Biomechanical analysis of staples for epiphysiodesis

  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 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2022 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons 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 33. F yd ýšek, K.; Michenko á, Š.; Ple a, L.; Kou ecký, J.; F ies, J.; Pe e ek Dˇedko á, K.; Madeja, R.; T e il, A.; K pec, P.; Halo, T.; e al. 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