Hip joint lubrication after injury in stochastic description of optimum standard deviations

• Autorzy: Wierzcholski, K. Ch.
• Języki publikacji: EN

Abstrakty

EN

The lubrication parameters of rough and used cartilage surface in human hip joint changes suddenly after its injury. Stochastic changes of the roughness of the surfaces of the head of bone and stochastic changes of the load imply the random changes of gap height. Hence, the pressure distributions and capacity as well as friction forces and friction coefficients radically decrease or increase in several microseconds after trauma. These changes are very difficult to measure, hence an appropriate numerical research in this field is very important. In order to obtain correct numerical results, we have to perform calculations using stochastic description with optimum standard deviations.

Słowa kluczowe

PL

staw biodrowy; chrząstka

EN

hip Joint impulsive lubrication; cartilage roughness; random changes

• Czasopismo: Acta of Bioengineering and Biomechanics
• Rocznik: 2005
• Tom: Vol. 7, nr 2
• Strony: 51-79
• Opis fizyczny: Bibliogr. 38 poz., il., rys., tab.

Twórcy

autor

Wierzcholski, K. Ch.

• Base Technique Department, Maritime University of Gdynia, 81-225 Gdynia, ul. Morska 83, Poland

Bibliografia

• [1] BERNSTEIN B., Hypo-elasticity and elasticity, Arch. Ration. Mech. Anal., 1960, 6, pp. 90–104.
• [2] DOWSON D., Bio-Tribology of Natural and Replacement Synovial Joints, [in:] Van Mow C., Ratcliffe A., Woo S.L-Y., Biomechanics of Diarthrodial Joint, Springer-Verlag, New York, Berlin, London, Paris, Tokyo, Hong Kong, 1990, Vol. 2, Chap. 29, pp. 305–345.
• [3] EBERHARDT A.W., KEER L.M., LEWIS J.L., VITHOONTIEN V., An analytical model of joint contact, ASME J. Biomech. Eng., 1990, 112, pp. 407–413.
• [4] FISZ M., Rachunek prawdopodobieństwa i statystyka matematyczna, PWN, Warszawa, 1969.
• [5] FUNG Y.C., Bioviscoelastic Solids, [in:] Biomechanics, Mechanical Properties of Living Tissues, Berlin, Springer-Verlag, 1993.
• [6] FUNG Y.C., The Meaning of Constitutive Equations, [in:] Biomechanics, Mechanical Properties of Living Tissues, Berlin, Springer-Verlag, 1993.
• [7] FUNG Y.C., Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York, 1993, pp. 220–241.
• [8] FUNG C.A., First course in continuum mechanics: for physical and biological engineers and scientists, 3-rd ed., Englewood Cliffs, NJ, Prentice-Hall, 1993.
• [9] FUNG C., Biomechanics, Motion, Flow, Stress and Growth, Springer-Verlag, New York, Hong Kong, 1993.
• [10] GARCIA J.J., ALTIERO N.J., HAUT R.C., Estimation of in Situ Elastic Properties of Biophasic Cartilage Based on a Transversely Isotropic Hypo-Elastic Model, Journal of Biomechanical Engineering, February 2000, Vol. 122, pp. 1–8.
• [11] HOLMES M.H., Finite deformation of soft tissue: Analysis of a mixture model in uni-axial compression, ASME J. Biomech. Eng., 1986, 108, pp. 372–381.
• [12] JEMIOàO S., TELEGA J.J., MICHALAK C., Hyperelastic anisotropic model of soft tissues, Acta Bioeng. Biomechanics, 2000, 2 Suppl. 1, pp. 235–240.
• [13] JOHNSON G.A., RAJAGOPAL K.R.Y., WOO S.L., A Single Integral Finite Strain (sifs) Model of Ligaments and Tendons, Advances in Bioengineering, 1992, 22, pp. 245–248.
• [14] KĄCKI E., Równania różniczkowe cząstkowe w zagadnieniach fizyki i techniki, WNT, Warszawa, 1989.
• [15] KNOPP K., Szeregi nieskończone, PWN, 1956.
• [16] MAUREL W., WU Y., THALMANN D., Biomechanical Models for Soft Tissue Simulation, SpringerVerlag, Berlin, Heidelberg, 1998.
• [17] MOW V.C., HOLMES M.H., LAI, Fluid transport and mechanical properties of articular cartilage, Journal of Biomechanics, 1984, 17, pp. 337–394.
• [18] MOW V.C., RATCLIFFE A., WOO S., Biomechanics of Diarthrodial Joints, Springer-Verlag, Berlin, Heidelberg, New York, 1990.
• [19] MOW V.C., SOSLOWSKY L.J., Friction, lubrication and wear of diarthrodial joints, [in:] Mow V.C., Hayes W.C. (eds.), Basic Orthopedic Biomechanics, New York, Raven Press, 1991, pp. 254–291.
• [20] MOW V.C., GUILAK F., Cell Mechanics and Cellular Engineering, Berlin, Heidelberg, New York, Springer-Verlag, 1994
• [21] NOWACKI W., Teoria sprĊĪystoĞci, PWN, Warszawa, 1970.
• [22] RALSTON A., A First Course in Numerical Analysis, McGraw-Hill Co., New York, Toronto, London, Sydney, 1965.
• [23] STEINHAGEN J., KURZ B., NIGGEMEYER O., BRUNS J., The pathophysiology of cartilage diseases, Ortopedia, Traumatologia, Rehabilitacja, 2001, Vol. 3, No. 2, pp. 163–168.
• [24] SOBCZYK M., Statystyka, PWN, Warszawa, 1996.
• [25] TEIPEL I., The Impulsive Motion of a Flat Plate in a Viscoelastic Fluid, Acta Mechanica, SpringerVerlag, 1981, 39, pp. 277–279.
• [26] TRUESDELL C., A First Course in Rational Continuum Mechanics, Maryland, John Hopkins University, Baltimore, 1972.
• [27] TRUESDELL C., Hypo-elasticity, J. Rational Mechanics and Analysis, 1955, 4, pp. 83–133.
• [28] UNGETHÜM M., WINKLER-GNIEWEK W., Tribologie in Medizin, Tribologie Schmierungstechnik, 1990, 5, pp. 268–277.
• [29] WIERZCHOLSKI K., PYTKO S., Metoda wyznaczania parametrów bioáoĪyska smarowanego cieczą nienewtonowską (in Polish), Tribologia, 1993, 1, pp. 9–12.
• [30] WIERZCHOLSKI K., PYTKO S., Analytical calculations for experimental dependences between shear rate and synovial fluid viscosity, Proc. of Internat. Tribology Conference, Japan, Yokohama, 1995, Vol. 3, pp. 1975–1980.
• [31] WIERZCHOLSKI K., Oil velocity and pressure distribution in short journal bearing under Rivlin Ericksen lubrication, SAMS, System Analysis Modeling and Simulations, OPA Overseas Publishers Assoc., N.V., 1998, Vol. 32, pp. 205–228.
• [32] WIERZCHOLSKI K., The method of solutions for hydrodynamic lubrication by synovial fluid flow in human joint gap, Control and Cybernetics, 2002, Vol. 31, No. 1, pp. 91–116.
• [33] WIERZCHOLSKI K., Capacity of deformed human hip joint gap in time dependent magnetic field, Acta of Bioengineering and Biomechanics, 2003, Vol. 5, No. 1, pp. 43–65.
• [34] WIERZCHOLSKI K., Pressure distribution in human joint gap for elastic cartilage and time dependent magnetic field, Russian Journal of Biomechanics, Perm, 2003, Vol. 7, No. 1, pp. 24–46.
• [35] WIERZCHOLSKI K., Tribologie für menschliche Gelenke, Tribologie und Schmierungstechnik, 2002, 5, pp. 5–13.
• [36] WIERZCHOLSKI K., Theory of viscoelastic lubrication of hip joint in stochastic description for periodic motion, Tribologia, 2004, 4(196), pp. 327–338.
• [37] WOO S.-Y., JOHNSON G.A., SMITH B.A., Mathematical Modeling of Ligaments and Tendons, Journal Biomechanical Engineering, 1993, 115, pp. 468–473.
• [38] XIAO H., BRUHNS O.T., MEYERS A., Hypo-elasticity model based upon the logarithmic stress rate, J. Elast., 1997, 47, pp. 51–68.