A patient-specific numerical model of the ankle joint has been developed using open-source software with realistic material properties that mimics the physiological movement of the foot during the stance phase of the gait cycle. The patient-specific ankle geometry has been segmented as a castellated surface using 3DSlicer from the computed tomography image scans of a subject with no congenital or acquired pathology; subsequently, the bones are smoothed, and cartilage is included as a uniform thickness extruded layer. A high-resolution Cartesian mesh has been generated using cfMesh. The material properties are assigned in the model based on the CT image Hounsfield intensities and compared to a sandwich-based material model. Gait data of the same subject was obtained and used to relatively position the tibia, talus, and calcaneus bones in the model. The stance phase of the gait cycle is simulated using a cell-centred finite-volume method implemented in open-source software OpenFOAM. The predicted peak contact pressures occur in the range of 4.85–5.53 MPa with average pressures in the range of 1.56–1.95 MPa, and the contact area ranges between 429 and 707.8 mm2 for the entire stance phase with the mid-stance phase predicting the maximum contact area. These predictions are in agreement with results from the literature. The effect of arthritis on the contact characteristics of the ankle joint has also been examined. A concentrated increase in pressure was predicted that could be manifested as pain, thereby leading to reduced motion in the ankle. The model, with continued development, has the capability to understand the effect of joint degradation and furthermore, could help provide a tool to predict the efficiency of therapeutic surgical procedures as well as guide the development of next generation ankle prostheses. The work would be made available in the University College Dublin depository (https://github.com/laxmimurali/anklejoint) as well as research gate once the article has been published.
QianZRenLDingY, et al. A dynamic finite element analysis of human foot complex in the sagittal plane during level walking. PLoS ONE2013; 8(11): e79424.
2.
DalstraMHuiskesRvan ErningL.Development and validation of a three-dimensional finite element model of the pelvic bone. J Biomech Eng1995; 117: 272–278.
3.
AndersonAEPetersCLTuttleBD, et al. Subject-specific finite element model of the pelvis: development, validation and sensitivity studies. J Biomech Eng2005; 127: 364–373.
4.
AndersonAEEllisBJMaasSA, et al. Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip. J Biomech2010; 43: 1351–1357.
5.
BachtarFChenXHisadaT.Finite element contact analysis of the hip joint. Med Biol Eng Comput2006; 44: 643–651.
6.
MajumderSRoychowdhuryAPalS.Variations of stress in pelvic bone during normal walking, considering all active muscles. Trend Biomater Artif Organ2004; 17(2): 48–53.
7.
SilvestriC.Development and validation of a knee-thigh-hip LSDYNA model of a 50th precentile male. PhD Thesis, Worcester Polytechnic Institute, Worcester, MA, 2008.
8.
AndersonAEEllisBJMaasSA, et al. Validation of finite element predictions of cartilage contact pressure in the human hip joint. J Biomech Eng2008; 130: 051008.
9.
AndersonAEEllisBJPetersCL, et al. Cartilage thickness: factors influencing multidetector CT measurements in a phantom study. Radiology2008; 246(1): 133–141.
10.
CardiffPKaracAFitzPatrickD, et al. Development of mapped stress-field boundary conditions based on a hill-type muscle model. Int J Numer Method Biomed Eng2014; 30(9): 890–908.
11.
CardiffPKaracAFitzPatrickD, et al. Development of a hip joint model for finite volume simulations. J Biomech Eng2014; 136(1): 011006.
12.
DemirdžićIMartinovićDIvankovićA.Numerical simulation of thermal deformation in welded workpiece. Zavarivanje1988; 31: 209–219 (in Croatian).
13.
DemirdžićIMuzaferijaS.Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology. Comput Method Appl Mech Eng1995; 125(1–4): 235–255.
14.
FryerYDBaileyCCrossM, et al. A control volume procedure for solving elastic stress-strain equations on an unstructured mesh. Appl Math Model1991; 15(11–12): 639–645.
15.
TukovićVIvankovićAKaraćA.Finite-volume stress analysis in multi-material linear elastic body. Int J Numer Method Eng2013; 93: 400–419.
16.
DemirdžićIDžafarovićEIvankovićA.Finite-volume approach to thermoviscoelasticity. Numer Heat Trans Part B: Fund2005; 47(3): 213–237.
17.
CardiffPKaraćAIvankovićA.Development of a finite volume contact solver based on the penalty method. Comput Mater Sci2012; 64: 283–284.
18.
TropsaVGeorgiouIIvankovicA, et al. OpenFOAM in non-linear stress analysis: modelling of adhesive joints. In: Proceedings of the 1st OpenFOAM workshop, Zagreb, 26–28 January 2006. University Park, PA: Penn State University.
19.
CardiffP.Development of the finite volume method for hip joint stress analysis. PhD Thesis, University College Dublin, Dublin, 2012.
20.
IvankovićAMuzaferijaADemirdžićI.Finite volume method and multigrid acceleration in modelling of rapid crack propagation in full-scale pipe test. Comput Mech1997; 20(1–2): 46–52.
21.
KaraćAIvankovićA.Investigating the behaviour of fluid-filled polyethylene containers under base drop impact: a combined experimental/numerical approach. Int J Impact Eng2009; 36(4): 621–631.
22.
JasakHWellerHG.Application of the finite volume method and unstructured meshes to linear elasticity. Int J Numer Method Eng2000; 48: 267–287.
23.
JasakHWellerH.Finite volume methodology for contact problems of linear elastic solids. In: Proceedings of 3rd international conference of Croatian society of mechanics, Dubrovnik, 20–21 September, 2000, pp.253–260.
24.
WellerHGTaborGJasakH, et al. A tensorial approach to computational continuum mechanics using object orientated techniques. Comput Phys1998; 12(6): 620–631.
PieperSLorensenBSchroederW, et al. The NA-MIC Kit: ITK, VTK, pipelines, grids and 3D slicer as an open platform for the medical image computing community. In: Proceedings of the 3rd IEEE international symposium on biomedical imaging: from nano to macro, vol. 1, Arlington, VA, 6–9 April 2006, pp.698–701. New York: IEEE.
MillingtonSAGrabnerMWozelkaR, et al. Quantification of ankle articular cartilage topography and thickness using a high resolution stereophotography system. Osteoarth Cartil2007; 15(2): 205–211.
33.
OtaTYamamotoIMoritaR.Fracture simulation of the femoral bone using the finite-element method: how a fracture initiates and proceeds. J Bone Miner Metabol1999; 17(2): 108–112.
34.
YosibashZPadanRJoskowiczL, et al. A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments. J Biomech Eng2007; 129(3): 297–309.
35.
TaddeiFMartelliSReggianiB, et al. Finite-element modeling of bones from CT data: sensitivity to geometry and material uncertainties. IEEE T Biomed Eng2006; 53(11): 2194–2200.
36.
OrwollESMarshallLMNielsonCM, et al. Finite element analysis of the proximal femur and hip fracture risk in older men. J Bone Miner Res2009; 24(3): 475–483.
37.
CattaneoPMDalstraMFrichLH.A three-dimensional finite element model from computed tomography data: a semi-automated method. Proc IMechE, Part H: J Engineering in Medicine2001; 215(2): 203–212.
38.
SnyderSMSchneiderE.Estimation of mechanical properties of cortical bone by computed tomography. J Orthop Res1991; 9(3): 422–431.
39.
Gonzalez-CarbonellRAOrtiz-PradoAJacobo-ArmendarizVH, et al. 3D patient-specific model of the Tibia from CT for orthopedic use. J Orthop2015; 12(1): 11–16.
40.
MorganEFBayraktarHHKeavenyTM.Trabecular bone modulus-density relationships depend on anatomic site. J Biomech2003; 36(7): 897–904.
41.
MesfarWShirazi-AdlA.Biomechanics of the knee joint in flexion under various quadriceps forces. Knee2005; 12: 424–434.
42.
RussellMEShivannaKHGroslandNM, et al. Cartilage contact pressure elevations in dysplastic hips: a chronic overload model. J Orthop Surg Res2006; 1: 6.
43.
WuGSieglerSAllardP, et al. ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion: part I: ankle, hip, and spine. J Biomech2002; 35(4): 543–548, http://www.sciencedirect.com/science/article/pii/S0021929001002226
44.
CardiffPKaraćATukovićV, et al. Development of a finite volume based structural solver for large rotation of non-orthogonal meshes. In: Proceedings of the 7th OpenFOAM workshop, Darmstadt, 25–28 June 2012. Darmstadt: Technische Universitat Darmstadt.
45.
KuraHKitaokaHBLuoZP, et al. Measurement of surface contact area of the ankle joint. Clin Biomech1998; 13(4–5): 365–370.
46.
MillingtonSGrabnerMWozelkaR, et al. A stereophotographic study of ankle joint contact area. J Orthop Res2007; 25(11): 1465–1473.
47.
AndersonDDGoldsworthyJKShivannaK, et al. Intra-articular contact stress distributions at the ankle throughout stance phase-patient-specific finite element analysis as a metric of degeneration propensity. Biomech Model Mechanobiol2006; 5(2–3): 82–89.
48.
SuckelAMullerOWachterN, et al. In vitro measurement of intraarticular pressure in the ankle joint. Knee Surg Sports Traumatol Arthrosc2010; 18(5): 664–668.
49.
CaputoAMLeeJYSpritzerCE, et al. In vivo kinematics of the tibiotalar joint after lateral ankle instability. Am J Sports Med2009; 37(11): 2241–2248.
50.
CalhounJHLiFLedbetterBR, et al. A comprehensive study of pressure distribution in the ankle joint with inversion and eversion. Foot Ankle Int1994; 15(3): 125–133.
51.
DriscollHLChristensenJCTencerAF.Contact characteristics of the ankle joint: part 1: the normal joint. J Am Podiatr Med Assoc1994; 84(10): 491–498.
WuJZHerzogWEpsteinM.Effects of inserting a pressensor film into articular joints on the actual contact mechanics. J Biomech Eng1998; 120(5): 655–659.
54.
RamseyPLHamiltonW.Changes in tibiotalar area of contact caused by lateral talar shift. J Bone Joint Surg Am1976; 58(3): 356–357.
55.
KimizukaMKurosawaHFukubayashiT.Load bearing pattern of the ankle joint: contact area and pressure distribution. Arch Orthop Trauma Surg1980; 96: 45–49.
56.
GreenwaldASMatejczykMBKepplerL, et al. Preliminary observations on the weight-bearing surfaces of the human ankle joint. Surg Forum1976; 27(62): 505–506.
57.
CorazzaFStagniRCastelliVP, et al. Articular contact at the tibiotalar joint in passive flexion. J Biomech2005; 38(6): 1205–1212.
58.
WanLde AslaRJRubashHE, et al. Determination of in-vivo articular cartilage contact areas of human talocrural joint under weightbearing conditions. Osteoarth Cartil2006; 14(12): 1294–1301.
59.
MichelsonJDChecconeMKuhnT, et al. Intra-articular load distribution in the human ankle joint during motion. Foot Ankle Int2001; 22(3): 226–233.
60.
AndersonAE.Computational modeling of hip joint mechanics. PhD Thesis, The University of Utah, Salt Lake City, UT, 2007.
61.
MuralidharanL.Development of a numerical model to understand the contact pressure characteristics in the ankle joint. PhD Thesis, University College Dublin, Ireland, 2019.
62.
Alonso-RasgadoTJimenez-CruzDKarskiM.3-D computer modelling of malunited posterior malleolar fractures: effect of fragment size and offset on ankle stability, contact pressure and pattern. J Foot Ankle Res2017; 10: 13.
TochigiYRudertMJSaltzmanCL, et al. Contribution of articular surface geometry to ankle stabilization. J Bone Joint Surg Am2006; 88(12): 2704–2713.
65.
AteshianGLaiWZhuW, et al. An asymptotic solution for the contact of two biphasic cartilage layers. J Biomech1994; 27(11): 1347–1360.
66.
CardiffPKaraćAFlavinR, et al. Modelling the muscles for hip joint stress analysis using a finite volume methodology. In: Proceedings of the 18th bioengineering in Ireland, Belfast, Northern Ireland, 2012.
