Biomechanical assessment of cannulated nails for the treatment of proximal femur fractures
Abstract
This article focuses on a type of surgical implant used in orthopaedics and traumatology-cannulated femoral nails. Femoral nails are used in medical treatment for purposes of osteosynthesis, i.e., when treating various types of complicated fractures, in this case fractures of the femur. The article investigates cases in which a nail has been implanted in the proximal part of the femur for a short time (with the fracture still not healed), compared with cases in which the bone has already healed. According to AO classification, examined fractures are described as AO 31B3 AO 32A3. The main focus is on strength-deformation analysis using the finite element method (FEM), which makes it possible to determine the behaviour of the femur-implant system. FEM analysis was used to compare 1.4441 steel nails made by two manufacturers, Medin (Czech Republic) and Tantum (Germany). Boundary conditions including external loading, prescribed supports and elastic foundation are defined. There were solved FEM analyses for five cases of healed femur and five cases of broken femur both including implants with prescribed collo-diaphyseal angles. The results of the analysis were used to assess stress-deformation states from the perspective of appropriateness for clinical treatment, biomechanical reliability and safety. All examined femoral nails are compared, safe and suitable for patient treatment.
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Citation: Frydrýšek, K.; Halo, T.; ˇ Cepica, D.; Machalla, V.; Šimeˇcková, K.; Skoupý, O.; Madeja, R.; Havlíˇcek, M.; Dostálová, K.; Trefil, A.; et al. Biomechanical Assessment of Cannulated Nails for the Treatment of Proximal Femur Fractures. Appl. Sci. 2022,12, 7470. https:// doi.org/10.3390/app12157470 Academic Editor: Gaetano Isola Received: 15 April 2022 Accepted: 22 June 2022 Published: 25 July 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). applied sciences Article Biomechanical Assessment of Cannulated Nails for the Treatment of Proximal Femur Fractures Karel Frydrýšek 1,2 , Tomáš Halo 1,2,* , Daniel ˇ Cepica 1,2, Vojtˇech Machalla 1,2, Kateˇrina Šimeˇcková1,2 , Ondˇrej Skoupý1,2, Roman Madeja 2,3, Miroslav Havlíˇcek 4, Kamila Dostálová5, Antonín Trefil 1, Leopold Pleva 2,3, Zuzana Murˇcinkova 6, Pavel Krpec 7and Josef Hlinka 8 1Faculty of Mechanical Engineering, VSB—Technical University of Ostrava, 17. listopadu 15/2172, 70800 Ostrava-Poruba, Czech Republic; kar[email protected] (K.F.); [email protected] (D. ˇ C.); [email protected] (V.M.); [email protected] (K.Š.); [email protected] (O.S.); [email protected] (A.T.) 2Faculty of Medicine, University of Ostrava, Syllabova 19, 70300 Ostrava-Vítkovice, Czech Republic; [email protected] (R.M.); [email protected] (L.P.) 3Trauma Centre, University Hospital Ostrava, 17. listopadu 1790, 70852 Ostrava-Poruba, Czech Republic 4Medin, a.s, Vlachovicka 619, 59231 NovéMˇesto na Moravˇe, Czech Republic; miroslav[email protected] 5 Centre for Advanced Innovative Technologies, VSB—Technical University of Ostrava, 17. listopadu 15/2172, 70800 Ostrava-Poruba, Czech Republic; [email protected] 6Department of Design and Monitoring of Technical Systems, Technical University of Košice, Letná9, 04200 Košice, Slovakia; [email protected] 7V-NASS, a.s., Halasova 2938/1a, 70300 Ostrava-Vítkovice, Czech Republic; [email protected] 8Faculty of Materials Science and Technology, VSB—Technical University of Ostrava, 17. listopadu 15/2172, 70800 Ostrava-Poruba, Czech Republic; [email protected] *Correspondence: [email protected] Abstract: This article focuses on a type of surgical implant used in orthopaedics and traumatology—cannulated femoral nails. Femoral nails are used in medical treatment for purposes of osteosynthesis, i.e., when treating various types of complicated fractures, in this case fractures of the femur. The article investigates cases in which a nail has been implanted in the proximal part of the femur for a short time (with the fracture still not healed), compared with cases in which the bone has already healed. According to AO classification, examined fractures are described as AO 31B3 AO 32A3. The main focus is on strength-deformation analysis using the finite element method (FEM), which makes it possible to determine the behaviour of the femurimplant system. FEM analysis was used to compare 1.4441 steel nails made by two manufacturers, Medin (Czech Republic) and Tantum (Germany). Boundary conditions including external loading, prescribed supports and elastic foundation are defined. There were solved FEM analyses for five cases of healed femur and five cases of broken femur both including implants with prescribed collodiaphyseal angles. The results of the analysis were used to assess stress-deformation states from the perspective of appropriateness for clinical treatment, biomechanical reliability and safety. All examined femoral nails are compared, safe and suitable for patient treatment. Keywords: proximal femoral nailing; osteosynthesis; numerical simulation; traumatology; FEM analysis; biomechanics; short reconstructive nails 1. Introduction In medical practice, nails are used to treat various types of limb fractures. Femoral nails are used to treat fractures of the proximal and distal femur. This article presents an analysis of nails used to treat proximal femoral fractures located in the vicinity of the pelvis. It also draws significance to the usage of short reconstructive nails in the treatment of specific proximal femur fractures. The examined nails are manufactured by Medin ( NovéMˇesto na Moravˇe, Czech Republic ) and Tantum (Neumünster, Germany). It draws Appl. Sci. 2022,12, 7470. https://doi.org/10.3390/app12157470 https://www.mdpi.com/journal/applsci
Appl. Sci. 2022,12, 7470 2 of 16 on previous theoretical and practical studies concerning the proximal femur [ 1 , 2 ]. In the AO classification, the fractures in this region are fractura mediocervicalis femoris AO 31B3 and fractura subtrochanterica femoris AO 32A3 [ 3 ]. These are among the most frequent fractures of long bones, human trauma and they present the greatest risk to the elderly population. A substantial majority of patients with these fractures are over the age of 50, and cases occur among women 2–3 times more frequently than among men [ 4 ]. For these reasons, it is beneficial to conduct stress-deformation analyses and to assess the suitability of femoral nails for clinical treatment. The nails currently in use differ primarily in their design (collodiaphyseal angle 120–135 ◦ , see Figure 1a) and also depending on the producer and the materials used (compatibility with the human body). Appl.Sci.2022,12,xFORPEERREVIEW2of17 (NovéMěstonaMoravě,CzechRepublic)andTantum(Neumünster,Germany).Itdraws onprevioustheoreticalandpracticalstudiesconcerningtheproximalfemur[1,2].Inthe AOclassification,thefracturesinthisregionarefracturamediocervicalisfemorisAO31B3 andfracturasubtrochantericafemorisAO32A3[3].Theseareamongthemostfrequent fracturesoflongbones,humantraumaandtheypresentthegreatestrisktotheelderly population.Asubstantialmajorityofpatientswiththesefracturesareovertheageof50, andcasesoccuramongwomen2–3timesmorefrequentlythanamongmen[4].Forthese reasons,itisbeneficialtoconductstress‐deformationanalysesandtoassessthesuitability offemoralnailsforclinicaltreatment.Thenailscurrentlyinusedifferprimarilyintheir design(collo‐diaphysealangle120–135°,seeFigure1a)andalsodependingonthe producerandthematerialsused(compatibilitywiththehumanbody). (a)(b) Figure1.(a)Anatomyoffemurbone(a—liniaintertrochanterica;b—trochantermajor;c—caput femoris;d—foveacapitisfemoris;e—collumfemoris;f—tuberositasglutea;g—trochanterminor; h—tuberculumadductorium;i—epicondylusmedialis;j—condylusmedialis;k—faciespatellaris; l—condyluslateralis;m—epicondyluslateralis;n—proximalend;o—diaphysis;p—distalend).(b) Proximalfemurplacedinacetabulum(X‐raysnapshot). Thefemur(seeFigure1)isthelargestandheaviestboneinthehumanbody.The proximalpartofthefemurconsistsmainlyofthealmostsphericalfemoralhead(caput femoris),whichisseatedwithintheacetabulumofthepelvis;thefemoralneck(collum femoris),whichformstheneck‐shaftangle(collo‐diaphysealangle)withthemainaxial lengthofthefemur(usually125–135°);andtheeminencesofthegreaterandlesser trochanter(trochantermajorandtrochanterminor)andtheadjacentareas,wherethe muscleattachmentsarelocated[1].Theanteversionofthefemoralnecktothefrontal anatomicalplaneisapproximately15°. Proximalfemoralfracture(PFF)isoneofthemostcommontypesoflongbonefracture anditpresentsaparticularrisktoelderlypatients.WeknowthatPFFsaccountforalarge proportionofhospitalisationsandpossiblecomplicationsamongtraumacases[2]. Morepreciseclassificationsofthesefractureshavebeendeveloped,facilitating practicaldescriptionandenablingdifferenttreatmentcentrestosharetheirclinical experiences.Historically,oneofthebest‐knownclassificationsoftrochantericfractures wasdevelopedbyEvans[5],whodividesthemprimarilyintostableandunstable Figure 1. ( a ) Anatomy of femur bone (a—linia intertrochanterica; b—trochanter major; c—caput femoris; d—fovea capitis femoris; e—collum femoris; f—tuberositas glutea; g—trochanter minor; h—tuberculum adductorium; i—epicondylus medialis; j—condylus medialis; k—facies patellaris; l—condylus lateralis; m—epicondylus lateralis; n—proximal end; o—diaphysis; p—distal end). (b) Proximal femur placed in acetabulum (X-ray snapshot). The femur (see Figure 1) is the largest and heaviest bone in the human body. The proximal part of the femur consists mainly of the almost spherical femoral head (caput femoris), which is seated within the acetabulum of the pelvis; the femoral neck (collum femoris), which forms the neck-shaft angle (collo-diaphyseal angle) with the main axial length of the femur (usually 125–135 ◦ ); and the eminences of the greater and lesser trochanter (trochanter major and trochanter minor) and the adjacent areas, where the muscle attachments are located [ 1 ]. The anteversion of the femoral neck to the frontal anatomical plane is approximately 15◦. Proximal femoral fracture (PFF) is one of the most common types of long bone fracture and it presents a particular risk to elderly patients. We know that PFFs account for a large proportion of hospitalisations and possible complications among trauma cases [2]. More precise classifications of these fractures have been developed, facilitating practical description and enabling different treatment centres to share their clinical experiences. Historically, one of the best-known classifications of trochanteric fractures was developed by Evans [ 5 ], who divides them primarily into stable and unstable fractures and into several types. Figure 2a shows a classification of a fracture based on this system compared with the equivalent AO classification.
Appl. Sci. 2022,12, 7470 3 of 16 Appl.Sci.2022,12,xFORPEERREVIEW3of17 fracturesandintoseveraltypes.Figure2ashowsaclassificationofafracturebasedonthis systemcomparedwiththeequivalentAOclassification. (a)(b) Figure2.(a)Pertrochantericfractureoffemur(Evans5,AO31A2.3);(b)fracturetreatmentvianail. Femoralneckfractureshavebeendescribedbynumerousauthors.Oneofthemost frequentlyusedclassificationsisbyGarden[6],whodividesfracturesintofourgrades:I. incomplete,II.completebutnon‐displaced,III.completeandpartiallydisplacedandIV. completeandfullydisplaced. AnotherclassificationofPFFs(andotherfractures)istheinternationalAO/OTA system,developedbytheSwissAO(ArbeitsgemeinschaftfürOsteosynthesefragen)and theOTA(OrthopedicTraumaAssociation).Thissystemusesnumbersandlettersto designatedfracturetypes.PFFsaredenotedbynumbersfrom31upwards3. Eachofthesetypesofproximalfemoralfracturerequiresspecialmethodsof treatment,eachtypehasitsownspecificsetofpossiblecomplicationsandcontroversies regardingoptimalmanagementmethods.Formoreinformationonthevariousissues involvedintheappropriatemanagementofPFFs,pleasereadthefollowing1,2,4]. PFFsamongelderlypeoplearemainlycausedbysimplefalls.Inyoungerpatients, PFFsaremostfrequentlycausedbyhigh‐energyinjuries,usuallysustainedduetotraffic accidents,fallsfromheights,sportinginjuriesoroccupationalinjuries. Nowadays,suchfracturesarealmostalwaystreatedsurgically(osteosynthesis, alloplasty);exceptionsareincaseswhenpatientshavecontraindicationstogeneralor regionalanaesthesia.Thetextbelowfocusesmainlyonosteosynthesis. Surgeryinvolvestherepositioningandsubsequentosteosynthesisofthebroken bone,withmetalimplantsusedtofixthefracturedpartsoftheboneinplace;thesemay beeitherexternalorinternalfixators[7,8].Assurgicalmethodshaveevolved,sotoohave theimplantsusedforosteosynthesisinproximalfemoralfractures[9].Inthepast,plates withloadscrewswereused[10].Nowadays,osteosynthesisisusuallyachievedbyusing nailswithseveralloadscrews[11].Thereliabilityofosteosynthesisdependsonanumber offactors,includingthequalityofthebonetissue(anditsporosityorotherdegradation), Figure 2. ( a ) Pertrochanteric fracture of femur (Evans 5, AO 31 A2.3); ( b ) fracture treatment via nail. Femoral neck fractures have been described by numerous authors. One of the most frequently used classifications is by Garden [ 6 ], who divides fractures into four grades: I. incomplete, II. complete but non-displaced, III. complete and partially displaced and IV. complete and fully displaced. Another classification of PFFs (and other fractures) is the international AO/OTA system, developed by the Swiss AO (Arbeitsgemeinschaft für Osteosynthesefragen) and the OTA (Orthopedic Trauma Association). This system uses numbers and letters to designated fracture types. PFFs are denoted by numbers from 31 upwards [3]. Each of these types of proximal femoral fracture requires special methods of treatment, each type has its own specific set of possible complications and controversies regarding optimal management methods. For more information on the various issues involved in the appropriate management of PFFs, please read the following [1,2,4]. PFFs among elderly people are mainly caused by simple falls. In younger patients, PFFs are most frequently caused by high-energy injuries, usually sustained due to traffic accidents, falls from heights, sporting injuries or occupational injuries. Nowadays, such fractures are almost always treated surgically (osteosynthesis, alloplasty); exceptions are in cases when patients have contraindications to general or regional anaesthesia. The text below focuses mainly on osteosynthesis. Surgery involves the repositioning and subsequent osteosynthesis of the broken bone, with metal implants used to fix the fractured parts of the bone in place; these may be either external or internal fixators [ 7 , 8 ]. As surgical methods have evolved, so too have the implants used for osteosynthesis in proximal femoral fractures [ 9 ]. In the past, plates with load screws were used [ 10 ]. Nowadays, osteosynthesis is usually achieved by using nails with several load screws [ 11 ]. The reliability of osteosynthesis depends on a number of factors, including the quality of the bone tissue (and its porosity or other degradation), the character of the fracture and the properties and shape of the implant used. The healing of the fracture is also affected by other factors, such as the patient’s overall physical and
Appl. Sci. 2022,12, 7470 4 of 16 mental state, the condition of the soft tissue, the hormonal stability of the organism, possible infections, etc. The choice of an appropriate implant, its properties and its shape have a substantial influence on the possible emergence of early and later postoperative complications, as well as on the duration of the healing process. In this article, there are ten solved cases (i.e., ten numerical simulations) of fractured and healed femur with femoral nail implants with variability in collo-diaphyseal angles. Finite element method (FEM) was used to assess the suitability and reliability of all examined implants. FEM is widely used and accepted numerical method for solution of problems in mechanics and biomechanics. Quite a good review of FEM approach applied in lower limbs biomechanics can be seen in [ 12 ]. Similar numerical simulations were presented in reference [13]. 2. Materials and Methods Figure 3briefly describes the process behind Materials and Methods chapter in pictures and is further explained in the following text below. Appl.Sci.2022,12,xFORPEERREVIEW4of17 thecharacterofthefractureandthepropertiesandshapeoftheimplantused.Thehealing ofthefractureisalsoaffectedbyotherfactors,suchasthepatient’soverallphysicaland mentalstate,theconditionofthesofttissue,thehormonalstabilityoftheorganism, possibleinfections,etc. Thechoiceofanappropriateimplant,itspropertiesanditsshapehaveasubstantial influenceonthepossibleemergenceofearlyandlaterpostoperativecomplications,as wellasonthedurationofthehealingprocess. Inthisarticle,therearetensolvedcases(i.e.,tennumericalsimulations)offractured andhealedfemurwithfemoralnailimplantswithvariabilityincollo‐diaphysealangles. Finiteelementmethod(FEM)wasusedtoassessthesuitabilityandreliabilityofall examinedimplants.FEMiswidelyusedandacceptednumericalmethodforsolutionof problemsinmechanicsandbiomechanics.QuiteagoodreviewofFEMapproachapplied inlowerlimbsbiomechanicscanbeseenin[12].Similarnumericalsimulationswere presentedinreference[13]. 2.MaterialsandMethods Figure3brieflydescribestheprocessbehindMaterialsandMethodschapterin picturesandisfurtherexplainedinthefollowingtextbelow. Figure3.Workflowdiagram. Themechanicalpropertiesoftheboneareconsideredtobeisotropicand homogeneous;theyareidenticalinallcasesforthepurposesofFEManalysis.Allpartsof thenailsareproducedfrom1.4441steel,whichiscommonlyusedinimplantsandis biocompatible[14–16].MechanicalpropertiesareshowninTable1. Table1.Mechanicalpropertiesofmaterialsused. MaterialModulusofTensile Elasticity/MPa/ Poisson’s Constant/1/ OffsetYieldStrength Rp0.2/MPa/ TensileStrength Rm/MPa/ Bone13,0000.3‐ ‐ 1.4441steel200,0000.298001000 Thecollo‐diaphysealangleoftheanatomicalmodelofthefemur(Figures1aand4) obtainedfromaCTimageis125°[17].Thecollo‐diaphysealanglesoftheinvestigatednails withvariantsofthefemurareshowninTable2.Thisvariabilitywasdiscussedwithmedics. Figure 3. Workflow diagram. The mechanical properties of the bone are considered to be isotropic and homogeneous; they are identical in all cases for the purposes of FEM analysis. All parts of the nails are produced from 1.4441 steel, which is commonly used in implants and is biocompatible [ 14 – 16 ]. Mechanical properties are shown in Table 1. Table 1. Mechanical properties of materials used. Material Modulus of Tensile Elasticity/MPa/ Poisson’s Constant/1/ Offset Yield Strength Rp0.2/MPa/ Tensile Strength Rm/MPa/ Bone 13,000 0.3 - - 1.4441 steel 200,000 0.29 800 1000 The collo-diaphyseal angle of the anatomical model of the femur (Figures 1a and 4) obtained from a CT image is 125 ◦ [ 17 ]. The collo-diaphyseal angles of the investigated nails with variants of the femur are shown in Table 2. This variability was discussed with medics.
Appl. Sci. 2022,12, 7470 5 of 16 Appl.Sci.2022,12,xFORPEERREVIEW5of17 Figure4.Collo‐diaphysealangleofanatomicalCADfemur. Notethedifferencebetweenthecollo‐diaphysealangleofthefemur(whichisa constant125°)andthecollo‐diaphysealanglesofthenails(rangingfrom120°to135°) [18,19].Accordingtotheanatomyofapatient,themanufacturercanproduceimplants withvariouscollo‐diaphysealangles.Otherdimensionsmayalsovarydependingonthe patient’sanatomy,fromwhichsomearedepictedinFigure5. (a)(b) Figure5.Generaldimensionsofexaminedimplants.(a)Medin;(b)Tantum. Table2.Cannulatednailsunderinvestigation. Medina.s. Nailcollo‐diaphysealangle125°HealedfemurFigure6a BrokenfemurFigure7a Nailcollo‐diaphysealangle130°HealedfemurFigure6b BrokenfemurFigure7b Nailcollo‐diaphysealangle135°HealedfemurFigure6c BrokenfemurFigure7c Tantum Nailcollo‐diaphysealangle120°HealedfemurFigure6d BrokenfemurFigure7d Nailcollo‐diaphysealangle125°HealedfemurFigure6e BrokenfemurFigure7e Figure 4. Collo-diaphyseal angle of anatomical CAD femur. Note the difference between the collo-diaphyseal angle of the femur (which is a constant 125 ◦ ) and the collo-diaphyseal angles of the nails (ranging from 120 ◦ to 135 ◦ ) [ 18 , 19 ]. According to the anatomy of a patient, the manufacturer can produce implants with various collo-diaphyseal angles. Other dimensions may also vary depending on the patient’s anatomy, from which some are depicted in Figure 5. Appl.Sci.2022,12,xFORPEERREVIEW5of17 Figure4.Collo‐diaphysealangleofanatomicalCADfemur. Notethedifferencebetweenthecollo‐diaphysealangleofthefemur(whichisa constant125°)andthecollo‐diaphysealanglesofthenails(rangingfrom120°to135°) [18,19].Accordingtotheanatomyofapatient,themanufacturercanproduceimplants withvariouscollo‐diaphysealangles.Otherdimensionsmayalsovarydependingonthe patient’sanatomy,fromwhichsomearedepictedinFigure5. (a)(b) Figure5.Generaldimensionsofexaminedimplants.(a)Medin;(b)Tantum. Table2.Cannulatednailsunderinvestigation. Medina.s. Nailcollo‐diaphysealangle125°HealedfemurFigure6a BrokenfemurFigure7a Nailcollo‐diaphysealangle130°HealedfemurFigure6b BrokenfemurFigure7b Nailcollo‐diaphysealangle135°HealedfemurFigure6c BrokenfemurFigure7c Tantum Nailcollo‐diaphysealangle120°HealedfemurFigure6d BrokenfemurFigure7d Nailcollo‐diaphysealangle125°HealedfemurFigure6e BrokenfemurFigure7e Figure 5. General dimensions of examined implants. (a) Medin; (b) Tantum. Table 2. Cannulated nails under investigation. Medin a.s. Nail collo-diaphyseal angle 125◦Healed femur Figure 6a Broken femur Figure 7a Nail collo-diaphyseal angle 130◦Healed femur Figure 6b Broken femur Figure 7b Nail collo-diaphyseal angle 135◦Healed femur Figure 6c Broken femur Figure 7c Tantum Nail collo-diaphyseal angle 120◦Healed femur Figure 6d Broken femur Figure 7d Nail collo-diaphyseal angle 125◦Healed femur Figure 6e Broken femur Figure 7e
Appl. Sci. 2022,12, 7470 6 of 16 Appl.Sci.2022,12,xFORPEERREVIEW6of17 (a)(b)(c)(d)(e) Figure6.ModifiedCADmodelsofahealedfemurwithnails—(a–c)Medin;(d,e)Tantum. (a)(b)(c)(d)(e) Figure7.ModifiedCADmodelsofabrokenfemurwithnails—(a–c)Medin;(d,e)Tantum. InordertoattainanacceptablelevelofsimplificationintheFEMsimulation,theCAD modelsweremodifiedappropriately(seeFigure8).Thisreducescomputingtimebuthas nosubstantialimpactontheanalyticalresults.Thescrewsweremodelledaspin‐type structures;thescrewthreadwasreplacedbyacylindricalportionwiththesamediameter astheminorthreaddiameter(onthesideofsafety).Thethreadsofthefixationscrews weremodifiedtoapproximatelythemeandiameterofthescrewthreads(representingan acceptablesimplification),exceptatthepointofcontactwiththenail,wherethemajor threaddiameterwasretained(foraccuraterepresentationofthecontact).Thescrewheads weremodifiedtocylindricalvolumesinordertosimplifythesimulation(thisdoesnot affecttheresults). (a) (b) (c) Figure 6. Modified CAD models of a healed femur with nails—(a–c) Medin; (d,e) Tantum. Appl.Sci.2022,12,xFORPEERREVIEW6of17 (a)(b)(c)(d)(e) Figure6.ModifiedCADmodelsofahealedfemurwithnails—(a–c)Medin;(d,e)Tantum. (a)(b)(c)(d)(e) Figure7.ModifiedCADmodelsofabrokenfemurwithnails—(a–c)Medin;(d,e)Tantum. InordertoattainanacceptablelevelofsimplificationintheFEMsimulation,theCAD modelsweremodifiedappropriately(seeFigure8).Thisreducescomputingtimebuthas nosubstantialimpactontheanalyticalresults.Thescrewsweremodelledaspin‐type structures;thescrewthreadwasreplacedbyacylindricalportionwiththesamediameter astheminorthreaddiameter(onthesideofsafety).Thethreadsofthefixationscrews weremodifiedtoapproximatelythemeandiameterofthescrewthreads(representingan acceptablesimplification),exceptatthepointofcontactwiththenail,wherethemajor threaddiameterwasretained(foraccuraterepresentationofthecontact).Thescrewheads weremodifiedtocylindricalvolumesinordertosimplifythesimulation(thisdoesnot affecttheresults). (a) (b) (c) Figure 7. Modified CAD models of a broken femur with nails—(a–c) Medin; (d,e) Tantum. In order to attain an acceptable level of simplification in the FEM simulation, the CAD models were modified appropriately (see Figure 8). This reduces computing time but has no substantial impact on the analytical results. The screws were modelled as pin-type structures; the screw thread was replaced by a cylindrical portion with the same diameter as the minor thread diameter (on the side of safety). The threads of the fixation screws were modified to approximately the mean diameter of the screw threads (representing an acceptable simplification), except at the point of contact with the nail, where the major thread diameter was retained (for accurate representation of the contact). The screw heads were modified to cylindrical volumes in order to simplify the simulation (this does not affect the results). Appl.Sci.2022,12,xFORPEERREVIEW6of17 (a)(b)(c)(d)(e) Figure6.ModifiedCADmodelsofahealedfemurwithnails—(a–c)Medin;(d,e)Tantum. (a)(b)(c)(d)(e) Figure7.ModifiedCADmodelsofabrokenfemurwithnails—(a–c)Medin;(d,e)Tantum. InordertoattainanacceptablelevelofsimplificationintheFEMsimulation,theCAD modelsweremodifiedappropriately(seeFigure8).Thisreducescomputingtimebuthas nosubstantialimpactontheanalyticalresults.Thescrewsweremodelledaspin‐type structures;thescrewthreadwasreplacedbyacylindricalportionwiththesamediameter astheminorthreaddiameter(onthesideofsafety).Thethreadsofthefixationscrews weremodifiedtoapproximatelythemeandiameterofthescrewthreads(representingan acceptablesimplification),exceptatthepointofcontactwiththenail,wherethemajor threaddiameterwasretained(foraccuraterepresentationofthecontact).Thescrewheads weremodifiedtocylindricalvolumesinordertosimplifythesimulation(thisdoesnot affecttheresults). (a) (b) (c) Figure 8. Cont.
Appl. Sci. 2022,12, 7470 7 of 16 Appl.Sci.2022,12,xFORPEERREVIEW7of17 (d) Figure8.ModificationsofCADmodelsforFEManalysis.(a)Medinloadscrew;(b)Tantumload screw;(c,d)Fixationscrews. IntheFEManalysis,fracturesAO31B1andAO32A3(indicatedintheprecedingtext anddepictedinFigure7)werecreatedintheCADmodelofthefemoralbonebydividing thebonemodelalongtwoplanes,asindicatedinFigure9.DoctorsfromtheUniversity HospitalinOstravawereconsultedregardingthelocationofthisdivisionandapproved thedivision. Figure9.LocationoffracturesintheanatomicalCADmodelofthefemur(Spaceclaim). 3.FiniteElementAnalysis TheFEManalysiswasconductedusingAnsysWorkbench2020R2software[20]. Contactsweredefinedforthepurposeofsimulatingmechanicalcontactsinall investigatedmodels(seeFigures6and7).Inprinciple,thecontactsarethesameinallthe analyses,thoughtherearedifferencesbetweenthehealedandbrokenfemurs,inthelatter typethereisalsocontactbetweenthebonefragments(onthefracturesurfaces).The contactsareshowninTable3. Table3.Contacts(AnsysWorkbenchMechanicalsoftware). ElementFemurScrew HealedfemurFemur(Onebody)Bonded NailBondedBonded BrokenfemurFemurFrictionlessBonded NailBondedNoseparation Forthehealedfemur,itwasconsideredthatbonetissuehasgrownaroundallparts ofthescrewsandnails,whichmeansthatneitherthenailasawholenoranypartofit moveswithinthefemur,sothenailcanbeconsideredapartofthebone.Forthisreason, thecontactsweredefinedas“Bonded”. Forthebrokenfemur,thecontacttypeswerechoseninordertosimulateasituation inwhichthepatientbeginstoplaceweightontheaffectedlimb.Innormalcircumstances, weight‐bearingbegins6weeksaftertheimplantisfittedandthepatientshouldplaceno morethanone‐thirdoftheirtotalbodyweightonthehealinglimb.(Informationgained Figure 8. Modifications of CAD models for FEM analysis. ( a ) Medin load screw; ( b ) Tantum load screw; (c,d) Fixation screws. In the FEM analysis, fractures AO 31B1 and AO 32A3 (indicated in the preceding text and depicted in Figure 7) were created in the CAD model of the femoral bone by dividing the bone model along two planes, as indicated in Figure 9. Doctors from the University Hospital in Ostrava were consulted regarding the location of this division and approved the division. Appl.Sci.2022,12,xFORPEERREVIEW7of17 (d) Figure8.ModificationsofCADmodelsforFEManalysis.(a)Medinloadscrew;(b)Tantumload screw;(c,d)Fixationscrews. IntheFEManalysis,fracturesAO31B1andAO32A3(indicatedintheprecedingtext anddepictedinFigure7)werecreatedintheCADmodelofthefemoralbonebydividing thebonemodelalongtwoplanes,asindicatedinFigure9.DoctorsfromtheUniversity HospitalinOstravawereconsultedregardingthelocationofthisdivisionandapproved thedivision. Figure9.LocationoffracturesintheanatomicalCADmodelofthefemur(Spaceclaim). 3.FiniteElementAnalysis TheFEManalysiswasconductedusingAnsysWorkbench2020R2software[20]. Contactsweredefinedforthepurposeofsimulatingmechanicalcontactsinall investigatedmodels(seeFigures6and7).Inprinciple,thecontactsarethesameinallthe analyses,thoughtherearedifferencesbetweenthehealedandbrokenfemurs,inthelatter typethereisalsocontactbetweenthebonefragments(onthefracturesurfaces).The contactsareshowninTable3. Table3.Contacts(AnsysWorkbenchMechanicalsoftware). ElementFemurScrew HealedfemurFemur(Onebody)Bonded NailBondedBonded BrokenfemurFemurFrictionlessBonded NailBondedNoseparation Forthehealedfemur,itwasconsideredthatbonetissuehasgrownaroundallparts ofthescrewsandnails,whichmeansthatneitherthenailasawholenoranypartofit moveswithinthefemur,sothenailcanbeconsideredapartofthebone.Forthisreason, thecontactsweredefinedas“Bonded”. Forthebrokenfemur,thecontacttypeswerechoseninordertosimulateasituation inwhichthepatientbeginstoplaceweightontheaffectedlimb.Innormalcircumstances, weight‐bearingbegins6weeksaftertheimplantisfittedandthepatientshouldplaceno morethanone‐thirdoftheirtotalbodyweightonthehealinglimb.(Informationgained Figure 9. Location of fractures in the anatomical CAD model of the femur (Spaceclaim). 3. Finite Element Analysis The FEM analysis was conducted using Ansys Workbench 2020 R2 software [20]. Contacts were defined for the purpose of simulating mechanical contacts in all investigated models (see Figures 6and 7). In principle, the contacts are the same in all the analyses, though there are differences between the healed and broken femurs, in the latter type there is also contact between the bone fragments (on the fracture surfaces). The contacts are shown in Table 3. Table 3. Contacts (Ansys Workbench Mechanical software). Element Femur Screw Healed femur Femur (One body) Bonded Nail Bonded Bonded Broken femur Femur Frictionless Bonded Nail Bonded No separation For the healed femur, it was considered that bone tissue has grown around all parts of the screws and nails, which means that neither the nail as a whole nor any part of it moves within the femur, so the nail can be considered a part of the bone. For this reason, the contacts were defined as “Bonded”. For the broken femur, the contact types were chosen in order to simulate a situation in which the patient begins to place weight on the affected limb. In normal circumstances, weight-bearing begins 6 weeks after the implant is fitted and the patient should place no more than one-third of their total body weight on the healing limb. (Information gained from consultation with doctors) In some cases, the bone may suffer renewed damage at the location of the fracture, as it has not yet completely healed. In such cases there is no
Appl. Sci. 2022,12, 7470 8 of 16 displacement of the bone fragments, though the fragments may move slightly against each other. For this reason, the contact was defined as “Frictionless”; this enables both tangential and normal displacement (separation). The contact is without a coefficient of friction, as the coefficient of friction between bones is not known. Moreover, in this case it is not necessary, as the entire movement of the bone is represented by the nail and its parts. Because this is a simulation of the state of the femur after 6 weeks of treatment, it is considered that the bone tissue has already grown around all the recesses on the nails and their parts; the contact is thus defined as “Bonded”. For load screws and fixation screws, this contact would be provided by means of self-tapping screws during the initial implantation process. Other boundary conditions used in the FEM analyses are shown in Figure 10. The hip joint region is subjected to compressive force F (C) and this is also the location of a contact permitting displacement only in the direction of the force application (B). Force F replaces the transfer of the patient’s weight—in this case a patient standing on one leg (extreme condition). For the purposes of the analysis, this force is considered to be static load with value of 1 N, and the necessary calculations are also carried out for other loading. In the knee joint region there is a boundary condition with a Winkler elastic foundation (D) with stiffness k = 0.13 N/mm3 simulating the compressibility of joints (the reduction in the size of the spaces between the joints under loading) and a boundary condition only permitting displacement in the direction of the force application (A). Experiences of using elastic foundations were drawn from previous studies [1,2]. Appl.Sci.2022,12,xFORPEERREVIEW8of17 fromconsultationwithdoctors)Insomecases,thebonemaysufferreneweddamageat thelocationofthefracture,asithasnotyetcompletelyhealed.Insuchcasesthereisno displacementofthebonefragments,thoughthefragmentsmaymoveslightlyagainsteach other. Forthisreason,thecontactwasdefinedas“Frictionless”;thisenablesbothtangential andnormaldisplacement(separation).Thecontactiswithoutacoefficientoffriction,as thecoefficientoffrictionbetweenbonesisnotknown.Moreover,inthiscaseitisnot necessary,astheentiremovementoftheboneisrepresentedbythenailanditsparts. Becausethisisasimulationofthestateofthefemurafter6weeksoftreatment,itis consideredthatthebonetissuehasalreadygrownaroundalltherecessesonthenailsand theirparts;thecontactisthusdefinedas“Bonded”.Forloadscrewsandfixationscrews, thiscontactwouldbeprovidedbymeansofself‐tappingscrewsduringtheinitial implantationprocess. OtherboundaryconditionsusedintheFEManalysesareshowninFigure10.The hipjointregionissubjectedtocompressiveforceF(C)andthisisalsothelocationofa contactpermittingdisplacementonlyinthedirectionoftheforceapplication(B).ForceF replacesthetransferofthepatient’sweight—inthiscaseapatientstandingononeleg (extremecondition).Forthepurposesoftheanalysis,thisforceisconsideredtobestatic loadwithvalueof1N,andthenecessarycalculationsarealsocarriedoutforother loading.InthekneejointregionthereisaboundaryconditionwithaWinklerelastic foundation(D)withstiffnessk=0.13 N/mmsimulatingthecompressibilityofjoints(the reductioninthesizeofthespacesbetweenthejointsunderloading)andaboundary conditiononlypermittingdisplacementinthedirectionoftheforceapplication(A). Experiencesofusingelasticfoundationsweredrawnfrompreviousstudies[1,2]. Figure10.Boundaryconditions. Themainelementusedincreatingthefiniteelementmeshwasaten‐nodequadratic tetrahedralelementwiththreedegreesoffreedominaxesX,Y,Zineverynode(solid187, Ansyssoftware[20]).Thiselementissuitableforthemeshingofirregularshapes,which isbeneficialinthiscase.Themeshalsousedlocalrefinementintheregionsofcontactand theregionsofexpectedstressconcentration.ThisinitialmeshisshownforaMedin125° cannulatednailinFigure11,withdetailsofthemeshrefinementshowninFigure12.The meshpropertiesfortheindividualsystemsareshowninTable4. Figure 10. Boundary conditions. The main element used in creating the finite element mesh was a ten-node quadratic tetrahedral element with three degrees of freedom in axes X, Y, Z in every node (solid 187, Ansys software [ 20 ]). This element is suitable for the meshing of irregular shapes, which is beneficial in this case. The mesh also used local refinement in the regions of contact and the regions of expected stress concentration. This initial mesh is shown for a Medin 125 ◦ cannulated nail in Figure 11, with details of the mesh refinement shown in Figure 12. The mesh properties for the individual systems are shown in Table 4. Appl.Sci.2022,12,xFORPEERREVIEW9of17 Figure11.FiniteelementmeshforaMedin125°nail. Figure12.LocalmeshrefinementforaMedin125°nail. Table4.Meshproperties. ΣofElementsΣofNodes Medina.s. Nailcollo‐diaphysealangle125°Healedfemur111,447188,515 Brokenfemur114,990193,606 Nailcollo‐diaphysealangle130°Healedfemur101,685172,160 Brokenfemur103,090174,794 Nailcollo‐diaphysealangle135°Healedfemur102,524173,702 Brokenfemur104,092176,498 Tantum Nailcollo‐diaphysealangle120°Healedfemur113,942190,439 Brokenfemur109,578183,865 Nailcollo‐diaphysealangle125°Healedfemur110,558185,967 Brokenfemur110,746186,860 4.Results ThevaluesshowninTable5expresstheevaluatedandmaximumvaluesofHMH stressinMPa(occurringatthelocationswithstressconcentrators,i.e.,notches).The equivalentHMHstressisgenerallydeterminedbymeansofEquation(1).Extremestress valuesoccurlocallyinverysmallareas.Theanalysisalsotakesintoaccounttheso‐called evaluatedstressvaluesoccurringinthevicinityofthemaximum(seeFigure13). Generally,thestressesoccurringinthenailsystemsareconsiderablylower. Figure 11. Finite element mesh for a Medin 125◦nail.
Appl. Sci. 2022,12, 7470 9 of 16 Appl.Sci.2022,12,xFORPEERREVIEW9of17 Figure11.FiniteelementmeshforaMedin125°nail. Figure12.LocalmeshrefinementforaMedin125°nail. Table4.Meshproperties. ΣofElementsΣofNodes Medina.s. Nailcollo‐diaphysealangle125°Healedfemur111,447188,515 Brokenfemur114,990193,606 Nailcollo‐diaphysealangle130°Healedfemur101,685172,160 Brokenfemur103,090174,794 Nailcollo‐diaphysealangle135°Healedfemur102,524173,702 Brokenfemur104,092176,498 Tantum Nailcollo‐diaphysealangle120°Healedfemur113,942190,439 Brokenfemur109,578183,865 Nailcollo‐diaphysealangle125°Healedfemur110,558185,967 Brokenfemur110,746186,860 4.Results ThevaluesshowninTable5expresstheevaluatedandmaximumvaluesofHMH stressinMPa(occurringatthelocationswithstressconcentrators,i.e.,notches).The equivalentHMHstressisgenerallydeterminedbymeansofEquation(1).Extremestress valuesoccurlocallyinverysmallareas.Theanalysisalsotakesintoaccounttheso‐called evaluatedstressvaluesoccurringinthevicinityofthemaximum(seeFigure13). Generally,thestressesoccurringinthenailsystemsareconsiderablylower. Figure 12. Local mesh refinement for a Medin 125◦nail. Table 4. Mesh properties. Σof Elements Σof Nodes Medin a.s. Nail collo-diaphyseal angle 125◦Healed femur 111,447 188,515 Broken femur 114,990 193,606 Nail collo-diaphyseal angle 130◦Healed femur 101,685 172,160 Broken femur 103,090 174,794 Nail collo-diaphyseal angle 135◦Healed femur 102,524 173,702 Broken femur 104,092 176,498 Tantum Nail collo-diaphyseal angle 120◦Healed femur 113,942 190,439 Broken femur 109,578 183,865 Nail collo-diaphyseal angle 125◦Healed femur 110,558 185,967 Broken femur 110,746 186,860 4. Results The values shown in Table 5express the evaluated and maximum values of HMH stress in MPa (occurring at the locations with stress concentrators, i.e., notches). The equivalent HMH stress is generally determined by means of Equation (1). Extreme stress values occur locally in very small areas. The analysis also takes into account the so-called evaluated stress values occurring in the vicinity of the maximum (see Figure 13). Generally, the stresses occurring in the nail systems are considerably lower. σHMH =qσ2 1+σ2 2+σ2 3−(σ1σ2+σ2σ3+σ1σ3), (1) where σi(MPa) are principle stresses. Table 5. Stress values at F = 1 N results in 10−2MPa. Nail Material Femur (HMH)·10−2/MPa/ Medin Tantum 125◦130◦135◦120◦125◦ 1.4441 steel Healed femur σev ÷σmax 11.15 ÷12.55 5.69 ÷6.41 8.51 ÷9.58 7.46 ÷8.40 8.18 ÷9.21 Broken femur σev ÷σmax 7.22 ÷8.12 5.58 ÷6.28 9.84 ÷11.07 5.45 ÷6.13 8.56 ÷9.63
Appl. Sci. 2022,12, 7470 16 of 16 28. Nizamuddin, M.K.; Kirthana, S. Reconstruction of human femur bone from CT scan images using CAD techniques. IOP Conf. Ser. Mater. Sci. Eng. 2018,455, 012103. [CrossRef] 29. Materialise. Mimics Innovation Suite. Medical Image Analysis Software. Available online: https://www.materialise.com/en (accessed on 21 April 2022).