A Porous Media Approach to Finite Deformation Behaviour in Soft Tissues

References

• Almeida , S. and Spilker , R. L. ( 1997 ). Mixed and penalty finite element methods for the nonlinear behaviour of biphasic tissues in finite deformation Part 1-Alternate formulations . Comp. Meth. Biomech. Biomed. Eng. , 1 , 25 - 46 .
   PubMedGoogle Scholar
• Argoubi , M. and Shirazi-Adl , A. ( 1996 ). Poroelastic creep response analysis of a lumbar motion segment in compression . J. Biomech. , 29 , 1331 - 1339 .
   PubMed Web of Science ®Google Scholar
• Athesian , G. A. , Warden , W. H. , Kim , J. J. , Grelsamer. R. P. and Mow , V. C. ( 1997 ). Finite deformation biphasic material properties of bovine articular cartilage from confined compression experiments . J. Biomech. , 30 , 1157 - 1164 .
   Google Scholar
• Barry , S. I. and Aldis , G. K. ( 1990 ). Comparison of models for flow induced deformation of soft biological tissue . J. Biomech. , 23 , 647 - 654 .
   PubMed Web of Science ®Google Scholar
• Best , B. A. , Guilak , F. , Setton , L. A. , Zhu , W. , Saed-Nejad , F. , Ratcliffe , A. , Weidenbaum , M. and Mow , V. C. ( 1994 ). Compressive mechanical properties of the human anulus flbrosus and their relationship to biochemical composition . Spine , 19 , 212 - 221 .
   PubMed Web of Science ®Google Scholar
• Biot , M. A. ( 1941 ). General theory of three dimensional consolidation , J. Appl. Phys. , 12 , 155 - 164 .
   Web of Science ®Google Scholar
• Broberg , K. B. ( 1993 ). Slow deformation of intervertebral disc . J. Biomech. , 26 , 501 - 512 .
   PubMed Web of Science ®Google Scholar
• Carter , D. R. and Hayes , W. C. ( 1977 ). The compressive behavior of bone as a two-phase porous structure . J. Bone Jt. Surg. , 59-A , 954 - 962 .
   Web of Science ®Google Scholar
• Cassidy , J. J. , Silverstein , M. S. , Hiltner , A. and Baer , E. ( 1990 ). A water transport model for the creep response of the intervertebral disc . J. Mot. Sci. Mat. Med. , 1 , 81 - 89 .
   Google Scholar
• Cheng , W. F. and Tsui , Y. ( 1992 ). Limitations to the large strain theory . Int. J. Num. Meth. Eng. , 33 , 101 - 114 .
   Google Scholar
• Dienes , J. K. ( 1979 ). On the analysis of rotation and stress rate in deforming bodies , Acta Mech. , 32 , 217 - 232 .
   Web of Science ®Google Scholar
• Dillaman , R. M. , Roer , R. D. and Gay , D. M. ( 1991 ). Fluid movement in bone theoretical and empirical . J. Biomech. , 24 , 163 - 177 .
   PubMed Web of Science ®Google Scholar
• Hidalgo-Ovejero , A. M. , Martinez-Grande , M. and Garcia-Mata , S. ( 1994 ). Disc herniation with gas . Spine , 19 . 2210 - 2212 .
   Google Scholar
• Holmes , M. H. and Hukins , D. W. L. ( 1996 ). Analysis of load-relaxation in compressed segments of lumbar spine . Med. Eng. Phys. , 18 , 99 - 104 .
   PubMed Web of Science ®Google Scholar
• Holmes , M. H. and Mow , V. C. ( 1990 ). The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration . J. Biomech. , 23 , 1145 - 1156 .
   PubMed Web of Science ®Google Scholar
• Iatridis , J. C. , Weidenbaum , M. , Setton , L. A. and Mow , V. C. ( 1996 ). Is the nucleus pulposus a solid or a fluid? Mechanical behaviors of the nucleus pulposus of the human intervertebral disc . Spine , 21 , 1174 - 84 .
   PubMed Web of Science ®Google Scholar
• Johnstone , B. , Urban , J. P. , Roberts , S. and Menage , J. ( 1992 ). The fluid content of the human intervertebral disc. Comparison between fluid content and swelling pressure profiles of discs removed at surgery and those taken postmortem . Spine , 17 , 412 - 416 .
   PubMed Web of Science ®Google Scholar
• Kafka , V. ( 1993 ). On hydraulic strengthening of bones , J. Biomech. , 26 , 761 - 762 .
   Google Scholar
• Kazarian , L. E. ( 1975 ). Creep characteristics of the human spinal column . Orth. Clin. N. Amen , 6 , 3 - 18 .
   PubMed Web of Science ®Google Scholar
• Kenyon , D. E. ( 1979 ). A mathematical model for water flux through aortic tissue . Bull. Math. Biol. , 41 , 79 - 90 .
   Google Scholar
• Kwan , M. K. , Lai , W. M. and Mow , V. C. ( 1990 ). A finite deformation theory for cartilage and other soft hydrated connective tissues-I Equilibrium results . J. Biomech. , 23 , 145 - 155 .
   PubMed Web of Science ®Google Scholar
• Lai , W. M. , Hou , J. S. and Mow , V. C. ( 1991 ). A triphasic theory for the swelling and deformation behaviors of articular cartilage . J. Biomech. Eng. , 113 , 245 - 258 .
   PubMed Web of Science ®Google Scholar
• Laible , J. P. , Pflaster , D. , Krag , M. H. , Simon , B. R. and Haugh , L. D. ( 1993 ). A poroelastic-swelling finite element model with applications to the intervertebral disc . Spine , 18 , 659 - 670 .
   PubMed Web of Science ®Google Scholar
• Laible , J. P. , Pflaster , D. , Simon , B. R. , Krag , M. H. , Pope , M. and Haugh , L. D. ( 1994 ). A dynamic material parameter estimation procedure for soft tissue using a poroelastic finite element model . J. Biomech. Eng. , 116 , 19 - 29 .
   PubMed Web of Science ®Google Scholar
• Li , S. , Patwardham , A. G. , Amirouche , F. M. , Havey , R. and Meade , K. P. ( 1995 ). Limitations of the standard linear solid model of intervertebral discs subject to prolonged loading and low-frequency vibration in axial compression . J. Biomech. , 28 , 779 - 790 .
   PubMed Web of Science ®Google Scholar
• Lunardi , P. , Mastronardi , L. , Puzzilli , F. and Missori , P. ( 1993 ). Gas-containing lumbar disc herniation a case report and review of the literature . Spine , 18 . 2533 - 2536 .
   Google Scholar
• Martinez , J. B. , Oloyede , V. O. and Broom , N. D. ( 1997 ). Biomechanics of load-bearing of the intervertebral disc an experimental and finite element model . Med. Eng. Phys. , 19 , 145 - 56 .
   PubMed Web of Science ®Google Scholar
• Meroi , E. ( 1993 ). Comportamento non lineare per geometria di mezzi porosi parzialmente saturi . Ph.D. thesis . Istituto di Scicnza e Tecnica delle Costruzioni. Universita di Padova .
   Google Scholar
• Meroi , E. A. , Natali , A. N. and Schrefler , B. A. ( 1996 ). A poroelastic approach to the analysis of spinal motion segment . In Computer Methods in Biomechanics and Biomedical Engineering , (Eds J. Middleton et ai) , Gordon and Breach Publishers , Amsterdam , 325 - 338 .
   Google Scholar
• Meroi , E. A. , Natali , A. N. and Schrefler , B. A. ( 1997 ). A partially saturated formulation of intervertebral segment undergoing large deformations, Proc. Joint Conference of GIMC and AMC , Padova , 241 - 244 .
   Google Scholar
• Meroi , E. A. and Schrefler , B. A. , ( 1995 ). Large strain analysis of porous media . In Modern issues in non-saturated soils (eds. A. Gens et al.) , Springer-Verlag , Wien , C.9 , 397 - 447 .
   Google Scholar
• Meroi , E. A. Schrefler , B. A. and Zienkiewicz , O. C. ( 1995 ). Large strain static and dynamic semisaturated soil behaviour . Int. J. Num. Anal. Meth. Geomech. , 19 , 81 - 106 .
   Google Scholar
• Molenkamp , F. ( 1986 ). Limits to the Jaumann stress rate . Int. J. Num. Anal. Meth. Geomech. , 10 , 151 - 176 .
   Google Scholar
• Mow, V. C. Kuei , S. C., Lai , W. M. rmstrong. C. G. ( 1980 ). Biphasic creep and stress relaxation of articular cartilage in compression theory and experiment . J. Biomech. Eng. , 102 , 73 - 84 .
   Google Scholar
• Natali , A. N. and Meroi , E. A. ( 1989 ). A review of the biomechanical properties of bone as a material . J. Biomed. Eng. , 11 , 266 - 276 .
   PubMedGoogle Scholar
• Natali , A. and Meroi , E. ( 1990 ). Nonlinear analysis of intervertebral disk under dynamic load . J. Biomech. Eng. , 112 , 358 - 363 .
   PubMed Web of Science ®Google Scholar
• Natali , A. N. and Meroi , E. A. ( 1993 ). The mechanical behaviour of bony endplate and annulus in prolapsed disc configuration . J. Biomed. Eng. , 15 , 235 - 239 .
   PubMedGoogle Scholar
• Ochoa , J. A. , Sanders , A. P. , Heck , D. A. and Hillberry , B. M. ( 1991 ). Stiffening of the femoral head due to intertra-becular fluid and intraosseous pressure . J. Biomech. Eng. , 113 , 259 - 262 .
   Google Scholar
• Oomens , C. W. J. , Van Campen , D. H. and Grootenboer , H. J. ( 1987 ). A mixture approach to the mechanics of skin . J. Biomech. , 20 , 877 - 885 .
   PubMed Web of Science ®Google Scholar
• Schrefler , B. A. ( 1995 ). F.E. in environmental engineering coupled thermo-hydro-mechanical processes in porous media including pollutant transport . Archives of Computational Methods in Engineering 2-3 1 - 54 .
   Google Scholar
• Shirazi-Adl , S. A. , Shrivastava , S. C. and Ahmed , A. M. ( 1984 ). Stress analysis of the lumbar disc-body unit in compression—a three dimensional nonlinear finite element study . Spine , 9 , 120 - 135 .
   PubMed Web of Science ®Google Scholar
• Simon , B. R. ( 1988 ). Poroelastic finite element models in biomechanics—an overview . Interfaces in Medicine and Mechanics—II (eds. K. R. Williams et al.) , Elsevier Applied Science 279 - 288 .
   Google Scholar
• Simon , B. R. , Kaufmann , M. V. , McAfee , M. A. and Baldwin , A. L. ( 1993 ). Finite clement models for arterial wall mechanics . J-Biomcch-Eng. 115 , 489 - 496 .
   PubMed Web of Science ®Google Scholar
• Simon , B. R. , Liable , J. P. , Pilaster , D. , Yuan , Y. and Krag , M. H. ( 1996 ). A poroelastic finite element formulation including transport and swelling in soft tissue structures . J. Biomech. Eng. , 118 , 1 - 9 .
   PubMed Web of Science ®Google Scholar
• Simon , B. R. , Wu , J. S. S. , Carlton , M. W. , Evans , J. H. and Kazarian , L. E. ( 1985 ). Structural models for human spinal motion segments based on a poroelastic view of the intervertebral disk . J. Biomech. Eng. , 207 , 327 - 335 .
   Google Scholar
• Simon , B. R. , Wu , J. S. S. , Carlton , M. W. , Kazarian , L. E. , France , E. P. , Evans , J. H. and Zienkievich , O. C. ( 1985 ). Poroelastic dynamic structural models of Rhesus spinal motion segments . Spine , 10 , 494 - 507 .
   PubMed Web of Science ®Google Scholar
• Spilker , R. L. , Suh , J. K. and Mow , V. C. ( 1992 ). A finite clement analysis of the indentation stress-relaxation response of linear biphasic articular cartilage . J. Biomech. Eng. , 114 , 191 - 201 .
   PubMed Web of Science ®Google Scholar
• Spilker , R. L. , Donzelli , P. S. and Mow , V. C. ( 1992 ). A transversely isotropic finite element model of the meniscus . J. Biomech. , 25 , 1027 - 1045 .
   PubMed Web of Science ®Google Scholar
• Spilker , R. L. and Suh , J. K. ( 1990 ). Formulation and evaluation of a finite element model for the biphasic model of hydrated soft tissues , Comp. Struct. , 35 , 425 - 439 .
   Web of Science ®Google Scholar
• Suh , J. K. , Li , Z. and Woo , S. L. ( 1995 ). Dynamic behavior of a biphasic cartilage model under cyclic compressive loading . J. Biomech. , 28 , 357 - 364 .
   PubMed Web of Science ®Google Scholar
• Wayne , J. S. , Woo , S. L. and Kwan , M. K. ( 1991 ). Application of the u-p finite element method to the study of articular cartilage . J. Biomech. Eng. , 113 , 397 - 403 .
   PubMed Web of Science ®Google Scholar
• Wu , J. S. and Chen , J. H. ( 1996 ). Clarification of the mechanical behaviour of spinal motion segments through a three-dimensional poroelastic mixed finite element model . Med. Eng. Phys. , 18 , 215 - 224 .
   PubMed Web of Science ®Google Scholar
• Zienkiewicz , O. C. and Taylor , R. L. ( 1991 ). The finite element method , 2 , McGraw-Hill Book Company , London .
   Google Scholar