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Ci a ion: Paulino, M.F.; Rosei o, L.M.;
Balacó, I.; Ne o, M.A.; Ama o, A.M.
E alua ion o Bone Consolida ion in
Ex e nal Fixa ion wi h an
Elec omechanical Sys em. Appl. Sci.
2022,12, 2328. h ps://doi.o g/
10.3390/app12052328
Academic Edi o : An onio Sca ano
Recei ed: 10 Janua y 2022
Accep ed: 16 Feb ua y 2022
Published: 23 Feb ua y 2022
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applied
sciences
A icle
E alua ion o Bone Consolida ion in Ex e nal Fixa ion wi h an
Elec omechanical Sys em
Ma ia F. Paulino 1,* , Luis M. Rosei o 1,2 , Inês Balacó3, Ma ia A. Ne o 1and Ana M. Ama o 1
1Depa men o Mechanical Enginee ing, Cen e o Mechanical Enginee ing,
Ma e ials and P ocesses (CEMMPRE), Uni e si y o Coimb a, 3030-788 Coimb a, Po ugal;
l osei [email p o ec ed] (L.M.R.); [email p o ec ed] (M.A.N.); ana.ama [email p o ec ed] (A.M.A.)
2Poly echnic o Coimb a, ISEC, Rua Ped o Nunes–Quin a da No a, 3030-199 Coimb a, Po ugal
3
Pedia ic O hopedics Se ice o he Pedia ic Hospi al o Coimb a—CHUC, EPE, 3004-561 Coimb a, Po ugal;
[email p o ec ed]
*Co espondence: [email p o ec ed]; Tel.: +351-239-790-700
Fea u ed Applica ion: The indings o his wo k can help doc o s decide when i is app op ia e
o emo e he ex e nal ixa o .
Abs ac :
The moni o ing o ac u e o os eo omy healing is i al o o hopedis s o help ad ise, i
necessa y, seconda y ea men s o imp o ing healing ou comes and minimizing pa ien su e ing. I
has been decades since os eo omy s i ness has been iden i ied as one main pa ame e o quan i y and
quali y he ou come o a egene a ed callus. S ill, adiog aphic imaging emains he cu en s anda d
diagnos ic echnique o o hopedis s. Hence, wi h ecen echnological ad ancemen s, enginee s
need o use he new b anches o knowledge and imp o e o inno a e diagnos ic echnologies. An
elec omechanical sys em was de eloped o help diagnose changes in os eo omy s i ness ea ed
wi h he ex e nal ixa o LRS O ho ix
®
. The concep was e alua ed expe imen ally and nume ically
du ing ac u e healing simula ion using wo di e en models: a simpli ied model o a human ibia,
consis ing o a nylon ba wi h a diame e o 30 mm, and a syn he ic ibia wi h he ana omical model
om ou h-gene a ion Sawbones
®
. Mo eo e , Sawbones
®
blocks wi h di e en densi ies simula ed
he mechanical cha ac e is ics o he egene a ed bone in many s ages o bone callus g ow h. The
expe imen al measu emen s using he de eloped diagnos ic we e compa ed o he nume ically
simula ed esul s. Fo his ex e nal ixa o , i was possible o show ha he displacemen in os eo omy
was always lowe han he displacemen p esc ibed in he elonga o . Ne e heless, a ela ionship
was es ablished be ween he ene gy consump ion by he elec omechanical sys em used o pe o m
callus s imulus and he deg ee o os eo omy consolida ion. Hence, his echnology may lead o
me hodologies o mechanical s imula ion o egene a ing bone, which will play a ele an ole o
bed idden indi iduals wi h mobili y limi a ions.
Keywo ds:
ex e nal ixa ion; mic omo emen s; bone callus; elec omechanical sys em; bone
consolida ion
1. In oduc ion
Ex e nal ixa o s a e a su gical me hod o bone immobiliza ion commonly applied
o allow a ac u e o heal app op ia ely, p o iding s abili y o long bones and so issue
a e a se e e ac u e. Howe e , hey can also be used o p o ec so issues a e a
bu n o se e e inju y and as a p ocedu e o co ec bone misalignmen and es o e limb
leng h, o example, in he case o dwa ism. The main ad an age o ex e nal ixa ion is
ela ed o he quickness and acili y o i s applica ion. S ill, because i in ol es a su gical
p ocedu e, i needs o be pe o med by an o hopedic su geon. When an ex e nal ixa ion
sys em is applied, he isk o in ec ion a he ac u e si e is minimal. Howe e , he e
is some hypo hesis ha disease may occu a he connec ion be ween he ods and he
Appl. Sci. 2022,12, 2328. h ps://doi.o g/10.3390/app12052328 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2022,12, 2328 2 o 17
skin [
1
]. Ex e nal ixa ion sys ems es ablish a link in he agmen ed bone, allowing load
ans e be ween he pa s and p omo ing in e agmen a y mo emen s o bone healing [
2
].
The in e agmen a y mo emen is he ela i e mo emen be ween he bone agmen s,
which can appea du ing a pa ien ’s weigh -bea ing ac i i ies. These mic omo emen s
in he ac u e si e a e c ucial o p omo ing bone callus g ow h and he con ol o bone
egene a ion [
3
]. Hence, he con olled physical ac i i y o he pa ien migh ep esen a
mechanical s imula ion ha con ibu es o bone healing. Ne e heless, i is also wo h
s a ing ha excessi e mobili y would dis u b bone consolida ion and pe u b he healing
p ocess, leading o in ec ions and bone misalignmen s [
4
–
6
]. Hence, hese in e agmen a y
mo emen s a e c ucial o he complex p ocess o consolida ing ac u e [7].
Ne e heless, mechanical s imula ion by pa ien s’ weigh -bea ing ac i i ies is only
possible in people who can walk. In he case o bed idden pa ien s o o hose wi h
educed mobili y, he bone union is mo e complica ed and may e en be inhibi ed by
o he heal h p oblems in he pa ien s ha migh cause imp ope o impai ed bone healing,
leading o a signi ican inc ease in ea men ime. Hence, all biomechanical de ices
ha can in oduce con olled mic omo emen s a he ac u e si e, con ibu ing o he
ehabili a ion o pa ien s and educing he eco e y ime, a e an al e na i e o help hose
pa ien s. Acco ding o Ba cik and Epa i [
8
], he mechanical manipula ion o he local
ac u e en i onmen can signi ican ly dec ease ac u e pa ien s’ healing ime, sugges ing
ha addi ional expe imen s should be conduc ed o de e mine he bes pa ame e s. Fo
ins ance, i is necessa y o know when he in e agmen a y mo ion needs o be s opped
o allow o consolida ion and es ablish he bes s imula ion/ es a io. As adiog aphic
e alua ion shows some limi a ions, se e al au ho s a e ying o de elop me hods o healing
assessmen ha can gi e in o ma ion abou he p og ession o he mechanical p ope ies o
he ac u e epai issue. Fo example, using implan s wi h sensing capabili ies [
9
,
10
] o
ins umen ed implan s can imp o e he clinical ou come o o al hip eplacemen s [11,12].
These inno a i e implan s can be implemen able, p o ide he apeu ic bene i s, and ha e
diagnos ic capabili ies.
Su gical p ocedu es in ol ing bone egene a ion and he iden i ica ion o bone consol-
ida ion will help de ine he exac momen o emo e he ixa ion sys em. Righ now, his
iden i ica ion is assu ed by equipmen ha ing adia ion emissions, such as densi ome y
o omog aphy. Hence, he de elopmen o ools allowing an ea ly iden i ica ion o he
consolida ion phase has applicabili y in e es in he scope o pa ien eco e y, pa icula ly
o bed idden si ua ions. This s udy in ends o con ibu e o he in oduc ion o mic o-
mo emen s and he ea lie iden i ica ion o he healing phase o he egene a ed bone
h ough an elec omechanical sys em. The p esen ed elec omechanical sys em may also
play an essen ial ole in bone s e ching, as i can eplace he manual in oduc ion made
by he pa ien , au oma ing his p ocess. The p o o ype was de eloped in he O ho ix
®
monoplane ex e nal ixa ion sys em, bu he concep can ex end o ano he ex e nal ixa ion
ype whe e linea mo emen migh occu .
2. Ma e ials and Me hods
2.1. Expe imen al Models
This s udy conside ed a ibial os eo omy model in he cen al a ea o he diaphysis,
s abilized using a unila e al ex e nal ixa o LRS (Limb Recons uc ion Sys em), om
O ho ix
®
(Munich, Ge many), supplied by O ho ix GmbH, Munich, Ge many, used in
a wide a ie y o si ua ions. Two expe imen al models we e implemen ed, one using a
syn he ic ibia, and ano he using a single od ep esen ing a simpli ied ibia geome y [
3
].
The models did no include so issue. Figu e 1illus a es he expe imen al model se wi h
simpli ied and ana omical ea u es.
Appl. Sci. 2022,12, 2328 3 o 17
Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 o 17
Figu e 1. Ana omical model/ ibial simpli ied—ex e nal ixa ion.
The ana omical model used a ou h-gene a ion Sawbones® ibia, whose geome y
has he CAD e e ence #3401. The model conside ed he mechanical cha ac e is ics o he
co ical and abecula bone as iso opic wi h he p ope ies gi en in Table 1. The os eo -
omy ixa ion included he LRS unila e al ex e nal ixa o applica ion and he a ached
elec omechanical sys em. Schanz pins o 6 mm in diame e and 150 mm in leng h allowed
connec ing he ixa o o he bone. Schanz pins a e p oduced in AISI 316L s eel, and hei
mechanical p ope ies a e shown in Table 1.
Table 1. Mechanical p ope ies o co ical and abecula bone. Mechanical p ope ies o he ex e nal
ixa o .
Designa ion
Densi y [kg/m3]
Young Modulus
[GPa]
Coe icien o Poisson
T abecula Bone, [13]
300
0.7
0.20
Co ical Bone, [13]
1800
17.0
0.30
Ex e nal ixa o O ho ix® LRS (AISI 7075 T6), [14]
2810
72.0
0.33
Schanz pin (AISI 316L), [14]
8027
200.0
0.27
As shown in Figu e 1, he os eo omy was pe pendicula o he mechanical axis o he
bone, and he wo opposi e aces we e a a dis ance o 10 mm. The axis o he ixa o was
70 mm away om he mechanical axis o he ibia [15,16]. The closes dis ance om he
Schanz pin o he os eo omy was 28 mm. All alues we e de ined acco ding o he indica-
ion o he medical eam ha suppo ed he wo k.
The elec omechanical sys em p esen ed in Figu e 1 includes a mo o and an elec-
onic con ol uni , bo h placed in a box and coupled o he end o he mobile clamp o he
as ene . The wo m sc ew o he elonga o is connec ed o he mo o sha and assu es he
axial mo emen o he wo m sc ew. The p incipal componen s o he elec omechanical
sys em a e p esen ed in Figu e 2. The sys em consis s o a mic omo o wi h he e e ence
Rail
Shanz pin
Fixed Clamp
Os eo omy (10 mm)
Elonga o
Mobile clamp
Elec omechanical
Sys em
Fixa ion Sys em
O ho ix®
Fixa ion Sys em
O ho ix®
Tibial Mechanical Axis
Figu e 1. Ana omical model/ ibial simpli ied—ex e nal ixa ion.
The ana omical model used a ou h-gene a ion Sawbones
®
ibia, whose geome y
has he CAD e e ence #3401. The model conside ed he mechanical cha ac e is ics o
he co ical and abecula bone as iso opic wi h he p ope ies gi en in Table 1. The
os eo omy ixa ion included he LRS unila e al ex e nal ixa o applica ion and he a ached
elec omechanical sys em. Schanz pins o 6 mm in diame e and 150 mm in leng h allowed
connec ing he ixa o o he bone. Schanz pins a e p oduced in AISI 316L s eel, and hei
mechanical p ope ies a e shown in Table 1.
Table 1.
Mechanical p ope ies o co ical and abecula bone. Mechanical p ope ies o he ex e -
nal ixa o .
Designa ion Densi y [kg/m3]Young Modulus [GPa] Coe icien o Poisson
T abecula Bone, [13] 300 0.7 0.20
Co ical Bone, [13] 1800 17.0 0.30
Ex e nal ixa o O ho ix®LRS
(AISI 7075 T6), [14]2810 72.0 0.33
Schanz pin (AISI 316L), [14] 8027 200.0 0.27
As shown in Figu e 1, he os eo omy was pe pendicula o he mechanical axis o
he bone, and he wo opposi e aces we e a a dis ance o 10 mm. The axis o he ixa o
was 70 mm away om he mechanical axis o he ibia [
15
,
16
]. The closes dis ance om
he Schanz pin o he os eo omy was 28 mm. All alues we e de ined acco ding o he
indica ion o he medical eam ha suppo ed he wo k.
The elec omechanical sys em p esen ed in Figu e 1includes a mo o and an elec onic
con ol uni , bo h placed in a box and coupled o he end o he mobile clamp o he as ene .
The wo m sc ew o he elonga o is connec ed o he mo o sha and assu es he axial
mo emen o he wo m sc ew. The p incipal componen s o he elec omechanical sys em
Appl. Sci. 2022,12, 2328 4 o 17
a e p esen ed in Figu e 2. The sys em consis s o a mic omo o wi h he e e ence A-max
16, Maxon
®
(Sachseln, Suíça), P ecious Me al B ushes CLL, 2 Wa , wi h a 16 mm diame e ,
which gua an ees he axial displacemen induc ion i he mobile clamp is loose, bu also
he blocking o he mo emen i equi ed. The mic omo o is con olled h ough a con ol
uni de eloped on he A duíno®p og amming pla o m.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 4 o 17
A-max 16, Maxon® (Sachseln, Suíça), P ecious Me al B ushes CLL, 2 Wa , wi h a 16 mm
diame e , which gua an ees he axial displacemen induc ion i he mobile clamp is loose,
bu also he blocking o he mo emen i equi ed. The mic omo o is con olled h ough
a con ol uni de eloped on he A duíno® p og amming pla o m.
The elec omechanical sys em was powe ed wi h a ba e y and elec onically ac i-
a ed using an Encode MR Type M, 32 CPT, 2/3 Channel o posi ional con ol. The ha d-
wa e sys ems o he A duino® boa d used a DRV8801 pla e om Texas Ins umen s® (Dal-
las, TX, USA), allowing he bidi ec ional con ol o a b idged DC mic omo o . The boa d
could supply a di ec cu en up o 1 A, ole a ing peak cu en s ha migh , o a ew
seconds, each alues o 2.8 A. Two conduc o s we e needed o powe he mic omo o o
he DRV8801 boa d, which would ecei e a ol age o 12 V be ween he “VMM” e he
“GND”. The passage o elec ic cu en be ween he boa d and he mic omo o was as-
su ed h ough he “mo o +” e “mo o −“ pins.
Addi ionally, an encode coupled o he mic omo o ob ained esul s in he elonga-
o ’s ins an closing o opening posi ion. The de eloped so wa e in eg a es an in e ace
implemen ed h ough he Azande® p og am allowing he use o de ine some pa ame e s,
such as mo o speed and posi ion. This p og am enables he selec ion o mo emen ype,
choosing he linea eloci y o he mo emen , he displacemen dis ance, and he numbe
o epe i ions o be pe o med.
Figu e 2. Connec ion o he elec omechanical sys em in o he ex e nal ixa o O ho ix®.
Because he mic omo o needed a powe supply o ensu e he mechanical s imulus,
he e was also a mechanical esis ance, and he mo o cu en consump ion was ela ed o
he mechanical esis ance. Al hough he esis ance depends on se e al ac o s, such as he
sliding ic ion among se e al su aces, he esis ance opposi ion in he os eo omy mainly
con ibu es o he sys em’s mechanical esis ance. Hence, i is c ucial o ind a ela ionship
be ween he igidi y o he os eo omy and he ene gy o supply o he mo o ha gua an-
ees he necessa y mechanical s imulus. Mo eo e , a e calib a ion, he elec omechanical
sys em c ea es displacemen ela ionships be ween he ixa o clamp and he os eo omy.
A suppo pla o m buil -in Aluminum p o ile o Mini ec® (30 × 30) was de eloped
o he wo models, allowing he posi ional adjus men o he componen s. This s uc u e
in ended o eplica e, in a simpli ied way, he posi ioning o he lowe limb in he ho i-
zon al posi ion, like in a bed idden pa ien . I included a ixed suppo , ep esen ing he
posi ion o knee connec ion, and a ee axial suppo , which mimicked he ela ionship
wi h he oo and guided he axial mo emen in oduced in he assembly, as shown in
Figu e 3. The os eo omy’s displacemen was cha ac e ized using a Mi u oyo® analogue
compa a o , wi h a measu emen accu acy o 1 µm and loca ed on one o he aces o
Sawbones® block.
Mobile Clamp Elec omechanical Sys em
Figu e 2. Connec ion o he elec omechanical sys em in o he ex e nal ixa o O ho ix®.
The elec omechanical sys em was powe ed wi h a ba e y and elec onically ac i a ed
using an Encode MR Type M, 32 CPT, 2/3 Channel o posi ional con ol. The ha dwa e
sys ems o he A duino
®
boa d used a DRV8801 pla e om Texas Ins umen s
®
(Dallas,
TX, USA), allowing he bidi ec ional con ol o a b idged DC mic omo o . The boa d
could supply a di ec cu en up o 1 A, ole a ing peak cu en s ha migh , o a ew
seconds, each alues o 2.8 A. Two conduc o s we e needed o powe he mic omo o
o he DRV8801 boa d, which would ecei e a ol age o 12 V be ween he “VMM” e he
“GND”. The passage o elec ic cu en be ween he boa d and he mic omo o was assu ed
h ough he “mo o +” e “mo o −“ pins.
Addi ionally, an encode coupled o he mic omo o ob ained esul s in he elonga-
o ’s ins an closing o opening posi ion. The de eloped so wa e in eg a es an in e ace
implemen ed h ough he Azande
®
p og am allowing he use o de ine some pa ame e s,
such as mo o speed and posi ion. This p og am enables he selec ion o mo emen ype,
choosing he linea eloci y o he mo emen , he displacemen dis ance, and he numbe
o epe i ions o be pe o med.
Because he mic omo o needed a powe supply o ensu e he mechanical s imulus,
he e was also a mechanical esis ance, and he mo o cu en consump ion was ela ed o
he mechanical esis ance. Al hough he esis ance depends on se e al ac o s, such as he
sliding ic ion among se e al su aces, he esis ance opposi ion in he os eo omy mainly
con ibu es o he sys em’s mechanical esis ance. Hence, i is c ucial o ind a ela ionship
be ween he igidi y o he os eo omy and he ene gy o supply o he mo o ha gua an ees
he necessa y mechanical s imulus. Mo eo e , a e calib a ion, he elec omechanical
sys em c ea es displacemen ela ionships be ween he ixa o clamp and he os eo omy.
A suppo pla o m buil -in Aluminum p o ile o Mini ec
®
(30
×
30) was de eloped
o he wo models, allowing he posi ional adjus men o he componen s. This s uc u e
in ended o eplica e, in a simpli ied way, he posi ioning o he lowe limb in he ho izon al
posi ion, like in a bed idden pa ien . I included a ixed suppo , ep esen ing he posi ion
o knee connec ion, and a ee axial suppo , which mimicked he ela ionship wi h he
oo and guided he axial mo emen in oduced in he assembly, as shown in Figu e 3. The
os eo omy’s displacemen was cha ac e ized using a Mi u oyo
®
analogue compa a o , wi h
a measu emen accu acy o 1 µm and loca ed on one o he aces o Sawbones®block.
Appl. Sci. 2022,12, 2328 5 o 17
Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 o 17
Figu e 3. Ho izon al suppo ing pla o m: (a) suppo condi ions o he simpli ied model; (b) sup-
po condi ions o he ana omic ibia.
This s udy used he Sawbones® blocks (Sawbones®, Malmö, Sweden, 2019) wi h di -
e en densi ies o simula e di e en os eo omy igidi ies. Acco ding o he adema k,
hese ma e ials allow o a good simula ion o he mechanical cha ac e is ics o he egen-
e a ed bone in he many s ages o bone callus g ow h [17], ep oducing he a ia ion in
bone callus s i ness. The mechanical p ope ies and he designa ion o he se e al ma e-
ials a e in Table 2. This ma e ial is applied in os eo omy o ca y ou ad ancemen es s.
These es s a e in ended o e alua e he esis ance capaci y o he ma e ial when subjec ed
o comp ession.
Table 2. Mechanical p ope ies o he ma e ials used in he os eo omy [18].
Solid Foam
10 PCF
15 PCF
20 PCF
30 PCF
40 PCF
50 PCF
Densi y
[g/cm3]
0.16
0.24
0.32
0.48
0.64
0.80
Tensile S eng h
[MPa]
2.1
3.7
5.6
12.0
19.0
27.0
Young Modulus ( ac ion)
[GPa]
0.086
0.173
0.284
0.592
1.0
1.469
Comp essi e S eng h
[MPa]
2.2
4.9
8.4
18.0
31.0
48.0
Young Modulus (Comp.)
[GPa]
0.058
0.123
0.210
0.445
0.759
1.148
Coe icien o Poisson
0.3
0.3
0.3
0.3
0.3
0.3
The Sawbones® ma e ials ha e igidi ies (s i ness exp essed in Young’s comp ession
Modulus) be ween hose o ib ous issue, imma u e bone, and ma u e bone. Table 3 com-
pa es he Sawbones s i ness alues a di e en densi ies wi h bone cha ac e is ics in he
a ious phases. Se e al au ho s [19,20] used hese egene a ed bone p ope ies o ep e-
sen bone egene a ion in ma hema ical models, whe eas o he esea che s c ea ed nu-
me ical models based on he same in o ma ion [21–23].
The p ima y pu pose o his expe imen al se up was o s udy he ela ionship be-
ween igidi y and mic omo emen s on he os eo omy o he loading condi ions de ined
a he mic omo o . Mo eo e , i was also essen ial o e alua e he mic omo o ene gy con-
sump ion (CEMo o ) in o wa d and backwa d mo emen s o de e mine i s ela ionship
wi h he ma e ial’s s i ness a he os eo omy. Hence, h ee di e en displacemen s we e
imposed in he os eo omy, co esponding o 1, 1.5, and 2 mm, and, o gua an ee epea a-
bili y and ep oducibili y, i e es s o each displacemen we e pe o med. Se e al au-
ho s a gue ha he eco e y ime can be educed i os eo omy s imula ion is p omo ed
wi h displacemen s o 1 mm/day [13,24–29].
(a)
(b)
(a)
(b)
Figu e 3.
Ho izon al suppo ing pla o m: (
a
) suppo condi ions o he simpli ied model; (
b
) suppo
condi ions o he ana omic ibia.
This s udy used he Sawbones
®
blocks (Sawbones
®
, Malmö, Sweden, 2019) wi h
di e en densi ies o simula e di e en os eo omy igidi ies. Acco ding o he adema k,
hese ma e ials allow o a good simula ion o he mechanical cha ac e is ics o he e-
gene a ed bone in he many s ages o bone callus g ow h [
17
], ep oducing he a ia ion
in bone callus s i ness. The mechanical p ope ies and he designa ion o he se e al
ma e ials a e in
Table 2
. This ma e ial is applied in os eo omy o ca y ou ad ancemen
es s. These es s a e in ended o e alua e he esis ance capaci y o he ma e ial when
subjec ed o comp ession.
Table 2. Mechanical p ope ies o he ma e ials used in he os eo omy [18].
Solid Foam 10 PCF 15 PCF 20 PCF 30 PCF 40 PCF 50 PCF
Densi y
[g/cm3]0.16 0.24 0.32 0.48 0.64 0.80
Tensile S eng h
[MPa] 2.1 3.7 5.6 12.0 19.0 27.0
Young Modulus ( ac ion)
[GPa] 0.086 0.173 0.284 0.592 1.0 1.469
Comp essi e S eng h
[MPa] 2.2 4.9 8.4 18.0 31.0 48.0
Young Modulus (Comp.)
[GPa] 0.058 0.123 0.210 0.445 0.759 1.148
Coe icien o Poisson 0.3 0.3 0.3 0.3 0.3 0.3
The Sawbones
®
ma e ials ha e igidi ies (s i ness exp essed in Young’s comp ession
Modulus) be ween hose o ib ous issue, imma u e bone, and ma u e bone. Table 3
compa es he Sawbones s i ness alues a di e en densi ies wi h bone cha ac e is ics
in he a ious phases. Se e al au ho s [
19
,
20
] used hese egene a ed bone p ope ies o
ep esen bone egene a ion in ma hema ical models, whe eas o he esea che s c ea ed
nume ical models based on he same in o ma ion [21–23].
The p ima y pu pose o his expe imen al se up was o s udy he ela ionship be ween
igidi y and mic omo emen s on he os eo omy o he loading condi ions de ined a he
mic omo o . Mo eo e , i was also essen ial o e alua e he mic omo o ene gy consump ion
(CEMo o ) in o wa d and backwa d mo emen s o de e mine i s ela ionship wi h he
ma e ial’s s i ness a he os eo omy. Hence, h ee di e en displacemen s we e imposed
in he os eo omy, co esponding o 1, 1.5, and 2 mm, and, o gua an ee epea abili y and
ep oducibili y, i e es s o each displacemen we e pe o med. Se e al au ho s a gue ha
he eco e y ime can be educed i os eo omy s imula ion is p omo ed wi h displacemen s
o 1 mm/day [13,24–29].

Appl. Sci. 2022,12, 2328 6 o 17
Table 3. S i ness o he ma e ial used o ep esen os eo omy/ egene a i e bone [18,20].
S i ness [MPa]
Fib ous Tissue 0.2
Sawbones®10 58
→S imula ion
Sawbones®15 123
Sawbones®20 210
Sawbones®30 445
Sawbones®40 759
Imma u e Bone 1000
Sawbones®50 1148
Ma u e Bone 6000
Co ical Bone 20,000
The expe imen al esul s a e p esen ed using he ollowing no a ion:
{PA6 ; AN}Si jdk(1)
whe e PA6 ep esen s he simpli ied model’s esul s, and AN hose o he ana omical model.
The index i ep esen s he ype o Sawbones
®
ma e ial, i.e., 10, 20, 30, 40, and 50, he index j
iden i ies he speed imposed on he mic omo o (2 mm/min), and he index kis ela ed o
he le el o displacemen se , i.e., 1 mm, 1.5 mm, and 2 mm.
2.2. Nume ical Models
The geome ical models we e c ea ed based on he expe imen al simpli ied and
ana omical models. Each one o he wo model iles was impo ed in o he ADINA Sys em
o linea and nonlinea ini e elemen analysis (ADINA AUI e sion 9.3.1, ADINA R&D
Inc., Wa e - own, NY, USA). Figu e 4illus a es he ex e nal ixa ion models ha eplica e
he expe imen al condi ions. Since hese models we e based on he s imula ion concep
pe o med on pa ien s wi h educed mobili y, he bounda y condi ions mimicked hese
physical limi a ions. Hence, he main mo emen es ic ions we e in he knee a ea, while
he suppo in he oo was less es ic i e, and he displacemen loading condi ion was
assu ed a he mobile clamp. Figu e 4also shows he nume ical bounda y condi ions. The
h ee ansla ional deg ees o eedom in he ibia condyles egions and he displacemen s
in he XX and ZZ axis in he oo a ea we e es ic ed, allowing only axial mo emen .
The con ac among su aces ensu ed he ma e ial con inui y be ween he aces o
he bone and he aces o he os eo omy ma e ial, be ween he pin su aces and he inne
su aces o he hole bone. E en knowing ha he ixa ion o he clamp o he ail was
assu ed h ough a sc ew, he bonded con ac allowed simpli ying he nume ical model.
Ma e ial con inui y gua an eed he connec ion be ween he pins and he clamps. The
ela i e mo emen among he aces in ol ed on he emaining con ac s was included.
Figu e 5shows he se e al con ac su aces o he nume ical models.
A mesh sensi i i y s udy was assu ed, assuming ha g id displacemen independence
was achie ed o a ia ions in he o de o 5%. Assignmen o he mesh densi y o he
se e al bodies o each model was suppo ed by equally spaced subdi isions o he bodies,
using he desi ed edge leng h dimensions be ween 1 mm e 3 mm. In some cases, he
subdi ision o speci ic aces was ecalcula ed wi h smalle sizes o assu e a mo e e ined
mesh in a eas equi ing highe p ecision o he esul s. The Delaunay ee- o m meshing
algo i hm gua an eed disc e iza ion o he domains, gene a ing an eigh -node hexahed al
elemen . Addi ional displacemen deg ees o eedom we e allowed by selec ing he
incompa ible modes op ion. The o al numbe o nodes and elemen s o each model a e
de ailed in Table 4.
Appl. Sci. 2022,12, 2328 7 o 17
Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 o 17
Figu e 4. Fini e elemen s models: Ana omical model (AN); Simpli ied model (PA6).
The con ac among su aces ensu ed he ma e ial con inui y be ween he aces o he
bone and he aces o he os eo omy ma e ial, be ween he pin su aces and he inne su -
aces o he hole bone. E en knowing ha he ixa ion o he clamp o he ail was assu ed
h ough a sc ew, he bonded con ac allowed simpli ying he nume ical model. Ma e ial
con inui y gua an eed he connec ion be ween he pins and he clamps. The ela i e
mo emen among he aces in ol ed on he emaining con ac s was included. Figu e 5
shows he se e al con ac su aces o he nume ical models.
Figu e 5. Con ac su aces included in he nume ical models: Ana omical model (AN); Simpli ied
model (PA6).
A mesh sensi i i y s udy was assu ed, assuming ha g id displacemen independ-
ence was achie ed o a ia ions in he o de o 5%. Assignmen o he mesh densi y o
he se e al bodies o each model was suppo ed by equally spaced subdi isions o he
bodies, using he desi ed edge leng h dimensions be ween 1 mm e 3 mm. In some cases,
PA6
AN
PA6
AN
Figu e 4. Fini e elemen s models: Ana omical model (AN); Simpli ied model (PA6).
Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 o 17
Figu e 4. Fini e elemen s models: Ana omical model (AN); Simpli ied model (PA6).
The con ac among su aces ensu ed he ma e ial con inui y be ween he aces o he
bone and he aces o he os eo omy ma e ial, be ween he pin su aces and he inne su -
aces o he hole bone. E en knowing ha he ixa ion o he clamp o he ail was assu ed
h ough a sc ew, he bonded con ac allowed simpli ying he nume ical model. Ma e ial
con inui y gua an eed he connec ion be ween he pins and he clamps. The ela i e
mo emen among he aces in ol ed on he emaining con ac s was included. Figu e 5
shows he se e al con ac su aces o he nume ical models.
Figu e 5. Con ac su aces included in he nume ical models: Ana omical model (AN); Simpli ied
model (PA6).
A mesh sensi i i y s udy was assu ed, assuming ha g id displacemen independ-
ence was achie ed o a ia ions in he o de o 5%. Assignmen o he mesh densi y o
he se e al bodies o each model was suppo ed by equally spaced subdi isions o he
bodies, using he desi ed edge leng h dimensions be ween 1 mm e 3 mm. In some cases,
PA6
AN
PA6
AN
Figu e 5.
Con ac su aces included in he nume ical models: Ana omical model (AN); Simpli ied
model (PA6).
Table 4. Desc ip ion o he o al numbe o elemen s and nodes pe model.
Simpli ied Ana omic
Elemen s 272075 373624
Nodes
This s udy assumed iso opic linea elas ic p ope ies o all componen s, and hei
mechanical p ope ies we e hose p e iously p esen ed in Table 1. The loading, ep esen ing
he elec omechanical s imulus, was included by p esc ibing a 2 mm displacemen a he
holes o he ee clamp, whe e he elonga o was connec ed, as indica ed in Figu e 4.
Appl. Sci. 2022,12, 2328 8 o 17
3. Resul s
3.1. Expe imen al Resul s
Figu e 6compa es he esul s o he se e al ypes o Sawbones
®
(10, 15, 20, 30, 40, 50)
blocks using he no a ion p esen ed in Equa ion (1). The sawbones s i ness o he di e en
blocks is shown in he g aphic wi h he o ange line; Figu e 6a p esen s he esul s ela ed o
he simpli ied models, whe eas Figu e 6b p esen s hose ela ed o he ana omical model.
The wo se s o esul s showed ha , as he s i ness o he os eo omy ma e ial inc eased, he
displacemen a he os eo omy dec eased; hence, bo h lines show nega i e slopes.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 o 17
he subdi ision o speci ic aces was ecalcula ed wi h smalle sizes o assu e a mo e e-
ined mesh in a eas equi ing highe p ecision o he esul s. The Delaunay ee- o m
meshing algo i hm gua an eed disc e iza ion o he domains, gene a ing an eigh -node
hexahed al elemen . Addi ional displacemen deg ees o eedom we e allowed by selec -
ing he incompa ible modes op ion. The o al numbe o nodes and elemen s o each
model a e de ailed in Table 4.
Table 4. Desc ip ion o he o al numbe o elemen s and nodes pe model.
Simpli ied
Ana omic
Elemen s
272075
373624
Nodes
This s udy assumed iso opic linea elas ic p ope ies o all componen s, and hei
mechanical p ope ies we e hose p e iously p esen ed in Table 1. The loading, ep esen -
ing he elec omechanical s imulus, was included by p esc ibing a 2 mm displacemen a
he holes o he ee clamp, whe e he elonga o was connec ed, as indica ed in Figu e 4.
3. Resul s
3.1. Expe imen al Resul s
Figu e 6 compa es he esul s o he se e al ypes o Sawbones® (10, 15, 20, 30, 40,
50) blocks using he no a ion p esen ed in Equa ion (1). The sawbones s i ness o he
di e en blocks is shown in he g aphic wi h he o ange line; Figu e 6a p esen s he esul s
ela ed o he simpli ied models, whe eas Figu e 6b p esen s hose ela ed o he ana om-
ical model. The wo se s o esul s showed ha , as he s i ness o he os eo omy ma e ial
inc eased, he displacemen a he os eo omy dec eased; hence, bo h lines show nega i e
slopes.
(a)
(b)
Figu e 6. Displacemen a he os eo omy in he wo expe imen al models: (a) he simpli ied model;
(b) he ana omic model.
Figu e 6 shows ha i he os eo omy ma e ial wi h he lowe s i ness was unde an
imposed displacemen o 2 mm h ough he wo m sc ew, i ecei ed only 18% o he 2
mm. This pe cen age o displacemen was calcula ed by compa ing he displacemen
measu ed in os eo omy wi h he displacemen imposed in he mic omo o . Figu e 7a com-
pa es he os eo omy displacemen o he Sawbones®20 ma e ial when h ee di e en al-
ues o p esc ibed displacemen we e de ined a he wo m sc ew o bo h ixa o models.
The beha io o bo h models was qui e simila , and he di e ences we e mainly ela ed
o he geome ical dimensions o he wo models. Mo eo e , hese esul s con i med ha ,
as he os eo omy’s s i ness inc eased, he discha ge o he o ce be ween he bone and he
y = -0.0105x + 0.5854
R² = 0.9678
y = -0.0078x + 0.3948
R² = 0.9611
0
0.2
0.4
0.6
0.8
1
1.2
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
10 20 30 40 50
S i ness [GPa]
Displacemen [mm]
Sawbones® ma e ial
d2
d1.5
Sawbones® da a
Linea (d2)
Linea (d1.5)
Figu e 6.
Displacemen a he os eo omy in he wo expe imen al models: (
a
) he simpli ied model;
(b) he ana omic model.
Figu e 6shows ha i he os eo omy ma e ial wi h he lowe s i ness was unde an
imposed displacemen o 2 mm h ough he wo m sc ew, i ecei ed only 18% o he 2 mm.
This pe cen age o displacemen was calcula ed by compa ing he displacemen measu ed
in os eo omy wi h he displacemen imposed in he mic omo o . Figu e 7a compa es he
os eo omy displacemen o he Sawbones
®
20 ma e ial when h ee di e en alues o
p esc ibed displacemen we e de ined a he wo m sc ew o bo h ixa o models. The
beha io o bo h models was qui e simila , and he di e ences we e mainly ela ed o he
geome ical dimensions o he wo models. Mo eo e , hese esul s con i med ha , as
he os eo omy’s s i ness inc eased, he discha ge o he o ce be ween he bone and he
ixa o was di e en , as desc ibed by se e al wo ks [
30
–
32
]. Table 5con ains he alues o
Figu e 7a and he p esc ibed displacemen a io measu ed a he os eo omy.
The es s ca ied ou on he simpli ied and ana omical models allowed eco ding he
ene gy consump ion o he mic omo o (CEMo o ) in he a ia ions o displacemen e sus
s i ness a he os eo omy. Figu e 7b shows he alues o he CEMo o a iable o he
simpli ied and ana omy models o assu e a p esc ibed displacemen o 2 mm a he wo m
sc ew and using a 2 mm/min eloci y.
Figu e 7b allows he quan i ica ion o he CEMo o a iable o se e al os eo omy
s i nesses. In he ini ial phase o healing, pa icula ly, he e was a highe inc ease in he
s i ness and, simul aneously, in he alue o he CEMo o a iable. A e his ini ial phase,
he CEMo o a iable showed a s abiliza ion wi h sligh a ia ions.
Appl. Sci. 2022,12, 2328 9 o 17
Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 o 17
ixa o was di e en , as desc ibed by se e al wo ks [30–32]. Table 5 con ains he alues o
Figu e 7a and he p esc ibed displacemen a io measu ed a he os eo omy.
The es s ca ied ou on he simpli ied and ana omical models allowed eco ding he
ene gy consump ion o he mic omo o (CEMo o ) in he a ia ions o displacemen e -
sus s i ness a he os eo omy. Figu e 7b shows he alues o he CEMo o a iable o he
simpli ied and ana omy models o assu e a p esc ibed displacemen o 2 mm a he wo m
sc ew and using a 2 mm/min eloci y.
Table 5. Ra io o he p esc ibed displacemen s a he os eo omy o he Sawbones®20 ma e ial.
P esc ibed [mm]
PA6 Model
AN Model
Os eo omy [mm]
Ra io [%]
Os eo omy [mm]
Ra io [%]
2
0.33
17%
0.37
19%
1.5
0.19
13%
0.21
14%
1
0.1
10%
0.16
16%
(a)
(b)
Figu e 7. (a) Displacemen a he os eo omy in he wo expe imen al models using he Sawbones®
20 ma e ial a he os eo omy; (b) a ia ion o CEMo o a iable wi h he s i ness o he ma e ial a
he os eo omy.
Figu e 7b allows he quan i ica ion o he CEMo o a iable o se e al os eo omy
s i nesses. In he ini ial phase o healing, pa icula ly, he e was a highe inc ease in he
s i ness and, simul aneously, in he alue o he CEMo o a iable. A e his ini ial phase,
he CEMo o a iable showed a s abiliza ion wi h sligh a ia ions.
3.2. Nume ical Resul s
The simula ions o he wo models comple ed all ime s eps. The displacemen s o e
each axes di ec ions and i s magni ude we e analyzed. The i s analysis was based on he
displacemen dis ibu ion in he os eo omy when 2 mm o p esc ibed displacemen we e
de ined a he wo m sc ew. Since he y-axis is pa allel o he solici a ion di ec ion and he
ixa o axes, he a e age y displacemen s a he os eo omy ace i s ly loaded a e p esen ed
in Table 6. The a e age alues we e e alua ed conside ing all nodes o he os eo omy ace
o bo h models. In addi ion, he maximum displacemen alue on he same ace is also
p esen ed. I is possible o obse e ha as he s i ness o he os eo omy ma e ial inc eased,
he displacemen dec eased, wi h bo h models showing simila beha io .
Fo bo h models, Figu es 8 and 9 show he dis ibu ion o y-displacemen a he in-
e ace whe ein he con ac appea ed i s ly. The dis ibu ion pa e n a ied wi h he ma-
e ial’s s i ness. The homogenei y o he displacemen s inc eased as he os eo omy s i -
ness inc eased, sugges ing ha s imula ion would be mo e challenging o implemen as
0
0.1
0.2
0.3
0.4
1.0 1.5 2.0
Os eo omy displacemen [mm]
Wo m sc ew displacemen [mm]
AN
PA6
70
75
80
85
90
95
100
105
110
115
120
58 258 458 658 858 1058
CEMo o [mA]
Os eo omy s i ness [MPa]
AN 2d2E
PA6 2d2E
Figu e 7.
(
a
) Displacemen a he os eo omy in he wo expe imen al models using he Sawbones
®
20 ma e ial a he os eo omy; (
b
) a ia ion o CEMo o a iable wi h he s i ness o he ma e ial a
he os eo omy.
Table 5. Ra io o he p esc ibed displacemen s a he os eo omy o he Sawbones®20 ma e ial.
P esc ibed [mm] PA6 Model AN Model
Os eo omy [mm] Ra io [%] Os eo omy [mm] Ra io [%]
2 0.33 17% 0.37 19%
1.5 0.19 13% 0.21 14%
1 0.1 10% 0.16 16%
3.2. Nume ical Resul s
The simula ions o he wo models comple ed all ime s eps. The displacemen s o e
each axes di ec ions and i s magni ude we e analyzed. The i s analysis was based on he
displacemen dis ibu ion in he os eo omy when 2 mm o p esc ibed displacemen we e
de ined a he wo m sc ew. Since he y-axis is pa allel o he solici a ion di ec ion and he
ixa o axes, he a e age ydisplacemen s a he os eo omy ace i s ly loaded a e p esen ed
in Table 6. The a e age alues we e e alua ed conside ing all nodes o he os eo omy ace
o bo h models. In addi ion, he maximum displacemen alue on he same ace is also
p esen ed. I is possible o obse e ha as he s i ness o he os eo omy ma e ial inc eased,
he displacemen dec eased, wi h bo h models showing simila beha io .
Table 6. A e age and maximum Y-displacemen in he ace o he os eo omy i s ly loaded.
Os eo omy
Ma e ial
PA6 Model [mm] AN Model [mm]
A e age Maximum A e age Maximum
S10 0.35 0.49 0.55 0.59
S15 0.30 0.43 0.48 0.52
S20 0.29 0.38 0.42 0.46
S30 0.20 0.29 0.30 0.34
S40 0.12 0.18 0.14 0.17
S50 0.11 0.16 0.11 0.14
Fo bo h models, Figu es 8and 9show he dis ibu ion o y-displacemen a he
in e ace whe ein he con ac appea ed i s ly. The dis ibu ion pa e n a ied wi h he
ma e ial’s s i ness. The homogenei y o he displacemen s inc eased as he os eo omy
s i ness inc eased, sugges ing ha s imula ion would be mo e challenging o implemen
as bone egene a ion occu ed. The image on he igh -hand side o bo h igu es shows he
Appl. Sci. 2022,12, 2328 16 o 17
Acknowledgmen s:
This esea ch was sponso ed by na ional unds h ough FCT—Fundação pa a a
Ciência e a Tecnologia, unde he p ojec UIDB/00285/2020.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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