Hyper-elastic modelling of intervertebral disc polyurethane implant

• Autorzy: Pawlikowski M. , Skalski K. , Sowiński T.
• Języki publikacji: EN

Abstrakty

EN

Artificial materials including various kinds of polymers like polyurethanes are more and more widely used in different branches of science and also in biomedical engineering. The paper presents the process of creating a constitutive equation for a polyurethane nanocomposite which is considered to be hyper-elastic. The constitutive modelling was conducted within the range of application of the material as one of the components of lumbar intervertebral disc prosthesis. In the paper, the biomechanics of the lumbar spine and the most frequently applied intervertebral disc prostheses are described. Also a polyurethane nanocomposite as a new material to be applied in prostheses is presented. The way of formulating a constitutive equation by means of mathematical formulae is described. Four various hyper-elastic potential functions are considered, i.e., Ogden, Neo-Hookean, Yeoh and Mooney–Rivlin. On the basis of monotonic compression tests the best hyper-elastic model for the material considered was chosen and hyper-elastic constants were calibrated. Finally, the constitutive model was validated on the basis of FE analysis. The paper ends with a conclusion and presentation of further plans of research directed towards the development of a constitutive equation and its application in computer simulations by means of the finite element method.

Słowa kluczowe

EN

constitutive equation; curve fitting; hyperelastic constants

PL

równanie konstytutywne; dopasowywanie krzywej

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Acta of Bioengineering and Biomechanics
• Rocznik: 2013
• Tom: Vol. 15, no. 2
• Strony: 43--50
• Opis fizyczny: Bibliogr. 26 poz., tab., wykr., il.

Twórcy

autor

Pawlikowski M.

• Warsaw University of Technology, Institute of Mechanics and Printing, Warszawa, Poland

autor

Skalski K.

• Warsaw University of Technology, Institute of Mechanics and Printing, Warszawa, Poland

autor

Sowiński T.

• Military Institute of Medicine, Department of Orthopaedics, Warszawa, Poland

Bibliografia

• [1] AHRENS J., SHELOKOV A.P., CARVER J.L., Normal joint mobility is maintained with an artificial disc prosthesis, New York: North Am. Spine Society, 1997.
• [2] AKESON W.H., WOO S.L., TAYLOR T.K., GHOSH P., BUSHELL G.R., Biomechanics and biochemistry of the intervertebral disks: the need for correlation studies, Clin. Orthop., 1977, Vol. 129, 133–140.
• [3] BERTAGNOLI R., SCHONMAYR R., Surgical and clinical results with the PDN prosthetic disc-nucleus device, Eur. Spine J., 2002, Vol. 11 (Suppl. 2), S143–148.
• [4] BORKOWSKI P., MAREK P., KRZESIŃSKI G., RYSZKOWSKA J.L., WAŚNIEWSKI B., WYMYSŁOWSKI P., ZAGRAJEK T., Finite element analysis of artificial disc with an elastomeric core in the lumbar spine, Acta Bioeng. Biomech., 2012, Vol. 14, 59–66.
• [5] CASPI I., LEVINKOPF M., NERUBAY J., Results of lumbar disk prosthesis after a follow-up period of 48 months, Isr. Med. Assoc., 2003, Vol. 5, 9–11.
• [6] CINOTTI G., DAVID T., POSTACCHINI F., Results of disc prosthesis after a minimum follow-up period of 2 years, Spine, 1996, Vol. 21, 995–1000.
• [7] GAMRADT S.C., WANG J.C., Lumbar disc arthroplasty, The Spine Journal, 2005, Vol. 5, 95–103.
• [8] GOH S.M., CHARALAMBIDES M.N., WILLIAMS J.G., Determination of the Constitutive Constants of Non-Linear Viscoelastic Materials, Mech. Time-Depend Mat., 2004, Vol. 8, 255–268.
• [9] GORDON J., DMITRIEV A.E., HU N., MCAFFEE P.C., Biomechanical evaluation of total disc arthroplasty: an in-vitro human cadaveric model, New Orleans, LA: American Academy of Orthopaedic Surgeons, 2003.
• [10] KLARA P.M., RAY C.D., Artificial nucleus replacement: clinical experience. Spine, 2002, Vol. 27, 1374–1377.
• [11] KRAG M.H., SEROUSSI R.E., WILDER D.G., POPE M.H., Internal displacement distribution from in vitro loading of human thoracic and lumbar spinal motion segments: experimental results and theoretical predictions, Spine, 1987, Vol. 12, 1001–1007.
• [12] LINK H.D., History, design and biomechanics of the LINK SB Charité artificial disc, Eur. Spine J., 2002, Vol. 11 (Suppl. 2), S98–S105.
• [13] ŁODYGOWSKI T., KĄKOL W., WIERSZYCKI M., Finite element analysis of artificial disc with an elastomeric core in the lumbar spine, Acta Bioeng. Biomech., 2005, Vol. 7, 29-37.
• [14] MAKSIMOV R.D., IVANOVA T., KALNINS M., ZICANS J., Mechanical properties of high-densitypolyethylene/chlorinated polyethylene blends, Mech. Comp. Mat., 2004, Vol. 40, 331–340.
• [15] MCNALLY D.S., ADAMS M.A., Internal intervertebral disc mechanics as revealed by stress profilometry, Spine, 1992, Vol. 17, 66–73.
• [16] OGDEN R., SACCOMANDI G., SGURA I., Fitting hyperelastic models to experimental data, Comput. Mech., 2004, Vol. 34, 484–502.
• [17] OSTI O.L., VERNON-ROBERTS B., MOORE R., FRASER R.D., Annular tears and disc degeneration in the lumbar spine. A post-mortem study of 135 discs, J. Bone Joint Surg. Br, 1992, Vol. 74, 678–682.
• [18] PAWLIKOWSKI M., Cortical Bone Tissue Viscoelastic Properties and Its Constitutive Equation – Preliminary Studies, Arch. Mech. Eng., 2012, LIX:31-52
• [19] PAWLIKOWSKI M., KLASZTORNY M., SKALSKI K., Studies on constitutive equation that models bone tissue, Acta Bioeng. Biomech., 2008, Vol. 10, 39–47.
• [20] PIOLETTI D.P., RAKOTOMANANA L.R., BENVENUTI J.F., LEYVRAZ P.F., Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons, J. Biomech., 1998, Vol. 31(8), 753–757.
• [21] POPE M.H., WILDER D.G., MATTERI R.E., FRYMOYER J.W., Experimental measurements of vertebral motion under load, Orthop. Clin. North. Am., 1977, Vol. 8, 155–167.
• [22] POPE M.H., FRYMOYER J.W., LEHMANN T.R., Structure and function of the lumbar spine, [in:] M.H. Pope, G.B.J. Anderson, J.W. Frymoyer, D.B. Chaffin (eds.), Occupational low back pain: assessment, treatment, and prevention, St. Louis, MO: CV Mosby, 1991, 95–113.
• [23] ROLANDER S.D., Motion of the lumbar spine with special reference to the stabilizing effect of posterior fusion. An experimental study on autopsy specimens, Acta Orthop. Scand., 1966, Vol. (Suppl. 90), 1–144.
• [24] SIMON S.R., Kinesiology, [in:] S.R. Simon (ed.), Orthopaedic basic science, Rosemont, Il: American Academy of Orthopaedic Surgeons, 1994, 519–622.
• [25] YUAN S.W., Y-X.: Optimization theory and methods, Nonlinear Programming, Springer, 2006.
• [26] TROPIANO P., HUANG R.C., GIRARDI F.P., MARNAY T., Lumbar disc replacement: preliminary results with ProDisc II after a minimum follow up period of 1 year, J. Spinal Disord. Tech., 2003, Vol. 16, 362–368.