Intro to Biomechanics
Professors:
Thomas S. Buchanan (lecture)
Kurt Manal (lab)
TA: Justin Cowder
Lab Goal
 Muscles are the motors of the human
body. Our goal is to explore how
muscles’ generate force. Specifically:
 How does maximal muscle force
change as a function of its length?
 How does maximal muscle force
change as a function of its velocity?
Outline
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How muscle works
How muscle force changes with length
How muscle force changes with velocity
How these relate to strength & speed
How we measure these things
Wilkie on Muscle
A notice of a lecture presented by Professor D.R. Wilkie to the Institution of
Electrical Engineers in London. The subject is muscle:
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Muscles actuate movement by
development of tension
 That is, muscles pull
they don’t push.
 Muscles are grouped
into antagonist pairs.
 Movement involves
coordination of many
muscles.
Muscle Structure
Muscle Fascicles Myofibers
Sarcomeres
Fascicles are groups of fibers
 One can dissect out
muscle fascicles
 Under a light
microscope a
stripped pattern is
seen
 A muscle cell may
be 10-100mm in
diameter and 1-30
cm long
Muscle fibers are
comprised of myofibrils
 Under an electron
microscope, one
can clearly see
individual myofibrils
(threads)
 The sources of the
stripped patterns
are also seen
Structure of Individual Fiber
Sarcomeres
 Sarcomeres—the fundamental units of
muscle contraction. They are arranged in
series, hence the total change in length of a
muscle may be great while that of the
individual sarcomeres is small. They are
comprised of contractile filaments (thick and
thin filaments). Together these form a stripped
pattern when viewed under a light
microscope, which is why skeletal muscle is
sometimes called “striated” muscle.
Structure of the Sarcomere
Myofibril
Schematic of Sarcomere
Schematic of Sarcomere
Electron Microscope View
Force is developed at the actinmyosin cross bridge
 Thick filament is
made of myosin
(head and tail)
 Actin is the
primary
component of
thin filaments
(10nm diameter)
Sarcomere structure
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A-band
I-band
Z-line
H-zone
M-line
or M-region
Sarcomere Structrure
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A-band
I-band
Z-line
H-zone
M-line
or M-region
Outline



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How muscle works
How muscle force changes with length
How muscle force changes with velocity
How these relate to strength & speed
How we measure these things
Length-Tension Relationship
 The tension a sarcomere can generate
is a function of its length.
– When the sarcomeres are very long, only
a few of the myosin heads on each thick
filament can reach a thin filament, so little
force can be exerted.
Length-Tension Relationship
 At intermediate lengths, all of the
myosin heads are within reach of the
thin filaments, so maximum force can
be exerted.
Length-Tension Relationship
 With further shortening, the ends of the
thin filaments reach beyond the midpoints of the thick ones, to myosin
heads that face the wrong direction and
push on them instead of pulling. This
reduces the force that the muscle fiber
can exert.
Length-Tension Relationship
 Eventually, as shortening continues, the
thick filaments collide with the Z-disks.
Any further shortening distorts the
filaments and the force falls rapidly.
Length-Tension Relationship
 The tension a sarcomere can generate
is a function of its length.
Length-Tension Relationship
This is at 2.2 mm
for a frog. “Optimal
length” is about 2.8
mm for humans.
 There is an active and passive
component to the L-T relationship.
Outline





How muscle works
How muscle force changes with length
How muscle force changes with velocity
How these relate to strength & speed
How we measure these things
Force-Velocity Relationship
 The force a muscle can exert depends
upon how fast it is shortening as well as
the sarcomere length.
 The faster it is shortening, the less force
it can exert. This is why you cannot lift
heavy weights quickly.
 However, a muscle that is being forcibly
stretched exerts increased force.
Force-Velocity Relationship
Force-Velocity Relationship
Concentric
Eccentric
 F-V curve for isotonic contractions.
 Note that it is typically plotted with increases
in length being negative.
Hill Equation
 The Hill equation describes shortening
muscle:
(F + a)v = b(Fo - F)
 Here, a and b are constants,
Fo is maximum force, F
Hill Model
o
F is force, and
F
r
c
v is velocity.
0
e
Vmax
-b
-a
V elocit y
Outline





How muscle works
How muscle force changes with length
How muscle force changes with velocity
How these relate to strength & speed
How we measure these things
Whole Muscle Parameters
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Fiber Length
Pennation Angle
Cross Sectional Area
Moment Arm
Muscle Architecture
Muscle Architecture
Parallel Fibered
Pennate Muscle
Pennation Angle
 This is the angle between the muscle
fibers and the line of action
Cross Sectional Area
 Cross Sectional Area is related to the
# of muscle fibers in parallel.
 Hence, it should take into account the
pennation angle, as shown below:
Muscle Moment Arms
 Moment arm of
a muscle is the
length from the
joint center to
the muscle.
This is not a
constant.
 M=rxF
For Muscle #1
Joint Moment
 For each muscle, maximal
joint moment changes with
joint angle.
 It is the product of the
moment arm curve and the
muscle force curve.
 “Strength” is the sum of the
joint moment curves for
every muscle that acts at
the joint.
MA
Angle
Force
Angle
Moment
Angle
Moment
Contributions
 Note that large Peak
Forces (OPF) or
large Moment Arm
(SAR) does not
necessarily result in
large Moments.
Static Properties
The fiber length and pennation angle of
muscles can vary considerably.
Gastrocnemious has short,
pennate fibers and a long
tendon
Sartorius has long, parallel
fibers and very little tendon
Excursion vs Force
Parallel fibers:
Pennate fibers:
Long excursion,
Lower forces
Short excursion,
Higher forces
Outline





How muscle works
How muscle force changes with length
How muscle force changes with velocity
How these relate to strength & speed
How we measure these things
Lab Goal #1
 Q> How does maximal muscle force change
as a function of its length?
 To answer this we will measure maximal joint
moment as a function of joint angle
 We will provide estimates of muscle moment
arms from literature.
 You will take your measured joint moments
and the supplied moment arms to estimate
muscle force as a function of joint angle.
Lab Goal #2
 Q> How does maximal muscle force change
as a function of its velocity?
 To answer this we will measure maximal joint
moment at different velocities
 You will take your measured joint moments &
velocities and the supplied moment arms to
estimate muscle force as a function of
velocity.
Joint Moment
 We will measure joint moment using a
Biodex Dynometer
– Statically
– Dynamically
Muscle Parameters
 Other muscle parameters
can be measured in living
people using an
ultrasound machine:
– Pennation Angle
– Fiber length
Muscle Activity
 Muscle activation can be measured by
putting electrodes on (or into) a muscle.
 This is called electromyography and the
resulting signals are called EMGs.
EMG
EMG and Muscle Force
 EMG is related to muscle force
 The relationship is nonlinear
– EMG to muscle activation
– Muscle force-length relationship
– Muscle force-velocity relationship
 Mathematical models describing this
relationship are the topic of my research
(in part)
Details
 Instructions on how to use the Biodex
will be provided at the lab session.
 Lab will be in Room 209 Spencer.
 Dr. Kurt Manal will coordinate the lab
sessions.
Many graphics in this talk are from “How Animals Move” by R. McNeil Alexander