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Gait & Posture 23 (2006) 383–390 Muscle mechanical work and elastic energy utilization during walking and running near the preferred gait transition speed Kotaro Sasaki, Richard R. Neptune * Department of Mechanical Engineering,
  Muscle mechanical work and elastic energy utilization during walkingand running near the preferred gait transition speed Kotaro Sasaki, Richard R. Neptune*  Department of Mechanical Engineering, The University of Texas at Austin, 1 University Station C2200, Austin, TX 78712, USA Received 17 January 2005; received in revised form 18 May 2005; accepted 23 May 2005 Abstract Mechanical and metabolic energy conservation is considered to be a defining characteristic in many common motor tasks. During humangait, the storage and return of elastic energy in compliant structures is an important energy saving mechanism that may reduce the necessarymuscle fiber work and be an important determinant of the preferred gait mode (i.e., walk or run) at a given speed. In the present study, themechanical work done by individual muscle fibers and series-elastic elements (SEE) was quantified using a musculoskeletal model andforward dynamical simulations that emulated a group of young healthy adults walking and running above and below the preferred walk-runtransitionspeed(PTS),andpotentialadvantagesassociatedwiththemusclefiber-SEEinteractionsduringthesegaitmodesateachspeedwereassessed. The simulations revealed that: (1) running below the PTS required more muscle fiber work than walking, and inversely, walkingabovethe PTS requiredmore muscle fiberworkthan running,and (2)SEE utilization inrunning was greater abovethan belowthe PTS. Theseresults support previous suggestions that muscle mechanical energy expenditure is an important determinant for the preferred gait mode at agiven speed. # 2005 Elsevier B.V. All rights reserved. Keywords:  Muscle work; Musculoskeletal model; Forward dynamic simulation; Preferred gait mode 1. Introduction Muscle mechanical energy expenditure is an importantquantity to analyze human locomotion since it reflects theneuromotor strategies used by the nervous system and isdirectly related to the efficiency of the task. Energyconservation is a defining characteristic in many commonmotor tasks and generally leads to a preferred mode inperformingagivenlocomotortask [1].Previousstudieshavesuggestedthatthetwoprimaryenergysavingmechanismsinwalking are the passive exchange of potential and kineticenergy (e.g. [2]) and elastic energy utilization (e.g. [3]). Assuming that walking can be modeled as an inverted-pendulum, the maximum theoretical efficiency of theenergetic exchange between kinetic and potential energy(i.e., energy recovery) is only as high as 65% and variesdepending on walking speed [4] and stride frequency [5]. In addition,recentsimulationanalyses using amulti-segmentalmusculoskeletalmodel foundthat considerable musclework is needed to produce the inverted pendulum-like motion [6].Thus, the passive energy exchange mechanism in normalwalking may not be as significant as that observed in simpleinverted-pendulum models.Elastic energy utilization that stores and returnsmechanical energy is considered to be an importantmetabolic energy saving mechanism, especially in running(e.g. [3,7]). Gravitational potential and kinetic energy havethe potential to be stored as elastic energy in compliantconnectivetissue and tendinous structures,and subsequentlyreleased to do positive work at a later point in the gait cycle.The Achilles tendon is one of the most widely studiedstructures, and previous studies have estimated that nearly50% of the total mechanical energy of the body is stored inthe tendon and arch of the foot during the stance phase inrunning [8,9]. Other tendons that are rapidly stretched during the loading response (e.g., knee extensor tendons) arealso assumed to play an important role [10].Tendons not only store and return elastic energy, but alsoact to reduce the corresponding muscle’s fiber shortening & Posture 23 (2006) 383–390* Corresponding author. Tel.: +1 512 471 0848; fax: +1 512 471 8727. E-mail address: (R.R. Neptune).0966-6362/$ – see front matter # 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.gaitpost.2005.05.002  velocity to allow the fibers to operate at a more favorablecontractilestate.Thereductioninfibervelocityincreasesthecontraction efficiency and reduces the correspondingmetabolic cost [10]. Such reductions in fiber velocitieshave been observed in the distal extensor muscles in vivo inhopping and running animals [11,12] and humans duringwalking [13]. With the reduction of metabolic cost, elastic energy storage and return has been suggested as animportant determinant for the preferred gait mode (i.e.,walking or running) at a given speed [14,15]. Indeed, the metabolic cost of running is lower than walking at speedsabove the preferred walk-run transition speed (PTS), andinversely, running becomes more costly than walking atspeeds below the PTS (e.g. [16,17]). However, no study hasquantified the relative fiber to tendon work ratios in walkingandrunningandwhetherthe increaseinmetaboliccostistheresult of increased muscle fiber work.Previousstudieshavemeasuredmuscleforceandlengthinvivo in animals [11,12] and humans (e.g. [18,19]). Methodologically, force and length measurement in vivo isextremely difficult and limited to a few local muscles, eitherbysurgicallyimplantingforceandlengthsensorsintomuscles[11,12] or using complex imaging techniques to obtain fiberlengths and estimating the corresponding musculotendonforces(e.g.[20–22]).Earlierstudieshaveusedtraditionalgaitanalysis techniques to compute changes in segmentalmechanical energy (e.g. [23–25]) as an indirect approachforestimatingfiberandtendonwork.However,thesemethodscannot account for co-contractions of antagonistic musclegroups and separate individual muscle fiber and tendoncontributions to mechanical energy of the system [26].In contrast, a detailed musculoskeletal model withindividual musculotendon actuators including contractile(CE) and series elastic (SEE) elements and forwarddynamical simulations can be used to estimate thecontributions of muscle fibers and elastic structures to themechanical energetics of a given motor task  [6,27]. Theoverall goal of this study was to use simulations of walkingand running at speeds above and below the PTS to examinemuscle fiber mechanical work and SEE utilization. Ourspecific objectives were to assess the hypotheses that: (1)total muscle fiber work is higher in walking than runningabove the PTS, and inversely, fiber work is higher in runningthan walking below the PTS, and (2) SEE utilization duringstance isgreaterinrunningabovethan belowthe PTS. Theseresults will provide insight into the role muscle mechanicalenergy expenditure plays in determining the preferred gaitmode at a given speed. 2. Methods 2.1. Musculoskeletal model A sagittal-plane musculoskeletalmodelwith ninedegreesof freedom (e.g. [28]) was used to generate forwarddynamical simulations emulating young healthy adultswalking and running above and below the PTS. Themusculoskeletal model was developed using SIMM (Mus-culoGraphics Inc., Evanston, IL) and a forward dynamicalsimulation was generated using Dynamics Pipeline (Muscu-loGraphics Inc., Evanston, IL). The model consisted of atrunk (head, arms, torso and pelvis), both legs (femur, tibia,patella and foot per leg) and fifteen Hill-type musculotendonactuators per leg representing the major lower-extremitymuscle groups. Each actuator consisted of a contractileelement (CE) that represents the active force generatingproperties of the muscle fibers governed by force-activation-length-velocity relationships, a non-linear elastic elementparallel to the CE representing the passive properties of themusclefibers(PEE),andanon-linearelasticelementinserieswiththePEE andCEthatrepresentsthepassivepropertiesof thetendonandaponeurosis(SEE)[29].TheSEEforce-length relationship was scaled by CE maximum isometric forceandSEE slack length [29]. These muscles were combined intonine functional groups based on anatomical classification,withmuscleswithineachgroupreceivingthesameexcitationsignal. The groups were defined as: GMAX (gluteusmaximus, adductor magnus), IL (iliacus, psoas), HAM(biceps femoris long head, medial hamstrings), VAS (threevasti muscles), RF (rectus femoris), BFsh (biceps femorisshort head), TA (tibialis anterior), GAS (medial and lateralgastrocnemius) and SOL (soleus). Each muscle’s excitationwas defined using surface EMG-based patterns (see  Dataacquisition and processing  below). Since no surface EMGdatawereavailableforILandBFsh,blockexcitationpatternswere used. The muscle excitation-activation dynamics wasdescribed using a first-order differential equation [30] withactivation and deactivation time constants of 5 and 10 ms,respectively. These relatively short time constants werechosenbecausetheEMG-basedpatternswerealreadyheavilylow-pass filtered. Passive torques representing the ligamentsand other connective tissues were applied to each joint [31].The contact between the foot and ground was modeled usingthirty visco-elastic elements attached to each foot [32]. 2.2. Dynamic optimization Well-coordinated walking and running simulations overthe gait cycle (i.e., from right foot-strike to right foot-strike)were generated using dynamic optimization to fine-tune theonset, duration and magnitude of the muscle excitationpatterns. A simulated annealing algorithm [33] was used tominimize the difference between the simulation andexperimentally measured group-averaged kinematics andground reaction forces (GRFs) (e.g. [34]; see  Dataacquisition and processing  below). 2.3. Muscle fiber and SEE mechanical work  Muscle fiber (CE) and SEE power were computedindependently as the product of the corresponding force and K. Sasaki, R.R. Neptune/Gait & Posture 23 (2006) 383–390 384  velocity at each instant in time over the gait cycle.Subsequently, positive (concentric), negative (eccentric)and total mechanical work done by the individual musclefibers and SEEs during the stance and swing phases wereobtained by time-integration of the corresponding powerduring each phase of the gait cycle asMechanical work  ¼ Z   t  2 t  1 P d t   (1)where  P  is the positive or negative power in the fiber andSEE and  t  1  and  t  2  define the duration of positive or negativepower within the stance and swing phases. The total fiberwork was obtained by summing the positive and absolutevalue of the negative fiber work over the gait cycle across allmuscles. The net fiber work was computed by summing thepositiveandnegativefiberworkacrossallmuscles.SincetheSEEs are perfectly elastic, the negative SEE work (energystored) equals the positive SEE work (energy released).Therefore, only the positive SEE work is presented.SEE utilization was defined as the ratio of the positiveSEE to positive fiber work during each muscle’s activeregionduringthestancephase(i.e.,whenthemuscle’sactivestate exceeded 3% of its maximum activation) asSEE utilization ¼ 100   positive SEE work positive fiber work    (2)To assess the total elasticity utilization of all muscles,the same ratio was computed for the total positive SEE andtotal positive fiber work for all muscles during the stancephase. 2.4. Experimental data collection Body segment kinematic, GRF and EMG data duringwalking and running above and below the PTS werecollected from 10 healthy subjects (5 males and 5 females:age 29.6  6.1 years old, height 169.7  10.9 cm, bodymass 65.6  10.7 kg). The two speeds examined were 80%and 120% of the subject’s PTS, which correspond to speedswhere the difference in metabolic cost between walking andrunning is clearly observed (e.g. [17]). The PTS wasdetermined using a step protocol [35]. Informed consentapproved by the Cleveland Clinic Foundation and TheUniversity of Texas at Austin was obtained from eachsubject before participating in the experiments. All datawere collected at the Cleveland Clinic Foundation inCleveland, OH. 2.5. Data acquisition and processing The kinematic, GRF and EMG data used in the dynamicoptimization were sampled at 120, 480 and 1200 Hz,respectively, for 15 s near the end of a randomly assignedone-minute trial of walking or running on a split-belttreadmill with embedded force plates (Tecmachine,Andre´zieux-Bouthe´on, France). The kinematic data werecaptured using a motion capture system (Motion AnalysisCorp, Santa Rosa, CA) with a modified Helen Hayes markerset (one-inch diameter reflective markers). The EMG datawere collected using the guidelines provided by Perotto [36]from the gluteus maximus, rectus femoris, vastus medialis,biceps femoris long head, medial gastrocnemius, soleus andtibialis anterior of the right leg. Disposable surface bi-polarEMG electrodes were used (Noraxon, Scottsdale, AZ; 1 cmdiameter, 2 cm inter-electrode distance). All data weredigitally filtered using fourth-order zero-lag Butterworthfilters. The cut-off frequencies for the kinematic and GRFdatawere6and20 Hz,respectively(e.g.[37,38]).EMG datawere processed using a band-pass filter (20–400 Hz), fullrectification and low-pass filter (10 Hz) (e.g. [39]). Theresultant EMG linear envelopes were then normalized toeachmuscle’smaximumvalueduringthegaitcycle.Alldatawere time-normalized to a full gait cycle, and were averagedwithin each subject and then across subjects to obtain agroup average. 3. Results The group-average PTS was 1.96  0.17 m/s, yieldingsimulations of walking and running at 1.6 and 2.4 m/s thatcorresponded to speeds of 80% and 120% of the PTS,respectively. Hereinafter, walking and running at the slowand fast speeds will be labeled as W80, R80, W120 andR120, respectively. The corresponding walking and runningsimulations emulated the experimental data almost alwayswithin   2 S.D. of the group-average (Fig. 1) using theoptimized EMG-based muscle excitation patterns. 3.1. Comparison between W80 and R80 The total fiber work done by the muscles in running atthe slow speed was 25 J greater than in walking (Table 1:Fiber Total, W80 < R80). The difference was primarilydue to an increase in VAS negative work in stance dur-ing running (  22 J) (Fig. 2: VAS, Fiber-Negative,W80 < R80). The total positive work done by all SEEswashigherinrunningthaninwalking(Table1:PositiveSEEWork Total), with the difference due primarily to the ankleplantar flexors (SOL, GAS) and VAS (Fig. 2: SOL, GAS,VAS - SEE-Positive). Overall, the SEE utilization wasgreater in running than in walking due primarily to thegreater SEE work in R80 (Table 1: SEE Utilization,W80 < R80). 3.2. Comparison between W120 and R120 The total muscle fiber work was slightly lower in runningcompared to walking (4 J, Table 1: Fiber Total,W120 > R120). In running, GAS positive work (  3 J)and VAS positive and negative work (  10 and 14 J, K. Sasaki, R.R. Neptune/Gait & Posture 23 (2006) 383–390  385  respectively) increased during stance (Fig. 2: GAS, VAS –Fiber-Positive, Fiber-Negative, W120 < R120), while SOLand HAM positive work output decreased (  5 and 8 J,respectively) (Fig. 2: SOL, HAM – Fiber-Positive,W120 > R120). Consequently, fiber negative work increased while overall positive work remained unchangedduringstance (Table1:FiberStance–NegativeandPositive,compare W120 and R120).In swing, marked decreases inIL(  15 J), and to a lesser degreein GMAX and HAM, positivework was observed in running (Fig. 3: IL, GMAX, HAM – Fiber-Positive, W120 > R120). Positive SEE work duringstance increased 17 J in running (Table 1: SEE Stance),primarily due to increased plantar flexor SEE work (Fig. 2:SOL, GAS – SEE-Positive, W120 < R120). Overall, theSEEutilizationwasgreaterinrunningthaninwalkingduetothe increased positive SEE work (Table 1: SEE Utilization,W120 < R120). K. Sasaki, R.R. Neptune/Gait & Posture 23 (2006) 383–390 386Fig. 1. Hip, knee and ankle joint angles (units:  8 ) and vertical (vGRF) andhorizontal (hGRF) ground reaction forces (units: normalized to bodyweight) in walking (W80) and running (R80) simulations (dashed line)and experimental data (solid line, average  2 S.D.). Positive anglesindicate flexion, extension and dorsiflexion in the hip, knee and ankle joints,respectively.Similartrackingresultswereobtainedforthe120%PTSwalking and running conditions.Table 1Mechanical work (units: J) done by all muscle fibers and SEEs duringstance,swingandoverthegaitcyclein walking(W)andrunning(R)at80%and 120% PTSW80 R80 W120 R120Fiber stancePositive 58 65 67 67Negative 29 52 34 51Fiber swingPositive 28 22 44 27Negative 13 14 30 26Fiber total 128 153 175 171Fiber net 44 21 47 17SEE stancePositive 23 34 31 48SEE swingPositive 2 2 7 6Positive SEE work total 25 36 38 54SEE utilization (%) 40 52 46 72SEE Utilization is the percent ratio of positive SEE work to positive fiberwork during stance.Fig. 2. Mechanical work done by individual muscle fibers and SEEs during stance in walking (W) and running (R) at 80% and 120% PTS.
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