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 (L m ) Fascicle length (L f ) 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 – F m = T s * PCSA Prism approximation – Volume = b*d – B sin(  ) = V/L f – PCSA = V/ L f = M/  /L f Project force to tendon – F t = F m cos(  ) = Ts*M/  /L f * cos(  ) LfLf d b  PCSA FmFm FtFt

Test PCSA Spector & al., 1980 – Cat soleus and medial gastrocnemius Powell & al., 1984 – Guinnea pig: 8 calf muscles PoPo/gPo/pcsaPo/Ft Soleus MG Relative measure 130% 41% 6%0.7% Measured force Predicted Ft (o) Predicted PCSA (●) Powell Spector

Are pennate muscles strong? F t = T s *M/  /L f * cos(  ) cos(  ) is always ≤1 F t ≤ 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 Fiber shortens from f  f 1 – Rotates from    1 – b*d constant – b*f*sin(  ) = b*f 1 *sin(  1 ) – h = f*cos(  )-f 1 *cos(  1 ) Fractional shortening in muscle is greater than the fractional shortening of fascicles – If the fascicles rotate much – eg: 15° fibers, fascicle shorten 25%  muscle 27% f d f1f1  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 and biochemistry influence Vmax – Fiber type: 2x – Fiber length: 12x

Other Geometries Point origin, point insertion Elastic aponeurosis – Increase length with force – V m = V a + V f 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., 1994 Purslow & 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 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