Forty-hertz Midlatency Auditory Evoked Potential Activity Predicts Wakeful Response during Desflurane and Propofol Anesthesia in Volunteers 

We enrolled 22 healthy male volunteers aged 21–30 yr with their informed consent and approval from the University of California, San Francisco, Committee on Human Research. Details of patient recruitment, anesthetic technique, and wakeful response testing have been described previously. 18Each volunteer was anesthetized twice, once with desflurane (Baxter Pharmaceutical Products Division, Liberty Corner, NJ) and once with a continuous intravenous solution of propofol (Stuart Pharmaceuticals, Wilmington, DE). Order of anesthetic administration was randomized, with 5 days between administrations. Each drug was delivered in concentration steps maintained for 15 min.

Desflurane administration began with a single-step increase to an end-tidal concentration of 2.0%, as determined by a respiratory gas analyzer (Capnomac, Datex, Helsinki, Finland) calibrated using secondary (cylinder) standards. Volunteers were tested for responsiveness as defined by their response to a verbal request to squeeze an investigator's hand one, two, or three times. Desflurane end-tidal concentration was increased step-wise, 0.5 vol%, at 15-min intervals until the volunteer failed to respond appropriately. MAC^Awakefor each volunteer equaled the mean of the concentrations just permitting and preventing appropriate response to command. 17For the final concentration step, end-tidal desflurane concentration was increased to 1.5 or 2.0 times MAC^Awakefor that volunteer.

For volunteers receiving propofol, intravenous delivery of propofol from a syringe pump (Ohmeda 9000, Ohmeda, Madison, WI) was computer-controlled using an infusion rate–time profile 29to deliver targeted step increases of arterial propofol, beginning with a single-step increase to a target concentration of 1.5 μg/ml, after which concentration was increased step-wise 0.5 μg/ml at 15-min intervals until the volunteer did not respond appropriately to the hand-squeeze request. For each volunteer, Cp50^Awake(analogous to MAC^Awake) was calculated as the mean of the target concentrations just permitting and preventing appropriate response to command. For the final concentration step, target propofol concentration was increased to 1.5 or 2.0 times Cp50^Awakefor each volunteer. We determined propofol concentrations in heparinized arterial blood samples withdrawn from the left radial artery. The samples were analyzed with high-performance liquid chromatography using the technique of Plummer. 30 

After abrading the skin (OmniPrep, DO Weaver, Denver, CO), silver–silver chloride electrodes were placed at the vertex (active), on both mastoids (reference), and overlying the right clavicle (ground). Contact impedance differed by less than 2 kΩ between electrodes. A Pathfinder I (Nicolet Instruments, Madison, WI) was used for acoustic stimulation and recording of MLAEPs. A 150-μs unidirectional rectangular wave pulse provided a binaural rarefraction click at 80 dB with a frequency of 9.3 Hz via  acoustically shielded headphones (Telephonics TDH 39P, Huntington, NY). MLAEPs were recorded from 0 to 100 ms (512 data points) using a 15- to 1,500-Hz bandpass filter. Individual trials with response signal >90% of amplifier voltage limit were automatically rejected as artifacts. The average from 1,000 stimulations obtained over a 2- to 3-min period provided the MLAEP.

We recorded one, two, or three MLAEPs 9 min after each 0.5% or 0.5 μg/ml step increase. Volunteers were tested for responsiveness after recording MLAEPs.

Further MLAEP analysis was conducted on a Macintosh computer (Apple Computer, Cupertino, CA). If replicated MLAEPs were available, we averaged the MLAEPs to obtain a single waveform and used that single waveform for subsequent data analysis. We defined the waveform occurring just before loss of responsiveness as Resp, that occurring just after loss of responsiveness as NoResp, and that occurring 1.5–2.0 times MAC^Awake(or Cp50^Awake) as NoResp^next. For each volunteer and anesthetic agent, we defined a waveform set as the Resp, NoResp, and NoResp^nextwaveforms.

For each MLAEP waveform, we calculated MLAEP power spectrum indices using joint time–frequency analysis (JTFA)31(LabVIEW, National Instruments, Austin, TX), using the short-time Fourier transform and a Hanning window. We used JTFA because the standard Fourier transform–based methods of measuring the MLAEP frequency spectrum usually incorporate a “window” function 32that accentuates information at the center latency of the MLAEP sweep (e.g. , 50 ms of a 100-ms duration acquisition). Because maximally predictive information may be in frequency spectra calculated with nonstandard windowing, we used JTFA to vary the latency of the window center. Like standard Fourier transform–based methods, JTFA measures power as a function of frequency, and in addition as a function of window-center latency. After appropriate scaling, the JTFA calculated the two-sided power density spectrum, also sometimes termed power spectra , in microvolts squared per hertz (μV²/Hz), for a range of windows centering at specified latencies; for a window center at 50 ms, the width of the window at half power was ±18 ms and the frequency width was ±7 Hz. The JTFA used zero padding to 200 ms to obtain a frequency spacing of 5 Hz. For each MLAEP waveform, we calculated power density spectra for windows centered from 20–74 ms, at 3-ms intervals. Then, for each of these power density spectra, we measured power density over the range from 20–80 Hz, at 5-Hz intervals, to obtain indices of power density at each frequency bin and latency interval (e.g. , Pwr^{40-Hz38 ms}).

To compare our JTFA results with more conventional fast Fourier transform (FFT) analysis, we used AcqKnowledge (ver. 3.0, BIOPAC Systems, Goleta, CA) to calculate power density at 40 Hz. The FFTs were calculated using a standard Hanning window, centered at 50 ms, and zero padding was added to extend the epoch to 200 ms. After appropriate scaling, the two-sided power density of each FFT spectrum was measured in microvolts squared per hertz (μV²/Hz) at 40 Hz to create an index we termed Pwr^FFT40-Hz.

To compare the predictive performance of these MLAEP power indices with that of standard MLAEP latency and amplitude indices, we measured latency and amplitude values using AcqKnowledge for each MLAEP. The waveforms were passed through a 511-coefficient Finite Impulse Response (FIR) highpass filter with Blackman −61-dB windowing and a −6-dB cutoff at 15 Hz. We identified the MLAEP peaks by simultaneously displaying all three waveforms of a volunteer's set and then selecting peaks according to the expected latency (e.g. , the Na peak was the maximum negative voltage between 17 and 22 ms) and the similarity in appearance of the peaks among the three waveforms, considering the tendency for peak latency to progressively increase from Resp to NoResp to NoResp^next. Latency was measured from stimulus presentation to the peak voltages (e.g. , Nb) to create MLAEP indices (e.g. , Lat^Nb). 33Amplitude was measured from the zero-voltage baseline to the peaks (e.g. , Nb to create Amp^Nb). We also calculated the peak-to-peakvoltage of Amp^Pa−(Amp^Na+ Amp^Nb)/2 to createAmp^NaPaNb. 34 

After finding that Lat^Nbwas the best-performing latency index and Amp^NaPaNbthe best-performing amplitude index, and hypothesizing that these indices contained independently predictive information, we combined Lat^Nband Amp^NaPaNbinto a new single-number index:

In preparation for statistical analysis, for each anesthetic, we created a response group that consisted of pooled Resp waveforms, and a no-response group that consisted of the pooled NoResp and NoResp^nextwaveforms. We called the combined response and no-response groups for each anesthetic the complete group for that anesthetic. Because the MLAEP waveforms of some volunteers were missing or appeared artifactual (which might unfairly degrade predictive performance), we created an extended group for each anesthetic by selecting from the complete group the two thirds (14 of 21) of the volunteers having complete sets of waveforms that were relatively free of artifacts. We also created a bracketed group for each anesthetic, containing the MLAEPs that just bracketed wakeful response (i.e. , Resp and NoResp waveforms in the extended group and excluding NoResp^nextwaveforms).

We used P^K27,28to calculate predictive performances of MLAEP and concentration indices. For example, consider two randomly selected Nb latency values, one a Resp and one a NoResp. The P^Kis the probability that the Nb latency values correctly predict which waveform is the Resp and which is the NoResp. A P^Kof 0.50 means that the index correctly predicts responsiveness 50% of the time (e.g. , by chance) and a P^Kof 1.00 implies that the index predicts responsiveness perfectly.

Having calculated a large array of spectral power densities over a range of frequency bins and latency intervals, we sought to determine the optimum frequency and latency for separating responding and nonresponding volunteers. To do so, we calculated the P^Kvalues at each frequency bin and latency interval for each anesthetic and then examined topographic surfaces of P^Kas a function of frequency and latency to identify the peak in P^Kvalues; the optimum frequency and latency values were defined as those corresponding to the P^Kpeak.

We also used P^Kto compare predictive performance of MLAEP and concentration indices, for each database. To compare the P^Kvalue of each MLAEP index with the P^Kvalue of the corresponding desflurane or propofol concentration, we calculated the difference and statistical significance of the difference at the P = 0.05 and 0.01 criteria levels (two-tail test, no Bonferroni correction). For each MLAEP index, we also calculated the statistical significance of the difference for predictions of desflurane and propofol groups combined. To do so, we pooled the P  value of the difference during desflurane anesthesia with that during propofol anesthesia to calculate a product that has a chi-square–like distribution, and then we tested the significance at the P = 0.05 and 0.01 criteria levels. 35We also compared the predictive performance of the best-performing MLAEP power indices with that of the MLAEP latency and amplitude indices by similarly calculating differences between P^Kvalues and the statistical significances of the differences.

To calculate specific indicator values for predicting a volunteer's probability of nonresponsiveness, we applied logistic regression analysis 36(SPSS, Chicago, IL) to each extended group to calculate the probability of wakeful response as a function of indicator value. Logistic regression analysis provided β, a measure of the steepness (slope) of the logistic regression curve, and Indicator⁵⁰and Indicator⁹⁵, the values of the indicators at which the probability of nonresponse equals 0.50 and 0.95. 37Before applying logistic regression analysis, we appropriately transformed indicator scales 27,38(see Appendix). We calculated logistic regressions for anesthetic concentrations, Pwr^40-Hz38ms, Pwr^40-Hz50ms, and Lat^Nb. To display logistic regression curves for these indices over comparable value ranges, we calculated linear regressions of Pwr^{40-Hz38 ms}and Lat^Nbagainst log¹⁰(concentration), for desflurane and propofol.

Twenty-one volunteers received desflurane and 22 received propofol (one volunteer did not complete the desflurane portion of the study because of a respiratory infection). Figure 1is a representative illustration of the progressive increase in latency and decrease in amplitude with decreasing responsiveness in a volunteer receiving propofol. Most sets showed a similar pattern of change between Resp and NoResp, but two sets showed no change, and one set showed a reversed change (decreased latency and increased amplitude). Figure 1also shows the FFT power density spectra of the MLAEPs from the volunteer receiving propofol. Multiple MLAEPs for a given volunteer, averaged to create a single MLAEP for that volunteer, were frequently recorded at the NoResp^nextlevel (13 of 21 desflurane volunteers, 15 of 22 propofol volunteers) but infrequently at the Resp level (1 of 21 desflurane, 1 of 22 propofol) and NoResp level (0 of 21 desflurane, 1 of 22 propofol).

Figure 2shows the JTFA spectrograms of the MLAEPs shown in figure 1.

Figures 3 and 4show all the MLAEP waveforms in the response and no-response groups of the desflurane and the propofol extended groups.

Figure 5shows topographic maps of P^Kvalues for power density over the latency range of 20–74 ms and the frequency range of 25–60 Hz for desflurane and propofol, for the bracketed groups. The P^Kvalues peaked in the region of 38 ms and 40–45 Hz for desflurane, and 50 ms and 40–45 Hz for propofol. The P^Kvalues for the extended groups peaked at the same latencies and frequencies as the corresponding bracketed groups. The P^Kvalues for these highest performing power density indices were 0.96 ± 0.03 (P^Kvalue ± SE) for Pwr^{40-Hz38 ms}during desflurane (table 1), and 0.96 ± 0.02 for Pwr^{40-Hz50 ms}during propofol. We term these indices Pwr^40-Hz.

The alternative ∼40-Hz indicator calculated using a conventional FFT, Pwr^FFT40-Hz, had nearly the same high level of performance as Pwr^40-Hz(table 1). (Comparisons of P^Kvalues must be made within a response–no-response group pair, i.e. , within the desflurane column or the propofol column. 27)

The P^Kvalue for concentration of desflurane was 0.91 ± 0.05 (table 1) and for measured propofol was 0.94 ± 0.03. The P^Kvalues for Pwr^40-Hzindices were not greater than those for corresponding concentrations, at P = 0.05.

The P^Kvalues for all MLAEP latency or amplitude indices in the extended groups were less than for corresponding concentrations of desflurane and propofol (table 1), although not all differences achieved statistical significance at P = 0.05. Of the latency and amplitude indices, Lat^Nbhad the highest prediction performance: P^K= 0.86 ± 0.06 during desflurane and 0.88 ± 0.06 during propofol. The P^Kvalues for Pwr^40-Hzcompared with P^Kvalues for Lat^Nbyielded P = 0.16 during desflurane anesthesia, P = 0.14 during propofol anesthesia, and pooled P = 0.10 for groups combined. The P^Kvalues for Pwr^40-Hzcompared with those for the next best-performing latency and amplitude index, Lat^Pb, yielded pooled P < 0.05.

Combining the best latency index, Lat^Nb, and amplitude index, Amp^NaPaNb, into a composite single-number index, Lat^NbAmp^NaPaNb, improved prediction; P^K= 0.95 ± 0.03 during desflurane and 0.93 ± 0.04 during propofol.

For the bracketed group, the P^Kvalues for concentration and for all MLAEP indices decreased compared with their corresponding values in the combined groups. (Like other measures of correlation, P^Kis sensitive to data range. By deleting Resp^next, the data range decreased for all indices, and thus all P^Kvalues would also be expected to decrease. 27) The P^Kvalue for desflurane was 0.82 ± 0.09 and for propofol was 0.88 ± 0.06. The corresponding P^Kvalue for Pwr^{40-Hz38 ms}was 0.91 ± 0.06 and for Pwr^{40-Hz50 ms}was 0.92 ± 0.05. The P^Kvalues for these Pwr^40-Hzindices compared with P^Kvalues for concentration were not significantly different, yielding P = 0.44 during desflurane anesthesia, P = 0.44 during propofol anesthesia, and pooled P = 0.50 for groups combined. For Lat^Nb, the corresponding P^Kvalues were 0.81 ± 0.08 and 0.81 ± 08.

Table 2shows the logistic regression analysis results for concentration, Pwr^{40-Hz38 ms}, Pwr^{40-Hz50 ms}, and Lat^Nb, in terms of the values of Indicator⁵⁰, Indicator⁹⁵, and β slope 37for the extended groups. The Indicator⁵⁰value, analogous to MAC^Awake, for concentration of desflurane was 2.45 ± 0.11 vol% and of propofol was 2.55 ± 0.10 μg/ml, consistent with previously published results. 18The Indicator⁵⁰value for Pwr^{40-Hz38 ms}during desflurane was −3.36 ± 0.11 log¹⁰(μV²/Hz) and during propofol was −3.28 ± 0.09 log¹⁰(μV²/Hz). The Indicator⁹⁵value, analogous to MAC^Awake05, for Pwr^{40-Hz38 ms}during desflurane was −4.02 ± 0.25 log¹⁰(μV²/Hz) and during propofol was −3.80 ± 0.19 log¹⁰(μV²/Hz). Consistent with the P^Kvalues in table 1, during desflurane anesthesia, the slope for Pwr^{40-Hz38 ms}was steeper than that for Pwr^{40-Hz50 ms}; during propofol anesthesia, the slope for Pwr^{40-Hz50 ms}was steeper than for Pwr^40-Hz38-ms.

Figure 6shows logistic regression curves for anesthetic concentration, Pwr^{40-Hz38 ms}, and Lat^Nbduring desflurane and propofol. The curves graphically display results shown in table 2. 37Although the prediction performance of an indicator is shown by the steepness of the slope of the curve, because of the assumptions used for scaling indices and determining comparable value ranges, we did not attempt to compare differences between the curves.

As calculated from Indicator⁵⁰and Indicator⁹⁵in table 2, for Pwr^{40-Hz38 ms}a change of nonresponsiveness from 50 to 95% was associated with a change of 0.66 log¹⁰(μV²/Hz) during desflurane (a 20% change from the Indicator⁵⁰value) and 0.52 log¹⁰(μV²/Hz) during propofol (a 16% change).

Although many MLAEP features have been proposed as indicators of wakeful responsiveness, few comparisons of the predictive performances of these indicators have been made. Such comparisons constitute one of the primary contributions of the present work, and P^Kallows such comparisons. 27,28We found that the best-performing indicators were the ∼40-Hz power (Pwr^40-Hz), a composite Nb latency and NaPaNb amplitude index (Lat^NbAmp^NaPaNb), and Nb latency (Lat^Nb).

After finding good predictive performance of ∼40-Hz power measured by the JTFA spectrogram, we confirmed that a more conventional FFT analysis of ∼40-Hz power of the MLAEP provided similar high performance.

We found that 40–45 Hz was the range of the optimal frequency of the MLAEP power for predicting response to command. This finding confirms previous reports associating ∼40-Hz activity and wakefulness. 4,26,39–48The optimal latency for measuring the MLAEP power was 38 ms during desflurane and 50 ms during propofol. These latency values were obtained by inspecting the topographic surfaces of P^Kvalues (fig. 5). We did not attempt to calculate the confidence limits of these values. Inspection and comparison of individual power density spectra suggest that the difference in these latency values would not be statistically significant.

Figure 6provides an example of specific ∼40-Hz activity values that could be used to guide the administration of anesthesia.

Of the latency and amplitude indices, Lat^Nbhad the highest prediction performance, validating previous reports about the efficacy of this index. 1,2,5,22,49The Lat^Nbdid not predict as well as anesthetic concentration, although the differences were not statistically significant. In contrast, Tooley et al.  49reported that Nb latency predicted eyelash response better than concentration of propofol.

Combining Lat^Nband Amp^NaPaNbinto a new single-number index, Lat^NbAmp^NaPaNb, improved predictive performance slightly. To create the formula for calculating Lat^NbAmp^NaPaNb, we calculated P^Kvalues for alternative combinations of Lat^Nband Amp^NaPaNband found that the best performance was by a formula summing the increase in latency (in microseconds) of Lat^Nband decrease in amplitude (in microvolts) of Amp^NaPaNb, in which amplitude was normalized by a factor of 10 so that latency and amplitude had equally weighted changes over the concentration ranges.

It would be of interest to compare the 40-Hz auditory steady-state response (ASSR) with the ∼40-Hz power of the MLAEP. Although Plourde and Villemure 50compared the ASSR with latency and amplitude indices of the MLAEP, the ∼40-Hz activity of the MLAEP was not reported. Compared with the ∼40-Hz power of the MLAEP, the ASSR and the coherent frequency may have advantages as predictors because, for an individual subject, the optimum stimulus frequency for evoking the response could be determined while a subject was awake, and the magnitude of that optimum response used to normalize the values during anesthesia. 24–26,39,40In contrast, MLAEP is measured using a fixed, relatively slow stimulus rate, 9.3 Hz for example, which may not be optimal for the inherent response of all individuals. Individualization for response frequency may be important because, although the optimum frequency of auditory stimuli of a group of 16 awake subjects studied by ASSR was 40 Hz, the range was 20–50 Hz. 51Similarly, the range of coherent frequency for a group of 10 awake subjects was 34–44 Hz. 40After individualizing the ASSR stimulus, Plourde et al.  25found that the predictive value for loss of consciousness by ASSR was the same as that by isoflurane concentration.

We created two groups to evaluate predictive performances, the extended group and the bracketed group. The extended groups consisted of one response (Resp) and two nonresponse (NoResp and NoResp^next) MLAEPs, reflecting our interest in determining MLAEP indices that could identify patients emerging from deeper anesthetic levels to wakefulness. Although we created the extended group to provide a group for analysis that contained a complete set of waveforms for each volunteer and a reduced number of artifactual waveforms, even some waveforms in the extended groups appeared irregular and of marginally acceptable quality, as seen in figures 2 and 3.

We created the bracketed groups to enhance our ability to evaluate whether MLAEP indices could predict better than concentration, which would suggest a reflection of basic neurophysiologic mechanisms related to wakefulness. Bracketed groups were created by deleting the NoResp^nextMLAEPs from the extended groups, decreasing the range of index values, and, as expected, 27decreasing the P^Kvalues of MLAEP and concentration indices. Although P^Kvalues of ∼40-Hz power exceeded those of anesthetic concentrations, the differences were not statistically significant. If we had found significantly higher P^Kvalues for ∼40-Hz power, this would have suggested that prediction performance by ∼40-Hz power may not simply reflect concentration, and that ∼40-Hz power may reflect basic neurophysiologic mechanisms related to wakeful response.

If ∼40-Hz activity reflects mechanisms related to wakefulness, what might those mechanisms be? The brain generates gamma oscillations, also called ∼40-Hz oscillations, although the oscillations may range from 20–90 Hz. 42Gamma oscillations arise from the thalamocortical system and are modulated by the intralaminar nuclei of the thalamus, which are in turn influenced by the midbrain reticular activating system. 48,52Although gamma oscillations may occur during anesthesia and non–rapid eye movement sleep, gamma oscillations markedly increase during rapid eye movement sleep, arousal, and awakening, occurring more frequently, increasing in amplitude, and becoming synchronous over widespread areas of the cerebral cortex. 41–47,53In awake humans, auditory stimuli reset the synchronicity of gamma oscillations, producing coherent oscillations over the cortex. 41,43,44Further investigation might reveal whether the ∼40-Hz activity we measured from extracranial scalp electrodes is related to the gamma oscillations.

Although we speculate that ∼40-Hz activity may reflect mechanisms related to wakeful response, ∼40-Hz activity may not reflect the mechanism underlying responsiveness, because for three volunteers the ∼40-Hz power of NoResp exceeded that of Resp. However, as discussed subsequently, a subject may not respond even though wakeful, and such a lack of response could help explain the reversed change in ∼40-Hz power for these three volunteers. Also against the possibility that ∼40-Hz power reflects the mechanism underlying wakefulness is the observation by Steriade et al.  46that ∼40-Hz synchronization of cortical electroencephalographic activity of awake cats disappeared and reappeared without a detectable reason, although wakefulness appeared to be uninterrupted.

We chose hand squeezing to demonstrate a volunteer's ability for cognitive processing and because failure to appropriately respond indicates probable suppression of memory formation. 7–16We did not distinguish between a brief and a sustained duration of wakefulness, although this distinction may better indicate the potential for memory formation. 14,15Occasionally, a person may be wakeful and yet not respond to command, 2,54and this failure to respond might explain some cases in which MLAEP indices showed little or no change between Resp and NoResp (i.e. , the NoResp should then have been labeled a Resp). We did not choose eye opening on command as the endpoint of wakefulness 17because eye opening may be an orienting or startle-like response instead of one that indicates cognitive processing.

There were other shortcomings in our methods that also could be avoided in future studies. Replicate MLAEPs (which increase confidence in the waveforms) were infrequently recorded because of time restraints. We studied volunteers during induction of anesthesia rather than emergence from anesthesia. If MLAEPs during emergence differ from those during induction (i.e. , hysteresis), our findings might not hold for emergence. Other reports suggest that hysteresis might not be a problem: Nb latency provides similar results during repeated transitions from consciousness to unconsciousness and back again. 5Finally, we studied volunteers who did not receive noxious stimulation, such as surgical stimulation. Surgical stimulation can alter MLAEP waveforms, causing increased amplitude of the peaks. 55 

Although MLAEP indices did not predict significantly better than anesthetic concentration, electroencephalographic indices that performed well, such as ∼40-Hz activity or bispectral index, 11,32could offer advantages over anesthetic concentration. During clinical anesthesia, the usefulness of anesthetic concentration as a predictor is confined to the inhaled anesthetics, in which end-tidal concentrations can be measured on line. If intravenous agents contribute significantly to production of anesthesia, measurement of the concentration of inhaled agents does not suffice as an adequate predictor. Additional limitations result from changes in inhaled and intravenous agent delivery after which pharmacokinetics limit the capacity to estimate cerebral anesthetic concentrations. Thus, an electrophysiologic index that predicts wakefulness independent of these variables would be valuable, even though it does not necessarily predict significantly better than steady-state anesthetic concentration. Of note, at the present, the determination of MLAEP requires more technical expertise and effort than electroencephalographic (or bispectral index) monitoring.

In summary, of the MLAEP indices we studied, ∼40-Hz power of the MLAEP frequency spectrum provided the highest prediction performance of wakeful responsiveness in volunteers receiving desflurane and propofol. The composite Lat^NbAmp^NaPaNbindices provided the next best performances, and Lat^Nbthe third best. The ∼40-Hz power is an objective measure that can be obtained from readily available instruments and may find clinical application for predicting wakeful responsiveness.

The authors thank H. L. Bennett, Ph.D., for advice about data acquisition and M. H. Valizadeh, M.S., for help with data analysis.

To appropriately apply logistic regression analysis, criteria about distribution of data need to be satisfied; if the criteria are not met, data may be transformed by nonlinear rescaling. To examine the appropriateness of the scaling of MLAEP indices, we compared the data points of each index with their corresponding logarithmically scaled concentration data points. We did so because logarithmically scaled concentration data meet the criteria and provide the best fit for constructing concentration–response logistic regression curves. 38Scaling of MLAEP indices were compared with log¹⁰(concentration) by visually examining x–y scatter plots for nonlinear trends and verifying improvements in indicator scale transformations by increases in correlation coefficients (r) found by comparing the transformed indicators with log¹⁰(concentration). In this way, acceptable scaling was obtained with log¹⁰(Pwr^{40-Hz38 ms}), log¹⁰(Pwr^{40-Hz50 ms}), Lat^Nb, and Lat^NbAmp^NaPaNb.