

Ci a ion: F yd ýšek, K.; ˇ
Cepica, D.;
Halo, T.; Skoupý, O.; Ple a, L.;
Madeja, R.; Pome lo á, J.; Lose o á,
M.; Kou ecký, J.; Michal, P.; e al.
Biomechanical Analysis o S aples o
Epiphysiodesis. Appl. Sci. 2022,12,
614. h ps://doi.o g/10.3390/
app12020614
Academic Edi o : Claudio Bel ede e
Recei ed: 9 Decembe 2021
Accep ed: 6 Janua y 2022
Published: 9 Janua y 2022
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A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
applied
sciences
A icle
Biomechanical Analysis o S aples o Epiphysiodesis
Ka el F yd ýšek 1,2,* , Daniel ˇ
Cepica 1,2, Tomáš Halo 1,2 , Ondˇ ej Skoupý1,2, Leopold Ple a 1,3,
Roman Madeja 1,3, Jana Pome lo á1,3 , Monika Lose o á4,5 , Jan Kou ecký5, Pa el Michal 5, Voj ˇech Ha las 6,
Šimon K aus 6,7, Dominik ˇ
Du ica 7, Ka eˇ ina Pe e ek Dˇedko á8, Ma ek Pagáˇc 9, Pa el K pec 10 and
Paweł Osemlak 11
1Ins i u e o Eme gency Medicine, Facul y o Medicine, Uni e si y o Os a a, Syllabo a 19,
703 00 Os a a-Ví ko ice, Czech Republic; [email p o ec ed] (D. ˇ
C.); [email p o ec ed] (T.H.);
[email p o ec ed] (O.S.); [email p o ec ed] (L.P.); [email p o ec ed] (R.M.);
[email p o ec ed] (J.P.)
2
Depa men o Applied Mechanics, Facul y o Mechanical Enginee ing, VSB—Technical Uni e si y o Os a a,
17. Lis opadu 2172/15, 708 00 Os a a, Czech Republic
3T auma Cen e , 17., Uni e si y Hospi al Os a a, Lis opadu 1790, 708 52 Os a a-Po uba, Czech Republic
4Facul y o Ma e ials Science and Technology, VSB—Technical Uni e si y o Os a a, 17. Lis opadu 2172/15,
708 00 Os a a, Czech Republic; [email p o ec ed]
5Medin, a.s, Vlacho icka 619, 592 31 No éMˇes o na Mo a ˇe, Czech Republic; [email p o ec ed] (J.K.);
[email p o ec ed] (P.M.)
6Mo ol Uni e si y Hospi al, V Ú alu 84, 150 06 P ague 5, Czech Republic;
[email p o ec ed] (V.H.); [email p o ec ed] (Š.K.)
7Depa men o O hopaedics, Second Facul y o Medicine, Cha les Uni e si y, V Ú alu 84,
150 06 P ague 5, Czech Republic; [email p o ec ed]
8
Cen e o Ad anced Inno a ion Technologies, VSB—Technical Uni e si y o Os a a, 17. Lis opadu 15/2172,
708 00 Os a a-Po uba, Czech Republic; ka e ina.pe e [email p o ec ed]
9Depa men o Machining, Facul y o Mechanical Enginee ing, VSB—Technical Uni e si y o Os a a,
Assembly and Enginee ing Me ology, 17. Lis opadu 2172/15, 708 00 Os a a, Czech Republic;
[email p o ec ed]
10 V-NASS, a.s., Halaso a 2938/1a, 703 00 Os a a-Ví ko ice, Czech Republic; [email p o ec ed]
11 Pedia ic Uni e si y Hospi al Named by P o . An oni G˛ebala in Lublin, ul. P o . A. G˛ebali 6,
Depa men o Pedia ic Su ge y and T auma ology, Medical Uni e si y o Lublin, 20-093 Lublin, Poland;
[email p o ec ed]
*Co espondence: ka [email p o ec ed]; Tel.: +420-597323495; Fax: +420-596916490
Abs ac :
Limb asymme y can, and o en does, cause a ious heal h p oblems. Bloun bone s aples
(clips) a e used o co ec such une en g ow h. This a icle analyzes he pe o mance o a biome-
chanical s aple du ing bone ( ibia) g ow h a es . The s aples conside ed in his s udy we e made o
1.4441 s ainless s eel, he model o ibia consis ed o wo ma e ials ep esen ing co icalis and spongio-
sis. Hooke’s law was used o modeling ma e ials’ beha io s o ini e elemen analysis (FEA). The
maxima o s ess and o al s aple displacemen we e e alua ed using he ini e elemen me hod and
e i ica ion o he esul s, along wi h he de e mina ion o he maximum loading (g owing) o ce ha
he s aples a e capable o wi hs anding, was pe o med expe imen ally. The p esen ed me hod can be
used o de e mine he sa e y and usabili y o s aples o bone g ow h a es . Acco ding o ou esul s,
he design o Bloun s aples conside ed in his pape is sa e and sui able o o hopedic ea men .
Keywo ds: biomechanics; o hopedics; Bloun s aple; FEA; expe imen ; epiphysiodesis
1. In oduc ion
The g ow h de o mi ies, one o which is Bloun ’s disease, a e globally among he mos
common condi ions o p esen in pedia ic o hopedic clinics [
1
,
2
]. These de o mi ies can,
al hough a ely, be associa ed also wi h childhood obesi y, i.e., high body mass index (BMI);
o u he in o ma ion, see [3].
Appl. Sci. 2022,12, 614. h ps://doi.o g/10.3390/app12020614 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2022,12, 614 2 o 16
These g ow h de o mi ies ha e been, o many yea s, ea ed su gically, u ilizing he
manipula ion o na u al g ow h capabili ies o he bone; see [
1
]. Epiphyseal s apling is
one o he mos commonly and adi ionally used me hods o such co ec ion, using ine
me al s aples (clips) implan ed in o a speci ic pa o a child’s long bone o empo a ily
p e en i s g ow h. Hence, epiphyseal s apling (also known as epiphysiodesis, Bloun
epiphysiodesis, bone g ow h es ic ion, o bone g ow h su ge y) in ol es placing such
s aples in a way o b idge he g ow h pla e o slow down he g ow h o he long bone;
see [1,4]. This sho su gical p ocedu e is pe o med unde gene al anes hesia.
The e a e no compa able nonsu gical al e na i es o epiphyseal s apling. Su gical
al e na i es include leg sho ening (i.e., a su ge y du ing which a sec ion o he bone is cu
ou and agmen s a e joined oge he wi h a pla e), pe cu aneous epiphysiodesis, see [
5
],
open epiphysiodesis, and, ecen ly, ension band echnique.
Epiphyseal s apling was in oduced by Wal e Bloun in 1949, see [
6
], and since hen,
i has become a common p ocedu e o co ec ing, in pa icula , angula de o mi ies o he
knee (genu a um o genu algum) in child en. The g ow h o he child’s o adolescen ’s
bone is associa ed mainly wi h physis, i.e., a ca ilage s uc u e nea join s; see [
1
,
4
]. Bloun
s aples a e also used o pseudoa h osis ea men [7].
Using s aples, he physis (epiphyseal pla e) can be ela i ely simply es ained ei-
he on bo h sides when co ec ing limb leng h disc epancy (i.e., “epiphysiodesis”) o
only on one side when co ec ing angula de o mi ies (i.e., “hemiepiphyseodesis”) (see
Figu es 1and 2
). Unlike he i e e sible me hod o pe manen epiphysiodesis, see [
8
], epi-
physeal s apling does no des oy he epiphyseal pla e and, he e o e, allows esump ion o
he g ow h once he op imal co ec ion is achie ed; see [4].
Appl. Sci. 2022, 12, x FOR PEER REVIEW 2 o 16
These g ow h de o mi ies ha e been, o many yea s, ea ed su gically, u ilizing he
manipula ion o na u al g ow h capabili ies o he bone; see [1]. Epiphyseal s apling is one
o he mos commonly and adi ionally used me hods o such co ec ion, using ine
me al s aples (clips) implan ed in o a speci ic pa o a child’s long bone o empo a ily
p e en i s g ow h. Hence, epiphyseal s apling (also known as epiphysiodesis, Bloun
epiphysiodesis, bone g ow h es ic ion, o bone g ow h su ge y) in ol es placing such
s aples in a way o b idge he g ow h pla e o slow down he g ow h o he long bone; see
[1,4]. This sho su gical p ocedu e is pe o med unde gene al anes hesia.
The e a e no compa able nonsu gical al e na i es o epiphyseal s apling. Su gical al-
e na i es include leg sho ening (i.e., a su ge y du ing which a sec ion o he bone is cu
ou and agmen s a e joined oge he wi h a pla e), pe cu aneous epiphysiodesis, see [5],
open epiphysiodesis, and, ecen ly, ension band echnique.
Epiphyseal s apling was in oduced by Wal e Bloun in 1949, see [6], and since hen,
i has become a common p ocedu e o co ec ing, in pa icula , angula de o mi ies o he
knee (genu a um o genu algum) in child en. The g ow h o he child’s o adolescen ’s
bone is associa ed mainly wi h physis, i.e., a ca ilage s uc u e nea join s; see [1,4]. Bloun
s aples a e also used o pseudoa h osis ea men [7].
Using s aples, he physis (epiphyseal pla e) can be ela i ely simply es ained ei he
on bo h sides when co ec ing limb leng h disc epancy (i.e., “epiphysiodesis”) o only on
one side when co ec ing angula de o mi ies (i.e., “hemiepiphyseodesis”) (see Figu es 1
and 2). Unlike he i e e sible me hod o pe manen epiphysiodesis, see [8], epiphyseal
s apling does no des oy he epiphyseal pla e and, he e o e, allows esump ion o he
g ow h once he op imal co ec ion is achie ed; see [4].
Figu e 1. Pa s o he g owing bone ( ibia).
Figu e 1. Pa s o he g owing bone ( ibia).
Recen ly, he ension band echnique, in oduced by S e ens in 2007 [
9
], using non-
locking pla es (simila o hose used o os eosyn hesis) and sc ews almos in he same
posi ion as s aples, has g adually become a p e e able al e na i e o s apling. Howe e ,
Bloun ’s o iginal me hod s ill emains an e ec i e means o he ea men o lowe limb
de o mi ies in adolescen s; see [1,4,10].
Acco ding o [
1
,
4
], besides accu a e diagnosis con i med by a adiog am o he whole
limb (see Figu e 2), good iming o he ea men is also e y impo an . The su gical
p ocedu e in ol es a sho longi udinal incision h ough so issues o e he physis and
ex ape ios eal implan a ion o he s aple using a special ins umen unde adiog aphy
con ol [
11
] (see Figu e 3). The s aple mus b idge he physis bu no pene a e i o p e en
i s impai men (see Figu e 4).
The s aples should no be es ic ing he physis o longe han 2 yea s o p e en
pe manen g ow h cessa ion [
12
]. O he complica ions du ing ea men , such as damaging
he physis by imp ecise s aple implan a ion, mechanical ailu e o he s aple (bending, a ely
b eak), o s aple mig a ion can occu . The las one is also he mos common complica ion
and disad an age compa ed wi h he ension band echnique; see [1,4].
Appl. Sci. 2022,12, 614 3 o 16
Appl. Sci. 2022, 12, x FOR PEER REVIEW 2 o 16
These g ow h de o mi ies ha e been, o many yea s, ea ed su gically, u ilizing he
manipula ion o na u al g ow h capabili ies o he bone; see [1]. Epiphyseal s apling is one
o he mos commonly and adi ionally used me hods o such co ec ion, using ine
me al s aples (clips) implan ed in o a speci ic pa o a child’s long bone o empo a ily
p e en i s g ow h. Hence, epiphyseal s apling (also known as epiphysiodesis, Bloun
epiphysiodesis, bone g ow h es ic ion, o bone g ow h su ge y) in ol es placing such
s aples in a way o b idge he g ow h pla e o slow down he g ow h o he long bone; see
[1,4]. This sho su gical p ocedu e is pe o med unde gene al anes hesia.
The e a e no compa able nonsu gical al e na i es o epiphyseal s apling. Su gical al-
e na i es include leg sho ening (i.e., a su ge y du ing which a sec ion o he bone is cu
ou and agmen s a e joined oge he wi h a pla e), pe cu aneous epiphysiodesis, see [5],
open epiphysiodesis, and, ecen ly, ension band echnique.
Epiphyseal s apling was in oduced by Wal e Bloun in 1949, see [6], and since hen,
i has become a common p ocedu e o co ec ing, in pa icula , angula de o mi ies o he
knee (genu a um o genu algum) in child en. The g ow h o he child’s o adolescen ’s
bone is associa ed mainly wi h physis, i.e., a ca ilage s uc u e nea join s; see [1,4]. Bloun
s aples a e also used o pseudoa h osis ea men [7].
Using s aples, he physis (epiphyseal pla e) can be ela i ely simply es ained ei he
on bo h sides when co ec ing limb leng h disc epancy (i.e., “epiphysiodesis”) o only on
one side when co ec ing angula de o mi ies (i.e., “hemiepiphyseodesis”) (see Figu es 1
and 2). Unlike he i e e sible me hod o pe manen epiphysiodesis, see [8], epiphyseal
s apling does no des oy he epiphyseal pla e and, he e o e, allows esump ion o he
g ow h once he op imal co ec ion is achie ed; see [4].
Figu e 1. Pa s o he g owing bone ( ibia).
Figu e 2.
(
a
) Long adiog am o p eope a i e genu algum and (
b
) consecu i e co ec ion wi h s aples
in emu ; see [4].
Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 o 16
Figu e 2. (a) Long adiog am o p eope a i e genu algum and (b) consecu i e co ec ion wi h s a-
ples in emu ; see [4].
Recen ly, he ension band echnique, in oduced by S e ens in 2007 [9], using non-
locking pla es (simila o hose used o os eosyn hesis) and sc ews almos in he same
posi ion as s aples, has g adually become a p e e able al e na i e o s apling. Howe e ,
Bloun ’s o iginal me hod s ill emains an e ec i e means o he ea men o lowe limb
de o mi ies in adolescen s; see [1,4,10].
Acco ding o [1,4], besides accu a e diagnosis con i med by a adiog am o he whole
limb (see Figu e 2), good iming o he ea men is also e y impo an . The su gical p o-
cedu e in ol es a sho longi udinal incision h ough so issues o e he physis and ex-
ape ios eal implan a ion o he s aple using a special ins umen unde adiog aphy con-
ol [11] (see Figu e 3). The s aple mus b idge he physis bu no pene a e i o p e en
i s impai men (see Figu e 4).
Figu e 3. Implan a ion o s aples.
Figu e 4. Posi ion o s aples b idging he physis in emu .
The s aples should no be es ic ing he physis o longe han 2 yea s o p e en
pe manen g ow h cessa ion [12]. O he complica ions du ing ea men , such as damag-
ing he physis by imp ecise s aple implan a ion, mechanical ailu e o he s aple (bending,
a ely b eak), o s aple mig a ion can occu . The las one is also he mos common com-
plica ion and disad an age compa ed wi h he ension band echnique; see [1,4].
The e is a lack o in o ma ion ega ding he biomechanical aspec o Bloun ’s s aples;
hence, one o he goals o ou publishing is o ill he gap in his ield.
The e a e wo main me hods o sol ing biomechanical p oblems:
• Nume ical app oach—( he main subjec o his pape ).
• Expe imen al app oach (used and desc ibed only ma ginally he e).
In his pape , he s ess and de o ma ion o s aples du ing epiphysiodesis a e e alu-
a ed by a nume ical app oach using ini e elemen analysis (FEA). The ini e elemen
me hod (FEM) is a ecognized ins umen o nume ical analysis widely used in
Figu e 3. Implan a ion o s aples.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 o 16
Figu e 2. (a) Long adiog am o p eope a i e genu algum and (b) consecu i e co ec ion wi h s a-
ples in emu ; see [4].
Recen ly, he ension band echnique, in oduced by S e ens in 2007 [9], using non-
locking pla es (simila o hose used o os eosyn hesis) and sc ews almos in he same
posi ion as s aples, has g adually become a p e e able al e na i e o s apling. Howe e ,
Bloun ’s o iginal me hod s ill emains an e ec i e means o he ea men o lowe limb
de o mi ies in adolescen s; see [1,4,10].
Acco ding o [1,4], besides accu a e diagnosis con i med by a adiog am o he whole
limb (see Figu e 2), good iming o he ea men is also e y impo an . The su gical p o-
cedu e in ol es a sho longi udinal incision h ough so issues o e he physis and ex-
ape ios eal implan a ion o he s aple using a special ins umen unde adiog aphy con-
ol [11] (see Figu e 3). The s aple mus b idge he physis bu no pene a e i o p e en
i s impai men (see Figu e 4).
Figu e 3. Implan a ion o s aples.
Figu e 4. Posi ion o s aples b idging he physis in emu .
The s aples should no be es ic ing he physis o longe han 2 yea s o p e en
pe manen g ow h cessa ion [12]. O he complica ions du ing ea men , such as damag-
ing he physis by imp ecise s aple implan a ion, mechanical ailu e o he s aple (bending,
a ely b eak), o s aple mig a ion can occu . The las one is also he mos common com-
plica ion and disad an age compa ed wi h he ension band echnique; see [1,4].
The e is a lack o in o ma ion ega ding he biomechanical aspec o Bloun ’s s aples;
hence, one o he goals o ou publishing is o ill he gap in his ield.
The e a e wo main me hods o sol ing biomechanical p oblems:
• Nume ical app oach—( he main subjec o his pape ).
• Expe imen al app oach (used and desc ibed only ma ginally he e).
In his pape , he s ess and de o ma ion o s aples du ing epiphysiodesis a e e alu-
a ed by a nume ical app oach using ini e elemen analysis (FEA). The ini e elemen
me hod (FEM) is a ecognized ins umen o nume ical analysis widely used in
Figu e 4. Posi ion o s aples b idging he physis in emu .
The e is a lack o in o ma ion ega ding he biomechanical aspec o Bloun ’s s aples;
hence, one o he goals o ou publishing is o ill he gap in his ield.
The e a e wo main me hods o sol ing biomechanical p oblems:
•Nume ical app oach—( he main subjec o his pape ).
•Expe imen al app oach (used and desc ibed only ma ginally he e).
In his pape , he s ess and de o ma ion o s aples du ing epiphysiodesis a e e al-
ua ed by a nume ical app oach using ini e elemen analysis (FEA). The ini e elemen
me hod (FEM) is a ecognized ins umen o nume ical analysis widely used in enginee -
Appl. Sci. 2022,12, 614 4 o 16
ing mechanics (see, e.g., [
13
]) and biomechanics. I has been p e iously used o a ious
biomechanical asks [14–16], including Bloun s aple applica ions in epiphysiodesis [17].
To e i y he esul s o he nume ical solu ion, i.e., o assess he usabili y o s aples
unde he chosen loading (g owing) o ce, and o ind he maximum loading (g owing)
o ce ha he s aples can wi hs and, a simple expe imen al app oach was also used in his
pape . Expe imen s can be used in combina ion wi h FEA (as we do he e o , e.g., in [
18
]), o
expe imen s can se e as a s andalone ool o simula ion o eali y, see, e.g., [19].
Ou app oach can be u he used o ano he ypes o modi ica ions o Bloun ’s
s aples, pla es, and simila implan a es.
2. Ma e ials and Me hods
The bone g ow h occu s in he epiphyseal pla e, whe e a new bone mass is c ea ed.
Conside ing his ac , he simula ion o he g owing p ocess u ned ou o be di icul .
Fo his eason, we came up wi h a solu ion whe e he a i icial bone ( ibia) is cu in
wo a he posi ion o he epiphyseal pla e; u he mo e, we assume ha he bone g ows
p edominan ly in he di ec ion o he bone axis (i.e., only opposi ional g ow h is conside ed),
which means ha g ow h can be simula ed by pulling he wo bone segmen s away om
each o he .
Models o he s aples, bo h 3D CAD and physical, we e p o ided by MEDIN, a.s.; see
Figu e 5and [20].
Appl. Sci. 2022, 12, x FOR PEER REVIEW 4 o 16
enginee ing mechanics (see, e.g., [13]) and biomechanics. I has been p e iously used o
a ious biomechanical asks [14–16], including Bloun s aple applica ions in epiphysi-
odesis [17].
To e i y he esul s o he nume ical solu ion, i.e., o assess he usabili y o s aples
unde he chosen loading (g owing) o ce, and o ind he maximum loading (g owing)
o ce ha he s aples can wi hs and, a simple expe imen al app oach was also used in his
pape . Expe imen s can be used in combina ion wi h FEA (as we do he e o , e.g., in [18]),
o expe imen s can se e as a s andalone ool o simula ion o eali y, see, e.g., [19].
Ou app oach can be u he used o ano he ypes o modi ica ions o Bloun ’s s a-
ples, pla es, and simila implan a es.
2. Ma e ials and Me hods
The bone g ow h occu s in he epiphyseal pla e, whe e a new bone mass is c ea ed.
Conside ing his ac , he simula ion o he g owing p ocess u ned ou o be di icul . Fo
his eason, we came up wi h a solu ion whe e he a i icial bone ( ibia) is cu in wo a he
posi ion o he epiphyseal pla e; u he mo e, we assume ha he bone g ows p edomi-
nan ly in he di ec ion o he bone axis (i.e., only opposi ional g ow h is conside ed),
which means ha g ow h can be simula ed by pulling he wo bone segmen s away om
each o he .
Models o he s aples, bo h 3D CAD and physical, we e p o ided by MEDIN, a.s.; see
Figu e 5 and [20].
Figu e 5. Physical model and 3D CAD model wi h main dimensions (mm), supplied by MEDIN,
a.s.
2.1. Fini e Elemen Analysis
The nume ical analysis is pe o med using he Ansys Wo kbench 2020 R2 sw; see
[21]. Homogenous and iso opic ma e ial models a e assumed o be good app oxima ions
o eali y. S aples a e made o biocompa ible s ainless s eel 1.4441 (AISI 316L), see [4], and
he a i icial bone model consis s o co icalis and spongiosis (i.e., he co ical and spongy
pa s); mechanical p ope ies we e aken om [22], whe e Young’s modulus o spongiosis
was epo ed o ange be ween 0.1 and 0.5 GPa and o co icalis be ween 12 and 18 GPa.
F om his, alues close o he uppe limi we e chosen; his can, o example, illus a e
obesi y (i.e., s onge bones o accommoda e o highe body mass). Used ma e ial models
a e p esen ed in Table 1.
Table 1. Ma e ial models o bone and s ainless s eel.
Ma e ial
Young’s Modulus (GPa)
Poisson’s Ra io (1)
Yield S eng h
(MPa)
Ul ima e S eng h
(MPa)
1.4441
183
0.33
690
800
Co icalis
16.1
0.3
Spongiosis
0.4
0.3
Figu e 5.
Physical model and 3D CAD model wi h main dimensions (mm), supplied by MEDIN, a.s.
2.1. Fini e Elemen Analysis
The nume ical analysis is pe o med using he Ansys Wo kbench 2020 R2 sw; see [
21
].
Homogenous and iso opic ma e ial models a e assumed o be good app oxima ions o
eali y. S aples a e made o biocompa ible s ainless s eel 1.4441 (AISI 316L), see [
4
], and
he a i icial bone model consis s o co icalis and spongiosis (i.e., he co ical and spongy
pa s); mechanical p ope ies we e aken om [22], whe e Young’s modulus o spongiosis
was epo ed o ange be ween 0.1 and 0.5 GPa and o co icalis be ween 12 and 18 GPa.
F om his, alues close o he uppe limi we e chosen; his can, o example, illus a e
obesi y (i.e., s onge bones o accommoda e o highe body mass). Used ma e ial models
a e p esen ed in Table 1.
Table 1. Ma e ial models o bone and s ainless s eel.
Ma e ial Young’s
Modulus (GPa)
Poisson’s Ra io
(1)
Yield S eng h
(MPa)
Ul ima e
S eng h (MPa)
1.4441 183 0.33 690 800
Co icalis 16.1 0.3
Spongiosis 0.4 0.3
Appl. Sci. 2022,12, 614 5 o 16
Resea ch by Halo e al. [
4
] ocused on a simple bone ma e ial model, conside ing he
co ical pa as he only ma e ial o he bone. In he cu en pape , howe e , we imp o ed
he bone ma e ial model by di iding i in o co icalis and spongiosis pa s.
2.1.1. CAD and FEM Model
The used CAD model ob ained om a 3D scan and he bone model used in he
expe imen a e no 100% iden ical; ne e heless, hey a e su icien ly simila o allow
expe imen al e i ica ion o he calcula ion esul s; see Figu e 6. The model o he whole
bone is no necessa y o ou pu poses and, o his eason, only he p oximal pa o he
ibia was used in his calcula ion. This p oximal pa was hen “cu ” in wo a he si e o
he epiphyseal pla e. The s aples we e i ually placed in he bone in he way hey usually
a e du ing epiphysiodesis, i.e., in he gene al a ea b idging he physis.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 o 16
Resea ch by Halo e al. [4] ocused on a simple bone ma e ial model, conside ing he
co ical pa as he only ma e ial o he bone. In he cu en pape , howe e , we imp o ed
he bone ma e ial model by di iding i in o co icalis and spongiosis pa s.
2.1.1. CAD and FEM Model
The used CAD model ob ained om a 3D scan and he bone model used in he ex-
pe imen a e no 100% iden ical; ne e heless, hey a e su icien ly simila o allow expe -
imen al e i ica ion o he calcula ion esul s; see Figu e 6. The model o he whole bone
is no necessa y o ou pu poses and, o his eason, only he p oximal pa o he ibia
was used in his calcula ion. This p oximal pa was hen “cu ” in wo a he si e o he
epiphyseal pla e. The s aples we e i ually placed in he bone in he way hey usually a e
du ing epiphysiodesis, i.e., in he gene al a ea b idging he physis.
Figu e 6. 3D CAD model o he bone and s aples wi h main dimensions (mm).
The CAD model o s aple p o ided by MEDIN a.s. con ains no ches, which a e no
sui able o FEA. Fo his eason, sha p edges we e ounded; see Figu e 7. Howe e , hese
sha p edges a e impo an o p ope ly inse ing he s aple in a bone.
Figu e 7. 3D CAD model o he s aple wi h ounded sha p edges (mm).
Figu e 6. 3D CAD model o he bone and s aples wi h main dimensions (mm).
The CAD model o s aple p o ided by MEDIN a.s. con ains no ches, which a e no
sui able o FEA. Fo his eason, sha p edges we e ounded; see Figu e 7. Howe e , hese
sha p edges a e impo an o p ope ly inse ing he s aple in a bone.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 o 16
Resea ch by Halo e al. [4] ocused on a simple bone ma e ial model, conside ing he
co ical pa as he only ma e ial o he bone. In he cu en pape , howe e , we imp o ed
he bone ma e ial model by di iding i in o co icalis and spongiosis pa s.
2.1.1. CAD and FEM Model
The used CAD model ob ained om a 3D scan and he bone model used in he ex-
pe imen a e no 100% iden ical; ne e heless, hey a e su icien ly simila o allow expe -
imen al e i ica ion o he calcula ion esul s; see Figu e 6. The model o he whole bone
is no necessa y o ou pu poses and, o his eason, only he p oximal pa o he ibia
was used in his calcula ion. This p oximal pa was hen “cu ” in wo a he si e o he
epiphyseal pla e. The s aples we e i ually placed in he bone in he way hey usually a e
du ing epiphysiodesis, i.e., in he gene al a ea b idging he physis.
Figu e 6. 3D CAD model o he bone and s aples wi h main dimensions (mm).
The CAD model o s aple p o ided by MEDIN a.s. con ains no ches, which a e no
sui able o FEA. Fo his eason, sha p edges we e ounded; see Figu e 7. Howe e , hese
sha p edges a e impo an o p ope ly inse ing he s aple in a bone.
Figu e 7. 3D CAD model o he s aple wi h ounded sha p edges (mm).
Figu e 7. 3D CAD model o he s aple wi h ounded sha p edges (mm).

Appl. Sci. 2022,12, 614 6 o 16
The adius size o 0.25 mm, acco ding o Figu e 7, is qui e small, because his pa o
he s aple is ela i ely hin, and using bigge adius size (e.g., 0.5 mm) would esul in nea
comple e emo al o his pa .
In his pape , we used only he bone model and s aples o FEA. The eason o his
accep able simpli ica ion lies in he ac ha he limb g ow h is p ima ily de e mined by
he bone (o , mo e accu a ely, epiphyseal pla e). The bone is in ac (i.e., wi hou ac u e);
he e o e, he in luence o he muscles, ligamen s, menisci, and syno ia on bone g ow h is
negligible compa ed o he load on he bone.
Muscles, ligamen s, menisci, and syno ia could play a small ole in es ic ing he
s aple mig a ion, bu his e ec is no no iceable in ou s udy and hence is conside ed
negligible. Thus, muscle and o he issues and luids we e omi ed in his pape .
The in luence o ana omical pa s in ca i as a icula is (i.e., men ioned muscles, lig-
amen s, menisci, and syno ia) migh play signi ican ole in ambula ion o pa ien s wi h
Bloun s aples, see [23].
The ans o ma ion o he CAD model in o he FEM model is p esen ed in Figu e 8.
Conside ing he complexi y o he bone shape, he ibia was disc e ized by e ahed al
elemen s (SOLID187 in Ansys sw) wi h a global maximum size o 2.5 mm. The elemen size
in holes o s aples was locally e ined o mi o he elemen size o he s aples. In addi ion,
a e inemen o 0.5 mm was pe o med in a small ci cula a ea in he immedia e icini y
o holes o s aples. The global elemen size is ela i ely la ge as we a e ocusing on and
e alua ing only he s aple esponse, no ha o he bone. The co icalis and spongiosis FE
meshes a e con inuously connec ed by nodes and elemen s sha ing aces (i.e., con o mal
mesh achie ed by sha ed opology unc ion in Ansys SpaceClaim sw), see [21].
Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 o 16
The adius size o 0.25 mm, acco ding o Figu e 7, is qui e small, because his pa o
he s aple is ela i ely hin, and using bigge adius size (e.g., 0.5 mm) would esul in
nea comple e emo al o his pa .
In his pape , we used only he bone model and s aples o FEA. The eason o his
accep able simpli ica ion lies in he ac ha he limb g ow h is p ima ily de e mined by
he bone (o , mo e accu a ely, epiphyseal pla e). The bone is in ac (i.e., wi hou ac u e);
he e o e, he in luence o he muscles, ligamen s, menisci, and syno ia on bone g ow h
is negligible compa ed o he load on he bone.
Muscles, ligamen s, menisci, and syno ia could play a small ole in es ic ing he
s aple mig a ion, bu his e ec is no no iceable in ou s udy and hence is conside ed
negligible. Thus, muscle and o he issues and luids we e omi ed in his pape .
The in luence o ana omical pa s in ca i as a icula is (i.e., men ioned muscles, liga-
men s, menisci, and syno ia) migh play signi ican ole in ambula ion o pa ien s wi h
Bloun s aples, see [23].
The ans o ma ion o he CAD model in o he FEM model is p esen ed in Figu e 8.
Conside ing he complexi y o he bone shape, he ibia was disc e ized by e ahed al
elemen s (SOLID187 in Ansys sw) wi h a global maximum size o 2.5 mm. The elemen
size in holes o s aples was locally e ined o mi o he elemen size o he s aples. In
addi ion, a e inemen o 0.5 mm was pe o med in a small ci cula a ea in he immedia e
icini y o holes o s aples. The global elemen size is ela i ely la ge as we a e ocusing
on and e alua ing only he s aple esponse, no ha o he bone. The co icalis and spongi-
osis FE meshes a e con inuously connec ed by nodes and elemen s sha ing aces (i.e., con-
o mal mesh achie ed by sha ed opology unc ion in Ansys SpaceClaim sw), see [21].
Figu e 8. FEM model o he bone and s aples.
S aples we e disc e ized by a hex-dominan mesh (SOLID186 + some SOLID187 ele-
men s) wi h a global maximum elemen size o 0.5 mm. The elemen size was locally e-
ined on adii and in he immedia e icini y o hese a eas; see Figu e 9.
Figu e 8. FEM model o he bone and s aples.
S aples we e disc e ized by a hex-dominan mesh (SOLID186 + some SOLID187
elemen s) wi h a global maximum elemen size o 0.5 mm. The elemen size was locally
e ined on adii and in he immedia e icini y o hese a eas; see Figu e 9.
The p esen ed mesh in i s inal o m was used o he inal calcula ion and esul
e alua ion. The sensi i i y analysis s a ed wi h a coa se mesh, and a e each compu a ion,
a new, e ined, mesh wi h hal he elemen size o he p e ious mesh was c ea ed. This
p ocess was epea ed un il esul s o wo di e en meshes we e close (wi hin a 1% ma gin
o e o ); in his way, he mesh sensi i i y analysis was pe o med.
Addi ional in o ma ion abou FE mesh ega ding he numbe o elemen s and nodes
is p esen ed in Table 2.
Appl. Sci. 2022,12, 614 7 o 16
Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 o 16
The adius size o 0.25 mm, acco ding o Figu e 7, is qui e small, because his pa o
he s aple is ela i ely hin, and using bigge adius size (e.g., 0.5 mm) would esul in
nea comple e emo al o his pa .
In his pape , we used only he bone model and s aples o FEA. The eason o his
accep able simpli ica ion lies in he ac ha he limb g ow h is p ima ily de e mined by
he bone (o , mo e accu a ely, epiphyseal pla e). The bone is in ac (i.e., wi hou ac u e);
he e o e, he in luence o he muscles, ligamen s, menisci, and syno ia on bone g ow h
is negligible compa ed o he load on he bone.
Muscles, ligamen s, menisci, and syno ia could play a small ole in es ic ing he
s aple mig a ion, bu his e ec is no no iceable in ou s udy and hence is conside ed
negligible. Thus, muscle and o he issues and luids we e omi ed in his pape .
The in luence o ana omical pa s in ca i as a icula is (i.e., men ioned muscles, liga-
men s, menisci, and syno ia) migh play signi ican ole in ambula ion o pa ien s wi h
Bloun s aples, see [23].
The ans o ma ion o he CAD model in o he FEM model is p esen ed in Figu e 8.
Conside ing he complexi y o he bone shape, he ibia was disc e ized by e ahed al
elemen s (SOLID187 in Ansys sw) wi h a global maximum size o 2.5 mm. The elemen
size in holes o s aples was locally e ined o mi o he elemen size o he s aples. In
addi ion, a e inemen o 0.5 mm was pe o med in a small ci cula a ea in he immedia e
icini y o holes o s aples. The global elemen size is ela i ely la ge as we a e ocusing
on and e alua ing only he s aple esponse, no ha o he bone. The co icalis and spongi-
osis FE meshes a e con inuously connec ed by nodes and elemen s sha ing aces (i.e., con-
o mal mesh achie ed by sha ed opology unc ion in Ansys SpaceClaim sw), see [21].
Figu e 8. FEM model o he bone and s aples.
S aples we e disc e ized by a hex-dominan mesh (SOLID186 + some SOLID187 ele-
men s) wi h a global maximum elemen size o 0.5 mm. The elemen size was locally e-
ined on adii and in he immedia e icini y o hese a eas; see Figu e 9.
Figu e 9.
Re ined FE mesh: (
a
) De ail o he mesh in/a ound he hole o he s aple; (
b
) Mesh o he
s aple; (c) Elemen size on s aple (mm).
Table 2. Numbe o FE elemen s and nodes.
Pa Numbe o FE
Elemen s
Numbe o FE
Nodes
Tibia Epiphysis 66,083 102,706
Me aphysis-Diaphysis 80,183 126,033
S aple Medial 132,292 438,008
La e al 132,581 442,394
To al 411,139 1,109,141
2.1.2. Bounda y Condi ions
The global coo dina e sys em was o ien ed so ha he Z-axis is pa allel o he bone
axis. As men ioned abo e, we assumed ha he bone g ows p edominan ly in he di ec ion
o he bone axis (i.e., opposi ional g ow h) and, he e o e, he alignmen o he axes allows
simple loading o he bone segmen s in he epiphyseal pla e in he Zdi ec ion. We assumed
ha o he g ow h o occu , he loading o ce Fz needs o ma ch he weigh o he pe son.
As he bone g ow h happens in he ea ly s ages o li e (childhood, adolescence), we ha e
chosen ou bone o come om an adolescen s anding on one leg wi h a chosen 100 kg
body weigh equi alen o Fz = 980.7 N. In [
24
], he g owing o ce was de e mined o be
app oxima ely 500 N, i.e., ou o ce Fz was o e es ima ed o e on he side o sa e y. The
o ce bounda y condi ion is illus a ed in Figu e 10.
The dis al end o he cu ibia is ully ixed (i.e., p esc ibed displacemen s a e u
x
= u
y
= u
z
= 0); in he p oximal pa ; he e is a pa ial ixa ion (i.e., p esc ibed displacemen s u
x
=
u
y
= 0) allowing o a mo emen in he Z di ec ion. De o ma ion bounda y condi ions a e
shown in Figu e 11.
Apa om he o ce and de o ma ion bounda y condi ions, ic ional con ac s be ween
he s aples and he bone mus be conside ed. The Coulomb ic ion coe icien be ween
s ainless s eel and bone anges om app oxima ely 0.25 o 0.7, acco ding o [
25
]. The
ic ion coe icien is highly dependen , among o he hings, on he su ace quali y o bo h
bone and s eel, ha dness o bone, e c. In his analysis, he ic ion coe icien was se o 0.2
(es ima ed by an educa ed guess), gi ing he possibili y o s aples o mig a e ou o bone.
The ic ion coe icien used in his s udy is lowe han in [
25
], aking in o accoun he body
luids and issues educing he ic ion. Ne e heless, e en wi h he low ic ion coe icien
used in ou s udy, he displacemen in con ac a eas was e y small, so ic ion does no
ha e a majo e ec on s ess dis ibu ion.
Appl. Sci. 2022,12, 614 8 o 16
Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 o 16
Figu e 9. Re ined FE mesh: (a) De ail o he mesh in/a ound he hole o he s aple; (b) Mesh o he
s aple; (c) Elemen size on s aple (mm).
The p esen ed mesh in i s inal o m was used o he inal calcula ion and esul
e alua ion. The sensi i i y analysis s a ed wi h a coa se mesh, and a e each compu a-
ion, a new, e ined, mesh wi h hal he elemen size o he p e ious mesh was c ea ed.
This p ocess was epea ed un il esul s o wo di e en meshes we e close (wi hin a 1%
ma gin o e o ); in his way, he mesh sensi i i y analysis was pe o med.
Addi ional in o ma ion abou FE mesh ega ding he numbe o elemen s and nodes
is p esen ed in Table 2.
Table 2. Numbe o FE elemen s and nodes.
Pa
Numbe o FE Elemen s
Numbe o FE Nodes
Tibia
Epiphysis
66083
102706
Me aphysis-Diaphysis
80183
126033
S aple
Medial
132292
438008
La e al
132581
442394
To al
411139
1109141
2.1.2. Bounda y Condi ions
The global coo dina e sys em was o ien ed so ha he Z-axis is pa allel o he bone
axis. As men ioned abo e, we assumed ha he bone g ows p edominan ly in he di ec-
ion o he bone axis (i.e., opposi ional g ow h) and, he e o e, he alignmen o he axes
allows simple loading o he bone segmen s in he epiphyseal pla e in he Z di ec ion. We
assumed ha o he g ow h o occu , he loading o ce Fz needs o ma ch he weigh o
he pe son. As he bone g ow h happens in he ea ly s ages o li e (childhood, adoles-
cence), we ha e chosen ou bone o come om an adolescen s anding on one leg wi h a
chosen 100 kg body weigh equi alen o Fz = 980.7 N. In [24], he g owing o ce was
de e mined o be app oxima ely 500 N, i.e., ou o ce Fz was o e es ima ed o e on he
side o sa e y. The o ce bounda y condi ion is illus a ed in Figu e 10.
Figu e 10.
Fo ce bounda y condi ion— o ces Fz (equi alen o 100 kg) ac ing on he epiphyseal pla e.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 o 16
Figu e 10. Fo ce bounda y condi ion— o ces Fz (equi alen o 100 kg) ac ing on he epiphyseal
pla e.
The dis al end o he cu ibia is ully ixed (i.e., p esc ibed displacemen s a e ux = uy
= uz = 0); in he p oximal pa ; he e is a pa ial ixa ion (i.e., p esc ibed displacemen s ux
= uy = 0) allowing o a mo emen in he Z di ec ion. De o ma ion bounda y condi ions
a e shown in Figu e 11.
Figu e 11. De o ma ion bounda y condi ions.
Apa om he o ce and de o ma ion bounda y condi ions, ic ional con ac s be-
ween he s aples and he bone mus be conside ed. The Coulomb ic ion coe icien be-
ween s ainless s eel and bone anges om app oxima ely 0.25 o 0.7, acco ding o [25].
The ic ion coe icien is highly dependen , among o he hings, on he su ace quali y o
bo h bone and s eel, ha dness o bone, e c. In his analysis, he ic ion coe icien was se
o 0.2 (es ima ed by an educa ed guess), gi ing he possibili y o s aples o mig a e ou o
bone. The ic ion coe icien used in his s udy is lowe han in [25], aking in o accoun
he body luids and issues educing he ic ion. Ne e heless, e en wi h he low ic ion
coe icien used in ou s udy, he displacemen in con ac a eas was e y small, so ic ion
does no ha e a majo e ec on s ess dis ibu ion.
2.2. Expe imen
The expe imen was conduc ed o suppo he FEA and clinical applica ions, i.e., o
de e mine he maximum loading o ce Fz o he bone ha he s aples can wi hs and and
o pa ially con i m he indings o he nume ical analysis. Howe e , as he expe imen s
a e no he main goal o his a icle ( he main goal is FEA), hey we e pe o med only once
on an ana omical a i icial bone [26] and once using ce i ied bone oam blocks [27] and
will be only b ie ly desc ibed (see Sec ion 4: Resul s o he Expe imen ).
One o he men ioned expe imen s was pe o med on a i icial bones o he SAW-
BONES b and. The bones a e made o composi e ma e ial mimicking he p ope ies o a
eal human bone, i.e., hey a e sui able o expe imen al pu poses. Fo he use o compo-
si e bone models in expe imen al es ing, see, e.g., [28,29].
The expe imen was based on he same p inciples and assump ions as hose used in
he p esen ed FEA. The ull body o he a i icial ibia was cu o ob ain only he p oximal
pa , which was subsequen ly spli in o wo segmen s a he si e o he epiphyseal pla e.
Bo h bone segmen s we e mechanically adjus ed o allow o he use o a jig. The jig con-
sis ed o a sc ew wi h a washe and nu a ached o he uppe bone segmen (epiphysis)
and o a sel - apping sc ew holding he lowe bone segmen (me aphysis-diaphysis). S a-
ples we e inse ed in o he bone segmen s (in a simila loca ion as in FEA), b idging he
epiphyseal pla e. Bone segmen s we e hen pulled away om each o he using he jig.
Figu e 11. De o ma ion bounda y condi ions.
2.2. Expe imen
The expe imen was conduc ed o suppo he FEA and clinical applica ions, i.e., o
de e mine he maximum loading o ce Fz o he bone ha he s aples can wi hs and and o
pa ially con i m he indings o he nume ical analysis. Howe e , as he expe imen s a e
no he main goal o his a icle ( he main goal is FEA), hey we e pe o med only once on
an ana omical a i icial bone [
26
] and once using ce i ied bone oam blocks [
27
] and will
be only b ie ly desc ibed (see Sec ion 4: Resul s o he Expe imen ).
One o he men ioned expe imen s was pe o med on a i icial bones o he SAW-
BONES b and. The bones a e made o composi e ma e ial mimicking he p ope ies o a
eal human bone, i.e., hey a e sui able o expe imen al pu poses. Fo he use o composi e
bone models in expe imen al es ing, see, e.g., [28,29].
Appl. Sci. 2022,12, 614 9 o 16
The expe imen was based on he same p inciples and assump ions as hose used in he
p esen ed FEA. The ull body o he a i icial ibia was cu o ob ain only he p oximal pa ,
which was subsequen ly spli in o wo segmen s a he si e o he epiphyseal pla e. Bo h
bone segmen s we e mechanically adjus ed o allow o he use o a jig. The jig consis ed o
a sc ew wi h a washe and nu a ached o he uppe bone segmen (epiphysis) and o a
sel - apping sc ew holding he lowe bone segmen (me aphysis-diaphysis). S aples we e
inse ed in o he bone segmen s (in a simila loca ion as in FEA), b idging he epiphyseal
pla e. Bone segmen s we e hen pulled away om each o he using he jig. Figu e 12a
shows a schema ic d awing o he expe imen . Figu e 12b shows he ac ual expe imen .
Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 o 16
Figu e 12a shows a schema ic d awing o he expe imen . Figu e 12b shows he ac ual
expe imen .
Figu e 12. (a) A schema ic d awing o he expe imen (dimensions in mm); (b) Ac ual implemen a-
ion o he expe imen .
In he schema ic d awing, see Figu e 11a, dimension “A” de ails he dis ance o he
epiphyseal pla e om he op o he bone and he dimension “MAX. 90” is ela ed o he
limi s o he used es ing machine.
The uppe bone segmen in Figu e 11b was w apped in duc ape o acili a e manip-
ula ion be o e and du ing he expe imen .
Used equipmen :
• Model o ibia—SAWBONES, Tibia, 4 h Gen., Composi e, 17 PCF Solid Foam Co e;
see [27].
• S aples—p o ided by MEDIN, a.s.; see [20].
• Jig—M12 sc ew, M12 nu , washe (inne diame e 12 mm), ST12 sel - apping sc ew,
all p o ided by MEDIN, a.s.
• Uni e sal es ing machine—TESTOMETRIC M500-50CT; see [30].
The expe imen was conduc ed using de o ma ion-con olled loading wi h a con-
s an a e o jaw sepa a ion se o 10 mm/min.
3. Resul s o FEA
FEA was pe o med as desc ibed in Sec ion 2: Ma e ials and Me hods. The dis ibu-
ion o equi alen s ess ( on Mises) in he s aples was de e mined om he simula ion o
he bone g ow h es ic ion. The maximum s ess occu s in he s aple adius, see Figu es
13 and 14.
Figu e 12.
(
a
) A schema ic d awing o he expe imen (dimensions in mm); (
b
) Ac ual implemen a ion
o he expe imen .
In he schema ic d awing, see Figu e 11a, dimension “A” de ails he dis ance o he
epiphyseal pla e om he op o he bone and he dimension “MAX. 90” is ela ed o he
limi s o he used es ing machine.
The uppe bone segmen in Figu e 11b was w apped in duc ape o acili a e manipu-
la ion be o e and du ing he expe imen .
Used equipmen :
•
Model o ibia—SAWBONES, Tibia, 4 h Gen., Composi e, 17 PCF Solid Foam Co e;
see [27].
•S aples—p o ided by MEDIN, a.s.; see [20].
•
Jig—M12 sc ew, M12 nu , washe (inne diame e 12 mm), ST12 sel - apping sc ew, all
p o ided by MEDIN, a.s.
•Uni e sal es ing machine—TESTOMETRIC M500-50CT; see [30].
The expe imen was conduc ed using de o ma ion-con olled loading wi h a cons an
a e o jaw sepa a ion se o 10 mm/min.
3. Resul s o FEA
FEA was pe o med as desc ibed in Sec ion 2: Ma e ials and Me hods. The dis ibu-
ion o equi alen s ess ( on Mises) in he s aples was de e mined om he simula ion
o he bone g ow h es ic ion. The maximum s ess occu s in he s aple adius, see
Figu es 13 and 14.
The o al displacemen o s aples is p esen ed in Figu e 15. In ou case, he highes
o al displacemen is a he op end o he s aples and he maximum displacemen is highe
up in he medial s aple han in he la e al one. Based on he de ec ed de o ma ion, we can
measu e he dis ance be ween he bone segmen s om he epiphyseal pla e o ob ain a
ough es ima ion o how much he bone could g ow wi h he s aples applied. Figu e 16
shows he a e age maximum possible g ow h dis ance be ween bo h bone segmen s.
The acqui ed FEA esul s a e summa ized in Table 3.
Appl. Sci. 2022,12, 614 16 o 16
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