A CORRECTION PROCEDURE FOR THE VOLUME CONDUCTOR EFFECT IN THE COMPOUND ACTION POTENTIAL RECORDED...

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Intern. J. Neuroscience, 112:1013–1026, 2002Copyright 2002 Taylor & Francis0020-7454/02 $12.00 + .00DOI: 10.1080/00207450290026012

A CORRECTION PROCEDUREFOR THE VOLUME CONDUCTOR

EFFECT IN THE COMPOUND ACTIONPOTENTIAL RECORDED FROM

ISOLATED NERVE TRUNK

NIZAMETTIN DALKILIC

Selcuk UniversityFaculty of MedicineDepartment of BiophysicsKonya, Turkey

FERIT PEHLIVAN

Ankara UniversityFaculty of MedicineDepartment of BiophysicsAnkara, Turkey

The shape and magnitude of the compound action potential (CAP), whichis the linear summation of the single fiber action potentials, dependstrongly on the recording conditions. Volume conductor effect should beeliminated or corrected in order to get reliable information about thefunctional state of the nerve trunk. In the case of monophasic extra-cellular recordings, the integral of CAP recorded extracellularly tendsto decrease with the distance, because the extracellular resistance be-tween the stimulating and recording electrodes changes. To compensatefor this effect, we took into account the spatial deviation of the integralof CAP versus distance and defined a spatial correcting factor, g(x). By

Received 3 March 2002.This work was performed in the Department of Biophysics, Faculty of Medicine, Ankara

University, and was supported by Ankara University Research Fund (98.30.00.01).Address correspondence to Dr. Nizamettin Dalkilic, Selcuk Unv. Meram Tip Fak. Biyofizik

Anabilim Dali, 42080 Konya, Turkey. E-mail: [email protected]

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1014 N. Dalkilic and F. Pehlivan

applying g(x) to all CAPs, we get corrected CAP (cCAP) data for fur-ther evaluations. It is well known that the slope of the maximum deriva-tive of CAP versus distance curve would be a measure of conductionvelocity distribution for the fast conducting nerves in a nerve trunk. Theslopes of these curves for extracellular and suction techniques on thesame nerves are compared; we concluded that the difference betweenthe two techniques was not important for the correction procedure onextracellular records.

Keywords compound action potential, extracellular recording, sciaticnerve, suction techniques, volume conduction

It is known that the intracellular recording of action potentials isvery adequate in terms of sensitivity. Despite this fact, the extracel-lular technique still maintains its importance from both experimen-tal and clinical points of view (Hansen & Ulbricht., 1991; Lonnendonkeret al., 1990; Poulter et al., 1993; Tan, 1985; Tan & Caliskan, 1988;Tan & Tan, 1995, 1998).

Peripheral nerves consist of axons, which have different conduc-tion velocities and are confined in sheath. If one nerve is excited,linear summation of the action potentials contributing from eachnerve fiber make up the compound action potential (CAP).

The analysis of CAP, which is recorded from a peripheral nerveevoked by a supramaximal stimulation, can be successfully used todetermine the functional state of that particular nerve, diagnose anynervous disease, observe the nerve’s growth, or deduce the conduc-tion velocity distribution of the nerve.

Although different techniques, such as magnetically recorded com-pound action currents (Wijesinghe et al., 1991), are used to deter-mine the structural and functional state of the nerve, extracellularand suction techniques for recording CAP from isolated nerve arethe ones most widely used (Bostock & Grafe, 1985; Carley & Rey-mond, 1987; Masson et al., 1989; Mateu et al., 1997; Rendell et al.,1989). While these techniques appear mostly in the literature, bothhave pros and cons.

In order to deduce which of the techniques is most reliable andadvantageous, we recorded the CAPs from the isolated frog sciaticnerves by both techniques, and compared the results of numericanalysis on CAP data.

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Volume Conduction in Action Potential 1015

EXTRACELLULAR RECORDING

FIGURE 1. Schematic representation of an extracellular monophasic recording.

In order to minimize the volume conductor effect, isolated nervetrunks are the preferred source to record CAP (Mateu et al., 1997;Rubinstein & Shrager, 1990; Vladimirov et al., 1997). In the extra-cellular recording technique, the isolated nerve is laid on the record-ing and stimulating electrodes in the nerve chamber. Electricalactivity that results from the stimulation of the nerve is recorded asa potential difference between the reference and the exploring elec-trodes, and both electrodes are positioned on undamaged part of thenerve. This is called “extracellular biphasic recording technique.” Inthe “extracellular monophasic recording technique,” the referenceelectrode is positioned on the crushed and continuously depolarizedpart of the nerve, while the active electrode remains on the un-damaged part.

The potential difference that we recorded extracellularly dependsnot only on the voltage source, but on the conductive propertiesof the extracellular matrix. In order to reduce the effect of the un-desired second factor which is called “volume conductor effect,”the nerve is isolated from the conductive medium and hung floatingon air or placed in the paraffin oil. The conductive film coveringthe nerve is enough for the nervous conduction. A representativescheme for monophasic extracellular recording is given in Figure 1.

If the distance from the stimulating point to the recording pointis x, then (d – x) would be the distance between the reference and

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active electrodes, where d is the overall length between the stimu-lating and the reference electrodes. Assuming that the longitudinalresistance of the extracellular film covering the nerve changes lin-early with length, then the voltage source V

s(t) can be written as,

Vs(t) = R

0I + (d – x)ρ

xI (1)

where I is the total current, R0 is the total internal resistance of the

voltage source (including the membrane resistance and the axoplas-mic resistance), and ρ

x is the extracellular resistance per unit length

of the nerve. If we rearrange Eq. (l) for I, then

Vs(t)I = R0 + (d – x)ρ

x

(2)

The potential recorded at any point [Vg(t,x)] can be thought as

the potential difference originated by this current source on the ex-tracellular resistance [(d – x) ρ

x], that is V

g(t,x) = I. (d – x)ρ

x. Ac-

cording to Ohm’s law, under the condition of R0 >> (d – x)ρ

x, this

potential can be written as

Vg(t, x) = Vs(t) (d – x)ρ

xR0

(3)

This means that the recorded CAP is directly proportional to theextracellular resistance [(d – x)ρ

x], and so to the distance between

the recording electrodes.In the case of monophasic recording from an isolated nerve trunk,

the integral of CAP should be constant as the recording distancevaries under the ideal conditions where the volume conductor effectcan be neglected. In actual cases, however, the integrals of CAPrecorded extracellularly tend to decrease with the distance from thestimulating point because the extracellular resistance [(d – x)ρ

x]

changes. To compensate for this volume conductor effect, we tookinto account the spatial deviation of the integral of CAP from areference value. The integral of the CAP (t, x

0), which is recorded

from the point nearest to the stimulating point, is selected as thereference value. Then we defined a spatial correction factor as a

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value when multiplied by the integral of CAP for that distance wouldgive the reference value. That is,

∫tV

g(t,x

0) = g(x) • ∫

tV

g(t,x) (4)

Comparing this equation with Eq. (3), it can be seen that the1/g(x) linearly dependent on the distance and the uncertainty in g(x)becomes higher when the active electrode moves toward the refer-ence electrode,

∫tV

g(t,x)

g(x) =

∫tV

g(t,x

0)

= d – x

0(5)

By applying g(x) to all CAPs, one can get corrected CAP (cCAP)data for further evaluations.

1 d – x

SUCTION RECORDING

In electrophysiological studies, the suction technique is widely usedin tasks such as stimulating peripheral nerve, recording CAPs fromnerves, or recording single fiber action potentials (SFAPs) (Bakeret al., 1987; Bostock & Grafe, 1985; Carley & Raymond, 1987;Scholfield, 1989; Shao & Hochmuth, 1996). This technique has otherapplications, such as recording monophasic action potentials fromcardiac cells in electrophysiological and clinical studies (Cotoi &Dragulescu, 1975; Franz, 1991).

In the suction method, suction electrodes are constructed from lowmelting point glass capillary tubing by heating one end, which willlater be constricted approximately to the diameter of the nerve understudy. The barrels are filled with artificial salt solutions and an Ag/AgCl wire is inserted into capillary tubing connected to the record-ing system (Easton, 1993; Kettenmann & Grantyn, 1992). While oneend of the nerve is inserted into the constricted end of the capillary,the opposite end is positioned on the stimulating electrode.

An electrical model of the recording end of suction electrodewith a nerve-end inside can be represented as in Figure 2.

If we consider the nerve as a single large equivalent fiber, itsintracellular potential near the inserted end (V

e) may differ from

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intracellular potential outside the electrode (Vm). If E

0 represents

transmembrane potential outside the electrode and Em is the trans-

membrane potential at the end inside the capillary tube, the currentwill flow around the loop whenever V

e and V

m are different. As the

current flows, the electrode will sense the voltage drop V0, across R

0.

After some reductions, V0 can be written as,

V0 = R

0/R

i (V

m – V

e) (6)

where Ri is the internal resistance of the fiber and R

0 is the resis-

tance of the external medium (Stys et al., 1991).Since resistances R

i and R

0 are parallel and resistance of the ex-

ternal medium is much more than that of the intracellular compart-ment (i.e., R

0 >> R

i), parallel combination of R

0 and R

i (R

p) is equal

to R0 (R

p ≅ R

0). As such, V

0 can be given as,

V0 = R

p/R

i(V

m – V

e) (7)

Eq. (7) shows that V0 is directly proportional to the R

p (Stys et al.,

1991).

MATERIALS AND METHODS

Experiments were performed to record CAPs from isolated frogsciatic nerve by extracellular and suction techniques. The frogs weredissected approximately 1 h before experiments were started. During

FIGURE 2. Electrical model of recording end of a suction electrode with nerve in-serted (Stys et al., 1991).

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the dissection, frog Ringer’s solution was used to keep the nervemoist. One end of the dissected nerve was tied using threads, andthe nerve was transferred into bathing system of suction technique.The distal end of the bundle was drawn snugly into the barrel of asaline-filled glass pipette with a tip. The tip was thick enough topull a nerve inside with the actual application of suction to the freeend of the capillary. This capillary electrode was connected to adifferential amplifier.

The other tied end of the nerve was laid on the stimulating elec-trode, which was positioned on the upper side of the bath, with nocontact with the Ringer’s solution.

As the nerves were stimulated by a supramaximal electrical pulse,the action potentials were recorded using an isolated preamplifier(Harvard) that had a rather high input impedance. The CAP signalswere digitized with a 0.04 ms sampling period by an A/D converter(PCL 812PG) and 512 time samples per CAP record stored on ahard disk.

After completing the suction record, the nerve was moved to anextracellular moist chamber from the suction chamber. In order tostimulate the distal end of the bundle, the same experimental proce-dure followed for the suction record was used to record the extra-cellular CAP from the same nerve bundle.

The CAP data stored on hard disc were analyzed later. Numeri-cal analysis of both recorded signals was conducted and the resultshave been compared.

RESULTS

The CAPs belonging to the same nerve shown in Figure 3a and 3bwere recorded by suction and extracellular techniques at differentdistances (from 1.5 cm to 5.5 cm by .5 step). In order to see howthe integrals of CAPs change along the nerve, the integrals of extra-cellular and suction CAPs were calculated. The integrals of CAPversus distance curves for both techniques have been given in Fig-ure 4a and 4b, respectively.

For each experiment, by selecting the biggest integral of CAPfor the suction series and the integral of the nearest CAP for the

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extracellular series as references, correction factors for each dis-tance were calculated. Changes in correction factors with the dis-tances can be seen in Figure 5a and 5b for both extracellular andsuction techniques with the standard deviation.

For each experiment, by selecting suction CAP with the biggestintegral and the nearest extracellular CAP’s integral as references,correction factors for each distance were calculated. Changes in cor-rection factors with the distances can be seen in Figure 5a and 5b forboth extracellular and suction techniques with the standard deviation.

As mentioned in Eq. (5), the inverse of the correction function(1/(g(x)) should change linearly with the distance. To see how theexperimental data coincide with theoretical argument, 1/g(x)s for

FIGURE 3. The compound action potentials recorded by extracellular (a) and suction(b) techniques from 9 different distances. Each CAP has been shown in the same axis.

FIGURE 4. Integrals of CAPs recorded by extracellular (a) and suction (b) tech-niques from 9 different distances.

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each distance were calculated (Figure 6a). Since it is known thatthis change arises from the change in extracellular resistance be-tween reference and recording electrodes, their values were determinedfor each distance by using the resistance-measuring device that weconstructed. The resistance values between reference and recordingelectrodes were calculated for each distance, and relative extracellu-lar resistance versus distance values were found as in Figure 6b.

In order to correct volume conductor effect, the CAPs recordedby both techniques were multiplied by correction factors derived foreach distance. By doing this, the decrement caused by volume con-ductor effect was eliminated, and thus CAPs have been corrected as

FIGURE 5. The changes of extracellular (a) and suction (b) correction factors andstandard deviation with the distances for the average of 28 different nerve recordings.

FIGURE 6. Inverse of extracellular correction factor (a) and relative extracellularresistance predicted directly from experimental setup (b) and their standard deviations(n = 28).

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cCAPs. Since the change in values of the maximum derivatives ofcCAPs with distance give information about the conduction veloc-ity distribution or fiber diameter distribution for the fast conduct-ing fibers of that particular nerve (Dalkilic & Pehlivan, 1994), themaximum derivative of each cCAP has been calculated, and theresults have been given in Figure 7a and 7b. In these figures, eachpoint represents the average result of 28 different nerves. Such ahigh standard deviation is due to the fact that each nerve belongs toa different subject.

DISCUSSION

Extracellular and suction CAPs recorded by changing the distancebetween the stimulating and the recording electrodes from 1.5 to5.5 cm in steps of 0.5 cm are given in Figure 3. While the ampli-tude of the extracellular CAPs decrease sharply with distance, thedecrements in the amplitudes of suction CAPs are not as much asthose of the extracellular CAPs. The decrement in the amplitude ofextracellular CAPs is primarily due to the decrement in extracellu-lar resistance between reference and active electrodes (Dalkilic &Pehlivan, 1994). If this factor can be eliminated in an appropriateway, then the decrement in amplitude can be attributed to the con-duction velocity distribution. However, the decrement in suction

FIGURE 7. Derivatives of extracellular (a) and suction (b) of corrected CAPs (cCAP)and their standard deviations (n = 28).

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CAP amplitude can be attributed only to the conduction velocitydistribution.

Since the diameter of the axons that constitute the nerve are dif-ferent, with any change in the distance a decrement in amplitudeand an increment in CAPs duration could be expected. However, inideal conditions where a cylindrical nerve has no volume conductoreffect, no matter where the recording is made, the integral of CAPsshould be constant. The integrals of extracellular and suction CAPscalculated for different distances of a nerve are given in Figure 4.Whereas the suction CAP integrals for each distance are approxi-mately the same, the extracellular CAP integrals decrease dramati-cally with the distance from the stimulating site. If the area under aCAP is assumed to be constant, as would be in an ideal condition, itcan be thought that the suction CAP integrals are verifying ourexpectations. In the extracellular method, the decrement in CAP’sintegral can be attributed to the decrement in the extracellular resis-tance with the distance.

In order to determine to what extent the reduction in the CAPamplitude arises from the conduction velocity distribution, the fac-tors that cause amplitude reduction other than conduction velocitydistribution must be eliminated. To accomplish this task, relativecorrection factors (g(x)) were calculated for each distance, and g(x)versus distance curves for both suction and extracellular techniqueshave been sketched for all 28 experiments. In the g(x)-distance curvefor suction records, though little fluctuations were observed, g(x) isalmost stable and approximately equal to 1. Therefore, the decreasein suction CAP amplitude with distance can be attributed only tothe conduction velocity distribution. In the g(x)-distance curve forthe extracellular records, g(x) increases with the distance, and thisincrement becomes more evident as the active electrode approachesthe reference electrode. The standard deviation in g(x) also obvi-ously increases with distance. The necessity of a correction factor inextracellular technique, as discussed in the introduction, arises fromthe fact that extracellular resistance decreases with an increase indistance. According to Eq. (3), the recorded CAP(t,x) is directlyproportional to the external resistance.

So as to see to what extent our findings coincide with the varia-tion in theoretically discussed g(x), 1/g(x) values for extracellular

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records have been calculated and 1/g(x)-distance curves were plottedas shown in Figure 7. Extracellular 1/g(x) curves decrease with dis-tance linearly as expected. For the suction records, 1/g(x)-distancecurves were also drawn. Consequently, average slope of the extra-cellular 1/g(x) curves are much greater than those obtained fromsuction 1/g(x) curves. This difference is related to the volume conduc-tor effect that is exhibited explicitly in the extracellular technique.

The above discussion suggests that, contrary to the records takenby extracellular technique, there is no need for a correction procedurefor the suction records in order to reduce the volume conductor effect.

Theoretically, it is expected that the extracellular 1/g(x) varieswith the resistance between the two electrodes [(d – x)ρ

x] linearly.

Our findings also show that the extracellular 1/g(x) decreases withthe distance linearly as seen in Figure 7a. In order to verify thisconclusion directly, the extracellular resistance measured experi-mentally by the resistance reading system, and the resistance-distance curves are also drawn both for extracellular and suctionsystems. The slope of the decrement of the extracellular 1/g(x) andexperimental extracellular resistance can be considered as equal.Therefore, the approach we have introduced in theoretical discus-sion has been proved and our correction procedure proposal servesonly to reduce the volume conductor effect.

It is known that the change in maximum derivatives of CAPs canbe attributed to the conduction velocity distribution of nerve fibers(Dalkilic & Pehlivan, 1994; Biagetti et al., 1990; Roberge & Boucher,1990), at least for the fast conduction fibers. The corrected CAPs(cCAPs) were determined by multiplying both extracellular and suc-tion CAP records with the previously calculated correction factorsfor each distance, then the derivatives are determined on correctedcCAPs data. Maximum derivative of a cCAP-distance curve, whichgives information about the conduction velocity distribution, wasplotted. The slopes of maximum derivatives determined from theextracellular and suction cCAP-distance curves of 28 experimentswere found approximately equal to each other. If we make a pairedcomparison of maximum derivatives of cCAPs derived from extra-cellular and suction methods, some difference appears, but on theaverage of 28 experiments it can be seen that the results are almostthe same.

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As a result, in any work that consists of deriving informationabout the functional state of a whole nerve by using recorded CAPsdata, extracellular recording techniques are preferred, providing thatthe volume conductor effect should be corrected. Suction techniquescan be used preferentially in the studies of single nerve action po-tentials.

CONCLUSION

An important factor that affects the shape and magnitude of CAP isthe volume conductor effect and this effect should be eliminated orcorrected in order to get reliable information about the functionalstate of the nerve trunk from the recorded CAP data. Suction tech-nique is partly a manner for the elimination of this effect. In thecase of monophasic extracellular recording, our correction proce-dure gives the same results as the suction technique about the func-tional state of the same nerve trunk.

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A CORRECTION PROCEDURE FOR THE VOLUME CONDUCTOR EFFECT IN THE COMPOUND ACTION POTENTIAL RECORDED...

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