Faculdade de Engenha ia da Uni e sidade do Po o
Modelling he gai o heal hy and pos -s oke
indi iduals
Mo gana Pi es A onso
Mas e ’s deg ee in Bioenginee ing
Supe iso :
P o . João Manuel R.S. Ta a es
Mechanical Enginee ing Depa men , FEUP
Co-supe iso :
P o . And eia So ia Pinhei o Sousa
Physio he apy Depa men , ESTSP
Sep embe 2015
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© Mo gana Pi es A onso, 2015
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Resumo
A locomoção é uma a e a de g ande impo ância na ida das pessoas. Mesmo que odos
os indi íduos saudá eis ap esen em uma a iabilidade na u al nos pad ões da ma cha, é
possí el de ini um pad ão acei á el pa a “ma cha no mal”. Con udo, algumas pa ologias
podem induzi pad ões de ma cha ano mais que podem limi a a ida de uma pessoa, o nando-
a dependen e de ou os e, consequen emen e, eduzindo a sua qualidade de ida.
O aciden e ascula ence álico (AVE) a e a 15 milhões de pessoas em cada ano, das quais 50%
so em al e ações da ma cha não pe manen es, de aco do com a O ganização Mundial de
Saúde. A ma cha na sequência de um AVE é uma combinação de á ias anomalias que dependem
do indi íduo, da se e idade e da localização do dano e do empo deco ido após a oco ência.
A aplicação de um a amen o adequado nes es pacien es pode melho a com o conhecimen o
de como a pa ologia a e a os músculos e os con olos ne osos associados a eles, pe mi indo
desenha soluções especí icas e pe sonalizadas a cada pacien e. A análise expe imen al da
ma cha é de g ande u ilidade na ex ação de pa âme os de ma cha, oda ia, ap esen a
algumas agilidades. Simulações compu acionais dinâmicas, po ou o lado, êm um g ande
po encial nes e ipo de in es igação e, combinada com dados expe imen ais, pe mi em a
ealização de es udos causa-e ei o, sob e como músculos especí icos a e am o mo imen o, po
exemplo, em indi íduos que enham so ido um AVE.
Nes e abalho, duas simulações compu acionais o am desen ol idas usando o OpenSim, a
pa i de dados cinemá icos e ciné icos ob idos em ensaios de ma cha ealizados num indi íduo
saudá el e ou o na sequência de um AVE. Os dados expe imen ais o am ex aídos de um
ichei o com a ex ensão *.c3d e p é-p ocessados. Cada simulação começou com um modelo
musculosquelé ico, que oi adap ado de aco do com a massa e dimensões do indi iduo
pos e io men e o am de e minados os ângulos e momen os nas a iculações po cinemá ica e
dinâmica in e sa; as o ças e momen os esiduais o am eduzidos e inalmen e oi usado o
“Compu ed Muscle Con ol” pa a de e mina a con ibuição muscula dos p incipais lexo es
plan a es (soleus e gas ocnémio medial), lexo do sal ( ibial an e io ) e um músculo da coxa
i
(semimemb anoso). Os ângulos e momen os nas a iculações ela i os ao indi íduo saudá el
e ela am-se de aco do com a e e ência. No en an o, os músculos analisados mos a am
di e enças nos pad ões de a i ação. Na simulação en ol endo ao indi íduo pós AVE, e i icou-
se alguma edução do ângulo e momen o no o nozelo do memb o a e ado, mas a a i ação e
po ência dos lexo es plan a es só oi eduzida no gas ocnémio medial. Po ou o lado,
e i icou-se a i ação p olongada do semimemb anoso du an e a ase de apoio do memb o
a e ado.
Os a uado es muscula es não o am capazes de ge a a cinemá ica p e endida sem eco e a
o ças esiduais e de ese a e ainda oi e i icado um e o al o no ângulo do o nozelo di ei o.
Abs ac
Locomo ion is a ask wi h g ea impo ance in he li e o a pe son. E en hough e e y heal hy
indi idual shows na u al a iabili y in gai pa e ns, i is possible o de ine an accep able
pa e n o “no mal gai ”. Howe e , some pa hologies can induce abno mal gai pa e ns ha
can limi he li e o a pe son, making him/he dependen o o he s and consequen ly educing
his/he s quali y o li e. T ea men s in ol ing ehabili a ion o su gical p ocedu es can e e
o diminished he impai men s in gai , showing good imp o emen s on he people’s li e.
S oke o ce eb o ascula acciden (CVA) a ec s 15 million people each yea , om which 50%
su e non-pe manen gai impai men s, acco ding o he Wo ld Heal h O ganiza ion. Gai
a e s oke is a combina ion o se e al abno mali ies ha depend on he indi idual, he
se e i y and he loca ion o he inju y and he ime passed a e i s occu ence.
The applica ion o an adequa e ea men in hese pa ien s can be imp o ed wi h he
unde s anding o how he pa hology a ec s he muscles, and he neu al con ols associa ed
wi h i and allow o design speci ic solu ions o each pa ien . Expe imen al gai analysis is
use ul in measu ing impo an gai pa ame e s, bu i has limi ed capabili ies. Compu a ional
dynamic simula ions, on he o he hand, ha e g ea po en ial in his ype o in es iga ion and,
combined wi h he expe imen al da a, allow pe o ming cause-e ec s udies, abou how
speci ic muscles in luence he mo emen , o example, in indi iduals a ec ed in he sequence
o a s oke.
In he p esen wo k, wo compu a ional dynamic simula ions we e de eloped using OpenSim,
using kinema ic and kine ic da a collec ed om a gai ail pe o med on a heal hy and a pos -
s oke indi idual. The expe imen al da a was ex ac ed om a *.c3d ile and p ocessed. Each
simula ion s a ed om a musculoskele al model, scaled acco ding o he mass and dimensions
o each indi idual; ollowed he de e mina ion o he join angles and momen s by sol ing an
in e se kinema ics and dynamics p oblem; hen he esidual o ces we e educed and inally
Compu ed Muscle Con ol was used o de e mine he muscle con ibu ions o he gai o he
p incipal plan a lexo s (soleus and medial gas ocnemius) and do si lexo s ( ibialis an e io )

i
and one hams ing (semimemb anosus). The join angles and momen s ela i e o he heal hy
indi idual showed o be in ag eemen wi h he e e ence alues o no mal gai . Howe e , he
muscles analysed showed di e ences in he ac i a ion pa e ns. In he simula ion in ol ing a
pos -s oke indi idual i was e i ied lowe plan a lexo angle and momen bu he ac i a ion
and powe o he plan a lexo muscles we e only educed in he medial gas ocnemius o he
impai ed limb. On he o he hand i was e i ied ea ly ac i a ion o he plan a lexo s and
p olonged ac i a ion o he semimemb anosus om he impai ed limb du ing i s s ance.
The muscula ac ua o s we e no able o ack he kinema ics wi hou he use o esidual and
ese e o ces and he igh ankle had a high e o associa ed.
ii
Acknowledgmen s
I would like o hank o my supe iso and co-supe iso , P o esso D . João Ta a es
and D a. And eia Sousa, o hei a en ion, guidance and ad ice du ing he de elopmen o
his wo k.
Also I would like o hank o he Eng. Ped o Fonseca om he LABIOMEP o he p o ision o
he expe imen al da a and o he a en ion in answe ing my ques ions and o D a. Augus a
Sil a o he help analysing he esul s.
I would like o exp ess my since e g a i ude o my amily and iends, o hei cons an
suppo and ca e.
Finally I wan o hank o God o he oppo uni ies and people ha He pu in my pa h.
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x i

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Lis o ables
Table 2. 1. Common spacio- empo al, kinema ic and kine ic/EMG abno mali ies in gai o
pos -s oke pa ien s. ................................................................................. 17
Table 5.1. Gene al gai pa ame e s ob ained o he S udy 2 and S udy 1. ...................... 55
Table 5. 2 Ma ke e o (RMS) and maximum e o associa ed wi h he scaling p ocess o
he models in he S udy 2 and S udy 1 and he espec i e limi alues ecommended
in [50]. .................................................................................................. 56
Table 5. 3 Ma ke e o (RMS) and maximum e o associa ed wi h he scaling p ocess o
he models in he S udy 2 and S udy 1 and he espec i e limi alues ecommended
in [50]. .................................................................................................. 60
Table 5. 4 Maximum and RMS alues o he esidual o ces and momen s and o a ional
e o s ob ained o he RRA o he S udy 2 and S udy 1 and he ecommended [50]
op imal and maximum h esholds. ................................................................. 66
Table 5. 5 Maximum and RMS alues o he esidual o ces and momen s, ese e o ces
and ansla ional and o a ional e o s ob ained o he CMC o he S udy 2 and
S udy 1 and he ecommended [50] op imal and maximum h esholds. .................... 67
Table 6.1 Co espondence be ween he ma ke se used in he gai ial pe o med in he
LABIOMEP and he de aul ma ke se used in OpenSim. The X indica es ha a
ma ke is no included in he espec i e con igu a ion. ....................................... 85
x iii
xix
Abb e ia ions and Symbols
BTK Biomechanical ToolKi
CE Con ac ile Elemen
CMC Compu ed Muscle Con ol
COM Cen e o Mass
CONTRA Con ala e al
COP Cen e o P essu e
CPG Cen al Pa e n Gene a o
CVA Ce eb o ascula Acciden
DOF Deg ee o F eedom
EMG Elec omyog aphy
GRF G ound Reac ion Fo ce
ID In e se Dynamics
IK In e se Kinema ics
IPSI Ipsila e al
LED Ligh Emi ing Diode
MEDGAS Medial gas ocnemius
PEE Pa allel Elas ic Elemen
PWA Poin o W ench Applica ion
RRA Residual Reduc ion Algo i hm
SEE Se ies Elas ic Elemen
SEMEMB Semimemb anosus
SOL Soleus
TA Tibialis An e io
xx
i
Chap e 1
In oduc ion o he disse a ion and i s
s uc u e
1.1 - In oduc ion
Locomo ion is p esen in almos e e y animal and i is lea ned in he beginning o li e.
Te es ial locomo ion in humans, o gai , is o g ea impo ance in hei daily li e, since i is
he ehicle o many o he asks.
Biomechanical gai analysis can be based in expe imen al me hods ha allows he
de e mina ion o impo an gai pa ame e s (kinema ic, kine ic and elec omyog aphic).
Howe e , using uniquely his app oach i is di icul o es ablish cause-e ec ela ions be ween
a speci ic muscle’s ac ion and i s con ibu ion o he o e all mo emen . Dynamic simula ions
a e able o ill his gap since i enables he access o he inpu s ha gene a e he ou pu s
assessed expe imen ally: he o ces ha o igina ed he mo ions measu ed. This is due o he
ac ha he sys em (model) is known and is desc ibed ma hema ically. The desc ip ion o he
model is, howe e , complex and, as consequence, i is necessa y o use compu a ional ools o
sol e hese equa ions. OpenSim is an example o a so wa e designed o his pu pose and
allows pe o ming dynamical simula ions, using expe imen al da a.
The applica ion o gai analysis in he clinical ield, o example, in he cha ac e iza ions o
he impac o a pa hology in gai o e en as a diagnos ic ool is possible. Subjec s wi h s oke
p esen se e al gai impai men s ha a e dependen o nume ous ac o s: b ain a ea a ec ed,
ime a e he inju y, physical cha ac e is ics o he pa ien , e c. The s udy o he muscle
o ces in hese indi iduals pe mi s he iden i ica ion o he sou ce o he damages and allows
he c ea ion o sui able he apeu ic and/o su gical solu ion o each pa ien . Mo eo e , aking
in o accoun s udies pe o med in heal hy indi iduals, i con ibu es o he inc ease o he
knowledge abou he ou comes o his pa hology.

In oduc ion o he disse a ion and i s s uc u e
2
1.2 - Objec i es
The main objec i es o his monog aph we e he ollowing:
1. Explo e he undamen als o he human gai , aking in o accoun :
a. The musculoskele al sys em o he lowe limb in ol ed in he p ocess:
ana omical cons i u ion (bones, join s and muscles) and unc ion;
b. Unde s and he p ocess o gai as a coo dina ed mo emen as esul o a
complex sys em o neu omuscula con ol and s udy he gai cycle, by
decomposing i in he espec i e phases and subphases in o de o unde s and
he sequence o e en s.
c. Explo e he concep s o gai abno mali y and pa hological gai and de e mine
he consequences o a s oke in he ask o walking, conside ing p e ious
s udies.
2. Elabo a e a li e a u e e iew add essing he ollowing issues:
a. Me hodologies used cu en ly in expe imen al gai analysis;
b. Ma hema ical and mechanical models able o simula e he musculoskele al
sys em, he muscles and muscula con ol, de eloped o be used in
compu a ional simula ions o gai ;
3. De eloped dynamic simula ions o heal hy and pa hological gai in OpenSim, aking he
ollowing s eps:
a. Ex ac and p ocess expe imen al da a om a gai ial o a pos s oke
indi idual and p epa e i o use as inpu in OpenSim;
b. Execu e he OpenSim wo k low (choice o a musculoskele al model, scaling,
in e se kinema ics, in e se dynamics, educ ion o esiduals and compu ed
muscle con ol);
4. Compa e he esul s ob ained om he heal hy and pos s oke simula ion and wi h he
li e a u e.
1.3 - O ganiza ional S uc u e
This disse a ion is di ided in six chap e s, each one con aining he espec i e
in oduc ion and summa y. Nex , is p esen ed a b ie desc ip ion o each emainde
chap e .
Chap e 2 – Fundamen s o Human Gai
In his chap e he ana omical s uc u es composing he lowe limb and he pel is (bones,
join s and muscles) a e desc ibed wi h in e es in unde s anding hei ole in he walking
ask. In a second pa , i is desc ibed no mal gai and om he neu omuscula con ol
in ol ed, ollowing by he cha ac e is ic gai cycle and he espec i e phases and subphases.
O ganiza ional S uc u e
3
Finally, a e in oduced he concep s o gai abno mali y and pa hological gai . A speci ic ype
o pa hological gai , pos -s oke gai , is explo ed. Conside ing expe imen al s udies done wi h
pos -s oke indi iduals, he cha ac e is ics o his ype o gai a e enume a ed and g ouped
acco ding o hei spacio- empo al, kinema ic, kine ic and EMG na u e.
Chap e 3 – Li e a u e e iew
The s a e o a comp ises he expe imen al and compu a ional app oaches o cu en gai
analysis. In he i s opic, he assessmen o impo an gai pa ame e s by isual gai analysis
and he use o echnological ools o ex ac kinema ic and kine ic da a, and he elec ical
ac i i y o he muscles (EMG) is explained.
In he second opic, ega ding he compu a ional analysis o gai , he models designed o
simula e ma hema ically and mechanically he musculoskele al sys em, he muscle ension
pa hs, he ope a ion o he muscles and endons as an ac ua o , he muscula ac i a ion and
he neu omuscula con ol a e desc ibed.
Chap e 4 – Me hodology
In he i s pa o his chap e , he me hod used o ex ac ing he kine ic and kinema ic da a
om a *.c3d and he espec i e p ocessing is p esen ed. In he second pa , he compu a ional
en i onmen , OpenSim, and i s capabili ies a e in oduced. Then, each s ep o he
implemen ed wo k low is desc ibed: he choice o he musculoskele al model, he scaling
p ocess, he in e se kinema ics and dynamics s ep, he educ ion o he esiduals and, inally
he compu ed muscle con ol.
Chap e 5 – Resul s and discussion
In his chap e , he expe imen al da a ex ac ed om he *.c3d ile and p ocessed is analysed
and discussed, as well as he me hods used. Following he e o s and he esul s ob ained om
each s ep o he wo k low a e p esen ed and discussed, compa ing he simula ions de eloped
o he heal hy and he pos -s oke indi idual wi h he li e a u e.
Chap e 6 - Final conclusions and u u e de elopmen s
Being his he inal chap e , i p esen s he gene al conclusions o he p esen s udy, as well
as he limi a ions o his s udy and possible u u e de elopmen s.
In oduc ion o he disse a ion and i s s uc u e
4
Annex
In he annex, he da a ha complemen he unde s anding o he s udy is p esen ed:
a. Annex 1 lis o body ma ke s used in he LABIOMEP and in OpenSim;
b. Annex 2: plo s o he g ound eac ion momen s il e ed using di e en cu -o
equencies;
c. Annex 3: weigh s used o each ma ke in he scaling p ocess;
d. Annex 4: weigh s a ibu ed o each ma ke in he in e se kinema ics p ocess.
1.4 - Main Con ibu ions
The p esen wo k inc eases he knowledge abou he sequence o p ocedu es necessa y o
model gai , using OpenSim, s a ing wi h he gene a ion o he inpu iles in he app op ia e
o ma om a *.c3d ile, which is a s anda d o ma among he biomechanical communi y, un il
he s udy o he muscula beha iou . I also explo es he in luences in conside ing he
ho izon al momen s as pa o he ex e nal o ces and momen s in he simula ions o gai , ha
usually a e no aken in o accoun in some gai s udies.
5
Chap e 2
Fundamen s o Human Gai
2.1 - In oduc ion
The unde s anding o ana omical o ganiza ion o he lowe limb and pel is is undamen al in
gai s udies.
The bones a e igid s uc u es able o suppo he body and mo e. The mo emen is only
ensu ed because o he exis ence o join s connec ing he bones. Each join allows one o mo e
deg ees o eedom, depending on i s con o ma ion. The muscles in ol e he skele al sys em,
being linked o he bones in inse ion poin s h ough endons. Due o his con igu a ion,
muscula con ac ion is capable o gene a e mo emen o bones a ound he join s. When
se e al muscles a e con ac ing, coo dina ed by he neu al con ols, complex mo emen s can
be made, o example, walking.
No mal gai is di icul o de ine since he e is some a iabili y be ween heal hy subjec s,
depending on he on he pe son sex, age, body geome y. Thus, he e m “no mal” has se e al
de ini ions, acco ding o he cha ac e is ics o he indi idual unde s udy [1].
Gai is a complex ask ha in ol es ne ous con ol o ac i a e muscles and c ea e a
coo dina ed mo emen . The muscles a e ac i a ed by elec ic impulses a i ing h ough he
neu ons and sen om he mechanism con ols.
The high con ols o locomo ion a e loca ed in he b ain, consis ing in he b ain co ex, basal
ganglia and he ce ebellum, and a e esponsible o planned ac ions by he pe son. The spinal
co d is also impo an and i is he e we e he hy hmic and “au oma ic” mo emen s o walking
a e gene a ed. Ano he impo an aspec is ha he con ol o gai coun s wi h eedback
mechanisms ha help modula ing he muscle exci a ions, such as muscle spindles, Golgi o gans
and mechano ecep o s in he skin.
In o de o s udy he gai cycle, i is necessa y o ocus ou a en ion in one leg, since gai is
symme ical, and ollows i s mo emen s h ough he cycle. Then i is possible o di ide i in a
Fundamen s o Human Gai
12
The an e io compa men is o med by he quad iceps emo is g oup o muscles ha ha e
inse ion in he pa ella endon: ec us emo is, as us la e alis, medialis and in e medius. The
sa o ius, he longes muscle o he body is also pa o his compa men [2].
The medial compa men is o med by he adduc o muscles (b e is, longus and magnus), he
g acilis and he pec ineus, while he pos e io , also called hams ing muscles include he biceps
emo is, he semimemb anosus and he semi endinosus [2].
Las ly, he muscles loca ed in he leg, esponsible o he mo emen s o he ankle, oo and
oes a e classi ied in ex insic and in insic. The ex insic a e also di ided in o h ee g oups
[2], based on hei loca ion:
An e io compa men : includes he ex enso digi o um longus and hallucis longus, ibialis
an e io and ibula is e ius and is esponsible o do si lexion and e e sion o in e sion o he
oo and ex ension o he oes;
La e al compa men : o med by he ibula is b e is and longus and in ol ed in e e sion o he
oo and also plan a lexion;
Pos e io compa men : has supe icial muscles, he gas ocnemius and soleus, which join he
plan a is and o m he calcaneal endon (commonly known as Achilles endon) and ha a e
in ol ed in plan a lexion o he oo . The deep muscles ( lexo digi o um longus and hallucis
longus, popli eus and ibialis pos e io ) ac in lexion and in e sion he oes.
The in insic muscles o he oo a e loca ed inside he oo , in a simila s uc u e o he hand
and a e esponsible o oe lexion, ex ension, adduc ion and abduc ion [2].
2.3 - No mal Gai
2.3.1 - Neu omuscula con ol
Skele al muscles a e well-o ganized complex s uc u es, composed by hund eds o ascicles,
which consis in hund eds o muscle ibbe s [1]. These a e, in u n, an a angemen o ilamen s
ac in and myosin, which cause muscula con ac ion when hey slide ela i ely o each o he
[1].
A mo o uni is conside ed o be he combina ion o a neu on, and he muscle ibbe s ene a ed
by i and i s b anches [1, 4]. The neu on ansmi s elec ical signals (ac i a ion po en ial) o
each muscle ibbe , causing he elease o calcium ions, which will igge he muscle
con ac ion and gene a e mo emen , wi h consump ion o me abolic ene gy [1, 4]. Muscula
con ac ion can be isome ic, i he muscle gene a es ension, bu does no change i s leng h;
iso onic i he leng h changes, bu he ension gene a ed does no ; concen ic i he con ac ion
causes muscle sho ening; and eccen ic i i causes leng hening [1].

No mal Gai
13
The walking mo emen was desc ibed as a complex in e ac ion be ween sup aspinal, spinal
and a e en eedback mechanisms [5]. The sup aspinal mechanisms a e associa ed wi h he
“ ine con ol” o walking [6] and include [1, 7]:
Mo o co ex, which gene a es olun a y mo emen ;
Basal ganglia, esponsible o planning and con olling pa allel sequences o mo emen s o
p oduce complex mo emen s;
Ce ebellum, esponsible o he iming o muscula ac i i ies, namely in he smoo h and apid
ansi ion om one mo emen o ano he , hus being in ol ed in he equilib ium o he body.
Also helps in he con ol o in ensi y o muscula con ac ion.
The spinal co d is esponsible o he c ea ion o e lexes ha a e as eac ions o a s imulus,
de ec ed by he a e en eedback mechanisms [1, 6]. The a e en eedback mechanisms
include: muscle spindles, senso ial ecep o s loca ed in he muscles esponsible o muscle
leng h and eloci y eedback; Golgi o gans, in cha ge o o ce eedback; and
mechano ecep o s in he join s and skin, which gi e cu aneous eedback [5]. These mechanisms
allow he adap a ion o gai o he en i onmen s imuli [8].
In he spinal co d, he e a e also Cen al Pa e n Gene a o s (CPG), which consis in ne wo ks
o ne ous cells [1, 8, 9]. Associa ed wi h he a e en eedback mechanism, he CPG p oduce
hy hmic mo emen s like walking, wi hou conscious e o [6]. E en hough he exis ence o
hese in quad uped animals was al eady p o ed, he e idence o hose in human s ills indi ec
[6, 10].
2.3.2 - Gai Cycle
Gai cycle is de ined as he in e al be ween wo successi e occu ences in he p ocess o
walking. Fo example, i i is conside ed he con ac o he igh oo wi h he g ound (“ini ial
con ac ”) as he beginning o he cycle, hen he cycle ends in he nex con ac be ween he
igh oo and he g ound [1, 11]. This pe iod is cha ac e ized by a s ance phase, du ing which
he oo is in con ac wi h he g ound, and a swing phase, whe e he limb swings in he ai [1,
11]. When one leg is he s ance phase, he opposi e is in swing phase, excluding he momen
o double con ac , in which bo h a e in s ance phase (Figu e 2.4).
Fundamen s o Human Gai
14
Figu e 2.4. Diag am o he gai phases o le and igh legs [1].
The s ance phase las s app oxima ely 60% o he gai cycle [11] and begins wi h he ini ial
con ac and ends wi h he oe o o he same leg. I comp ises ou subphases (Figu e 2.5) [1,
11]:
1. Ini ial con ac : he ini ial s age o he loading esponse, when he heel o he igh oo
con ac s wi h he g ound. I is cha ac e ized by hip lexion, knee ex ension and neu al
do si lexion o he ankle. The g ound eac ion o ce has upwa ds di ec ion;
2. Loading esponse: occu s a e he ini ial con ac and be o e opposi e oe-o , when
bo h ee a e in con ac wi h he g ound and he weigh o he body is ans e ed om
he le leg o he igh one. In his phase he ankle p esen s plan a lexion and he
g ound eac ion o ce inc eases i s magni ude and di ec ion om upwa ds o upwa ds
and backwa ds;
3. Mid-s ance: occu s a e he opposi e oe-o and be o e he heel ise. I co esponds
o he momen when he le leg is in he swing phase and passes he igh one. The hip
inc eases he ex ension, which is achie ed mainly because o he ine ia and g a i y,
while he knee is eaches he highes lexion poin o he s ance phase be o e i s a s
o ex end. The ankle, which was in plan a lexion changes o do si lexion. The g ound
eac ion o ce mo es o wa d along he oo , om he momen when he oo is in ull
con ac wi h he g ound [1];
4. Te minal s ance: co esponds o he momen when he heel o igh oo s a s o lea e
he g ound, be o e he le oo oe con ac s wi h i [11]. The heel ise is cha ac e ized
by peaks o hip and knee ex ension and ankle do si lexion. In opposi e ini ial con ac ,
he hip eaches he highes ex ension angle, while he knee s a s lexing and he ankle
mo es in o plan a lexion. Du ing his phase, he g ound eac ion o ce mo es o wa d
[1];
No mal Gai
15
5. P e-swing: is cha ac e ized by double suppo , since he le oo con ac s wi h he
walking su ace and he body weigh is sha ed be ween he wo legs and i las s un il
he oe o momen , which sepa a es he s ance phase om he swing phase [1, 11].
The emaining 40% o he cycle consis s in he swing phase (Figu e 2.4), which is sub-
di ided in:
1. Ini ial swing: occu s when he igh oo lea es he g ound. The hip is lexed as well as
he knee, and he ankle eaches he peak o plan a lexion immedia ely a e he oe-
o . The g ound eac ion o ce is posi ioned behind he knee and becomes ze o when
he oo lea es g ound [1];
2. Mid-swing: s a s wi h he ee adjacen , when he igh and le legs a e side by side
and ends wi h he ibia e ical. In he i s s ep, he hip con inues o lex and he knee
is also lexed, mos ly as consequence o he hip lexion. The ankle mo es o an a i ude
conside ed neu al o do si lexed. The g ound eac ion o ce is null, since he igh oo
is in he ai [1];
3. Te minal swing: begins wi h ibia e ical, consis ing on he ibia o he igh leg being
in a e ical posi ion. The lexion o he hip ends, he knee is passi ely ex ended, and
he ankle is be ween sligh plan a lexion and do si lexion. This phase ends wi h he
ini ial con ac , which ma ks he beginning o a new cycle [1].
Figu e 2.5. S ance and swing phases diag am and he espec i e subphases [1].
Fundamen s o Human Gai
16
2.4 - Gai Dis u bance
2.4.1 - Abno mal and pa hological gai
Some gai cha ac e is ics a y om pe son o pe son; howe e , i is possible o quan i y some
a iables ha allow o de ine o accep able ange o alues ha cha ac e ize a no mal gai
pa e n [1].
Gai is gene ally accomplished by ou main asks [1, 12]:
- Main enance o he balance o he unk, a ms and head ei he s a ically o
dynamically;
- The s ance leg mus be able o suppo he body weigh ;
- The swinging leg mus ad ance o a posi ion in o de o accep he body weigh
ans e ence;
- The ene gy supply mus be enough o allow he o wa d mo emen s.
I is conside ed ha i a leas one o hese equi emen s is no ul illed o he indi idual can
pe o m all he asks, bu wi h ex a ene gy consump ion o wi h he need o walking aids ( o
example, canes), has a gai abno mali y [1].
I is impo an o dis inguish he e m gai abno mali y om pa hological gai . Gai abno mali y
is he desc ip ion o some gai cha ac e is ics ha can be isually iden i ied o by using
expe imen al gai analysis me hods (discussed in he chap e 3) and can include, o example:
unk bending, ci cumduc ion, hip hiking, aul ing, abno mal hip o a ion, excessi e knee
ex ension/ lexion, inadequa e do si lexion con ol, abno mal oo con ac , insu icien push-
o , abno mal walking base, hy hmic dis u bances, e c. [1] Pa hological gai is ela ed wi h a
pa hology, such as ce eb al palsy, myelomeningocele, Pa kinson’s disease, s oke, e c. [1]. The
gai pa e ns associa ed can include a single abno mali y o a combina ion o se e al, which
can in e ac be ween hem and may change wi h ime and he apy and a y om pe son o
pe son [1, 13].
In pa hological gai , an abno mali y may esul di ec ly om any muscula o neu al impai men
such as muscle weakness, some de o mi y o spas ici y, o be he consequence o a
compensa ion o an impai men , being named in his case as adap a ion [1, 12].
2.4.2 - Pos -s oke gai
Ce eb o ascula acciden (CVA), commonly e e ed as s oke, is he dea h o b ain issue as
consequence o a dis u bance o he a e ial blood supply [2, 12]. The e a e wo ypes o s oke:
haemo hagic s oke ha esul s om a e y bleeding inside he b ain and ischemic s oke ha
is consequence o he blockage o b ain a e ies by a h ombus, a blood clo , a a globule o
a gas bubble [2]. The ou comes o a s oke a e dependen on he a ea o he b ain which su e s
Gai Dis u bance
17
he empo a y p i a ion o blood and can include loss o communica ion and ision capabili ies
and abno mali ies in he mo o sys em. The mos equen case is he one in which one o he
sides o he e i o y i iga ed by he middle ce eb al a e y is a ec ed and some mo o
unc ions a e damaged, causing mo o con ol diso de s in he opposi e side o he body [14].
In addi ion, mo o unc ion can also be impai ed i he midb ain is inju ed because his can
block ne e conduc ion he pa hways be ween he b ain and spinal co d, a ec ing he senso ial
and mo o sys ems and, consequen ly, abno mal gai [7].
Pos -s oke pa ien s su e neu ological and mo o sequels, bu mo e han 85% o s oke
su i o s a e able o walk wi h o wi hou assis ance [15]. The e is some a iabili y o gai
abno mali ies be ween indi iduals ollowing s oke, and hey depend on he ime a e he
inju y, as well i he pa ien ecei ed ehabili a ion he apy [12, 13].
Hemipa esis, one o he mos common impai men s [16], is he a ec ion o one side o he
body due o de ec i e muscle ac i a ion [17]. In se e al s udies, muscle ac i i y was measu ed
by elec omyog aphy (EMG), showing al e a ions in he magni ude and phase o he muscula
ac i i y pa e ns, compa ing o heal h indi iduals and abno mali ies on bo h he con alesional
(CONTRA) and ipsilesional (IPSI) sides, leading o bila e al di e ences [18, 19].
P onounced asymme y in gai pa e n, due o hemipa esis, may change some empo al,
spacial, kine ic and kinema ic gai a iables [16]. Table 2.1 is p esen s a lis o gai common
impai men s associa ed o pos -s oke gai .
Table 2. 1. Common spacio- empo al, kinema ic and kine ic/EMG abno mali ies in gai o pos -s oke
pa ien s.
Gai modi ica ions
Spacio-
empo al
[12, 13]
- Reduced walking eloci y;
- Sho e s ide leng h;
- Longe gai cycle du a ion;
- Longe p opo ion o double-suppo phase and
s ance/swing phases o bo h legs.
Kinema ics
[19]
- Gene al dec ease o join peak displacemen s a he hip,
knee and ankle.
Sagi al plane
- Dec eased hip ex ension du ing s ance and dec eased hip
lexion du ing swing;
- Highe ankle plan a lexion a ini ial con ac [13];
- Knee hype ex ension du ing weigh accep ance;

Fundamen s o Human Gai
18
- Dec ease o knee lexion and absence o do si lexion a
swing phase.
Ho izon al plane
- La ge ex e nal o a ion o he pa e ic hip and knee;
F on al plane
- La ge abduc ion o he hip and la ge in e sion o he ankle
in he pa e ic side;
- La ge pel ic hiking and la e al displacemen .
EMG/Kine ics
- Weakness o he pa e ic muscles, sugges ed by he o e all
dec ease o EMG le els in he pa e ic side [12, 19];
- Reduc ion o he plan a lexion momen in bo h sides in he
co esponden la e s ance phases [17]:
- Pa e ic side: a ibu ed o he ea ly and educed EMG
ac i i y o he pa e ic plan a lexo s (namely medial
gas ocnemius);
- Ipsilesional side: ela ed wi h excessi e an agonis co-
ac i a ion as an adap a ion o pos u al ins abili y
caused by impai ed gai ;
- P olonged s ance co-ac i a ion o hams ings and he
quad iceps muscles in bo h sides (ac ing as compensa o y
mechanism o he weakness o he plan a lexo s, which ha e
been ound o ha e he la ges con ibu ion o suppo du ing he
single leg s ance phase [16, 20, 21] ;
- Hype ac i e s e ch e lexes ha may cause knee
hype ex ension and hinde do si lexion in la e s ance phase,
in e e ing wi h push-o [17]. Besides, plan a lexo s gene a e
la ge pa o he ene gy o mo e he limbs o wa d du ing he
push-o phase. This g oup o muscles, speci ically he soleus and
he gas ocnemius, showed insu icien powe gene a ion in he
con alesional side [22];
- Reduc ion o he do si lexion momen in he swing phase, in
he con alesional side caused by weakness o ankle do si lexo s,
namely ibilalis an e io , combined wi h inc eased plan a lexo
passi e s i ness [15, 17];
Gai Dis u bance
19
- Dynamic spas ici y o he plan a lexo s and weakness o he
do si lexo s du ing loading esponse a e esponsible o he
inc easing o he s ep leng h [15, 17, 23].
- Conce ning he powe i is e i ied di e ences be ween slow
and as walke s[17]:
- Slow walke s: Lowe la e s ance ankle pull-o (A2: second
ankle powe bu s ) and ea ly swing hip pull-o (H3: hi d
hip powe bu s ) p opulsi e powe bu s s on bo h sides;
- Fas walke s: La ge posi i e wo k by bo h hip ex enso s
in ea ly s ance (H1: i s hip powe bu s ) and, in he
con alesional side, by he H3 p opulsi e powe bu s .
Spas ici y is e i ied in 20-30% o he pos -s oke pa ien s [5, 12]. I is de ined as a “mo o
diso de by eloci y-dependen inc ease in onic s e ch e lexes (muscle one) wi h
exagge a ed endon je ks, esul ing om hype exci abili y o he endon e lex” [5]. Howe e ,
he e is con o e sy be ween he au ho s abou he con ibu ion o he spas ici y in pos -s oke
gai impai men s [15, 21].
These impai men s lead o a highe ene ge ic cos , a he biological (me abolic) and mechanic
le els [12, 13, 16]. The me abolic cos in hemiplegic gai was ound o be 50% o 97% highe
han in heal hy subjec s [18]. Lamon agne e al. [17] epo ed ha his gene al highe
ene ge ic cos may be ela ed o he excessi e co-ac i a ion o an agonis ic muscles.
2.5 - Summa y
The lowe limb is composed by se e al bones, join and muscles, o ganized simila ly o he
uppe limb in some aspec s.
The localiza ion o he muscles as well as hei inse ion in he bones is di ec ly linked wi h he
mo emen hey gene a e. Conside ing hei ac ion, muscles can also be g ouped, o example,
he g oup o he hip lexo s, which a e in ol ed in lexion o he hip.
The ac ha he join s in lowe limb (and also he uppe limb) sys em a e syno ial is impo an
conside ing ha he ela i e mo emen o he limbs and he simul aneous ask o suppo ing
Fundamen s o Human Gai
20
he body weigh lead o a high ic ion be ween he bones ha could inc ease he wea i he
join was no equipped wi h ca ilage, syno ial lub ican and o he mechanisms.
The hip, knee and ankle join s and associa ed bones and muscles mus ecei e special a en ion
since conside able amoun o mo emen a e gene a ed he e. On he o he hand, he join s in
he pel is and in he oo a e e y es ic i e o he mo ion, when compa ed o hese join s.
Human gai in ol es con ol by sup aspinal and spinal mechanisms ha ansmi elec ic signals
o he muscles in o de o gene a e he desi ed mo emen . In he pa icula case o locomo ion,
he e a e indi ec e idences o a con ol cen e in he spinal co d, esponsible o he
gene a ion o unconscious s epping. The gai cycle is di ided in he s ance and swing phases,
which in u n a e di ided in o i e and h ee subphases, espec i ely. This me hod allows he
s udy o he sequen ial e en s in e ms o momen s o he segmen s, g ound eac ion o ces
and muscles in ol ed o achie e he ask o locomo ion.
Gai abno mali ies ollowing s oke a e mos ly he consequence o he weakness o he muscles
o one side o he body. Spas ici y, howe e , has a neu al o igin, bu he e is s ill disag eemen
be ween he s udies pe o med, abou he in luence o i in pos -s oke gai .
In he sequence o hese disabili ies, he a ec ed indi idual de elops mechanisms o
compensa ion, wi h he objec i e o allowing his locomo ion. Ne e heless, hese a e also
classi ied as gai abno mali ies.
In he sequence o a s oke, pa ien s mus ecei e ehabili a ion he apy in o de o minimize
o elimina e i s ou comes and imp o e hei quali y o li e.
21
Chap e 3
Rela ed Wo k
3.1 - In oduc ion
Human gai can be s udied using an expe imen al app oach by measu ing se e al pa ame e s
ha cha ac e ize gai , wi h he aid o he la es echnologies a ailable o his pu pose. Many
esea ch labo a o ies and specialized clinics can pe o m his s udies o pu poses o esea ch
o o help in he p ocess o ehabili a ion.
Wi h he de elopmen o new complex models simula ing he human body and he de elopmen
o he compu e s, i became possible o combine he da a collec ed expe imen ally wi h
compu a ional models and make dynamic simula ions, able o es ima e, o example, he
indi idual muscle con ibu ions o he mo emen . S udies aiming o es hypo hesis (“wha i ”
s udies), such as see wha happens when a muscula exci a ion pa e n is modi ied [24] a e
also possible using compu a ional simula ions, which is ha d o implemen expe imen ally.
In his chap e , he expe imen al me hodologies o assess kinema ic, kine ic measu emen s
and muscle ac i i y a e e iewed. A e wa ds, he ma hema ical models cu en ly used wi h
he aim o ep esen he biological s uc u es (muscles, bones, ligamen s) and he espec i e
con ol a e analysed. Finally, an o e iew o OpenSim, he so wa e o be used, is gi en.
3.2 - Expe imen al me hods o gai analysis
Gai analysis is de ined as “ he sys ema ic measu emen , desc ip ion, and assessmen o hose
quan i ies hough o cha ac e ize human locomo ion” [25]. The s udy o human locomo ion has
been inc easingly used in he las decades in he ields o spo s, ehabili a ion [26] and in
esea ch [17].
Roy B. e al [25], in 1991, de ined clinical gai analysis as he use o gai analysis in which he
clinician quan i a i ely examines he ou comes o a ce ain disease o inju y su e ed o he
Rela ed Wo k
28
3.3.2 - Muscle pa hs
The muscles and endons a e assumed o be inse ed in a single poin in he bones and muscles
which inse in he bone h ough a la ge a ea a e modeled using mo e han one po ion wi h
only wo inse ion ex emi ies [35].
The o ces gene a ed by each muscle a e applied o he segmen s h ough a ensile pa h [39].
This pa h can be conside ed as a simple s aigh line, hough his me hod can lead o e o s
when he muscle w aps a ound ano he componen like a bone o ano he muscle [35]. Ano he
possibili y is o ep esen he muscle’s pa h h ough i s c oss-sec ional cen oids. Howe e , his
me hod p esen s se e al p oblems because i is ha d o de e mine hese poin s o e e y join
con igu a ion [40]. An al e na i e me hod consis s in es ablishing speci ic poin s along he
c oss-sec ional cen oid’s pa h, which a e ixed in he s uc u es whe e he muscle w aps and
a e linked by s aigh lines o cu ed segmen s [35] (Figu e 3.2).
Figu e 3.2. Th ee dimensional ep esen a ion o he shank, oo and oes and he ensile pa h o he
soleus muscle (single s aigh line) and o he pe oneus longus, wi h a se ies o line segmen s and
cons ained “ ia poin s” [41].
Ano he op ion is he obs acle-se app oach ha allows does no cons ain he muscle pa h in
he con ac wi h he o he segmen s (bones and/o muscles), allowing i o mo e eely o e
he neighbo ing s uc u es [40].
3.3.3 - Muscle- endon ac ua o model
The Hill- ype muscle- endon ac ua o model was widely adop ed in compu a ional dynamical
simula ions since i is conside ed e icien and usable in se e al mo emen s and has
compu a ional educed cos [4, 20, 22, 38]. O iginally, he model was de eloped by A. V. Hill
and i was only composed by wo elemen s [4], bu since hen i was imp o ed and he e sion
cu en ly used is composed by a muscle wi h h ee elemen s and a endon, as shown in Figu e

Compu a ional modelling and simula ion o he human gai
29
3.3. The CE is a con ac ile elemen , whe e he o ce is gene a ed and able o model he o ce-
leng h- eloci y p ope y, and he SEE and he PEE a e elas ic elemen s (sp ings) posi ioned,
espec i ely, in se ies and in pa allel [38]. The i s one is esponsible o modelling he muscle
ac i e s i ness and he la e one models muscle passi e s i ness [35]. In his model, he
endon is assumed o be an elas ic elemen . Howe e , i is known ha he o ce associa ed
a ies non-linea ly as he leng h o he endon changes and ha his simpli ica ion does no
a ec signi ican ly he o e all beha io [35].
Figu e 3.3. Hill- ype muscle- endon ac ua o , composed by a endon in se ies wi h he muscle. The
muscle is modeled by a con ac ile elemen (CE) in se ies wi h an elas ic elemen (SEE) and in pa allel
wi h ano he elas ic elemen (PEE) [38].
The muscle- endon dynamic beha io is go e ned by a single non-linea di e en ial equa ion
[38]:
𝐹󰇗𝑀𝑇=𝑓(𝐹𝑀𝑇,𝑙𝑀𝑇,𝑣𝑀𝑇,𝑎𝑚),0≤ 𝑎𝑚≤1 (3.2)
whe e: 𝐹𝑀𝑇 is musculo- endon o ce; 𝐹󰇗𝑀𝑇 is he a e o change o he muscle- endon o ce;
𝑙𝑀𝑇 is he musculo- endon leng h; 𝑣𝑀𝑇is he musculo- endon sho ening eloci y and 𝑎𝑚 is he
muscle ac i a ion.
Rela ed Wo k
30
3.3.4 - Muscle ac i a ion model
The exci a ion-con ac ion coupling has wo s eps (Figu e 3.4): ac i a ion dynamics, consis ing
in he ansduc ion o he neu al s imulus in o ac i a ion o he con ac ile elemen , and
con ac ion dynamics, he ans o ma ion o ac i a ion in o muscle con ac ion [39].
Figu e 3.4. Musculo- endon ac ua o dynamics [38].
The e is a delay in ime be ween he neu al signal (exci a ion) and he consequen muscle
ac i a ion (ac i a ion), due o he kine ics o chemical p ocesses in ol ing he calcium
molecules [35, 39]. Consequen ly, se e al s udies conce ning gai analysis ake in conside a ion
his p ocess [39], which is modeled by i s -o de di e en ial equa ion:
𝑎󰇗𝑚=(1
𝜏𝑟𝑖𝑠𝑒)(𝑢2−𝑢𝑎𝑚)+(1
𝜏𝑓𝑎𝑙𝑙)(𝑢−𝑎𝑚);𝑢=𝑢(𝑡); 𝑎𝑚=𝑎𝑚(𝑡) (3.3)
whe e: 𝑎𝑚 and 𝑎󰇗𝑚 a e he muscula ac i a ion and he a e o muscula ac i a ion,
espec i ely; 𝑢 is he muscle exci a ion; 𝜏𝑟𝑖𝑠𝑒 and 𝜏𝑓𝑎𝑙𝑙 a e he ime cons an s o ise and all,
espec i ely.
3.3.5 - Neu omuscula con ol model
Ha ing a musculoskele al model buil , i is necessa y o de ine he con ol o he muscle
exci a ion, so ha ealis ic mo emen s a e p oduced [38]. The e a e admi ed wo basic
app oaches o do his: a dynamic op imiza ion and a acking solu ion p oblem [33, 35, 38].
Using dynamic op imiza ion, i is necessa y o de ine clea ly an objec i e ask/ unc ion in o de
o ind he muscle con ols ha pe mi o achie e ha objec i e [33, 38]. In he spo s ield,
his me hod could be applied in s udies whe e he objec i e ask was, o example, he
maximum heigh jumping [42], maximum speed pedaling [43] and maximum dis ance h owing
[44].
In walking, Ande son and Pandy assumed ha he objec i e unc ion is he minimiza ion o he
me abolic ene gy consumed pe dis ance uni , and he esul s o hei s udy showed ha he
muscle unc ion can be well desc ibed by assuming his objec i e unc ion [45]. Howe e , when
we a e dealing wi h he human gai , he objec i e ask can be ambiguous in some cases [35].
An al e na i e me hod consis s in sol ing he op imal acking p oblem, by guiding he muscula
con ols in o de o ob ain he minimal di e ence be ween he simula ion da a and he
Compu a ional modelling and simula ion o he human gai
31
expe imen al da a, by means o a leas -squa es app oach [33, 38]. This solu ion is conside ed
o be he sui able in simula ions conce ning subjec -speci ic gai and pa hological gai and o
quan i y he muscle con ibu ions, iden i y join loading and inju ies [33, 38].
3.3.6 - Assessmen o he muscle o ces
The de e mina ion o muscle o ces and he unde s anding o how a muscle a ec s he
mo emen o he join s, and he segmen s can be done by using a musculoskele al model as
desc ibed in Figu e 3.5, applying a o wa d o in e se dynamics s a egy [35, 38].
Figu e 3.5. Diag am o he o wa d dynamics ( op) and he in e se dynamics (bo om) me hods [46].
In e se dynamics (Figu e 3.5) uses as inpu he body mo ions, which a e di e en ia ed and
used o compu e he muscle o ces, by using he g ound eac ion o ces and he join momen s
in he classical New on-Eule equa ions o mo ion [47]:
𝐹=𝑚𝑎 (3.4)
𝑀
󰇍
󰇍

=𝐼𝛼 (3.5)
whe e 𝐹 is he o ce; 𝑎 is he accele a ion; 𝑀
󰇍
󰇍

is he momen and is he angula accele a ion.
The o he app oach is o wa d dynamics, in which he inpu s o he sys em a e he muscle
exci a ions and when applied in he muscle- endon model ( aking in o accoun he coupling
Rela ed Wo k
32
exci a ion-ac i a ion) i is possible o ob ain he muscle o ces (Figu e 3.5). Using hese o ces
and he o he elemen s (musculoskele al model and skele al dynamics) i is possible o ob ain
he mo emen s gene a ed by he inpu exci a ions [35].
The numbe o muscles ac ing in one join is g ea e han i s numbe o DOF, consequen ly an
op imiza ion s a egy is usually used when conside ing hese wo app oaches. Using in e se
dynamics, he muscle o ces a e de e mined using s a ic op imiza ion, which sol es a di e en
op imiza ion p oblem a each ins an o he mo emen , o de e mine he muscle o ces om
he join kinema ics. On he o he hand, in he case o o wa d dynamics, i a goal o mo o
ask is de ined, i is possible o use dynamic op imiza ion, in which a single op imiza ion
p oblem is sol ed o he comple e cycle o he mo emen , being his app oach mo e expensi e
compu a ionally [35]. The e o e, dynamic op imiza ion is used, o example, in s udies ela ed
o spo pe o mance, in which he objec i e o ask desi ed is de ined and he muscle
ac i a ions a e known [35].
3.4 - Summa y
Expe imen al gai analysis echniques gi e use ul in o ma ion abou he quan i iable
cha ac e is ics o gai , bu he use o his da a in compu a ional simula ions is showing good
esul s in assessing quan i ies no measu able expe imen ally. These simula ions use
ma hema ical/mechanical models, desc ibed by complex equa ions, which need o be ea ed
and analyzed using compu e s.
33
Chap e 4
Me hodology
4.1 - In oduc ion
Biomechanical labo a o ies a ound he wo ld use di e en 3-D mo ion cap u e sys ems and
so wa e o collec hei da a, making mo e complica ed sha ing he da a be ween use s due
o p oblems o so wa e compa ibili y [48]. The si ua ion has changed wi h he in oduc ion o
he *.c3d ile o ma , ha began in 1987 and since hen i has been g adually adop ed by he
communi y, becoming a s anda d. *.c3d is a public domain ype o bina y ile o ma o eco d
and s o e synch onized 3D, analog and EMG aw da a, p ocessed da a ( o example gai e en s)
and gene al in o ma ion abou he ial (ins umen a ion and so wa e used and cha ac e is ics
o he subjec ) [48].
Compu a ional simula ions a e use ul o s udy human mo ion, which in ol es complex
mechanisms o con ol and ac ua ion and equen ly s a om expe imen al da a. OpenSim is
a ela i ely new so wa e ha can be used o pe o m his ype o simula ions since i pe mi s
he unde s anding o how muscle ac ua es o ep oduce a speci ic mo emen [39, 49, 50].
Thanks o i s e sa ili y (i allows o c ea e and change he models and add componen s), has
been used no only o s udy heal hy mo emen s o he human body, bu as well pa hological
mo ion [51, 52]. Typically, a simula ion s a s om choosing a model and he da a,
con enien ly ea ed and s o ed in he app op ia e ile o ma , se es as inpu . An OpenSim
simula ion consis s in a sequence o s eps, whe e he ou pu s om he p e ious s ep a e used
as inpu s in he ollowing, making necessa y o educe he e o s as possible o a oid i s
accumula ion.
OpenSim equi es, howe e , ha he expe imen al da a used as inpu o be in a speci ic o ma :
o he kinema ic da a uses he o ma *. c (T ack Row Column), c ea ed by Mo ion Analysis
Co po a ion and o he kine ic da a he o ma *.mo (Mo ion), c ea ed by he de elope s o
SIMM (So wa e o In e ac i e Musculoskele al Modelling) [50]. I he expe imen al da a is
s o ed in a *.c3d ile, is possible o ex ac i using, o example, he Biomechanical Toolki

Me hodology
34
(BTK), which is an open-sou ce and c oss-pla o m lib a y o unc ions o ead, w i e and modi y
acquisi ion iles. These ope a ions can be pe o med in Ma lab, by using he Ma lab w appe
[53] and w i ing he iles in he adequa e o ma o use as inpu .
The expe imen al da a ela i e o a pos -s oke indi idual was collec ed in he LABIOMEP and
sa ed in *.c3d o ma . Ma lab was used o ex ac and p ocess he da a and o ex ac he gai
e en s, necessa y o ob ain one gai cycle o pe o m he biomechanical simula ion ha will
be desc ibed in he Chap e 4.
In he second pa o his chap e , i will be desc ibed he each s ep o he wo k low o
biomechanical simula ion using OpenSim. A model o he head, o so and lowe limbs was used
o ep oduce he da a eco ded om a pos -s oke pa ien and a heal hy indi idual. The
kinema ics and join momen s we e de e mined, as well as he muscula ac i a ions and
powe s.
4.2 - Expe imen al da a ea men and analysis
4.2.1 - Kinema ic and kine ic da a
The kinema ic and kine ic da a ela i e o a pos -s oke subjec was p e iously collec ed in he
LABIOMEP, pe o ming a gai ail wi h a male subjec o 55 yea s old, 1,75 m heigh and 96Kg.
The pa ien has su e ed a CVA and he was mainly a ec ed in he uppe limbs. Consequen ly,
he lowe limb pe o mance in gai was no subs an ially impai ed. The pa ien pa hology
his o ical was no de ailed known, he only in o ma ion a ailable was ha his ea men
included he applica ion o bo ulin oxin only in he uppe limbs.
The kinema ic da a was acqui ed using a mo ion cap u e sys em 3D Qualisys™ Oqus Came a
Se ies sys em, ope a ing a 200 Hz wi h 12 came as e o e lec o s o in a ed ligh and 32
e lec o (passi e) body ma ke s. The ma ke da a was acqui ed using he na i e so wa e,
Qualisys T ack Manage . The con igu a ion o he ma ke s o he o so and lowe limbs is shown
in he Figu e 4.1.
Expe imen al da a ea men and analysis
35
Figu e 4.1. Loca ion o he ma ke s used in he gai ial pe o med in he LABIOMEP in a pos -s oke
pa ien : RAC – igh ac omion; LAC – le ac omion; C7 – e eb a C7; STERN – s e num; RASIS – igh
supe io iliac spine; LASIS – le supe io iliac spine; RPSIS – igh pos e io supe io iliac spine; LPSIS – le
pos e io iliac spine; RMK – igh medial knee; LMK – le medial knee; RLK – igh la e al knee; LLK – le
la e al knee; RMA – igh medial ankle; LMA – le la e al ankle; RLA – igh la e al ankle; LLA – le medial
ankle; RFOOT1 – igh oo p oximal phalange 5; LFOOT1 – le oo p oximal phalange 5; RFOOT4 – igh
oo p oximal phalange 5; LFOOT4 – le oo p oximal phalange 5; RBACKFOOT – igh back oo ;
LBACKFOOT – le back oo . (Only he ma ke s o he o so and lowe limbs, used in his s udy, a e
ep esen ed. The 10 ma ke s used in he lowe limbs a e no shown).
Du ing he ial, he subjec walked o e a se o six o ce pla o ms disposed as shown in he
Figu e 4.2, allowing he empo al synch oniza ion be ween he kinema ic and kine ic da a.
The pla o ms 1, 2 and 6 (Be ec FP4060) and 3, 4 (Be ec FP6090) we e ype 2 ex ensiome ic.
The pla o m 5 was piezoelec ic, ype 3 (Kis le 9281E). The subjec s epped in he pla o ms
2, 3, 4 and 6 and he da a was collec ed wi h a sampling equency o 2000 Hz.
Me hodology
36
Figu e 4.2. Fo ce pla o m disposi ion in he loo du ing he gai ial in he LABIOMEP. The o ce
pla o ms in which he subjec s epped a e shown in o ange (2, 3, 4 and 6). Image ob ained using he
so wa e Mokka.
4.2.2 - Da a ex ac ing and p e-p ocessing
The da a esul ing om he ial desc ibed abo e was s o ed in *.c3d o ma and, pos e io ly,
i was ex ac ed and p ocessed using Ma lab ®.
The e a e al eady a ailable unc ions de eloped by he OpenSim communi y, de eloped o
his pu pose [54]. In his wo k, he oolbox “c3d2OpenSim” de eloped by James Dunne in 2015
was used and adap ed o he da a. This oolbox uses as basis he unc ions o he Biomechanical
ToolKi (BTK).
In he Figu e 0.3 is shown he sequence o ac ions pe o med p epa e o use as inpu in
OpenSim.
Expe imen al da a ea men and analysis
37
Figu e 4.3.Sequence o s eps aken o ob ain he OpenSim inpu iles con aining he kinema ic and kine ic
da a (*. c and *.mo iles, espec i ely) ela i e o he pos -s oke indi idual.
The in o ma ion con ained in he *.c3d ile was ex ac ed and s o ed inside a Ma lab s uc
using a sequence o unc ions om he BTK. The unc ion b kGe Ma ke s ex ac s he posi ions
o he make s, de ined in he labo a o y coo dina e sys em. Then, his alues we e con e ed
o he OpenSim coo dina e sys em and inally, a *. c ile was p in ed wi h his in o ma ion.
Rega ding he o ce pla o m da a, he e a e wo me hods o ex ac ing he da a: he unc ion
Me hodology
44
I was necessa y o associa e o each body one o mo e make pai , so ha he co esponding
scale ac o was applied o ha body. In he case o using mo e han one ma ke pai , he scale
ac o is compu ed as he a e age be ween he ac o s compu ed o each one. In he Figu e
4.9 i is shown he Ma ke Se o he Scaling Tool o he S udy 2, showing each body and he
co esponding ma ke pai s associa ed.
Figu e 4.9. Display o he Measu emen Se o he Scaling Tool (S udy 2). A he le is p esen ed a lis o
he measu emen s, associa ed wi h he scale ac o s a e compu ed using he ma ke pai s shown a he
igh .
The o so and he pel is a e ecommended o be scaled non-uni o mly [50], his is, wi h
di e en scale ac o s in he h ee di ec ions. Fo ha eason, x and z di ec ion o he o so
was associa ed wi h he ma ke pai s RAC/LAC and RASIS/LASIS and o he y di ec ion ( e ical)
wi h C7/RPSIS and C7/LPSIS (Figu e 4.10). Al hough he ma ke s chosen o scale he e ical
di ec ion a e no aligned in he e ical di ec ion, hey a e be e indica o s o he o so’s
e ical leng h. A sac al ma ke would be mo e sui able o his pu pose.

Compu a ional Simula ion
45
45
Figu e 4.10. Ma ke s used o calcula e he e ical scale ac o o he o so. The dashed line ep esen s
he dis ances be ween he pai s C7/LPSIS and C7/RPSIS.
Conce ning he weigh , he Scaling Tool o e s has wo possible app oaches: p ese e he o al
mass o he subjec o he expe imen , main aining he ela i e masses o he bodies in he
model, o scaling each segmen mass aking in o accoun only he scale ac o s compu ed
be o e. In he las app oach he o al mass migh no ma ch he subjec 's eal mass. The i s
al e na i e was chosen, since mass modi ica ions could lead o e o s in he nex s eps, when
he g ound eac ion o ces measu ed a e conside ed. I impo an o no e ha he Scaling ool
adap s he mass dis ibu ion (ine ia ma ix) o each body, when changing i s mass and
dimensions and, using his op ion, he scale ac o s compu ed using he measu emen se (Figu e
4.9) a e no used o he mass scaling [50].
I is also necessa y o weigh each ma ke ela i ely o he o he s. La ge weigh s mean ha
he ma ke is acked mo e igh ly and he acking e o s a e mo e penalized. Fo his eason
he ma ke s ep esen ing bone landma ks and unc ional join cen es should ha e la ge
weigh s [50], which is he case o he ma ke s a he hip, knee and ankle join .The coo dina es
ep esen ing he sub ala and me a a sophalangeal join s we e locked in he neu al posi ion
(angle se o ze o) and weigh ed hea ily, so ha hey emain in ha posi ion du ing he
simula ions. In he OpenSim guide his s ep is ecommended [50] and he eason why his
ecommended is because he model does no possess enough muscles o con ol hese join s.
In he case o he S udy 1, he e was no need o change he de aul ma ke con igu a ion o
he OpenSim. I was used a s a ic ial ile o scaling and he Measu emen Se was al eady
Me hodology
46
de ined in a ile ha came wi h he da a. The weigh ing p ocess was done by a ibu ing la ge
weigh s he ma ke s loca ed in unc ional join cen es and bone landma ks, simila ly o he
S udy 2. The ela i e weigh s used in bo h s udies can be ound in annex.
A e de ining he pa ame e s desc ibed abo e in bo h s udies, he posi ion o he expe imen al
ma ke s was manually adjus ed o ma ch he i ual ma ke s, making se e al i e a ions un il
he RMS and he maximum e o we e minimized.
4.3.4 - In e se kinema ic (IK)
The In e se Kinema ics Tool allows o de e mine he join angles and ansla ions ha bes
ep oduce he expe imen al posi ion o he ma ke s. Fo each ame, i is sol ed a leas -squa es
p oblem, in o de o minimize he weigh ed e o o each coo dina e [49]:
𝑆𝑞𝑢𝑎𝑟𝑒𝑑 𝐸𝑟𝑟𝑜𝑟= ∑𝑤𝑖(𝑥𝑖𝑠𝑢𝑏𝑗𝑒𝑐𝑡−𝑥𝑖𝑚𝑜𝑑𝑒𝑙)2
𝑚𝑎𝑟𝑘𝑒𝑟𝑠
𝑖=1 +∑𝑤𝑗(𝜃𝑗𝑠𝑢𝑏𝑗𝑒𝑐𝑡−𝜃𝑗𝑚𝑜𝑑𝑒𝑙)2
𝑗𝑜𝑖𝑛𝑡 𝑎𝑛𝑔𝑙𝑒
𝑗=1 (4.6)
Whe e 𝑥𝑖𝑠𝑢𝑏𝑗𝑒𝑐𝑡 and 𝑥𝑖𝑚𝑜𝑑𝑒𝑙 a e he h ee-dimensional posi ions o he i h ma ke , o he subjec
and he model; 𝜃𝑗𝑠𝑢𝑏𝑗𝑒𝑐𝑡 and 𝜃𝑗𝑚𝑜𝑑𝑒𝑙 a e he angles o he j h join , o he subjec and he model;
and 𝑤𝑖 and 𝑤𝑗 a e he co esponding weigh s o he ma ke s and he join s.
This ool uses as inpu he make s posi ions s o ed in he *. c ile. The weigh ing o he ma ke s
was done by a ibu ing la ge weigh s o ma ke s less suscep ible o mo emen s due o skin
and so issue du ing gai [50]. The weigh s used in bo h simula ions can be consul ed in he
annex 3.
4.3.5 - In e se dynamics (ID)
The In e se Dynamics Tool calcula es he join momen s necessa y o make he model pe o m
he desi ed kinema ics, acco ding o he basic equa ions o mo ion (Equa ions 3.4 and 3.5).
Al hough, he ollowing s eps a e no dependen on he ID esul s, his s ep was done o analyse
he join momen s and he o ces ac ing in he pel is, be o e he educ ion o he esiduals.
The ou pu *.mo ile o he In e se Kinema ics s ep was used as inpu , as well as he *.mo ile
con aining he g ound eac ion o ces, momen s and he PWA/COP. The In e se Dynamics Tool
allows he possibili y o conside he in e ac ion wi h he g ound as a body o ce, which ac s
in he cen e o mass o a body o as a poin o ce ha ac s in he PWA/COP and p oduces a
o que. The second op ion was used in bo h simula ions. Du ing his and he ollowing s eps,
he sub ala and he me a a sophalangeal join we e locked in he Coo dina es Edi o , so ha
he model was consis en wi h he kinema ics ob ained h ough he In e se Kinema ics s ep
Compu a ional Simula ion
47
47
4.3.6 - Residual educ ion algo i hm (RRA)
Wi h he pu pose o educing he esidual o ces and momen s ac ing in he model, which a e
assumed o sol e he dynamic inconsis ency be ween he expe imen al da a and he model,
he Residual Reduc ion Algo i hm Tool was used. The esidual o ces a e de e mined as
desc ibed in he Equa ion 4.7, and he e o s associa ed a e ob ained by he Equa ion 4.8.
𝐹𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙=∑𝑚𝑖𝑎𝑖−𝐹𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑠𝑒𝑔𝑚𝑒𝑛𝑡𝑠
𝑖=1 (4.7)
Whe e 𝐹𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 is he ex e nal o ce ac ing on he model; 𝑚𝑖 and 𝑎𝑖 a e he masse and
accele a ion o he i h segmen and 𝐹𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 is he esidual o ce.
𝑆𝑞𝑢𝑎𝑟𝑒𝑑 𝐸𝑟𝑟𝑜𝑟= ∑Ω𝑖(𝑞󰇘𝑗𝑑𝑒𝑠𝑖𝑟𝑒𝑑−𝑞󰇘𝑗𝑚𝑜𝑑𝑒𝑙)2
𝑗𝑜𝑖𝑛𝑡𝑠
𝑗=1 (4.8)
Whe e 𝑞󰇘𝑗𝑑𝑒𝑠𝑖𝑟𝑒𝑑 and 𝑞󰇘𝑗𝑚𝑜𝑑𝑒𝑙 a e, espec i ely, he desi ed and he e ec i e accele a ion o he
j h join and Ω𝑖 is he weigh associa ed o ha join .
This algo i hm eplaces he muscles o he model by ideal ac ua o s ac ing in each coo dina e,
and each one has an op imal o ce and an exci a ion con ol associa ed. The o ce p oduced
by he ideal ac ua o is hen gi en by he Equa ion 4.9.
𝐹𝑜𝑟𝑐𝑒𝑖𝑑𝑒𝑎𝑙 𝑎𝑐𝑡𝑢𝑎𝑡𝑜𝑟=𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝐹𝑜𝑟𝑐𝑒× 𝐸𝑥𝑐𝑖𝑡𝑎𝑡𝑖𝑜𝑛 (4.9)
The ool uses as inpu s he iles con aining he kinema ics and he g ound eac ion o ces and
wo XML iles:
- Ac ua o s ile, whe e a e desc ibed he ideal ac ua o s and hei p ope ies: op imal o ce,
poin o applica ion ( o poin ac ua o s), bodies (in he case o o que ac ua o s) and he
minimum and maximum exci a ion;
- Tasks ile, which speci ies he ela i e weigh a ibu ed o each join .
Ini ially i was done an ini ial pass o e i y i he model was s ong enough o ep oduce he
kinema ics. Ac ua o s ha equi e lowe con ols o gene a e o ce a e less expensi e o he
algo i hm and, consequen ly, i elies in hese ac ua o s. Thus, in he ini ial pass, high op imal
o ces we e a ibu ed o esidual poin ac ua o s (Fx, Fy and Fz) and o esidual o que
ac ua o s (Mx, My and Mz) and he weigh s we e he same o each ac ua o . The esul s we e
analysed and he op imal o ces o esidual ac ua o s we e dec eased o o ce he algo i hm
o use he coo dina e ac ua o s (join ac ua o s) ins ead o he esidual ones. Fo each i e a ion
Me hodology
48
he e o associa ed o each coo dina e was e i ied and he weigh s o he coo dina es wi h
high e o we e inc eased o imp o e hei acking. This was done un il an op imal solu ion
was ound, in which he RMS and he maximum alues o he esiduals and he e o s we e
conside ed accep able, acco ding o [50]. I is impo an o e e ha , since he sub ala and
he me a a sophalangeal join s we e kep locked, he e we e no include in he asks ile,
because hey we e no acked. And he ac ua o s ac ing in hese join s we e emo ed.
A he end o he p ocess, OpenSim au oma ically adjus s he COM (Cen e o Mass) o he o so
and sugges s mass adjus men s o each one o he bodies, in o de o educe he esidual o ces,
which we e applied o he model be o e he nex s ep.
4.3.7 - Compu ed muscle con ol (CMC)
Compu ed Muscle Con ol Tool was used o de e mine how he muscles o he model ac ua es
o p oduce he mo emen . This algo i hm uses a combina ion o a p opo ional-de i a i e (PD)
con ol and s a ic op imiza ion, as shown in he scheme o he Figu e 4.11.
Figu e 4. 11. Scheme o he CMC algo i hm used in gai [59].
S a ic op imiza ion dis ibu es he load o he muscles, which a e syne gis ic ac ua o s, o
each ime ins an . This p ocess uses a pe o mance c i e ion ha is in ended o be minimized,
wi h wo possible o mula ions: slow and as a ge (Equa ion 4.10). The as a ge app oach,
gene ally ecommended by p oducing be e acking [50], was used in bo h simula ions.
𝐽=∑𝑥𝑖2𝑛𝑥
𝑖=1 ;𝐶𝑗=𝑞󰇘𝑗∗−𝑞󰇘𝑗∀𝑗 (4.10)
Whe e 𝐽 is he pe o mance c i e ion; 𝑥𝑖 is he exci a ion o he i h ac ua o ; 𝑞󰇘𝑗∗ and 𝑞󰇘𝑗 a e he
desi ed and he ob ained accele a ions o he j h join ; and 𝐶𝑗 is he equali y cons ain (C=0),
ha equi es he di e ence be ween he desi ed and ob ained accele a ion o be wi hin he
ole ance alue, in his case was used 0,00001.
Summa y
49
The ile inpu s o CMC a e:
- *.mo ile desc ibing he kinema ics, ob ained wi h he RRA;
- *.mo ile wi h g ound eac ion o ces ( he same used in ID);
- *.xml iles con aining:
- model ac ua o s: muscles, he ese e and esidual ac ua o s and hei p ope ies.
The ese e ac ua o s a e ideal ac ua o s ha
- con ol cons ain s, whe e a e speci ied he maximum and minimum exci a ion o
he ac ua o s desc ibed in he model ac ua o s ile;
- asks which con ains he ela i e weigh s o each coo dina e, simila ly o he asks
ile om RRA.
Simila ly o he RRA s ep, i was made an ini ial pass wi h la ge op imal o ces o esidual and
ese e ac ua o s and he same weigh s o each coo dina e. In he ollowing i e a ions he
op imal o ces o ese es and esiduals we e educed and he con ols cons ains inc eased,
so ha he con olle choose o ely on muscles ins ead o esidual and ese e o ces. The
i e a ions we e s opped when he esiduals, ese es and e o s associa ed we e educed
enough o accep able alues.
4.4 - Summa y
The da a om a gai ial pe o med wi h pos -s oke indi idual was ex ac ed om a *.c3d ile
and p ocessed using he BTK in Ma lab and a *. c and a *.mo ile we e ob ained. The i s one
s o es he ma ke ajec o y da a (kinema ic) and he second one s o es he g ound eac ion
o ce da a (kine ic). These wo iles we e used as inpu s in he OpenSim simula ion desc ibed
in he nex chap e .
Two gai simula ions we e pe o med using OpenSim, one wi h a subjec conside ed heal hy
and he o he wi h a pos -s oke indi idual. F om he co esponden expe imen al da a, i was
de e mined he join angles and o ques, using in e se kinema ics and in e se dynamics,
espec i ely, he esidual o ces and momen s ac ing in he model we e educed ( h ough RRA)
and inally, he muscula beha iou was de e mined using CMC.

50
51
Chap e 5
Resul s and discussion
5.1 - In oduc ion
In his chap e he esul s a e p esen ed and discussed. In he i s pa , he esul s om he
ex ac ion om a *.c3d ile and he p ocessing o he expe imen al da a used in he S udy 2
a e p esen ed. Secondly, he esul s ob ained in each s ep o he wo k low o he OpenSim a e
shown and analysed. In he case o he S udy 1, since i consis s in a simula ion o a heal hy
indi idual, he alues o he join angles and momen s and he muscle ac i a ions and powe s
we e compa ed wi h he a ailable e e ence alues in he li e a u e. Fo he S udy 2, hese
pa ame e s we e also compa ed wi h he li e a u e abou pos -s oke gai .
In bo h cases, an analysis o he muscula ac i a ion and powe s o he p incipal plan a lexo
muscles (soleus and medial gas ocnemius), he main do si lexo ( ibialis an e io ) and one
hams ing (semimemb anosus) was done and analysed oge he wi h he esul s o he
kinema ics.
5.2 - Expe imen al da a
The da a ep esen ing he 3D posi ion o he ma ke s was no subjec ed o p ocessing, since i
was no co up ed wi h noise. The so wa e used in he da a collec ion (Qualisys T ack Manage )
includes pos -p ocessing o he ma ke da a, elimina ing he need o il e ing o emo e he
noise [60]. Using he so wa e MLSViewe , a Mo ion Lab Sys ems So wa e © o display he
Resul s and discussion
52
con en s s o ed in a *.c3d ile [61], i is possible o isualize he eco ded ajec o y o he
ma ke s. In he Figu e 5.1 i is shown he ajec o y o he ma ke placed in he heel o le
oo (LBACKFOOT) in he h ee di ec ions (x, y and z o he labo a o y coo dina e sys em),
using MLSViewe , whe e is possible o see ha he da a is clean. Besides, his da a was
au oma ically il e ed in OpenSim when using he IK, ID and RRA Tools, as ecommended in he
OpenSim guide [50].
Figu e 5.1. Visualiza ion o he posi ion, in he h ee di ec ions x, y and z (labo a o y coo dina e sys em)
o he ma ke RBACKFOOT o he pos -s oke indi idual, in MLSViewe .
The o ce pla o ms used in he expe imen al ial and conside ed in his s udy we e o ype 2,
meaning ha each one has six ou pu channels o analog da a o he h ee componen s o he
o ce and o he momen s ac ing in he o igin o he o ce pla o m [48]. This da a was s o ed
in a *.c3d, which con ained also he scale ac o s and he calib a ion ma ixes necessa y o
con e he aw da a (elec ic ou pu ) in o o ce da a. This ope a ion has been done by using
he BTK, which has wo dis inc unc ions, bo h used in his wo k. Since he code o he
unc ions is no a ailable, i is no possible o analyse he each s ep o he ope a ions
pe o med. The ou pu o he unc ion b kGe Fo cePla o mW enches is he alue o he o ces
and momen s in he o igin o he o ce pla o m, consequen ly his unc ion only needs o
ans o m he elec ical signal o he o ce pla e, using he scale and calib a ion in o ma ion,
in o o ce and momen da a. On he o he hand, acco ding o he in o ma i e webpage o he
BTK [62], he unc ion b kGe G oundReac ionW enches, which gi es he o ces, loca ion o he
PWA and he momen s de ined in ha poin , in addi ion o his ans o ma ion, de e mines he
PWA and he momen s on i , by using he o mula de eloped by Shimba [63] which also was
desc ibed in Za sio sky [55].
Expe imen al da a
53
Rega ding he loca ion o he COP and he PWA, all h ee componen s o he posi ion did no
show conside able di e ences, sugges ing ha he dis ance be ween his wo poin s is no
ele an .
I was e i ied ha he alues o he o ces ob ained wi h he wo unc ions we e he same, as
expec ed. The e ical momen s showed small dissimila i ies which mean once mo e ha he
loca ion o he PWA and he COP is e y small. In ac , hese di e ence o posi ions is explained
by he ho izon al momen s abou he PWA ha , in his case, a e e y small (Figu e 5.2).
Figu e 5.2. G ound eac ion momen in he e ical di ec ion (My, conside ing he OpenSim coo dina e
sys em) in he PWA, ob ained using he unc ion b kGe G oundReac ionW enches (PWA Righ My and PWA
Le My) and he ee-momen ac ing in he COP, o he igh and le legs o he pos -s oke indi idual.
Rega ding he ho izon al momen s in he PWA (Figu e 5.3), i we e e i ied abno mal peaks in
he beginning and he end o he con ac phases. By analysing di ec ly he da a o he ho izon al
momen s ob ained wi h he unc ion b kGe G oundReac ionW enches, i was no iced ha he
ime o he beginning and o he end o he con ac , assumed o be whe e he e ical o ce is
highe han ze o, i does no coincide wi h he delimi a ion o he con ac in he ho izon al
momen s.
The ound peaks could be smoo hed by in e pola ing he da a a he ini ial and inal momen s
o con ac . Howe e , i is impo an o no ice ha he alue o he ho izon al momen s is e y
R_IC
L_TO
L_IC
R_TO
R_IC
L_TO
L_IC
R_TO
-6
-4
-2
0
2
4
6
1,0 1,1 1,3 1,4 1,5 1,6 1,8 1,9 2,0 2,1 2,3 2,4 2,5 2,7 2,8 2,9 3,0 3,2 3,3 3,4 3,6 3,7 3,8 3,9
Momen (N.m)
Time (s)
E en s PWA Righ My PWA Le MY COP Righ My COP le My
Resul s and discussion
60
The e o s associa ed wi h he acking o he ma ke s du ing he in e se kinema ics p ocess
we e sa is ac o y o he S udy 2, bu exceeded he ecommended limi s in he S udy 1 (Table
5.3). The maximum e o egis e ed in his s udy is associa ed wi h he ma ke R.Ac omium,
which had associa ed a lowe acking weigh .
The IK p ocess is e y dependen o he scaling p ocess [50] and consequen ly, he high e o s
egis e ed in he IK o he S udy 1 migh be ela ed wi h he e o s ob ained in he
co esponding scaling p ocess.
Table 5. 3 Ma ke e o (RMS) and maximum e o associa ed wi h he scaling p ocess o he models
in he S udy 2 and S udy 1 and he espec i e limi alues ecommended in [50].
S udy 1
S udy 2
Recommended limi s
Ma ke e o : RMS (cm)
2.25
1.19
< 2
Max e o (cm)
8.56 (R.Ac omium)
3.98 (RMK)
< 2-4
5.3.3- In e se dynamics
Using in e se dynamics, he model ied o ep oduce he mo emen de e mined by in e se
kinema ics in he p e ious s ep while subjec ed o he ex e nal o ces and momen s con ained
in he *.mo iles c ea ed.
Making a i s analysis o he o ce ha ac s in he pel is, highe peaks in he e ical o ce
(Fy) a e obse ed in he ins an s o ini ial con ac o he wo limbs (Figu e 5.6). I he e ical
g ound eac ion o ces a e plo ed in he same g aph as he o ces ac ing in he pel is, om
ID, (Figu e 5.7) he e is a coincidence wi h dec ease o he peaks and he beginning o he
con ac . Indeed, he e ical o ce ac ing in he pel is appea s o be compensa ing he
inexis ence o a o ce in he ins an s be o e Fy becomes di e en om ze o. This o ce is he
majo o ce componen and accoun s o he e ical accele a ion o he cen e o mass and
he cha ac e is ic cu e o his o ce includes a quick inc ease a e heel s ike [67]. Howe e
he e ical o ce ob ained has an ab up inc ease, e i ied in hese ins an s, which ise om
ze o o 130 N (in he le ini ial con ac ) and 125 N ( igh ini ial con ac ) in a small in e al o
ime. To minimize he e o s o igina ed om his, smoo hing he da a could be done in he
p ocessing s ep.

OpenSim Simula ion
61
Figu e 5. 6. Fo ces ac ing in he pel is, ob ained using ID, be o e educing he esiduals. The blue line
ep esen he e ical esidual o ce, he ed and he g een ep esen he ho izon al esidual o ces (Fx
and Fy).
Figu e 5. 7. Plo o he e ical GRF ac ing on he le ( ed) and igh (blue) legs and he o ce ac ing in
he pel is (g een).
Conside ing he di e ences be ween indi iduals in he size and weigh o he segmen s, in
o de o compa e he join momen s wi h he li e a u e is necessa y o scale hese alues in
new on-me e s pe kilog am body mass.
Resul s and discussion
62
Figu e 5. 8. Re e ence in e nal join momen s o he hip, knee and ankle acco ding o [1], in N.m/Kg,
o one gai cycle. The gai e en s a e ep esen ed as: IC – ini ial con ac ; OT – opposi e oe-o ; HR –
heel ise; OI – opposi e ini ial con ac ; TO – oe-o ; FA – ee -adjacen ; TV – ibia e ical
Compa ing he esul s o hip join momen s ob ained in he heal hy subjec om he S udy 1
(Figu e 5.9) wi h he alues ound in he li e a u e (Figu e 5.8), he momen cu e has a simila
shape, howe e , he wo legs show di e en ange alues: -0.8/ 0.5 N.m/Kg o he igh leg
and -0.6/0.6 N.m/Kg o he le leg. Also he knee momen ob ained in his simula ion is in
ag eemen wi h he e e ence, hough he e we e ound di e ences be ween he wo legs in
he maximum hip lexion, a ini ial con ac : he igh leg eached a momen o -0.7 N.m/Kg
and he le -0.6 N.m/Kg.
Rela i ely o he ankle, he maximum plan a lexo momen i was highe han he e e ence
alues (app oxima ely -1 N.m/Kg) in bo h limbs and he igh leg egis e ed a highe alue (-
1.77 N.m/Kg) han he le (1.50 N.m/Kg).
No mal gai is assumed o be symme ic, e en hough i is accep ed a small deg ee o
asymme y, which is negligible in heal hy subjec s [68]. The esul s do no show conside able
di e ences be ween bo h sides.
Rela i ely o he S udy 2, ID was pe o med using he ex e nal o ce da a conside ing he COP
and he PWA. Analysing he esul s ob ained, he e was no ound conside able di e ences
be ween hem. The cu es show he simila shape and maximum and minimum momen alues.
In he Figu e 5.9 he join momen s ob ained using he PWA a e shown. The maximum hip
lexion momen was highe o he IPSI limb (0.52 N.m/Kg) compa ing o he CONTRA limb (0.45
OpenSim Simula ion
63
N.m/Kg), while he maximum hip ex ension momen o he IPSI limb was -0.80 N.m/Kg and
o he CONTRA limb -0.70 N.m/Kg.
Rega ding he knee momen , i was ound a lowe knee lexo momen in he CONTRA limb (-
0.16 N.m/Kg) be o e he ini ial con ac , compa ing o he IPSI limb in he co esponden ini ial
con ac (-0.32 N.m/Kg). Howe e , i is obse ed high abno mal peaks happening du ing he
ini ial con ac , in bo h sides, ha also occu in he hip momen da a, highe han he ones ha
appea in he in e se dynamics esul s om he S udy 1.
The ankle plan a lexo maximum momen di e sligh ly om one limb o he o he (-1.47
N.m/Kg in he IPSI limb and -1.40 N.m/Kg in he CONTRA limb). In bo h limbs i was no ound
he do si lexo momen a e ini ial con ac as expec ed, by looking a he cu e ound in he
li e a u e. An abno mal peak appea ed in he IPSI limb du ing i s ini ial con ac .
Resul s and discussion
64
Figu e 5. 9. Hip, knee and ankle join momen s ob ained wi h in e se kinema ics, o he S udy 1 ( i s ow) and he S udy 2 (second ow). The blue line e e s o he igh
limb (IPSI limb in he S udy 2) and he ed line o he le limb (CONTRA limb in he S udy 2).
-1
-0,5
0
0,5
1
0 7 13 20 27 33 40 47 53 60 67 73 80 87 93 100
Momen (N.m.Kg)
Gai cycle (%)
Hip lexion momen
-1
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
0 7 13 20 27 33 40 47 53 60 67 73 80 87 93 100
Momen (N.m.Kg)
Gai cycle (%)
Knee ex ension momen
-2
-1,5
-1
-0,5
0
0,5
0 7 13 20 27 33 40 47 53 60 67 73 80 87 93 100
Momen (N.m.Kg)
Gai cycle (%)
Ankle do si lexion momen
-1
-0,5
0
0,5
1
014 28 43 57 71 85 99
Momen (N.m.Kg)
Gai cycle (%)
Hip lexion momen
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0,2
0,3
0,4
014 28 43 57 71 85 99
Momen (N.m.Kg)
Gai cycle (%)
Knee ex ension momen
-2
-1,5
-1
-0,5
0
0,5
1
014 28 43 57 71 85 99
Momen (N.m.Kg)
Gai cycle (%)
Ankle do si lexion momen
OpenSim Simula ion
65
5.3.4- Residual educ ion algo i hm
The educ ion o he esiduals was success ully accomplished in bo h s udies 1 and 2, acco ding
o he ecommended in he OpenSim guide [50], as i is possible o e i y by analysing he Table
5.4 . The bes esul s we e ob ained o he S udy 1, in which he alues o maximum and RMS
esiduals and e o s we e inside he op imal limi . In he S udy 2, h e esiduals o e passed he
op imal h eshold, howe e , dec easing esiduals would inc ease he e o s associa ed wi h he
kinema ics beyond he accep able alues. Analysing he plo o he esidual o ces in he S udy
2 (conside ing he PWA), i is possible o see peaks in he e ical o ce (Fy), in he poin o
he igh and le ini ial con ac , also e i ied in he in e nal momen s om ID. Howe e , i is
e i ied a dec ease o he magni ude o hese peaks, a e he educ ion o he esiduals (Figu e
5.10).
Figu e 5. 10. Residuals o ces ob ained in RRA o he S udy 1, using PWA. The blue line ep esen he
e ical esidual o ce, he ed and he g een ep esen he ho izon al esidual o ces (Fx and Fy).
In ID, he ac ion o ex e nal o ces (GRF) is balanced only wi h he body o ces, while in RRA
he esiduals ha a e he o ces and momen s ac ing in he pel is a e educed and,
consequen ly, his educ ion is compensa ed by changes in he ac ua ion o he o he join
ac ua o s.
The e a e no e e ence alues o e alua e he dimension o he o al mass adjus men
ecommended by a e he RRA s ep. In bo h cases i was less han 1%, being lowe o he
heal hy model (S udy 1). This migh no be ela ed wi h he pa hology, bu wi h he
expe imen al da a i sel , since he RRA in ends o compensa e o dynamic inconsis encies.

Resul s and discussion
66
Table 5. 4 Maximum and RMS alues o he esidual o ces and momen s and o a ional e o s ob ained
o he RRA o he S udy 2 and S udy 1 and he ecommended [50] op imal and maximum h esholds.
Rela i ely o he S udy 2, he RRA was also pe o med ha ing he GRF conside ing he COP and
he PWA, o e i y he in luence mainly he in luence o he ho izon al momen s in he
simula ion. In bo h cases i was used he same se ings o he ac ua o s and asks. Small
di e ences we e de ec ed in wha conce ns o he in e nal join momen s an he esiduals
ob ained. The highes di e ence e i ied be ween he wo analysis was ound in he maximum
o a ional e o associa ed wi h he igh ankle, which was 1,57º when he PWA is conside ed
and -3,00º o he analysis using he COP. The weigh associa ed wi h he igh ankle was
inc eased o a emp o diminish he e o in acking his join , howe e , he e o was no
diminished. This means ha he model canno ack he mo ion comple ely wi hou he ac ion
S udy 1
S udy 2
Absolu e
op imal
h eshold
Absolu e max
h eshold
COP
PWA
Max Residual
Fo ces (N)
-7,21
(Fx)
-19,00 (Fz)
-17,27 (Fz)
< 10
< 25
RMS Residual
Fo ces (N)
3,26
6,98
7,10
< 5
< 10
Max Residual
momen s (Nm)
-22,80
(Mz)
-62,13
(Mx)
-58,66
(Mx)
< 50
< 75
RMS Residual
Momen s (Nm)
9,08
15,17
16,32
< 30
< 50
Max ansla ional
e o (cm)
-1,09
(Pel is
x)
-2,89
(Pel is z)
-2,83
(Pel is z)
< 2
< 5
RMS ansla ional
e o (cm)
0,61
1,31
1,35
< 2
< 4
Max o a ional
e o (deg)
-0,40
(Righ
hip
lexion)
-3,00
(Righ
ankle
angle)
-1,57
(Righ
ankle
angle)
< 2
< 5
RMS o a ional
e o (deg)
0,16
0,64
0.58
< 2
< 5
To al mass
adjus men (Kg)
-0,05
-0,43
-0,56
-
-
To al mass
adjus men (%)
-0,07%
-0,45%
-0,58%
-
-
OpenSim Simula ion
67
o he esidual o ces and i s dec ease, pa icula ly in he ins an s we e he peaks exis , caused
e o s in acking he kinema ics.
In he nex s ep (CMC) i was used he PWA app oach o he ex e nal o ces, since he
maximum e o associa ed was lowe and i will dec ease he accumula ion o e o s in
kinema ics in he inal esul .
5.3.5- Compu e muscle con ol
The esul s o he kinema ics compu ed in he p e ious s ep we e used as he mo ion o ack
du ing CMC. Fo bo h s udies i was pe o med se e al i e a ions in o de o y o ind he
op imal solu ion, in which he esiduals, ese es and e o s we e inside he op imal, o a
leas , he accep able limi s. In he Table 5.5 a e shown he esul s o hese pa ame e s. The
esul s ela i e o he S udy 1 a e sa is ac o y since all he pa ame e s a e inside he op imal
h eshold. In he case o he S udy 2, he maximum alues o esidual momen s, o a ional
e o and ese e o ce su passed his op imal limi , bu s ill accep able. Howe e , i was
ob ained a peak o 130,60N o esidual e ical o ce (Fz) in he simula ion using he PWA, in
he igh ini ial con ac (Figu e5.11).
Table 5. 5 Maximum and RMS alues o he esidual o ces and momen s, ese e o ces and ansla ional
and o a ional e o s ob ained o he CMC o he S udy 2 and S udy 1 and he ecommended [50] op imal
and maximum h esholds.
S udy 1
S udy 2 (PWA)
Op imal
h eshold
Max
h eshold
Max Residual Fo ces (N)
-8,83 (Fx)
130,66 (Fz)
< 10
< 25
RMS Residual Fo ces (N)
3,37
12,85
< 10
< 25
Max Residual momen s
(Nm)
-22,39 (Mz)
59,31 (Mx)
< 50
< 75
RMS Residual Momen s
(Nm)
9,43
15,76
< 30
< 50
Max ansla ional e o
(cm)
-0,01 (Pel is z)
0,10 (Pel is z)
< 1
< 2
RMS ansla ional e o
(cm)
5,31E-3
0,02
< 1
< 2
Max o a ional e o
(deg)
-0,38
(Le knee
angle)
-6,54
(Righ ankle angle)
< 2
< 5
Resul s and discussion
68
RMS o a ional e o
(deg)
0,09
0,46
< 2
< 5
Max Rese e (N.m)
3.12
(Le ankle
angle)
-64,61
(Righ knee angle
ese e)
< 25
< 50
RMS Rese e (N.m)
0,12
2,96
< 10
< 25
Figu e 5. 11. G aph showing he alue o he esidual o ces Fx ( ed), Fy (blue) and Fz (g een) ac ing in
he pel is, esul ing om CMC.
The igh ankle had he highes acking e o associa ed (-6,54º). Looking a he cu e o he
igh ankle kinema ics a e RRA and a e CMC (Figu e5.12, i is possible o see ha he e o
s a s om he igh ini ial con ac , he ins an whe e he la ge esiduals we e ob ained,
sugges ing a ela ion be ween his occu ences. Simila ly, in he p e ious s ep (RRA) he la ges
acking e o was associa ed wi h he igh ankle angle, e en hough was inside he accep able
limi s. Also in he ins an o igh ini ial con ac i we e e i ied high ese e momen s in he
igh side: he igh knee ese e ac ua o eached he maximum ese e alue (-64,61 N.m)
and also he igh ankle egis e ed 50,20 N.m. Dec easing he op imal o ce o his ese e
ac ua o s, so ha he model would no use hem, leads o in e up ion o CMC p ocess, meaning
ha he model needs he ac ion o hese ac ua o s o ollow he kinema ics.
I could be hypo hesized ha he locking o he sub ala and me a a sophalangeal join s could
in luence he e o s in acking he ankle mo emen , bu i was no e i ied he same p oblem
in he le ankle, which was sa is ac o ily acked in he CMC (0.69º), making his hypo hesis
less plausible.
OpenSim Simula ion
69
Figu e 5. 12. Righ ankle angle e o . The ed line co esponds o he igh ankle angle ob ained a e
RRA and he blue line ep esen s he igh ankle angle a e CMC.
5.3.6- Muscle ac ion
The ou pu iles o he CMC include:
- Join kinema ics (posi ion and angula eloci y and accele a ion) and in he case
o he pel is also he linea eloci y and accele a ion;
- T acking e o s o he kinema ics;
- Ac ua o (muscle and ese es) o ces and powe s;
- Ac ua o (muscle and ese es) powe s;
- Con ols: exci a ion pa e ns o each ac ua o ;
- S a es: muscle ac i a ion and ibbe leng h.
The ac i a ion pa e n o each ese e and esidual ac ua o is di ec ly linked o he espec i e
exci a ion, since he ac i a ion is he esul o he p oduc o he exci a ion by he op imal
o ce [50]. In he case o he muscles, he ac i a ion is ob ained h ough he exci a ion-
ac i a ion dynamics (Figu e 3.4), desc ibed by he di e en ial equa ion 3.3, esul ing in some
ime delay be ween exci a ion and ac i a ion.
The analysis o he muscle o ce h ough ime is no enough o a be e unde s anding o he
beha iou o he muscles. Since a muscle can p oduce o ce isome ically (no ibbe leng h
changing), concen ically (p oduces o ce by con ac ing in he same di ec ion o he
mo emen ) and eccen ically p oduces o ce by leng hening in he di ec ion o he mo emen )
and also can change i s leng h and no exe o ce [1, 4]. Consequen ly, o do a mo e comple e
analysis is necessa y o s udy he muscle ac i a ion oge he wi h he kinema ics in he
espec i e ime, o e i y he ac i a ion and he di ec ion o he mo emen . When a muscle
con ac s concen ically, i p oduces ene gy, meaning ha i gene a es posi i e powe , while
eccen ic con ac ion leads o ene gy abso bing and, consequen ly nega i e powe [1]. Since
powe is he a ia ion o ene gy (joule) wi h ime, i s uni s a e joule pe second (J/s) wa (W).
Resul s and discussion
76
Figu e 5. 15. Ac i a ion and powe associa ed wi h he muscles SOL, MEDGAS, TA, SMEMB, ob ained in CMC (S udy 2). The ed line e e s o he CONTRA limb and he blue
line e e s o he IPSI limb.
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
011 24 37 47 55 63 76 89 98
Ac i a ion
Gai cycle (%)
TA ac i a ion
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
011 24 37 47 55 63 76 89 98
Ac i a ion
Gai cycle (%)
SMEMB ac i a ion
-300
-250
-200
-150
-100
-50
0
50
100
150
011 24 37 48 55 64 77 89 98
Powe ( W)
Gai cycle (%)
TA powe
-40
-30
-20
-10
0
10
20
30
40
50
60
011 24 37 48 55 64 77 89 98
Powe (W)
Gai cycle (%)
SMEMB Powe

Summa y
77
5.4 - Summa y
Two simula ions o gai we e de eloped, one using no mal gai and o he using pos -s oke gai .
The expe imen al da a used o simula e pos -s oke gai was ex ac ed om a *.cd3 ile and
he espec i e o ce pla o m da a was used o compu e he o ces and momen s ha ac in
he PWA and in he COP. The esul s showed no ele an di e ences be ween he loca ion o
hese poin s and he momen s in he ho izon al plane we e small compa ing o he e ical
momen .
The kinema ics and join momen s ob ained o he heal hy model e ealed o be in acco dance
wi h he e e ence. Howe e , he muscula ac i a ions showed some asymme y and, in he
case o he TA and he SMEMB, hese muscles we e ac i a ed in ins an s o he cycle whe e i
doesn’ happen in he e e ence.
The kinema ics o he pos -s oke model, howe e , showed only low plan a lexion as he main
impai men and he esul s om CMC o he plan a lexo muscles showed ea ly ac i a ion,
bu no diminished in he pa e ic side. These muscles appea ed o be able o gene a e he
necessa y powe be o e p opulsion. The hams ing muscle (SMEMB) om he CONTRA limb,
showed p olonged ac i a ion du ing s ance phase, which i is usually epo ed in he li e a u e
as a compensa o y mechanism o plan a lexo weakness.
This model had associa ed high acking e o o he igh ankle and high magni ude esiduals
and ese es a he ins an o igh ini ial con ac , sugges ing ha i was no able o ep oduce
i s kinema ics elying mainly in he muscula ac ua o s.
78
79
Chap e 6
Final conclusions and u u e
de elopmen s
6.1- Final conclusions
The aim o his disse a ion consis ed in simula e heal hy and a pa hological gai , speci ically
pos -s oke gai , using compu a ional me hods, s a ing om expe imen al da a.
Fi s ly, he undamen als o human gai we e explo ed, ega ding he ana omy and he
neu omuscula con ols in ol ed. A e ha , gai impai men s in he sequence o a s oke we e
s udied and desc ibed. The expe imen al me hodologies used o collec kine ic and kinema ic
da a and he ma hema ical models ha se e as undamen als o he compu a ional ools o
biomechanical modelling we e e iewed and desc ibed.
The p ocedu e o ob ain he expe imen al kinema ic and kine ic da a om a *.c3d ile was
desc ibed, as well as i s p ocessing and con e sion in o *. c and *.mo iles o use as inpu in
OpenSim. Following, he implemen a ion o he OpenSim wo k low desc ibed o each s ep o
bo h simula ions.
The esul s ob ained o he model o he heal hy indi idual we e in acco dance wi h he
li e a u e, when he join angles and momen s we e compa ed, despi e small asymme ies,
accep ed in heal hy subjec s. The muscula ac ua o s we e ac i a ed acco ding o he
e e ence, howe e he TA and SMEMB ac ua o s we e also ac i a ed in o he unp edic ed
ins an s.
Rega ding he pos -s oke model, he kinema ics associa ed e ealed low plan a lexion in he
CONTRA limb, cha ac e is ic om he pos -s oke gai . The hams ing muscle SMEMB also
Final conclusions and u u e de elopmen s
80
showed p olonged ac i a ion du ing CONTRA limb s ance, which migh be associa ed wi h he
g adual dec ease o hip lexion. Howe e , he muscle ac i a ions o he plan a lexo s only
showed diminished ac i a ion in he medial gas ocnemius and in bo h plan a lexo s, SOL and
MEDGAS, showed ea ly ac i a ion, as i is desc ibed in pos -s oke gai li e a u e. I is impo an
o conside ha he model was no able o comple ely ep oduce he kinema ics and e en
hough acking e o s we e expec ed, he igh ankle angle had associa ed an e o ha
o e passed he accep able limi s. Indeed, i was e i ied ha he model had o use he esidual
and ese e ac ua o s, e en hough hese ac ua o s we e mo e expensi e o he con olle .
6.1- Limi a ions
The limi a ions o he p esen wo k a e mainly ela ed wi h he expe imen al da a used. Less
was known abou he indi iduals and he condi ions o collec ion o expe imen al da a.
Conce ning he pos -s oke pa ien , impo an in o ma ion abou he pa hology his o ical was
unknown: se e i y and a ec ed b ain a ea, ime pas a e he acciden and i he had ecei ed
physio he apy. Also he pos -s oke indi idual used in he p esen wo k did no show
accen ua ed impai men s in gai , since he was mainly a ec ed in he uppe limbs.
6.2- Fu u e wo k
As u u e wo k i is p oposed o pe o m gai e alua ions o a heal hy and a pos -s oke
indi iduals wi h simila age, body heigh and weigh , in he same condi ions (use o he same
numbe o ma ke s, pe o m a s a ic ial o scaling, making measu emen s o body segmen s
and o al heigh and body mass) and use EMG o assess he muscula ac i a ion expe imen ally.
Taking pic u es o he indi idual and eco d in ideo he gai ial would help o ind subjec -
speci ic cha ac e is ics and o iden i y sou ces o e o ela ed o i .
Using he wo models could be pe o med an Induced Accele a ion Analysis (IAA) in OpenSim,
wi h he pu pose o ob aining he muscle con ibu ions o he accele a ion o he cen e o
mass. An addi ional s udy could be done, by s a ing om a heal hy model and diminishing he
ac i a ion o speci ic muscles ( o example he plan a lexo s and he do si lexo s) and analyse
he muscle compensa ions used by he model o ep oduce he heal hy gai .
81
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85
Annex
Annex 1 - Expe imen al body ma ke s
Table 6.1 Co espondence be ween he ma ke se used in he gai ial pe o med in he LABIOMEP and
he de aul ma ke se used in OpenSim. The X indica es ha a ma ke is no included in he espec i e
con igu a ion.
RIGHT BODY
LEFT BODY
HEAD AND TORSO
LABIOMEP
OPENSIM
LABIOMEP
OPENSIM
LABIOMEP
OPENSIM
RAC
R.Ac omium
LAC
L.Ac omium
X
Top.Head
RASIS
R.ASIS
LASIS
C7
X
RPSIS
X
LPSIS
X
STERN
S e num
X
R.Thigh.Uppe
X
L.Thigh.Uppe
X
V.Sac al
X
R. Thigh.F on
X
L. Thigh.F on
X
R. Thigh.Rea
X
L. Thigh.Rea
RLK
R.Knee.La
LLK
L.Knee.La
RMK
R.Knee.Med
LMK
L.Knee.Med
X
R.Shank.Uppe
X
L.Shank.Uppe
X
R.Shank.F on
X
L.Shank.F on
X
R.Shank.Rea
X
L.Shank.Rea
RLA
R.Ankle.La
LLA
L.Ankle.La
RMA
R.Ankle.Med
LMA
L.Ankle.Med
RFOOT1
X
LFOOT1
X
RFOOT4
X
LFOOT4
X
X
R.Mid oo .Sup
X
L.Mid oo .Sup
X
R.Mid oo .La
X
L.Mid oo .La
X
R.Toe.La
X
L.Toe.La
X
R.Toe.Med
X
L.Toe.Med
X
R.Toe.Tip
X
L.Toe.Tip
RBACKFOOT
R.Heel
LBACKFOOT
L.Heel