The aim of this work is to provide a computational tool for the mechanical characterization of the hindfoot ligaments. The investigation is performed by a coupled numerical and experimental approach. For this purpose, a numerical model that represents the complex structural configuration of the hindfoot and the typical features of the mechanical behaviour of the ligament tissue is developed. The geometrical analysis of the anatomical site is performed starting from the processing of computed tomography and magnetic resonance images. Accounting for morphometric measurements, the virtual solid model provides an averaged configuration of the hindfoot structure. In order to specify the mechanical behaviour of the ligament tissue, a fibre-reinforced visco-hyperelastic model is adopted. The formulation accounts for the anisotropic configuration, geometric non-linearity, non-linear elasticity and time-dependent phenomena. Numerical analyses are performed to evaluate the biological tissues and structure mechanics with regard to physiological boundary conditions, accounting for dorsiflexion and plantarflexion movements. In order to evaluate the reliability of the numerical model developed, the experimental data are compared with the numerical results. The numerical results are in agreement with the range of values obtained by experimental test confirming the accuracy of the procedure adopted.
CheungJTMZhangMLeungAK. Three-dimensional finite element analysis of the foot during standing – a material sensitivity study. J Biomech2005; 71: 1045–1054.
2.
CheungJTMNiggBM. Clinical applications of computational simulation of foot and ankle. Sport Orthop Traumatol2007; 23: 264–271.
3.
GonzalezAGBayodJFrutosJCPF. Finite-element simulation of flexor digitorum longus or flexor digitorum brevis tendon transfer for the treatment of claw toe deformity. J Biomech2009; 42: 1697–1704.
4.
TaoKWangDWangC. An in vivo experimental validation of a computational model of human foot. J Bionic Eng2009; 6: 387–397.
5.
YuJCheungJTMFanY. Development of a finite element model of female foot for high heeled shoe design. Clin Biomech2008; 23: S31–S38.
6.
FontanellaCGMatteoliSCarnielEL. Investigation on the load-displacement curves of a human healthy heel pad: in vivo compression data compared to numerical results. Med Eng Phys. Epub ahead of print 24January2012. DOI: 10.1016/j.medengphy.2011.12.013.
7.
FontanellaCGForestieroACarnielEL. Analysis of heel pad tissues mechanics at the heel strike in bare and shod conditions. Med Eng Phys. Epub ahead of print 10July2012. DOI: 10.1016/j.medengphy.2012.06.008.
8.
NataliANForestieroACarnielEL. Investigation of foot plantar pressure: experimental and numerical analysis. Med Biol Eng Comput2010; 48: 1167–1174.
9.
NataliANFontanellaCGCarnielEL. A numerical model for investigating the mechanics of calcaneal fat pad region. J Mech Behav Biomed Mater2012; 5(1): 216–223.
10.
AttarianDEMcCrackinHJDeVitoDP. Biomechanical characteristics of human ankle ligaments. Foot Ankle1985; 6(2): 54–58.
11.
FunkJRHallGWCrandallJR. Linear and quasi linear viscoelastic characterization of ankle ligaments. J Biomech Eng2000; 122: 15–22.
12.
PeñaEPeñaJADoblaréM. On modelling nonlinear viscoelastic effects in ligaments. J Biomech2008; 41: 2659–2666.
13.
HingoraniRVProvenzanoPPLakesRS. Nonlinear viscoelasticity in rabbit medial collateral ligament. Ann Biomed Eng2004; 32(2): 306–312.
14.
HolzapfelGA. Nonlinear solid mechanics: a continuum approach for engineering. New York: Wiley, 2000.
15.
BossAPHintermannB. Anatomical study of the medial ankle ligament complex. Foot Ankle Int2002; 23(6): 547–553.
16.
BurksRTMorganJ. Anatomy of the lateral ankle ligaments. Am J Sport Med1994; 22: 72–73.
17.
ButlerAMWalshWR. Mechanical response of ankle ligaments at low loads. Foot Ankle Int2004; 25(1): 8–12.
18.
MilnerCESoamesRW. Anatomical variations of the anterior talofibular ligament of the human ankle joint. J Anat1997; 191: 457–458.
19.
MkandawireCLedouxWRSangeorzanBJ. Foot and ankle ligament morphometry. J Rehabil Res Dev2005; 42(6): 809–820.
20.
Van den BekeromMPJOostraRJAlvarezPG. The anatomy in relation to injury of the lateral collateral ligaments of the ankle: a current concepts review. Clin Anat2008; 21: 619–626.
21.
OzekiSYasudaKKanedaK. Simultaneous strain measurement with determination of a zero strain reference for the medial and lateral ligaments of the ankle. Foot Ankle Int2002; 23(9): 825–832.
22.
ForestieroACarnielELNataliAN. Biomechanical behaviour of ankle ligaments: constitutive formulation and numerical modelling. Comput Methods Biomech Biomed Engin. Epub ahead of print 22May2012. DOI: 10.1080/10255842.2012.688105.
23.
KellerKNasrilariMFillerT. The anterior tibio-talar ligament: one reason for anterior ankle impingement. Knee Surg Sports Traumatol Arthrosc2010; 18: 225–232.
24.
KumaiTTakakuraYRufaiA. The functional anatomy of the human anterior talofibular ligament in relation to ankle sprains. J Anat2002; 200: 457–465.
25.
NataliANForestieroACarnielEL. Parameters identification in constitutive models for soft tissues mechanics. Russ J Biomech2009; 4(46): 29–39.
26.
ImhauserCWSieglerSUdupaJK. Subject specific models of the hindfoot reveal a relationship between morphology and passive mechanical properties. J Biomech2008; 41: 1341–1349.
27.
Al-AliDGraichenHFaberS. Quantitative cartilage imaging of the human hind foot: precision and inter-subject variability. J Orthop Res2002; 20(2): 249–256.
28.
MillingtonSAGrabnerMWozelkaR. Quantification of ankle articular cartilage topography and thickness using a high resolution stereophotography system. Osteoarthritis Cartilage2007; 15: 205–211.
29.
WelschGHMamischTCHughesT. In vivo biochemical 7.0 Tesla magnetic resonance: preliminary results of dGEMRIC, zonal T2, and T2 mapping of articular cartilage. Invest Radiol2008; 43(9): 619–626.
30.
BrownCPNguyenTCMoodyHR. Assessment of common hyperelastic constitutive equations for describing normal and osteoarthritic articular cartilage. Proc IMechE, Part H: J Engineering in Medicine2009; 223(6): 643–652.
31.
GarcíaJJCortésDH. A biphasic viscohyperelastic fibril-reinforced model for articular cartilage formulation and comparison with experimental data. J Biomech2007; 40(8): 1737–1744.
32.
BursacPMObitzTWEisenbergSR. Confined and unconfined stress relaxation of cartilage: appropriateness of a transversely isotropic analysis. J Biomech1999; 32: 1125–1130.
33.
AthanasiouKALiuGTLaveryLA. Biomechanical topography of human articular cartilage in the first metatarsophalangeal joint. Clin Orthop Relat Res1998; 348: 269–281.
34.
StuebnerMHaiderMA. A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage. J Biomech2010; 43: 1835–1839.
35.
HaiderMASchugartRC. A numerical method for the continuous spectrum biphasic poro-visco-elastic model of articular cartilage. J Biomech2006; 39: 77–183.
36.
AndersonDDGoldsworthyJKLiW. Physical validation of a patient-specific contact finite element model of the ankle. J Biomech2007; 40(8): 1662–1669.
37.
NataliANCarnielELPavanPG. Modelling of mandible bone properties in the numerical analysis of oral implant biomechanics. Comput Methods Programs Biomed2010; 100(2): 158–165.
38.
KnetsIVitinsVDobelisM. Ageing of compact bone tissue. J Biomech2006; 39(Supplement 1): S20.
39.
ShinJYueNUntaroiuCD. A finite element model of the foot and ankle for automotive impact applications. Ann Biomed Eng2012; 40(12): 2519–2531.
40.
GomezMANahumAM. Biomechanics of bone. In: NahumAMMelvinJW (eds) Accidental injury: biomechanics and prevention. New York: Springer-Verlag, 2002, pp.206–227.
41.
SieglerSUdupaJKRinglebSI. Mechanics of the ankle and subtalar joints revealed through a 3D quasi-static stress MRI technique. J Biomech2005; 38(3): 567–578.
42.
AllingerTLEngsbergJR. A method to determine the range of motion of the ankle joint complex, in vivo. J Biomech1993; 26(1): 69–76.
43.
FongCMBlackburnJTNorcrossMF. Ankle-dorsiflexion range of motion and landing biomechanics. J Athl Train2011; 46(1): 5–10.
44.
SieglerSChenJSchneckCD. The effect of damage to the lateral collateral ligaments on the mechanical characteristics of the ankle joint an in-vitro study. J Biomech Eng1990; 112(2): 129–137.
45.
KamiyaTHidejiKDaisukeS. Mechanical stability of the subtalar joint after lateral ligament sectioning and ankle brace application. A biomechanical experimental study. Am J Sports Med2009; 37(12): 2451–2458.
46.
LapointeSJSieglerSHillstromH. Changes in the flexibility characteristics of the ankle complex due to damage to the lateral collateral ligaments: an in vitro and in vivo study. J Orthop Res1997; 15: 331–341.
47.
KovaleskiJEHollisJMHeitmanRJ. Assessment of ankle-subtalar joint complex laxity using an instrumented ankle arthrometer: an experimental cadaveric investigation. J Athl Train2002; 37(4): 467–474.
48.
LuoZPKitaokaHBHsuHC. Physiological elongation of ligamentous complex surrounding the hindfoot joints: in vitro biomechanical study. Foot Ankle Int1997; 18(5): 277–283.
49.
RosenbaumDBeckerHPWilkeHJ. Tenodeses destroy the kinematic coupling of the ankle joint complex. A three dimensional in vitro analysis of joint movement. J Bone Joint Surg Br1998; 80(1): 162–168.
50.
NataliANPavanPGCarnielEL. Anisotropic elasto-damage constitutive model for the biomechanical analysis of tendons. Med Eng Phys2005; 27: 209–214.
51.
NataliANPavanPGCarnielEL. Characterization of soft tissue mechanics with ageing. IEEE Eng Med Biol Mag2008; 27(49): 15–22.
52.
NataliANFontanellaCGCarnielEL. Constitutive formulation and analysis of heel pad tissues mechanics. Med Eng Phys2010; 32: 516–522.
