BE 310 Final Project: Reflex Response of the Knee



BE 310 Final Project: Reflex Response of the Knee

Group M7: Ana Crespo, Jacquie Farag, Maureen Schriver

ABSTRACT

The reflex response of the knee was observed using a goniometer, to record angular movement, electrodes to record the EMG of the quadriceps muscle, and BioPac software. A reflex hammer was used to hit the patellar tendon and record the tapping force. Multiple trials were conducted with the same subject in an attempt to minimize differences between group members. Peak force vs. Maximum angular acceleration (which is proportional to torque) and Peak force vs. Integrated EMG graphs were constructed in order to determine a correlation between tapping force and these two parameters, as was modeled in the study by Zhang et al[1]. Based on linear regressions performed on the data, no correlation was determined between peak tapping force and either absolute integrated EMG or the maximum angular acceleration. Therefore, we were unable to confirm the results produced in the Zhang study.

BACKGROUND[2]

A reflex is an involuntary and relatively stereotyped response to a specific sensory stimulus. Two features of the sensory stimulus are particularly important in shaping the reflex response. First, the precise location of the stimulus determines in a fixed way the particular muscle that contract to produce the reflex response. Second the strength of the stimulus determines the amplitude of the response.

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Figure 1: Diagram of nerve response of the knee jerk reflex

The knee jerk reflex is a well known example of stretch reflex. Tapping the knee cap (patella) pulls on the tendon of the quadriceps femoris, which is an extensor muscle that extends the lower leg. When the muscle stretches in response to the pull of the tendon, information regarding this change in the muscle is conveyed by the afferent sensory neurons to the spinal cord and the central nervous system. In the spinal cord the sensory neurons act directly on motor neurons that contract the quadriceps. By the same token, they act indirectly, through inhibitory interneurons, to inhibit motor neurons that contract the antagonist muscle, the hamstring. The sensory neurons also end in projection interneurons that transmit information about the local neural activity to higher regions of the brain concerned with movement; the stretch reflex plays a central role in the maintenance of balance. It is called a monosynaptic reflex because it depends only on the simple connection between primary afferent fibers from muscle spindles and motor neurons innervating the same muscle. In other spinal reflexes such as those produced by cutaneous stimuli, one or more interneurons may be interposed between the primary afferent fibers and the motor neurons.

MATERIALS and METHODS

Materials

– BioPac MP30 hardware

– BioPac electrode lead set (SS2L)

– BioPac twin axis goniometer (SS20L)

– BioPac reflex hammer (SS36L)

– BioPac Pro Lesson H28 Software

– Conductive gel

– Tape and Velcro to fix goniometer to leg

Methods

The subject was fitted with the electrode equipment as shown in the picture below.[3]

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Figure 2: Diagram of experimental apparatus

The ground electrode lead (black) was positioned on the subject’s kneecap. The other two electrode leads were placed on the subject’s quadriceps muscle, approximately 8-10cm apart. The goniometer was fixed to the outside of the subject’s leg as shown in Figure 2, with care to ensure the spring at the center of the goniometer was not too taut nor too slack. Tape and Velcro were used to fix the plastic parts of the goniometer to the subject’s leg. The subject sat at the edge of a table, with her knee at a 90º angle when at rest.

The subject’s patellar tendon was localized with the experimenter’s thumb, and then struck at different points to determine the optimum reflex spot. This spot was then marked by a visible X to serve as a target for all subsequent trials. The goniometer was then calibrated for the leg positions at 0 and 90 degrees using the BioPac software.

To run a trial, the experimenter would start recording with the BioPac software, hit the market spot at a 90º angle, and wait for the leg to stop swinging. The hits were repeated with different force levels until 25-30 seemingly successful hits (appreciable leg swing) were obtained.

DATA ANALYSIS

All of the BioPac channel data was analyzed to determine peak hammer force, absolute integrated EMG and maximum angular acceleration as follows:

- Peak hammer force: highlight all the peaks corresponding to one hit and choose “max” for one of the calculation boxes above the channels. The peak force level will be displayed.

- Absolute integrated EMG: Highlight the entire EMG waveform, click on “Transform” in the tools menu, go down to “Math Functions” and select “Abs”. Then highlight the EMG corresponding to one hit from beginning to end and choose “integral” for one of the calculation boxes above the channels. The integrated EMG value will be displayed.

- Maximum angular acceleration: Assume each waveform corresponding to a hit is a periodic sine wave. Maximum angular acceleration is then the coefficient of the second derivative of a sine wave formula ( A(2(/T)2, where A is the amplitude and T is the period of the sine wave. For each hit, highlight the first trough-to-crest section (min to max) of the angular movement waveform. Choose “p-p” for one of the calculation boxes above the channels. This will display the peak to peak value in the y-direction, which is twice the amplitude of the waveform. In another calculation box, choose “delta T” and that will display half the period value. Using these values calculate A and T, then plug into the maximum angular acceleration formula.

RESULTS

The plot of the absolute integrated EMG response vs. the peak tapping force appears in Figure 2. This graph shows that there seems to be no direct correlation between peak tapping force and the integrated absolute EMG of the quadriceps response. A linear trendline of all the data points has an R2 value of 0.0948.

Figure 2: EMG vs. Tapping force plot

A plot for maximum angular acceleration vs. peak force was also constructed (see Figure 3). There does not appear to be a correlation between these two parameters. The R2 for this relationship was only 0.0426.

Figure 3: Maximum angular acceleration vs. peak force plot

Figure 4 shows the screen view of BioPac for all three channels. As can be seen in the diagram, channel one in red shows the tapping force. Channel 2 in blue shows the EMG response after the absolute value was taken. The third channel in green is the output from the goniometer. The obtained waveform was manipulated to determine the angular acceleration as stated above.

Figure 4: Screen view of BioPac

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DISCUSSION

The main purpose of this project was to develop an experiment that would allow some biological phenomenon to be analyzed through signals. Lesson H28 provided a base to the project by presenting a way to measure a biological phenomenon (reflex response), but after completing the entire lesson during the first week of this project, we found that the data analysis was too focused on the biological response (reflex response time) and did not utilize the signals for more than calculating a time delay.

In order to incorporate more of the information obtained from the EMG, hammer and goniometer signals, we modified the experiment based on the paper by Li-Qun Zhang et. al., System Identification of Tendon Reflex Dynamics1, and attempted to verify his results on the correlation between tapping force and both the integrated EMG signal and the torque applied to the leg. The integrated EMG signal represents the number of motor neurons firing in the quadriceps muscle. Instead of finding the torque applied to the leg by the quadriceps muscle, we found the maximum angular acceleration, which is proportional to the torque. The results of our experiment show that using this experimental setup, there is no correlation between the peak tapping force and the integrated EMG signal (R2=0.0948) or between the peak tapping force and the maximum angular acceleration of the leg (R2=0.0426). Zhang found there to be a linear correlation between the tapping force and the EMG signals. Zhang also found a strong correlation between the tapping force and the reflex torque; this correlation was found to be linear as well.

We believe that this experimental setup presents some major setbacks and differences from Zhang’s setup that prevented the verification of his results. First of all, Zhang used a special device that tapped the leg at a constant angle and place every time. We found it very difficult to hit the subject’s knee at the same spot by hand, in spite of the visible mark. Moreover, the angle at which the subject’s knee was hit was much more difficult to control. We were already focusing on hitting the right spot and the arm movement of the person handling the hammer could not be described quantitatively. Zhang also used a dome shaped rubber pad, which was attached to the patient’s knee on the patellar tendon. The stiff dome acted as a visible target and also transmitted the force of the hammer to the most sensitive spot on the tendon, thereby making the procedure much more accurate.

Another setback experienced in our experiment was lack of knowledge about the subject’s tendon reflexes. Zhang found that the sensitive spot was more localized for patients with weak tendon reflexes and in contrast was larger for patients with strong tendon reflexes. If our subject had weak tendon reflexes, hitting the most sensitive spot could have been more difficult than the experimental setup already made it. Zhang also noted that at levels of too soft or too strong tapping forces do not follow the linear correlation between tapping force and EMG signals. He stated that there is a sub-threshold which does not transmit enough stretch to the muscle receptors and will not emit a response; there is also an above threshold that could drive tendon against underlying tissue and therefore not deliver a necessarily larger stretch to the muscle receptors. Each patient has a different maximum and minimum, and tapping force levels above and below these limits do not allow for a linear correlation. Zhang took note of these parameters and had linear correlations with R2 values equal to 0.736, 0.71, and 0.76. We had no way of measuring our subject’s thresholds, which made it impossible for us to eliminate any data points that deviated from a linear relationship due to this limitation. The torque vs. tapping is also restricted by the tapping strength parameters that restricted the EMG vs. tapping force.

Another problem we encountered during the experiment had to do with the calibration of the goniometer. For the first two weeks we calibrated the goniometer on a table as the BioPac lesson suggests, but when we analyzed the data we found that our subject’s leg was swinging more than 130º, which led to an erroneous calculation of the maximum angular acceleration. During the third week we decided to calibrate the goniometer on the subject’s leg, using the rest position as 90º and the stretched out position as 0º. Once this correction was made, the values obtained for the angle of leg motion were much more believable. This discrepancy may be due to how the goniometer stretches when it’s placed on the leg as opposed to how it stretches when one is manipulating it with one’s hands.

If this experiment were conducted in the future, there are several key changes that could be made to our set-up. The first would be to test multiple subjects in order to eliminate random errors in specific subjects. In addition, an apparatus could be formed that would quantify the angle at which the tendon is struck. Quantitative analysis of the hammer angle could yield categories of tapping force within the bulk data and aid in proving linear relationships among the data. A more signals-based approach could also be taken by creating a filter for the EMG and tapping force data. By determining the optimum sampling frequency of these values, our integrations could yield more relevant data and correct the artifacts in our sampling data. All of these methods would improve the precision in our data and clean up our experimental graphs to perhaps produce a more linear relationship and support the data from the Zhang et al study.

REFERENCES

1. Zhang, Li-Qun, et al., “System Identification of Tendon Reflex Dynamics”, IEEE Transactions on Rehabilitation Engineering, Vol. 7, No.2, June 1999.

2.

3. BioPac Pro Online Manual- Lesson H28:

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[1] See References

[2]

[3]

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Tapping force

EMG

Angular Displacement

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