Download 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 al1. 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.
1
See References
BACKGROUND2
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.
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)
2
http://ifcsun1.ifisiol.unam.mx/Brain/reflex.htm
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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
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.
3
http://www.biopac.com/bslprolessons/h28/h28.htm
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
EMG response vs. Peak tapping force (wk 3 trial 2)
0.012
y = 0.0005x + 0.0052
Integrated EMG signal (mV-sec)
2
R = 0.0948
0.01
0.008
0.006
0.004
0.002
0
0
1
2
3
4
5
Peak tapping force (mV)
6
7
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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
Max angular acceleration vs. Peak force
2000
Angular acceleration
(degrees/s^2)
1800
y = 42.426x + 971.85
R2 = 0.0426
1600
1400
1200
1000
800
600
400
200
0
0
1
2
3
4
5
6
7
8
Pe ak force (mV)
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
Tapping force
EMG
Angular Displacement
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 subthreshold 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. http://ifcsun1.ifisiol.unam.mx/Brain/reflex.htm
3. BioPac Pro Online Manual- Lesson H28:
http://www.biopac.com/bslprolessons/h28/h28.htm