Fiber architecture

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 ()• “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• Physiological cross-sectional area

– Sum fascicles perpendicular to axis– Not measurable– Fm = Ts * PCSA

• Prism approximation– Volume = b*d– B sin() = V/Lf

– PCSA = V/ Lf = M//Lf

• Project force to tendon– Ft = Fm cos() = Ts*M//Lf * cos()

Lf

d

b

PCSA

Fm

Ft

Test PCSA

• Spector & al., 1980– Cat soleus and medial gastrocnemius

• Powell & al., 1984 – Guinnea pig: 8 calf muscles

0.0

0.5

1.0

1.5

2.0

2.5

Po Po/g Po/pcsa Po/Ft

SoleusMG

Rel

ativ

e m

easu

re 130%

41%6% 0.7%

Measured force

Pre

dict

ed F

t (o

)

Pre

dict

ed P

CS

A (

●)

Powell

Spector

Are pennate muscles strong?

• Ft = Ts*M//Lf * cos()• cos() is always ≤1• Ft ≤ Fm

– Fiber packing– Series sarcomeres (A=1, F=1)– Parallel sarcomeres (A=6, F=6)– Pennate sarcomeres (A = 6, F=5.2)

Length change

• Fiber shortens from ff1

– Rotates from 1

– b*d constant– b*f*sin() = b*f1*sin(1)

– h = f*cos()-f1*cos(1)

• Fractional shortening in muscle isgreater than the fractional shorteningof fascicles– If the fascicles rotate much– eg: 15° fibers, fascicle shorten 25%muscle 27%

f

d

f1

b

h

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 andbiochemistry influenceVmax– Fiber type: 2x– Fiber length: 12x

Other Geometries

• Point origin, point insertion• Elastic aponeurosis

– Increase length with force– Vm = Va + Vf

• Multipennate muscles

Cos()Cos()

Cos()Cos()

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

Smits et al., 1994Purslow & Trotter, 1994

• MU localized longitudinal

Motor endplates in sternomanibularis

Fibers innervated by single MN are near one MEP band

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 controlof muscle lengths

– Measure both EDLorigin&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