Biomechanics of Skeletal Biomechanics of Skeletal MuscleMuscle

Professor Ming-Shaung Ju Professor Ming-Shaung Ju 朱銘祥朱銘祥

Dept. of Mechanical EngineeringDept. of Mechanical EngineeringNational Cheng Kung University, Tainan, TaiwNational Cheng Kung University, Tainan, Taiwan an

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ContentsContents

I. Composition & structure of skeletal I. Composition & structure of skeletal musclemuscle

II. Mechanics of Muscle ContractionII. Mechanics of Muscle Contraction

III. Force production in muscleIII. Force production in muscle

IV. Muscle remodelingIV. Muscle remodeling

V. SummaryV. Summary

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Muscle types: Muscle types: – cardiac muscle: composes the heartcardiac muscle: composes the heart– smooth muscle: lines hollow internal organssmooth muscle: lines hollow internal organs– skeletal (striated or voluntary) muscle: skeletal (striated or voluntary) muscle:

attached to skeleton via tendon & attached to skeleton via tendon & movementmovement

Skeletal muscle 40-45% of body weightSkeletal muscle 40-45% of body weight– > 430 muscles> 430 muscles– ~ 80 pairs produce vigorous movement~ 80 pairs produce vigorous movement

Dynamic & static workDynamic & static work– Dynamic: locomotion & positioning of Dynamic: locomotion & positioning of

segmentssegments– Static: maintains body postureStatic: maintains body posture

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I. Composition & I. Composition & structure of skeletal structure of skeletal musclemuscle

Structure & organization

• Muscle fiber: long cylindrical multi-nuclei cell 10-100 m

fiber endomysium fascicles perimysium

epimysium (fascia)

• Collagen fibers in perimysium & epimysium are continuous

with those in tendons

• {thin filament (actin 5nm ) + thick filament (myosin 15 nm )}

myofibrils (contractile elements, 1m ) muscle fiber

55

66

77

Bands of myofibrilsBands of myofibrils

A bands: thick filaments in cA bands: thick filaments in central of sarcomereentral of sarcomere

Z line: short elements that liZ line: short elements that links thin filamentsnks thin filaments

I bands: thin filaments not oI bands: thin filaments not overlap with thick filamentverlap with thick filamentss

H zone: gap between ends oH zone: gap between ends of thin filaments in center of thin filaments in center of A bandf A band

M line: transverse & longitudM line: transverse & longitudinally oriented linking proinally oriented linking proteins for adjacent thick filteins for adjacent thick filamentsaments

A bandI band

Z ZM

sarcomere

H

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Sarcoplasmic reticulumSarcoplasmic reticulum network of tubules & sacs; network of tubules & sacs; parallel to myofibrilsparallel to myofibrils enlarged & fused at junction enlarged & fused at junction

between A & I bands: transverbetween A & I bands: transverse sacs (terminal cisternae)se sacs (terminal cisternae)

Triad {terminal cisternae, tranTriad {terminal cisternae, transverse tubule}sverse tubule}

T system: duct for fluids & proT system: duct for fluids & propogation of electrical stimulupogation of electrical stimulus for contraction (action potes for contraction (action potential)ntial)

Sarcoplasmic reticulum store Sarcoplasmic reticulum store calciumcalcium

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Molecular composition Molecular composition of myofibrilof myofibril Myosin composed of indiviMyosin composed of indivi

dual molecules each has a dual molecules each has a globular head and tailglobular head and tail

Cross-bridge: actin & myosCross-bridge: actin & myosin overlap (A band)in overlap (A band)

Actin has double helix; twActin has double helix; two strands of beads spiralino strands of beads spiraling around each otherg around each other

troponin & tropomysin regtroponin & tropomysin regulate making and breakinulate making and breaking contact between actin & g contact between actin & myosinmyosin

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Molecular basis of muscle Molecular basis of muscle contractioncontraction Sliding filament theory: relative movement of aSliding filament theory: relative movement of a

ctin & myosin filaments yields active sarcomerctin & myosin filaments yields active sarcomere shorteninge shortening

Myosin heads or cross-bridges generate contraMyosin heads or cross-bridges generate contraction force ction force

Sliding of actin filaments toward center of sarcSliding of actin filaments toward center of sarcomere: decrease in I band and decrease in H zoomere: decrease in I band and decrease in H zone as Z lines move closerne as Z lines move closer

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Motor unitMotor unit

1212

1313

ATP

ATP

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Histology of muscleHistology of muscle

Eye muscle (Rectus lateralis); Myofibrillar ATPase stain, PH 4.3

Type I

Type IIA

Type IIB

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Muscle Differentiation (types of fibers)Muscle Differentiation (types of fibers)

I (I (slow-twitch slow-twitch oxidative)oxidative)

IIA IIA (fast-twitch (fast-twitch oxidative glycoloxidative glycolytic)ytic)

IIB IIB fast-twitch glycfast-twitch glycolyticolytic

Contraction speedContraction speed SlowSlow fastfast fastfast

Myosin-ATPase activitMyosin-ATPase activityy

LowLow HighHigh HighHigh

Primary source of Primary source of ATP productionATP production

Oxidative phosOxidative phosphorylationphorylation

Oxidative phosOxidative phosphorylationphorylation

Anaerobic glycolysiAnaerobic glycolysiss

Glycolytic enzyme actGlycolytic enzyme activityivity

LowLow IntermediateIntermediate HighHigh

No. of mitochondriaNo. of mitochondria ManyMany ManyMany FewFew

CapillariesCapillaries ManyMany ManyMany FewFew

Myoglobin contentsMyoglobin contents HighHigh HighHigh LowLow

Muscle ColorMuscle Color RedRed RedRed WhiteWhite

Glycogen contentGlycogen content LowLow IntermediateIntermediate HighHigh

Fiber diameterFiber diameter smallsmall IntermediateIntermediate LargeLarge

Rate of fatigueRate of fatigue slowslow IntermediateIntermediate FastFast

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Functional arrangement of Functional arrangement of musclemuscle

pinnated angle of muscle

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The Musculotendinous UniThe Musculotendinous Unitt Tendon- spring-like elastic Tendon- spring-like elastic

component in series with ccomponent in series with contractile component (protontractile component (proteins)eins)

Parallel elastic component Parallel elastic component (epimysium, perimysium, e(epimysium, perimysium, endomysium, sarcolemma)ndomysium, sarcolemma)

F

x

PEC: parallel elastic componentCC: contractile componentSEC: series elastic component

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II. Mechanics of Muscle II. Mechanics of Muscle ContractionContraction Neural stimulation – impulseNeural stimulation – impulse Mechanical response of a motor unit - twitchMechanical response of a motor unit - twitch

T

t

eT

tFtF

0)(

T: twitch or contraction time, time for tension to reach maximum

F0: constant of a given motor unit

Averaged T valuesTricep brachii 44.5 ms Soleus 74.0 msBiceps brachii 52.0 ms Medial Gastrocnemius 79.0 msTibialis anterior 58.0 ms

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Summation and tetanic contractionSummation and tetanic contraction

(ms)

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Generation of muscle Generation of muscle tetanustetanus

10 Hz

100Hz

Note: muscle is controlled by frequency modulation from neural input very important in functional electrical stimulation

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Wave summation & tetanizationWave summation & tetanization

Critical frequency

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Motor unit recruitmentMotor unit recruitmentAll-or-nothing event2 ways to increase tension:- Stimulation rate- Recruitment of more motor unit

Size principleSmallest m.u. recruited firstLargest m.u. last

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III. Force production in III. Force production in musclemuscle

Force –length characteristicsForce –length characteristics Force – velocity characteristicsForce – velocity characteristics Muscle ModelingMuscle Modeling Neuromuscular system dynamics Neuromuscular system dynamics

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3-1 Force-length curve of 3-1 Force-length curve of contractile componentcontractile component

Resting 2.0-2.25 um Resting 2.0-2.25 um max. no. of cross brimax. no. of cross bridges; max. tensiondges; max. tension

2.25-3.6 um no. of cr2.25-3.6 um no. of cross bridge oss bridge

< 1.65 um overlap of < 1.65 um overlap of actin no. of cross briactin no. of cross bridge dge

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Influence of parallel elastic Influence of parallel elastic componentcomponent

l0

Fc

Fp

Ft

Note: Fc is under voluntary control & Fp is always present

Fp

l0

Fc

Ft

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Overall force-length characteristics of a Overall force-length characteristics of a musclemuscle

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Series Elastic ComponentSeries Elastic Component

Tendon & other series tissueTendon & other series tissue Lengthen slightly in isometric contractionLengthen slightly in isometric contraction Series component can store energy when Series component can store energy when

stretched prior to an explosive shorteningstretched prior to an explosive shortening

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Quick-release for determining Quick-release for determining elastic constant of series elastic constant of series componentcomponent Muscle is stimulated to build Muscle is stimulated to build

tensiontension Release mechanism is Release mechanism is

activatedactivated Measure instantaneous Measure instantaneous

shortening x while force is shortening x while force is kept constantkept constant

Contractile element length Contractile element length kept constant during quick kept constant during quick releaserelease

F

x

FKSC

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In vivo force-length In vivo force-length measurementmeasurement Human Human in vivoin vivo experiments (MVC) experiments (MVC) Challenges:Challenges:

– Impossible to generate a max. Impossible to generate a max. voluntary contraction for a single voluntary contraction for a single agonist without activating remaining agonist without activating remaining agonistagonist

– Only moment & angle are Only moment & angle are measurable. Moment depends on measurable. Moment depends on muscle force and moment arm.muscle force and moment arm.

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3-2 Force-Velocity 3-2 Force-Velocity CharacteristicsCharacteristics Concentric contractionConcentric contraction

– Muscle contracts and shortening, positive Muscle contracts and shortening, positive work was done on external load by musclework was done on external load by muscle

– Tension in a muscle decreases as it Tension in a muscle decreases as it shortensshortens

Eccentric contractionEccentric contraction– Muscle contracts and lengthening, Muscle contracts and lengthening,

external load does work on muscle or external load does work on muscle or negative work done by muscle.negative work done by muscle.

– Tension in a muscle increases as it Tension in a muscle increases as it lengthens by external loadlengthens by external load

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Force-velocity Force-velocity characteristics of skeletal characteristics of skeletal muscle (Hill model)muscle (Hill model)

0

0

0

0

0

0Fwhen velocity max. v

heat shortening oft coefficien a

tensionisometric max. F

)(

F

vab

abv

baFF

eccentric concentricF

v

Increased tensions in eccentric due to:• Cross bridge breaking force > holding force at isometric length• High tendon force to overcome internal damping friction

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Length and velocity versus Length and velocity versus ForceForce

Note: maximum contraction condition; normal contractions are fraction of the maximum force

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Equilibrium of load and muscle Equilibrium of load and muscle forceforce

Muscle force is function Muscle force is function of of lengthlength, , velocityvelocity and and activationactivation

The load determines The load determines activation and length of activation and length of muscle by the muscle by the equilibrium conditionequilibrium condition

Load: Load: springspring-like, -like, inertialinertial, , viscousviscous damper damper

linear spring

Nonlinearspring

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3-3 Muscle Modeling3-3 Muscle ModelingElements of Hill model other than contractile element

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• Derive equations of motion• Estimated parameters based onExperimental data & modelSimulation (least squares). Numerical simulation

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3-4 Neuromuscular system 3-4 Neuromuscular system dynamicsdynamics

Muscle forceMuscle forceF = FF = F00 * Act * F * Act * FLTLT * F * FFVFV

T = r(T = r() * F(L() * F(L(), V, A)), V, A)FF00= F= F00(pinnated angle, PCSA, fiber type)(pinnated angle, PCSA, fiber type)

rmuscle

-15

-10

-5

0

5

10

15

20

brachialis biceps, long

passive

triceps, med.

triceps, lat.

triceps, long

biceps, short

brachioradialis

Tor

que

(N-m

)

0 0.5 1 1.5 2 2.5Angle (radian)

Max torque due to each muscle

Note: feedback mechanism in neuromuscular system

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Neuromuscular system Neuromuscular system modelingmodeling

ActivationDynamics

Central Command& reflexes

ContractionDynamics

TendonCompliance

TendonCompliance

Force

Muscle-TendonVelocity

Muscle-TendonLength

-

-

+

+

muscle

tendon

tendon

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Muscle fatigueMuscle fatigue

Drop in tension followed prolonged stimulation.Fatigue occurs when the stimulation frequency outstrips rate of replacement of ATP, the twitch force decreases with time

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V. Muscle RemodelingV. Muscle Remodeling Effects of Disuse and ImmobilizationEffects of Disuse and Immobilization

– Immediate or early motion may prevent muscle atroImmediate or early motion may prevent muscle atrophy after injury or surgeryphy after injury or surgery

– Muscle fibers regenerate in more parallel orientatioMuscle fibers regenerate in more parallel orientation, capillariaztion occurred rapidly, tensile strength rn, capillariaztion occurred rapidly, tensile strength returned more quicklyeturned more quickly

– Atrophy of quadriceps developed due to immobilizaAtrophy of quadriceps developed due to immobilization can not be reversed by isometric exercises.tion can not be reversed by isometric exercises.

– Type I fibers atrophy with immobilization; cross-secType I fibers atrophy with immobilization; cross-sectional area decreases & oxidative enzyme activity retional area decreases & oxidative enzyme activity reducedduced

– Tension in muscle afferent impulses from intrafusal Tension in muscle afferent impulses from intrafusal muscle spindle increases & leading to increase stimmuscle spindle increases & leading to increase stimulation of type I fiberulation of type I fiber

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Effects of Physical TrainingEffects of Physical Training– Increase cross-sectional area of muscle fibers, muIncrease cross-sectional area of muscle fibers, mu

scle bulk & strengthscle bulk & strength– Relative percentage of fiber types also changesRelative percentage of fiber types also changes– In endurance athletes % type I, IIA increaseIn endurance athletes % type I, IIA increase– Stretch out of muscle-tendon complex increases Stretch out of muscle-tendon complex increases

elasticity & length of musculo-tendon unit; store elasticity & length of musculo-tendon unit; store more energy in viscoelastic & contractile componmore energy in viscoelastic & contractile componentsents

– Roles of muscle spindle & Golgi tendon organs: inRoles of muscle spindle & Golgi tendon organs: inhibition of spindle effect & enhance Golgi effect to hibition of spindle effect & enhance Golgi effect to relax muscle and promote further lengthening.relax muscle and promote further lengthening.

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V. SummaryV. Summary

Structure unit of muscle: fiberStructure unit of muscle: fiber Myofibrils are composed of actin & myosinMyofibrils are composed of actin & myosin Sliding filament theory & cross-bridgeSliding filament theory & cross-bridge Calcium ion & contractivityCalcium ion & contractivity Motor unit: a single neuron & all muscle fiMotor unit: a single neuron & all muscle fi

bers innervated by itbers innervated by it Force production depends on length, veloForce production depends on length, velo

city, muscle composition & morphology (Hcity, muscle composition & morphology (Hill model)ill model)

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ReferencesReferences

D.A. Winter, Biomechanics and Motor ContD.A. Winter, Biomechanics and Motor Control of Human Movement, 2nd ed. John Wilrol of Human Movement, 2nd ed. John Wiley & Sons, NY, 1990. ey & Sons, NY, 1990.

M. Nordin & V.H. Frankel, Basic BiomechanM. Nordin & V.H. Frankel, Basic Biomechanics of the Musculoskeletal System, 2ne ed., ics of the Musculoskeletal System, 2ne ed., Lea & Febiger, London, 1989.Lea & Febiger, London, 1989.

Y.C. Fung, Biomechanics: Mechanical PropY.C. Fung, Biomechanics: Mechanical Properties of Living Tissues, 2nd ed., Speinger-erties of Living Tissues, 2nd ed., Speinger-Verlag, NY, 1993.Verlag, NY, 1993.