Muscle Force Experiment: Background
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
2.671 Measurement and Instrumentation
Muscle Force Experiment Background
Muscle is a remarkable motor. A whole muscle, such as your biceps muscle (that flexes the
forearm about the elbow joint), consists of a bundle of long cells called muscle fibers. In a typical adult
human skeletal muscle, the muscle fiber diameter is similar to adult human scalp hair diameter and
ranges from about 40 μm (similar to fine red hair) to over 100 μm (dark hair diameter) if you have
built up your muscle by, for example, weight lifting. If you train with weight lifting, the total number
of muscle fibers in a muscle remains essentially constant as the fiber diameter increases.
Objectives:
•
•
•
To characterize your own biceps muscle motor performance
To determine the relationship between electrical nerve signal to the muscle (“input”) and
muscle force (“output”)
To examine muscle fatigue
Instrumentation:
•
•
•
•
•
•
•
Optical table with crossbar mounted on two load cells (Omega Engineering LCCA-500)
Fluke 175 DMM
Agilent 33220A Function Generator
Gemini PM-100 active speaker
Op-amp circuits: differential amplifier, active half-wave rectifier, active low-pass filter
Electromyographic Preamplifier (Motion Lab Systems MA-311)
National Instruments A/D board
Description of Experimental Apparatus:
The apparatus comprises a 32 mm diameter rod mounted horizontally on two S-shaped load cells
(Omega Engineering Model LCCA-500), which measure the force exerted as you pull up on the bar. A
full-wave bridge is used to measure the average output of the pair of load cells. The EMG signal is
measured with a small probe that is held on your bicep with an ACE bandage.
References:
R. Rhoades and R. Pflanzer, “Human Physiology” (Saunders College Publishing, Philadelphia, 1989),
Chapter 9
http://www.myomo.com/technology/index.shtml (MIT spinoff company the uses EMG signals to assist
muscle force in partially paralyzed patients
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Muscle Force Experiment: Background
1. Background
In this section we describe the basics of muscle mechanics, biochemistry, and control. You will
also learn about some of the difficulties inherent in performing experiments with human (or animal)
subjects, including technical and ethical concerns. Obtaining repeatable data on a biological subject –
even if the subject is cooperative – can be difficult. Since you do not have the time to repeat all the
measurements a large number of times on different test subjects, you will find that your error analysis
is somewhat qualitative, and that your estimated errors may be a significant percentage of your results.
1.1 Anatomy of the Human Arm
In this experiment you will study the mechanics of flexing of the elbow, defined as motion that
decreases the angle between the upper arm and the forearm. Figure 1 shows the anatomy of the human
elbow joint, including the bones of the upper arm (humerus) and lower arm (radius and ulna).1
elbow flexion
upper arm
Humerus
Radius
forearm
Ulna
Figure 1: Structural anatomy of the human elbow joint (Ref. 1)
There are 5 major muscles involved in flexing the elbow: The biceps brachii, brachialis,
brachioradialis, pronator teres, and the extensor carpi radialis longus. The two largest muscles, the
biceps and the brachialis, account for about 70% of the torque-generating capacity of this group of
muscles, with the biceps responsible for 45% of the total torque.2 These muscles are shown in Fig. 2a
and in cross-section in Fig. 2b. The remaining three elbow flexors are smaller in cross-section and also
attach to the forearm much closer to the elbow, thus contributing less to the generated torque.
a)
b)
biceps
triceps
brachialis
Fig 2: Primary elbow flexors, the biceps brachii and brachialis shown (a) along the
humerus3 and (b) in cross-section through the upper arm4 (color added for clarity)
1
Gray, Henry. Anatomy of the Human Body. Philadelphia: Lea & Febiger, 1918; Bartleby.com, 2000,
www.bartleby.com/107/. [2/25/07], FIG. 331
2
W.M. Murray et al., “The isometric functional capacity of muscles that cross the elbow”, Journal of Biomechanics 33
(2000) 943.
3
Ref. 1, FIG 411
4
Ref. 1, FIG 413
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Muscle Force Experiment: Background
It is important to note that muscle fibers can only apply force in contraction. Therefore, for each
muscle or group of muscles in the human body there exists a muscle or group of muscles that provide
the opposite motion. These are called antagonistic muscles. The antagonistic muscle for the human
elbow flexors is the triceps, located at the back of the upper arm5 and shown in Fig. 2b.
1.2 Muscle Internal Structure and Biochemistry
Skeletal muscle comprises groups of muscle fibers surrounded by connective tissue. There are two
main types of motor fibers: red (“slow twitch”) and white (“fast twitch”). Red fibers store oxygen and
rely on aerobic metabolism to produce adenosine triphosphate (ATP) the primary energy source for
living cells. These fibers are common for sports that require endurance, such as running a marathon or
long distance swimming or cycling. White fibers use ATP more quickly to produce stronger forces
albeit for shorter times, and rely on both aerobic and anaerobic metabolism. This type of muscle fiber
is commonly used for weightlifting and sprinting. 6
The structure of muscle is shown in Fig. 3. Each muscle fiber is composed of myofibrils. These, in
turn, are comprised of myofilaments, which are organized into structures referred to as sarcomeres.
Two types of filaments are found in the sarcomeres: thick filaments (made of the myosin protein) and
thin filaments (actin protein). When the muscle contracts, the actin and myosin filaments do not
change length. Instead, they slide relative to one another, thus shortening the sarcomere length. The
force that can be exerted by each fiber decreases as the fiber length decreases.7
http://205.187.104.8/users/thiele/web/apbio/review/m
Figure 3: Organization of human biceps muscle
The actin molecules in each thin filament are organized into helices comprising two chains of
actin monomers. Each myosin molecule has a double globular head on one end, and a thin rod shaped
section, or tail, at the other end. These are arranged in a bundle with their heads protruding out to form
5
http://www.botany.uwc.ac.za/SCI_ED/grade10/manphys/skel_mus.htm
http://en.wikipedia.org/wiki/Skeletal_muscle
7
Maganaris, CN “Force-length characteristics of in vivo human skeletal muscle”, Acta Physiol Scand 172 (2001), 279
6
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Muscle Force Experiment: Background
crossbridges that connect to the actin filaments. These structures are shown in Fig. 4, and can be seen
in an online movie animation showing actin and myosin filaments during muscle contraction8. The
energy required to contract a muscle is provided by ATP.
Figure 4: Muscle biochemistry [Ref. 8]
1.3 Mechanics of Elbow Flexor Muscles
The maximum force generated by skeletal muscle per unit cross-sectional area is about 350 kN/m2
(this peak is essentially the same for all mammals). Dinosaur muscle was probably very similar to
human muscle and is likely to have generated the same peak stress (force per unit cross-sectional area).
A very strong human with a biceps muscle cross-sectional area of 10-2 m2 can thus generate a peak
force in the muscle of 3500 N. This is not the force exerted on a load in the hand, since the biceps
muscle acts on the arm through a lever, as shown in Fig. 1. The lever ratio is defined as the distance
from the elbow to the load divided by the distance from the elbow to the biceps insertion point. The
lever ratio for the human biceps is approximately 10, although it can vary somewhat from person to
person. For example, if the elbow joint to hand length is 0.4 m and if the biceps tendon insertion point
is 0.04 m from the elbow, the peak force measured at the hand in the case of the very strong human
will be 350 N. Consider your own biceps muscle. What are the advantages and disadvantages using a
Class III lever as shown in Fig. 1?
http://academic.uofs.edu/faculty/kosmahle1/courses/pt245/levbicep.htm
Figure 5: Diagram of human biceps.
8
http://www.sci.sdsu.edu/movies/actin_myosin_gif.html
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Muscle Force Experiment: Background
In reality the mechanics are more complicated than shown in Fig. 5 because, as stated in Sect. 1.1,
five distinct muscles contribute to the force that can be exerted on the hand during elbow flexion. An
added complication is that since the force applied by a muscle fiber depends on the length of the fiber,
the maximum force that can be applied by each of these muscles depends on the angle between the
upper arm and the forearm. Since each muscle has a distinct geometry relative to the elbow, the effect
of angle on muscle force is different for each muscle. The elbow angle is defined to be the angle
between the upper arm and a line extending from the back of the elbow parallel to the forearm and is
0° when the arm is straight. Measurements of anatomical data combined with detailed studies of
muscle properties have been used to develop a model to predict how the force of each muscle changes
with elbow angle,2 as shown in Fig. 6 for the biceps (BIC - both heads) and the brachialis (BRA).
Figure 6: Dependence of normalized force on elbow angle for the biceps (BIC) and brachialis (BRA) [Ref. 2].
As can be seen in Fig. 6, the biceps exerts 90% or more of its maximum force for elbow angle
θ between 20° and 45°. For θ = 80° the force ratio drops to 80%. For θ higher than 80°, the force drops
precipitously – at 100°, the force has dropped to 30% its maximum. Note that the brachialis muscle can
maintain larger force at larger angles with 90 – 100% of its maximum force up to 100°. Therefore, the
fraction of torque due to the biceps will decrease somewhat as θ increases. For example, at 100°, the
maximum force that can be applied by all elbow flexors decreases by about a factor of 2 from that at
20°, but the biceps contribution is still about 40%. The measurements you will perform in lab will be
made for an elbow flexion angle of 45°. At this angle it is reasonable to assume that 45% of the
measured force is due to the biceps.
In order to compare the maximum biceps force per unit area for a specific test subject with the
predicted value of 350 kN/m2 the cross-sectional area of the biceps must be estimated. As is evident in
Fig. 2b, the biceps is not cylindrical in the relaxed state. Well-developed biceps muscles will become
more cylindrical when flexed, and thus the area can be approximated by measuring the diameter across
the muscle (not across the bone). Students with less well-developed biceps muscles may wish to
estimate the degree of eccentricity of their biceps to obtain a better approximation to the area.
Recognizing that the measurement of biceps area will always have an associated uncertainty, there is
an additional factor affecting the muscle stress derived from measurements of force and area: not all of
the geometrical cross-section of the biceps contains muscle tissue, also referred to as contractile tissue.
Klein et al9 state that approximately 12% of the biceps cross-sectional area is non-contractile tissue,
and therefore should not be included when finding muscle stress. Combining this fact with the
realization that measurements on the exterior of the arm will most likely overestimate muscle diameter,
it is reasonable to assume that the relevant muscle cross-sectional area is approximately 85% that
estimated from the measured diameter.
9
Klein, CS, Marsh, GD, Petrella, RJ, and Rice, CL “Muscle fiber number in the biceps brachii muscle of young and old
men”, Muscle & Nerve, 28 (2003), 62.
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1.4 Muscle Control via Nerve Impulses
Finally, individual “motor units” in skeletal muscle are controlled by impulses from the central
nervous system. The concept of a motor unit was first introduced by Lidell and Sherrington10 in 1925.
A muscle motor unit comprises a single motor neuron, shown schematically in Fig. 7,11 and a group of
muscle fibers that are activated by one of the many branches of the neuron axon terminal.
Fig 7: Structure of a motor neuron [Ref. 11]. Each branch of the axon terminal is
connected to a single muscle fiber in the motor unit.
When an impulse reaches the axon terminal of a motor neuron, small packets of the
neurotransmitter acetylcholine are released into the synaptic clefts at the surface of the muscle fibers.
This causes a depolarization of the muscle membrane and triggers the generation of an “action
potential” to propagate on both sides of the synaptic junction along the muscle fiber. Transverse
tubules conduct the depolarization from the surface to the sarcoplasmic reticulum where calcium ions
(Ca++) are released. The calcium ions in turn control the attachment of the crossbridges between the
myosin complex and the actin helix (see Fig. 4) and therefore control the relative movement of actin
and myosin.12
The motoneuron action potential has a typical duration of 1 – 2 msec13 The additional electrical
pulses generated by the muscle fibers themselves sum up together leading to an electric pulse from the
motor unit as a whole with duration of 5 – 8 msec and amplitude of about 0.5 mV.13 This potential is
referred to as the Electromyographic potential, or EMG. The signal is usually quantified by
determining either the RMS (root-mean-square) or the ARV (average-rectified-value) of the nerve
impulses. Therefore, the EMG signal increases with the repetition rate of the impulses reaching the
motor neurons.
The brain has two methods by which it can generate a given muscle force. It can turn on (recruit) a
subset of the motor units for a particular muscle by activating the corresponding nerve fibers, and/or it
can vary the rate at which the motor units are stimulated. It turns out that for a large muscle like the
10
Lidell, E. G. T., and C. S. Sherrington. Recruitment and some other factors of reflex inhibition. Proc. R. Sot. London Ser.
B 97: 488-518, 1925.
11
http://en.wikipedia.org/wiki/Image:Neuron.svg
12
“Synaptic Transmission: A Four Step Process”, Multimedia Neuroscience Education Project, Williams College. Online:
http://www.williams.edu/imput/synapse/index.html [2/28/07].
13
Basmajian, JV “Normal Electromyography” in Muscle, ed. Paul WM, Daniel EE, Kay CM, Monckton G (Pergamon
Press, Oxford, 1965), pp. 479-486
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biceps, recruitment and rate are used to increase muscle force from rest (0 force) through 85% full
activation. Beyond this, all motor units have been recruited, and only rate can be used to increase
force. For small muscles recruitment and rate is used from rest to about 50% full activation at which
point rate alone is used.14 The efficiency of the human biceps muscle is about 35%, with the remainder
of the energy input to the muscle released as heat. Maximum efficiency typically occurs at about 30%
MVC.15
Each motor unit contracts as a whole, although all the component fibers to do not contract at
exactly the same time.13 The rate at which motor units receive impulses varies up to about 100
impulses per second (dependent upon the muscle). At higher stimulation rates the motor unit saturates
and no further force is produced. At lower stimulation rates the motor unit force will be lower
(although not proportionally so). This activation signal is an example of a point process, which means
that the amplitude and width of the pulses arriving at the motor neuron are unimportant. The extent of
stimulation of the motor unit is determined solely by the time between pulses.
For mammals, there is an orderly recruitment of muscle units. The “size principle of motor
recruitment”16 predicts that at low forces, the smaller slow-twitch units are activated, followed by the
medium-sized fast oxidative twitch units (at about 30% MVC for the biceps), and, finally, the large
fast glycolytic twitch units (at about 80% MVC for the biceps). In addition to having a lower activation
threshold, the slow twitch units are also hard to fatigue. However, once they have all been recruited,
the brain must recruit fast oxidative twitch units, which have a higher threshold and therefore require a
larger increase in EMG for a given increase in force. The fast-twitch units also fatigue more easily,
requiring additional recruitment and thus an increase in EMG with time simply to maintain a constant
force. You will examine these effects in the lab today by defining a quantity called Muscle Gain,
defined as the ratio of the force applied at the hand to the ARV of the EMG signal. The Muscle Gain
cannot be compared between test subjects or even for the same subject if the EMG sensor was
removed and then replaced on the biceps. Why not?
1.5 Experiments with Human Subjects
Since antiquity there have been ethical debates surrounding experiments involving human
subjects.17 The earliest extant statement on the subject may be the Hippocratic Oath, which is often
quoted as “above all, do no harm” and has been used to guide the practice of medicine for thousands of
years. In the modern era, the Food and Drug Act of 1938 required that drug safety be demonstrated
before marketing, which opened a need for human drug trials. The excesses of World War II prompted
the international adoption of the Nuremberg Code in 1947, which stipulates that informed consent
must be received for all experiments and that the benefits must be weighed against the risk to and
suffering of experimental subjects.17
In the United States, modern protocols were instigated with a US Surgeon General policy
statement in 1966 requiring that all experiments involving human subjects be approved by an
independent panel, called an Institutional Review Board (IRB).17 Specific IRB procedures were
defined in 1974 with the adoption by the 18th World Medical Assembly in Helsinki of “Regulations for
the Protection of Human Subjects of Biomedical and Behavioral Research”.
14
http://www2.fhs.usyd.edu.au/ess/gwinn/mm/Recruit%20&%20Rate%20Coding-2003.pdf
http://home.hia.no/~stephens/musfacts.htm
16
Denny-Brown, D. and Pennybacker, J. B. (1938). Fibrillation and fasciculation in voluntary muscle. Brain 61, 311–334.
17
Sparks, J “Timeline of Laws Related to the Protection of Human Subjects”, Office of NIH History, June 2002. Online:
http://history.nih.gov/01Docs/historical/2020b.htm [2/28/07].
15
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One of the requirements of this agreement relevant to the present experiment is the condition that
“Every precaution should be taken to respect the privacy of the subject, and to minimize the impact of
the study on the subject's physical and mental integrity, and on the personality of the subject.”
Therefore, when you report your results from the muscle force experiment, you must do so
anonymously (i.e. Subject A and Subject B), without compromising the right to privacy of yourself or
your lab partner.
1.6 Maximal Voluntary Contraction
In order to characterize the muscle as a motor, the maximum force output must be determined.
This quantity is referred to as the Maximal Voluntary Contraction (MVC), and varies depending on
muscle geometry (muscle size, lever ratio, etc.), muscle condition, and angle between the upper arm
and the forearm. We will define the MVC for the biceps as the maximum force that can be applied at
the hand, not the maximum force in the muscle (hence MVC depends on lever ratio, muscle area, and
elbow angle). Since MVC depends on muscle area, women typically have lower MVC than men. For
leg and trunk muscles, the MVC for the average woman is typically 60-75% that of the average men.
However, for arm muscles, the average MVC for women is typically half that of the average man. It is
important to note that there are wide distributions around this average, as shown in Fig. 8 (data taken
from previous classes of 2.671, available on the course website), so that it is not too difficult to find a
pair of people for which the woman has higher MVC than the man! More information on MVC is in
the short paper Static Muscle Force by TE Bernard, available on the 2.671 website.
Biceps MVC of 2.671 Students (both arms)
0.18
Female
0.16
Male
0.14
0.12
0.10
0.08
0.06
0.04
0.02
80
10
0
12
0
14
0
16
0
18
0
20
0
22
0
24
0
26
0
28
0
30
0
32
0
34
0
36
0
38
0
40
0
42
0
44
0
46
0
48
0
50
0
0.00
40
60
Fraction of Total Number of M or F Arms
0.20
Force (N)
Figure 8: Biceps muscle MVC for 37 female and 52 male 2.671 students (both arms),
age about 20. The elbow angle was fixed for these experiments at 45° and the load cells
were also mounted at 45°.
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2. Measurement of Force and EMG
2.1 EMG Sensor
EMG is most accurately measured with sensors inserted into the muscle, but can also be
monitored with a sensor placed on the skin above the muscle, as will be done in this experiment. The
experimental system includes an EMG Preamplifer (specifications in Lab Handouts page of 2.671
website at https://web.mit.edu/2.671/www/labs/ma300_preamp.pdf). The EMG Preamplifier is used to
measure the electrical signal input to the muscle. The placement of the EMG sensor on the arm has a
strong effect on the resultant EMG signal, as shown in Fig. 5, with the preferred location at the midline
of the muscle.18
1
2
3
4
Figure 5: The amplitude spectrum of the EMG signal as a function of location of the
EMG electrodes. The largest EMG signal is detected at location 2, at the midline of the
muscle. This location also provides the minimum detection of signals from adjacent
muscles.2
2.2 Calibration of load cells
We have calibrated the load cells for you by hanging 1 to 6 1-kg masses on the crossbar, as shown
in the photograph of Fig. 6. Figure 7 shows the dependence of output voltage on force applied to the
crossbar. The calibration equation obtained from a linear fit to the data of Fig. 7 is
F = 64.7(Vout − K 0 ) ,
(1)
18
C. J. De Luca, “The use of surface electromyography in biomechanics”, Journal of Applied Biomechanics, 13 (2), 1997,
pp. 135-16. Available at http://www.delsys.com/library/papers/Biomechanics.pdf
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where the output voltage, Vout, is in Volts, the force, F, is in Newtons. The constant K0 (in Volts)
depends on the temperature of the room and can be determined from the output voltage with no load on
the crossbar.
Figure 6: Photograph of experimental setup for calibration of load cells
20
Data
Linear Fit
Upward Force (N)
0
20
40
60
80
1.5
1
0.5
0
Output Voltage (V)
Figure 7: Calibration plot for load cells
3. Data Analysis
The following data analysis should be performed for all types of reports. Only after analyzing your
data thoroughly can you prioritize the importance of your various findings and determine what belongs
in your report, as suggested in the next section. The text in this and the following section refers to
experiments described in the Full Procedure instructions, which are more extensive than the Answer
Booklet and Individual Oral Report Procedures. If you are preparing an abstract and answer booklet
report or an individual oral report, simply ignore any text below that relates to experiments you did not
perform.
1. A description of differential amplifiers can be found in the OpAmp handout you received at the
beginning of the term. Make sure you understand how this circuit works. Refer to Fig. 1 in the
Procedure and calculate the gain of the differential amplifier. Record the gain in your lab
notebook or in your Answer Booklet. Do you understand how the circuit works?
2. Refer to the circuit diagrams in your lab notebook or Answer Booklet for the active rectifier
and low pass filter circuits. Compute the cutoff frequencies for the high pass filter on the
rectifier board and for the low-pass filter board and record these values in your lab notebook (or
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Answer Booklet). Compute the gain of the active low-pass filter from the indicated resistor
values and record in your lab notebook.
3. Determine your MVC in N for both arms.
4. Estimate your biceps cross-section from your diameter measurements. Compute the mean and
standard deviation of your measurements and record in your lab notebook or Answer Booklet.
Perform the t-statistic analysis outlined in the Soda Can Instructions to determine the precision
uncertainty (uD) in the diameter of your muscle from your multiple measurements.
5. Compute the stress in your (and your partner’s) biceps muscles from your MVC and estimated
cross-sectional area, assuming that 45% of the measured MVC is due to the bicepand the
muscle area is 85% that found from the diameter. You should use the lever ratio you estimated
for your own arms in lab. In other words, multiply your measured MVC by 0.45, divide by 0.85
times your estimated area, and multiply by the lever ratio for your specific arm. Compare the
computed stress to what you expect for mammals.
6. Use the method of propagation of errors to estimate the precision uncertainty in the calculated
stress in your muscle and quote your calculated stress with this uncertainty in your report. Just
include the uncertainty in diameter and lever ratio – since the maximum force is a single
number, not an average.
7. EMG vs. Force Data: Make sure to display EMG (on the vertical axis) as positive. Make the
horizontal axis Force in Percent MVC. Do not include the data points when you were relaxing
your bicep. Can you identify regions of linearity with different slopes, corresponding to the
recruitment of the different muscle fiber types? Refer to Sect 1.3: there should be an increase in
slope at about 30% MVC and another increase in slope at about 80% MVC. Remember that
these breakpoints are just guidelines and are expected to vary significantly from person to
person. Display fit lines on the plot corresponding to each region (refer to Sect. 3.1 below for
instructions). Compute the precision uncertainty for each slope. Is there a significant different
in slope between the regions?
8. For a Journal Article or Group Oral Report, you may wish to compare the EMG vs %MVC for
regions of increasing force to those for decreasing force.
9. Muscle Fatigue Data: Plot force vs time and EMG signal (inverted so that the values are
positive) vs time on two separate graphs. The data should show an increase in EMG in the
region of constant force. Or, if you were unable to hold a constant force, the data may show a
decrease in force for constant EMG. Print out copies of both plots and tape in your lab
notebook.
10. Plot Muscle Gain (defined as Muscle Force divided by positive EMG) vs. time for the fatigue
data and determine the percent change in the gain of your muscle during fatigue. For a Journal
Article or Group Oral Report, compare the fatigue data for the two different force regimes (less
than 30% and greater than 80%)
3.1 Analyze the Force vs EMG data
Plot both data columns (%MVC and +EMG) vs time (or versus point number). This is easily done
in Excel with a Line chart (rather than an X-Y scatter chart). In Excel, the resultant plot will appear
similar to that shown below (once you remove the default gray background)
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Hover the mouse over the first peak of the
force data to find out the point number and
then hover over the start of the next increase in
force, as shown below. In a COPY of your
original worksheet, delete the data between
these two points. Repeat so that the data set
comprises only regions of increasing force.
The plot should now appear as shown to the left below. Copy both columns of data and
Paste Special - Values so that the data columns are now numbers rather than formulae.
Sort the data in increasing order of %MVC to obtain the plot shown on the right below.
You are now ready to plot EMG vs %MVC and find the best-fit slope to the regions corresponding
to the three different types of muscle motor units. This is easily done in Logger Pro.
Copy the two data columns into Logger Pro. Verify
that the x-coordinate is force in %MVC and the ycoordinate is EMG (positive). Autoscale the graph as
necessary to view the entire data set. Highlight the
region of the graph that appears to correspond to the
slow oxidative twitch motor units (%MVC ≤ ~30%) as
shown to the right. Press the Linear Fit button
to perform a linear regression on the selected
data. Repeat for the fast oxidative twitch motor
units and, if visible, for the fast glycolytic motor units.
In the graph shown at the right, there are only two
regions of different slope visible, as shown in the
analyzed graph below.
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Refer to Sect 4.1 (p. 6) of the Uncertainty Analysis
handout found on the Resources page of the website
(the same as Sect. 3.4.1 in the Soda Can Experiment
Background, p. 13) to determine the uncertainty of
the linear fit parameters. When you quote the slope
in your lab report (or oral presentation), be sure to
include the 95% confidence interval in order to
discuss the significance (or non-significance) of any
observed differences between the three slopes.
breakpoint
4. Guidelines for Lab Report
The topics listed below can be included in all reports, depending on space or time available.
Obviously more items on the list will be included for longer reports than shorter ones. The first several
items in the list should be included in every report. It is left to you to prioritize these items and
determine what belongs in your report. There is no fixed list for each type of report, as the items that
should be included will depend on the overall focus of your report.
1. Clean schematic diagram (or photograph with labels) of experimental setup.
2. Theory section including the general properties of muscle and its activation by electrical signals
from the brain.
3. Your and your partners MVC for both arms and the corresponding stress in your (and your
partner’s) muscle. Compare the computed stress to what you expect for mammals. Include
the 95% confidence interval for your calculated stress.
4. The relationship between EMG and force (in % MVC) in your and your partner’s muscles,
showing regions of linearity (if any). If you fit lines to the separate linear regions, include best
fit values for slope with precision uncertainty.
5. Since you have normalized the force axis to %MVC, you can compare the relative increase in
slope at each transition and the %MVC at which each occurs for you and your partner.
6. Plots of measured force vs. time and EMG vs. time during muscle fatigue.
7. Plot of Muscle Gain vs time during Fatigue
p. 13 of 13
© I.W. Hunter and B.J. Hughey, 11/19/2007