Multivariate analysis of diaphragm EMG power spectral moments

COMPUTERS

AND

BIOMEDICAL

Multivariate J. MILTON

ADAMS,*

Departments

RESEARCH

17, 163-174 (1984)

Analysis of Diaphragm Spectral Moments T. K. ALDRICH,

N. S. ARORA,

EMG Power AND D. F. ROCHESTER

of Biomedical Engineering and Pulmonary-Allergy Medicine, University of Virginia, Charlottesville, Virginia 22908

Received July 20, 1983

A single derived index of the power spectrum of the diaphragm electromyogram (EMG) has been used in detecting fatigue. Additional information in the EMG could be used to study diaphragm function in other respiratory conditions. Diaphragm EMGs and calculated power spectra at 12 frequencies were measured in normal subjects and patients with severe chronic obstructive pulmonary disease during several respiratory maneuvers both before and after treadmill exercise to dyspnea. The power spectra were characterized by the first five moments. Changes in the EMG were similar when assessed by multivariate analysis of variance of the spectral estimates or of the moments. Factor analysis provided two latent variables that correlated with the first and second moment respectively. The first moment was found to be the most sensitive single discriminant of fatigue and is only slightly improved by adding other information. It is concluded that the first and second moments of the EMG power spectra provide a concise, parsimonious description of the changes in the EMG.

To detect fatigue, changes in the frequency distribution of power in the diaphragm electromyogram (EMG) have been used (5-7, II). These changes are often described by a single parameter which is usually either the ratio of high frequency power to low frequency power or the first moment, Ml, of the spectrum. This procedure has the advantage of simplicity but may neglect additional information which could describe diaphragm function under other respiratory conditions. By analogy with the mathematics of probability distributions, the power spectrum may be described by its moments. Although individual spectral estimates may be combined by factor or discriminate analysis to provide indicators, these may be difficult to interpret. We hypothesized that additional EMG information, if present, may be adequately represented by the spectral moments and therefore be interpreted as a center frequency (first moment), measure of dispersion (second), skewness (third), etc. Our objective was to assess * To whom correspondence should be sent at Divisionpf Biomedical Engineering, University of Virginia, Box 377, Medical Center, Charlottesville, Va. 22908. 163 0010-4809184 $3.00 Copyright 6 l!W by Academic Press, Inc. All rights of reproduction in any form reserved.

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the adequacy of spectral moments to describe the EMG spectra from several respiratory maneuvers in both health and disease. In addition we attempted to determine if some combination of measurements could detect fatigue better than the first moment alone. In a sample of normal subjects and patients with chronic obstructive pulmonary disease (COPD) under a variety of diaphragm maneuvers we found that the first five moments changed in a similar fashion as the power spectrum. Factor analysis revealed two latent variables, one related to high frequency power and correlated with Ml and a second factor related to low frequency power correlating with the second moment. The most sensitive discriminant of fatigue was MI which was only slightly improved by adding other information. METHODS

Subjects. Data were obtained from four untrained normal subjects, one of whom was measured on two occasions, and from four patients with COPD (Table I). Informed consent was obtained from each subject for all procedures. which had been approved by the Human Investigation Committee of the University of Virginia Medical Center. Measurements. EMGs were recorded from 20-mm-wide bipolar electrodes spaced 8 mm apart and incorporated into a double-lumen polyethylene catheter which was introduced transnasally. To measure transdiaphragmatic pressure thin-walled latex balloons were attached to the catheter at the distal end and 20 cm from the end, each communicating with one of the two catheter lumens. The EMG signal from the two electrodes was differentially amplified by a Hewlett-Packard 8811A preamplifier with a first-order bandpass filter set for a low cutoff of 15 Hz and a high cutoff of 1000 Hz. Surface electrocardiogram (ECG) was monitored from standard ECG leads, amplified by a Hewlett-Packard 8811A preamplifier, and displayed on an oscilloscope. Transdiaphragmatic pressure, Pdi, and mouth pressure were monitored using Validyne MP45 differential pressure transducers, and inspired volume was measured with an Ohio TABLE

I

PHYSIOLOGIC PARAMETERS FOR SUBJECTS IN THE STUDY” Normal Number Age (years) FEV,/FVC Pi Onax) (cm HzO) MVV (% pred.)

COPD

3M, I F

4M

5 34-t 0.79 t 0.04

63 t 2 0.43 k 0.05 49 t 3

131 r 9 96 k 16

16 t 3

Nope. Data are mean values 2 SE. a FEVJFVC. forced expired volume in first second divided by vital capacity; Pirmax,, maximum generated inspiratory pressure; MVV, maximum voluntary ventilation.

EMG

Spirometer. corder.

SPECTRAL

165

MOMENTS

All signals were recorded on a Honeywell

56OOC FM tape re-

Data analysis. EMG, ECG, volume, and pressure signals were replayed and analyzed using a PDP 11/20 digital computer with a Tektronix 4012 graphics terminal. The signals were sampled at 10 kHz, and every ten consecutive samples were averaged to produce a point every millisecond. Five-second sections of data were displayed on the graphics terminal and the initiation of each inspiratory effort and all of the QRS complexes in the ECG were identified. The time periods which contained QRS complexes or detectable motion artifact were edited out of the EMG. The remaining sections of data were divided into 256-msec segments and labeled with respect to time from the onset of the inspiratory effort. The power spectrum (P(J)) of each segment of data was then computed by applying a Blackman window and fast Fourier transform algorithm (3) to produce raw estimates at 65 frequencies between zero and 254 Hz. Frequencies below 20 Hz were deleted and the remaining values were smoothed over five adjacent frequencies to give intermediate power estimates at 12 frequencies (31, 51, 70, 90, 109, 129, 149, 168, 188, 207, 227, and 246 Hz). Intermediate estimates from 5 to 10 successive maneuvers (that occurred within a 256-msec block of time) were then averaged. The coefficient of variation of these final estimates ranges from ?32 to 14%. The moments of the spectra were calculated as Mk = [2

(h - Ml)kP(f;)/MO]“’

k = 2, 3, 4

[II

where MO = XP(Fi)

PI

Ml = CJ;P(J;)IMO.

[31

and

Statistical analysis. Multivariate analysis of variance (MANOVA) used the Model I design with a least-squares solution for unequal n’s (9). Hotelling’s criteria were used and tests were made at the 0.05 level of significance. Factor analyses were performed by three methods: inferred factors, unweighted least squares, and maximum likelihood; this reduces the chance that a solution is a sole result of the statistical model. Varimax rotation of the axes was applied. Discriminant analysis was performed using linear, stepwise addition of variables to discriminate between before and after exercise. All analyses were performed using a CDC 730 computer and a commonly available package of statistical programs (10). Experimental protocol. Diaphragm EMGs were recorded during three maneuvers: (1) spontaneous breathing, (2) maximal effort with an occluded airway (Muller maneuver), or (3) maximal effort without airway occlusion (inspiratory vital capacity). Each maneuver was repeated up to ten times before and at the conclusion of treadmill exercise, at 4 to 5 mph on a 15” grade in normals, or at 2

ADAMS

166

ET AL.

to 1 mph on a 0” grade in COPD patients. Exercise was continued until the subject felt short of breath and unable to continue. Data were analyzed only from subjects who developed respiratory muscle fatigue, defined as a 15% or greater decrease in postexercise Pdi. Measurements from spontaneous breaths were obtained just before exercise stopped and from maximal efforts immediately after exercise ceased.

NORMAL

C0 PD

SUBJECTS

SUBJECTS

Ob’ FREQUENCY

(Hz)

FREQUENCY

(Hz)

FIG. 1. Power spectra for four subjects and four patients. These were calculated by averaging all spectra for Muller maneuvers before or after exercise. Before exercise (0) and after exercise (0).

EMG

SPECTRAL

167

MOMENTS

RESULTS

The shapes of the spectra (Fig. 1) were consistent with the theoretical predictions of Lindstrom and Magnusson [7]. Observation of the shape of the spectra failed to reveal any consistent pattern of difference between patients and subjects. Using the power at the 12 frequencies as 12 variates describing the EMG, a multivariate analysis of variance (MANOVA) was performed. The factors were exercise (before and after), group (subject or patient), maneuver (spontaneous breath, Muller maneuver, or vital capacity) and time (400 msec or >500 msec after initiation of effort). This analysis revealed that EMG changes were significantly different from zero for the exercise x group x maneuver interaction (E X G X M in Table II) and for the time factor. The way the EMG changed depended upon whether it was obtained before or after exercise, and from which maneuver or which group the measurement came. The second column of Table II presents the significant effects when the 5 spectral moments are analyzed. The results are very similar to the analysis of the 12 powers except time is not a significant factor for the moments. The first four canonical correlations between the 12 spectral estimates and 5 moments were all greater than 0.95. To determine the dimensionality of these changes several factor analyses

TABLE F RATIOS

FOR ANOVA

II AND MANOVA”

MANOVA 12 powers TxMxGxEb TxMxE MxGxE TxGxE TxMxG GxE MxE MxG TxE TxG TxM E G M T L1Asterisks b T, time;

0.823 1.00 2.50* 1.21 1.46 0.77 2.13* 2.41* 0.86 0.91 1.51 1 .I9 5.33* 2.61* 2.73* mark significant effects M, maneuver; G, group;

ANOVA 5 moments 0.414 1.35 1.97* 1.64 1.60 1.67 2.67* 2.21* 1.10 2.00 0.84 3.71* 6.56* 3.36* 1.86

(P < 0.05). E, exercise;

x , interactions.

Ml

M2

0.02 2.28 0.96 0.00 3.16* 0.72 2.22 5.89* 0.001 0.52 0.05 12.39* 10.65* 9.01* 0.24

0.010 3.26* 0.55 0.046 0.73 0.73 11.39* 1.03 0.05 0.01 0.21 9.18* 24.66* 3.45* 0.56

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were performed. The first was of the 12 powers and the results are shown in Fig. 2. The 12 powers are plotted on the two factor axes which accounted for 73% of the variance of the changes. All but the first two frequencies had communalities greater than 0.60; power at the two lowest frequencies had communalities of 0.33 and 0.19, respectively. Thus, the common factors model fit the mid- and upper frequencies adequately but the lowest frequencies had a higher contribution of unique components. The first factor was highly correlated with high frequency power from 129 to 246 Hz and, before rotation. accounted for 50% of the variance. The second factor was not clearly associated with particular frequencies in the maximum likelihood solution, but with the inferred solution, correlated with power at 70 and 90 Hz. The unweighted least-squares solution revealed that the high frequency power split between the two factors. Subject to the limitations of the linear model, factor analysis finds two dimensions to the changes in the diaphragm EMG: one related to high frequency power and the other most nearly related to low frequency power. A similar analysis of the five moments of the moments of the spectrum did not converge for the maximum likelihood model but did for unweighted leastsquares and for the inferred factors (Fig. 3). One factor accounted for 81% of the variance and the other 17%, for a total of 98%. The second moment was

FACTOR

2

3 9

2 I

4 I

5 6

IO ’

FACTOR

I

FIG. 2. Plot of 12 powers on factors axes. This result was obtained by the maximum likelihood model and varimax rotation. The powers at each of the 12 frequencies are plotted at their locations given by the factor loadings and are identified by their number in ascending order of frequency.

EMG SPECTRAL

FACTOR

169

MOMENTS

2 MP

M4

MI

MO ,FACTOR

I

I

M3

A FIG. 3. Plot of five moments on factor axes; inferred solution. varimax rotation.

correlated with one factor while the remaining moments loaded on the other factor. Communalities were all greater than 0.80. We infer that MO, Ml, M3, and M4 associate with one dimension of the variance and M2 with a second independent dimension. When the moments were combined with the individual spectral estimates, the correlation matrix was nearly singular, indicating redundant information. Again, two factors were found accounting for a total of 79% of the variance; communalities were greater than 0.60 except for 31 and 51 Hz. The first factor was highly correlated with high frequency power (>129 Hz) and all moments except M2 (Fig. 4). The second factor was positively correlated with power at 70 and 90 Hz and negatively correlated with power at 31 Hz. Power at 110 Hz and M2 were moderately correlated within both factors. Thus, there were essentially two dimensions accounting for about threefourths of the variance of the diaphragm EMG. After rotation one factor was related to high frequency power (2129 Hz). The second factor was related to some low frequency power and to the second moment but it was not as clearly identifiable as the first. Further extraction of any information accounted for less variance than a single, independent variable. This factor analysis suggests that the second moment, in addition to the first, provides a concise and parsimo-

170

ADAMS FACTOR

3

ET AL. 2

4 5

8

2

MO

6’

9 ‘*MIFACTOR

pb3

I

II I2

I M2

FIG. 4. Plot of combined powers and moments on factor axes; unweighted least-squares solution. varimax rotation.

nious description of the EMG power spectrum under our experimental conditions. To determine how Ml and M2 characterize the EMG in comparison with the 12 spectral estimates, the univariate ANOVA of these two variables was compared to the MANOVA (columns 3 and 4 of Table II). Neither Ml nor M2 has the same significant third-order interaction terms as the MANOVA did. However, the second-order interaction and main effects that were significant in the MANOVA were in one of the single moments. The changes in Ml and M2 which were found to be significantly different from zero in Table II were examined further by the Newman-Keuls test (Table III). The first moment decreased after exercise and was higher for normal subjects breathing spontaneously in the early phase of an inspiration. On the other hand, M2 was lower in patients than subjects but increased in spontaneous breaths before exercise. Neither of the moments differed between the two maximal efforts but each indexed different facets of subject-patient and exercise comparisons for spontaneous breaths. Since detection of fatigue may be enhanced by additional information in the power spectrum, we performed a linear, stepwise discriminant analysis to separate data taken before and after exercise. The variable with the greatest discrimination power was the first moment; additional variables entered into the

EMG SPECTRAL TABLE VALUES

Time in breath: Disease: SBb MM vc Time in breath: Exercise: SB MM vc

OF

171

MOMENTS III

Ml

AND

M2

Ml: preexercise, 103.1; postexercise, 97.6” Early

Late

Normal

COPD

Normal

COPD

116.7‘ 100.0 98.4

97.7 99.0 97.8

108.1 102.3 100.3

106.1 99.3 96.4

M2: subjects, 60.5; patients, 57.9d Early

Late

Pre-

Post-

Pre-

Post-

63.7*’ 59.5 59.2

55.8 59.2 58.8

63.7* 59.8 59.0

45.5 58.2 58.7

a Ml decreased significantly after exercise in both groups, all maneuvers and both phases of the breath. b SB, spontaneous breathing; MM, Muller maneuver; VC, vital capacity. c Normal subjects breathing spontaneously had a significantly greater value of Ml in the early phase of the breath. d Subjects had higher values of M2 than patients regardless of the phase of a breath, exercise, or maneuver. p Preexercise values (*) of M2 were higher in spontaneous breaths of normal subjects.

discriminant function were power at 149 Hz and then power at 51 Hz. Classification results are in Table IV. Adding the two additional variables served primarily to correct 12 EMGs classified as before exercise (by only Ml) to the postexercise category. With Ml, 58.9% of the EMGs were correctly classified, while with the three variables a slight improvement to 65.8% was seen. DISCUSSION

We found essentially that two dimensions were required to describe a majority of the variance in the EMG spectra. The first and second moments of the spectra closely correlated with these two dimensions and changed similarly to the total spectrum. Some improvement in discrimination of exercise was found when power at 149 and 51 Hz was used in linear combination with Ml. Limitations. The primary limitation of this approach is that the variables are combined in a linear function. It is possible that nonlinear functions of the variables would be much better in parsimoniously describing the EMG or discriminating fatigue. This is a general limitation of the class of multivariate techniques; nonlinear transformations of variables are possible but principles

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TABLE DISCRIMINANT

ANALYSIS:

IV PREEXERCISE

vs

POSTEXERCISE

Classification results: Ml only Predicted Actual No. Before After Correctly classified

84 118

Before

After

4s 44

39 74 58.9%

Classification results: Ml, 149 Hz, 51 Hz Predicted Actual No. Before After Correctly classified

84 118

Before

After

47 32

37 86 65.8%

for choosing the best set of nonlinear transformations are not well established. Another obvious limitation is the small number of subjects used and the selected experimental conditions. Although a large number of measurements were made in each person, only four normal subjects and four patients were analyzed. It is reasonable to expect that further studies along these lines may find variation due to differences between subjects and conditions. We did find that if the data were separated into subject or patient groups the factor structure was not substantially changed. Thus, there does not appear to be a large systematic difference in dimensionality between types of subjects. We intentionally chose a minimal level of diaphragm exertion in order to be able to study patients with severe respiratory disease (8). This has the disadvantage of producing barely perceptible levels of fatigue but allows study of patients with small changes in diaphragm EMG parameters. Finally, a more subtle limitation may be present. We have implicitly ignored the effect of noise on the power spectral estimation and analysis. If, however, the variance of the noise changes or the noise is not white, some of the observed significant effects and covariance may be due to the changing signal-tonoise ratio (I, 13). This may also apply to the factor analyses of the spectra. If the signal level, particularly at high frequencies, drops below the noise level, some of the high frequency components may appear to be raised. We did not rigorously measure true noise spectra and are therefore unable to judge the magnitude of its effect. Interpretation and implications. The first moment of the power spectrum has been used to detect changes in the EMG previously (5-7, II). Our objective was twofold: (1) to determine if there was additional relevant information in the

EMG

SPECTRAL

MOMENTS

173

EMG beyond that contained in Ml, and if so, (2) to concisely and parsimoniously describe that information. Multivariate analysis of variance of the spectra assesses significant changes in the total spectrum and allows comparison of description by 12 frequencies and by 5 moments (12). Experimental effects which were significant when the 12 frequencies were used as variables were almost the same as when the moments were analyzed. High (>0.95) canonical correlations imply similar information content also. This indicates that the 5 moments, although much fewer in number, still characterize the spectrum well. Other attempts to reduce the number of variables needed to describe power spectra include using “Gaussian functions” to locate and characterize peaks in the EEG spectrum (4). This is well suited for spectra such as the EEG with multiple peaks but essentially reduces to calculating moments when spectra are shaped with one broad peak..Fitting time series models to EEGs has also been proposed (2). This is a time domain description which can be shown to be related to the power spectra. Gersch et al. (2) then transform the time series models and use an information measure (related to spectral coherence) to assess the relation between signals. Factor analysis revealed that two dimensions or latent variables account for about three-fourths of the variance of the spectrum; adding a third factor accounted for only 7% more. Although one factor was related to high frequency power, variables as descriptors of the spectra involve forming linear combinations of the 12 powers, These combinations may not be interpretable measurements. We attempted instead to choose a single moment that correlated well with each latent variable and use that to describe the spectra. The first and second moments fit this specification and, although they are not exactly orthogonal or uncorrelated, they are interpretable as the centroid and dispersion of the spectrum. They also appear to index different significant changes in the spectra (Table II). The first moment decreased after exercise to dyspnea as expected (1, 5, 6, II) (Table III) and also was higher in the early phase of spontaneous breaths of subjects. The physiologic reason for the latter is not clear, although the decrease of Ml after exercise is probably related to mild fatigue. Differences between subjects and patients as well as spontaneous and maximal efforts were evident in M2. If M2 is interpreted as an index of dispersion of the power spectrum then increases (decreases) in M2 mean that the spectrum is less (more) peaked; i.e., the power is more (less) evenly spread over the frequency range. The changes in M2 were small; so small changes in shape would be expected. Until more is understood about the relation between muscle function and the characteristics of the EMG, physiologic interpretation of M2 will remain difficult. Adding the second moment did not increase the ability to detect fatigue. Instead Ml was found to be the most sensitive indicator of fatigue and slight improvement was made by including power at 51 and 149 Hz. Other changes in the EMG such as differences between strength of the effort or between subjects

174

ADAMSETAL.

and patients may be indexed by A42. Further studies with more subjects, under different conditions and including an analysis of the contribution of the noise spectrum, are warranted. Conclusions. We conclude that further relevant information is contained in the diaphragm EMG power spectrum beyond that assessed by the first moment and is best represented by the second moment. The first moment, or centroid, of the EMG spectrum is the most sensitive measure of fatigue currently available from the EMG power spectrum. ACKNOWLEDGMENTS The authors thank Ellen Carabello supported by National Heart. Lung

and R. W. Sweeney for technical assistance. This work and Blood Institute Grants HL-22022 and HL-25606.

was

REFERENCES 1. ALDRICH, T. K., ADAMS, J. M., ARORA. N. S.. AND ROCHESTER, D. F. Power spectral analysis of the diaphragm electromyogram. J. Appl. Physiol. 54, 1579 (1983). 2. GERSCH, W.. YONEMOTO, J., AND NAITOH, P. Automatic classification of multivariate EEG’s using an amount of information measure and the eigenvalues of a parametric time series model features. Comput. Biomed. Res. 10, 297 (1977). 3. HARRIS, F. J. On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE. 66, 51 (1978). 1. KINGMA, Y. J., PRONK. C. N. A., AND SPARREBOOM. D. Parameter estimation of power spectra spectra using Gaussian function. Comput. Biomed. Res. 9, 591 (1976). 5. LINDSTROM. L.. MAGNUSSON, R., AND PETERSEN. 1. Muscular fatigue and action potential conduction velocity changes studied with frequency analyses of EMG signals. Electromyogr. C/in. Neurophysiol. 10, 341 (1970). 6. LINDSTROM, L., KADEFORS. R.. AND PETERSEN. 1. An electromyographic index for localized muscle fatigue. J. Appl. Physiol. 43, 750 (1977). 7. LINDSTROM, L., AND MAGNUSSON, R. I. Intepretation of myoelectric power spectra: A model and its application. Proc. IEEE. 65, 643 (1977). 8. MACKLEM. P. T.. AND Roussos, C. S. Respiratory muscle fatigue: A cause of respiratory failure? Clin. Sci. Molec. Med. 53, 419 (1977). 9. MORRISON, D. F. “Multivariate Statistical Methods.” McGraw-Hill, New York, 1976. IO. NIE, N. H., HULL, C. H., JENKINS, J. G.. STEINBRENNER. K. AND BENT, D. H. “SPSS.” McGraw-Hill, New York, 1975. II. SCHWEITZER, T. W., FITZGERALD, J. W.. BOWDEN, J. A.. AND LYNNE-DAVIES. P. Spectral analysis of human inspiratory diaphragmatic electromyograms. J. Appl. Physiol. 46, 152 (1979). 12. VILA, J. L., MARTINEZ, R., GIMENEZ, J., AND LLABRES, M. MANOVA of statistical moments in biopharmaceutical studies: A numerical example with three equally spaced doses of amoxicillin. J. Pharmacokinet. Biophnrmacol. 8, 411 (1980). 13. HARY, D., BELMAN, M. J., PROPST, J., AND LEWIS, S. A. Statistical analysis of the spectral moments used in EMG tests of endurance. J. Appl. Physiol. 53, 799 (1982).