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Time dependent human hip joint lubrication for periodic motion with stochastic asymmetric density function

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Języki publikacji
EN
Abstrakty
EN
The present paper is concerned with the calculation of the human hip joint parameters for periodic, stochastic unsteady, motion with asymmetric probability density function for gap height. The asymmetric density function indicates that the stochastic probabilities of gap height decreasing are different in comparison with the probabilities of the gap height increasing. The models of asymmetric density functions are considered on the grounds of experimental observations. Some methods are proposed for calculation of pressure distributions and load carrying capacities for unsteady stochastic conditions in a super thin layer of biological synovial fluid inside the slide biobearing gap limited by a spherical bone acetabulum. Numerical calculations are performed in Mathcad 12 Professional Program, by using the method of finite differences. This method assures stability of numerical solutions of partial differential equations and gives proper values of pressure and load carrying capacity forces occurring in human hip joints.
Rocznik
Strony
83--97
Opis fizyczny
Biblogr. 24 poz., rys., wykr.
Twórcy
  • Technical University of Koszalin, Institute of Technology and Education, Koszalin, Poland
Bibliografia
  • [1] CWANEK J., The usability of the surface geometry parameters for the evaluation of the artificial hip joint wear, Rzeszów University Press, Rzeszów, 2009.
  • [2] MOW V.C, RATCLIFFE A., WOO S., Biomechanics of Diarthrodial Joints, Springer Verlag, Berlin–Heidelberg–New York, 1990.
  • [3] KNOLL V.C., Trans-scaphoid perilunate fracture dislocation, Hand Surg. Am., 2005, Vol. 30A, 1145–1152.
  • [4] PAWLAK Z., URBANIAK W., GADOMSKI A., YUSUF K.Q., AFARA I.O., OLOYEDE A., The role of lamellate phospholipid bilayers In lubrication of joint, Acta Bioeng. Biomech., 2012, Vol. 14(4), 101–106.
  • [5] GADOMSKI A., BEŁDOWSKI P., RUBI M.P., URBANIAK W., AUGE W., SANTAMARIA-HOLEK I., PAWLAK Z., Some conceptual thoughts toward nanos cale oriented friction In a model of articular cartilage, Math. Biosc., 2013, Vol. 244, 188–200.
  • [6] WIERZCHOLSKI K., Stochastic impulsive pressure calculations for time dependent human hip joint lubrication, Acta Bioeng. Biomech., 2012, Vol.14(4), 81–100.
  • [7] WIERZCHOLSKI K., Comparison between impulsive and periodic non Newtonian lubrication of human hip joint, Engineering Transactions, 2005, Vol. 53(1), 69–114.
  • [8] WIERZCHOLSKI K., MISZCZAK A., Load carrying capacity of microbearings with parabolic, Journal Solid State Phenomena, Trans. Technical Publications, Switzerland, 2009, Vol. 147–149, 542–547.
  • [9] PAWLAK Z., URBANIAK W., OLOYEDE A., The relationship between friction and wettability in aqueous environment, Wear, 2011, Vol. 171, 1745–1749.
  • [10] WIERZCHOLSKI K., Non isothermal stochastic lubrication of human hip joint in periodic motion with various frequencies and amplitudes, Russ. J. Biomech., 2005,Vol. 9(4), 72–98.
  • [11] DOWSON D., Bio-Tribology of Natural and Replacement Synovial Joints, [in:] C. Van Mow, A. Ratcliffe, S.L.-Y. Woo, Biomechanics of Diarthrodial Joint, Springer-Verlag, New York–Berlin–Londyn–Paris–Tokyo–Hong Kong, 1990, Vol. 2, Chap. 29, 305–345.
  • [12] FUNG Y.C., Biomechanics: Mechanical Properties of Living Tissues, Springer Verlag, New York, 1993.
  • [13] FUNG Y.C., A First Course in Continuum Mechanics: for physical and biological engineers and scientists, 3rd ed., Englewood Cliffs, N.J. Prentice–Hall, 1994.
  • [14] FUNG Y.C., Biomechanics, Motion, Flow, Stress and Growth, Springer Verlag, New York–Hong Kong, 1990.
  • [15] 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, J. Biomech. Eng., 2000, Vol. 122(2), 1–8.
  • [16] OZEN M., SAYMAN O., HAVITCIOGLU H., Modeling and stress analyses of a normal foot-ankle and a prothetic foot-ankle complex, Acta Bioeng. Biomech., 2013, Vol. 15(3), 19–27.
  • [17] BŁAŻKIEWICZ M., Muscle force distribution during forward and backward locomotion, Acta Bioeng. Biomech., 2013, Vol. 15(3), 3–9.
  • [18] WIERZCHOLSKI K., Theory of visco-elastic lubrication of hip joint in stochastic description for periodic motion, Tribologia, 2004, Vol. 4(196), 327–338.
  • [19] FISZ M., Probability Theory and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1963.
  • [20] SOBCZYK M., Statystyka, PWN, Warszawa 1996.
  • [21] TRUESDELL C.A., First Course in Rational Continuum Mechanics, Maryland, John Hopkins University, Baltimore, 1972.
  • [22] RALSTON A., A First Course in Numerical Analysis, McGraw Hill Co., New York–Toronto–London–Sydney, 1965.
  • [23] WIERZCHOLSKI K., MISZCZAK A., Unsteady Lubrication of Deformed Spherical Human Joint, Polish J. of Environmental Studies, Vol. 17, No. 2, 2008, 106–113.
  • [24] WIERZCHOLSKI K., MISZCZAK A., Rheology and Remodeling of Human Joints and Micro-Bearing, Polish J. of Environmental Studies, Vol. 17, No. 2, 2008, 99–105.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-554a001f-f4bd-4336-9354-fb268cf74847
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