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Synovial fluid. Rheology and modelling Rheology and modelling Anna Kucaba-Pietal Rzeszow University of Technology Poland

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purpose of the work To examine whether the use of an isotropic micropolar model to describe the liquid crystal synovial fluid is appropriate Performing calculations tribological size biobearings on the basis of the theory of micropolar fluids for physiological data and comparison with the results of clinical observations

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coefficient of friction c x ~ , It works about 70 years Transfer the load from a few to 18MP cartilage Synovial fluid Biobearing hip joint

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cartilage

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5 Contentsvalue Dry matter 0,13 3,5 Density(20 o C) 1,0081 1,015 pH 7,2 7,4 viscosity (20 o C) water, g/kg hyaluronic acid (HA ) 2-3%2-3% The content of dry matter g/kg Albumins, globulins g/l Phospholipids, glycoprotein's 10,7 21,3 10,2 0,5 Mucyns, g/l 0,68 1,35 Glucoses, g/l jak w surowicy krwi Urynial Acid, mg/l 73,4 Synovial Fluid

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6 Sodium Hyaluronate, Hyaluronan Made up of repeating glucuronic acid and N-acetylglucosamine subunitsMade up of repeating glucuronic acid and N-acetylglucosamine subunits High molecular weight: 0.2 to 10 million DaltonHigh molecular weight: 0.2 to 10 million Dalton Major component of synovial fluidMajor component of synovial fluid Exhibits viscoelastic propertiesExhibits viscoelastic properties Synovial Fluid Main Factors affecting the rheological properties: a) Hyaluronic Acid concentation c) Molecular weigh of Hyaluronic Acid d) temperature

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7 efekt przędliwości własności lepkosprężyste – efekt Barusa The influence of HA concentration on viscosity coefficient of synovial fluid HA concentration effect on Synovial fluid rheology

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8 In normal joints synovial fluid shows higher elastic properties. For diseases such as Rheumatoid arthritis, seropositive and seronegative, it is observed to decrease in the elastic and viscous properties of synovial fluid In the elderly peoples and competitive athletes, a decrease in viscosity and reduced HA chain length is observed. Rheumatic Diseases

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9 Pathophysiological significance of biofluid rheology Develop an understanding of how the micro- and nano- structure of blood influences its rheology Explore to use of rheological parameters in diagnostics and menagement of clinical disorders and inoptimisation of blood processing Explore new methods of measurement suited for clinical application Maintain new type apparatus for such measurements Perspectives

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lk = – kl O The mathematical description of the liquid crystal medium versus micropolar fluid model

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Cartilage - construction 20 m 5 m 20 m 50 m 2 m

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The coefficient of friction during movement along (1) and perpendicular to Microgroove (2). (Kupchinov) Cartilage surface waviness exhibits Magn. X 300

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Synovial fluid - rheological properties dynamic viscosity coefficient of a HA solution coefficient of dynamic viscosity of synovial viscoelastic properties - Barus effect

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Cartilage - the construction 20 m 5 m 20 m 50 m 2 m

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Model Rivlina-Ericksena gdzie: –stress tensor p – pressure I – tensor jednostkowy, A 1 i A 2 – shear tensor Rivlina-Ericksena,,, – material constants of synovial

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ij = (-p + V k,k ) ij + (V i, j + V j, i ) + (V j, i - ijk k ), C ij = k, k ij + i, j + j, i. Micropolar fluid equations

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The dimensionless form of the m.f. equations

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L min = h/l min = 1000 L max = h/l max = 90. h = 40 m, a = 0.04 m = R/2 U = 0.01 m/s Effect legth of HA molecules on load N parameter N showing the synovial fluid concentrations of HA : L1, L2 - HA molecules long, L3, L4 - short molecules The calculated bearing capacity W for different lengths L of HA molecules pozaslaniaj synku na rysunkach polskie napisy Ten slajd proszę rozbi mi na dwa slajdy, tytul taki sam, Na jednym dwa z boku na drugim wykres.

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HA concentration effect on Synovial fluid rheology

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Effect of HA molecules on the surface of bone approaching time in biołożysku? Parameter N as a function of the synovial fluid: L1, L2 - HA molecules long, L3, L4 - short molecules Calculation of time approaching the surface of the bone s as a function of concentration and lenth of HA

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Nośność stawu biodrowego w funkcji parametru N dla pięciu wartości temperatury mazi Calculation of load capacity as a function of temperature

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Conclusions The calculation of the tribological joint quatities obtained under micropolar model applied to synovial fluid are qualitatively consistent with clinical observations. Mikropolarny fluid model of synovial remains in compliance with confirmed experimentally LCD model synovial fluid both in terms of physics of liquid crystals, as well as mathematical description. Describes the synovial fluid phase transitions.

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Thank you for your attention

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