title: Topology of calculating pressure and friction coefficients for time-dependent human hip joint lubrication.
abstract: The paper deals with the calculations of the unsteady, impulsive pressure distributions, carrying capacities and friction forces under unsteady conditions in a super-thin layer of biological synovial fluid inside the slide biobearing gap limited by a spherical bone head. Unsteady and random flow conditions for the biobearing lubrication are given. Moreover, the numerical topology of pressure calculation for a difference method is applied. From a mathematical viewpoint the present method for the solution of the modified Reynolds equation allows this problem to be resolved by the partial recurrence nonhomogeneous equation of the second order with variable coefficients. To the best of the author knowledge, an adaptation of the known numerical difference method to the spherical boundary conditions applied during the pressure calculations for a human hip bonehead seems to be decisive.
authors.affiliation: Pomeranian Academy of Słupsk, Institute of Applied Mathematics, Poland. krzysztof.wierzcholski@wp.pl
authors.forename: Krzysztof
authors.initials: K
authors.lastname: Wierzcholski
mesh_terms: D001696:Biomechanical Phenomena; D001698:Biomedical Engineering / Q000379:methods*; D004548:Elasticity; D017276:Friction; D006621:Hip Joint / Q000503:physiopathology*; D006801:Humans; D008153:Lubrication; D008954:Models, Biological; D008962:Models, Theoretical; D011312:Pressure; D013314:Stress, Mechanical; D013582:Synovial Fluid / Q000378:metabolism; D013997:Time Factors; D014783:Viscosity