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A Model for Intra-Articular Heat Exchange in a Knee Joint

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Abstract

A mathematical model has been developed for the understanding of temperature distribution in knee joint. Temperature rises in knee joint as a result of frictional energy. This heated synovial fluid enters into the articular cartilage by the process of filtration and supplies heat to cartilage and bone. This cooled fluid again mixes well with the lubricant in the joint cavity. The problem is formulated as a two-region flow and diffusion model: flow and thermal diffusion within the intra-articular gap; and within the porous matrix covering the approaching bones at the joint. The solution of the coupled mixed boundary value problem is solved by using perturbation method. It has been observed that, in certain diseased and or old synovial joints, the movement of the fluid into or out of the cartilage resisted, and therefore, the temperature does rise. The temperature does rise in old and diseased joints as observed by varying the values of parameters from its normal values. These values refer to old age and/or diseases affecting degeneration of synovial fluid and or cartilage.

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References

  1. Szwajczak, E., Kucaba-Pietal, A., Telega, J.J.: Liquid crystalline properties of synovial fluid. Eng. Trans. 49, 315–358 (2001)

    Google Scholar 

  2. Maroudas, A.: Hyaluronic acid films. Proc. Inst. Mech. Eng. 181, 122–124 (1967)

    Google Scholar 

  3. McCutchen, C.W.: The frictional properties of animal joints. Wear 5, 1–17 (1962)

    Article  Google Scholar 

  4. Mukherjee, K.K., Bose, K.K.: In: Tandon, P.N., Kapur J.N. (eds.) Studies in Biomechanics, pp. 111–114. HBTI Publications, India (1980)

  5. Rieker, C.: Sulzer Orthopaedics, personal communication (1999)

  6. Lu, Z., McKellop, H.: Frictional heating of bearing materials tested in a hip joint wear simulator. Proc. Inst. Mech. Eng. H 211, 101–108 (1997)

    Article  CAS  Google Scholar 

  7. Lu, Z., McKellop, H., Liao, P., Benya, P.: Potential thermal artefacts in hip joint wear simulators. J. Biomed. Mater. Res. 48, 458–464 (1999)

    Article  CAS  Google Scholar 

  8. Davidson, J.A., Schwartz, G., Lynch, M.G., Gir, S.: Wear creep and frictional heating of femoral implant articulating surfaces and the effect of long term performance part II, friction, heating and torque. J. Biomed. Mater. Res. 22, 69–91 (1988)

    Article  CAS  Google Scholar 

  9. Moss, S.G., Schweitzer, M.E., Jacobson, J.A., Brossmann, J.A., Lombardi, J.V., Dellose, S.M., Coralnick, J.R., Standiford, K.N., Resnick, D.: Hip joint fluid: detection and distribution at MR imaging and US with cadaveric correlation. Radiology 208, 43–48 (1998)

    CAS  Google Scholar 

  10. Liebergall, M., Simkin, A., Mendelson, S., Rosenthal, A., Amir, G., Segal, D.: Effect of mild hyperthermia on cell viability and mechanical. Clin. Orthop. 349, 242–248 (1998)

    Article  Google Scholar 

  11. Hlavacek, M.: Lubrication of the human ankle joint in running. Int. Rev. Mech. Eng. 3, 619–626 (2009)

    Google Scholar 

  12. Davidson, J.A., Gir, S., Paul, J.P.: Heat transfer analysis of frictional heat dissipation during articulation of femoral implants. J. Biomed. Mater. Res. 22, 281–309 (1988)

    Article  CAS  Google Scholar 

  13. Sawyer, W.G., Hamilton, M.A., Fregly, B.J., Banks, S.A.: Temperature modelling in a total knee joint replacement using patient specific kinematics. Tribol. Lett. 15, 343–351 (2003)

    Article  CAS  Google Scholar 

  14. Bergmann, G., Graichen, F., Rohlmann, A., Verdonschot, N., Van Lenthe, G.H.: Frictional heating of total hip implants. Part 1. Measurements in patients. J. Biomech. 34, 421–428 (2001)

    Article  CAS  Google Scholar 

  15. Bergmann, G., Graichen, F., Rohlmann, A., Verdonschot, N., Van Lenthe, G.H.: Frictional heating of total hip implants. Part 2. Finite element study. J. Biomech. 34, 429–435 (2001)

    Article  CAS  Google Scholar 

  16. Fialho, J.C., Fernades, P.R., Eca, L., Folgado, J.: Computational hip joint simulator for wear heat generation. J. Biomech. 40, 2358–2366 (2007)

    Article  Google Scholar 

  17. Tandon, P.N., Bali, R.: A study on temperature regulation in synovial joints. Tribol. Lett. 3, 209–213 (1997)

    Article  Google Scholar 

  18. Tandon, P.N., Gupta, R.S., Prakash, J.S.: Role of synovial fluid temperature regulation in human joints. Kanpur Univ. Res. J. Sci. 4, 41–52 (1983)

    Google Scholar 

  19. Bali, R., Shukla, A.K.: A simple model for temperature regulation in synovial joint. Ultra Sci. 15, 109–116 (2003)

    Google Scholar 

  20. Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. Wiley, New York (1960)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Harcourt Butler Technological Institute, Kanpur, 208 002, India

    Rekha Bali

  2. Department of Applied Sciences & Humanities, Kanpur Institute of Technology, Kanpur, 208 001, India

    S. K. Sharma

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  1. Rekha Bali
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  2. S. K. Sharma
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Correspondence to Rekha Bali.

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Bali, R., Sharma, S.K. A Model for Intra-Articular Heat Exchange in a Knee Joint. Tribol Lett 41, 379–386 (2011). https://doi.org/10.1007/s11249-010-9720-3

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  • DOI: https://doi.org/10.1007/s11249-010-9720-3

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