Anesth Analg 2004;98:698-702
© 2004 International Anesthesia Research Society
doi: 10.1213/01.ANE.0000100152.31854.2B
TECHNOLOGY, COMPUTING, AND SIMULATION
Spectral Analysis of Movement Patterns During Anesthesia
Steven L. Jinks, PhD,
Joseph F. Antognini, MD, and
Earl Carstens, PhD
From the Department of Anesthesiology and Pain Medicine and the Section of Neurobiology, Physiology and Behavior, University of California, Davis, Davis, California
Address correspondence to Steven L. Jinks, PhD, Department of Anesthesiology and Pain Medicine, TB-170, UC Davis, Davis, CA 95616. Address email to sljinks{at}ucdavis.edu
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Abstract
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It remains unclear how anesthetics produce immobility, an end-point used in determining anesthetic potency. Understanding how movement (in response to noxious stimulation) is ablated by anesthetics could be aided by using spectral analysis of the high and low frequency components of complex movement patterns. We therefore applied a spectral analysis to previously published movement data from rats anesthetized with isoflurane and halothane at 0.6, 0.9, and 1.1 minimum alveolar concentration (MAC). We recorded isometric forces of hindlimb movement elicited by noxious mechanical stimulation of the hindpaw. The movement patterns were subjected to spectral analysis to determine force amplitude for each frequency component. When halothane was increased from 0.6 to 0.9 MAC, force amplitude decreased only for the lowest-frequency (<1 Hz) components, in part related to the generally lower high-frequency forces at 0.6 MAC. Between 0.6 and 0.9 MAC isoflurane amplitude was reduced for most frequencies in the 0–10 Hz range. For both halothane and isoflurane at 1.1 MAC, as expected, force amplitude substantially decreased at all frequencies. We conclude that spectral analysis is useful to describe and quantify the effects of anesthetics on complex movement patterns resulting from noxious stimuli applied during anesthesia.
IMPLICATIONS: Complex movement can occur when a noxious stimulus is applied to an anesthetized animal. The frequency components of these movement patterns can be described and quantified by spectral analysis, thus providing a useful tool to investigate the immobilizing properties of anesthetics.
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Introduction
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Immobility is a critical goal of anesthesia and is a behavioral end-point with which to measure anesthetic potency (1). The minimum alveolar concentration (MAC) method uses an "all or none" determination of gross and purposeful movement elicited by a supramaximal noxious stimulus, although movement progressively decreases as anesthesia is increased (2). We have used a simple method to determine both movement force and pattern (2). The pattern, however, can be difficult to quantify because of its complexity. For example, rapid movements can be superimposed on slower movements (2).
The frequency components of a complex movement can be broken down by spectral analysis (3) (Fig. 1), a method that has been applied to electromyogram (EMG) data sets (4). The objectives of the present article were to describe how spectral analysis can be used to evaluate complex movement and to apply this analysis to evaluate anesthetic effects on various frequency components of movement using previously published data (2). We hypothesized that all frequency components of a complex movement would be depressed above MAC, but that there may be frequency-selective effects of different anesthetic (halothane and isoflurane) at sub-MAC concentrations.
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Figure 1. A, a waveform (left panel) that is a combination of 3 sine waves (1 Hz, 3 Hz, 10 Hz); the spectrum generated using spectral analysis shows 3 peaks at 1 Hz, 3 Hz, and 10 Hz (right panel). B, the 10-Hz component has been removed (left panel) and the corresponding spectrum (right panel) shows just the remaining 1-Hz and 3-Hz components.
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Methods
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We analyzed previously reported movement data from experiments approved by the local animal care and use committee (2). In brief, rats were anesthetized with isoflurane (n = 8) or halothane (n = 7), followed by tracheostomies and mechanical ventilation. Each animal’s MAC was determined from the average of concentrations that prevented and permitted gross purposeful movement in response to a noxious mechanical stimulus (hemostat) applied to the tail. Each limb was attached to a force transducer to permit recording of force generated by each limb during application of a hindpaw clamp (2 10-s applications 2–3 min apart) at 0.6, 0.9, and 1.1 MAC.
We used a commercially available program to perform spectral analysis (Spectrum function, Chart 4.2; ADInstruments, Colorado Springs, CO). The fast Fourier transform (FFT) size was set at 1024 with no overlap of FFTs; window tapering (e.g., cosine bell) was not used. We used the "Adjust to best fit" option in Chart4.2, which interpolated missing data points so that the waveform was unchanged (5). We analyzed the movement patterns of the stimulated hindlimb by importing the data into the Chart program as text files (i.e., the instantaneous force at each time point; 200 samples/s). Movement was analyzed from its beginning to its end. In a few instances movement persisted for more than 10 s after removal of the clamp, and we analyzed only for the movement occurring during and 10 s after clamp application. Most movement patterns were 
10–20 s long. Because the FFT size was 1024 and the sampling rate was 200/s, approximately 2–4 FFTs were produced from each movement pattern. These FFTs were averaged to obtain a spectrum of force amplitude every 0.2 Hz between 0–10 Hz.
For each anesthetic dose we summed the force amplitudes across all frequencies (0–10 Hz) as well as frequencies <1 Hz and frequencies 1–10 Hz. We then performed analysis of variance with Student-Newman-Keuls post hoc testing. We compared the summed values at each anesthetic dose and between anesthetics. We used a P < 0.05 for significance.
To validate the data transformation from the time to frequency domain, we performed the analysis on one raw movement waveform and then reconstructed the waveform from the resulting spectrum using a custom program (MatLab, Natick, MA), according to the general formula for the Fourier series:equation
where A = amplitude, f = frequency, and 
= the phase of each signal component summed in the reconstruction.
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Results
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The isoflurane MAC was 1.2% ± 0.1% and the halothane MAC was 1.0% ± 0.2%. Figure 2 shows raw force tracings from an animal anesthetized with isoflurane at 0.6, 0.9, and 1.1 MAC. Note that there is a progressive decrease in movement (force and number of movements) as the anesthetic is increased. The corresponding spectrum generated by spectral analysis of the 0.6 MAC force tracing shows that there are peaks in the 0–1 Hz region corresponding to the slower movements (every 2 s) and another set of peaks in the 2–6 Hz region corresponding to the superimposed faster movements. At 0.9 MAC there is loss of faster components, whereas at 1.1 MAC there is little movement.
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Figure 2. Raw tracings of isometric force of hindlimb movements from a rat anesthetized with isoflurane. A clamp was applied to the paw of the hindlimb for 10 s at 0.6, 0.9, and 1.1 MAC. The corresponding spectra indicate the frequencies that are primarily affected by the increase in isoflurane concentrations. Note that between 0.6 and 0.9 MAC there is a loss of force amplitude in the 1–10 Hz frequency range, whereas at 1.1 MAC there is loss at all frequencies.
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Figure 3 shows a raw movement waveform that has been subjected to spectral analysis. The waveform was accurately reconstructed by including all frequencies between 0 and 10 Hz (Fig. 3, right panel, thick line). When using only 0–3 Hz frequencies, as expected, the reconstructed waveform lost the higher frequency components (Fig. 3, right panel, thin line).
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Figure 3. The tracing in the left panel demonstrates the complex nature of a raw movement pattern. The spectrum of that movement is shown in the middle panel. The right panel shows the reconstruction of the waveform using frequencies between 0–10 Hz (bottom thick line) and frequencies between 0–3 Hz (top thin line). Note that when the frequency range 0–10 Hz is used there is faithful reconstruction of the original waveform, whereas using only the 0–3 Hz range results in loss of high frequency components, as expected.
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Summary data of the spectral analysis are shown in Figure 4 and Table 1. From 0.6 MAC to 0.9 MAC halothane there is a decrease in force amplitude of the low frequencies (<1 Hz; P < 0.05), whereas the amplitudes at greater frequencies were minimally affected, in part related to the already existing small amplitudes at these higher frequencies at 0.6 MAC. At 1.1 MAC, however, movement, in general, ceases and there is flattening of the spectrum. With isoflurane, however, the transition from 0.6 to 0.9 MAC affected most frequencies. The mean force amplitude in the entire frequency range at 0.6 MAC isoflurane was significantly greater than that at 0.6 MAC halothane (P < 0.05; Table 1).
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Figure 4. Summary data for the hindlimb forces generated during application of a clamp to the paw at 0.6, 0.9, and 1.1 MAC halothane (7 animals) and isoflurane (8 animals). Note that between 0.6 and 0.9 MAC there is a decrement in force amplitude in most frequencies for isoflurane but only in frequencies below 1 Hz for halothane; this is in part related to the lower amplitudes in the high frequency range at 0.6 MAC halothane. As expected, there is a large decrease at 1.1 MAC. The 0.9 MAC data are expressed as mean and 95% upper confidence interval (CI) and for clarity the 0.6 and 1.1 MAC data are shown only as means. The 0.6 MAC mean data for isoflurane are above the 0.9 MAC CI at most frequencies.
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Discussion
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Spectral analysis has been applied to a variety of biological data including the EMG, electroneurogram, and electroencephalogram, the latter application being most familiar to anesthesiologists. The present results show that complex movements can also be reliably expressed in terms of their frequency components. Analysis of our previous data (2) demonstrated that increasing the concentration of halothane from 0.6 MAC to 0.9 MAC did not affect movement frequencies >1 Hz, presumably because of the relatively small contribution of these frequencies to the overall movement. For isoflurane, however, most frequencies were uniformly depressed over the same concentration range. The present analysis also revealed a significantly greater force amplitude for 0.6 MAC isoflurane as compared with 0.6 MAC halothane (Table 1), consistent with our prior studies (2,6), suggesting that halothane has a more pronounced depressant effect on spinal sensorimotor processing at sub-MAC concentrations.
When examining a raw movement tracing it can be difficult to determine whether the movement is a single, forceful withdrawal, or whether it represents the summation of several rapid movements. Temporal summation occurs when motor responses to noxious stimuli summate over time, i.e., when one motor response builds on another. This has important implications because the degree of temporal summation of motor responses to noxious stimuli alters anesthetic requirements; e.g., increased temporal summation increases anesthetic requirements to prevent movement (7). Application of spectral analysis to such data might be useful in investigating anesthetic effects on neural circuits involved in temporal summation as well as circuits involved in locomotion and the flexion reflex. Spectral analysis potentially could also be used to evaluate diagnostic EMG data obtained in the operative setting. For example, the EMG is sometimes used to evaluate the effect of a neuromuscular blocking drug, and spectral analysis could be useful in determining the extent of the drug’s effect.
There are limitations to spectral analysis. For example, it works best when there is "stationarity," a term that describes the stability of the underlying pattern over time. In many biological systems this is not always the case. In the present study, we averaged FFTs that resulted from analysis of individual movement patterns, thus reducing any errors arising from nonstationarity (8). Averaging responses within animals (e.g., two stimulation trials) and across animals further reduced possible errors. The spectral analysis requires the FFT size to be a power of 2 (32, 64, 128, 256,...). If a 1-second signal is digitized at 200 samples/second and the FFT size is 256, then the FFT must "fill in" the last 56 points, usually by making the last 56 points zero, which can lead to artifacts on the spectrum. We inserted the remaining 56 points into the signal by interpolation so that the sample remained 1 second long and maintained its original pattern (5). It is still important to quantify the total number of movements, although this can sometimes be difficult when one movement appears to merge with another. In our prior study we reported force integrated over time, or the "area under the curve." This analysis is potentially ambiguous because some high amplitude rapid movements could yield the same value as weak and prolonged movements (e.g., the 0.6 MAC and 0.9 MAC movement tracings in Fig. 2). The former case would presumably have greater amplitude in the higher frequency range as compared with that in the latter case. Thus, spectral analysis in conjunction with other analytical methods provides a more accurate and complete description of movement patterns.
In summary, we have applied spectral analysis to quantify the frequency components of complex movements in anesthetized rats. Spectral analysis provides information on the relative contribution of different movement frequency components within the overall movement pattern and how anesthetics affect these various components.
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Acknowledgments
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Supported, in part, by grants from NSRA (to SLJ) and National Institutes of Health grants GM61283 and GM57970 (to JFA).
The authors thank William Miller, PhD, for his helpful comments.
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References
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- Jinks SL, Martin JT, Carstens E, et al. Peri-MAC depression of a nociceptive withdrawal reflex is accompanied by reduced dorsal horn activity with halothane but not isoflurane. Anesthesiology 2003; 98: 1128–38.[ISI][Medline]
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- Miller WL, Sigvardt KA. Spectral analysis of oscillatory neural circuits. J Neurosci Methods 1998; 80: 113–28.[ISI][Medline]
Accepted for publication September 22, 2003.
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Abstract
Introduction
