Supplementary,Material, MTJ,Tracking,Methods, WeestimatedAT,muscle,andMTUlengthchangesusingpreviouslypublishedMTJtrackingmethods (Hoffrén et al., 212; Lichtwark, 25; Lichtwark and Wilson, 26). The ultrasound transducer was placedoverthemglatmtj,thensecurelyaffixedtotheshankusinghypafix retentiontapeandace bandages(fig.%1b).toapproximateatorigin,thecharacteristic Y ofthemtjwasmanuallytrackedin eachultrasoundimage.acalcaneusmotioncapturemarkerapproximatedatinsertion.acustom3ld printedfixtureattachedtothetransducerallowedtrackingofitspositionandorientationwithrespect to the lab reference frame. The ultrasound field of view was assumed to be perpendicular to the longitudinalplaneofthetransducer.atlengthwasestimatedasthestraightlline3ddistancefromthe calcaneustothemtj.mgmusclelengthchangewasthenapproximatedasthedifferencebetweenmtu lengthchange(fromaregressionequationbasedonankleandkneeangles,hawkinsandhull,199)and ATlengthchange. MF,Tracking,Methods, We estimated AT, muscle, and MTU length changes using previously published MF tracking methods (CroninandLichtwark,213;FarrisandSawicki,212;Hoangetal.,27;Hoffrénetal.,212;Masaki Ishikawa et al., 25; M. Ishikawa et al., 25; Lichtwark et al., 27; Lichtwark and Wilson, 26; Sakumaetal.,211).ThetransducerwasplacedovertheMGmusclebelly,thensecurelyaffixedtothe shankusinghypafix retentiontapeandacebandages(fig.%1c).anautomatedaffineflowalgorithm was used to estimate timelvarying length of an individual MG muscle fascicle (Farris and Lichtwark, 216). Manual corrections of the fascicle endpoints were made for frames in which the automated calculation did not track the fascicle well, based on visual inspection of a trained researcher. If the fascicle extended beyond the field of view, the endpoint locations were estimated via linear extrapolation(i.e.,byextendingthelinesofthefascicleandaponeurosesbeyondthefieldofviewand findingtheintersectionpoint).pennationanglewascalculatedforeachframeastheanglebetweenthe superficialfasciaandthemusclefascicle.changesinfasciclelengthwerethencorrectedforpennation angletoapproximatechangesinmgmusclelengthalongthemuscle slineofaction.atlengthchange wasthenestimatedasthedifferencebetweenmtulengthchange(fromaregressionequationbasedon ankleandkneeangles,hawkinsandhull,199),andmglengthchange. EMG,Data,Collection,&,Analysis, EMGdatawerecollectedtosupplementprimaryoutcomemeasures,andusedtoconfirmthatmuscle activity was consistent with loading expectations for each task. Surface EMG sensors (Delsys Trigno) were placed unilaterally on the medial gastrocnemius (MG), lateral gastrocnemius (LG), soleus (SOL), andtibialisanterior(ta).emgsignalsweredemeaned,highlpassfilteredat15hz,rectified,andlowl passfilteredat1hz,andthennormalizedbasedonthemaximummuscleactivationmagnitudethat occurredduringthethreerecordedtasks(potvinandbrown,24;zeliketal.,215).theresultingemg envelopesfromeachcyclewerenormalizedto1datapoints(representingto1%ofthecycle). Foreachtask,onasubjectLspecificbasis,EMGenvelopeswereaveragedoverfivesequentialcycles(Fig.%
S3b).ForsubjectsinwhichMTJandMFtrackingtrialswereperformedseparately,EMGisonlyreported forthemftrackingtrials. Explanation,of,Model,Expectations,for,Each,Task, Below we summarize the expected behaviors of a common MTU model: a passive linear extension spring(representingtheatandassociatedaponeurosis)actinginserieswithanactuator(representing themuscle).inthisstudythemodelrepresentsthemgmtu,whichspansdistallyfromthecalcaneus (heel),posteriorlyacrosstheankleandkneejoints,andthenconnectsproximallytothethighsegment. Sinceexperimentaltaskswereperformedslowly(quasiLstatically)dynamiceffectsduetoinertiawere ignoredforthis simplemodel.itwasassumedthattheextensionspringremainedlinearanddidnot becomeslack(seeextendeddiscussionbelowonslacklength). The restricted joint calf contraction task is akin to fixing each end of the MTU model, then ramping up/downtheactuatorforce.asforceincreased,weexpectedthattheactuatorwouldshortenandthe series spring would lengthen by an equal magnitude (Fig.% 3a, top% row). Experimentally this task was achievedbyaffixingarigidbarabovethekneeandthigh.allsubjectsshowedactivationofthemg,lg, andsolthatwasinaccordancewithmuscleforcesrampingupandthendown(i.e.,theloadingpattern assumedinordertoderivemodelexpectations).allsubjects,exceptone(fig.%s3b,%column%1),showed negligible TA activation, indicating that antagonistic muscle contraction was not a significant confounding factor. Subjects also exhibited minimal change in ankle angle (Fig.% S3a,% column% 1), as expectedduetotherigidbar.however,duetosofttissuedeformationagainsttherigidbar,itwasnot possibletocompletelyrestrictjointmotion(bryantetal.,28;magnussonetal.,21).nonetheless, thesimplifiedmodelandexperimenttaskwerequalitativelyconsistent,eachcapturingthesamemain muscleandtendonlengthchangebehaviors. TheankleDF/PFwithfootinairtaskwasmodeledbyfixingtheMTUattheproximalend,hanginga smallmassatthedistalend,thenslowlydrivingtheactuatortoliftandlowerthemass.withthefootin theair,relativelylowatforcewasexpected,i.e.,onlyforceneededtocounteracttorqueduetothe massofthefootabouttheanklejointandtoovercomeanypassiveresistancefromantagonisticmtus. Themassofthebiologicalfootisabout1kgandthecenterofmassofthefootisabout6mmanterior totheankleinneutralposition.assumingananthropometricatmomentarmofabout5mm(honert andzelik,216;mcculloughetal.,211),<<1nmoftorqueisneededtosupportthemassofthefoot. Passivejointmomentshavebeenestimatedtoberelativelysmallacrossarangeofankleangles.For example,passiveanklemomentsareexpectedtobe<5nmatankleangles<9,and<1nmforthe maximumdorsiflexionanglesreachedduringthistask(basedonsilderetal.,27).againassumingan anthropometric AT moment arm, AT forces would typically be <1 N, and at most be about 2 N (whichisonlyabout7%oftheforceexperiencedbytheatduringwalkingatmoderatespeed,bogeyet al.,25).consistentwiththeexpectationoflowloading,emgfromthemgandotherplantarflexors wasrelativelylowthroughouttheentiredf/pfanklerangeofmotion(fig.%s3,%column%2).also,theta exhibited activity during dorsiflexion beyond neutral, but was inactive during plantarflexion beyond neutral(fig.%s3b,%column%1).additionalforcesduetojointfrictionwereassumedtobenegligible,since experimentsinvolvedyoung,healthysubjects.atstiffnessvaluesinliteratureareontheorderof13l 47 N/mm (Kubo et al., 27, p. 2; Lichtwark, 25; Maganaris and Paul, 22; Magnusson et al., 21;Muraokaetal.,25).Duetotheserelativelylowforcesactingonarelativelystifftendon,we
expectedatlengthchangetobesmall(i.e.,lessthanafewmm)throughoutthemovementcycleofthis DF/PFtask(Fig.%3a,%middle%row). HeelraisesweremodeledbyfixingtheMTUatoneend,withthedistalendfreetomoveastheactuator shortened/lengthened under relatively large force. We assumed that there was low loading on the actuatorandseriesspringatthebeginningofthecycle,thenforcesincreased.onemightintuitthatthe MTUforceprofileovertheheelraisecyclewouldincreasemonotonically(asoneliftsupfromtheflat footedposture),thenplateauatsomehigherforcewhiletheheelwasofftheground,thendecrease forceasapersonreturnedbacktofootlflat.theatforceprofileisactuallysomewhatmorecomplex:it isdoublelpeakedduetothedynamicallylchangingmomentarmfromtheanklejointtothecenterof pressure(cop),thepointofapplicationofthegroundreactionforce(grf).beginningfromfootlflat,as thecalfmusclesincreasetheirforceandlifttheheelsofftheground,thecopshiftsanteriorlytowards the distal end of the foot, increasing the ankleltolcop moment arm and causing a peak in AT force. Then,asthefootrotatesaboutthemetatarsophalangealjoints,theankleshiftsanteriorly,decreasing the ankleltolcop moment arm, and reducing the AT force. As the heel lowers, the cycle is reversed creatingasecondatforcepeak.weconfirmedthisdoublelpeakedforceprofileexperimentallyusing motionandgroundreactionforcedata(fig.%s1).atmomentarmvariesslightlywithankleangleand muscle activation level, but for the ~3 of ankle plantarflexion during the heel raise task, the AT momentarmisexpectedtoincreasebylessthan1mm(maganarisandpaul,2;mcculloughetal., 211).Evenwitha1mmincreaseinmomentarm,theATforceatpeakplantarflexion(~5%cycle) wouldonlybeabout15%(~11n)lessthanthatestimatedwithaconstantmomentarm.basedonat stiffness values in literature (Kubo et al., 27, p. 2; Lichtwark, 25; Maganaris and Paul, 22; Magnusson et al., 21; Muraoka et al., 25), this reduction in tendon force would reduce tendon length by <1 mm. Regardless of the precise force profile, the key model takeaway is that we would expectthespringtolengthenproportionallywithincreasingmtuforce(fig.%3a,%bottom%row).forthe heelraisetask,emgresultsconfirmedthatallsubjectsincreasedactivationofthemg,lg,andsolas the heel began lifting off the ground (Fig.% S3b,% column% 3), consistent with the model loading expectationssummarizedabove. % PostBHoc,Corrections,to,AT,Length,Change,Estimate, Formostsubjects,astheyplantarflexedtheiranklebeyondneutralintheankleDF/PFtaskweobserved aroughlylineardecreaseinatlength(fig.%3,%middle%row).itwasinitiallytemptingtousethisdf/pftask toderiveanatlengthchangecorrectionfactorbasedonankleangletoremovethistrend;however, thisapproachmaybeillladviseduntilthesourceoferrorisbetterunderstood;forreasonssummarized below. Numerically, we could approximate a proportional relationship between ankle angle and AT length change (Fig.% 4,% left% column) during this low force task, and treat it as a correction factor. We couldapplythiscorrectionfactor,afunctionofankleangle,bysubtractingitfromtheatestimates.asa result, AT length changes would become small throughout the entire DF/PF cycle (qualitatively consistentwithmodelexpectations).thecorrectionfactorderivedfromthelowforcetaskcouldalsobe usedtoadjustatlengthchangeestimatesfromtheheelraisetask(fig.%4,%right%column).thiswould shift the AT behavior towards lengthening, which would again make the experimental results more consistent with model expectations. However, this type of postlhoc adjustment to AT length change would also necessitate adjusting our estimate of either the muscle or MTU length change to compensate, in order to ensure that muscle length change plus tendon length change was still
equivalenttooverallmtulengthchange.presentlyitisnotclearif,orjustifiedwhy,eitherthemuscleor MTUestimateshouldbeadjustedposthoc.Therefore,beforeapplyinganysuchcorrectionfactorswe advisethatitwouldbeprudenttofirstdiscernwhythisatlengthchangevs.ankleangletrendexistsat all.weanticipatethatthisdeeperunderstandingwillinformourconceptualmodelofmtudynamics,or motivatespecificrefinementsintheempiricalmethodsusedtoestimateatlengthchange. Extended,Discussion,of,Slack,Length,&,StraightBLine,Tendon,Assumption, SlackeningoftheMGand/orAT(Hugetal.,213,Hoangetal.,27,Muraokaetal.22)havebeen estimatedtooccuratabout2l4 ofplantarflexionbeyondneutral(i.e.,at5l7 infig.%4),whenthe ankle is passively rotated. Thus, AT slackening may degrade the accuracy of tendon length estimates during the DF/PF task, a low force ankle rotation task, when ankle angle is less than about 5L7 ; highlightingtheimportanceofconsideringslacklengthforcertaintasks.however,slacklengthdoesnot seemtoexplainthesubstantialtendonshortening(~1mm)astheankleplantarflexedfrom9 to7 inthedf/pftask,norsimilarshorteningreportedinpriorliteratureonpassiveanklerotation(csapoet al., 213). Furthermore, slack length wouldnotseemtoexplain the shortening observed during heel raiseswhenthemgwasactivelycontracting(fig.%s3).regressionlbasedestimatesofoverallmtulength (Grieve, 1978; Hawkins and Hull, 199) are based on cadaver studies, assuming straightlline approximationsandthatmtulengthisonlyafunctionofjointangles(yuenandorendurff,26).prior studies(fukutanietal.,214;stosicandfinni,211),foundthatwhenusingalinearapproximation,the ATappearedtoshortenby3mmmorethanwhenusinganestimatethataccountedforcurvature(for 3 ofplantarflexionbeyondneutral).however,this3mmerrorwassmallcomparedtothe15mmof ATshorteningweobservedforasimilar3 ofplantarflexion(duringankledf/pf,fig.%3,%middle%row). Toapproximatetheeffectofcurvatureonourestimates,weaddedavirtualwaypoint5mmposterior totheanklejointcenterthatrotatedwiththefootsegment.wethenusedthecalcaneus,waypoint,and MTJpositionstocalculateapiecewisetendonlength.Usingthispiecewisetendonestimateaccounted for less than 4% of the total shortening for both the ankle DF/PF and heel raise task at peak plantarflexion,indicatingthat curvature alone does not appeartoexplainthemajorityofthetendon shortening. Potential confounds discussed above do not reflect a comprehensive list. Other potential estimationissueshavebeendescribedinpriorliterature(e.g.,croninandlichtwark,213;epsteinand Herzog,23;Herbertetal.,211;ZelikandFranz,217). Supplementary,Material,References, Bogey,R.A.,Perry,J.,Gitter,A.J.,25.AnEMGLtoLforceprocessingapproachfordeterminingankle muscleforcesduringnormalhumangait.ieeetrans.neuralsyst.rehabil.eng.13,32 31. https://doi.org/1.119/tnsre.25.851768 Bryant,A.L.,Clark,R.A.,Bartold,S.,Murphy,A.,Bennell,K.L.,Hohmann,E.,MarshallLGradisnik,S., Payne,C.,Crossley,K.M.,28.Effectsofestrogenonthemechanicalbehaviorofthehuman Achillestendoninvivo.J.Appl.Physiol.15,135 143. https://doi.org/1.1152/japplphysiol.1281.27 Cronin,N.J.,Lichtwark,G.,213.Theuseofultrasoundtostudymuscle tendonfunctioninhuman postureandlocomotion.gaitposture37,35 312. https://doi.org/1.116/j.gaitpost.212.7.24 Csapo,R.,Hodgson,J.,Kinugasa,R.,Edgerton,V.R.,Sinha,S.,213.Anklemorphologyamplifies calcaneusmovementrelativetotricepssuraemuscleshortening.j.appl.physiol.115,468 473. https://doi.org/1.1152/japplphysiol.395.213 Epstein,M.,Herzog,W.,23.Aspectsofskeletalmusclemodelling.Philos.Trans.R.Soc.BBiol.Sci.358, 1445 1452.https://doi.org/1.198/rstb.23.1344
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Figure,Captions, Fig.%S1.%Heel%raise%kinematics%and%kinetics.$(a)Ankle&angle&vs.&movement&cycle.&(b)Estimated)AT# force& vs.& movement& cycle.& AT& force& (F AT )" was" estimated" by" dividing" ankle" moment" (from" standard'inverse'dynamics)'by'at'moment'arm'about'the'ankleand$expressed$as$percentage$of$ body% weight% (%BW)." Depicted are interlsubject means and standard deviations (shaded regions). (c) Simplified) moment) balance) about) the) ankle) joint.) The) doublelpeaked& AT& force& profile( occurs( because( the( AT( has( a( roughly( constant( moment( arm( about( the( ankle( whereas( there% is% a% dynamicallylchanging' moment' arm' from' the' ankle' to' the' center' of' pressure' (the' point&of&application&of&the&ground&reaction&force,&f GRF ). Fig.%S2.%Subject=specific'results.AT#(thick#blue),#MG#muscle#(dashed#red)#and#MTU#(thin#black)# length'changes'vs.'movement#cycle.major&columns&are&tasks.&unshaded&columns&show&the&mtj& method'results'and'shaded'columns'show'the'mf'method'results.'the'top'row'represents'the' mean%and%standard%deviation%across%subjects.%remaining%rows%each%represent%subjectlspecific' average&results. Fig.%S3.%Kinematics%and%subject=specific%EMG.%(a)%Ankle(solidgreen)andknee(dashedgreen) jointanglesvs.movementcycle,averagedacrosseightsubjects.(b)medialgastrocnemius(mg, red),lateralgastrocnemius(lg,green),soleus(sol,blue),andtibialisanterior(ta,orange), muscleactivationvs.movementcycle.emgmagnitudesarereportedasapercentageofthe maximumactivationobservedduringthesethreetasks.eachcolumnisatask.eachrow representssubjectlspecificaverageresults.
(a) heel raises b) (c) ankle angle (deg) AT Force (%BW) 12 9 6 3 2 1 1 % cycle F AT F AT 1 F AT F GRF F GRF F GRF
Δlength (mm) restricted joint MTJ anke DF/PF MF 2-2 2-2 2-2 2-2 2 (excluded) (excluded) -2 2-2 2-2 2-2 2-2 % cycle 1 MTJ heel raises MF MTJ MF 2-2 -4 2-2 -4 2-2 -4 2-2 -4 S1 2-2 -4 2-2 -4 S2 2-2 -4 2-2 -4 S3 2-2 -4 2-2 -4 S4 2-2 -4 2-2 -4 S5 2-2 -4 2-2 -4 S6 2-2 -4 2-2 -4 S7 2-2 -4 2-2 -4 S8 avg
restricted joint anke DF/PF heel raises 1 % cycle (a) 12 ANKLE 12 KNEE 12 9 9 9 angle (deg) 6 3 6 3 6 3 (b) MG LG SOL TA 5 S1 5 S2 5 S3 5 (excluded) S4 EMG (%max) 5 S5 5 S6 5 S7 5 S8