Download Fiber architecture - Georgia Institute of Technology

Fiber architecture
• Quantification of muscle structure
• Relationship to functional capacity
– Muscle as one big sarcomere
– Independent fibers/fascicles
Terminology
• Attachments
– Origin
– Insertion
• Muscle belly
– Aponeurosis (internal tendon)
– Fascicle (Perimysium)
– Compartment
– Pennation
Connective tissue layers
• Endomysium
• Perimysium
• Epimysium
Purslow & Trotter 1994
Muscles are 3-D structures
Structural definition
• Qualitative
– Epimysium
– Discrete tendon
• Insertion (gastroc)
• Origin (extensor digiti longus)
– Easy to separate
• Electrophysiological
– Common nerve
– Common reflex
3-D structures
•
•
•
•
Curved (centroid) paths
Curved fiber paths
Distributed attachments
Varying fascicle length
Categorizing
• Pennation
– Longitudinal
– Unipennate
– Bipennate
– Multipennate
• Approximation
– Fascicle length
– Force capacity
Historical
• Stensen (1660)
• Borelli (1680)
• Gosch (1880)
Idealized muscles
•
•
•
•
•
Muscle mass (M)
Muscle length (Lm)
Fascicle length (Lf)
Pennation angle (q)
“Physiological” cross sectional area (PCSA)
The Gans & Bock Model
• Vastus Intermedius
– Identical facsicles
– Originate directly from bone
– Insert into tendon that lies parallel to bone
• Geometrical constraints
– Tendon moves parallel to bone
– Constant volume
– 2-D approximation
• No change “into the paper”
• Constant area
Force capacity
d
• Physiological cross-sectional area
– Sum fascicles perpendicular to axis
– Not measurable
– Fm = Ts * PCSA
b
• Prism approximation
– Volume = b*d
– B sin(q) = V/Lf
– PCSA = V/ Lf = M/r/Lf
• Project force to tendon
– Ft = Fm cos(q) = Ts*M/r/Lf * cos(q)
q
Lf
Fm
PCSA
Ft
Test PCSA
• Spector & al., 1980
– Cat soleus and medial gastrocnemius
• Powell & al., 1984
Powell
– Guinnea pig: 8 calf muscles
Soleus
MG
130%
41%
1.5
6%
0.7%
1.0
0.5
0.0
Po
Po/g
Po/pcsa Po/Ft
Predicted Ft (o)
Relative measure
2.0
Predicted PCSA (●)
Spector
2.5
Measured force
Are pennate muscles strong?
• Ft = Ts*M/r/Lf * cos(q)
• cos(q) is always ≤1
• Ft ≤ F m
– Fiber packing
– Series sarcomeres (A=1, F=1)
– Parallel sarcomeres (A=6, F=6)
– Pennate sarcomeres (A = 6, F=5.2)
Length change
d
• Fiber shortens from ff1
– Rotates from q  q1
– b*d constant
– b*f*sin(q) = b*f1*sin(q1)
– h = f*cos(q)-f1*cos(q1)
f1
b
h
q
• Fractional shortening in muscle is
q1
greater than the fractional shortening
f
of fascicles
– If the fascicles rotate much
– eg: 15° fibers, fascicle shorten 25%muscle 27%
Operating range
• Muscle can shorten ~50% (Weber, 1850)
– Operating range proportional to length
– Spasticity
– Reduced mobility (Crawford, 1954)
• Length-tension relationship
– Useful range strongly
dependent on Lo
– Pennate fibers shorten
less than their muscle
Velocity
• Force-velocity relationship
– Shortening muscle produces less force
– Power = force * speed
– Acceleration
• Architecture and
biochemistry influence
Vmax
– Fiber type: 2x
– Fiber length: 12x
Other Geometries
• Point origin, point insertion
• Elastic aponeurosis
– Increase length with force
Cos(a-q)
Cos(q)
– Vm =
Va +
Vf
Cos(a)
Cos(a)
• Multipennate muscles
Other subdivisions
• Multiple bellies
– Digit flexors/extensors
– Biceps/Triceps
– Multiple discrete attachments
• Compartments
– Most “large” muscles
– Internal connective tissue
– Internal nerve branches
Multiple bellies
• Rat EDL
– 4 insertion tendons
– 2 nerve branches
• Glycogen depletion
– Discrete branch territories
– Mixing at ventral root
Balice-Gordon & Thompson 1988
Compartments
• Cat lateral
gastrocnemius
– Dense internal
connective tissue
– Surface texture
– Internal nerve
branches
English & Ledbetter, 1982
LG Compartments
• Motor unit
– Axon+innervated fibers
– Constrained to
compartment
English & Weeks, 1984
Neural view
• Does NS use the same divisions as
anatomists?
• Careful training can control single motoneuron
• Behavioral recruitment spans muscles
– Mechanical tuning
– Training
Anatomical vs neural division
• Muscle
– Easily separated
– Separately innervated
• Multi-belly
– Partly separable
– Slight overlap of nerve territories
• Compartment
– Inseparable
– Slight overlap of nerve territories
Fibers and fascicles
• Rodents
– Fiber = fascicle
– Easiest experimental model
• Small animals
– Fascicle 5-10 cm
– Fiber 1-2 cm (conduction velocity ~2-5 m/s)
Motor unit distribution
• MU localized longitudinal
Fibers innervated by single
MN are near one MEP band
Motor endplates in sternomanibularis
Purslow & Trotter, 1994
Smits et al., 1994
3-D reconstruction
• Relatively straight fibers
• Taper-in, taper-out
1 mm
Ounjian et al., 1991
Mechanical independence
• Bag of spaghetti model
– Independent muscle/belly/compartment/fiber
– Little force sharing
• Fiber composite model
– Adjacent structures coupled elastically
– Lateral force transmission
Fiber level force transmission
• Sybil Street, 1983
• Frog sartorius
– All but one fiber removed from half muscle
– Anchor remaining fiber ends
– Anchor segment and “clot”
– Same force
“Belly” level force transmission
• Huijing & al., 2002
• Rat EDL
– Separate digit tendons
– Cut one-by-one (TT)
– Pull bellies apart (MT)
– Little force change with
tenotomy only
Muscle level force transmission
• Maas & al., 2001
• Rat TA and EDL
– Separate control
of muscle lengths
– Measure both EDL
origin&insert F
– 10% EDL-TA trans
Summary
•
•
•
•
•
Architectural quantification: M, Lm, Lf, q
Estimates of force production: PCSA (Fm), Ft
Simple models are “pretty good”
Sub-muscular structures: compartments
Neural structure is not the same as muscle
structure