Knee ligaments mechanics
From experiments to FE simulations
Keywords:
knee ligaments, failure, damage, behavior lawAbstract
Acting as track rod for joints, knee ligaments are viscoelastic complex structures which are loaded up to damage and failure during trauma situations. This paper presents 10 years of joint research at the Laboratory of Biomechanics and Application and the Laboratory of Acoustics and Mechanics in investigating the mechanical behaviour of such structures. Staring from clinical knowledge, we show, how experimental, histological, theoretical and FE simulation approaches have been performed to investigate such the behaviour of such structures.
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References
Andrieux F., Sur les milieux visco-hyperelastiques endommageables, Ph. D. Thesis,
Université de Technologie de Compiègne, 1996.
Arnoux P.J., Modélisation des ligaments des membres porteurs, Ph D. Thesis, Université de
la Méditerranée, 2000.
Arnoux P.J., Cavallero C., Chabrand P., Brunet C., “Knee ligaments failure under dynamic
loadings”, International Journal of Crashworthiness, Vol. 7, No 3, 2002, pp. 255-268.
Arnoux P.J., Chabrand P., Jean M., Bonnoit J., “A visco-hyperelastic model with damage for
the ligaments of the knee under dynamic constraints”, International Journal on Computer
Methods in Biomechanics and Biomedical Engineering, Vol. 5, No. 2, 2002, pp. 167-174.
Arnoux P.J., Pithioux M., Chabrand P., Jean M., Bonnoit J., “Numerical damage models in
biological tissues using a structural approach”, European Journal of Physics, Vol. 17,
No. 1, 2002, pp. 65-73.
Behr M., Arnoux P.J., Thollon L., Serre T., Cavallero C., Brunet C., “Towards integration of
muscle tone in lower limbs subjectes to impacts”, IX International Symposium on
Computer Simulation in Biomechanics, Sydney, Australia, 2003.
Behr M., Description et modélisation du comportement musculaire du membre pelvien,
Application à la sécurité routière, Ph D. Thesis, Université de la Méditerranée, 2004.
Bidal S., Reconstruction tridimensionnelle d’éléments anatomiques et génération automatique
de maillages éléments finis optimisés, PhD thesis, Université de la Méditerranée, 2003.
Bingham D. N., Dehoff P. H., “A constitutive equation for the canine anterior cruciate
ligament”, J. Biomechanical Engineering, 101, 1979, pp. 15-22.
Butler D.L, Noyes F.R, Grood E. S., “Measurement of the mechanical properties of the
ligaments”, CRC Handbook of Engineering in Medicine and Biology, Section B:
Instruments and Measurements, 1992.
Cardot J., Masson C., Arnoux P.-J., Brunet C., “Experimental and numerical studies of frontal
impact to the lower limb”, International Crashworthiness and Design Symposium, 2003.
Chaboche J. L., “Continuum damage mechanics, Part I : General concepts”, J. Applied
Mechanics., 55, 1987, pp. 59-64.
Comminou M., Yannas I., “Dependence of stress-strain nonlinearity of connective tissues on
the geometry of collagen fibers”, Journal of Biomechanics, Vol. 9, 1976, pp. 427-433.
Dehoff H., “On the non linear viscoelastic behaviour of soft biological tissues”,
J. Biomechanics, Vol. 11, 1978, pp. 35-40.
Demiray H., “A note on the elasticity of soft biological tissues”, J. Biomechanics, Vol. 5,
, pp. 309-311.
Diamant J., Keller A., Baer E., Litt M., Arridge R., “Collagen ultrastructre and its relations to
mechanical properties as a function of ageing”, Proceedings of Research Society, London,
Vol. B180, 1972, pp. 293-315.
Frisen M., Mägi M., Sonnerup L., Viidik A., “Rheological analysis of soft collagenous tissue-
Part 1 : Theoretical considerations”, Journal of Biomechanics, Vol. 2, 1969, pp. 13-20.
Folkhard W., Mosler, E., Geercken, W., Knorzer, E., Nemetscheck-Gansler, H.,
Nemetscheck, Th., Koch, H. J., “Quantitative analysis of the molecular sliding mechanism
in native tendon collagen-time resolved dynamic studies using synchroton radiation”,
International Journal of Biological Macromolecules, Vol. 9, 1987, pp. 169-175.
Fung Y. C., “Biorheology of soft tissues”, Biorheology, Vol. 10, 1973, pp. 139-155.
Fung Y. C., Biomechanics, Mechanical properties of living tissues, Second edition, Springer,
Germain P., Cours de mécanique des milieux continus, T. 1-2, Masson, Paris, 1986.
Hodge A., Petruska, J., Electron microscopy, Academic Press, New York, 1962.
Holden J., Grood E., Korvich D., Cummings J., Butler D., Bylski-Austrow D., “In vivo forces
in the anterior cruciate ligament : direct mesurements during walking and trotting in a
quadruped”, Journal of Biomechanic, Vol. 27, No. 5, 1994, pp. 517-526.
Humphrey J., Yin, F., “A new constitutive formulation for characterizing the mechanical
behaviour of soft tissues”, Journal of Biophysics, Vol. 52, 1987, pp. 563-570.
Hurschler C., Loitz-Ramage B., Vanderby R., “A structurally based stress stretch relationship
for tendon and ligament”, Journal of Biomechanical Engineering, Vol. 119, 1997,
pp. 392-399.
Jundt J., Modèles d’endommagement et de rupture des tissus biologiques, Ph D. thesis in
preparation, 2004.
Kachanov L. M., Time of the rupture process under creep conditions, Z. W. Akad. Nauk.,
S. S. R., 1958.
Kwan M., Woo S., “Technical brief: a structural model to describe the nonlinear stress-strain
behaviour for parallel-fibered collagenous tissues”, J. Biomechanical Engineering,
/361, 1989, pp. 361-363.
Lam T., Thomas C., Shrive N., Frank C., Sabiston C., “The effects of temperature on the
viscoelastic properties of the rabbit medial collateral ligament”, Journal of Biomechanical
Engineering, Vol. 112, 1990, pp. 147.
Lanir Y., “Constitutive equations for fibrous connective tissues”, Journal of Biomechanics,
, 1, 1983, pp. 1-12.
Lanir Y., “A microstructure model for the rheology of mammalian tendon”, J. Biomechanical
Engineering, 102, 1980, pp. 332-339.
Liao H., Belkoff S., “A failure model for ligaments”, Journal of Biomechanics, Vol. 32,
, pp. 183-188.
Liorzou G., Le genou ligamentaire, Springer Verlag, 1990.
Maes M., Vanhuyse V., Decraemer W., Raman E., “A thermodynamically consistent
constitutive equation for the elastic force-length relation of soft biological materials”,
Journal of Biomechanics, 22, 11/12, 1989, pp. 1203-1208.
Mansat Ch., Jaeger J.H, Bonnel F., Le genou traumatique, Les ligaments du genou (de
l’anatomie à la biomécanique), ed. Masson, 1989, pp. 8-16.
Martin B., Burr D.B, Sharkey N.A., Skeletal tissue mechanics, 1998, Springer.
Mommersteeg T.J.A., “The effect of variables relative insertion orientation of human knee
bone-ligament-bone complex on the tensile stiffness”, Journal of Biomechanics, Vol. 28,
No. 6, 1995, pp. 745-752.
Mommersteeg T.J.A., “Characterisation of the mechanical behavior of human knee ligaments:
a numerical experimental approach”, Journal of Biomechanics, Vol. 29, No 2, 1996,
pp. 151-160.
Mosler E., Folkhard W., Knorzer E., “Stress induced molecular rearrangement in tendon
collagen”, Journal of Molecular Biology, 182, 1985, pp. 589-596.
Noyes F., Delucas J., Torvik P., “Biomechanisc of anterior cruciate ligament failure, an
analysis of strain-rate sensitivity and mechanisms of failure in primates”, Journal of Bone
and Joint Surgery, Vol. 56-A, 1975, pp. 236-253.
Noyes F. R., Grood E. S., “The strength of the anterior cruciate ligament in humans and
rhesus monkeys”, Journal of bone and Joint Surgery, 1976, pp. 1074-1081.
Pioletti D., Viscoelastic Properties of Soft Tissues: Application to knee ligament and tendon,
Ph. D; Thesis, Lausanne, EPFL, 1997.
Race A., “The mechanical properties of the two bundles of the human posterior cruciate
ligament”, Journal of Biomechanics, Vol. 27, No. 1, 1994, pp. 13-24.
Sasaki N., Odajima S., “Strain-Stress curve and Yung’s modulus of a collagen molecule as
determined by the X-ray diffraction technique”, Journal of Biomechanics, Vol. 29, No. 5,
, pp. 655-658.
Sasaki N., Odajima S., “Elongation mechanism of collagen fibrils and force strain relations of
tendon at each level of structural hierarchy”, Journal of Biomechanics, Vol. 29, No. 9,
, pp. 1131-1136.
Subit D., Modélisation de la liaison os-ligament dans l’articulation du genou, PhD thesis,
Université de la Méditerranée, 2004.
Viidik A., “Functionnal properties of collagenous tissues”, International Review of
Connective Tissue Research, Vol. 6, Academic Press, New York, 1973.
Winckler G., Manuel d’Anatomie Topographique et Fonctionnelle, 2e ed. Masson, Paris,
Woo S., “Mechanical properties of tendons and ligaments”, Fourth international congress of
biorheology, Vol. 19, 1982, pp. 285-396.
Woo S., Young E., Kwan M., “Fundamental studies in knee ligament mechanics”, Knee
Ligaments: Structure, Function, Injury and Repair, Edited by D. Daniel, by Raven Press,
, pp. 115-134.
Woo S., Hollis M., Adams O., Lyon M., Takai S., “Tensile properties of the human femur
anterior cruciate ligament-tibia complex, the effects of specimen age and orientation”, The
American Journal of Sport and Medicine, Vol. 29, No. 3, 1991, pp. 217-225
Woo S., “Mathematical modeling of ligaments and tendons”, ASME, Vol. 115, 1993, pp. 468-
Zuinen C., Le genou traumatique, De Boeck Université, 1991.