LABORATORY REPORT COVER PAGE - Penn Engineering



PROJECT FINAL REPORT COVER PAGE

GROUP NUMBER T3

PROJECT TITLE: Force Development in Posterior Superficial Leg Muscle;

Guidelines for Rehabilitation of Gastrocnemius

DATE SUBMITTED 12/18/2000

ROLE ASSIGNMENTS

ROLE GROUP MEMBER

FACILITATOR……………………….. Elizabeth Bucholz

TIME & TASK KEEPER……………… Adam Engler

SCRIBE……………………………….. Matt Fink

PRESENTER…………………………. Amy Rosen

Summary of Project Conclusions

The force, measured in body mass units (BMU), generated in the gastrocnemius muscle was determined to be linearly related to speed, stride length, stride rate, length of leg for walking gait. The experimentally derived equation expressing this relationship was determined to be: Fw = (1.7379 ( 0.0737)*v – (2.3536 ( 0.1718)*r – (0.9832 ( 0.0364)*s – (0.0074 ( 0.00004)*l + (2.6235 ( 0.1968) where F is measured in BMU, v is speed in m/s, r is stride rate in 1/s, s is stride length in m, and l is length of leg in m. An R2 = 0.7866 was found for the correlation of the forces predicted by this equation with experimentally determined forces after multiple linear regressions of all measured variables. The equation for force generated in the gastrocnemius as a function of running was determined to be: Fr = (0.7384 ( 0.0222)*s/l – (0.5394 ( 0.0200)*s – (2.6276 ( 0.6692)*f + (1.2833 ( 0.0773) where the additional variable f is foot length, the distance between the ball of the foot and the heel measured in meters. The R2 was determined to be 0.5774 for after multiple linear regression analysis. These two equations can be used to predict forces in the gastrocnemius during different gait cycles for healthy individuals in their early twenties. The weaker correlation of the variables for running was due to unmeasured variables such as maximum height reached and sway at greater speeds. Further investigation of these and other variables would give a more accurate prediction of the forces generated in the gastrocnemius muscle while running.

Objectives

The goal of this experiment was to determine the relevant physiological parameters responsible for generation of force in the gastrocnemius during walking and running. An experiment was designed to measure electrical signals from the gastrocnemius muscle of the leg using surface electromyography (EMG). The EMG signals were to be correlated to forces developed in the muscle during dynamic loading conditions through a calibration scheme relating force to mean integrated EMG. Force was predicted to be a function of speed, stride length, length of leg, and stride rate.

It was further hypothesized that right and left legs would not be statistically different in their calibration graphs, since one leg is not usually favored as could be the case with the hand or arm.

The specific aims of the experiment were two-fold. First, it was necessary to determine the statistically significant factors affecting force in the gastrocnemius muscle and compute formulas relating force to these variables for walking and running conditions. These equations could be used for rehabilitation and training situations. A non-invasive, quantitative force measurement was expected to assist patients in recovery and training by limiting the possibility of muscle injury/re-injury from overexertion.

Background

Biological:

The medial head of the gastrocnemius has its origin at the posterior nonarticular surface of the femoral condyle, while the lateral head originates at the lateral surface of the femoral condyle. The two heads unite to form the bulk of the muscle and finally unite with the tendon of the underlying soleus muscle to form the Achilles tendon, which inserts into the heel. The gastrocnemius muscle is a fusiform muscle, a long muscle with fibers that aid in contraction and motor recruitment1.

This muscle functions to create a powerful flexor of the ankle. Contraction of the muscle pushes the foot downward, giving the force used to propel the body forward during walking and running. The major complication to gastrocnemius EMG is apparent cross talk between the underlying soleus muscle and the gastrocnemius muscle. Since the soleus muscle controls the end of the gait cycle, it is known to have a “pick up” effect for the muscle, carrying through the stride when the gastrocnemius completes its contraction2,3. However, this cross talk in the EMG signal is only present during dynamic situations and can be isolated by low-pass filtration after the end of the gastrocnemius muscle contraction.

Stride Mechanics:

The gastrocnemius muscle is in contraction for 62% of the walking/running cycle, and continues the contractile cycle with the flexing of the knee when completing the stride. Since it is responsible for pushing the foot off of the ground, most of the force that it generates is a product of the muscle and the torque of the ankle-foot lever4. Beyond simple contractile cycles, the gastrocnemius itself has remained relatively unstudied, with no comparable literature values for any levels of contraction. However, the stride of the subject is complicated by other physiological concerns, namely the natural tension in the Achilles Tendon, which anchors the gastrocnemius muscle to the heel. Davis et al. noted in cadaver trials that the human Achilles Tendon contributes from 70 – 80 N for normal plantarflexion (1999).

Theory and Methods of Calculations

JMP IN version 4.0 was used to statistically analyze the data as it allowed multiple linear regression. Multiple linear regression allows multiple variables, such as speed, stride length, stride rate, length of leg and other factors to play a role in predicting the data acquired. The R2 value determines how well the predicted force relates to the actual force using analysis of variance. The variables impacting force were expected to be linear since no prior data had suggested that they were not.

Methods and Materials

Calibration of subjects and experimental trials were performed using BIOPAC Student Lab Pro Software (BIOPAC Systems, Inc.; Santa Barbara, CA) with a program written to measure two EMG signals in channels 1 and 2 and simultaneously display their integrated EMG values in two additional channels, 40 and 41. BIOPAC SS2L electrodes, leads and model MP30 signal conditioner were used to conduct and filter the signal. To calibrate all of the subjects free weights of 5, 10, and 25 lbs were used along with 2 bathroom scales (Thinner model P0005) to record forces generated in each gastrocnemius. A Spacesaver Treadmill Model 83129401 was used to conduct the dynamic gait trials, while allowing the subjects to walk and run in place. For all data, JMP IN v4.0 statistical analysis software (SAS Institute Inc.; Cary,NC) was utilized.

Subjects were calibrated each time an experimental trial was performed. Electrodes were connected to the skin overlying the gastrocnemius muscle in a triangular orientation (negative – upper lateral head, ground – lower lateral head, positive – lower medial head) on both the left and right calves. Subjects were positioned with their legs spread apart equidistant to the width of the hips in order to best equilibrate their weight distribution (so that the angle ( = 0 with respect to the center of mass), and a scale was placed under each leg. Toe-lift exercises, which isolated the gastrocnemius muscle’s contraction, were repeated for five times per weight while EMG and force measurements in the muscle were taken from both legs. To vary body mass, additional weights were added maintaining the initial center of mass. After calibrations were performed at each weight, the subject rested for two minutes in between each increment to eliminate any effects of fatigue. The force vs. mean integrated EMG curve was then plotted for six to eight different weights, ranging from forces of one half to twice body mass.

Subjects participated in the experimental running and walking trials with EMG, speed, and trial time data taken for both legs. Subjects walked at an initial speed of 1.0 miles/hr for twenty to twenty-five strides. The speed was then increased in increments of 0.5 miles/hr until the subject could no longer maintain walking, which was defined as maintaining one foot on the ground at all times. To assist both the subject and researchers, a motion capture system was used to observe the walking trials to ensure consistent gait. Walking trials continued until the subject’s maximum speed, 6.0 miles/hr for most subjects, was reached. The same protocol was used for running trials, with the speeds ranging from 4.0 miles/hr to 8.0 miles/hr.

For each trial, the mean integrated EMG and time of twenty strides were taken at each speed and converted to force using the subject’s calibration. Analysis of Variance (ANOVA) was carried out to determine which of the variables mentioned were significant for the force generated in the gastrocnemius. The dependant variable, force, which was a function of the subject’s mass and applied weight on each gastrocnemius muscle was normalized to body mass units (BMU) across all subjects. JMP IN software found equations of BMU as a function of a combination of several variables including speed, stride rate, stride length, length of leg and foot length. The BMU predicted from the equation was then plotted against the experimentally determined value. As different variables were added or removed, the R2 of this Predicted Force vs. Actual Force curve were noted. After testing the data with ANOVA, the equation yielding the most linear fit was chosen for both walking and running.

Results

Calibration data for Force and EMG were obtained by increasing the forces supported by the gastrocnemius muscle through an increase in applied free weights, while the subsequent mean Integrated EMG was recorded. Depending on the trial and subject, between twenty and thirty data points were obtained for each calibration run. A linear relationship was found to exist between Force and mean Int.EMG for each subject, and regression analysis determined the values of the coefficients for this relationship.

Figure 1: Representative Linear Plot of Force vs. mean Int.EMG; Subject AR O+

Figure 1 above shows the linear relationship between Force and mean Int.EMG. Slopes, representing muscle unit recruitment in N/mV, were independent for each subject. Correlations ranged from a low of 71% to a high of 92%, with the mean correlation at 82.02% and a standard deviation of ( 7.13%.

Table 1: Coefficients and Correlations for Each Calibration Trial

Table 1 lists the coefficients and correlations of the calibration equation for each trial and subject. The calibration equation is represented by the formula:

[pic] (1)

For subjects MF, EB, and AR the confidence intervals between left leg and right leg slopes overlap, indicating no significant difference in muscle unit recruitment between the two legs. Subject AE, however, exhibited significant differences in recruitment between his left and right legs. For subjects AE and MF calibrations were repeated during a second trial. For both legs of both subjects, confidence intervals between the two trials overlap, indicating no significant change in recruitment between the repeated calibrations.

For walking and running trials, EMG data was collected as treadmill speeds increased. Equations determined in individual calibrations were applied to the mean Int.EMG at each speed to determine the average magnitude of force generated in the gastrocnemius muscle at that speed. For each trial, several parameters were measured and calculated. Using the JMP IN v4.0 statistical analysis software, a series of multivariable regressions were performed to fit the average force to the variables of speed, v, stride rate, r, stride length, s, leg length, l, and foot length, f, for all subjects. The recorded forces in the gastrocnemius were normalized for body weight by dividing the force generated by the weight of the subject to yield the force, F, measured in body mass units (BMU's).

[pic] (2)

Table 2: Variable Selection Table

The above table illustrates how the variables were chosen for inclusion in the predicted force equations for walking and running. For each line in the table, a multivariable regression was performed including each indicated variable, and the correlation between the predicted data and actual data was calculated. From top to bottom are listed increasingly effective predictions, based on the efficacy of each variable and the correlation to actual data. A variable is considered effective if its inclusion increases the correlation by more than 0.5%. From these tables it is clear that that the most accurate equations for determination of force in the gastrocnemius during walking and running are:

[pic][pic] and [pic]

Table 3: Variable Coefficients w/ 95% Confidence Intervals - WALKING

Multivariable regression analysis on walking forces and the variables determined to be maximally effective yields the coefficients with 95% confidence intervals listed above. These coefficients are used in the equation for the force generated in gastrocnemius during walking:

[pic] (3)

Plotting the walking forces predicted by this equation against the measured forces generated in the gastrocnemius muscle during experimental trials is expected to yield a straight line with a slope of 1 and an intercept of 0, the R2 of which represents the correlation of the equation to the actual data.

Figure 2: Plot of Actual Gastrocnemius Force against Forces Predicted by Equation - WALKING

Linear regression of the Actual BMU's vs. the Predicted BMU's results in a slope with 95% confidence interval of 1.0015 ( 0.1068 and an intercept of 0.0000 ( 0.0963. The correlation of the walking model to the actual data is R2 = 0.7866.

Table 4: Variable Coefficients w/ 95% Confidence Intervals - RUNNING

Multivariable regression analysis on running forces and the variables determined to be maximally effective yields the coefficients with 95% confidence intervals listed above. These coefficients yield an equation for the force generated in gastrocnemius during running cases of:

[pic] (4)

Figure 3: Plot of Actual Gastrocnemius Force against Forces Predicted by Equation - RUNNING

Linear regression of the Actual BMU's vs. the Predicted BMU's results in a slope with 95% confidence interval of 1.0015 ( 0.2059 and an intercept of 0.0000 ( 0.2695. The correlation of the running model to the actual data is R2 = 0.5774.

Discussion

The calibration curves of force verses integrated EMG were linear, and for three out of four of the subjects, the differences in slope of force per unit recruitment were not statistically significant as predicted. The one subject who had legs that were statistically different from each other had lower recruitment in his right leg. An explanation for this discrepancy is that the subject has recently been using a Scooter as a mode of transportation and usually uses his right leg to propel himself. As seen from Table 1, the two subjects, MF and AE who repeated the calibration on a different day also exhibited no significant difference between the first two trials, indicating the experiment was reproducible.

Two criteria were used to determine the best equation that related the force in body mass units to the multiple variables. The R2 value determined how well the variables in question predicted the force. Significance of each variable determined its inclusion in the final equation and was based on a 0.5% increase in R2. If upon its incorporation into the equation the R2 did not increase significantly (+0.005), a given variable was not included in the equation. The number of variables used was also a factor as incorporating less variables makes the equation more functional. These two criteria determined the ultimate equations used to predict force.

For walking, incorporating all the variables, the R2 was 0.788, as opposed to the R2 of 0.787 for the incorporating only stride length, stride rate, length of leg and speed. Including stride length/length of leg and foot length would make the equation more complicated and would not predict force better in any dramatic way. The correlation between the predicted and actual force only goes up by 0.001 by incorporating these variables, which was determined to be insignificant for the purposes of this experiment. The choice of using the equation with length of leg instead of stride length/length of leg also made the equation simpler without taking away any correlation. The variables were also dependent on each other, which is why many of the predicted force equations yielded the same correlation. Stride length was equal to speed divided by stride rate; stride length over length of leg also incorporated two variables.

The highest correlation found for running was an R2 of 0.578 when speed, stride length, stride length/length of leg, and foot length were the variables. If speed was removed from the prediction of force, the R2 decreased to 0.577, a decrease in correlation of 0.001. Incorporating speed was not necessary as it did not increase the R2 value significantly. Including variables such as stride rate and length of leg also did not significantly increase the R2 value therefore they were excluded from the final equation for running. The variables that determined the equation were therefore stride length, stride length divided by length of leg, and foot length.

Several of the data points were excluded from the data set used to predict the force for running. The data points excluded showed no correlation. For each data set, the subject (AR) performed four trials all of which were analyzed separately to determine their correlation. The three other trials had a very high correlation (R2 above 0.92). For this one trial, however, the correlation between force and the variables had a R2 of 0.043, significantly lower than the other three trials. This indicated that there was some flaw in the performance of this trial. The subject was having difficulty with the electrodes during this trial, to the extent that they had to be replaced multiple times. Electrode movement can change the value of the signal and is most likely the reason for the variation.

From the equation for walking, speed showed a positive linear correlation with force, which was expected. As speed increases, the force required to propel oneself increases as well because the same distance has to be covered in less time. Stride rate was shown to have a negative linear correlation with force as increasing one’s stride rate increases the number of steps to get to the same distance. In a sense, the subject is dividing the amount of force required by the number of strides they take. The more strides taken means that less force is produced per stride for the same distance. The stride length was also shown to have a negative linear correlation with force, indicating that the longer the stride length, the lower the force. This was unexpected, but also can be explained. Since stride length is equal to speed divided by stride rate, which have positive and negative correlations to force, respectively, the correlation of stride length to force will also be negative. The length of leg was determined to play an important role as seen in table 3. This was also predicted, as the larger the leg, the easier it is to run with larger strides, as the person who has a leg of 80 cm has to generate more force than the person who has legs 100 cm long.

The equation for running showed that speed was not necessary to accurately determine force in the gastrocnemius muscle. The final equation used stride length, stride length divided by length of leg, and length of foot to predict force. Stride length divided by length of leg showed a positive linear correlation with force. As in walking, the length of leg is an important factor in standardizing stride length. By dividing stride length by length of leg, it was possible to normalize small-legged and long-legged people such that stride length in relation to subject could be analyzed. Larger stride means longer time in the air, which requires more force at push-off. The normalized stride length relationship showed the correlation that was originally anticipated, but as in the walking trials, stride length alone was negatively correlated to force. The length of foot was also a determining factor of force. The longer foot the subject had, the less force required. Two reasons could explain this. Foot length usually is an indicator of height and leg length, and leg length has been shown from walking trials to be negatively correlated to force. Foot length outperformed leg length in the running trials, however as a predictor for force. As foot length increases, the net force decreases because the subjects pushed off using the balls of their feet, which were at varying distances from their ankle. The force on the foot from the ground produced a torque, which in turn generated a force in the gastrocnemius muscle. The torque depends on the radius from the ankle to the point where force was applied. People with larger feet have larger radii, and therefore lower force as torque equals force times radius. If torque remains constant, force must decrease to account for increased radius.

In previous studies the cross-talk between the gastrocnemius and soleus EMG data has presented difficulty in analyzing each muscle separately. It was noted from experimental observation of the gait cycle that large, significant increase in Int. EMG readings occurred at the end of the cycle, when the toe pushes off the ground propelling the legs forward. It is this flexion that the gastrocnemius muscle is responsible for, as opposed to the extension of the ankle facilitated by the soleus muscle.2,3 Therefore, we can say that the large increase in Int. EMG during the end of the gait cycle is solely generated by the gastrocnemius muscle. It was this section of data that was recorded and used in our analysis, and for this reason we can definitively state that our analysis includes forces only in the gastrocnemius muscle. In addition, because the soleus muscle is located beneath the gastrocnemius, in reference to our electrode placement, any EMG data from it would be masked and obscured by overlying tissue.

The R2 value for running was very low. Several factors which played a role in lowering the R2 value were the fact that the treadmill was only 40.5 cm wide, while the average hip measurement of the subjects was 37.2 ( 0.5 cm. Since the treadmill barely accommodated the natural stance of the subjects, this caused unnaturally gait, which would thereby distort force. A wider treadmill is necessary to correct the gait. After the experiment, several variables were discovered that would play a crucial role in determination of force had they been measured. One of the most noteworthy variables is the maximum height that one attains after push off during running. Since a person, especially at lower speeds, tends to jump while running, the inclusion of this variable would significantly impact the R2 value.

Having an equation that determines the force (in BMU) generated in the gastrocnemius muscle as a function of speed, stride length, stride rate and length of leg can prove useful for applications of rehabilitation. The high R2 value for walking shows that the force can be predicted accurately and can be used to predict forces given certain physiological parameters. Thus, a physical therapist can utilize the equation for walking to set limitations on patient mobility to avoid overexertion and possible re-injury. Further analysis of running would have to be explored in order to apply the running equation to physical therapy, as the lower R2 value shows other factors still need to be quantified. However, since re-injury is most likely in extremely delicate cases, the walking equation will generally have more applications in physical therapy than running, which still can be applied despite the study’s limitations.

Conclusions

1. A method for separating gastrocnemius EMG data from the cross-talk of the soleus muscle using low-pass filtration and isolation of surface EMG was developed and utilized to obtain the data in this experiment.

2. A relationship (R2 = 0.7866) between the force generated in the gastrocnemius muscle of the leg during walking cases and the variables of speed, stride rate, stride length, and length of leg was determined, represented by:

[pic]

3. A relationship (R2 = 0.5774) between the force generated in the gastrocnemius muscle of the leg during running cases and the variables of stride length, stride length/length of leg, and foot length was determined, represented by:

[pic]

References

1. Richardson, Michael L., PhD, Teitz, Carol C., MD, Graney, Daniel O., PhD, "Online Muscle Atlas", University of Washington, 1997,

2. Toft, E.; Sinkjaer, T.; Andreassen, S; and Larsen, K. “Mechanical and Electromyographic Responses to Stretch of the Human Ankle Extensors.” J. Neurophys. 65(6): 1402-1410, 1991 June.

3. Perry, J; Esterday, C.S.; and Antonelli, D.J. “Surface Versus Intramuscular Electrodes for Electromyography of Superficial and Deep Muscles.” J. Physical Therapy 1:7-15, 1981.

4. Czerniecki, J.M. ”Foot and Ankle Biomechanics in Walking and Running: A Review” Am. J. of Phys. Med. & Rehab. 1988: p. 246-252.

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