Temporal, kinematic, and kinetic variables related to gail speed in subjects with hemiplegia: a regression approach.

The importance of clinical gait analysis has been controversial during the several decades of its development. There have been many calls for researchers to rationalize the information arising from gait analyses and to attempt to interpret the phenomena observed.[1] Investigators attempting to interpret the gait variations that are seen in pathologies face the problems of identifying which variables are "meaningful" among the scores that are available. We suggest that variables must be helpful in understanding the nature of the problem - or have what Cappozzo[1] has termed "explicative capacity" to be meaningful. Among the more interesting of these variables are those that the practitioner has some hope of modifying to effect a change in status of a patient or a group of patients.

The gait speed that a patient selects is a well-known indicator of overall gait performance,[2] and it is commonly used to monitor performance and evaluate the effects of treatment. Unfortunately, when used alone, gait speed neither assists in understanding the nature of the gait deficiencies nor is it helpful in directing training. That is, gait speed has no explicative capacity. Identification of the characteristics that distinguish the faster-walking patients from the slower patients, however, would assist in understanding the nature of the gait and could, in some instances, provide a focus for training.

Although a majority of gait studies of patients with hemiplegia have examined temporal variables,[3-5] some have studied kinematic variables,[6] kinetic variables,[7] mechanical energy,[8,9] and work and power.[10] A considerable amount of work has been reported on electromyographic characteristics.[6,11,12] Gait following stroke is grossly characterized by decreased speed of walking, increased stance time on the unaffected side, and decreased stance time on the affected side.[3,6] Joint-angle disturbances include reduction or loss of the knee flexion phase in stance, reduction of knee flexion in the swing phase,[13] sometimes loss of dorsiflexion of the ankle in the swing phase and at initial contact,[14] and generally reduced joint excursions.[15]

Lehmann et all[15] have reported a greater-than-normal internal knee flexion moment at mid-stance in persons with hemiplegia, a feature that was thought to be related to anterior movement of the center of gravity. ("Internal" moments are expressed as those "internal" to the link-segment model; "external" moments are expressed as those acting upon the link-segment model.) The internal moment is usually the result of muscle activity, though tension of structures posterior to the knee may also be involved if the knee is fully extended. Patients with hemiplegia exhibit disturbed mechanical energy patterns and overall energy costs that are above normal.[8,9] The affected limb characteristically has shown tonic extensor activity, coactivation of major muscle groups, and loss of selective muscle control during stance.[6,11] The patterns of activity and the presence of coactivation during walking have been used to classify the gait of subjects with hemiplegia.[11] Muscle power patterns at major lower-limb joints during walking have been near normal in shape but reduced in amplitude, with the muscles of the affected side providing about 40% of the positive work.[10]

Winter[16] has developed a "diagnostic chart" listing observed abnormalities of gait. Four causes of short step length, and therefore of low speed, have been identified: weak push-off prior to swing, weak hip flexors at toe-off and early swing, excessive deceleration of the leg in late swing, and above-normal contralateral hip extensor activity during contralateral stance. Although many descriptions of hemiparetic gait are present in the literature and causes of limitations have been suggested, few attempts have been made to quantitatively relate the detailed biomechanics of gait to general gait performance. The purpose of this study was to use multiple linear regression to assess the strength of association of temporal, kinematic, and kinetic gait variables with high walking speeds in patients with hemiplegia.

Method

Subjects

A total of 32 ambulatory adults with hemiplegia secondary to a cerebrovascular accident were studied in the Human Motion Laboratory of the School of Rehabilitation Therapy at Queen's University (Kingston, Ontario, Canada). The subjects constituted a sample of convenience drawn from patients of the Stroke Rehabilitation Unit of St Mary's of the Lake Hospital in Kingston. To be included in the study, subjects had to be ambulatory, able to follow instructions and to tolerate a testing session of about 2 hours with rests, and willing to participate. All subjects gave informed consent to participate in the study. The 20 male and 12 female subjects had an average age of 61 years (SD=12, range=24-78). The average time since stroke was 11 months (SD=14, range=2-88), and the subjects walked with an average speed of 0.45 m/s (SD=0.2, range=0.13-1.01). All subjects had previously been treated as inpatients in the Stroke Rehabilitation Unit of St Mary's of the Lake Hospital. Three subjects wore ankle-foot orthoses consistently. Ten subjects used no walking aids, 20 used a straight cane, and 2 walked with a quad cane. Twenty-seven subjects were fully independent when indoors; that is, they could walk safely more than 400 m with or without a straight cane. Five subjects required supervision. Outdoors, 21 subjects were fully independent, 8 required supervision, and 3 required minimal assistance. On stairs, 20 subjects were fully independent, 9 required supervision, and 3 required minimal assistance. Individual subject characteristics are shown in Table 1.

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Data Collection

Data collection consisted of filming the subjects as they walked along a walkway containing an embedded force platform(*) of standard size. The subjects walked in their own low-heeled shoes at their own comfortable, natural cadence while data were collected from one good stride in each of six walkway trials, three for each side of the body. They were allowed to hold a straight cane or an attendant's hand if extra guidance was required. A trial was deemed to be good if the camera-side foot was entirely contained within the force platform without the other foot and cane making contact. Prior to data collection, reflective markers were placed on the following camera-side landmarks to provide joint positional information from the film; head of the fifth metatarsal, ankle lateral malleolus, lateral epicondyle of the femur, greater trochanter at the hip joint level, and acromioclavicular joint. Background markers on the wall behind the walkway provided a reference so the body coordinates could be scaled and represented as absolute coordinates.

(*) Advanced Mechanical Technology Inc, 141 California St, Newton, MA 02158.

Filming of each subject was conducted using a cinematographic camera [dagger] (50 frames per second) located 480 cm from the walkway. The camera was mounted on a tracking cart and was guided manually along a track, which ran parallel to the walkway, to follow the subject as he or she walked. At the same time, data were sampled at a rate of 500 Hz from the force platform positioned midway along the runway, which operated in a voltage range of [+ or 1] 10 V. These data were converted to digital form using a custom-built A/D board in a range of [+ or -] 4,096 units and were stored on a desktop computer([double dagger]) along with a synchronizing signal from the camera. Simultaneously, the synchronizing signal produced a digital code on each frame of the film, providing the capability of matching the cinematographic and force platform data in time. When combined with the cinematographic data, information from the force plate permitted calculation of the vertical and fore-aft shear ground reaction forces and the center of pressure of the force vector.

([double dagger]) Model 9845, Hewlett-Packard (Canada) Ltd, 2670 Queensview Dr, Ottawa, Ontario, Canada K2B 8K1.

Coordinates of the body and background markers from a stride were extracted from the cinematographic film using a digitizer([sections]) interfaced to a desktop computer([parallel]) and custom-made software. Raw coordinate data were scaled and corrected for parallax error between the plane of progression of the subject and the plane of the background reference markers using the background markers as a spatial reference. The coordinate data were digitally filtered using a cutoff frequency corresponding to the fifth harmonic of the gait cycle frequency, a selection that is validated by Pezzack et al.[17] A standard seven-segment link-segment model was used in a computer program adapted from Winter[18] to calculate the kinematic and kinetic variables. The fact that a simple two-dimensional model was used means that the hip movements occurring between the pelvis and the spine and between the spinal segments are ascribed to the hip joint.

([sections]) GTCo Datalizer, GTCo Corp, 1055 First St, Rockville, MD 20850.

([parallel]) Model 50, Zenith Data Systems Corp, Hilltop Rd, St Joseph, Mi 49085.

Anthropometric constants, including segmental inertias, were obtained from Dempster[19] and based on each subject's height and body mass. Net joint powers were calculated for each instant in time as the product of net moment across the joint and the relative angular velocity between the adjacent limb segments. The integrals of positive and negative portions of net joint power curves yielded positive and negative work performed across each joint.[19] All kinetic data were normalized to body mass.

The variables selected for statistical analysis were grouped into three categories. The variables and conventions that are not self-evident are defined below.

Category 1-Temporal and

Kinematic Variables

Double support. Difference between stance and percentage of stride at which contact of the other foot occurred. Normal=60%-50%=10%. Value relates specifically to affected or unaffected side.

Maximum dorsiflexion. Maximum angle of dorsiflexion occurring during stance, with positive values indicating degrees of dorsiflexion over anatomical position.

Maximum plantar flexion. Maximum angle of plantar flexion occurring during stance, with negative values indicating degrees of plantar flexion in excess of 90 degrees.

Maximum knee stance. Maximum flexion of the knee occurring during stance phase.

Maximum knee swing. Maximum flexion of the knee occurring during swing phase.

Maximum hip flexion. Maximum flexion of the hip occurring during the gait cycle.

Maximum hip extension. Maximum extension of the hip occurring during the gait cycle.

Category 2-Moments

The polarity convention used for all moments was positive for internal extension moments of the hip and knee and for plantar-flexion moments of the ankle. All data were normalized to body mass.

Category 3-Mechanical Work

and Power

The instantaneous power of the hip, knee, and ankle joints (in watts per kilogram) for each frame of the film was calculated as the product of the net moment and the angular velocity of the joint,[20] normalized by dividing by body mass. The positive work and negative work (in joules per kilogram) performed by the muscles across each joint for each stride were determined by integrating the power curve that had been normalized by dividing each value by the subject's body mass.

Positive sum. Sum of positive work done at all joints normalized to body mass.

Negative Sum. Sum of negative work done at all joints normalized to body mass.

Data Analysis

Statistical Analysis Software (SAS) routines[21] were used to calculate averages for all variables on each side of the body for each subject. Descriptive statistics and sample correlations were obtained. Stepwise regression was used as an exploratory technique to provide evidence as to the best predictors of gait speed rather than to establish predictors with any degree of certainty. The rationale for use of this statistical procedure is provided at the end of this section.

Stepwise regression was used to select 3 or 4 of the 29 variables available that would best be able to account for the differences in speed among the 32 subjects. For each variable, on each side of each subject, the averages over the three runs were used. We chose to include only those variables with levels of significance less than about .001. The reason we chose only 1/50th of the conventional .05 level was that we were choosing the best among 29 possible regressor variables. At any stage, any 1 of the 29 variables could be entered into the regression, and we would have about 30 times the chance of obtaining a value below .05 than we would if only 1 variable were available. This analysis was exploratory in nature; we were seeking to obtain variables that suggest useful lines of approach in understanding gait speed in patients following a stroke.

Once three or four explanatory variables were chosen, the data were reexamined using these variables. Partial regression plots were made and examined for outliers and influential observations so that problems would be identified as a result of data failing to satisfy assumptions. The variables of age, time since stroke, gender, and side of dominance were added to the derived equations to determine whether demographic effects were influencing the results.

Finally, because stride speed is the product of cadence and stride length, any explanation of speed is accomplished through an explanation of stride length and cadence. To investigate these variables, each variable was used in turn instead of stride speed in our regression equations.

The analysis of the subject averages investigated how the different gait variables that typify different patients led to different average speeds. That is, this was an examination of between-subject variations. A second approach used within-subject variations to provide information regarding how the faster or slower strides of an individual subject could be accounted for by larger or smaller values of the gait variables obtained from the stepwise regression. Because these differences are independent of the averages, the within-subject analysis provided an independent check that the variables selected by the stepwise procedure were really important. The much smaller differences in speed, however, would be affected more by carryover from the previous stride, and the statistical significance for these data is limited.

Stepwise Regression

Among the B variables measured, it is possible to pick a few that seem to account for most of the differences in speed among subjects. For example, by calculating correlations for all 29, variables with speed, it is possible to find the best single predictor of speed. However, if we were seeking the best four variables to use together to predict speed, there would be 23,751 possible combinations to test. Such an approach is impractical. Stepwise regression is a technique for finding good combinations of predictor variables without trying all possibilities. We have used the SAS "maximum R[2]" method, which examines more possibilities and consequently provides slightly better variable selections than the more familiar stepwise methods.[22,23]

Results

Examples of profiles of joint angles, net moments, and joint powers are shown in Figures 1, 2, and 3, respectively. Descriptive statistics are presented in Tables 2 through 4. Table 5 presents the Pearson product-moment sample correlations between stride speed and the average from three strides for each of the variables. Because the nonparametric correlations (Spearman and Kendall) were not substantially different from the Pearson correlations, the Pearson values were not likely to be produced by outliers and the conclusions about statistical significance are not likely to be misleading.

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Many variables were highly correlated with stride speed; some deserve particular mention. The single temporal variable relating most closely with speed was the proportion of stance on the unaffected side - the smaller the proportion of the gait cycle occupied by the stance phase, the higher the speed. Among joint kinematic variables, maximum extension of the hip on the affected side was important. The maximum hip flexion moment, which occurs near the time of greatest hip extension on the affected side, was also highly related, as was the hip moment range. Interestingly, the maximum hip extension moment on the affected side was unrelated, whereas that on the unaffected side was highly related. in general, power variables related more closely to speed than moment variables. Of particular note are maximum ankle and hip power on both sides and the sum of positive work on both sides. Contrary to expectations, the positive work of the knee was not significantly correlated with speed on either side. Comparing the two sides of the body, most of the power and work variables of the affected side were more strongly related to speed than were corresponding values of the unaffected side.

Between-Subject Analysis

Table 6 shows the variables selected in the first four stages of a stepwise linear regression using the variables listed. As previously mentioned, we are cautious about using more than three or four of these variables, so we suggest the following equations that may be used to predict walking speed on either the affected or unaffected side of the patient with hemiplegia due to a stroke:

(1) Walking Speed (affected Side) = 0.35 - 0.45 of Maximum Hip Flexion Moment + 0.24 of Ankle Moment Range - 0.24 of Knee Moment Range - 0.007 of Double Support

(2) Walking Speed (Unaffected Side) = 1.34 - 0.015 of Stance + 0.09 of Maximum Ankle Power + 0.24 of Maximum Hip Power As shown in Table 6, these models gave adjusted [R.sup.2] values of .941 and .921, with probability values of [less than or equal to], for each of the variables in the equations.

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Our study of influential observations and outliers revealed that the subject exhibiting the highest speed was influential in regression analyses on both sides of the body and that observations on a second subject were influential on the unaffected side. We examined the extent to which these two observations influenced our results by removing them from the data and found that the [R.sup.2] values were reduced by 2% to 5% but that all variables included in the equations remained significant.

When the demographic variables (age, time since stroke, gender, dominant side) were added to the regression equations, none of them showed significance at the .05 level. This finding indicated that demographic information provided no additional information about stride speed to that already contained in the predictor variables.

When cadence was regressed separately on the chosen predictor variables, 32% of the variation was explained on the unaffected side and 51% was explained on the affected side. The variables explained 73% of the stride length variation on the unaffected side and 60% on the affected side. These findings indicate that the variables have more explanatory power for stride length than for cadence, but that the explanatory power for stride speed is derived from both factors.

Within-Subject Analysis

The second regression analysis made on the deviations of measures of individual subjects from their averages, within-subject variation, confirmed to a large extent the choices made by the stepwise selection on the between-subject variation. All three variables selected on the unaffected side had probability values of <.001, and together they explained 52% of the variation. On the affected side, however, only the first two variables - maximum hip flexion moment and ankle moment range - were significant at the .01 level, and they explained 23% of the variation. The regression equations obtained were as follows:

(3) Deviation in Walking Speed (Affected Side) = 0.07 of Deviation in Ankle Moment Range - 0.13 of Deviation in Maximum Hip Flexion Moment

(4) Deviation in Walking Speed (Unaffected Side) = 0.06 of Deviation in Maximum Ankle Power + 0.11 of Deviation in Maximum Hip Power - 0.007 of Deviation in Stance

Notice that although the equations are similar for those derived among subjects, the coefficients are less than half of those of equations 1 and 2.

Discussion and Conclusions

Limitations

There are a number of limitations to the methodology used in this study. First, the model representing the body was a simple one. The use of a single-segment upper body with no separate pelvis means that pelvic motion could not be assessed independently of the whole upper body. Adding the pelvic segment is a further refinement of this type of modeling, however, and it is unlikely that its inclusion would have provided additional insight at this stage of our knowledge about the kinetics of hemiparetic gait.

Second, the analysis was limited to two dimensions. Because motion occurring in the frontal plane was invisible, one might expect that significant underestimation of work and power would occur. The best reassurance that this is not the case was provided by a study of six subjects with gait pathologies, some of whom had very obvious non-sagittal-plane motions.[24] The three-dimensional analysis yielded few energy differences from the two-dimensional evaluation. Further, the component of most interest during walking is the mechanical work that moves the body in the line of progression, that is, in the sagittal plane. If the lower limb is laterally (externally) rotated, however, so that the adductors contribute substantially to hip flexion, then the work would be wrongly attributed to the hip flexors, although the work is correctly attributed within the plane. The same argument applies to the ankle. If there is some lateral rotation of the limb, only the component of power accomplished in the sagittal plane will be recorded. This is the component in which we are most interested because it is responsible for forward progression. None of the subjects in this study had grossly rotated lower limbs.

A third potential problem is the error caused by manually digitizing the film data. Although some human error is involved in selecting the centers of reflective markers, the magnitude of the error in this and similar laboratories[25] has been found to be about 1 mm RMS (root mean square, or the square root of the average squared difference values for a series of digitized data points). This magnitude consistently produces test-retest reliability in this laboratory greater than .985 (pearson product-moment correlation) for kinematic data.

A further limitation to be considered is the reliance on anthropometric constants for kinetic analysis that were derived from healthy individuals but applied in this study toward persons with hemiplegia due to a stroke.

These constants were not adjusted for the comparatively smaller mass of the affected limb during our kinetic analyses because the resulting differences were considered to be small, due to the slow speed of movement of these subjects.

Other methodological limitations are present in this type of analysis. Some are related to human factors. For example, despite using landmarks for marker placement, there is some unavoidable variation in placement from subject to subject. Others are caused by the simplification of complex problems and the assumptions that are made to achieve workable solutions. For example, in the model used in this study, the camera is assumed to be keeping the subject centered within the frame at a constant distance from the background plane. Variations will produce some error in the results.

Comparisons

The subject group showed many of the temporal characteristics reported to be associated with hemiparetic gait. The walking speed was slightly higher than that of a group of subjects studied by Brandstater et al,[3] judged to be at a stage of recovery that is identified by some selective control of movements outside synergistic patterns (stage 5). With reference to the variables of stance and double support, the averages of our study group were between stages 4 and 5, characterized by the ability to perform some movement other than gross synergies.

Correlations

The emphasis that rehabilitation therapists place on striving for early, definite, and complete transference of weight bearing from the unaffected limb to the affected limb and vice versa is supported by the high negative correlations between walking speed and the variables stance and double support. This relationship has been reported by others.[3,4]

Of the joint-angle variables, maximum extension of the affected hip bore the strongest relationship to speed (4=.61); the greater the angle of hip extension reached in late stance, the greater the speed. Because the temporal and kinematic measures are consequences of kinetic input, they yield little insight into the causes of the speed variations. Because we use temporal and kinematic indicators of performance to achieve change and to monitor progress, however, knowledge of their associations is valuable.

There was also a very strong association (r=.86) between speed and the maximum hip flexion moment, which occurs near the same time as maximum hip extension. During this period, the hip flexor muscles serve to control the extending thigh and subsequently to contract concentrically and start pull-off of the limb.[25] It is reasonable, then, that faster walking with greater hip extension should be associated with a larger hip flexion moment. Further, the moments at the hips have been shown to bear a close relationship to the forward acceleration of the trunk segment,[26] providing support for the hypothesis that the hip muscles are the prime controllers of the balance of the torso on the hips. This is a satisfying, if partial, explanation for the strong association between speed and hip flexion moment. The speed of walking may be determined by the ability of the subject with hemiplegia to provide moments of sufficient magnitude and modulation to control the upper body. As hip flexor strength is usually impaired in these subjects,[27,28] this inability may be a factor that limits gait speed. Such an explanation is consistent with the finding that the speed of walking chosen by patients with stroke is related to the strength of the affected limb.[5]

The number of power and work variables of both sides of the body that were strongly related to speed emphasizes their functional significance. Of particular importance were the ankle positive powers and the positive ankle work from both sides, which are produced by the ankle plantar flexors at push-off. This result is consistent with the observation of the importance of the ankle plantar flexors in normal walking.[20] The high correlations of maximum hip power and positive work of the hip with speed is also noteworthy. The maximum hip power is achieved during late stance and early swing phase (ie, during pull-off), and most of the positive work of the hip is attributable to this phase. In healthy subjects, the hip flexors provide the second largest contribution to the work of walking.[25]

Regression Models

The models produced give a picture of which variables, when taken together, best predict walking speed. Based on data from the affected side, a fast walker should have a long period of weight bearing and a large hip flexion moment at the end of stance phase, which is consistent with a large hip extension angle at that time. The person should also demonstrate a large range between the dorsiflexor and plantar-flexor moments of the ankle, but a small range of knee moments. Based on data from the unaffected side, a fast walker should have a short period of weight bearing, substantial ankle plantar-flexor power at push-off, and a strong pull-off by the hip flexors.

Many of the variables we measured were highly correlated with one another. This finding suggests that some variables selected for the model could be replaced with other variables with which they were highly correlated without much loss of predictive ability. This quality of the variables is described by statisticians as "multicollinearity." Although multicollinearity can be a problem in some regression modeling, it does not interfere here because we only selected one out of a set of correlated variables. Stepwise procedures mitigate against the retention of highly correlated predictor variables.

A consequence of these highly correlated variables is that many regression models that successfully account for most of the variation in velocity are possible. Using stepwise regression on a second data set might well give rise to a model that involves different variables, with both models fitting both data sets well. We can regard the groups of variables that were identified in each step as discrete, but not unique, descriptions of the self-selected walking speed, much as we might regard a sculpture from a number of points of view.

A potential concern of our analysis is that we selected predictor variables from a large collection of possibilities. In spite of using very low significance levels (P<.0001 in most cases), there is still a lingering sense that these variables are not subject to the usual methods of hypothesis testing. Our approach, however, has used only the average values for each subject, and the residuals for these averages (differences among three trials on each subject and their mean) constitute an independent data set. When we regressed these residuals for stride speed on the residuals for the seven selected predictor variables, we found that five of them (those with P<.0001) were significant at the .01 level. This finding confers additional support for these five variables (minimum hip moment and ankle moment range on the affected side; stance, maximum ankle power, and maximum hip power on the unaffected side).

Table 7 shows some of the effects on walking speed to be ascribed to changes in the predictor variables, according to the regression equations. The last column shows the change in speed to be expected if the variable in the equation is changed by one standard deviation. Typically, the change is between 0.05 and 0.1 m/s, or about 10% to 20% of the average speed. For individuals able to attain levels of one standard deviation better than average on all variables, the improvement in speed would be 0.30 m/s (66%) on the affected side and 0.25 m/s (53%) on the unaffected side. individuals achieving levels one standard deviation below average on all the variables would have correspondingly smaller average speeds.

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In order to effect changes in patients' performances, the important question is, "Do individuals improve their walking speed when the values of their predictor variables change in the appropriate direction?" rather than our initial question of "Which variables predict the walking speeds of different subjects the best?" The regression analysis done on the subjects, deviations from their averages (ie, the within-subject analyses) is appropriate to the first question because it shows that the walking speed of a subject increases with appropriate changes in these variables. It is important to study the extent to which equations derived between subjects give information about modifying an individual's gait. However, it is possible that the predictor variables characterizing the walking speed of individuals (selected to answer the second question) might not vary from stride to stride in individuals, and consequently would be useless in helping to train subjects to improve their walking. For example, if 30 subjects were at the limit of their range for their minimum hip moment, there would be little variation in minimum hip moment within subjects, but there would still be considerable variation between subjects. in this example, minimum hip moment would contribute significantly to between-subject variation in speed but would not be significant in explaining within-subject variation. Therapeutic programs such as biofeedback that are directed toward changing specific variables have potential only if the within-subject variation relates predictably to speed.

The coefficients of the within-subject equations (0.07 and -0.13 from equation 3 and 0.06, 0.11, and -0.007 from equation 4) are generally less than half those for the between-subject equations (0.24 and -0.24 from equation 1 and 0.09, 0.25, and -0.015 from equation 2). The differences in coefficients are partly attributable to measurement error. Because the residuals are differences in observations rather than averages of three observations, the residuals from individual averages contain relatively large measurement errors. To examine the effect of the increased error, we made a number of simulations with coefficients the same, but with errors in the predictor variables. We found that the values of the within-subject coefficients were typically reduced to about 60% of their true values. Thus, the results of equations 1 through 4 are not incompatible, with the within-subject equations being the same as the between-subject equations (except for the two variables that failed to appear). As we have noted in the minimum hip moment example, however, there is no a priori reason why the true coefficients should be equal.

Certain variables are notable by their failure to be significantly correlated with speed, or their absence from the models. For example, a great deal of time is spent in gait training of "knee control," or controlled flexion of the knee during stance phase, yet knee flexion in stance was poorly related to speed and no knee variables appeared in the models. The minimum power of the knee, however, was itself highly correlated with speed on the affected side. This knee power phase, which absorbs energy, occurs late in stance and results from eccentric quadriceps femoris muscle activity while the knee is flexing and the foot remains on the ground.(#) This result seems paradoxical; we would expect that energy absorption would relate negatively to speed. Our results, however, indicate that unless this knee flexion occurs, the subject cannot achieve a functional push-off at the ankle, nor an effective pull-off by the hip.

(#) Electromyography of the quadriceps femoris musculature has show low levels of activity late in the stance phase, particularly in the rectus femoris muscle.[25] Because mechanical power is the product of the moment generated by this low level of activity and the angular velocity of knee flexion, the eccentric power that results is substantial.

Versatility and Compensation

A linear regression model based on several predictor variables inherently contains ambiguity about the method by which a specified speed is produced. Thus, high values of one predictor variable and low values of a second predictor variable may produce the same speed as low values of the first variable and high values of the second variable. For example, an individual might be able to achieve a speed of 0.735 m/s using either a maximum hip flexion moment of -0.72 N.m/kg and an ankle moment range of 0.25 N.m/kg or a maximum hip flexion moment of -0.10 N.m/kg and an ankle moment range of 1.42 N.m/kg (Fig. 4). We would describe such a subject as versatile. Because we have used a stepwise procedure to derive our regression equations and the variables selected are not likely to be highly correlated, it is very likely that there will be versatility among individuals, indicating that different subjects will produce the same speed by different means.

Compensation may be observed in a subject who is unable to increase the ankle moment range beyond 0.68 N.m/kg, but can still reach a reasonable speed by producing a maximum hip flexion moment of -0.95 N.m/kg. This would be an example of one-sided compensation within the affected side. Our study sheds some light on between-limb compensation in this subject group - the compensation of the unaffected limb for deficiencies of the affected limb. The magnitude of the explanatory power of one side alone is quite surprising, and indicates a redundancy of information and a consistency in relationship between the events of the two sides. Because the affected side carries information that allows us to predict the speed accurately, we deduce that the unaffected limb cannot compensate independently of the affected limb. Because of this interdependence, we cannot rely on compensation by the unaffected side alone to increase walking ability, as sometimes has been suggested,[29] but must also increase the performance of the affected side. It is tempting to hypothesize that the gait performance of subjects with hemiplegia is determined within a very narrow range by the performance components of the affected limb.

Applications

These results suggest that experimental studies are needed to assess the effects of treatment aimed at increasing ankle power and hip power and at decreasing the stance time on the affected side. Richards and colleagues[30] have reported positive outcomes for an experimental group of patients whose treatment included isokinetic exercise and treadmill walking. It would be helpful to conduct a similar study, focusing treatment specifically on the variables identified by our study, to determine whether the model is useful in prescribing effective interventions. The data also suggest the need for examination of an intervention directed at obtaining a larger hip flexion moment and a larger ankle moment range on the unaffected side. In designing these intervention studies, our study suggests that compensation involves all of these factors, from both sides of the body, and that the intervention should not be focused on training a single "weak link," but should target all of the predictor variables.

The degree to which these regression equations are specific to the disability of stroke is not known. It does not seem likely that the equations would describe differences in the walking speed of healthy subjects. Although we do not have comparable data on healthy subjects, such an exploration promises interesting insight into these questions.

Many questions remain unanswered. Information gained simultaneously from both sides of the body might yield more economical explanations of the walking speed than the models presented. The questions surrounding symmetry and its role in gait could be addressed. Information about the relationships between the two sides would also be helpful in understanding the nature and degree of compensatory mechanisms that are used. In addition, this information would account for more within@subject variation. This approach has the potential of revealing many aspects about the manner in which individual subjects can improve their own gait performance, and may give further insight into methods of gait reeducation.

Acknowledgments

We acknowledge the assistance of Cally Martin, BSc(PT), and Pat Cross, BSc(PT), and the patients from the Physiotherapy Department of St Mary's of the Lake Hospital.

References

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