Consideration of anisotropic elasticity minimizes volumetric rather than shear deformation in human mandible

References

• Ashman , R.B. and van Buskirk , W.C. 1987 . Elastic properties of a human mandible . Adv. Dental Res. , 1 : 64 – 67 .
   PubMedGoogle Scholar
• Bornemann , F. , Erdmann , B. and Kornhuber , R. 1993 . Adaptive multilevel-methods in three space dimensions . Int. J. Numer. Methods Eng. , 36 : 3187 – 3203 .
   Web of Science ®Google Scholar
• Christiansen , D.L. , Huang , E.K. and Silver , F.H. 2000 . Assembly of type I collagen: fusion of fibril subunits and the and the influence of fibril diameter on mechanical properties . Matrix Biol. , 19 : 409 – 420 .
   PubMed Web of Science ®Google Scholar
• Cowin , S.C. 1999 . Bone poroelasticity . J. Biomech. , 32 : 217 – 238 .
   PubMed Web of Science ®Google Scholar
• Cowin , S.C. 2003 . A recasting of anisotropic poroelasticity in matrices of tensor components . Transport Porous Media , 50 : 35 – 56 .
   Web of Science ®Google Scholar
• Cowin , S.C. , Weinbaum , S. and Zeng , Y. 1995 . A case for bone canaliculi as the anatomical site of strain generated potentials . J. Biomech. , 28 : 1281 – 1297 .
   PubMed Web of Science ®Google Scholar
• Deuflhard , P. , Leinen , P. and Yserentant , H. 1989 . Concepts of an adaptive hierarchical finite element code . Impact Comput. Sci. Eng. , 1 : 3 – 35 .
   Google Scholar
• Dillaman , R. , 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
• Erdmann , B. , Lang , J. and Roitzsch , R. 1993 . “ KASKADE-manual ” . In Technical Report TR 93-05 Konrad–Zuse–Zentrum Berlin (ZIB)
   Google Scholar
• Erdmann , B. , Kober , C. , Lang , J. , Deuflhard , P. , Zeilhofer , H.-F. and Sader , R. 2002 . “ Efficient and reliable finite element methods for simulation of the human mandible ” . In Proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields , Germany : CDRom, Ulm .
   Google Scholar
• Gatzka , C. , Schneider , E. , Knothe Tate , M.L. , Knothe , U. and Niederer , P. 1999 . A novel ex vivo model for investigation of fluid displacements in bone after endoprosthesis implantation . J Materials Sci: Materials Med. , 10 : 801 – 806 .
   PubMedGoogle Scholar
• Hart , R.T. , Hennebel , V.V. , Thongpreda , N. , van Buskirk , W.C. and Anderson , R.C. 1992 . Modeling the biomechanics of the mandible: a three-dimensional finite element study . J. Biomech. , 25 : 261 – 286 .
   PubMed Web of Science ®Google Scholar
• Hellmich , C. and Ulm , F.-J. 2002 . Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments . J. Biomech. , 35 : 1199 – 1212 .
   PubMed Web of Science ®Google Scholar
• Hellmich , C. and Ulm , F.-J. 2003 . Average hydroxyapatite concentration is uniform in the extracollageneous ultrastructure of mineralized tissues: evidence at the 1–10 microns scale . Biomech. Modeling Mechanobiol. , 2 : 21 – 36 .
   PubMed Web of Science ®Google Scholar
• Hellmich , C. and Ulm , F.-J. 2005a . Drained and undrained poroelastic properties of healthy and pathological bone: a poro-micromechanical investigation . Transport Porous Media , 58 : 243 – 268 .
   Web of Science ®Google Scholar
• C. Hellmich and F.-J. Ulm, “Microelasticity-based investigation of poromechanical couplings in bone: implications for load-induced fluid flow in intertrabecular, vascular, and extravascular pore spaces”, in preparation 2005b.
   Google Scholar
• Helnwein , P. 2001 . Some remarks on the compressed matrix representation of symmetric second-order and fourth-order tensors . Comput. Methods Appl. Mech. Eng. , 190 : 2753 – 2770 .
   Web of Science ®Google Scholar
• Jacobs , C.R. , Yellowley , C.E. , Davis , B.R. , Zhou , Z. , Cimbala , J.M. and Donahue , H.J. 1998 . Differential effects of steady versus oscillating flow on bone cells . J. Biomech. , 31 : 969 – 976 .
   PubMed Web of Science ®Google Scholar
• Keanini , R.G. , Roer , R.D. and Dillaman , R.M. 1995 . A theoretical model of circulatory interstitial fluid flow and species transport within porous cortical bone . J. Biomech. , 28 : 901 – 914 .
   PubMedGoogle Scholar
• Knothe Tate , M.L. 2003 . Whither flows the fluid in bone?—an osteocyte's perspective . J. Biomech. , 36 : 1409 – 1424 .
   PubMed Web of Science ®Google Scholar
• Knothe Tate , M.L. and Knothe , U. 2000 . An ex vivo model to study transport processes and fluid flow in loaded bone . J. Biomech. , 33 : 247 – 254 .
   PubMedGoogle Scholar
• Knothe Tate , M.L. , Niederer , P. and Knothe , U. 1998 . In vivo tracer transport through the lacunocanalicular system of rat bone in an environment devoid of mechanical loading . Bone , 22 : 107 – 117 .
   PubMedGoogle Scholar
• Knothe Tate , M.L. , Steck , R. , Forwood , M.R. and Niederer , P. 2000 . In vivo demonstration of load-induced fluid flow in the rat tibia and its potential implications for processes associated with functional adaptation . J. Exp. Biol. , 203 : 2737 – 2745 .
   PubMedGoogle Scholar
• Kober , C. , Erdmann , B. , Sader , R. and Zeilhofer , H.-F. 2003 . “ Simulation (FEM) of the human mandible: a comparison of bone mineral density and stress/strain profiles due to the masticatory system ” . In Proceedings 10th Workshop, The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields , Germany : Ulm .
   Google Scholar
• Kober , C. , Erdmann , J. , Lang , B. , Sader , R. and Zeilhofer , H.-F. 2004 . Sensitivity of the temporomandibular joint capsule for the structural behaviour of the human mandible . Biomed. Technik , 49 : 372 – 373 .
   Google Scholar
• Korioth , T.W. , Romilly , D.P. and Hannam , A.G. 1992 . Three dimensional finite element stress analysis of the dentate human mandible . Am. J. Phys. Anthropol. , 88 : 69 – 96 .
   PubMed Web of Science ®Google Scholar
• Lees , S. , Heeley , J. and Cleary , P. 1979 . A study of some properties of a sample of bovine cortical bone using ultrasound . Calcified Tissue Int. , 29 : 107 – 117 .
   PubMed Web of Science ®Google Scholar
• Mackerle , J. 2004 . Finite element modelling and simulations in dentistry: a bibliography 1990–2003 . Comput. Methods Biomech. Biomed. Eng. , 7 : 277 – 303 .
   PubMedGoogle Scholar
• Martin , R.B. , Burr , D.B. and Sharkey , N.A. 1998 . Skeletal Tissue Mechanics , New York Berlin Heidelberg : Springer-Verlag .
   Google Scholar
• McCullough , R.L. 1990 . “ Introduction to anisotropic elasticity ” . In Delaware Composites Design Encyclopedia , Edited by: Carlsson , L.A. and Gillespie , J.W. Vol. 2 , Lancaster (PA) : Technomic Publishers Co. .
   Google Scholar
• Müller-Hannemann , M. , Kober , C. , Sader , R. and Zeilhofer , H.-F. 2001 . “ Anisotropic validation of hexahedral meshes for composite materials in biomechanics ” . In Proceedings of the 10th International Meshing Roundtable , 249 – 260 . USA : Newport Beach .
   Google Scholar
• National Library of Medicine . 1995 . The Visible Human Project http://www.nlm.nih.gov/research/visible/visible_human.html
   Google Scholar
• O'Mahony , A.M. , Willimans , J.L. and Spencer , P. 2000 . Anisotropic elastic properties of cancellous bone from a human edentulous mandible . Clin. Oral Implants Res. , 11 : 415 – 421 .
   PubMed Web of Science ®Google Scholar
• O'Mahony , A.M. , Willimans , J.L. and Spencer , P. 2001 . Anisotropic elasticity of cortical and cancellous bone in the posterior mandible increases peri-implant stress and strain under oblique loading . Clin. Oral Implants Res. , 12 : 648 – 657 .
   PubMed Web of Science ®Google Scholar
• Piekarski , K. and Munro , M. 1977 . Transport mechanism operating between blood supply and osteocytes in long bones . Nature , 269 : 80 – 82 .
   PubMed Web of Science ®Google Scholar
• Pothuaud , L. , van Rietbergen , B. , Charlot , C , Ozhinsky , E. and Majumdar , S. 2004 . A new computational efficient approach for trabecular bone analysis using beam models generated with skeletonized graph technique . J. Comput. Methods Biomech. Biomed. Eng. , 7 : 205 – 213 .
   PubMedGoogle Scholar
• Qin , Y.-X. , Lin , W. and Rubin , C. 2002 . The pathway of bone fluid flow as defined by in vivo intramedullary pressure and streaming potential measurements . Ann. Biomed. Eng. , 30 : 693 – 702 .
   PubMed Web of Science ®Google Scholar
• Qin , Y.-X. , Kaplan , T. , Saldanha , A. and Rubin , C. 2003 . Fluid pressure gradients, arising from oscillations in intramedullary pressure, is correlated with the formation of bone and inhibition of intracortical prorsity . J. Biomech. , 36 : 1427 – 1437 .
   PubMed Web of Science ®Google Scholar
• Rong , Q. Finite element simulation of the bone modeling and remodeling process around a dental implant . Ph.D. Thesis . Univ. Karlsruhe
   Google Scholar
• Reilly , D.T. and Burstein , A.H. 1975 . The elastic and ultimate properties of compact bone tissue . J. Biomech. , 8 : 393 – 405 .
   PubMed Web of Science ®Google Scholar
• Salzstein , R.A. and Pollack , S.R. 1987 . Electromechanical potentials in cortical bone—II. Experimental analysis . J. Biomech. , 20 : 271 – 280 .
   PubMed Web of Science ®Google Scholar
• Salzstein , R.A. , Pollack , S.R. , Mak , A.F.T. and Petrov , N. 1987 . Electromechanical potentials in cortical bone—I. A continuum approach . J. Biomech. , 20 : 261 – 270 .
   PubMed Web of Science ®Google Scholar
• Smit , T.A. , Burger , E.H. and Huyghe , J.M. 2002 . A case strain-induced fluid flow as a regulator of BMU-coupling and osteonal alignment . J. Bone Mineral Res. , 17 : 2021 – 2029 .
   PubMed Web of Science ®Google Scholar
• Stalling , D , Westerhoff , M. and Hege , H.-C. 2005 . “ The visualization handbook ” . In Amira: A Highly Interactive System for Visual Data Analysis , Edited by: Hansen , Charles D. and Johnson , Christopher R. Vol. 38 , Elsevier .
   Google Scholar
• Turner , C.H. , Cowin , S.C. , Rho , J.Y. , Ashman , R.B. and Rice , J.C. 1990 . The fabric dependency of the orthotropic elastic constants of cancellous bone . J. Biomech. , 23 : 549 – 561 .
   PubMed Web of Science ®Google Scholar
• Weinbaum , S. , Cowin , S.C. and Zeng , Y. 1994 . A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses . J. Biomech. , 27 : 339 – 360 .
   PubMed Web of Science ®Google Scholar
• Widera , G.E.O. , Tesk , J.A. and Priviter , E. 1976 . Interaction effects among cortical bone, cancellous bone and peridontal membrane of natural teeth and implants . J. Biomed. Material Res. , 7 : 613 – 623 .
   Google Scholar
• You , L. , Cowin , S.C. , Schaffler , M.B. and Weinbaum , S. 2001 . A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix . J. Biomech. , 34 : 1375 – 1386 .
   PubMed Web of Science ®Google Scholar