Muscle Mechanics
APA 6903
October 28, 2014
Olivia Zajdman
Michael Del Bel
• Muscle Anatomy Review
• What is a Motor Unit?
– Recruitment
– Fiber Type
• The Hill Model
– 3 Components
– Force-Length
– Force-Velocity
• Tendon Stretch-Shortening
• Musculoskeletal Model
Organization/Structure of Muscle
• Fiber = Structural unit of muscle
– Consist of many myofibrils
• Myofibrils = Basic unit of contraction
– Consist of sarcomeres, which contain thin (actin),
thick (myosin), elastic (titin) and inelastic (nebulin
and titin) filaments.
Organization/Structure of Muscle
Organization/Structure of Muscle
• Sarcomeres extend between Z-Lines
– Actin filaments extend length of sarcomere
– Myosin filaments are located in the center of the
– Titin and nebulin filaments form part of the
intramyofibrillar cytoskeleton
Sliding Filament Theory
• Actin and myosin “slide” along one another to shorten
the sarcomere.
• Myofilaments remain the same length.
• All sarcomeres per muscle fiber contract, in a wave-like
manner, shortening the fiber as whole.
What is a Motor Unit?
• The functional unit of skeletal muscle;
allows for movement!
• Consists of…
– Single motor neuron
– All of the muscle fibers innervated
• Fibers may not be adjacent to each other.
• Contractile component of the Hill Model.
• All-or-nothing principal: All muscle
fibers in MU are same type and all
contract when stimulated.
• Motor Unit Action Potential:
electrical twitch from MU recorded
via EMG.
• Henneman Size Principal: smallest
MU recruited first.
– Use spatial or temporal
summation to increase force
produced .
• Slow twitch (slow oxidative) and
fast twitch (fast glycolytic,
fatigable) fibers.
Hill Model
(P+a)(V+b) = (P0+a)b
P0 = maximum isometric tension
a = coefficient of shortening heat
b = a* V0/P0
V0 = maximum velocity (when P = 0).
• Primarily describes concentric contraction.
• Displays relationship between force and velocity in
physiological environment.
Winter, 2009
Hill Model
• Contractile component (CC)
– Active
• Parallel elastic component (PEC)
– Passive
• Series elastic component (SEC)
– Passive
Nordin and Frankel, 2012
Hill Model
• Contractile component (CC)
-”Active” force component,
generated by actin/myosin
interactions (sarcomeres).
-Fully extended when inactive.
-Shortened when activated.
Nordin and Frankel, 2012
Hill Model
• Parallel elastic component (PEC)
– Consists of connective tissue
(fascia, epimysium,
perimysium, endomysium)
surrounding the muscle.
– Represents the passive
muscle force that connective
tissues are responsible for.
Nordin and Frankel, 2012
Hill Model
• Series elastic component (SEC)
– Consists of the tendon and
elasticity of the
intramyofibrillar cytoskeleton.
– Similar function as PEC.
– Lengthens as force increases,
maintaining constant muscle
– Spring-like
Nordin and Frankel, 2012
Force vs. Length
• Force production proportional to
number of actin-myosin cross
• Lengthening or shortening to a
degree decreases number of
binding sites
• PEC contributes tension as it
becomes taut as muscle lengthens
• PEC passive force always present,
while CC voluntarily controlled
• Amplitude of force dependent on
amount of excitation
Force vs. Velocity
– Force decreases as muscle
shortens under load (cross
bridges break & reform).
– Fluid viscosity (CC/PEC)
creates friction -> requires
force to overcome -> reduce
tendon force.
– Force increases as muscle
lengthening velocity increases.
• Greater force to break
cross-bridge links than to
hold together.
Tendon Stretch-Shortening
Toe region: elongation reflect
change in wavy pattern of relaxed
Elastic/linear region: increase
stiffness in tissue.
Plastic region: some permanent
damage after load removed
Yield point: intersection of stressstrain (max).
Failure point: fibers sustain
irreversible damage.
Ultimate load: highest load
structure can withstand before
Slope: Elasticity modulus
Viscoelasticity Characteristics
Load Relaxation
Creep phenomenon
Musculoskeletal Model
• Representation of entire system’s
• Bones represent basis of
modeling body (rigid segments)
– Important to be accurate!
• Muscle Architecture (structure
reflects function)
– Pennation angle
– Physiological cross-section
– Fiber length/type
– Tendon morphology
Musculoskeletal Model
• Inverse dynamics
– Bone segments are controlled by estimated resultant
joint moments.
– Muscle forces are then estimated for sequences of
motions, while behaviour can be attributed through
inclusion of the Hill Model.
Problems with EMG-Driven Models
• Data from surface EMG electrodes may not fully
represent muscle’s activity.
• Impossible to measure deep muscle activity.
• Models generally simplify reality
– Model = 6-8 muscles for a jump
– Reality = >40 muscles involved
Nordin, M., & Frankel, V. (2012). Biomechanics of Tendons and
Ligaments and Biomechanics of Skeletal Muscle. In Basic
Biomechanics of the Musculoskeletal System(4th ed., pp. 102-180).
Baltimore, MD: Lippincott Williams & Wilkins.
Robertson, D., Caldwell, G., Hamil, J., Kamen, G., & Whittlesey, S.
(2004). Muscle Modeling. In Research Methods in Biomechanics (pp.
183-207). United States: Human Kinetics.
Winter, D. (2009). Muscle Mechanics. In Biomechanics and Motor
Control of Human Movement (4th ed., pp. 224-247). Hoboken, New
Jersey: John Wiley & Sons.

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