Far-field potentials generated by action potentials of isolated frog sciatic nerves in a spherical volume

Single neuron contributions to the auditory brainstem EEG

The auditory brainstem response (ABR) is an acoustically evoked EEG potential that is an important diagnostic tool for hearing loss, especially in newborns. The ABR originates from the response sequence of auditory brainstem nuclei, and a click-evoked ABR typically shows three positive peaks ('waves') within the first six milliseconds. However, an assignment of the waves of the ABR to specific sources is difficult, and a quantification of contributions to the ABR waves is not available. Here, we exploit the large size and physical separation of the barn owl first-order cochlear nucleus magnocellularis (NM) to estimate single-cell contributions to the ABR. We simultaneously recorded NM neurons' spikes and the EEG, and found that > 5,000 spontaneous single-cell spikes are necessary to isolate a significant spike-triggered average response at the EEG electrode. An average single-neuron contribution to the ABR was predicted by convolving the spike-triggered average with the cell's peri-stimulus time histogram. Amplitudes of predicted contributions of single NM cells typically reached 32.9 nV (mean, range: 2.5 - 162.7 nV), or 0.07% (median, range: 0.01 - 4.0%) of the ABR amplitude. The time of the predicted peak coincided best with the peak of the ABR wave II, and this coincidence was independent of the click sound level. Our results suggest that wave II of the ABR is shaped by a small fraction of NM units.

Correlates of a single cortical action potential in the epidural EEG

To identify the correlates of a single cortical action potential in surface EEG, we recorded simultaneously epidural EEG and single-unit activity in the primary somatosensory cortex of awake macaque monkeys. By averaging over EEG segments coincident with more than hundred thousand single spikes, we found short-lived (≈ 0.5 ms) triphasic EEG deflections dominated by high-frequency components > 800 Hz. The peak-to-peak amplitude of the grand-averaged spike correlate was 80 nV, which matched theoretical predictions, while single-neuron amplitudes ranged from 12 to 966 nV. Combining these estimates with post-stimulus-time histograms of single-unit responses to median-nerve stimulation allowed us to predict the shape of the evoked epidural EEG response and to estimate the number of contributing neurons. These findings establish spiking activity of cortical neurons as a primary building block of high-frequency epidural EEG, which thus can serve as a quantitative macroscopic marker of neuronal spikes.

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Cortical spikes are coincident with short-lived (~ 0.5 ms) EEG deflections.

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Cortical spikes produce ~  80 nV epidural EEG deflections at a distance of ~ 5 mm.

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EEG potentials due to spikes are dominated by high-frequency (> 800 Hz) components.

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High-frequency (> 800 Hz) EEG is a genuine macroscopic marker of spiking activity.

The origin of the premotor potential recorded from the second lumbrical muscle in normal man

OBJECTIVE

When recording with a palm electrode, a premotor potential precedes the compound muscle action potential (CMAP), evoked from the second lumbrical (2L) muscle following median nerve stimulation. The purpose of this study was to determine the origin of the premotor potential from the 2L.

METHODS

We recorded potentials with multi-channel electrodes in the palm and finger in a bipolar or referential manner, stimulating the second digit or median nerve at the wrist.

RESULTS

We recorded the traveling nearfield sensory nerve action potential (SNAP) and stationary negative potential in the palm. The peak latency of the stationary negative potential was the same as the one of the near-field potential of the digital sensory fibers at the base of the second finger. The onset of the premotor potential from the 2L muscle is aligned to the palmar SNAP in a bipolar manner by antidromic stimulation.

CONCLUSIONS

We conclude that the premotor potential from the 2L muscle is composed of a SNAP arising from antidromically activated palm sensory branches and a far-field potential generated by the median digital nerve fibers as they pass from the palm into the second finger.

SIGNIFICANCE

Our results might be useful for evaluating the 2L-interossei test for diagnosing carpal tunnel syndrome.

Nonlinear interactions of high-frequency oscillations in the human somatosensory system

OBJECTIVE

The source of somatosensory evoked high-frequency activity at about 600 Hz is still not completely clear. Hence, we aimed to study the influence of double stimulation on the human somatosensory system by analyzing both the low-frequency activity and the high-frequency oscillations (HFOs) at about 600 Hz.

METHODS

We used median nerve stimulation at seven interstimuli intervals (ISIs) with a high time resolution between 2.4 and 4.8 ms to investigate the N15, N20 and superimposed HFOs. Simultaneously, the electroencephalogram and the magnetoencephalogram of 12 healthy participants were recorded. Subsequently, the source analysis of precortical and cortical dipoles was performed.

RESULTS

The difference computations of precortical dipole activation curves showed in both the low- and high-frequency range a correlation between the ISI and the latency of the second stimulus response. The cortical low-frequency response showed a similar behavior. Contrarily, in the second response of cortical HFOs this latency shift could not be confirmed. We found amplitude fluctuations that were dependent on the ISI in the low-frequency activity and the HFOs. These nonlinear interactions occurred at ISIs, which differ by one full HFO period (1.6 ms).

CONCLUSIONS

Low-frequency activity and HFOs originate from different generators. Precortical and cortical HFOs are independently generated. The amplitude fluctuations dependent on ISI indicate nonlinear interference between successive stimuli.

SIGNIFICANCE

Information processing in human somatosensory system includes nonlinearity.

Human sensory-evoked responses differ coincident with either "fusion-memory" or "flash-memory", as shown by stimulus repetition-rate effects

BACKGROUND

A new method has been used to obtain human sensory evoked-responses whose time-domain waveforms have been undetectable by previous methods. These newly discovered evoked-responses have durations that exceed the time between the stimuli in a continuous stream, thus causing an overlap which, up to now, has prevented their detection. We have named them "A-waves", and added a prefix to show the sensory system from which the responses were obtained (visA-waves, audA-waves, somA-waves).

RESULTS

When A-waves were studied as a function of stimulus repetition-rate, it was found that there were systematic differences in waveshape at repetition-rates above and below the psychophysical region in which the sensation of individual stimuli fuse into a continuity. The fusion phenomena is sometimes measured by a "Critical Fusion Frequency", but for this research we can only identify a frequency-region [which we call the STZ (Sensation-Transition Zone)]. Thus, the A-waves above the STZ differed from those below the STZ, as did the sensations. Study of the psychophysical differences in auditory and visual stimuli, as shown in this paper, suggest that different stimulus features are detected, and remembered, at stimulation rates above and below STZ.

CONCLUSION

The results motivate us to speculate that: 1) Stimulus repetition-rates above the STZ generate waveforms which underlie "fusion-memory" whereas rates below the STZ show neuronal processing in which "flash-memory" occurs. 2) These two memories differ in both duration and mechanism, though they may occur in the same cell groups. 3) The differences in neuronal processing may be related to "figure" and "ground" differentiation. We conclude that A-waves provide a novel measure of neural processes that can be detected on the human scalp, and speculate that they may extend clinical applications of evoked response recordings. If A-waves also occur in animals, it is likely that A-waves will provide new methods for comparison of activity of neuronal populations and single cells.

Classification of the extracellular fields produced by activated neural structures

BACKGROUND

Classifying the types of extracellular potentials recorded when neural structures are activated is an important component in understanding nerve pathophysiology. Varying definitions and approaches to understanding the factors that influence the potentials recorded during neural activity have made this issue complex.

METHODS

In this article, many of the factors which influence the distribution of electric potential produced by a traveling action potential are discussed from a theoretical standpoint with illustrative simulations.

RESULTS

For an axon of arbitrary shape, it is shown that a quadrupolar potential is generated by action potentials traveling along a straight axon. However, a dipole moment is generated at any point where an axon bends or its diameter changes. Next, it is shown how asymmetric disturbances in the conductivity of the medium surrounding an axon produce dipolar potentials, even during propagation along a straight axon. Next, by studying the electric fields generated by a dipole source in an insulating cylinder, it is shown that in finite volume conductors, the extracellular potentials can be very different from those in infinite volume conductors. Finally, the effects of impulses propagating along axons with inhomogeneous cable properties are analyzed.

CONCLUSION

Because of the well-defined factors affecting extracellular potentials, the vague terms far-field and near-field potentials should be abandoned in favor of more accurate descriptions of the potentials.

Different origins of low- and high-frequency components (600 Hz) of human somatosensory evoked potentials

OBJECTIVE

Human median nerve somatosensory evoked potentials (SEPs) contain a low-amplitude (<500 nV) high-frequency (approximately 600 Hz) burst of repetitive wavelets (HFOs) which are superimposed onto the primary cortical response 'N20.' This study aimed to further clarify the cortical and subcortical structures involved in the generation of the HFOs.

METHODS

128-Channel recordings were obtained to right median nerve stimulation of 10 right-handed healthy human subjects and in 7 of them additional to right ulnar nerve. Data were evaluated by applying principal component analysis and dipole source analysis.

RESULTS

Different source evaluation strategies provided converging evidence for a cortical HFO origin, with two different almost orthogonally oriented generators being active in parallel, but with a phase shift of a quarter of their oscillatory period, while the low-frequency 'N20' is adequately modeled by one tangential dipole source. Median and ulnar derived low-frequency and HFO cortical sources show a somatotopic order. Additionally, generation of the HFOs was localized in subcortical, near-thalamic and subthalamic source sites. The near-thalamic dipole was located at significantly different sites in HFO and low-frequency data.

CONCLUSIONS

The cortical HFO source constellation points to a 'precortical' source in terminals of thalamocortical fibers and a second intracortical HFO origin. Furthermore, HFOs are also generated at subcortical and even subthalamic sites. Near-thalamic, the HFO and low-frequency signals are generated or modulated by different neuron populations involved in the thalamocortical outflow.

Origin of the binaural interaction component in wave P4 of the short-latency auditory evoked potentials in the cat: evaluation of serial depth recordings from the brainstem

There is no general agreement on the origin of the binaural interaction (BI) component in auditory brainstem responses (ABRs). To study this issue the ABRs to monaural and binaural clicks with various interaural time differences (ITDs) were simultaneously recorded from the vertex and from a recording electrode aiming at the superior olive (SO) in cats. Electrode path was along the fibers of the lateral lemniscus (LL). Binaural difference potentials (BDPs), which were computed by subtracting the sum of the two monaural responses from the binaural response, were obtained at systematic depths and across a range of ITD values. It was observed that only a specific BDP deflection recorded at the level at which lemniscal fibers terminate in the nuclei of LL coincided in time with the most prominent BDP in the cat's vertex-recorded ABRs, the BDP in their wave P4. As ITD was increased, the latency shifts and amplitude decrements of the scalp-recorded far-field BDP wave exactly followed those recorded at this lemniscal near-field BDP locus. The data support our hypothesis that the BI component in wave P4 results from a binaural reduction in dischargings of axons ascending in the LL, with this reduction due to contralateral inhibition of the discharge activity of the inhibitory-excitatory units in the lateral nucleus of the SO. Furthermore, at the level of the SO, the BDP in the responses to contra-leading binaural clicks always had larger magnitudes than those evoked by ipsi-leading ones. This bilateral asymmetry is consistent with the view that the BDP in scalp-recorded ABRs is related to the function of sound lateralization.

Short latency visual evoked potentials in occupational exposure to organic solvents

OBJECTIVES

Short latency visual evoked potentials (SVEP), in response to high-intensity flashes from light emitting diodes (LED), were used to detect subclinical effects along the visual pathway in four groups of subjects with different levels of exposure to gasoline, all within legally acceptable limits.

METHODS

Potentials and exposure levels were obtained from 31 subjects with different occupational exposure levels to gasoline fumes, as well as from 17 non-exposed control subjects. SVEP were recorded from four electrode sites (infra-orbital, Cz, Pz, Oz), in response to flashes presented to each eye in turn from goggle-mounted LEDs. SVEP components were defined after digital filtering, which eliminated the high-frequency oscillatory potentials and accentuated five major components: a periocular P30, attributed to the retina; a fronto-central N50, attributed to the optic nerve; centro-parietal P65 and N85, attributed to the optic tracts and radiation; and an occipital, cortical P105.

RESULTS

The latencies of successive SVEP components of the exposed subjects showed a significant latency prolongation compared to controls, beginning with activity attributed to the optic nerve and increasing cumulatively with the later components. Retinal components were not affected by the exposure to organic solvents. Among the exposed groups, differences in latency prolongation corresponded to occupational exposure.

CONCLUSION

The low-frequency components of SVEP were reliably measured and proved to be sensitive to subclinical effects of organic solvents on conduction along the visual pathway. These components are likely to be sensitive to other subcortical visual pathway lesions, but their clinical promise needs further verification.

Refractory properties of auditory brain-stem responses evoked by electrical stimulation of human cochlear nucleus: evidence of neural generators

In this study of electrically-evoked auditory brain-stem responses (EABRs) elicited by cochlear nucleus stimulation, 3 waves were identified after the initial wave that is directly initiated by the electric stimulus. Varying the rate of periodic stimulation or the interval between pairs of stimuli revealed that the shorter the latency of a wave, the faster it recovered from activation (i.e. shorter refractory period). The slow recovery of the third wave and an accompanying contribution to the second wave could be accounted for by postsynaptic generation in the two medial superior olivary nuclei (MSO); the faster recovery of another contribution to the second wave by generation in an axonal tract bending around the contralateral MSO; and the fastest recovery of the first wave by another axonal pathway having larger axons. Comparison with the relative latencies and spatial distribution of an acoustically-evoked auditory brain-stem response (AABR) indicated that the third wave corresponds to wave V, the second to wave IV (called IVb), and the first to a wave that precedes wave IV (called IVa). The anatomical interpretations for the two later waves of the EABR are consistent with most of the extant data on the neural generators of AABR waves IV and V. Thus, the present data and analysis strengthen the identification of the electrically evoked responses as EABRs and provide a firmer foundation for intra-operative EABR monitoring to assist auditory brain-stem implant placement.

High-frequency (600 Hz) SEP activities originating in the subcortical and cortical human somatosensory system

Digitally high-pass filtered median nerve SEP show an oscillatory burst of low-amplitude high-frequency (600 Hz) wavelets superimposed on the N20 component which itself is generated by excitatory postsynaptic potentials of area 3b pyramidal cells. Prior studies using magnetoencephalography (MEG) localized one wavelet generator close to the primary somatosensory hand cortex. Since MEG recordings are biased towards tangentially oriented and superficial generators, a dipole source analysis of 32-channel electric SEP recordings was employed here to test for the possibility of deep and/or radially oriented burst generators: in 10 normal subjects low noise (16,000 averages) median nerve SEP were evaluated using dipole source analysis before and after applying a digital 475 Hz high-pass filter. Two main oscillatory 600 Hz burst sources were modeled; (i) a deep burst source close to the thalamus, most active in a time window between the brain-stem P14 and the cortical N20 sources, detectable in 7 of 10 subjects; most probably, this activity originates from deep axon segments of thalamocortical fibers; and (ii) a subsequent burst source timed around the N20 and located in the vicinity of the primary somatosensory hand cortex in all subjects, which was already known from MEG data. This superficial oscillatory source may be dominated by repetitive activity conducted in the terminal segments of the thalamocortical projection fibers initiated by the thalamic burst generator.

Generation of far field potentials from the trigeminal nerve in the cat

This study provides evidence that far field potentials (FFPs) are generated from the trigeminal nerve in the cat. By stimulating the main mental nerve, three components (component 1, 0.59 +/- 0.06 ms; component 2, 0.81 +/- 0.06 ms; and component 3, 0.98 +/- 0.07 ms) were identified from surface electrodes. These three components were thought to be positive and negative FFPs because each component had a stationary peak and was distributed on the head being divided into positive and negative fields. Results of a study of lesions and recording compound action potentials (CAPs) defined the neural origins of those potentials as follows: component 1, the mandibular nerve at the mandibular foramen; component 2, the mandibular nerve at the foramen ovale; and component 3, somewhere between the gasserian ganglion and the trigeminal root. The amplitude of component 2 decreased when the mandibular nerve at the foramen ovale was immersed in cerebrospinal fluid (CSF) after opening the foramen and recovered to the prior level after closing the foramen with beeswax. We concluded that this transformation resulted in the change in electrical resistance of the volume conductor around the nerve.

Near- and far-fields: source characteristics and the conducting medium in neurophysiology

It is possible to appreciate the production of far-field potentials by considering constant current dipolar source voltage distributions in bounded volumes, especially when they are stretched in one direction, e.g., a cylinder. An essentially nondeclining voltage is detected when the recording electrodes are on opposite sides of, and relatively far from, the dipolar source. This voltage maintains its (a) latency, (b) amplitude, (c) morphology, and (d) polarity even if recordings are performed a whole body length away. These four criteria define far-field potentials. A propagating action potential (AP) can be conceptualized as a linear quadrupole or the summation of two dipoles "back-to-back" (+ - - +). The far-field components of the summated dipoles cancel resulting in the anticipated triphasic waveform for APs with only near-field characteristics, not meeting the first three criteria above. Far-field potentials can be transiently generated when any propagating AP constitutes a net "real" or "virtual" dipolar source. "Real" dipolar sources can occur if an AP encounters the termination of excitable tissue, an alteration in conduction velocity, curvature in excitable tissue resulting in a change in propagation direction, or an abrupt change in resistance of the excitable tissue. Virtual dipolar sources may be produced if an AP encounters a change in the size or shape of the extracellular medium or a transition in extracellular conductivity.

Interaural delay-dependent changes in the binaural difference potential in cat auditory brainstem response: implications about the origin of the binaural interaction component

Auditory brainstem responses (ABRs) evoked by dichotic clicks with 12 different interaural delays (ITDs) between 0 and 1500 microsecond(s) were recorded from the vertices of 10 cats under ketamine anesthesia. The so-called binaural difference potential (BDP), considered to be an indicator of binaural interaction (BI), was computed by subtracting the sum of the two monaural responses from the binaural one. The earliest and most prominent component of BDP was a negative deflection (DN1) at a latency between 4 and 4.8 ms. Like all the other components of BDP, DNI was also due to binaural reduction rather than enhancement of the corresponding ABR wave, P4 in this case. Furthermore, the way its latency increased as a function of ITD was also not compatible with what would be predicted by the delay-line coincidence detector models based on the excitatory-excitatory units in the medial superior olive (MSO). We therefore proposed an alternative hypothesis for the origin of this BI component based on the inhibitory-excitatory (IE) units in the lateral superior olive (LSO). The computational model designed closely simulated the ITD-dependent attenuation and latency shifts observed in DN1. It was therefore concluded that the origin of this BI component in the cat's vertex-ABR could be the lateral lemniscal output of the LSO, although the delay lines which have been shown to exist also in the mammalian brain may play an important role in encoding ITDs.

Generator sources for the early and late ulnar hypothenar premotor potentials: short segment electrophysiologic studies and cadaveric dissection

OBJECTIVE

Determine the generator sources for the ulnar hypothenar premotor potentials (PMPs).

DESIGN

Observational.

SETTING

EMG laboratory.

SUBJECTS

Ten asymptomatic adult volunteers, three cadaver hands.

MAIN OUTCOME MEASURE

Far-field versus near-field characteristics of recorded PMPs as determined by bipolar and referential recording electrode montages. A possible anatomic basis for any observed differences between ulnar PMPs and previously studied median PMPs were explored through cadaveric dissection.

RESULTS

An early PMP (E-PMP) had a latency that varied with changes in the position of G1 only. A late PMP (L-PMP was seen only when G1 and G2 were on different volumes (palm vs fifth digit, or second digit vs fifth digit); its latency did not vary significantly with changes in the position of G1 and G2.

CONCLUSIONS

(1) E-PMP is a near-field potential generated by the ulnar nerve passing near the G1 electrode. (2) L-PMP represents a far-field potential generated by the ulnar digital nerves as they traverse from the hand volume containing G1 to the finger volume containing G2. (3) Greater L-PMP-to-CMAP separation in the median than in the ulnar nerve was explained by cadaveric dissection, which revealed that the motor branch (responsible for the trailing CMAP) is longer in the median nerve than in the ulnar nerve relative to each nerve's corresponding digital sensory branch (responsible for the preceding L-PMP). (4) The PMP that is typically recorded with G1 at the hypothenar motor point and G2 on the fifth digit most likely represents E-PMP. (5) Any proposed diagnostic use of the ulnar PMPs must take into consideration these generator sources.

Short latency visual evoked potentials to flashes from light-emitting diodes

Short latency visual evoked potentials (SVEPs) have been described in response to high-intensity, strobe flashes. High-intensity flashes can now be generated from goggle-mounted light emitting diodes (LEDs) and the SVEPs to such flashes have been shown to be reproducible across subjects, avoiding photic spread to the examination room and acoustical artifacts from the strobe stimulator. In this study, SVEPs from multichannel records are described in terms of normative latencies and amplitudes, as well as scalp distributions, to explore their generators. Potentials were recorded from 10 young male subjects, from 16 scalp locations, in response to flashes from goggle-mounted LEDs. Flashes were presented to each eye in turn, as well as binocularly. The latencies, scalp distributions and intersubject variabilities of the LED evoked SVEPs were similar to those obtained with strobe flashes. SVEP components were divided into 3 groups, according to their latency and the electrodes at which they were recorded with the largest amplitudes: periocular (under 40 msec latency), fronto-central (40-55 msec) and parieto-occipital (55-80 msec latency). The scalp distributions observed in this study suggest subcortical generators along the visual pathway, beginning at the retina. The use of goggle-mounted LEDs should promote routine evaluation of the integrity of the visual pathway between retina and cortex using SVEPs.

Generators of the early and late median thenar premotor potentials

The generator sources of the median thenar premotor potentials (PMPs) have remained elusive despite debate in the literature. By studying the median nerve in the hand with a variety of bipolar and referential recording montages, we systematically examined the possible near-field and far-field sources that may determine these potentials. The results suggest that the early PMP is a near-field potential recorded by G1 and generated by the median nerve traversing the distal carpal tunnel. The late PMP represents a far-field potential generated by the median digital nerve fibers as they pass from the palm volume into the thumb volume. Characteristics of the late PMP are explained using the leading/trailing dipole (L/TD) model of far-field potential generation. The diagnostic utility of these PMPs is questionable, since they are recorded from "regions" along the nerve rather than from more clearly defined sites.

The origin of the human auditory brain-stem response wave II

Auditory brain-stem responses (ABRs) were recorded from human subjects undergoing neurosurgical procedures which exposed the auditory nerve. Scalp recordings indicated that the latency of the negativity between waves I and II (In) and the latency of positive peak II (IIp) were shorter when the nerve was suspended in air than when the nerve was submerged in cerebrospinal fluid or saline, while earlier and later waves remained unaffected. These results could not be attributed to changes in stimulus or recording parameters or conduction velocity. Computational and somatosensory experimental evidence of stationary potentials generated by physical properties of the volume conductor, including changes in conductivity or geometry, are presented to develop a model of wave IIp generation. The results of this study suggest that wave IIp (and probably In) are manifestations of current flux asymmetries across conductivity boundaries created by the temporal bone-cerebrospinal fluid intradural space-brain-stem interfaces. The current flux asymmetries are generated as the propagating auditory nerve action potential crosses the conductivity boundaries. These results also indicate that the physical characteristics of the volume conductor and neural pathways must be considered when interpreting surface recorded evoked potentials.

Short latency median nerve somatosensory evoked potential (SEP): increase in stimulation frequency from 3 to 30 Hz

Somatosensory evoked potentials were obtained by electrical stimulation of the median nerve in 10 normal subjects at 3 and 30 Hz. At the higher rate of stimulation, a reduction was observed in amplitudes and prolongation of latencies of the N9, N/P13 and N20 components as well as increase of the interpeak latency N9-N/P13. A significant increase between the onsets of the N11 and N20 components was also seen; however, no significant increase of the N/P13-N20 interpeak latency was observed. Analysis suggested that an important reason for this last finding was related to the fact that in some cases different fast frequency components (FFC) determined the N20 peak in the different situations. It was further observed that, in those cases in which at least 3 peaks in the fast frequency components were detected (7/10), a significantly different increase in latency between the first and the third peaks was noted. A possible thalamo-cortical generation of the FFC is discussed.

A fast method to compute surface potentials generated by dipoles within multilayer anisotropic spheres

Berg and Scherg's fast computation method is extended to multilayer anisotropic spheres. The Berg parameters can be dependent upon a dipole radial parameter or not, depending on the actual sphere conductivities and the layer the dipole is within. To find the Berg parameters, no specific electrode locations are required. Berg and Scherg's method is generally applicable whenever de Munck and Peters's addition-subtraction method can be used.

Visualization of a moving quadrupole with magnetic measurements of peripheral nerve action fields

Magnetic compound action fields (CAFs) over the right arm were measured from 63 sensor positions with two 7-channel SQUID gradiometer systems following electrical stimulation of the median nerve at the wrist. The field mapping of the CAFs revealed a propagating quadrupolar pattern with the leading depolarization and trailing repolarization fronts. The average distribution of the CAFs in the longitudinal direction was 9.0 cm in length for the depolarization field and 7.3 cm for the repolarization field in good agreement with a theoretical prediction based on the duration (3 msec) of the CAFs and the conduction velocity of the nerve (50 m/sec). The distance between the maxima of the depolarization front and the minima of the repolarization front was 6.3 cm. This spatial separation of the leading and trailing dipole locations suggests in part mutual cancellation of the fields with opposite polarity at or near the depolarized segment of nerve fibers.

Model misspecification detection by means of multiple generator errors, using the observed potential map

Due to model misspecification, currently-used Dipole Source Localization (DSL) methods may contain Multiple-Generator Errors (MulGenErrs) when fitting simultaneously-active dipoles. The size of the MulGenErr is a function of both the model used, and the dipole parameters, including the dipoles' waveforms (time-varying magnitudes). For a given fitting model, by examining the variation of the MulGenErrs (or the fit parameters) under different waveforms for the same generating-dipoles, the accuracy of the fitting model for this set of dipoles can be determined. This method of testing model misspecification can be applied to evoked potential maps even when the parameters of the generating-dipoles are unknown. The dipole parameters fitted in a model should only be accepted if the model can be shown to be sufficiently accurate.

Insidious errors in dipole parameters due to shell model misspecification using multiple time-points

Insidious errors in dipole modeling due to shell model misspecification in a spherical model were examined analyzing multiple time-points using the constraints of a commonly-used DSL (Dipole Source Localization) method. The computer simulation examined the differences in the fit dipole parameters for the same generator under two circumstances: 1) when computed as a single dipole active alone, and 2) when computed as a member of a simultaneously-active dipole pair. The computations were done using a simplification by which the dipole parameters computed from multiple time-points can be correctly assessed by computing dipole parameters at only two virtual time-points. Using multiple time-points in the DSL generally resulted in less error than if only a single time-point was used. However, how much improvement cna be achieved by using multiple time-points, as compared with a single time-point, is a function of many factors, such as the location and orientation of the dipoles, and the relative magnitudes and overlap of the waveforms (i.e., time-varying magnitudes) of the dipoles, as well as the model used in the fitting. Further, it was shown that it is incorrect to assume that a multiple-time-point DSL will compute a zero magnitude for generators during quiescent intervals. Additionally, it was shown that a "correction" to reduce error for one pair of waveforms will not be applicable to other waveforms. Also, even if location errors are eliminated, magnitude and orientation errors can still be shown to be present. Finally, iterative reduction of the least-square error between the observed and predicted surface maps leads to increasing errors in dipole parameters. We conclude that a DSL with model misspecification can contain insidious (undetectable) errors.

[Evoked potentials by median nerve stimulation (SSEP): subcortical components]

Este estudo constitui uma revisão de literatura realizada com a finalidade de se relacionar a designação, as características dos campos de potencial e os geradores implicados, para os componentes subcorticais do potencial evocado somatossensorial por estimulação do nervo mediano no punho.

Uniqueness of the generators of brain evoked potential maps

This study considers the uniqueness of neuronal generators of human brain evoked potentials measured on the scalp using the physical and mathematical properties of the volume conductor model. The results are applicable to a realistic, nonhomogeneous head shape where the potential map is known on a continuous set of points on the scalp. It is shown that sources which occupy "zero volume" in space such as point dipoles or sources distributed on an open surface or a line are uniquely defined by the potential maps. Finite volume nonoverlapping sources are also uniquely defined by their potential map. However, there are infinitely many different but overlapping sources which can create the same map. Several examples of such sources are provided. It is shown that there is a unique, minimum volume source which can be defined in this case. Results suggest that if a reconstruction of the sources starts from a continuous scalp map (obtained by interpolation of the data between electrode sites), one can obtain unique results concerning the source parameters that are not available in a search for a source whose potential map fits only at a discrete set of points.

Far-field potential production by quadrupole generators in cylindrical volume conductors

Far-field potentials have been observed clinically and recognized as such for approximately 30 years. Unfortunately a complete understanding of far-field potential generation is not yet at hand. An attractive model is the representation of an action potential by a quadrupole consisting of a leading and trailing dipole with respect to the direction of propagation. This investigation physically models an action potential by using a quadrupole constant current source and substantiates the concept that an action potential as modeled by two dipoles back-to-back is capable of producing far-field potentials in cylindrical volume conductors. The 4 postulated mechanisms of generating far-field potentials are validated, i.e., an action potential encountering (1) different size volume conductors, (2) the termination of excitable tissue, (3) a change in conducting medium conductivity, and (4) a bend in the nerve. A fifth postulated but previously not demonstrated method of far-field production, neural branching, is shown by the quadrupole model to also be capable of yielding far-field potentials. The termination of a volume conductor is also shown to be capable of generating a voltage difference across the quadrupole. Any of the above 6 conditions create an alteration in the symmetry of the leading and trailing dipole moments resulting in a transient potential difference across the quadrupole as recorded with a far-field recording montage. The potential difference produced by the asymmetric electric field between the leading and trailing dipoles recorded distantly in areas of low potential gradient is the so-called far-field potential. This investigation substantiates the utility of the leading/trailing dipole model of far-field production and offers a simple model of passive voltage distributions secondary to dipolar moment imbalances to better understand the generation of far-field potentials in cylindrical volume conductors.

Far-field potentials in cylindrical and rectangular volume conductors

The occurrence of a transient dipole is one method of producing a far-field potential. This investigation qualitatively defines the characteristics of the near-field and far-field electrical potentials produced by a transient dipole in both cylindrical and rectangular volume conductors. Most body segments of electrophysiologic interest such as arms, legs, thorax, and neck are roughly cylindrical in shape. A centrally located dipole generator produces a nonzero equipotential region which is found to occur along the cylindrical wall at a distance from the dipole of approximately 1.4 times the cylinder's radius and 1.9 times the cylinder's radius for the center of the cylinder. This distance to the equi-potential zone along the surface wall expands but remains less than 3.0 times the cylindrical radius when the dipole is eccentrically placed. The magnitude of the equipotential region resulting from an asymmetrically placed dipole remains identical to that when the dipole is centrally located. This behavior is found to be very similar in rectangular shallow conducting volumes that model a longitudinal slice of the cylinder, thus allowing a simple experimental model of the cylinder to be utilized. Amplitudes of the equipotential region are inversely proportional to the cylindrical or rectangular volume's cross-sectional area at the location of dipolar imbalance. This study predicts that referential electrode montages, when placed at 3.0 times the radius or greater from a dipolar axially aligned far-field generator in cylindrical homogeneous volume conductors, will record only equipotential far-field effects.

Far-field potentials

Far-field potentials are produced by neural generators located at a distance from the recording electrodes. These potentials were initially characterized incorrectly as being of positive polarity, widespread distribution, and constant latency; however, recent advances have clearly demonstrated that far-field potentials may be either positive or negative depending upon the location of the electrodes with respect to the orientation of the dipole generator. Additionally, peak latencies in the far-field can vary with alterations in body position and the spatial distribution of far-field potentials, while widespread, is not uniform. Recent studies of far-field potentials suggest how such waveforms are produced when the symmetry of an action potential, as recorded by distant electrodes, is broken by such factors as differing conductivities of volume conductor compartments, direction of action potential propagation, size differentials in adjoining body segments, or the termination of action potential propagation in excitable tissue. Human, animal, and computer experiments support the preceding generalizations. These new explanations are directly applicable to such far-field potentials as the short latency somatosensory-evoked potential. Furthermore, since far-field potentials can also occur in muscle tissue, one should expect that these generalizations will hold with respect to electromyographic potentials.

Far-field potentials in circular volumes: the effect of different volume sizes and intercompartmental openings

Preliminary investigations of circular volume conductors suggested that far-field potential magnitude declines progressively slower with increasing radial distance from a current source and follows a cosine function with angular displacement of the recording electrode from the electrical generator's axis. Using circular volumes of 6 differing radii, the mathematical relationship between angle, radii, and far-field potential amplitude is determined. Previous theoretical relationships of amplitude versus dipolar spacing, current, and distance from a dipole generator in a bounded volume conducting medium are verified for the near-field. Far-field potentials in circular volumes are found to become constant at radii greater than 75% of the bounded volume's radius. Additionally, an adjoining volume conductor acts simply as a passive fluid-filled electrode (wick electrode) to the circular volume containing the generator until the intercompartmental opening to the circular volume exceeds 20% of its circumference. This finding was clinically supported by recording similar P9 somatosensory-evoked far-field potentials generated caudal to the foramen magnum from various portions of the cranium, whose connections to the torso, foramen magnum, and neck, average 6.2% and 17.8%, respectively. Finally, 3 circular volume conductors were connected in series by channels less than 20% of the volume conductor's circumference. Both adjoining circular volumes were equipotential to the far-field potential present at the boundary of the first circular volume containing the dipole generator. This observation supports the clinical finding of far-field potential transmission through multiple human bodies in conductive contact.

Possible model for generation of P9 far-field potentials

The distribution of P9 far-field somatosensory evoked potentials, after stimulation of the median nerve with a knee reference, was examined to determine the mechanism of the generation of P9 potentials. In addition to positive potentials (P9s), we found a negative potential (N9) recorded from the chest ipsilateral to the stimulation. The simulation of the distribution of these P9/N9 potentials by an electrical circuit diagram suggested the validity of this model for generation of the P9s.

Far-field potentials in circular volumes: evidence to support the leading/trailing dipole model

The leading/trailing dipole model explains the production of far-field potentials as an asymmetry in the leading and trailing dipole moments of a propagating action potential detected by a referential montage. This investigation documents the production of far-field potentials produced by a pure dipole generator in a circular volume conductor. Multiple equipotential waveforms are recorded in an adjoining circular volume conductor attached to the one in which the dipole generator is located. This finding substantiates the "wick electrode" effect that explains the equipotential and instantaneous distribution of far-field potentials over relatively large distances in volume conductors. The present findings support a number of the leading/trailing dipole model proposals which explain far-field potential generation.

Far-field potentials in muscle

Far-field potentials have been predicted by computer simulations as well as demonstrated in both animals and humans with respect to the peripheral and central nervous systems. Computer simulations have also predicted far-field potentials originating at the termination of muscle tissue. This investigation demonstrates the occurrence of 2 far-field potentials in the human biceps muscle resulting from action potential termination at the musculotendonous junctions. A monophasic potential is produced at both the muscle's origin and insertion, and the polarity is entirely dependent upon the recording montage. Sequential stimulation of the biceps muscle at 2.5-cm increments resulted in the 2 far-field potentials and their respective latencies changing proportional to the distance between the stimulus site and the 2 musculotendonous junctions. Various stimulation and recording montages are used to investigate the properties of these far-field potentials. The leading/trailing dipole model is utilized to explain the production and polarity of far-field potentials generated by muscle tissue.