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Perioperative Medicine  |   May 2009
Influence of Auditory Stimulation Rates on Evoked Potentials during General Anesthesia: Relation between the Transient Auditory Middle-latency Response and the 40-Hz Auditory Steady State Response
Author Affiliations & Notes
  • Richard R. McNeer, M.D., Ph.D.
    *
  • Jorge Bohórquez, Ph.D.
  • Özcan Özdamar, Ph.D.
  • *Assistant Professor, Department of Anesthesiology, University of Miami School of Medicine, Miami, Florida; Department of Biomedical Engineering, University of Miami, Coral Gables, Florida. †Research Assistant Professor, Department of Biomedical Engineering, University of Miami, Coral Gables, Florida. ‡Professor and Chair, Department of Biomedical Engineering, University of Miami, Coral Gables, Florida; Departments of Otolaryngology, Pediatrics and Neuroscience, University of Miami School of Medicine, Miami, Florida.
Article Information
Perioperative Medicine / Central and Peripheral Nervous Systems
Perioperative Medicine   |   May 2009
Influence of Auditory Stimulation Rates on Evoked Potentials during General Anesthesia: Relation between the Transient Auditory Middle-latency Response and the 40-Hz Auditory Steady State Response
Anesthesiology 5 2009, Vol.110, 1026-1035. doi:10.1097/ALN.0b013e31819dad6f
Anesthesiology 5 2009, Vol.110, 1026-1035. doi:10.1097/ALN.0b013e31819dad6f
AUDITORY evoked potentials consist of electrical activity in the brain that is linked to (or evoked from) auditory stimuli. Two types of potentials or responses have been studied in relation to anesthetic effect: (1) the auditory middle-latency response and (2) the 40-Hz auditory steady state response (ASSR). (1) The auditory middle-latency response—hereafter referred to as transient  —is usually recorded with auditory stimulation rates of 10-Hz or less1,2 and has amplitude and phase components that vary with time and eventually disappear. It has been shown that the transient is affected in a consistent, concentration-dependent manner by most anesthetics.3 Various waveform peaks in the transient are correlated to responsiveness or memory formation4–9 and predict the wakeful response during anesthesia.10 (2) The 40-Hz ASSR is an approximately sinusoid waveform with phase and amplitude components that remain nearly constant over time, and is obtained when auditory stimuli are presented at 40 Hz—a rate sufficiently high so that overlapping of individual transients occurs. Anesthetic attenuation of the 40-Hz ASSR amplitude has been shown to correlate with depth of anesthesia produced by most anesthetics.11–14 
It is suggested that the 40-Hz ASSR and the transient share the same generators in the subcortical and cortical structures of the brain,2,15,16 and that the 40-Hz ASSR is simply a composite or linear superimposition of the transient waveform.17 In support of this, deliberate superposition or convolution  of the transient waveform has been shown to reasonably predict the amplitude of the recorded 40-Hz ASSR when obtained in awake, nonmedicated subjects.18–20 However, when recorded in anesthetized subjects, convolution of the transient consistently overestimates the amplitude of the recorded 40-Hz ASSR.21 This prediction discrepancy  during anesthesia has lead to several hypotheses evoking a stimulation rate–dependent property of anesthetic action21 or an adaptation of the auditory apparatus.22 There are also source localization (magnetoencephalographic) data23 that suggest the existence of separate neurogenerators for the transient and 40-Hz ASSR.
Historically, the transient was recorded at auditory stimulation rates limited to 10 Hz or less—significantly lower than 40 Hz. This limitation existed because in the brain, at higher stimulation rates, each individual evoked transient overlaps with the next, generating a complicated convolved response. Traditional time-domain averaging to extract the evoked signal above electroencephalographic background from the convolved response can be problematic or ineffective. Recently, a method known as continuous-loop averaging deconvolution  (CLAD) was described that can be used to extract or deconvolve  evoked transients from convolved responses.24,25 With CLAD, we recently recorded transients using 40-Hz stimulation in awake subjects,26 and henceforth, we will refer to this evoked response as the 40-Hz transient  to distinguish it from transients evoked at lower, more traditional stimulation rates (e.g.  , 5-Hz transient).
In this study, we investigated the basis of the prediction discrepancy. We simultaneously recorded the 40-Hz ASSR, 5-Hz transient, and 40-Hz transient in surgical patients undergoing general anesthesia. We then convolved the 5- and 40-Hz transients to obtain “predicted” 40-Hz ASSRs. Phasor analysis and statistical tests were used to compare the predicted and recorded waveforms. The results reveal the basis of the prediction discrepancy and strongly support the assertion that the transient and 40-Hz ASSR are generated by the same underlying neuronal structures.
Materials and Methods
Patient Recruitment
Approval for this study was obtained from the institutional review boards at the University of Miami and Jackson Memorial Hospital (Human Subject Research Office, Miami, Florida). With informed/written consent, we enrolled healthy subjects, with American Society of Anesthesiologists physical status I or II, scheduled to have either elective inguinal hernia repair or laparoscopic cholecystectomy. Subjects were excluded with a history positive for seizures or hearing impairment.
Study Design
Patients were premedicated with midazolam (2 mg) and fentanyl (100 μg) and were induced with propofol (1–2 mg/kg) and either vecuronium (0.1 mg/kg) or succinylcholine (0.5–1 mg/kg) followed by trachea intubation with an endotracheal tube. A combination of nitrous oxide and/or sevoflurane and intermittent boluses of fentanyl as needed was used to maintain general anesthesia. For all surgeries, anesthesiologists, who were not directly involved in the study and who were blinded to specific study details and outcome measures, were asked to follow standard of care in maintaining adequate anesthetic depth. Titration of anesthetic concentrations was accomplished, but was not limited to, monitoring of patient vital signs, expired concentration of inhalational anesthetic(s), ventilator parameters, and patient movement. Recording experiments (fig. 1) were initiated at least 20 min after induction and at least 5 min after establishment of constant expired concentrations of inhalational anesthetics. Each experiment consisted of three or more recording sets, and each set consisted of three interleaved rounds of 512 sweeps that used traditional, medium jitter, and isochronic auditory stimulation sequences (described in the following section) to generate the 5-Hz transient, 40-Hz transient, and 40-Hz ASSR, respectively. Summarizing (fig. 1), (1) three interleaved recording windows (each 512 sweeps in length and corresponding to each type of evoked response) formed a set, (2) three or more sets were considered to constitute an experiment, and (3) each experiment corresponded to a single constant level of anesthetic. Because during a typical surgery several different anesthetic concentrations occurred because of changing anesthetic requirements, data from any single patient often consisted of several different experiments and expired anesthetic concentrations (table 1).
Fig. 1. Schematic of study design. At least 20 min after induction of anesthesia (Ind.) and establishment of a steady state level of expired concentration of nitrous oxide and/or sevoflurane, the first recording experiment (Exp. #1) was begun. The recording continued until a change in anesthetic concentration occurred. Each subsequent experiment (  e.g.  , Exp. #2) was begun at least 5 min after a new steady state anesthetic level was established. Each experiment consisted of three or more sets. Each set consisted of three interleaved recordings pertaining to the 5-Hz conventional (conv.) isochronic, 40-Hz jittered continuous-loop averaging deconvolution (CLAD), and 40-Hz steady state (SS) isochronic auditory click stimulating sequences, respectively. Emerg. = emergence. 
Fig. 1. Schematic of study design. At least 20 min after induction of anesthesia (Ind.) and establishment of a steady state level of expired concentration of nitrous oxide and/or sevoflurane, the first recording experiment (Exp. #1) was begun. The recording continued until a change in anesthetic concentration occurred. Each subsequent experiment (  e.g.  , Exp. #2) was begun at least 5 min after a new steady state anesthetic level was established. Each experiment consisted of three or more sets. Each set consisted of three interleaved recordings pertaining to the 5-Hz conventional (conv.) isochronic, 40-Hz jittered continuous-loop averaging deconvolution (CLAD), and 40-Hz steady state (SS) isochronic auditory click stimulating sequences, respectively. Emerg. = emergence. 
Fig. 1. Schematic of study design. At least 20 min after induction of anesthesia (Ind.) and establishment of a steady state level of expired concentration of nitrous oxide and/or sevoflurane, the first recording experiment (Exp. #1) was begun. The recording continued until a change in anesthetic concentration occurred. Each subsequent experiment (  e.g.  , Exp. #2) was begun at least 5 min after a new steady state anesthetic level was established. Each experiment consisted of three or more sets. Each set consisted of three interleaved recordings pertaining to the 5-Hz conventional (conv.) isochronic, 40-Hz jittered continuous-loop averaging deconvolution (CLAD), and 40-Hz steady state (SS) isochronic auditory click stimulating sequences, respectively. Emerg. = emergence. 
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Table 1. Experimental Recording Conditions and Subject Demographics 
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Table 1. Experimental Recording Conditions and Subject Demographics 
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Auditory Stimulus Sequence Description
Auditory stimuli consisted of rarefaction clicks that were presented monaurally to the right ear using an insert earphone (ER-3A Ethmotic Research, Elk Grove Village, IL). A stimulus sound level of 82 peak dB sound pressure level was calibrated in a 2-ml acoustic coupler using a precision sound level meter (Quest Model 1800; Quest Technologies, Oconomowoc, WI). A full description of auditory stimulus generation and evoked response recording using CLAD can be found elsewhere.27 Briefly, three stimulus sequences were used in this study and are shown schematically (fig. 1). Two sequences consisted of clicks presented with no jitter at constant (isochronic) rates of 4.9 and 39.1 Hz. These sequences were used to record the 5-Hz transient and 40-Hz ASSR, respectively. To generate the 40-Hz transient, a 39.1-Hz sequence of medium-jittered clicks was used.27 Jittering is a requirement of CLAD so that the deconvolution matrix has a unique solution.24 The SmartEP system (Intelligent Hearing Systems, Miami, FL) was used to generate all sequences.
Recording Setup and Conditions
The electroencephalographic recordings were obtained using the SmartEP system. Disposable electrodes (Vermed, Bellows Falls, VT) were applied to FPz (positive), the right mastoid (negative), and the forehead (ground). Signals were amplified (gain: 100,000), band-pass filtered (10–1,500 Hz, 6 dB/oct), and digitized at 200-μs sampling time, with each sweep consisting of 1,024 data points with a duration of 204.8 ms. Artifact rejection was set at 30 μV. The ASSRs and 5-Hz transients were calculated by using traditional nonoverlapping 204.8-ms sweep averaging. The 40-Hz transients were calculated by averaging the convolved recordings for each jittered sequence, and then deconvolving using CLAD. Any low-frequency noise remaining after analog filtering, averaging, and deconvolution was removed using a spectral digital high-pass filter cutting frequencies of 15 Hz and below.
Convolution of Recorded Transients to Generate Predicted 40-Hz ASSRs
Five- and 40-Hz transients were linearly superimposed (convolved) to generate predicted 40-Hz ASSRs—5-Hz predicted ASSR  and 40-Hz predicted ASSR  , respectively. The method used is similar to those described elsewhere.18,21,28 Initially, a transient (204.8 ms, 1,024 points) was demarcated into eight equal segments of 25.6 ms or 128 points. The demarcated transient was circularly time shifted 25.6 ms (one segment) to generate a second. The time shifting was repeated for the second recording, and so on until eight recordings were obtained that could be wrapped around to form a continuous loop. These eight recordings were then convolved (summed linearly) to generate a predicted ASSR. Because the convolution process can generate small artifactual peaks, the predicted ASSRs were digitally denoised (comb filtered) so that only the main frequency (f0= 39.06 Hz) and the first two harmonics (f1= 78.12 Hz and f2= 117.18 Hz) remained (refer to the next section). For consistency, this denoising was also applied to the recorded ASSRs (fig. 2).
Fig. 2. Time and frequency domain signal treatment. (  A  ) The recorded 40-Hz auditory steady state response (ASSR) was denoised. (  B  ) Fourier transformation (FFT) of the waveforms before and after denoising were performed to illustrate the effect of denoising in the frequency domain. The Fourier theorem can be used to show that most signal energy is contained in the 40-, 80-, and 120-Hz harmonic components (  black bars  ) . Denoising removes the remaining noise frequencies harmonics (  gray bars  ). (  C  ) The recorded 5-Hz transient waveform was convolved as described in the text to generated a predicted ASSR, which was denoised as in  A  . (  D  ) FFT of these predicted waveforms was obtained. Note that phase information is not represented in this FFT, but both phase and amplitude data are important and were used in the phasor and statistical analyses outlined in the text and illustrated in  figure 3. (  E  and  F  ) The same procedure was applied to the 40-Hz transient waveform. 
Fig. 2. Time and frequency domain signal treatment. (  A  ) The recorded 40-Hz auditory steady state response (ASSR) was denoised. (  B  ) Fourier transformation (FFT) of the waveforms before and after denoising were performed to illustrate the effect of denoising in the frequency domain. The Fourier theorem can be used to show that most signal energy is contained in the 40-, 80-, and 120-Hz harmonic components (  black bars  ) . Denoising removes the remaining noise frequencies harmonics (  gray bars  ). (  C  ) The recorded 5-Hz transient waveform was convolved as described in the text to generated a predicted ASSR, which was denoised as in  A  . (  D  ) FFT of these predicted waveforms was obtained. Note that phase information is not represented in this FFT, but both phase and amplitude data are important and were used in the phasor and statistical analyses outlined in the text and illustrated in  figure 3. (  E  and  F  ) The same procedure was applied to the 40-Hz transient waveform. 
Fig. 2. Time and frequency domain signal treatment. (  A  ) The recorded 40-Hz auditory steady state response (ASSR) was denoised. (  B  ) Fourier transformation (FFT) of the waveforms before and after denoising were performed to illustrate the effect of denoising in the frequency domain. The Fourier theorem can be used to show that most signal energy is contained in the 40-, 80-, and 120-Hz harmonic components (  black bars  ) . Denoising removes the remaining noise frequencies harmonics (  gray bars  ). (  C  ) The recorded 5-Hz transient waveform was convolved as described in the text to generated a predicted ASSR, which was denoised as in  A  . (  D  ) FFT of these predicted waveforms was obtained. Note that phase information is not represented in this FFT, but both phase and amplitude data are important and were used in the phasor and statistical analyses outlined in the text and illustrated in  figure 3. (  E  and  F  ) The same procedure was applied to the 40-Hz transient waveform. 
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Phasor Analysis
Phasor analysis29 was used to decompose recorded and predicted ASSR waveforms. For this study, we used the first three harmonics (40, 80, and 120 Hz), which we have found to contain most of the signal energy (figs. 2A and B). Each harmonic, a pure cosine wave, is obtained as a single beam of the Fourier decomposition. The cosine wave is defined by the real and imaginary components of a complex number. These components can be represented as phasors (vectors) on a phasor diagram (fig. 3A). As such, each ASSR is describable as a six-dimensional array  , consisting of a real and imaginary number for each of the three harmonics (40, 80, and 120 Hz). Because it is not easy to graphically represent six-dimensional arrays, for the purpose of data presentation, each array is depicted as three projections corresponding to the three harmonics (fig. 3A). Phasor arrays are amenable to algebraic manipulation and statistical comparison testing (fig. 3B).
Fig. 3. Statistical analysis description. (  A  ) A difference phasor (  thin black vector  ) is calculated for each frequency component (  e.g.  , 40-Hz) by subtracting the recorded (  thick gray  ) and predicted (  black  )phasors containing the origin. The difference phasor represents the difference between the predicted and recorded signals in terms of amplitude and phase. The phasor analysis presented here for illustration pertains to data from an individual recording experiment from the current study. (  B  )The 40-Hz difference phasor from  A  (  circumscribed asterisk in the left lower quadrant  ) is plotted with the difference phasors (  asterisks  )from all recording experiments. The Hotelling  T  2test is used to determine whether the average difference phasor (  single vector containing the origin  ) is significantly different from zero. Ellipses centered around the phasor tip are calculated that correspond to specific  P  values. A difference phasor is statistically different from the origin if the ellipse does not contain the origin. The conclusion for this particular example is that the recorded and predicted phasors (and the corresponding time-domain waveforms) are statistically different from each other (  P  < 0.01). Note that ellipse size is inversely proportional to  P  value. Here for example, for  P  = 0.001, the corresponding ellipse contains the origin. ASSR = auditory steady state response. 
Fig. 3. Statistical analysis description. (  A  ) A difference phasor (  thin black vector  ) is calculated for each frequency component (  e.g.  , 40-Hz) by subtracting the recorded (  thick gray  ) and predicted (  black  )phasors containing the origin. The difference phasor represents the difference between the predicted and recorded signals in terms of amplitude and phase. The phasor analysis presented here for illustration pertains to data from an individual recording experiment from the current study. (  B  )The 40-Hz difference phasor from  A  (  circumscribed asterisk in the left lower quadrant  ) is plotted with the difference phasors (  asterisks  )from all recording experiments. The Hotelling  T  2test is used to determine whether the average difference phasor (  single vector containing the origin  ) is significantly different from zero. Ellipses centered around the phasor tip are calculated that correspond to specific  P  values. A difference phasor is statistically different from the origin if the ellipse does not contain the origin. The conclusion for this particular example is that the recorded and predicted phasors (and the corresponding time-domain waveforms) are statistically different from each other (  P  < 0.01). Note that ellipse size is inversely proportional to  P  value. Here for example, for  P  = 0.001, the corresponding ellipse contains the origin. ASSR = auditory steady state response. 
Fig. 3. Statistical analysis description. (  A  ) A difference phasor (  thin black vector  ) is calculated for each frequency component (  e.g.  , 40-Hz) by subtracting the recorded (  thick gray  ) and predicted (  black  )phasors containing the origin. The difference phasor represents the difference between the predicted and recorded signals in terms of amplitude and phase. The phasor analysis presented here for illustration pertains to data from an individual recording experiment from the current study. (  B  )The 40-Hz difference phasor from  A  (  circumscribed asterisk in the left lower quadrant  ) is plotted with the difference phasors (  asterisks  )from all recording experiments. The Hotelling  T  2test is used to determine whether the average difference phasor (  single vector containing the origin  ) is significantly different from zero. Ellipses centered around the phasor tip are calculated that correspond to specific  P  values. A difference phasor is statistically different from the origin if the ellipse does not contain the origin. The conclusion for this particular example is that the recorded and predicted phasors (and the corresponding time-domain waveforms) are statistically different from each other (  P  < 0.01). Note that ellipse size is inversely proportional to  P  value. Here for example, for  P  = 0.001, the corresponding ellipse contains the origin. ASSR = auditory steady state response. 
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Statistical Analysis
For each experiment we calculated a difference-phasor array  by subtracting the predicted from the recorded ASSR phasor arrays (fig. 3A). Our null hypothesis was as follows: The difference-phasor array is statistically different than zero, i.e.  , the origin (0, 0, 0, 0, 0, 0). Rejection of this null hypothesis would indicate that the predicted and recorded phasor arrays (and therefore the corresponding ASSR waveforms) are not statistically different from each other. We tested the null hypothesis by performing the Hotelling T  2test,30 a multivariate analog of the Student t  test. The T  2test gives the likelihood that a vector signal is greater than background residual noise. In our study, the vector signal is the grand-averaged difference-phasor array calculated from the difference-phasor arrays from each experiment (fig. 3B). With the T  2test, confidence limits are represented as ellipses centered at the grand-averaged difference-phasor array tips. If the origin is not contained in the ellipse, the difference phasor is considered to be significantly different than zero for a specified P  value. All phasor and statistical calculations were performed in MATLAB Release 13 (The Mathworks, Inc., Natick, MA). The T  2test was performed using a program available at .1
Results
Qualitative Effect of 5- and 40-Hz Stimulation Rates on Transient Responses
A total of 13 subjects (1 female) aged between 26 and 66 yr participated (table 1). As was done previously,31 in this article, the auditory brainstem and middle-latency responses are included in the presentation of transient response waveforms to allow voltage comparisons across recordings. Adequate brainstem responses were obtained for all subjects during recording confirming adequate delivery of auditory stimuli and effectively ruling out the presence of significant hearing impairment to the rarefaction clicks (fig. 4, first two columns). A total of 24 steady state experiments were conducted. The concentrations of anesthetic ranged from 0.7 to 2.0% ± nitrous oxide (42–70%), indicating that both intersubject and intrasubject differences in the anesthetic concentrations were required to maintain adequate anesthetic depth (table 1). Transient signals in the microvolt range were readily recorded in every experiment (fig. 4). For each experiment, peak V of the brainstem response was similar for 5- and 40-Hz transients. Qualitative differences in amplitudes and latencies of the 5- and 40-Hz transient components (middle-latency range) are apparent on visual inspection (fig. 4). The peak amplitudes of the 40-Hz transient components were generally more attenuated compared to those of the 5-Hz transient. In addition, in many of the 5-Hz transients, an early peak (approximately 20 ms) was also observed, and was rarely observed in the 40-Hz transients. These qualitative differences were more easily appreciated in the grand-averaged waveforms (fig. 4). An additional difference was the latency of the first peak after the brainstem response in the 40-Hz transient, which had a shorter latency than the comparable peak in the 5-Hz transient.
Fig. 4. Recorded transients and auditory steady state responses and predicted auditory steady state responses obtained for each of the 24 experiments. The grand average (Av) for each waveform type is shown in the  bottom row  . Cross-reference of patient information and anesthetic concentrations can be accomplished by concomitant study of this figure (see experiment numbers,  left  )and  table 1. Av = grand average. 
Fig. 4. Recorded transients and auditory steady state responses and predicted auditory steady state responses obtained for each of the 24 experiments. The grand average (Av) for each waveform type is shown in the  bottom row  . Cross-reference of patient information and anesthetic concentrations can be accomplished by concomitant study of this figure (see experiment numbers,  left  )and  table 1. Av = grand average. 
Fig. 4. Recorded transients and auditory steady state responses and predicted auditory steady state responses obtained for each of the 24 experiments. The grand average (Av) for each waveform type is shown in the  bottom row  . Cross-reference of patient information and anesthetic concentrations can be accomplished by concomitant study of this figure (see experiment numbers,  left  )and  table 1. Av = grand average. 
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Qualitative Comparison of Recorded and Predicted 40-Hz ASSRs
The 5-Hz predicted ASSRs (i.e.  , ASSRs predicted by the 5-Hz transient), the 40-Hz predicted ASSRs (i.e.  , ASSRs predicted by the 40-Hz transients), and the recorded ASSRs from each experiment (and grand averages) are shown alongside the 5- and 40-Hz transients (fig. 4). The 5-Hz predicted ASSR peak-to-peak amplitudes were generally larger than those of 40-Hz predicted ASSRs. In addition, the 40-Hz predicted ASSRs closely resembled the recorded ASSRs for each experiment. These qualitative findings were more easily appreciated in the grand-averaged predicted and recorded ASSRs (fig. 4, bottom waveforms). Of considerable note, regular oscillations seem to be present in the transient waveforms. Fourier analysis (data not shown) reveals these oscillations are centered around 20 Hz for both 5- and 40-Hz stimulation conditions; however, the power appears greater in the former.
Quantitative Comparison of Recorded and Predicted ASSR Waveforms
The complex numbers (real and imaginary) that describe the recorded and synthetic phasor arrays from each experiment (and grand averages) are presented in table 2. Five- and 40-Hz difference-phasor arrays were calculated from these data, and their projections are shown in figures 5A and B, respectively. Confidence intervals (P  < 0.05 and P  < 0.01) are represented by ellipses that surround the grand-averaged difference-phasor array projections. Referring to the 5-Hz difference-phasor array projections (fig. 5A), the origin is not contained in any of the ellipses (except for the ellipse (P  < 0.01) corresponding to the 120-Hz harmonic projection), indicating that the grand-averaged difference-phasor array is significantly different from zero. The null hypothesis as tested on the six-dimensional difference-phasor array is retained (T  2= 38.919, F = 5.076, P  = 0.003). However, referring to the 40-Hz difference-phasor array projections (fig. 5B), the origin is contained in all ellipses, indicating that this six-dimensional array is not significantly different from zero (T  2= 2.626, F = 0.343, P  = 0.905).
Table 2. Phasor Component Values Used in the Hotelling  T  2Analysis 
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Table 2. Phasor Component Values Used in the Hotelling  T  2Analysis 
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Fig. 5. Results of Hotelling  T  2analysis of difference-phasor arrays calculated from grand averaged recorded auditory steady state responses and predicted auditory steady state responses convolved from 5-Hz transient (  A  ) and 40-Hz transient (  B  ) waveforms. The  T  2, F, and  P  values are shown below each harmonic component projection. Results of the  T  2analysis of the six-dimensional difference-phasor arrays corresponding to the 5- and 40-Hz predicted responses are  T  2= 38.919, F = 5.076,  P  = 0.003 and  T  2= 2.626, F = 0.343,  P  = 0.905, respectively. 
Fig. 5. Results of Hotelling  T  2analysis of difference-phasor arrays calculated from grand averaged recorded auditory steady state responses and predicted auditory steady state responses convolved from 5-Hz transient (  A  ) and 40-Hz transient (  B  ) waveforms. The  T  2, F, and  P  values are shown below each harmonic component projection. Results of the  T  2analysis of the six-dimensional difference-phasor arrays corresponding to the 5- and 40-Hz predicted responses are  T  2= 38.919, F = 5.076,  P  = 0.003 and  T  2= 2.626, F = 0.343,  P  = 0.905, respectively. 
Fig. 5. Results of Hotelling  T  2analysis of difference-phasor arrays calculated from grand averaged recorded auditory steady state responses and predicted auditory steady state responses convolved from 5-Hz transient (  A  ) and 40-Hz transient (  B  ) waveforms. The  T  2, F, and  P  values are shown below each harmonic component projection. Results of the  T  2analysis of the six-dimensional difference-phasor arrays corresponding to the 5- and 40-Hz predicted responses are  T  2= 38.919, F = 5.076,  P  = 0.003 and  T  2= 2.626, F = 0.343,  P  = 0.905, respectively. 
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Determination of Transient Component Contribution to the 40-Hz ASSR Waveform
Based on the observed qualitative differences between the 5- and 40-Hz transient waveforms, we set out to estimate the contributions of the transient components to the final ASSR waveforms (figs. 6 and 7), similar to what was done previously.26 The recorded grand-averaged 5- and 40-Hz transients are shown in figures 6 and 7, respectively, with tentative labeling of component waveforms (e.g.  , Px, Ny, Py). The transient waveforms were altered to generate various curtailed waveforms (figs. 6A and 7A). Each curtailed waveform was convolved to generate a predicted ASSR (figs. 6B and 7B, solid traces). Finally, each predicted ASSR was converted to its 40-Hz harmonic phasor. The phasors were arranged tip to end in order of increasing curtailed waveform length (figs. 6C and 7C). Referring to figure 6B, none of the 5-Hz predicted ASSRs (solid traces) seems to visually resemble the recorded ASSR (dashed traces). However, in figure 7B, curtailed waveforms (b–d) yield predicted ASSRs that visually resemble the recorded ASSR. The phasor diagram (fig. 7C) shows that the curtailed phasor (c) resides closest to the recorded ASSR phasor—about as close as the grand-averaged (whole) ASSR phasor. These data suggest that it is the early components of the transient response that contribute the most to the generation of the ASSR waveform.
Fig. 6. Prediction of 40-Hz auditory steady state response (ASSR) using selected portions of the 5-Hz transient grand average waveform. (  A  ) Five-Hz grand averaged transient from  figure 4with peak labels tentatively assigned and (  B  ) predicted (  dashed  )and recorded (  solid  )40-Hz ASSR. The whole 5-Hz transient waveform and portions thereof (labeled  a    d  )were convolved to generate predicted waveforms. (  C  ) Phasor diagrams showing the corresponding and similarly labeled predicted (  solid  ,  bold  ) and recorded (  dashed  ) vectors. Avg = grand average. 
Fig. 6. Prediction of 40-Hz auditory steady state response (ASSR) using selected portions of the 5-Hz transient grand average waveform. (  A  ) Five-Hz grand averaged transient from  figure 4with peak labels tentatively assigned and (  B  ) predicted (  dashed  )and recorded (  solid  )40-Hz ASSR. The whole 5-Hz transient waveform and portions thereof (labeled  a  –  d  )were convolved to generate predicted waveforms. (  C  ) Phasor diagrams showing the corresponding and similarly labeled predicted (  solid  ,  bold  ) and recorded (  dashed  ) vectors. Avg = grand average. 
Fig. 6. Prediction of 40-Hz auditory steady state response (ASSR) using selected portions of the 5-Hz transient grand average waveform. (  A  ) Five-Hz grand averaged transient from  figure 4with peak labels tentatively assigned and (  B  ) predicted (  dashed  )and recorded (  solid  )40-Hz ASSR. The whole 5-Hz transient waveform and portions thereof (labeled  a    d  )were convolved to generate predicted waveforms. (  C  ) Phasor diagrams showing the corresponding and similarly labeled predicted (  solid  ,  bold  ) and recorded (  dashed  ) vectors. Avg = grand average. 
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Fig. 7. Same as  figure 6except that the predicted 40-Hz auditory steady state response is instead derived from portions of the 40-Hz transient grand average waveform. ASSR = auditory steady state response. Avg = grand average. 
Fig. 7. Same as  figure 6except that the predicted 40-Hz auditory steady state response is instead derived from portions of the 40-Hz transient grand average waveform. ASSR = auditory steady state response. Avg = grand average. 
Fig. 7. Same as  figure 6except that the predicted 40-Hz auditory steady state response is instead derived from portions of the 40-Hz transient grand average waveform. ASSR = auditory steady state response. Avg = grand average. 
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Discussion
The current study is the first to address the prediction discrepancy by using the 40-Hz transient response to predict the 40-Hz ASSR waveform during general anesthesia. The major finding is that there was no statistical difference between the predicted ASSRs (obtained after convolving the 40-Hz transient) and the recorded ASSRs. This result strongly suggests that the transient response and ASSR are generated by the same underlying neuronal structures. There are conflicting data in the literature regarding the relation between ASSR and transient responses in humans. In support of a common neurogenesis, numerous studies have shown a close correspondence of superimposed transient (electrical) responses and ASSR.17–19,32,33 However, evidence contrary to these results comes from magnetoencephalographic human studies,23,34 in which the components of the transient field were shown to be tonotopically distinguishable from the ASSR (field), and from animal studies.35 The reason for these conflicting data may depend on differences in the methodologies and analyses used in those studies to address the question. At the outset of the current study, our concern was that if we were to find a poor agreement between predicted and recorded ASSRs (i.e.  , corroboration of the prediction discrepancy), it would be difficult or impossible to dismiss differences in the recording conditions used to obtain transient and steady state waveforms as confounding factors. Hence, we used interleaving recording schedules, only recorded during steady state anesthetic concentrations and averaged over multiple recording epochs. To the best of our knowledge, the only difference in recording conditions was between the jittered stimulation sequence used to obtain the 40-Hz transient and the isochronic stimulation sequence used to obtain the ASSR. We were relieved after our initial qualitative, time-domain results showed that there seemed to be a strong likeness of the predicted and recorded ASSR waveforms. We subsequently wanted to dismiss this finding as due to chance by performing quantitative, frequency domain statistical analysis. We adapted the Hotelling T  2test to develop a statistical method to test whether the difference-phasor arrays derived from predicted and recorded ASSR waveforms were statistically greater than zero (e.g.  , an indication that the predicted and recorded waveforms were different). This would seem to be the first use of such a test in this context. The statistical results allow us to state with a high degree of certainty that the differences between predicted and recorded ASSRs are not statistically significant and, by inference, that the 40-Hz ASSR is a composite (or epiphenomenon) of the transient waveform.
The underlying explanation for the prediction discrepancy is that the morphology of the transient response varies with the rate of auditory stimulation during general anesthesia, and previous studies that reported a prediction discrepancy used 5- or 10-Hz (not 40-Hz) transient waveforms to predict the 40-Hz ASSR. For the purposes of reporting the differences between 5- and 40-Hz transient waveforms, we elected to give tentative labels to the middle latency components of the 40-Hz transient (fig. 7A) and the first positive peak after peak V of the 5-Hz transient (fig. 6A). As such, the main differences between the 5- and 40-Hz transient responses obtained in anesthetized subjects involve the early middle-latency peaks from 15 to 60 ms: (1) There is an additional peak (at approximately 20 ms), Px, that is only observed in 5-Hz transient recordings. (2) In 40-Hz transient recordings, a peak, Pyis present that has a shorter latency than Pain 5-Hz transient recordings. (3) The middle-latency component amplitudes in the 40-Hz transient are generally smaller than those in the 5-Hz transient. When selected portions of the 40-Hz transient are time shifted and summed, it seems that mainly the early peaks V (of the brainstem response), Ny, and Pycontribute to the generation of the steady state waveform (fig. 7). If Nyand Pycorrespond to Naand Pa, this finding is consistent with suggestions17 and evidence15 from others that it is these early peaks that lead to the ASSR waveform. It also suggests that the neurogenerators shared by transient response and ASSR are the lateral lemniscus (V), and/or mesencephalic structures including the inferior colliculus (Na) and the primary auditory cortex (Pa). It would be premature to report on how the peaks in the 5- and 40-Hz transients relate definitively. Our study was not designed to elucidate the anesthetic dose dependency of component latencies and amplitudes; we only analyzed recordings obtained during constant expired concentrations of anesthetic. The question of whether the 40-Hz transient peaks Ny, Py, Nz, and Pzare equivalent to Na, Pa, Nb, and Pb, respectively, will be answered by investigating the dynamic changes of component amplitudes and latencies as a function of the concentration of anesthetic, similar to the study reported by others36 for sevoflurane. We are currently working on such a study.
It is possible that Px, observed here in the 5-Hz transient during anesthesia, corresponds to the early middle-latency peak P0observed by others.37 The peak P0is not consistently seen in transient recordings. Others have observed P0recorded from anesthetized subjects. For example, Schwender et al.  36 studied dose dependency of component latency and amplitude in 9.3-Hz transient recordings during sevoflurane anesthesia. Though not explicitly reported, P0appears in their grand-averaged waveforms with all concentrations of sevoflurane. This finding, along with our data, preliminarily suggests that P0is present during anesthesia at lower stimulation rates (e.g.  , 5 Hz, 9.3 Hz) and that it disappears at higher stimulation rates (e.g.  , 40 Hz). It should be noted that in the 40-Hz transient, P0, may in fact be present (fig. 7A, see asterisk label) within the ascending portion of Py, which seems to have a shorter latency than Pain the 5-Hz transient response, though this is purely speculative. Electrode placement may be important for observing evoked potential signals. For this study, we used FPz and mastoid (positive and negative electrodes, respectively) and forehead (ground). Others have used alternate locations for the negative electrode. Our laboratory has obtained preliminary results showing that P0is observable in unanesthetized, awake volunteers when the negative electrode is placed at the inion. It would seem that movement of the negative electrode from the mastoid to the inion serves to diminish Na, which perhaps reveals the P0peak (verbal unpublished data, June 2008, Jorge Bohorquez, Ph.D., Department of Biomedical Engineering, Neurosensory Laboratory, University of Miami, Coral Gables, Florida). Future studies will address how electrode placement affects evoked potentials.
We observed what seems to be an oscillatory activity in the 5- and 40-Hz transient recordings obtained from subjects under general anesthesia, and we do not observe similar oscillations in unanesthetized, awake subjects.26 To the best of our knowledge, this is the first time such activity has been observed in a transient waveform; typical use of recording window lengths of 100 ms or less in previous studies, and the decreased sensitivity of shorter window lengths for detection of oscillatory activity are probable explanations. With CLAD, window lengths can be as long as 800 ms, and for this study, we used window lengths of 200 ms. We believe that the absence and presence of oscillatory activity in the transient waveform during the awake and anesthetized states, respectively, are consistent with the presence of neurons that can engage in a resonance with periodic stimulation. We hypothesize that anesthetics allow certain neurons to become entrained so that resulting evoked electrical activity becomes phase locked with the auditory stimulus. The significance and full characterization of this oscillatory activity remains to be established, and we are currently working in this regard.
The results presented here may help to explain an unexpected finding from a previous study. The 40-Hz ASSR amplitude was reported to be attenuated in the presence of nitrous oxide with isoflurane11 and enflurane.21 However, in the latter report, attenuation was found not to be dose dependent, and to vary in a nonmonotonic way.21 Our results show that the 40-Hz ASSR can be adequately described and reconstructed from 40-Hz transient and that both transient waveform amplitude and latency are important considerations. We hypothesize that the nonmonotonic relation observed by others can be explained by anesthetic effects on transient component latencies that are endogenously convolved during constant 40-Hz stimulation. If, for example, transient latencies increase with enflurane concentration, the degree of constructive (or destructive) summation of waveforms (and ultimately ASSR amplitude) will vary according to a polar—not linear—scale. This is illustrated in figure 8. The ASSR amplitude would vary nonmonotonically even if a linear anesthetic dose dependency for latency exists. In this model, the ASSR phase would also vary nonmonotonically. If our hypothesis is true, it would indicate that the 40-Hz ASSR, albeit an easily obtained steady state evoked potential that is unequivocally related to anesthetic depth, may offer a subset of the information that can be obtained from the transient waveform.
Fig. 8. Hypothetical explanation of nonmonotonous response of auditory steady state response (ASSR) amplitude to anesthetic dose. (  A  ) An idealized transient waveform (  a  ) is “stretched” to simulate increases in peak latencies (  b    d  ) as is known to occur with increasing levels of anesthetic. (  B  ) Each idealized transient is convolved generating predicted 40-Hz ASSRs. (  C  ) The root-mean-square (RMS) amplitudes (in arbitrary units) are calculated for each ASSR and plotted for each steady state waveform. This figure illustrates how linear variance of latencies in transient waveforms, with respect to anesthetic concentration, can lead to nonmonotonic changes in amplitude of the steady state waveforms as was observed for enflurane by Plourde and Villemure.  21 
Fig. 8. Hypothetical explanation of nonmonotonous response of auditory steady state response (ASSR) amplitude to anesthetic dose. (  A  ) An idealized transient waveform (  a  ) is “stretched” to simulate increases in peak latencies (  b  –  d  ) as is known to occur with increasing levels of anesthetic. (  B  ) Each idealized transient is convolved generating predicted 40-Hz ASSRs. (  C  ) The root-mean-square (RMS) amplitudes (in arbitrary units) are calculated for each ASSR and plotted for each steady state waveform. This figure illustrates how linear variance of latencies in transient waveforms, with respect to anesthetic concentration, can lead to nonmonotonic changes in amplitude of the steady state waveforms as was observed for enflurane by Plourde and Villemure.  21
Fig. 8. Hypothetical explanation of nonmonotonous response of auditory steady state response (ASSR) amplitude to anesthetic dose. (  A  ) An idealized transient waveform (  a  ) is “stretched” to simulate increases in peak latencies (  b    d  ) as is known to occur with increasing levels of anesthetic. (  B  ) Each idealized transient is convolved generating predicted 40-Hz ASSRs. (  C  ) The root-mean-square (RMS) amplitudes (in arbitrary units) are calculated for each ASSR and plotted for each steady state waveform. This figure illustrates how linear variance of latencies in transient waveforms, with respect to anesthetic concentration, can lead to nonmonotonic changes in amplitude of the steady state waveforms as was observed for enflurane by Plourde and Villemure.  21 
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It would have been useful to obtain baseline auditory evoked potentials in the awake state for comparison. Unfortunately, we found it extremely difficult to perform recordings on our awake subjects awaiting surgery in the holding area. To study the prediction discrepancy—a phenomenon observed only during general anesthesia—it was not important to have baseline recordings. In addition, we assume that awake recordings would be similar to those found in the literature and in a study similar to this one performed with awake subjects, recently reported by our group.26 We are unable to exclude the effect of muscle relaxant use on our recording because we were unable to determine relaxation status during the continuum of each of the surgeries. However, with our study design, which included common electrode placement, interleaving of recordings, and use of time-domain and phasor analyses, we believe that any myogenic response or artifact would affect all recordings equally and would not confound our data interpretation. A potential limitation of this study is the large range of anesthetic concentrations that were not targeted to a quantitative endpoint (e.g.  , expired percentage concentration). We decided to target anesthetic concentration to patient requirement to maintain general anesthesia. This target endpoint reduces the risk of either overdosing or underdosing anesthetic. It is also likely to have more real-world significance for future studies that will attempt to correlate evoked potential measures with awareness.
In summary, the 40-Hz ASSR is a composite or epiphenomenon of the evoked, transient waveform. The inability of 5- or 10-Hz transients to predict the 40-Hz ASSR is explained by an apparent stimulation rate-dependent effect on the morphology of the transient waveform recorded during anesthesia. It is likely that the ASSR amplitude can vary in a nonmonotonic (nonlinear) way even though changes in the transient amplitude and latency likely vary monotonically with anesthetic concentration. The use of CLAD was instrumental in accomplishing these studies, and its use contributed to our serendipitous observation of oscillations in both 5- and 40-Hz transients during anesthesia. The significance of these oscillations (which are not evident in awake recordings), as it relates to anesthetic action and depth, remains to be investigated.
The authors thank the Stanley Glaser Foundation; Alexander Castro, M.S., Graduate Student (Department of Biomedical Engineering, University of Miami, Coral Gables, Florida); and David Lubarsky, M.D., M.B.A., Professor and Chair, David Birnbach, M.D., Professor, Albert Varon, M.D., Professor, Shawn Banks, M.D., Assistant Professor, Kim Blumberg, M.D., Assistant Professor, Nick Nedeff, M.D., Assistant Professor, Edgar Pierre, M.D., Assistant Professor, Sripad Rao, M.D., Assistant Professor, and Christian Diez, M.D., Assistant Professor (all at the Department of Anesthesiology, University of Miami School of Medicine, Miami, Florida).
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Fig. 1. Schematic of study design. At least 20 min after induction of anesthesia (Ind.) and establishment of a steady state level of expired concentration of nitrous oxide and/or sevoflurane, the first recording experiment (Exp. #1) was begun. The recording continued until a change in anesthetic concentration occurred. Each subsequent experiment (  e.g.  , Exp. #2) was begun at least 5 min after a new steady state anesthetic level was established. Each experiment consisted of three or more sets. Each set consisted of three interleaved recordings pertaining to the 5-Hz conventional (conv.) isochronic, 40-Hz jittered continuous-loop averaging deconvolution (CLAD), and 40-Hz steady state (SS) isochronic auditory click stimulating sequences, respectively. Emerg. = emergence. 
Fig. 1. Schematic of study design. At least 20 min after induction of anesthesia (Ind.) and establishment of a steady state level of expired concentration of nitrous oxide and/or sevoflurane, the first recording experiment (Exp. #1) was begun. The recording continued until a change in anesthetic concentration occurred. Each subsequent experiment (  e.g.  , Exp. #2) was begun at least 5 min after a new steady state anesthetic level was established. Each experiment consisted of three or more sets. Each set consisted of three interleaved recordings pertaining to the 5-Hz conventional (conv.) isochronic, 40-Hz jittered continuous-loop averaging deconvolution (CLAD), and 40-Hz steady state (SS) isochronic auditory click stimulating sequences, respectively. Emerg. = emergence. 
Fig. 1. Schematic of study design. At least 20 min after induction of anesthesia (Ind.) and establishment of a steady state level of expired concentration of nitrous oxide and/or sevoflurane, the first recording experiment (Exp. #1) was begun. The recording continued until a change in anesthetic concentration occurred. Each subsequent experiment (  e.g.  , Exp. #2) was begun at least 5 min after a new steady state anesthetic level was established. Each experiment consisted of three or more sets. Each set consisted of three interleaved recordings pertaining to the 5-Hz conventional (conv.) isochronic, 40-Hz jittered continuous-loop averaging deconvolution (CLAD), and 40-Hz steady state (SS) isochronic auditory click stimulating sequences, respectively. Emerg. = emergence. 
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Fig. 2. Time and frequency domain signal treatment. (  A  ) The recorded 40-Hz auditory steady state response (ASSR) was denoised. (  B  ) Fourier transformation (FFT) of the waveforms before and after denoising were performed to illustrate the effect of denoising in the frequency domain. The Fourier theorem can be used to show that most signal energy is contained in the 40-, 80-, and 120-Hz harmonic components (  black bars  ) . Denoising removes the remaining noise frequencies harmonics (  gray bars  ). (  C  ) The recorded 5-Hz transient waveform was convolved as described in the text to generated a predicted ASSR, which was denoised as in  A  . (  D  ) FFT of these predicted waveforms was obtained. Note that phase information is not represented in this FFT, but both phase and amplitude data are important and were used in the phasor and statistical analyses outlined in the text and illustrated in  figure 3. (  E  and  F  ) The same procedure was applied to the 40-Hz transient waveform. 
Fig. 2. Time and frequency domain signal treatment. (  A  ) The recorded 40-Hz auditory steady state response (ASSR) was denoised. (  B  ) Fourier transformation (FFT) of the waveforms before and after denoising were performed to illustrate the effect of denoising in the frequency domain. The Fourier theorem can be used to show that most signal energy is contained in the 40-, 80-, and 120-Hz harmonic components (  black bars  ) . Denoising removes the remaining noise frequencies harmonics (  gray bars  ). (  C  ) The recorded 5-Hz transient waveform was convolved as described in the text to generated a predicted ASSR, which was denoised as in  A  . (  D  ) FFT of these predicted waveforms was obtained. Note that phase information is not represented in this FFT, but both phase and amplitude data are important and were used in the phasor and statistical analyses outlined in the text and illustrated in  figure 3. (  E  and  F  ) The same procedure was applied to the 40-Hz transient waveform. 
Fig. 2. Time and frequency domain signal treatment. (  A  ) The recorded 40-Hz auditory steady state response (ASSR) was denoised. (  B  ) Fourier transformation (FFT) of the waveforms before and after denoising were performed to illustrate the effect of denoising in the frequency domain. The Fourier theorem can be used to show that most signal energy is contained in the 40-, 80-, and 120-Hz harmonic components (  black bars  ) . Denoising removes the remaining noise frequencies harmonics (  gray bars  ). (  C  ) The recorded 5-Hz transient waveform was convolved as described in the text to generated a predicted ASSR, which was denoised as in  A  . (  D  ) FFT of these predicted waveforms was obtained. Note that phase information is not represented in this FFT, but both phase and amplitude data are important and were used in the phasor and statistical analyses outlined in the text and illustrated in  figure 3. (  E  and  F  ) The same procedure was applied to the 40-Hz transient waveform. 
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Fig. 3. Statistical analysis description. (  A  ) A difference phasor (  thin black vector  ) is calculated for each frequency component (  e.g.  , 40-Hz) by subtracting the recorded (  thick gray  ) and predicted (  black  )phasors containing the origin. The difference phasor represents the difference between the predicted and recorded signals in terms of amplitude and phase. The phasor analysis presented here for illustration pertains to data from an individual recording experiment from the current study. (  B  )The 40-Hz difference phasor from  A  (  circumscribed asterisk in the left lower quadrant  ) is plotted with the difference phasors (  asterisks  )from all recording experiments. The Hotelling  T  2test is used to determine whether the average difference phasor (  single vector containing the origin  ) is significantly different from zero. Ellipses centered around the phasor tip are calculated that correspond to specific  P  values. A difference phasor is statistically different from the origin if the ellipse does not contain the origin. The conclusion for this particular example is that the recorded and predicted phasors (and the corresponding time-domain waveforms) are statistically different from each other (  P  < 0.01). Note that ellipse size is inversely proportional to  P  value. Here for example, for  P  = 0.001, the corresponding ellipse contains the origin. ASSR = auditory steady state response. 
Fig. 3. Statistical analysis description. (  A  ) A difference phasor (  thin black vector  ) is calculated for each frequency component (  e.g.  , 40-Hz) by subtracting the recorded (  thick gray  ) and predicted (  black  )phasors containing the origin. The difference phasor represents the difference between the predicted and recorded signals in terms of amplitude and phase. The phasor analysis presented here for illustration pertains to data from an individual recording experiment from the current study. (  B  )The 40-Hz difference phasor from  A  (  circumscribed asterisk in the left lower quadrant  ) is plotted with the difference phasors (  asterisks  )from all recording experiments. The Hotelling  T  2test is used to determine whether the average difference phasor (  single vector containing the origin  ) is significantly different from zero. Ellipses centered around the phasor tip are calculated that correspond to specific  P  values. A difference phasor is statistically different from the origin if the ellipse does not contain the origin. The conclusion for this particular example is that the recorded and predicted phasors (and the corresponding time-domain waveforms) are statistically different from each other (  P  < 0.01). Note that ellipse size is inversely proportional to  P  value. Here for example, for  P  = 0.001, the corresponding ellipse contains the origin. ASSR = auditory steady state response. 
Fig. 3. Statistical analysis description. (  A  ) A difference phasor (  thin black vector  ) is calculated for each frequency component (  e.g.  , 40-Hz) by subtracting the recorded (  thick gray  ) and predicted (  black  )phasors containing the origin. The difference phasor represents the difference between the predicted and recorded signals in terms of amplitude and phase. The phasor analysis presented here for illustration pertains to data from an individual recording experiment from the current study. (  B  )The 40-Hz difference phasor from  A  (  circumscribed asterisk in the left lower quadrant  ) is plotted with the difference phasors (  asterisks  )from all recording experiments. The Hotelling  T  2test is used to determine whether the average difference phasor (  single vector containing the origin  ) is significantly different from zero. Ellipses centered around the phasor tip are calculated that correspond to specific  P  values. A difference phasor is statistically different from the origin if the ellipse does not contain the origin. The conclusion for this particular example is that the recorded and predicted phasors (and the corresponding time-domain waveforms) are statistically different from each other (  P  < 0.01). Note that ellipse size is inversely proportional to  P  value. Here for example, for  P  = 0.001, the corresponding ellipse contains the origin. ASSR = auditory steady state response. 
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Fig. 4. Recorded transients and auditory steady state responses and predicted auditory steady state responses obtained for each of the 24 experiments. The grand average (Av) for each waveform type is shown in the  bottom row  . Cross-reference of patient information and anesthetic concentrations can be accomplished by concomitant study of this figure (see experiment numbers,  left  )and  table 1. Av = grand average. 
Fig. 4. Recorded transients and auditory steady state responses and predicted auditory steady state responses obtained for each of the 24 experiments. The grand average (Av) for each waveform type is shown in the  bottom row  . Cross-reference of patient information and anesthetic concentrations can be accomplished by concomitant study of this figure (see experiment numbers,  left  )and  table 1. Av = grand average. 
Fig. 4. Recorded transients and auditory steady state responses and predicted auditory steady state responses obtained for each of the 24 experiments. The grand average (Av) for each waveform type is shown in the  bottom row  . Cross-reference of patient information and anesthetic concentrations can be accomplished by concomitant study of this figure (see experiment numbers,  left  )and  table 1. Av = grand average. 
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Fig. 5. Results of Hotelling  T  2analysis of difference-phasor arrays calculated from grand averaged recorded auditory steady state responses and predicted auditory steady state responses convolved from 5-Hz transient (  A  ) and 40-Hz transient (  B  ) waveforms. The  T  2, F, and  P  values are shown below each harmonic component projection. Results of the  T  2analysis of the six-dimensional difference-phasor arrays corresponding to the 5- and 40-Hz predicted responses are  T  2= 38.919, F = 5.076,  P  = 0.003 and  T  2= 2.626, F = 0.343,  P  = 0.905, respectively. 
Fig. 5. Results of Hotelling  T  2analysis of difference-phasor arrays calculated from grand averaged recorded auditory steady state responses and predicted auditory steady state responses convolved from 5-Hz transient (  A  ) and 40-Hz transient (  B  ) waveforms. The  T  2, F, and  P  values are shown below each harmonic component projection. Results of the  T  2analysis of the six-dimensional difference-phasor arrays corresponding to the 5- and 40-Hz predicted responses are  T  2= 38.919, F = 5.076,  P  = 0.003 and  T  2= 2.626, F = 0.343,  P  = 0.905, respectively. 
Fig. 5. Results of Hotelling  T  2analysis of difference-phasor arrays calculated from grand averaged recorded auditory steady state responses and predicted auditory steady state responses convolved from 5-Hz transient (  A  ) and 40-Hz transient (  B  ) waveforms. The  T  2, F, and  P  values are shown below each harmonic component projection. Results of the  T  2analysis of the six-dimensional difference-phasor arrays corresponding to the 5- and 40-Hz predicted responses are  T  2= 38.919, F = 5.076,  P  = 0.003 and  T  2= 2.626, F = 0.343,  P  = 0.905, respectively. 
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Fig. 6. Prediction of 40-Hz auditory steady state response (ASSR) using selected portions of the 5-Hz transient grand average waveform. (  A  ) Five-Hz grand averaged transient from  figure 4with peak labels tentatively assigned and (  B  ) predicted (  dashed  )and recorded (  solid  )40-Hz ASSR. The whole 5-Hz transient waveform and portions thereof (labeled  a    d  )were convolved to generate predicted waveforms. (  C  ) Phasor diagrams showing the corresponding and similarly labeled predicted (  solid  ,  bold  ) and recorded (  dashed  ) vectors. Avg = grand average. 
Fig. 6. Prediction of 40-Hz auditory steady state response (ASSR) using selected portions of the 5-Hz transient grand average waveform. (  A  ) Five-Hz grand averaged transient from  figure 4with peak labels tentatively assigned and (  B  ) predicted (  dashed  )and recorded (  solid  )40-Hz ASSR. The whole 5-Hz transient waveform and portions thereof (labeled  a  –  d  )were convolved to generate predicted waveforms. (  C  ) Phasor diagrams showing the corresponding and similarly labeled predicted (  solid  ,  bold  ) and recorded (  dashed  ) vectors. Avg = grand average. 
Fig. 6. Prediction of 40-Hz auditory steady state response (ASSR) using selected portions of the 5-Hz transient grand average waveform. (  A  ) Five-Hz grand averaged transient from  figure 4with peak labels tentatively assigned and (  B  ) predicted (  dashed  )and recorded (  solid  )40-Hz ASSR. The whole 5-Hz transient waveform and portions thereof (labeled  a    d  )were convolved to generate predicted waveforms. (  C  ) Phasor diagrams showing the corresponding and similarly labeled predicted (  solid  ,  bold  ) and recorded (  dashed  ) vectors. Avg = grand average. 
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Fig. 7. Same as  figure 6except that the predicted 40-Hz auditory steady state response is instead derived from portions of the 40-Hz transient grand average waveform. ASSR = auditory steady state response. Avg = grand average. 
Fig. 7. Same as  figure 6except that the predicted 40-Hz auditory steady state response is instead derived from portions of the 40-Hz transient grand average waveform. ASSR = auditory steady state response. Avg = grand average. 
Fig. 7. Same as  figure 6except that the predicted 40-Hz auditory steady state response is instead derived from portions of the 40-Hz transient grand average waveform. ASSR = auditory steady state response. Avg = grand average. 
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Fig. 8. Hypothetical explanation of nonmonotonous response of auditory steady state response (ASSR) amplitude to anesthetic dose. (  A  ) An idealized transient waveform (  a  ) is “stretched” to simulate increases in peak latencies (  b    d  ) as is known to occur with increasing levels of anesthetic. (  B  ) Each idealized transient is convolved generating predicted 40-Hz ASSRs. (  C  ) The root-mean-square (RMS) amplitudes (in arbitrary units) are calculated for each ASSR and plotted for each steady state waveform. This figure illustrates how linear variance of latencies in transient waveforms, with respect to anesthetic concentration, can lead to nonmonotonic changes in amplitude of the steady state waveforms as was observed for enflurane by Plourde and Villemure.  21 
Fig. 8. Hypothetical explanation of nonmonotonous response of auditory steady state response (ASSR) amplitude to anesthetic dose. (  A  ) An idealized transient waveform (  a  ) is “stretched” to simulate increases in peak latencies (  b  –  d  ) as is known to occur with increasing levels of anesthetic. (  B  ) Each idealized transient is convolved generating predicted 40-Hz ASSRs. (  C  ) The root-mean-square (RMS) amplitudes (in arbitrary units) are calculated for each ASSR and plotted for each steady state waveform. This figure illustrates how linear variance of latencies in transient waveforms, with respect to anesthetic concentration, can lead to nonmonotonic changes in amplitude of the steady state waveforms as was observed for enflurane by Plourde and Villemure.  21
Fig. 8. Hypothetical explanation of nonmonotonous response of auditory steady state response (ASSR) amplitude to anesthetic dose. (  A  ) An idealized transient waveform (  a  ) is “stretched” to simulate increases in peak latencies (  b    d  ) as is known to occur with increasing levels of anesthetic. (  B  ) Each idealized transient is convolved generating predicted 40-Hz ASSRs. (  C  ) The root-mean-square (RMS) amplitudes (in arbitrary units) are calculated for each ASSR and plotted for each steady state waveform. This figure illustrates how linear variance of latencies in transient waveforms, with respect to anesthetic concentration, can lead to nonmonotonic changes in amplitude of the steady state waveforms as was observed for enflurane by Plourde and Villemure.  21 
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Table 1. Experimental Recording Conditions and Subject Demographics 
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Table 1. Experimental Recording Conditions and Subject Demographics 
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Table 2. Phasor Component Values Used in the Hotelling  T  2Analysis 
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Table 2. Phasor Component Values Used in the Hotelling  T  2Analysis 
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