Engineering Transactions, 51, 2-3, pp. 267–306, 2003

Heat Transfer Problems in Orthopaedics

M. Stańczyk
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

J.J. Telega
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

The present paper presents a comprehensive review of the heat transfer problems in or-thopaedics. The emphasis is put on presenting clinically relevant issues along with the purpose and motivation for studying the presented problems. The available experimental methods and results are presented and the modelling approaches are described – mathematical formulations and numerical results.

The first of the problems studied is the bone cement heating during cemented implantations, special attention being paid to modelling the kinetics of the acrylic bone cement polymerisation. Next, the heat production during drilling and sawing of the bone is discussed. Eventually, the results concerning frictional heating of the articulating joints are presented.
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References

T. ALBREKTSSON, L. LINDER, Bone injury caused by curing bone cement, Glin. Orth. Rei. Res., 183, 280–287, 1984.

M. BALEANI, R. POGNANI, A. TONI, In vitro study of the influence of stem insertion rate and stem temperature on cement mantle porosity in cemented hip replacements, In 12th Annual Meeting of the European Orthopaedic Research Society, Lausanne, Switzerland (2002), P. F. LEYYRAZ, D. PIOLETTI, T. QUINN, and P. ZYSSET, [Eds.] P–5.

B. R. BALIGA, P. L. ROSE, A. M. AHMED, Thermal modeling of polymerizing polymethylmethacrylate, considering temperature-dependent heat generation, J. Biomech. Eng., 114, 251–259, 1992.

G. BERGMANN, F. GRAICHEN, A. ROHLMANN, In vivo measurement of temperature rise in a hip implant, 37th Annual Meeting Orthopaedic Research Society.

G. BERGMANN, F. GRAICHEN, A. ROHLMANN, N. YERDONSCHOT, G.H. VAN LENTHE, Frictional heating of total hip implants, Part 2: finite element study, J. Biomech., 34, 4, 429–435, 2001.

G. BERGMANN, F. GRAICHEN, A. ROHLMANN, N. YERDONSCHOT, G.H. VAN LENTHE, Frictional heating of total hip implants, Part 1: measurements in patients, J. Błomech., 34, 4, 421–428, 2001.

N.E.BISHOP, S. FERGUSON, S. TEPIĆ, Porosity reduction in bone cement at the cementstem interface, J. Bone Joint Surg. [Br], 78, 3, 349–356, 1996.

S. BIYIKLI, M F. MODEST, R. TARR, Measurements of thermal properties for human femora, J. Biomed. Mat. Res., 1986, 20, 1335–1345, 1986.

A. BORZACCHIELLO, L. AMBROSIO, L. NlCOLAIS, E. J. HARPER, K. E. TANNER, W. BONFIELD, Comparison between the polymerisation behavior of a new bone cement and a commercial one: modelling and in vitro analysis, J. Mat. Sci.: Materials in Medicine, 9, 835–838, 1998.

H.S. CARSLAW, J.C. JAEGER, Conduction of heat in solids, Oxford University Press, 1954.

M.J. CHAMPAGNE, P. DUMAS, P. ORLOY, M.R. BENETT, P. HAMET, J. TREMBLAY, Protection against necrosis by heat stress proteins in vascular smooth muscle cells: Evidence for distinct modes of cell death, Hypertension, 33, 906–913, 1999.

T. CHEN, R. P. KUSY, Effect of methacrylic acid: methyl methacrylate monomer ratios on polymerization rates and properties of polymethyl methacrylates, J. Biomed. Mat. Res., 36, 2, 190–199, 1997.

R. CLATTENBURG, J. COHEN, S. CONNER, N. COOK, Thermal properties of cancellous bone, J. Biomed. Mat. Res., 9, 169–182, 1975.

J.A. DAYIDSON, S. GIR, J. PAUL, Heat transfer analysis of frictional heat dissipation during articulation of femoral implants, J. Biomed. Mat. Res., 22, 281–309, 1988.

J.A. DAYIDSON, G. SCHWARTZ, G. LYNCH, S. GIR, Wear, creep, and frictional heating of femoral implant articulating surfaces and the effect on long-term performance–Part II: Friction, heating, and torgue, J. Biomed. Mat. Res., 22, 69–91, 1988.

E.D. DAYIS, D J. Doss, J.D. HUMPHREY, N.T. WRIGHT, Effects of heat-induced damage on the radial component of thermal diffusivity of bovine aorta, J. Biomech. Eng., 122, 3, 283–286, 2000.

D.A. DENNIS, R. KOMISTEK, E.J. NORTHCUT, J.A. OCHOA, A. RITCHIE, 'In vivo' determination of hip joint separation and the forces generated due to impact loading conditions, J. Biomech., 34, 5, 623–629, 2001.

H. DERAMOND, N.T. WRIGHT, S.M. BELKOFF Temperature elevation caused by bone cement polymerisation during vertebroplasty, Bone, 25, (2 Suppl.), 17S–21S, 1999.

J.A. DIPISA, G.S. SIH, A. BERMAN, The temperature problem at the bone-acrylic cement interface of the total hip replacement, Glin. Orth., 121, 95–98, 1976.

D. DOWSON, Ed., Advances in medical tribology. Orthopaedic implants and implant materials, Mechanical Engineering Publications Limited, London UK, 1998.

L.S. FLETCHER, Recent developments in contact conductance heat transfer, J. Heat Transfer, 110, 1059–1070, 1988.

H. FUKUSHIMA, Y. HASHIMOTO, S. YOSHIYA, M. KUROSAKA, M. MATSUDA, S. KAWAMURA, T. IWATSUBO, Conduction analysis of cement interface temperature in total knee arthroplasty, Kobe J. Med. Sci., 48, 63–72, 2002.

D.P. FYHRIE, J H. KIMURA, Cancellous bone biomechanics, J. Biomech., 32, 11, 1139–1148, 1999.

S.B. GOODMAN, J. SCHATZKER, G. SUMNER-SMITH, V.L. FORNASIER, N. GOFTEN, C. HUNT, The effect of polymethylmethacrylate on bone: an experimental study, Arch. Orthop. Trauma. Surg., 104, 3, 150–154, 1985.

F. GRAICHEN, G. BERGMANN, A. ROHLMANN, Hip endoprosthesis for in vivo measurement of joint force and temperature, J. Biomech., 32, 10, 1113–1117, 1999.

R.M. HALL, A. UNSWORTH, Friction in hip prostheses, Biomaterials, 18, 1017–1026, 1997.

E. HANSEN, Modelling heat transfer in a bone-cement-prosthesis system, J. Biomech., 36, 787–795, 2003.

N.J. HOLM, The formation of stress by acrylic bone cements during fixation of the acetabular prosthesis, Acta Orth. Scan., 51, 719–726, 1980.

R. HUISKES, Some fundamental aspects of human joint replacement, Acta Orth. Scan., 185, 1980.

J.M. HUYGHE, R. VAN LOON, F.T P. BAAIJENS, P.M. VAN KEMENADE, T. . SMIT, We are all porous media, [in:] Poromechanics II, J.-L. AURIAULT, C. GEINDREAU, P. ROYER, J.-F. BLOCH, C. BOUTIN and J. LEWANDOWSKA (Eds.), Balkema Publishers, Lisse, 2002.

K. IESAKA, W. JAFFE, H. COOPER, F. KUMMER, The effects of intra operative stem warming on the strength of the cement-prosthesis interface, In 48th Annual Meeting of the Orthopaedic Research Society.

W.L. JAFFEE, R M. ROSE, E.L. RADIN, On the stability of the mechanical properties of self-curing acrylic bone cement, J. Bone Jt. Surg., Am. Vol., 56, 1711–1714, 1974.

C.D. JEFFERISS, A J. LEE, R.S. LING, Thermal aspects of self-curing polymethylmethacrylate, J. Bone Joint Surg. [Br], 1975, 57, 4, 511–518, 1975.

W.R. KRAUSE, D.W. BRADBURY, J.E. KELLY, E.M. LUNCEFORD, Temperature elevations in orthopaedic cutting operations, J. Biomech., 15, 4, 267–275, 1982.

R.P. KUSY, Characterization of self-curing acrylic bone cements, J. Biomed. Mat. Res., 12, 271–305, 1978.

E.P. LAUTENSCHLAGER, G.W. MARSHALL, Mechanical strength of acrylic bone cements impregnated with antibiotics, J. Biomed. Mater. Res., 10, 837–845, 1976.

A.J.C. LEE, R.S.M. LING, S.S. YANGALA, The mechanical properties of bone cements, J. Med. Eng. Tech., 2, 137–140, 1977.

A.B. LENNOM, P.J. PRENDERGAST, Residual stress due to curing can initiate damage in porous bone cement: experimental and theoretical evidence, J. Biomech., 35, 311–321, 2002.

A.B. LENNON, P.J. PRENDERGAST, M.P. WHELAN, R.P. KENNY, C. CAYALLI, Modelling of temperature history and residual stress generation due to curing in polymethylmethacrylate, [in:] Proceedings of the 12th Conference of the European Society of Biomechanics (2000), P. J. PRENDERGAST, A. J. CARR, and T. C. LEE [Eds.], Royal Academy of Medicine in Ireland, Dublin, p. 253.

L. LINDER, Reaction of bone to the acute chemical trauma of bone cement, J. Bone Joint Surg., 59–A, l, 82–87, 1977.

J.X. LU, Z.W. HUANG, P. TROPIANO, B.C. D'ORVAL, M. REMUSAT, J. DEJOU, J. P. PROUST, D. POITOUT Human biological reactions at the interface between bone tissue and polymethylmethacrylate cement, J. Mat. Sci.: Materials in Medicine, 13, 803–809, 2002.

Z. LU, H. McKELLOP, Frictional heating of bearing materials tested in a hip joint wear simulator, [in:] Advances in Medical Tribology. Orthopaedic implants and implant materials, D. DOWSON, [Ed.] Mechanical Engineering Publications Ltd, pp. 193–200, 1998.

L.S. MATTHEWS, C. HIRSCH, Temperatures measured in human cortical bone when drilling, 3. Bone Joint Surg. [Am], 54, 2, 297–308, 1972.

S. MAZZULLO, M. PAOLINI, C. VERDI, Numerical simulation of thermal bone necrosis during cementation of femoral prostheses, J. Math. Biol., 29, 5, 475–494, 1991.

L.G. MERCURI, Measurement of the heat of reaction transmitted intracranially during polymerization of methylmethacrylate cranial bone cement used in stabilization of the fossa component of an alloplastic temporomandibular joint prosthesis, Oral Surg. Oral Med. Oral Pathol., 74, 2, 137–142, 1992.

D.D. MOSSER, J. DUCHAINE, L. BUORGET, L.H. MARTIN, Changes in heat shock proteins synthesis and heat sensitivity during mouse thymocyte development, Developmental Genetics, 14, 148–158, 1993.

V.C. MOW, A. RATCLIFFE, Structure and function of articular cartilage and meniscus, [in:] Basic Orthopaedic Biomechanics, V C. MOW and W.C. HAYES [Eds.), Lippincot– Raven Publishers, 113–177, Philadelphia 1997.

N. NUÑO, G. AVANZOLINI, Residual stresses at the stem-cement interface of an idealized cemented hip system, J. Biomech., 35, 6, 849–852, 2002.

M. OHTA, S. TSUTSUMI, S H. HYON, Y.B. KANG, H. TANABE, Y. MIYOSHI, Residual stress measurements of ultra-high molecular weight polyethylene for artificial joints, Rus. J. Biomech., 4, 2, 30–38, 2000.

E.M. ORTT, D J. DOSS, E. LEGALL, N.T. WRIGHT, J.D. HUMPHREY, A device for evaluating the multiaxial finite strain thermomechanical behavior of elastomers and soft tissues, J. Appl. Mech., 67, 465-471, 2000.

H.H. PENNES, Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiology, l, 93–122, 1948.

P.J. PRENDERGAST, Biomechanical techniques for pre-clinical testing of prostheses and implants, Lecture notes at Centre of Excellence for Advanced Materials and Structures, Institute for Fundamental Technological Research, Polish Academy of Sciences, Warsaw 2000.

N. RAMANIRAKA, Thermal bone necrosis at the bone-cement interface after cemented total hip arthoplasty: a finite element analysis. In 12th Annual Meeting of the European Orthopaedic Research Society, Lausanne, Switzerland (2002), P.F. LEYVRAZ, D. PIOLETTI, T. QUINN, and P. ZYSSET [Eds.], pp. O–23.

F.W. RECKLING, W.L. DILLON, The bone-cement interface temperature during total joint replacement, J. Bone Joint Surg., 59-A, l, 80–82, 1977.

J. ROJEK, J.J. TELEGA, Contact problems with friction, adhesion and wear in orthopaedic biomechanics. Part I – general developments, J. Theor. Appl. Mech., 39, 3, 655–677, 2001.

J. ROJEK, J.J. TELEGA, S. STUPKIEWICZ, Contact problems with friction, adhesion and wear in orthopaedic biomechanics. Part II – numerical implementation and application to implanted knee joints, J. Theor. Appl. Mech., 39, 3, 679–706, 2001.

S. SAHA, S. PAL, Mechanical properties of the bone cement: A review, J. Biomed. Mat. Res., 18, 435–462, 1984.

M. SAITO, A. MARUOKA, T. MORI, N. SUGANO, K. HINO, Experimental studies on a new bioactive bone cement: hydroxyapatite composite resin, Biomaterials, 15, 2, 156–160, 1994.

J. SCHATZKER, J.G. HORNE, G. SUMNER-SMITH, R. SANDERSON, J. P. MURNAGHAN, Metylmethacrylate cement: its curing temperature and effect on articular cartilage, Canadian J. Surg., 18, 172–178, 1975.

Y. SENAHA, T. NAKAMURA, J. TAMURA, K. KAWANABE, H. IIDA, T. YAMAMURO, Intercalary replacement of canine femora using a new bioactive bone cement, J. Bone Joint Surg., 78, l, 26–31, 1996.

A. SHITZER, S. BELLOMO, L. A. STROSCHEIN, R. R. GONZALEZ, K. B. PANDOLF, Simulation of a cold-stressed finger including the effects of wind, gloves and cold-induced vasodilatation, J. Biomech. Eng., 120, 389–394, 1998.

A.V. SOTIN, Y.V. AKULICH, R.M. PODGAYETS, The calculation of loads acting on the femur during normal human walking, Rus. J. Biomech., 4, l, 49–61, 2000.

P. SPENCER, C.M. COBB, D.M. WIELICZKA, A.G. GLAROS, P.J. MORRIS, Change in temperature of subjacent bone during soft tissue laser ablation, J. Periodontol, 69, 11, 1278–1282, 1998.

M. STAŃCZYK, Modelling of PMMA bone cement polymerisation, J. Biomech., submitted.

M. STAŃCZYK, J.J. TELEGA, Thermal problems in artificial joints: influence of bone cement polymerization, Acta Bioengng. Biomech., 3, 489–496, 2001.

M. STAŃCZYK, J.J. TELEGA, Modelling of heat transfer in biomechanics — a review. Port I. Soft tissues, Acta Bioengng. Biomech., 4, l, 31–61, 2002.

G.R. STARKE, C. BIRMIE, P.A. VAN DEN BLINK Numerical modelling of cement polymerisation and thermal bone necrosis, [in:] Computer Methods in Biomechanics and Biomedical Engineering – 2, J. MIDDLETON, M.L. JONES, and G.N. PANDE [Eds.] 1998, 163–172.

L.W. SWENSON JR, D.J. SCHURMAN, R. PIZIALI, Finite element temperature analysis of a total hip replacement and measurement of PMMA curing temperatures, J. Biomed. Mat. Res., 15, l, 83–96, 1981.

E. SZWAJCZAK, A. KUCABA-PIETAL, J.J. TELEGA, Liquid crystalline properties of synovial fluid, Engng Trans., 49, 315–358, 2001.

K. TAKEGAMI, T. SANO, H. WAKABAYASHI, J. SONODA, T. YAMAZAKI, S. MORITA, T. SHIBUYA, A. UCHIDA, New ferromagnetic bone cement for local hyperthermia, J. Biomed. Mat. Res., 43, 2, 210–214, 1998.

S. TEPIC, T. MACIROWSKI, R.W. MANN, Experimental temperature rise in human hip joint in vitro, in simulated walking, J. Orthop. Res., 3, 516–520, 1985.

S. TOKSVIG-LARSEN, H. FRANZEN, L. RYD, Cement interface temperature in hip arthoplasty, Acta Orth. Scan., 62, 2, 102–105, 1991.

S. TOKSVIG-LARSEN, L. RYD, A. LINDSTRAND, On the problem of heat generation in bone cutting, J. Bone Joint Surg. [Br], 73, l, 13–15, 1991.

S. TOKVYIG-LARSEN, L. RYD, A. LINDSTRAND, Temperature influence in different or- thopaedic saw blades, J. Arthoplasty, 7, (1), 21–24, 1992.

B. VAZQUEZ, M.P. GINEBRA, F.J. GIL, J.A. PLANELL, A. LÓPEZ BRAYO, J. SAN ROMAN, Radiopaque acrylic cements prepared with a new acrylic derivative of iodoquinoline, Biomaterials, 20, 2047–2053, 1999.

S. WEINBAUM, L.M. JUI, A new simplified bioheat equation for the effect of blood flow on local average tissue temperature, J. Biomech. Eng., 107, 131–139, 1985.

M.P. WHELAN, R.P. KENNY, C. CAYALLI, A.B. LENNOM, P.J. PRENDERGAST, Application of the optical fibre Bragg grating sensors to the study of PMMA curing, [In:] Proceedings of the 12th Conference of the European Society of Biomechanics (2000), P. J. PRENDERGAST, A.J. CARR, and T.C. LEE [Eds.], Royal Academy of Medicine in Ireland, Dublin, pp. 252.

H.G. WILLERT, J. LUDWIG, M. SEMLITSCH, Reaction of bone to methacrylate after hip arthoplasty, J. Bone Joint Surg., 56-A, 7, 1368–1382, 1974.

S. WIŚNIEWSKI, T. WIŚNIEWSKI, Heat transfer (in Polish), Wydawnictwa Naukowo Techniczne, Warszawa 1997.

Y.L. WU, S. WEINBAUM, L.M. JUI, A new analytic technique for 3-D heat transfer from a cylinder with two or more axially interacting eccentrically embedded vessels with application to countercurrent blood flow, J. Heat Mass Transfer, 36, 4, 1073–1083, 1993.

A.G.M. WYKMAN, Acetabular cement temperature in arthroplasty. Effect of water cooling in 19 cases, Acta Orth. Scan., 63, 5, 543–544, 1992.

T.H. YOUNG, C.K. CHENG, Y.M. LEE, L.Y. CHEN, C.H. HUANG, Analysis of ultrahigh molecular weight polyethylene failure in artificial knee joints: Thermal effect on long-term performance, J. Biomed. Mat. Res., 48, 2, 159–164, 1999.

M. ZHU, S. WEINBAUM, L.M. JUI, Heat exchange between unequal counter current vessels asymmetrically embedded in a cylinder with surface connection, J. Heat Mass Transfer, 33, 10, 2275–2284, 1990.

M. ZHU, S. WEINBAUM, D.E. LEMONS, A three-dimensional variable geometry counter current model for whole limb heat transfer, J. Biomech. Eng., 114, 3, 366–376, 1992.




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