. The derivation of the method is based on the presumption that the pdf is a member of a family of distributions very often named as the generalized exponential (GE) class of distributions. Based on high reliability estimations obtained in short simulation/measurement times, the low probably events are estimated accurately by extrapolation. The suggested method can be applied to some distributions that are different from GE distributions, such as noncentral chi-square distributions, to extrapolate to low probability events, with some extrapolation error. It can also be applied to BER estimation. The method is in particular helpful for estimating channels suffering from both severe signal distortion causing undesired intersymbol interference (ISI) of several symbols, and from severe noise. Such conditions prevail, for example, in metro and long haul high-speed optical fiber communication systems. So the method may be implemented in particular in maximum-likelihood sequence estimation (MLSE) optical receivers using nonparametric channel model estimation. A special use of the extrapolation method is explained for practical systems using trellis branch metrics derived from the estimated pdf to decode the transmitted sequence of symbols.     

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.     

Evaluating the noise in electrically evoked compound action potential measurements in cochlear implants

Electrically evoked compound action potentials (ECAPs) are widely used to study the excitability of the auditory nerve and stimulation properties in cochlear implant (CI) users. However, ECAP detection can be difficult and very subjective at near-threshold stimulation levels or in spread of excitation measurements. In this study, we evaluated the statistical properties of the background noise (BN) and the postaverage residual noise (RN) in ECAP measurements in order to determine an objective detection criterion. For the estimation of the BN and the RN, a method currently used in auditory brainstem response measurements was applied. The potential benefit of using weighted (Bayesian) averages was also examined. All estimations were performed with a set of approximately 360 ECAP measurements recorded from five human CI users of the CII or HiRes90K device (advanced bionics). Results demonstrated that the BN was normally distributed and the RN decreased according to the square root of the number of averages. No additional benefit was observed by using weighted averaging. The noise was not significantly different either at different stimulation intensities or across recording electrodes along the cochlea. The analysis of the statistical properties of the noise indicated that a signal-to-noise ratio of 1.7 dB as a detection criterion corresponds to a false positive detection rate of 1% with the used measurement setup.     

On the Nature and Elimination of Stimulus Artifact in Nerve Signals Evoked and Recorded Using Surface Electrodes

The electrical stimulus pulse and the surface electrodes commonly used to study compound action potentials of peripheral nerves give rise to an artifact consisting of an initial spike and a longer lasting tail which often interferes with the recorded signal. The artifact has four sources: 1) the voltage gradient between the recording electordes caused by stimulus current flowing through the limb, 2) the common-mode voltage of the limb caused by current escaping through the ground electrode, 3) the capacitive coupling between the stimulating and recording leads, and 4) the high-pass filtering characteristics of the recording amplifier. This paper models these sources and presents several methodological rules for minimizing their effects. Also presented are three computer-based methods for subtracting the residual artifact from contaminated records using estimates of the artifact obtained from: 1) subthreshold stimulation, 2) a second recording site remote from the nerve, or 3) stimulation during the refractory period of the nerve.     

A method to improve the estimation of conduction velocitydistributions over a short segment of nerve

Accurate, noninvasive determination of the distribution of conduction velocities (DCV) among fibers of a peripheral nerve has the potential to improve both clinical diagnoses of pathology and longitudinal studies of the progress of disease or the efficacy of treatments. Current techniques rely on long distances of propagation to increase the amount of temporal dispersion in the compound signals and reduce the relative effect of errors in the forward model. The method described in this paper attempts to reduce errors in DCV estimation through transfer function normalization and, thereby, eliminate the need for long segments of nerve. Compound action potential (CAP) signals are recorded from several, equally spaced electrodes in an array spanning only a 10-cm length of nerve. Relative nerve-to-electrode transfer functions (NETF's) between the nerve and each of the array electrodes are estimated by comparing discrete Fourier transforms of the array signals. NETF's are normalized along the array so that waveform differences can be attributed to the effects of temporal dispersion between recordings, and more accurate DCV estimates can be calculated from the short nerve segment. The method is tested using simulated and real CAP data. DCV estimates are improved for simulated signals. The normalization procedure results in DCV's that qualitatively match those from the literature when used on actual CAP recordings.     

Recording from a Single Motor Unit During Strong Effort

During strong voluntary effort it is rarely possible to identify the action potentials from single motor units. In large muscles the most selective recordings are obtained with bipolar wire electrodes. To elucidate this experimental finding we have calculated the extracellular field around a single muscle fiber from an intracellular muscle action potential. This model showed that the selectivity of a bipolar electrode is high provided: i) the diameter of the recording surfaces is less than half the diameter of the muscle fibers; ii) the center distance between the recording surfaces is of the same order or smaller than the diameter of the muscle fibers, and when iii) the center-line between the recording surfaces is oriented perpendicular to the direction of the muscle fibers.     

Simulation Techniques in Electromyography

A motor unit action potential (MUAP) recorded in clinical electromyography (EMG) is the spatial and temporal summation of the action potentials (AP's) from all muscle fibers in a motor unit (MU). An important determinant of MUAP waveform characteristics is the size of the recording electrode. In this paper, we have described the use of a modified line source model of single muscle fiber action potentials to simulate MUAP's as recorded by single fiber (SF) EMG, concentric needle (CN) EMG, and macro-EMG electrodes. Results indicate that SFEMG recordings from a normal MU contain mainly the AP's of the closest one to three muscle fibers of the MU. The amplitude, area, and duration of the simulated CNEMG MUAP's are determined mainly by the number and size of muscle fibers within a semicircular territory of 0.5, 1.5, and 2.5 mm, respectively, around the tip of the electrode. The amplitude and area of simulated macro-EMG MUAP's increase with the number of muscle fibers in the MU.     

Effects of electrode-to-fiber distance on temporal neural response with electrical stimulation

This paper presents an analysis of the effects of the electrode-to-fiber distance on the temporal response properties of an auditory nerve fiber stimulated by electric current pulses. This analysis was based upon results from a computational model of a mammalian auditory nerve fiber axon having 50 nodes of Ranvier, each consisting of 130 stochastic sodium channels and 50 stochastic potassium channels, making it possible to represent the temporal fluctuations of action potential initiation and conduction. A monopolar stimulus electrode was located above a central (26th) node at electrode-to-fiber distances of 1, 4, and 7 mm, while the recording electrode was located at the 36th node. Action potentials (spikes) were generated by the biophysical model using the Crank-Nicholson method to solve a diffusive partial differential equation. By observing the occurrence times of spikes in response to 2000 cathodic monophasic stimulus pulses, temporal jitter (i.e., the standard deviation of spike times) was calculated and the poststimulus time (PST) histogram was generated as well. Furthermore, by computing the PST histogram for each initiation node as functions of space (node number) and time (PST), it was shown that spike initiation was distributed not only spatially but also temporally for stimulus levels producing firing efficiencies (FEs) near 0.5. However, at levels producing FEs near 0.99, while temporal variations approached zero, the spatial distribution of initiating nodes was comparable to that observed for the FE near 0.5. As temporal fluctuations are important for speech coding in cochlear implants, we conclude that spatial characteristics of the electrode-auditory nerve fiber interface may play a significant role in influencing these stochastic temporal processes.     

A Procedure for Decomposing the Myoelectric Signal Into Its Constituent Action Potentials?Part I: Technique, Theory, and Implementation

A technique has been developed which enables the decomposition (separation) of a myoelectric signal into its constituent motor unit action potential trains. It consists of a multichannel (via one electrode) myoelectric signal recording procedure, a data compression algorithm, a digital filtering algorithm, and a hybrid visual-computer decomposition scheme. The algorithms have been implemented on a PDP 11/34 computer. Of the four major segments of the technique, the decomposition scheme is by far the most involved. The decomposition algorithm uses a-sophisticated template matching routine and details of the firing statistics of the motor units to identify motor unit action potentials in the myoelectric signal, even when they are super-imposed with other motor unit action potentials. In general, the algorithms of the decomposition scheme do not run automatically. They require input from the human operator to maintain reliability and accuracy during a decomposition.