Skeletal Muscle
•  Muscle is the material that really sets
biomechanics apart from other branches of
mechanics
•  3 Types:
– skeletal (voluntary)
– cardiac (involuntary)
– smooth (involuntary)
}striated
}striated
}unstriated
•  The main difference between skeletal and
cardiac muscle is that skeletal muscle can exhibit
a sustained ‘tetanic’ contraction whereas
cardiac muscle ‘beats.’
Structure
of
Skeletal Muscle
Structure
of
Skeletal Muscle
Myofibril (1µm Ø):
•  100’s-1000’s per myofiber
•  ~ 1500 thick filaments
•  ~ 3000 thin filaments
Fascicle:
Surrounded by
collagen sheath
Muscle cell (fiber):
•  10-80 µm 𝜙
•  multinucleated
•  sarcolemma
•  sarcoplasm
•  sarcoplasmic
reticulum
•  striated
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The Muscle Fiber (cell)
Key Components:
•  Multinucleated
•  Longitudinally arranged, circular cross
section
•  Sarcolemma (plasma membrane)
Terminal Cisternae
•  Sarcoplasm (cytosol)
•  Sarcoplasmic Reticulum (ER)
•  Mitochrondria (ATP powerhouse)
•  Transverse (T) Tubule
•  Terminal Cisternae
•  Network of Triads (T-tubule + 2 Terminal
Cisternae)
Myofibrils
• 
• 
• 
• 
1 µm Ø
~1500 thick filaments 12nm Ø
~3000 thin filaments 6 nm Ø
surrounded by sarcoplasmic
reticulum
•  A (optically anisotropic) band
•  I (optically isotropic) band
•  Z-line
The Sarcomere
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The Sarcomere
Anisotropic
Isotropic
~ 2.0 µm
to polarized light
The Sarcomere
The “Contractile Unit”
•  Thick Myosin Filaments
•  Thin Actin Filaments
•  Z-line to Z-line
•  A and I bands
•  Sliding Filament Theory
•  Titin
a.  Molecular Spring
b.  Connects Z-line to M-line,
allows for force transmission.
c.  Limits range of motion of sarcomere in tension, primary
contributor to passive stiffness.
Hexagonal Arrangement of
Myofilaments in Cross-Section
3
Myofilaments
•  Thick myosin filaments (180
myosin molecules polymerized)
•  Thin actin filaments
•  They interdigitate to form the
SARCOMERE
Actin
•  F-actin molecule
formed from G-actin
•  Twisted with a period of
70 nm - double helix
•  Two strands of
tropomyosin
•  Globular troponin
molecules (with a
strong affinity for Ca2+)
attached to
tropomyosin strands,
every 7 G-actin
monomers
Myosin
•  Subdomains:
Heavy Meromyosin HMM
Light Meromyosin LMM
S1-Head
•  Myosin leads protrude in
pairs at 180º
•  There are about 50 pairs
of cross-bridges at each
end of the thick filament
•  The filament makes a
complete twist 310º every
3 pairs
•  14.3 nm internal between
pairs
4
On each muscle fiber,
a nerve ending
terminates near the
center (at the muscle
end-plate).
Each nerve has from
2-3 to 150 fibers or
more depending on
the type of muscle.
At the end-plate is the
neuromuscular
junction.
Stimulus is transmitted
by neurotransmitter
Acetylcholine (mopped
up by cholinesterase).
The Motor Unit
Excitation-Contraction Coupling
Key Features
•  Negative resting membrane potential
- 
- 
High Intracellular [K+]
High Extracellular [Na2+]
•  Action Potential travels along sarcolemma
and down the T-tubule activates DHP.
• 
What is the DHP receptor?
a.  L-type (long-lasting) calcium voltage
gated channel
b.  Mechanically connected to the
Ryandine receptors (RyRs).
c.  How is cystosolic [Ca2+] increased?
• 
What is the primary difference in Ca2+ release between skeletal and cardiac
muscle?
- Calcium Induced Calcium Release (CICR)
Calcium Activation
Key Features
•  Force-development is highly
dependent on [Ca2+]. How is this
regulated?
•  Ca2+ binds to troponin-C sites,
which are separated by neighboring
troponin-C sites every 7 nm
(Cooperative Activity).
•  What is cooperative activity?
•  How does [Ca2+] regulate forcerelaxation? How is this achieved?
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The Crossbridge
Crossbridge Cycle
Crossbridge Cycle
Step 1: Cross-bridge (high-energy state) is formed
Step 2: Release of stored chemical energy is transferred
to mechanical motion, myosin head “power strokes” to it’s
rigor position (45 o). Actin slides towards the M-line.
Step 3: In rigor conformation, ATP molecule binds to
myosin head, releasing myosin (rigor state) from actin
filament.
Step 4: ATP hydrolysis (ATP à ADP + PI) supplies
potential energy to the myosin head. Myosin head is in it’s
upright position (90 o) and awaits for next open binding site
of actin to form crossbridge.
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Muscle Architecture
Flexor, Extensor, Belly, Tendon, Aponeurosis
Muscle Architecture:
Collagen Matrix
Muscle Architectures
Parallel (fusiform)
Convergent
Pennate
Circular (areolar)
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Muscle Architecture
Figure 9.2:2 from textbook. Diagram illustrating
(a) parallel-fibered and (b) pinnate muscles. (c)
and (d) illustrate pinnate muscle contraction.
Muscle Mechanics
• 
• 
• 
• 
• 
• 
• 
Twitch
Tetanus
Isometric contraction
Isotonic contraction
Concentric contraction
Eccentric contraction
Transient loading
Tests of Contractile Mechanics
Isometric - constant length
Isotonic - constant force
Transient
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Isometric (constant length) Preparations
Frog Semitendinosis Muscle
Force (N)
0.4
0
Active
Total
Passive
Time (s)
Fast vs. Slow Twitch Muscle
Duration of twitch corresponds to
functional requirements of muscle
Fast twitch muscle
White muscle
lower concentrations of RBCs
and myoglobin,
e.g. ocular muscle
T
Slow twitch muscle
Red muscle
e.g. soleus muscle
Isometric Twitch Tension T
Ocular (eye)
Gastrocnemius (calf)
Soleus (calf)
10
100
time (ms)
Stimulation Frequency
•  Increasing stimulus frequency will result into wave
summation of multiple twitches.
•  As frequency occurs, tetanus can occur (unfused/fused)
•  Fused tetanus occurs via recruitment of multiple
muscle fibers at high stimulation frequencies, resulting
in a maximum force development (>> twitch) that is
sustained over time.
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Passive Properties
Non-Stimulated Skel. Muscle:
•  Soft mechanical tissue
•  Nonlinear stress/strain
•  Viscoelastic properties:
(1)  Hysteresis
(2)  Stress Relaxation
(3)  Creep
Major Contributors:
•  ECM proteins
-  Collagen
-  Elastin
•  Titin
•  Vinculin
•  Fiber arrangement
(anisotropy)
Isometric Length-Tension
Relationships
Tension-length curves
for frog sartorius
muscle at 0ºC
Fixed length
Electrical Stimulation
Measure Force Generation
Isometric Tension: Sliding Filament
Theory
L
max
Developed tension
versus length for a
single fiber of frog
semitendinosus
muscle
Ascending limb is
dependent on Ca2+
concentration
Results in Isometric
Length-Tension
Relationship of muscle
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Isotonic (constant force) Preparations
F
L
Muscle shortens
Time (ms)
Reality: Isometric + Isotonic
The majority of skeletal muscles under go both:
•  Isometric Contraction (constant length):
Tmuscle < afterload
•  Isotonic Contraction (constant force):
Tmuscle > afterload
Force
Time
Isometric
Isotonic
Eccentric and Concentric Contraction
L0
Concentric Contraction:
•  Muscle shortens as it
generates tension.
•  Tmuscle > afterload
L < L0
L > L0
Eccentric Contraction:
•  Muscle lengths as it
generates.
•  Tmuscle < afterload
•  Serves to decelerate
muscle velocity as it
lengthens.
•  Ex: placing
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Hill’s Force-Velocity Curve
• The shortening part
(V>0) of the curve was
computed from Hill’s
equation with c = 4
• The asymptotes for
Hill’s hyperbola
(broken lines) are
parallel to the T/T0 and
V/Vmax axes
• Mechanical power
output is the product of
T and V
Hill's Equation
Original Form:
(T+a)(V+b)=b(T0+a)
a,b = asymptotes
Dimensionless forms:
1 − T T0
V
=
Vmax 1 + c (T T0 )
T0=Isometric force
1 − V Vmax
T
=
T0 1 + c (V Vmax )
(ranges from 1.2-4.0)
Vmax= velocity at T = 0
c = T0/a
Vmax
T0
Hill's Three Element Model
Fundamental Assumptions:
•  Resting length-tension relation is
governed by an elastic element in
parallel with a contractile element.
In other words, active and passive
tensions add. The parallel elastic
element is the passive properties.
•  Active contractile element is
determined by active length-tension
and velocity-tension relationships
only.
Fig 9.8:1 from text.
Hill’s functional model
of muscle
•  Series elastic element becomes
evident in quick-release
experiments.
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Hill's Three-Element Model
(basic equations)
L
T
h
D
T
stress contributed by the parallel elastic element
T(
P)
= P (L )
stress contributed by the activated actin − myosin filaments:
T(
S)
= S ( η, Δ )
S ( η, Δ ) is identically zero when the muscle is at rest; so that
S ( η, Δ ) <> 0
when η <> 0
and
S ( η, Δ ) = 0
when η = 0
Limitations of Hill Model
Division of forces between parallel and series elements and
division of displacements between contractile and elastic
elements is arbitrary (i.e. division is not unique). Structural
elements cannot be identified for each component.
Hill model is only valid for steady-shortening of tetanized
muscle.
1) For a twitch we must include the time-course of
activation and hence define "active state"
2) Transient responses observed not reproduced
Series elasticity is not observed. Properties of tendon and
crossbridge itself
Small Length Step Response
Tetanized single frog muscle fiber at 0ºC during a 1%
shortening step lasting 1 ms
13
Instantaneous and Plateau Tension
Solid lines: sarcomere length = 2.2 mm (near maximal myofilament
overlap). Broken lines: sarcomere length = 3.1 mm (39% myofilament
overlap). Thus instantaneous tension T1 reflects crossbridge stiffness and
number of attached crossbridges which varies with myofilament overlap.
Huxley and Simmons Model (1971)
Two stable attached
states of S-1 head. Thin
filament displacement y
stretches S-2 spring
generating force.
Calculated curves of T1
and T2 versus length
step y showing
predictions of Huxley
and Simmons model
Hill's Two Element Model
T
Fundamental Assumptions:
•  model consists of linear elastance
in series with contractile element.
T1
L1
L
T2
c.e.
L2
T
•  Active contractile element (c.e.)
depends on both muscle length
and shortening velocity.
•  Velocity can be determined from
Hill’s equation.
L = L1 + L2
T = T1 = T2
L’ = L1’ + L2’
T1 = α*ΔL1
L’ = L1’ + Vc.e.
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Hill’s 2-element model cont.
L’ = L1’ + Vc.e; ; where Vc.e. = L2’ (shortening velocity of
contractile element)
From Hill’s Equation: Vc.e. = - b (P-P0)/(P+a)
T = α*ΔL1 à T’ = α L1’ = α (L’ – Vc.e.)
T = α (L’ + b(P-P0)/(P+a)
Typical Parameters (Hill 1927, Holmes 2005):
a = 380 * 0.098 [mN/mm2]
b = 0.325 [mm/s]
P0 = a/0.257 [mN/mm2]
Vmax = b/a * P0 [mm/s]
Ls.e. 0 = 0.3; assume Ls.e. 0 is 30% of length
Solving in MATLAB
Input Time and
Length Profile
Define Parameters
Initialize Variables
(Element Lengths,
Tension)
Numerical Solver
(generic form)
Ref: Holmes 2005 (AJP)
MATLAB Output (Isometric)
S.E. à linear elastic
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MATLAB Output (Quick Release)
Both Elastic Elements are Inside the
Contractile Element
Actin
Myosin
Titin
Z-line
T
T
Skeletal Muscle: Summary of Key
Points
•  Skeletal muscle is striated and voluntary
•  It has a hierarchical organization of myofilaments forming
myofibrils forming myofibers (cells) forming
fascicles (bundles) that form the whole muscle
•  Overlapping parallel thick (myosin) and thin (actin)
contractile myofilaments are organized into sarcomeres in
series
•  Thick filaments bind to thin filaments at crossbridges which
cycle on and off during contraction in the presence of ATP
•  Nerve impulses trigger muscle contraction via the
neuromuscular junction
•  The parallel and/or pennate architecture of muscle fibers
and tendons affects muscle performance
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Muscle Mechanics: Summary of
Key Points
•  Skeletal muscle contractions can be twitches or
tetani, isometric or isotonic, eccentric or concentric
•  Twitch duration varies 10-fold with muscle fiber type
•  Tetanic contraction is achieved by twitch summation
•  The isometric length-tension curve is explained by
the sliding filament theory
•  Isotonic shortening velocity is inversely related to
force in Hill’s force-velocity equation
•  Hill’s three-element model assume passive and
active stresses combine additively
•  The series elastance is Hill’s model is probably
experimental artifact, but crossbridges themselves
are elastic
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