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Biomechanics of Skeletal Muscle

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Biomechanics of Skeletal Muscle BiomechanicsBiomechanics ofof SkeletalSkeletal MuscleMuscle www.fisiokinesiterapia.biz ContentsContents I.I. CompositionComposition && structurestructure ofof skeletalskeletal musclemuscle II.II. MechanicsMechanics ofof MuscleMuscle ContractionContraction III.III. ForceForce productionproduction inin musclemuscle IV.IV. MuscleMuscle remodelingremodeling V.V. SummarySummary 2 MuscleMuscle types:types: –– cardiaccardiac muscle:muscle: composescomposes thethe heartheart –– smoothsmooth muscle:muscle: lineslines hollowhollow internalinternal organsorgans –– skeletalskeletal (striated(striated oror voluntary)voluntary) muscle:muscle: attachedattached toto skeletonskeleton viavia tendontendon && movementmovement SkeletalSkeletal musclemuscle 4040--45%45% ofof bodybody weightweight –– >> 430430 musclesmuscles –– ~~ 8080 pairspairs produceproduce vigorousvigorous movementmovement DynamicDynamic && staticstatic workwork –– Dynamic:Dynamic: locomotionlocomotion && positioningpositioning ofof segmentssegments –– Static:Static: maintainsmaintains bodybody postureposture 3 I.I. CompositionComposition && structurestructure ofof skeletalskeletal musclemuscle Structure & organization • Muscle fiber: long cylindrical multi-nuclei cell 10-100 μm φ fiber →endomysium → fascicles → perimysium → epimysium (fascia) • Collagen fibers in perimysium & epimysium are continuous with those in tendons • {thin filament (actin 5nm φ) + thick filament (myosin 15 nm φ )} → myofibrils (contractile elements, 1μm φ) →muscle fiber 4 5 6 BandsBands ofof myofibrilsmyofibrils A band H I band A bands: thick filaments in central of sarcomere Z line: short elements that links thin filaments I bands: thin filaments not overlap with thick filaments H zone: gap between ends of thin filaments in center of A band M line: transverse & M Z Z longitudinally oriented linking proteins for sarcomere adjacent thick filaments 7 SarcoplasmicSarcoplasmic reticulumreticulum network of tubules & sacs; parallel to myofibrils enlarged & fused at junction between A & I bands: transverse sacs (terminal cisternae) Triad {terminal cisternae, transverse tubule} T system: duct for fluids & propogation of electrical stimulus for contraction (action potential) Sarcoplasmic reticulum store calcium 8 MolecularMolecular compositioncomposition ofof myofibrilmyofibril Myosin composed of individual molecules each has a globular head and tail Cross-bridge: actin & myosin overlap (A band) Actin has double helix; two strands of beads spiraling around each other troponin & tropomysin regulate making and breaking contact between actin & myosin 9 MolecularMolecular basisbasis ofof musclemuscle contractioncontraction SlidingSliding filamentfilament theory:theory: relativerelative movementmovement ofof actinactin && myosinmyosin filamentsfilaments yieldsyields activeactive sarcomeresarcomere shorteningshortening MyosinMyosin headsheads oror crosscross--bridgesbridges generategenerate contractioncontraction forceforce SlidingSliding ofof actinactin filamentsfilaments towardtoward centercenter ofof sarcomeresarcomere:: decreasedecrease inin II bandband andand decreasedecrease inin HH zonezone asas ZZ lineslines movemove closercloser 10 MotorMotor unitunit 11 12 ATP ATP 13 HistologyHistology ofof musclemuscle Type IIA Type IIB Type I 14 Eye muscle (Rectus lateralis); Myofibrillar ATPase stain, PH 4.3 MuscleMuscle DifferentiationDifferentiation (types(types ofof fibers)fibers) I (slow-twitch IIA (fast-twitch IIB fast-twitch oxidative) oxidative glycolytic glycolytic) Contraction speed Slow fast fast Myosin-ATPase activity Low High High Primary source of ATP Oxidative Oxidative Anaerobic glycolysis production phosphorylation phosphorylation Glycolytic enzyme Low Intermediate High activity No. of mitochondria Many Many Few Capillaries Many Many Few Myoglobin contents High High Low Muscle Color Red Red White Glycogen content Low Intermediate High Fiber diameter small Intermediate Large Rate of fatigue slow Intermediate Fast 15 FunctionalFunctional arrangementarrangement ofof musclemuscle α pinnated angle of muscle 16 TheThe MusculotendinousMusculotendinous UnitUnit Tendon- spring-like elastic component in series with contractile component F (proteins) Parallel elastic component x (epimysium, perimysium, endomysium, sarcolemma) PEC: parallel elastic component CC: contractile component SEC: series elastic component 17 II.II. MechanicsMechanics ofof MuscleMuscle ContractionContraction NeuralNeural stimulationstimulation –– impulseimpulse MechanicalMechanical responseresponse ofof aa motormotor unitunit -- twitchtwitch t t − F(t) = F e T 0 T T: twitch or contraction time, time for tension to reach maximum F0: constant of a given motor unit Averaged T values Tricep brachii 44.5 ms Soleus 74.0 ms Biceps brachii 52.0 ms Medial Gastrocnemius 79.0 ms Tibialis anterior 58.0 ms 18 SummationSummation andand tetanictetanic contractioncontraction (ms) 19 GenerationGeneration ofof musclemuscle tetanustetanus 100Hz 10 Hz Note: muscle is controlled by frequency modulation from neural input very important in functional electrical stimulation 20 WaveWave summationsummation && tetanizationtetanization Critical frequency 21 MotorMotor unitunit recruitmentrecruitment All-or-nothing event 2 ways to increase tension: - Stimulation rate - Recruitment of more motor unit Size principle Smallest m.u. recruited first Largest m.u. last 22 III.III. ForceForce productionproduction inin musclemuscle ForceForce ––lengthlength characteristicscharacteristics ForceForce –– velocityvelocity characteristicscharacteristics MuscleMuscle ModelingModeling NeuromuscularNeuromuscular systemsystem dynamicsdynamics 23 33--11 ForceForce--lengthlength curvecurve ofof contractilecontractile componentcomponent RestingResting 2.02.0--2.252.25 umum max.max. no.no. ofof crosscross bridges;bridges; max.max. tensiontension 2.252.25--3.63.6 umum no.no. ofof crosscross bridgebridge ↓↓ << 1.651.65 umum overlapoverlap ofof actinactin no.no. ofof crosscross bridgebridge ↓↓ 24 InfluenceInfluence ofof parallelparallel elasticelastic componentcomponent Fc Ft Ft Fp Fp l0 Fc l0 25 Note: Fc is under voluntary control & Fp is always present OverallOverall forceforce--lengthlength characteristicscharacteristics ofof aa musclemuscle 26 SeriesSeries ElasticElastic ComponentComponent TendonTendon && otherother seriesseries tissuetissue LengthenLengthen slightlyslightly inin isometricisometric contractioncontraction SeriesSeries componentcomponent cancan storestore energyenergy whenwhen 27 stretchedstretched priorprior toto anan explosiveexplosive shorteningshortening QuickQuick--releaserelease forfor determiningdetermining elasticelastic constantconstant ofof seriesseries component component Muscle is stimulated to F build tension Release mechanism is activated Measure instantaneous shortening x while force is kept constant Contractile element length kept constant during quick release F K SC = x 28 InIn vivovivo forceforce--lengthlength measurementmeasurement HumanHuman inin vivovivo experimentsexperiments (MVC)(MVC) Challenges:Challenges: –– ImpossibleImpossible toto generategenerate aa max.max. voluntaryvoluntary contractioncontraction forfor aa singlesingle agonistagonist withoutwithout activatingactivating remainingremaining agonistagonist –– OnlyOnly momentmoment && angleangle areare measurable.measurable. MomentMoment dependsdepends onon musclemuscle forceforce andand momentmoment arm.arm. 29 33--22 ForceForce--VelocityVelocity CharacteristicsCharacteristics ConcentricConcentric contractioncontraction –– MuscleMuscle contractscontracts andand shortening,shortening, positivepositive workwork waswas donedone onon externalexternal loadload byby musclemuscle –– TensionTension inin aa musclemuscle decreasesdecreases asas itit shortensshortens EccentricEccentric contractioncontraction –– MuscleMuscle contractscontracts andand lengthening,lengthening, externalexternal loadload doesdoes workwork onon musclemuscle oror negativenegative workwork donedone byby muscle.muscle. –– TensionTension inin aa musclemuscle increasesincreases asas itit lengthenslengthens byby externalexternal loadload 30 ForceForce--velocityvelocity characteristicscharacteristics ofof skeletalskeletal musclemuscle (Hill(Hill model)model) eccentric concentric F (F + a)b F = 0 − a v + b F0 = max. isometric tension a = coefficient of shortening heat v0 = max. velocity when F = 0 a v b = 0 F0 v Increased tensions in eccentric due to: • Cross bridge breaking force > holding force at isometric length 31 • High tendon force to overcome internal damping friction LengthLength andand velocityvelocity versusversus ForceForce Note: maximum contraction condition; normal contractions are fraction 32 of the maximum force EquilibriumEquilibrium ofof loadload andand musclemuscle forceforce Muscle force is function of length, velocity and activation The load determines Nonlinear spring activation and length of muscle by the equilibrium linear spring condition Load: spring-like, inertial, viscous damper 33 33--33 MuscleMuscle ModelingModeling Elements of Hill model other than contractile element 34 • Derive equations of motion • Estimated parameters based on Experimental data & model Simulation (least squares) . Numerical simulation 35 33--44 NeuromuscularNeuromuscular systemsystem dynamicsdynamics Muscle force F = F0 * Act * FLT * FFV 0 LT FV Max torque due to each muscle T = r(θ) * F(L(θ), V, A) 20 F0= F0(pinnated angle, PCSA, fiber type) 15 brachialis biceps, long 10 biceps, short 5 brachioradialis
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