Validi y o ecu en neu al ne wo ks o p edic pedal o ces and lowe
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limb kine ics in cycling
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Juan Co de o-Sánchez1, Rod igo Bini2, Gil Se ancolí3*
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1Depa men o Physio he apy, Facul y o Medicine and Heal h Science, Uni e si y o
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Alcalá, Alcalá de Hena es, Spain. h ps://o cid.o g/0000-0002-5890-2635
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2La T obe Ru al Heal h School, La T obe Uni e si y, Bendigo, Aus alia.
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h ps://o cid.o g/0000-0002-2138-7350
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3Simula ion and Mo emen Analysis Lab (SIMMA Lab), Depa men o Mechanical
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Enginee ing, Uni e si a Poli ècnica de Ca alunya, Ba celona, Ca alonia.
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h ps://o cid.o g/0000-0001-5034-2445
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Wo d coun : 3437
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*Co esponding au ho :
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Gil Se ancolí
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Depa men o Mechanical Enginee ing, Uni e si a Poli ècnica de Ca alunya
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A . Edua d Ma is any 16, A8.40
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08019 Ba celona
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gil.se anc[email p o ec ed]
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Abs ac
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Dynamic a iables con ibu e o unde s and he mechanics o pedalling and can assis wi h inju y
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p e en ion. Measu ing pedal o ces and join momen s and powe s has a high cos , which can
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be mi iga ed by using ained a i icial neu al ne wo ks (ANN) o p edic o ces om kinema ics.
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Thus, his s udy aimed a aining and alida ing ecu en ANN o p edic 3D pedal o ces, lowe
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limb join momen s and powe s om lowe limb kinema ics. E gome e pedalling da a om
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se en een cyclis s eco ded in a single labo a o y session we e used o ain he ANN, whe e
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a ious e gome e powe ou pu s and cadences we e combined. A di e en da ase wi h en
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cyclis s was u ilized o es he ANN´s pe o mance. S a is ical Pa ame ic Mapping (SPM) was
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pe o med o explo e signi ican co ela ions be ween measu ed and p edic ed kine ic a iables
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h oughou he pedal cycle. Mean co ela ion alues anged om 0.79 o 0.96 and all a iables
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exhibi ed signi ican posi i e co ela ions a hei peak absolu e alues (p<0.05), excep o he
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an e opos e io (p = 0.28) and mediola e al (p = 0.51) pedal o ces and he knee lexion powe
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(p = 0.33). The maximum p edic ion e o s o he ANN in he sagi al plane we e 12.1% o he
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pedal o ces, 17.2% o he ne join momen s and 9.4% o he join powe s, while o non-
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sagi al plane we e 13.0%, 28.9% and 24.0%, espec i ely. Thus, he ANN p oduces kine ic da a
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in cycling wi hin he e o s expec ed om he a iabili y be ween assessmen days.
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Keywo ds: Machine lea ning, dynamics, pedalling, join momen s and powe s
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In oduc ion
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The analysis o biomechanical a iables du ing cycling can help iden i y abno mali ies which, i
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co ec ed in ime, can p e en inju ies as i is he case whe e cyclis s wi h knee pain had much
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la ge knee momen s (Bini e al., 2011; Callaghan, 2005; P iego Quesada e al., 2019). The e o
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exe ed by he cyclis a each join can be quan i ied h ough an in e se dynamics analysis. The
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esul ing da a on join momen s and join powe a indi idual join s can help p e en o e use
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inju ies and educe he isk o join pain (Mu ay, 2023). Lowe limb join momen s and powe s
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a e some o he mos s udied a iables o analysing cycling echnique (Bini and Hume, 2023;
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Yamaguchi e al., 2023). Pedal o ces a e essen ial o op imizing aining and ehabili a ion
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p og ams as hey a e co ela ed wi h lowe limb muscle ac i i y and join eac ion o ces
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(Ahmadi e al., 2024). Howe e , accu a e measu emen s o pedal o ces a e pa icula ly
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challenging, leading some s udies o use cus om-made ins umen s o esea ch pu poses (Bini
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e al., 2014). Besides, al hough he equi ed a iables o pe o m in e se dynamics such as join
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angles and pedal o ces can be collec ed bo h inside and ou side labo a o ies using wea able
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echnology such as ine ial senso s and ins umen ed pedals (Ál a ez and Vinyolas, 1996; Bini
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and Hume, 2013; Chen e al., 2005; E ans e al., 2022; Ma uyama e al., 2019; Mo bey e al.,
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2024; Wooles e al., 2005), hei cos and a ailabili y pose limi a ions o bo h spo s and
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indus ial applica ions (McDe i e al., 2022). In addi ion, pe o ming in e se dynamics analyses
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using physics-based biomechanical models in ol es he pe sonaliza ion o skele al models and
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he compu a ion o he equa ions o mo ion. The e o e, besides he high cos o pedal o ce
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senso s, hese p ocesses a e no quickly applicable in spo s p ac ice and a e ime-consuming
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(Cecchini e al., 2014; Maye ho e e al., 2024).
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A i icial neu al ne wo ks (ANN) o e an al e na i e me hod o ob ain dynamics da a. An ANN
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can be ained o p edic ex e nal o ces, join momen s and powe s using only kinema ics da a,
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which a e mo e accessible o spo s scien is s and coaches (S e e e al., 2020; Seung e al.,
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2013; Koma is e al., 2019; Mund e al., 2020a; Al ai e al., 2023). ANNs a e a subse o machine
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lea ning echniques inspi ed by he ne wo ks o biological neu ons in ou b ains, consis ing o
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ainable unc ions ha es ima e ou pu a iables om inpu a iables wi hou equi ing speci ic
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knowledge o hei in e ac ions. The use o ANNs equi es iden i ying he inpu a iables ha
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mos signi ican ly con ibu e o he ou pu s (Çolak, 2021) and p o iding a su icien amoun o
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quali y da a (Klein and Rossin, 1999). One o he ad an ages o applying ANNs o cycling is ha
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hey may no equi e he use o musculoskele al models and hei pe sonaliza ion (Maye ho e
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e al., 2024), o he use o sophis ica ed expe imen al echniques o eco d dynamics da a (i.e.
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ins umen ed pedals o c anks). This also acili a es assessmen ou side labo a o y se ings.
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Despi e hese ad an ages, ew s udies ha e been published on he applica ion o ANNs o cycling
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biomechanics. Mos s udies p edic ing dynamics- ela ed da a we e ocused on single ime-
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independen pa ame e s (i.e. ze o-dimensional analysis), like he index o e ec i eness (IE) o
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posi i e impulse p opo ion (PIP) (To es e al., 2024). The p edic ion o empo al pa e ns o
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join momen s o join con ac o ces, as pe o med in musculoskele al-based s udies
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(Thompson e al., 2020) wi hou he need o pe o m complex measu emen s, would acili a e
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he analyses. Besides, as cycling is a widely p ac iced spo ha enhances pe o mance (A kinson
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e al., 2015) and heal h (Somma e al., 2022), p o iding daily bicycle use s wi h access o his
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knowledge could make cycling sa e and encou age i s p ac ise.
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Thus, his s udy aimed o ain and alida e ecu en ANN o p edic h ee-dimensional (3D)
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pedal o ces, lowe limb join momen s and powe s om lowe limb kinema ics. We
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hypo hesised ha he ained model will accu a ely p edic bo h pedal o ces and join kine ics.
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Me hods
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Da ase s
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The da ase used o ain he ANN came om he s udy o Bini and Hume (2023). I con ains da a
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om se en een cyclis s aged 24 ± 6 yea s-old, wi h a body mass o 75 ± 8 kg and a s a u e o 181
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± 6 cm, pedalling in a cycle e gome e o one minu e a nine andomised combina ions o powe
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ou pu s (1.5, 2.5 and 3.5 W/kg o body mass) and cadences (60, 80 and 100 pm). Da a collec ion
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om hese pa icipan s was ca ied ou wi h he app o al o he e hics commi ee om La T obe
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Uni e si y (HEC17-085).
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In o de o assess he alidi y o he ained model, a sepa a e da ase o en ec ea ional cyclis s
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( ou emales and six males: 24.4 ± 5.9 yea s, 175 ±8 cm, 72.5 ± 12.8 kg) pedalling on a cycle
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e gome e a 2.5 W/kg and 90 pm was used in his s udy, which was app o ed by he Uni e si y
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E hics Commi ee (HEC19-001). Da a om hese pa icipan s was p e iously u ilised in a
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publica ion (Bini, 2021). This sample size was calcula ed based on he in e -session a iabili y
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epo ed in a p io s udy o pedal o ce ou pu s (i.e. le pedal index o e ec i eness (Bini and
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Hume, 2020)). The s a is ical model in ol ed a co ela ion aiming o an e ec size o 0.78, based
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on he in e -sessions ICC om Bini and Hume (2020). The esul ing model indica ed ha eigh
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cyclis s would be equi ed, and we op ed o expand o en pa icipan s o a oid any missing da a
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poin s in he alida ion componen . Sample size calcula ion was conduc ed using GPowe
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s a is ical package (Faul e al., 2007).
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Da a analysis
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Join momen s used o ain he ANNs we e ob ained using a musculoskele al model (Lai e al.
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2017) scaled o each pa icipan om s a ic poses. This model was composed o 22 body
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segmen s and 37 deg ees o eedom (DoF) including he main lowe body DoF in cycling. This
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model is sui able o mo emen s in ol ing high hip and knee lexion as is he case o pedalling.
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Kinema ics (i.e. join coo dina es and hei de i a i es) and ex e nal o ces (i.e. pedal o ces)
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we e used o pe o m in e se kinema ics and in e se dynamics in OpenSim (Delp e al., 2007).
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Pedal o ces we e il e ed using a ze o-lag ou -o de lowpass Bu e wo h digi al il e a a cu o
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equency o 10 Hz. Mo ion da a we e lowpass il e ed a 10 Hz using he OpenSim In e se
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Dynamics ool. Join mechanical powe s we e compu ed o he igh lowe limb a each deg ee
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o eedom as he scala p oduc o he join momen by i s angula eloci y. The deg ees o
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eedom analysed we e hip lexion-ex ension, adduc ion-abduc ion, in e nal-ex e nal o a ion,
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knee lexion-ex ension and ankle do si-plan a lexion. Da a we e ime no malized o 101 da a
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poin s o each pedal cycle.
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Neu al ne wo ks
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Recu en neu al ne wo ks (RNN) we e ained o p edic pedal o ces and ne join momen s.
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The implemen ed RNN we e a sequen ial model composed o one laye wi h 64 long sho - e m
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memo y (LSTM) cells ollowed by a dense laye wi h 8 neu ons. The ec i ied linea uni (ReLU)
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ac i a ion unc ion was used due o i s as compu a ion and because i does no sa u a e o
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posi i e alues. Finally, a one-neu on dense laye wi h a linea ac i a ion unc ion was added o
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p oduce a single ou pu pe ime s ep. The adap i e momen es ima ion (Adam) algo i hm
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(Kingma and Ba, 2015) was used as op imize (wi h a lea ning a e o 1x10-4) due o i s good
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con e gence quali y and speed, while ea ly s opping was implemen ed o egula ize he lea ning
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p ocess. The RNN’s s uc u e and he lea ning a e we e selec ed acco ding o he G idSea ch
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algo i hm using c oss- alida ion o e alua e all he possible combina ions among he numbe o
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laye s (1, 2 o 3) and LSTM cells (32, 64 o 128) and he lea ning a e (1x10-2, 1x10-3 o 1x10-4).
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The inpu s o he RNN we e he hip, knee and ankle lexion-ex ension and hip o a ion join
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angles. The hip abduc ion join angle was emo ed om he inpu s, as including i inc eased he
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ANN p edic ion e o s by app oxima ely 20% o e all. Addi ionally, powe ou pu , cadence and
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pa icipan s’ body mass we e included in he inpu s, as hese ac o s a ec pedal o ces, join
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momen s and powe s (Bini e al., 2010b; E ema e al., 2009; Mo nieux e al., 2007). Each
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a iable was no malized by hei maximum absolu e alue o ensu e ha all a iables ha e a
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simila magni ude, he eby acili a ing he lea ning p ocess o he RNN. Da a analysis and RNN
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aining we e ca ied ou in Py hon ( 3.11.5) wi h Tenso Flow and Ke as using an In el i9-9880H
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CPU compu e wi h 32GB RAM and a N idia GeFo ce RTX 2080 wi h Max-Q Desing GPU.
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S a is ical analysis
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Pea son’s co ela ion and he oo mean squa ed e o (RMSE) we e calcula ed o e alua e he
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ag eemen be ween he measu ed (i.e. da a om en ec ea ional cyclis s) and he p edic ed
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pedal o ce and join momen and powe a iables. We compu ed he mean and s anda d
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de ia ion o he co ela ion and RMSE be ween cu es ac oss all pa icipan s. Addi ionally, e o
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pe cen ages we e compu ed as he mean RMSE no malized o he alue ange o he es da ase
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o each a iable (Equa ion 1).
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𝑒𝑟𝑟𝑜𝑟 (%)= 𝑚𝑒𝑎𝑛 𝑅𝑀𝑆𝐸
𝑟𝑎𝑛𝑔𝑒 𝑥 100 ( 1)
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Co ela ion was anked as poo (0–0.5), mode a e (0.5–0.75), good (0.75–0.90) and excellen
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(> 0.9) (Dancey and Reidy, 2004). A eg ession analysis using S a is ical Pa ame ic Mapping
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(SPM) (Pa aky e al., 2015) was pe o med in Py hon o compa e he measu ed and p edic ed
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ime-dependen a iables. A eg ession es (using spm1d.s a s. eg ess) was pe o med o assess
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whe he he co ela ion coe icien s we e signi ican ly di e en om ze o (p- alue <.05) a each
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ins an o he pedal cycle.
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Resul s
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Good o excellen ag eemen was ound o pedal o ces, ne join momen s and join powe s.
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Excellen ag eemen was obse ed o ankle lexion powe (Table 1). Mean RMSE anged
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be ween 9.90-13.0 % o pedal o ces, 12.10-28.90 % o ne join momen s and 5.50-24.0 %, o
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join powe s (Table 1).
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Table 1. Mean and s anda d de ia ion o he co ela ions and RMSE be ween measu ed and p edic ed a iables. The
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e o pe cen age is he RMSE no malized o he ange o he unde lying da a o each a iable.
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Co ela ion
RMSE
An e opos e io Pedal Fo ce
0.77 ± 0.12
25.5 ± 14.8 N (9.9 ± 5.7 %)
Ve ical Pedal Fo ce
0.89 ± 0.13
58.9 ± 21.8 N (12.1± 4.5 %)
Mediola e al Pedal Fo ce
0.82 ± 0.14
9.1 ± 3.1 N (13.0 ± 4.3 %)
Hip Flexion Momen
0.79 ± 0.12
29.7 ± 10.0 Nm (17.2 ± 5.8 %)
Hip Abduc ion Momen
0.77 ± 0.11
31.4 ± 26.4 Nm (28.9 ± 24.5 %)
Hip Ro a ion Momen
0.79 ± 0.12
15.9 ± 14.1 Nm (28.4 ± 25.5 %)
Knee Flexion Momen
0.88 ± 0.11
13.3 ± 4.7 Nm (15.4 ± 5.4 %)
Ankle Flexion Momen
0.88 ± 0.08
7.9 ± 2.7 Nm (12.1 ± 4.1 %)
Hip Flexion Powe
0.89 ± 0.1
87.4 ± 37.9 W (9.4 ± 4.0 %)
Hip Abduc ion Powe
0.75 ± 0.14
18.5 ± 14.1 W (24.0 ± 18.5 %)
Hip Ro a ion Powe
0.80 ± 0.17
10.8 ± 7.44 W (13.9 ± 9.6 %)
Knee Flexion Powe
0.86 ± 0.11
51.9 ± 22.4 W (9.1 ± 3.9 %)
Ankle Flexion Powe
0.96 ± 0.06
8.7 ± 4.1 W (5.5 ± 2.7 %)
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Figu e 1 and Figu e 2 show he mean measu ed and p edic ed pedal o ces and ne join
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momen s and join powe s, espec i ely. The e was good ag eemen be ween hem in e ms o
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co ela ion and RMSE. Acco ding o he eg ession SPM esul s (Figu e 1), he pe cen age o he
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cycle wi h signi ican co ela ions a ied o each a iable. The an e opos e io pedal o ce
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showed signi ican posi i e co ela ion a ound 30% o he pedal cycle wi h a mean e o below
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5.0 N (Figu e A1, Appendix A). Howe e he e was signi ican nega i e co ela ion be ween he
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40% and 95% wi h a maximum mean e o o 15.0 N. F om he 10 o 65% o he pedal cycle he e
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we e signi ican posi i e co ela ion o he e ical pedal o ces wi h a maximum mean e o o
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50.0 N. The mediola e al pedal o ce showed, om he beginning o he 22% and om he 75%
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o he end, signi ican posi i e co ela ions wi h mean e o s below 3.0 N. Be ween 25% and 52%
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o he pedal cycle he signi ican co ela ion was nega i e showing a mean e o smalle han 6.0
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N. Hip lexion and abduc ion momen s as well as ankle lexion momen displayed signi ican
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posi i e co ela ion o he mos o pedalling cycle. Thei maximum mean e o s we e 30.0 Nm,
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15.0 Nm and 8.0 Nm, espec i ely. On he con a y, hip o a ion momen and knee lexion
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momen only epo ed signi ican posi i e co ela ions be ween 21-32% and 25-53% o he pedal
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cycle, espec i ely. Howe e , hei mean e o s we e below 10.0 Nm. In a simila way, excep o
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he knee lexion powe , he e we e signi ican posi i e co ela ions o mos o he pedalling
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cycle (Figu e 2) wi h maximum mean e o s o 100.0 W, 25.0 W, 14.0 W and 13.0 W o he hip
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lexion, abduc ion and o a ion powe s and ankle lexion powe , espec i ely. Only hip lexion
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(abou 60%) and o a ion (abou 15% and 95%) powe s epo ed signi ican nega i e di e ences
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wi h maximum mean e o s o 50.0 W and 14.0 W, espec i ely. Knee lexion powe showed
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signi ican posi i e co ela ion be ween 35% and 55 % wi h mean e o smalle han 20.0 W. On
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he o he hand, signi ican nega i e co ela ions we e ound om 0% o 15% and om 58% o
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he end o he pedal cycle epo ing a maximum mean e o o 45.0 W.
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In addi ion, all a iables exhibi ed signi ican posi i e co ela ions a hei peak absolu e alues
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(i.e. wi hin he powe phase), excep o he an e opos e io and mediola e al pedal o ces and
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he knee lexion powe . Depending on he phase o he pedal cycle, he RNN p edic ions ei he
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o e es ima ed o unde es ima ed he measu ed da a (Figu e A1, Appendix A). A he maximum
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peaks o he cu es, he p edic ions ended o unde es ima e. The hip, knee and ankle lexion
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momen s we e unde es ima ed a he s a and end o he pedal cycle, while om app oxima ely
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be ween 20% o 60% o he cycle, hey we e o e es ima ed. The opposi e pa e n was obse ed
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o he e ical pedal o ce. The es o he a iables did no show such as clea pa e n.
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Figu e 1. Mean ( hick lines) and s anda d de ia ion (shadowed a eas) o he measu ed (blue) and p edic ed ( ed)
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pedal o ces and ne join momen s. Pe cen age o cycle s and o he posi ion o he pedal in he pedal cycle. The
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ins an s o 0 and 100% co espond o he op posi ion and he 50 % co espond o he bo om one. The SPM plo s
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display he s a is ic ou pu s (solid lines) whils he dashed ed lines show he c i ical alue o signi ican
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co ela ions.
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