Fiber architecture

1
Fiber architecture

• Quantification of muscle structure
• Relationship to functional capacity
• Muscle as one big sarcomere
• Independent fibers/fascicles

2
Terminology

• Attachments
• Origin
• Insertion
• Muscle belly
• Aponeurosis (internal tendon)
• Fascicle (Perimysium)
• Compartment
• Pennation

3
Connective tissue layers

• Endomysium
• Perimysium
• Epimysium

Purslow Trotter 1994
4
Muscles are 3-D structures
5
Structural definition

• Qualitative
• Epimysium
• Discrete tendon
• Insertion (gastroc)
• Origin (extensor digiti longus)
• Easy to separate
• Electrophysiological
• Common nerve
• Common reflex

6
3-D structures

• Curved (centroid) paths
• Curved fiber paths
• Distributed attachments
• Varying fascicle length

7
Categorizing

• Pennation
• Longitudinal
• Unipennate
• Bipennate
• Multipennate
• Approximation
• Fascicle length
• Force capacity

8
Historical

• Stensen (1660)
• Borelli (1680)
• Gosch (1880)

9
Idealized muscles

• Muscle mass (M)
• Muscle length (Lm)
• Fascicle length (Lf)
• Pennation angle (q)
• Physiological cross sectional area (PCSA)

10
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

11
Force capacity
d

• Physiological cross-sectional area
• Sum fascicles perpendicular to axis
• Not measurable
• Fm Ts PCSA
• Prism approximation
• Volume bd
• B sin(q) V/Lf
• PCSA V/ Lf M/r/Lf
• Project force to tendon
• Ft Fm cos(q) TsM/r/Lf cos(q)

b
q
Fm
Lf
PCSA
Ft
12
Test PCSA

• Spector al., 1980
• Cat soleus and medial gastrocnemius
• Powell al., 1984
• Guinnea pig 8 calf muscles

Powell
Spector
130
41
Predicted PCSA (?)
Predicted Ft (o)
6
0.7
Relative measure
Measured force
13
Are pennate muscles strong?

• Ft TsM/r/Lf cos(q)
• cos(q) is always 1
• Ft Fm
• Fiber packing
• Series sarcomeres (A1, F1)
• Parallel sarcomeres (A6, F6)
• Pennate sarcomeres (A 6, F5.2)

14
Length change
d

• Fiber shortens from f?f1
• Rotates from q ? q1
• bd constant
• bfsin(q) bf1sin(q1)
• h fcos(q)-f1cos(q1)
• Fractional shortening in muscle isgreater than
  the fractional shorteningof fascicles
• If the fascicles rotate much
• eg 15 fibers, fascicle shorten 25?muscle 27

f1
b
h
q
q1
f
15
Operating range

• Muscle can shorten 50 (Weber, 1850)
• Operating range proportional to length
• Spasticity
• Reduced mobility (Crawford, 1954)
• Length-tension relationship
• Useful range stronglydependent on Lo
• Pennate fibers shortenless than their muscle

16
Velocity

• Force-velocity relationship
• Shortening muscle produces less force
• Power force speed
• Acceleration
• Architecture andbiochemistry influenceVmax
• Fiber type 2x
• Fiber length 12x

17
Other Geometries

• Point origin, point insertion
• Elastic aponeurosis
• Increase length with force
• Vm Va Vf
• Multipennate muscles

Cos(a-q) Cos(a)
Cos(q) Cos(a)
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Other subdivisions

• Multiple bellies
• Digit flexors/extensors
• Biceps/Triceps
• Multiple discrete attachments
• Compartments
• Most large muscles
• Internal connective tissue
• Internal nerve branches

19
Multiple bellies

• Rat EDL
• 4 insertion tendons
• 2 nerve branches
• Glycogen depletion
• Discrete branch territories
• Mixing at ventral root

Balice-Gordon Thompson 1988
20
Compartments

• Cat lateral gastrocnemius
• Dense internal connective tissue
• Surface texture
• Internal nerve branches

21
LG Compartments

• Motor unit
• Axoninnervated fibers
• Constrained tocompartment

English Weeks, 1984
22
Neural view

• Does NS use the same divisions as anatomists?
• Careful training can control single motoneuron
• Behavioral recruitment spans muscles
• Mechanical tuning
• Training

23
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

24
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)

25
Motor unit distribution
Fibers innervated by single MN are near one MEP
band

• MU localized longitudinal

Motor endplates in sternomanibularis
Smits et al., 1994
Purslow Trotter, 1994
26
3-D reconstruction

• Relatively straight fibers
• Taper-in, taper-out

Ounjian et al., 1991
27
Mechanical independence

• Bag of spaghetti model
• Independent muscle/belly/compartment/fiber
• Little force sharing
• Fiber composite model
• Adjacent structures coupled elastically
• Lateral force transmission

28
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

29
Belly level force transmission

• Huijing al., 2002
• Rat EDL
• Separate digit tendons
• Cut one-by-one (TT)
• Pull bellies apart (MT)
• Little force change withtenotomy only

30
Muscle level force transmission

• Maas al., 2001
• Rat TA and EDL
• Separate controlof muscle lengths
• Measure both EDLorigininsert F
• 10 EDL-TA trans

31
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