Journal of Orthopaedic Research 8259-265 Raven Press, Ltd., New York 0 1990 Orthopaedic Research Society

Dynamic Electromyography . 11. Normal Patterns During Gait M. E. Wootten, M. P. Kadaba, and G. V. B. Cochran Orthopaedic Engineering and Research Center, Helen Hayes Hospital, West Haverstraw, New York, New York, U.S.A.

Summary: Human gait is a complex phenomenon. Many descriptors are needed to completely describe gait in terms of the biomechanics involved. The descriptors, when expressed as a function of the gait cycle, are complex waveforms. For each of these variables, a single “normal” pattern with bands of deviation has generally been accepted as a reference in clinicdresearch use to explain the abnormalities in a patient’s walking pattern. In fact, one observes many “normal” patterns, and a body of research has been devoted to explaining the differences between these patterns in terms of walking speed, age, cadence, sex, etc. It would be simpler in one sense to start with the fact that different people walk with different patterns, not one pattern with bands of deviation. Numerical representation of the waveforms simplifies the analysis and interpretation of waveform data and facilitates comparison between subjects or groups of subjects. When combined with pattern recognition techniques, it also is useful for identifying subpatterns within a group. In this article, the numerical representation of electromyographic data by KarhunenLoeve expansion are combined with cluster analysis to obtain patterns of dynamic phasic activity of 10 muscles of the lower extremity. From the 35 normal subjects walking at self-selected speed, two to four patterns are developed for each of the muscles and the physiological significance of the patterns are discussed. Key Words: Gait-Dynamic electromyography-Cluster analysis-Pattern recognition-K-means.

The results of quantitative gait analysis are beginning to be widely used to assess gait disabilities, select treatment, and evaluate efficacy of treatment. The gait descriptors, when expressed as a function of the gait cycle, are complex waveforms whose interpretation can often be complicated by the fact that patterns tend to vary significantly between individuals belonging to the same population. This is particularly true for the phasic muscle activity since the flexibility and redundancy afforded by the monoarticular and biarticular muscles of the

lower extremity facilitate different combinations of muscle activity patterns to yield similar lower limb kinematics. Winter and Yack (17), Shiavi et al. (12), and more recently Arsenault et al. (1) showed that phasic activity patterns tend to vary significantly for certain muscles of the lower extremities even among normal individuals. Interpretation of gait data would be simplified if a range of patterns of phasic muscle activity for each muscle or muscle group could be identified within each subject population. Numerical representation of waveform data together with clustering analysis have been used extensively to identify patterns of physiological data in a group Of subjectsOr patients (4)-Shiavi and Griffin (11) uscd clustering analysis on a numerical

Received October 21, 1987; accepted April 26, 1989. Address correspondence and reprint requests to Ms. M. E. Wootten at Gait Analvsis Laboratorv. Helen Haves Hosuital. . Route 9W, W. Hnverslraw, N.Y. 10993, U.S.A. .

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M . E. WOOTTEN ET AL.

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representation of muscle activity timing to derive patterns for various muscles of the lower extremity during level walking. Wong et al. (18) developed and used a hybrid clustering algorithm on a Fourier coefficient representation of lower-extremity jointangle motion data. They identified homogeneous subgroups within a population of cerebral palsy patients using combined joint-angle data from hip, knee, and ankle joints. In this article, we present an application of cluster analysis techniques to phasic electromyographic (EMG) data from a group of normal subjects for identifying homogeneous patterns or subgroups. Principal component analysis, described in Part I of this article (19), is used for the numericaI representation of phasic muscle activity. We develop patterns for each of the 10 muscles of the lower extremity and demonstrate that the numerical representation in conjunction with cluster analysis can yield patterns that are physiologically meaningful. METHODS

Electromyographic data recorded from 10 muscles of 35 normal subjects evaluated 3 times on each of 3 different test days were used to identify patterns of phasic muscle activity. The rectified, smoothed, and averaged data (averaged over 9 runs or 27 cycles) from 10 muscles were represented as a 32-point vector. The principal components of EMG data were determined and the first three to five weighting coefficients (features) were used to represent the average EMG pattern for each subject. The features from each muscle of the 35 normal subjects were used as input into cluster analysis algorithm. Two clustering algorithms, namely the one-way split ( 5 ) and k-means (6), were used to form the patterns based on the features. The one-way split algorithm starts with all the subjects in one group and splits them into subgroups (clusters) on the basis of the variance of the variables that, in this study, are the weighting coefficients of each muscle for each subject. The algorithm works on one cluster at a time and finds the split that maximizes the absolute differences in the averages of the two groups. Once the cluster is split, the variance of the variables is again calculated. If the variance within a variable is small (less than a given threshold), then that variable is not considered in the next split. If it is below the threshold for all variables, the algorithm proceeds to the next cluster. If any variable still has a variance

J Orthop Res, Vol. 8 , No. 2 , 1990

greater than the threshold, the group is split again. The result of this type of cluster analysis is a hierarchical structure of subgroups. The k-means algorithm is a standard algorithm; the details about the technique and implementation can be found in several references on clustering ( 3 3 . Briefly, the procedure iteratively regroups the subjects into k clusters so the overall mean square distance to each group center is minimized. The distance measure used is the Euclidean distance of the individual cases to the center of the group. The starting cluster centers and the number of clusters are provided by the operator. A cluster center, which is the mean of the cases in the cluster, is computed at each iteration. The algorithm stops if the subsequent regrouping does not reduce the overall distance. The critical considerations when using the k-means algorithm are the initial cluster centers and the number of groups/clusters in the partition, which are input into this algorithm; in this study, both were varied to determine the final clusters. The clusters reported in this article were calculated using the k-means algorithm and checked against the results of the one-way split. Three considerations were used to develop the final groups: the stability of the groups, the number of groups (clusters), and the similarity of the final clusters computed using the two different clustering algorithms. The groups were considered stable if different initial cluster centers yielded identical groups. To determine the number of clusters, Hartigan ( 5 ) suggested using the overall mean sum of square ratio (MSSR) as a criterion. The MSSR is defined as: MSSR

=

{[e[P(m,k)l/e[P(m,k x ( m - k + 1)

+

I)]]

-

1)

(1)

where e [P(m,k)] is the sum of the squares of the Euclidean distances in partitioning m cases into k clusters. If the ratio when splitting into k + 1 instead of k groups is high (by a factor of about lo), then the split into k + 1 clusters is appropriate (5). This rule was applied to determine the number of subgroups in the final partition. Finally, the clusters were considered to be reliable if the k-means and the oneway algorithms yielded identical or nearly identical clusters. The centers of the final clusters were used to reconstruct the representative linear envelope of muscle activity for the groups. The sum of the matrix product of the weighting coefficients of the cen-

DYNAMIC ELECTROMYOGRAPHY 11

261

clusters were chosen. The final clusters selected using the k-means algorithm were approximately similar to clusters determined using the one-way algorithm. The members of the groups were often identical; but even when not identical, the reconstructed mean vectors for the groups had no perceivable differences. Therefore, only the results from the kmeans algorithms are presented here. The squared correlation coefficients between the pairs of mean vectors of each subgroup are shown in Table 2, and are presented as a measure of similarity/dissimilarity between the groups. The patterns of muscle activity identified for the muscles evaluated in this study are shown in Figs. 1-5, and the number of subjects in each subgroup are shown as a percentage of the total number of subjects. For the gluteus maximus (Fig. l), only minor differences were apparent between groups 1 and 3, which combined, represented 86% of the subjects. The pattern of activity for subjects in group 2 was continuous, and the highest level of the activity occurred just after heel strike for all three groups. Some activity was present during preswing, which presumably is used to control the flexion of the hip. For the gluteus medius, the phasic pattern of muscle activity was similar to the pattern reported by other investigators (13,14,16), except that the subjects in this study did not depict any activity during stance/swing transition. These results are in concurrence with the results reported by Lyons et al. (9). For the first group, there was an increased level of activity during midstance, which is most likely used for lateral hip stability. Three distinct patterns were identified for the adductors (Fig. 2). The pattern for the first group showed very little activity during loading response and most of the activity occurred during preswing,

ter and the associated basis vectors were used as the representative vector for each cluster. In addition, correlation coefficients between pairs of representative vectors were also computed as a measure of similarity between groups.

RESULTS In the k-means algorithm, a random number generator was used to pick the initial centers and the clustering was repeated 20 different times, each time using different initial centers. For most muscles, when splitting into two clusters, the choice of initial centers did not change the composition or the number of subjects in each of the subgroups. Generally, when splitting into three clusters, the composition of the subgroups differed by one or two subjects. In this case, the partition that most frequently yielded the same subgroup composition was chosen; in all cases, this also depicted a minimum within cluster total sum of squares. However, with increasing partition size (i.e., >5), the composition, as well as the number of subjects in each of the subgroups was highly variable. In these cases, the partition with the minimum within total cluster sum of squares was again selected. Table 1 shows the overall MSSR calculated using eq. 1. The MSSR results depict clear stopping points for most of the muscles evaluated in this study, with the exception of the gluteus maximus and the vastus lateralis. According to the criterion suggested by Hartigan, all the muscles have possible stopping points in clustering at a partition size of 2 clusters. The gluteus maximus has possible stopping points at 2, 3, and 5 clusters, and the vastus lateralis at 2, 3, and 6. Three clusters were chosen for all the muscles, with the exception of gluteus medius, for which only 2

TABLE 1. Ratio of mean within sums of squares R for k:k

+

1 clusters

Muscle

1:2

2:3

3:4

4:5

5%

Gluteus maximus Gluteus medius Adductor longus Vastus lateralis Rectus femoris Vastus medialis Medial hamstring Lateral hamstring Anterior tibialis Gastrocnemius

27.9 22.3" 19.4 15.9 14.9 15.5 15.8 12.6 17.9 17.3

15.3" 8.4 9.9" 10.4" 12.7" 10.3" 15.6" 13.5" 12.8" 14.0"

4.8 7.9 6.3 5.2 8.5 6.7 7.0 6.2 8.4 8.5

11.0 6.5 5.9 7.8 6.4 6.7 5.5 6.7 4.5 7.7

5.4 4.9 4.6 10.8 3.9 6.2 6.9 6.0 3.2 6.7

Selected stopping point.

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TABLE 2. Correlation coefficients (?) between the clusters identified for each muscle Muscle

Groups 1 and 2

Groups 1 and 3

Groups 2 and 3

0.76 0.86

0.91

0.92

-

-

0.27

0.60

0.86 0.83

0.90

0.61 0.88 0.64

0.92

0.92 0.69 0.05

0.92

0.80 0.76

0.77

Gluteus maximus Gluteus medius Adductor longus Vastus lateralis Rectus femoris Vastus medialis Medial hamstring Lateral hamstring Anterior tibialis Gastrocnemius

0.35 0.03 0.86 0.77

0.76

0.36 0.60 0.80

which is thought to control hip abduction as the weight shifts to the opposite limb. The second and third groups had muscle activity at foot contact and two additional peaks of activity, one during double limb support and another during swing phase. The difference between these two groups was mainly in the location of the peaks, i.e., the maximum peak for group 2 occurred during swing phase, whereas that for group 3 occurred during preswing. During preswing, the adductors eccentrically contract to stabilize the pelvis as weight is shifted to the opposite limb and concentrically contract during swing as the thigh adducts in preparation for foot contact (8). The differences for the adductors in the three groups may therefore be attributed to varying relative levels of eccentric and concentric contraction during the preswing and swing portions of the gait cycle. The adductor muscle group also displayed a

G l u t e u s Maximus

higher intra- and intersubject variability (7), compared with other muscles evaluated in this study. Figure 3 shows the patterns identified for each of the muscles in the quadriceps group. The patterns for the vastus lateralis and medialis were very similar. Within each of these muscles, there was a difference in the patterns of muscle activity between terminal stance and preswing, and there were slight differences in the timing of activity during swing/ stance transition. The differences in the patterns for the rectus femoris muscle were mostly characterized by variable amounts of activity at stancehwing transition. The patterns for the medial and lateral hamstrings (biceps femoris-long head) are shown in Fig. 4. For the medial hamstring, all three groups had major activity during terminal swing, which is used to decelerate the shank in preparation for foot contact. For group 1, the major activity continued through loading response, whereas for group 3 , the activity terminated just after heel strike. For the lateral hamstring, group 2 had maximum activity during terminal swing, whereas group 3 had a maximum at foot contact. There was also considerable activity during stance starting after loading response and lasting until preswing in group 2 for the medial hamstring and group 1 for the lateral hamstring. The average walking speed of these two groups (Table 3) was high compared with the overall average. In the groups identified for the anterior tibialis, the waveforms were essentially similar with differ-

Gluteus Medius 49%

46%

-?A

!a,_____/ I

I I

0

G

I " " " ' P " " " i " ' " ' ' l

FIG. 1. Patterns of activity for the gluteus maximus and glut e u s m e d i u s ( a v e r a g e of groups). The number of subjects in each subgroup is shown as a percentage of the total number of subjects (35 subjects).

54%

14%

qfi 0

37%

0

PERCENT Of CYCLE

J Orthop Res, Vol. 8, N o . 2 , 1990

100

PERCENT OF CYCLE

I00

DYNAMIC ELECTROMYOGRAPHY 11 Adductor Longus

263

was continuous throughout stance phase.The patterns of activity for the gastrocnemius was similar to the traditional pattern reported in the literature, with activity slightly delayed in group 3 relative to group 2. Group 1 had two bursts of activity during stance to more actively decelerate the forward rotation of the tibia following weight acceptance (10,15) and then allow the foot to dorsiflex and stay in relative dorsiflexion during stance.

31% A

26%

DISCUSSION

43%

-

I

I'"""I"""'I

E

IBE

PERCENT OF CYCLE

FIG. 2. Patterns of activity for the adductor muscles (adductor longus) (average of groups). The number of subjects in each subgroup is shown as a percentage of the total number of subjects (35 subjects).

ing relative magnitudes. The groups had peak activity at foot contact, which may be responsible for preventing foot slap, and varying amounts of activity during swing phase, which allows dorsiflexion of the foot. The drop in activity during swing apparently allows the foot to evert during mid-swing (2). The pattern of activity for the subjects in group 3 Vastus Lateralis

In this article, we demonstrated the utility of a numerical representation in conjunction with cluster analysis for determining patterns of phasic activity of the muscles of lower extremity during level walking in a group of normal subjects. We showed that the technique is sensitive enough to represent a wide range of differences in the phasic muscle activity patterns. The results also confirm that for each muscle, there is more than one pattern of muscle activity for this group of 35 normal subjects. The results are in general agreement with those of Shiavi and Griffin (1I), except that the smaller number of subgroups or patterns were identified for each muscle. This may be due to the composite binary representation used by Shiavi and Griffin compared with the area vector representation of EMG used in this study. The patterns identified for each muscle appear to be reasonable from a physiological point of view

V a s t u s Medialis

47%

40%

Rectus Femoris

37%

14%

11%

I

e

m w a CYUE

63%

J

I 88

R

mw ff CYCLE

lea

e

m w OF C Y a E

1RR

FIG. 3. Patterns of activity for the quadricep muscles (average of groups). The number of subjects in each subgroup is shown as a percentage of the total number of subjects (35 subjects).

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264

L a t e r a l Hamstring

Medial Hamstring

57%

7

l

9%

i

"

~

~

~

~

~

l

"

'

*

'

~

u

~

46% I I

I I

~

~

-

~

~

34%

*

~

,

~

I

~

~

~

'

'

~

~

l

FIG. 4. Patterns of activity for the medial hamstring (semitendinosus) and lateral hamstring (long head of b i c e p s f e m o r i s ) (average of groups). The number of subjects in each subgroup is shown as a percentage of the total number of sub~ * ~ * , ~ ~ ~ ~ jects (35 subjects).

48%

A PERCENT OF CYCLE

E

and may be interpreted in terms of the biomechanics of lower extremity. Based on the correlation coefficient results (Table 2), it appears that the groups (clusters) for the biarticular muscles are more distinct from each other than those for monoarticular muscles. These results are supported by the intersubject variability results of Winter (17), which show that the phasic activity patterns of biarticular muscles are much more variable than monoarticular muscles. Our own results (7) also confirm these findings. Another factor that may affect the pattern of phasic muscle activity is the walking speed (12). Even though the subjects in this study were instructed to walk at their natural or preferred speed, no attempt was made to control the speed with vi-

I aa

sual or aural cues. It is therefore possible that the differences in the patterns could be due to the differences in walking speeds between the groups. Table 3 shows the mean walking speed for the subjects in each group for each muscle. For the subjects evaluated in this study, the group membership between the muscles were not similar. In other words, subjects in a particular group of one muscle did not cluster into a single group for other muscles. However, when pairs of agonists or agonist/antagonist muscle groups were examined, the constituents of the subgroups were related. For example, in the case of gluteus maximus and medial hamstring (agonist pair in hip extension), 77% of the subjects in group 3 of gluteus

Anterior T i h i a l i s

FIG. 5. Patterns of activity for the anterior tibialis and gastrocnemius (medial head) (average of groups). The number of subjects in each subgroup is shown as a percentage of the total number of subjects (35 subjects).

j ei._/:,_.._ (I

I

I " " " ' I " " " ' I " " " l I

28%

12%

E

PERCENT OF CYCLE

J Orthou Res, Vol. 8, No. 2 , 1990

I00

E

PERCWT OF CYCLE

I00

~

'

~

I

265

DYNAMIC ELECTROMYOGRAPHY 11 TABLE 3 . Average walking speed of each group f o r each muscle (cmls) Muscle

Group 1

Group 2

Group 3

Gluteus maximus Gluteus medius Adductor longus Vastus lateralis Rectus femoris Vastus medialis Medial hamstring Lateral hamstring Anterior tibialis Gastrocnemius

133 128 133 134 129 134 124 156 129 138

125 132 118 123 114 131 145 127 126 131

128 134 127 138 122 136 129 143 123

maximus were found in group 1 of the medial hamstring muscle. Similarly, 50% of the subjects in group 1 of gluteus maximus were found in group 3 for the medial hamstring muscle. As an example of an antagonist pair of muscles, 66% of those in group 3 , rectus femoris, are in group 2, lateral hamstring, and 68% of those in group 1, rectus femoris, are in group 3 , lateral hamstring. Similar results were obtained for other agonist/antagonist pairs. The two clustering algorithms used in this study yielded similar results. In the one-way split algorithm, the variances within each of the variables (features) are directly used as the criteria determining the clusters, and the search algorithm is more exhaustive. The only uncertainty in using this algorithm is the lack of a rigorous and objective stopping criteria for partitioning the groups. In comparison, the k-means algorithm, a generalized stopping criteria proposed by Hartigan (3,could be used to determine the number of clusters. In summary, the results from this study suggest that there are similarities and differences in the manner in which locomotion is achieved in normal subjects. Numerical representation facilitates comparison of data across groups to define key differences. The clustering algorithms investigated are more than adequate in identifying subtle differences within groups. For this group of normal subjects, some of the differences in subgroups are so slight they do not appear to have clinical significance; for example, groups 1 and 3 for vastus lateralis and groups 1 and 2 for vastus medialis. This only confirms that the combined technique of principal component representation and cluster analysis can identify very subtle differences in waveforms within a group, which are difficult to identify by visual in-

spection. Understanding the synergy of muscle activity patterns may be useful in understanding the abnormal forces and moments generated and thus help determine the cause and/or effect in resulting kinematics and kinetics. REFERENCES 1. Arsenault AB, Winter DA, Marteniuk RG: Is there a “normal” profile of EMG activity in gait? Med Biol Eng Comput 24:337-343, 1985 2. Basmajian JV, DeLuca CJ: Muscles Alive, Baltimore: Williams & Wilkens, 1985 3. Chen CH: Statistical Pattern Recognition, New Jersey: Spartan Books, 1973 4. Cohen A: Biomedical Sinnal Processina, - Vol. 11. Boca Raton, Florida: CRC Press: Inc., 1986 5. Hartigan J: Clustering Algorithms, New York: John Wiley & Sons, 1975 6. Hartigan J, Wong MA: A K-means clustering algorithm. In: Applied Statistics Algorithms, ed by Griffiths P and Hill ID, West Sussex, England: Ellis Honvood Limited, 1985, pp 192-202 7. Kadaba MP, Ramakrishnan HK, Wootten ME, Gainey J, Gorton G, Cochran GVB: Repeatability of kinematic, kinetic and electromyographic data in normal adult gait. J Orthop Res 1988 (in press) 8. Knutsson E, Richards C: Different types of disturbed motor control in gait of hemiparetic patients. Brain 102:405430, 1979 9. Lyons K, Perry J, Gronley J, Barnes L, Antonelli D: Timing and relative intensity of hip extensor and abductor muscle action during level and stair ambulation. Phys Ther 63:15971605, 1983 10. Murray MP, Guten GN, Sepic SB, Gardner GM, Baldwin JM: Function of the triceps surae during gait. J Bone Joint Surg [Am] 60:473476, 1978 11. Shiavi R, Griffin P: Representing and clustering electromyographic gait patterns with multivariate techniques. Med Biol Eng Comput 19:60&611, 1981 12. Shiavi R, Champion S, Freeman F, Griffin P: Variability of EMG patterns for level-surface walking through a range of self-selected speeds. Bull Prosthetic Res 185-14, 1981 13. Shiavi R: Electromyographyic patterns in adult locomotion: a comprehensive review. J Rehabil R D 223-98, 1985 14. Soderberg G, Dostal W: Electromyographic study of three parts of the gluteus medius muscle during functional activities. Phys Ther 58:691496, 1978 15. Sutherland DH, Cooper L, Daniel D: The role of the ankle plantar flexors in normal walking. J Bone Joint Surg [Am] 62:354-363, 1980 16. Winter DA: The Biomechanics of Motor Control of Human Gait, Ontario: Waterloo Press, 1987, p 50 17. Winter DA, Yack HJ: EMG profiles during normal human walking: stride-to-stride and inter-subject variability. Electroencephalogr Clin Neurophysiol67:402411, 1987 18. Wong MA, Simon S, Olshen R: Statistical analysis of gait patterns of persons with cerebral palsy. Stat Med 2:345-354, 1983 19. Wootten ME, Kadaba MP, Cochran GVB: Dynamic electromyography . I. numerical representation using principal component analysis. J Ortho Res 8:247-258, 1990

J Orthop Res, Vol. 8, No. 2 , 1990