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Estimation of random bio-hydrodynamic lubrication parameters for joints with phospholipid bilayers

Wierzcholski Krzysztof, Miszczak Andrzej

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 1

art. no. e135834

EN

This paper presents a new form of a mathematical estimation of stochastic bio-hydrodynamic lubrication parameters for real human joint surfaces with phospholipid bilayers. In this work, the authors present the analytical and stochastic considerations, which are based on the measurements of human joint surfaces. The gap is restricted between two cooperating biological surfaces. After numerous experimental measurements, it directly follows that the random symmetrical as well as unsymmetrical increments and decrements of the gap height in human joints influence the hydrodynamic pressure, load-carrying capacity, friction forces, and wear of the cooperating cartilage surfaces in human joints. The main focus of the paper was to demonstrate the influence of variations in the expected values and standard deviation of human joint gap height on the hydrodynamic lubrication parameters occurring in the human joint. It is very important to notice that the new form of apparent dynamic viscosity of synovial fluid formulated by the authors depends on ultra-thin gap height variations. Moreover, evident connection was observed between the apparent dynamic viscosity and the properties of cartilage surface coated by phospholipid cells. The above observations indicate an indirect impact of stochastic changes in the height of the gap and the indirect impact of random changes in the properties of the joint surface coated with the phospholipid layers, on the value of hydrodynamic pressure, load carrying capacity and friction forces. In this paper the authors present a synthetic, comprehensive estimation of stochastic bio-hydrodynamic lubrication parameters for the cooperating, rotational cartilage bio-surfaces with phospholipid bilayers occurring in human joints. The new results presented in this paper were obtained taking into account 3D variations in the dynamic viscosity of synovial fluid, particularly random variations crosswise the film thickness for non-Newtonian synovial fluid properties. According to the authors’ knowledge, the obtained results are widely applicable in spatiotemporal models in biology and health science.

2

Modeling and control of capacities in human joint gap for unsteady periodic motion and magnetic field

Wierzcholski K. C.

Journal of Applied Computer Science

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2004

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Vol. 12, nr 1

127-148

EN

This paper presents numerical modeling and control for synovial fluid unsymmetrical hvdrodynamic lubrication of human joints in periodically changed time and unsteady magnetic field. We assume that bonehead in human joint moves in two different directions. Basic equations are solved on the analytical and numerical way. Numerical calculations are performed in Mathcad 2000 Professional Program, using the method of Finite Differences. Stability of numerical solutions of partial differential equations was examined.

3

Method of solutions of synovial fluid squeeze flow in magnetic field for human joint gap

Wierzcholski K.

Journal of Applied Computer Science

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2002

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Vol. 10, nr 2

119-138

EN

In this paper are considered mathematical methods of solution of synovial fluid velocity components and pressure distribution for unsymmetrical squeeze flow in magnetic field in human joint gap between two rotational orthogonal. curvilinear bone surfaces.

4

Behavior of synovial fluid squeeze film in biobearing gap.

Wierzcholski K.

Zagadnienia Eksploatacji Maszyn

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1998

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Vol. 33, nr 2

325-332

EN

The various biobearing models accuring in human hip joint, knee joint, shoulder joint are lubricated not only by means o classical hydrodynamic lubrication as well by means of squeeze synovial fluid. In this paper we present a model of squeeze synovia film as a new one in such tribology application. The analytical solutions of synovial fluid velocity components and pressure functions are in this paper performed. Moreover we consider the influence of the synovial fluid velocity changes on the joint lubrication problem.

PL

Praca przedstawia wstępne rozważania na temat rozwiązań problemu wyciskania cieczy synowialnej w szczelinie biołożyska człowieka. W niniejszej pracy uzyskano pewne rozwiązania analityczne tego problemu przy pomocy uproszczonych równań podstawowych hydromechaniki w układzie współrzędnych prostokątnych. Uzyskane rozwiązania analityczne biorą pod uwagę wpływ ciśnienia na zmiany lapkości dynamicznej cieczy synowialnej. Obliczenia numerycznej w tej pracy nie zostały przeprowadzone.