49
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Adaptive Finite Element Analysis of the Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics

, , , &
Pages 215-229 | Received 19 Mar 1999, Accepted 03 Sep 1999, Published online: 28 Mar 2007

References

  • Adjerid , S. and Flaherty , J. E. , ( 1986 ). A Moving Mesh Finite Element Method with Local Refinement for Parabolic Partial Differential Equations. Comp. Meths. Appl. Mech. Engrg. , 55 , 3 – 26 .
  • Adjerid , S. , Aiffa , M. , Flaherty , J. E. , Hudson , J. B. and Shephard , M. S. , ( 1997 ). Modeling and Adaptive Numerical Techniques for Oxidation of Ceramic Composites. Ceramic Engng. andSci. Procs. , 18 , 315 – 322 .
  • Adjerid , S. , Aiffa , M. and Flaherty , J. E. , ( 1998 a). Hierarchical Bases for Triangular and Tetrahedral Elements. In preparation .
  • Adjerid , S. , Flaherty , J. E. , Hudson , J. B. and Shephard , M. S. , ( 1999 b). Modeling and the Adaptive Solution of CVD Fiber-Coating Processes. Comp. Meths. Appl. Mech. Engrg. , 172 , 293 – 308 .
  • Adjerid , S. , BabuSka , I. and Flaherty , J. E. , ( 1999 b). A Posteriori Error Estimation for the Finite Element Method-of-Lines Solution of Parabolic Problems. Mathematical Models and Methods in Applied Science , 9 , 261 – 286 .
  • Adjerid , S. , Belguendouz , B. and Flaherty , J. E. , ( 1998 d). A Posteriori Finite Element Error Estimation for Diffusion Problems , SIAM J. Sci. Comput. To appear .
  • Aiffa , M. , ( 1997 ). Adaptive Hp-Refinement Methods for Singularly-Perturbed Elliptic and Parabolic Systems. Ph.D. thesis, Dept. of Math. Sci. , Rensselaer Polytechnic Institute .
  • Ainsworth , M. and Oden , J. T. , ( 1993 ). A Unified Approach to A Posteriori Error Estimation Using Element Residual Methods. Numer. Math. , 65 , 23 – 50 .
  • Barocas , V. H. ranquillo, R, T., ( 1997 a). An Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics the Interplay Among Cell Traction, Fibrillar Network Deformation, Fibril Alignment, and Cell Contact Guidance. J. Biomech. Engng. , 119 , 137 – 145 .
  • Barocas , V. H. and Tranquillo , R. T. , ( 1997b ). A Finite Element Solution for the Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics The Effect of Contact Guidance on Isometric Cell Traction Measurement. J. Biomech. Engng. , 119 , 261 – 269 .
  • Barocas , V. H. , Moon , A. G. and Tranquillo , R. T. , ( 1995 ). The Fibroblasl-Populated Microsphere Assay of Cell Traction Force — Part 2. Measurement of the Cell Traction Coefficient. J. Biomech. Engng. , 117 . 161 – 170 .
  • Barocas , V. H. , Girton , T. S. and Tranquillo , R. T. , ( 1998 ). Engineered Alignment in Media-Equivalents Magnetic Prealignment and Mandrel Compaction. J. Biomech. Engng. , 120 , 660 – 666 .
  • Bcall , M. W. and Shephard , M. S. , ( 1997 ). A General Topology-Based Mesh Data Structure. Int. J. Num. Meth. Engng. , 40 , 1573 – 1596 .
  • Bcall , M. W. and Shephard , M. S. , ( 1998 ). An Object-Oriented Framework for Reliable Numerical Simulations, Engrg. with Computers. Accepted for publication .
  • Bell , E. , Ivarsson , B. and Merrill , C. , ( 1979 ). Production of a Tissue-like Structure by Contraction of Collagen Lattices by Human Fibroblasts of Different Proliferative Potential in Vivo. Proc. of the National Academy of Sciences of the USA , 76 , 1274 – 8 .
  • Brenan , K. E. , Campbell , S. L. and Petzold , L. R. , ( 1996 ). Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM .
  • Brenner , S. C. and Scott , L. R. , ( 1994 ). The Mathematical Theory of Finite Element Methods. Springer-Verlag .
  • Brczzi , F. ort in , M. , ( 1991 ). Mixed and Hybrid Finite Element Methods. Springer-Verlag .
  • Carncvali , P. , Morris , R. B. , Tsuji , Y. and Taylor , G. , ( 1993 ). New Basis Functions and Computational Procedures for p-Vcrsion Finite Element Analysis. Int. J. Num. Meth. Engng , 36 , 3759 – 3779 .
  • Ciarlct , P. G. and Raviarl , P.-A. , ( 1972 ). The Combined Effect of Curved Boundaries and Numerical Integration in Isoparametric Finite Element Methods. Pages 409–474 of Aziz, A. K. (ed) , The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. Academic Press .
  • Dembo , M. and Harlow , F. , ( 1986 ). Cell Motion, Contractile Networks, and the Physics of Interpenetrating Reactive Flow. Bio-phys. J. , 50 , 109 – 121 .
  • Dey , S. , Flaherty , J. E. , Ohsumi , T. K. and Shephard , M. S. , ( 1998 ). An Efficient Integration Method for p-Version Finite Elements in Curved Domains. In preparation .
  • Dickenson , R. B. , Guido , S. and Tranquillo , R. T. , ( 1994 ). Biased Cell Migration of Fibroblasts Exhibiting Contact Guidance in Oriented Collagen Gels. Ann. of Biomed. Engng. , 22 , 342 – 356 .
  • Dunavant , D. A. , ( 1985 ). High Degree Efficient Symmetrical Gaussian Quadrature Rules for the Triangle. Int. J. Num. Meth. Engng. 21 . 1129 – 1148 .
  • Ehrlich , H. P. and Rajaratnam , J. B. M. , ( 1990 ). Cell Locomotion Forces Versus Cell Contraction Forces for Collagen Lattice Contraction An In Vitro Model of Wound Contraction. Tissue and Cell , 22 , 407 – 417 .
  • Fix , G. J. , ( 1972 ). Effects of Quadrature Errors in Finite Element Approximation of Steady State, Eigenvalue, and Parabolic Problems. Pages 525–556 of Aziz, A. K. (ed) , The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. Academic Press .
  • Grinncll , F. , ( 1994 ). Fibroblasts, Myofibroblasts, and Wound Contraction. J. Cell Biol. 124 , 401 – 404 .
  • Guidry , C. and Grinncll , F. , ( 1986 ). Contraction of Hydrated Collagen Gels by Fibroblasts Evidence of Two Mechanism by Which Collagen Fibrils Arc Stabilized. Collagen and Related Research , 6 , 515 – 529 .
  • Gursky , S. E. and Sherman , M. S. , ( 1977 ). Yale Sparse Matrix Package — II. Nonsymmetric Codes. Tech. rept. trl 14. Dept. of Comp. Sci. , Yale University .
  • Hirai , J. , Kanda , K. , Oka , T. and Matsuda , T. , ( 1994 ). Highly oriented, Tubular Hybrid Vascular Tissue for a Low Pressure Circulatory System. ASAIO J. , 40 , 383 – 388 .
  • Huang , D. , Chang , T. R. , Aggarwal , A. , Lee , R. C. and Ehrlich , H. P. , ( 1993 ). Mechanisms and Dynamics of Mechanical Strengthening In Ligament-Equivalent Fibroblast-Populated Collagen Matrices. Ann. Biomed. Eng. , 22 , 289 – 305 .
  • Ilin , A. V. , Bagheri , B. , Metcalfe , R. W. and Scott , L. R. , ( 1997 ). Error Control and Mesh Optimization for High-Order Finite Element Approximation of Incompressible Viscous Flow. Comp. Meths. Appl. Mcch. Engrg. , 150 , 313 – 325 .
  • Knapp , D. M. , Barocas , V. H. , Moon , A. G. , Yoo , K. , Petzold. L. R. and Tranquillo , R. T. , ( 1997 ). Rheology of Reconstituted Type 1 Collagen Gel in Confined Compression. J. of Rheology , 41 , 971 – 993 .
  • Kolodney , M. S. and Elson , E. L. , ( 1993 ). Correlation of Myosin Light Chain Phosphorylation with Isometric Contraction of Fibroblasts. J. of Biol. Chem. , 268 , 23850 – 23855 .
  • Lawson , J. , Berziris , M. and Dew , P. M. , ( 1991 ). Balancing Space and Time Errors In the Method of Lines for Parabolic Equations. SIAMJ. Sci. Stat. Comput. , 12 , 573 – 594 .
  • L'Heureux , N. , Germain , L. , Labbe , R. and Auger , F. A. , ( 1993 ). In Vitro Construction of a Human Blood Vessel from Cultured Vascular Cells A Morphologic Study. J. of Vase. Surg. , 17 , 499 – 509 .
  • Lopez Valle , C. A. , Auger , F. A. , Rompre , P. , Bouvard , V. and Germain , L. , ( 1992 ). Peripheral Anchorage of Dermal Equivalents. Br. J. Dermatology , 127 , 365 – 371 .
  • Madri , J. A. and Pratt , B. M. , ( 1986 ). Endothelial Cell–Matrix Interactions In Vitro Models of Angiogenesis. J. Histochem. Cytochem. , 34 , 85 – 91 .
  • Moon , A. G. and Tranquillo , R. T. , ( 1995 ). The Fibroblast-Populated Collagen Microsphere Assay of Cell Traction Force — Part 1. Continuum Model. AlChE J. , 39 , 163 – 177 .
  • Mow , V. C. , Kuei , S. C. , Lai , W. M. and Armstrong , C. G. , ( 1980 ). Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression Theory and Experiments. J. Biomech. Engng. , 102 , 73 – 84 .
  • Oster , G. F. , Murray , J. D. and Harris , A. K. , ( 1983 ). Mechanical Aspects of Mesenchymal Morphogenesis. J. Emh. Exp. Res. , 78 , 83 – 125 .
  • Shephard , M. S. and Georges , M. K. , ( 1991 ) Automatic Three-Dimensional Mesh Generation by the Finite Octree Technique. Int. J. Num. Meth. Engng. , 32 , 709 – 749 .
  • Stopak , D. and Harris , A. K. , ( 1982 ). Connective Tissue Morphogenesis by Fibroblast Traction, I. Tissue Culture Observations. Dev. Biol. , 90 , 383 – 398 .
  • Strang , G. , ( 1972 ). Variational Crimes in the Finite Element Method , Pages 689–710 of Aziz, A. K. (ed) , The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. Academic Press .
  • Strang , G. and Fix , G. J. , ( 1973 ). An Analysis of the Finite Element Method. Prentice-Hal I, Inc .
  • Strouboulis , T. and Haque , K. A. , ( 1992 ). Recent Experiences with Error Estimation and Adaptivity, Part I Review of Error Estimators for Scalar Elliptic Problems. Comp. Meths. Appl. Mech. Engrg. , 97 , 399 – 436 .
  • Szabo , B. A. and BabuSka , I. , ( 1991 ). Finite Element Analysis. John Wiley and Sons Ltd .
  • Tranquillo , R. T. , Girton , T. S. , Bromberek , B. A. , Triebes , T. G. and Mooradian , D. L. , ( 1996 ). Magnetically-Oriented Tissue-Equivalent Tubes Application to a Circumferentially-Oriented Media-Equivalent. Biomaterials , 17 , 349 .
  • Verfiiith , R. , ( 1996 ). A Review of Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Stuttgart Teubner-Wiley .
  • Wait , R. and Mitchell , A. R. , ( 1985 ). Finite Element Analysis and Applications. John Wiley and Sons Ltd .
  • Wang , Y. , ( 1991 ). An Adaptive Local HPR-Refinement Finite Element Method for Parabolic Partial Differential Equations. Ph.D. thesis, Dept. Math. Sci. , Rensselaer Polytechnic Institute .
  • Wilkins , L. M. , Watson , S. R. , Prosky , S. J. , Meunier , S. F. and Parenteau , N. L. , ( 1994 ). Development of a Bilayered Living Skin Construct for Chemical Applications. Biotech, and Bioeng. , 43 , 747 – 756 .
  • Yu , D.-H. , ( 1991 a). Asymptotically Exact A-Posteriori Error Estimators for Elements of Bi-Even Degree. Chinese J. Math, and Appl. , 13 , 64 – 78 .
  • Yu , D.-H. , ( 1991 b). Asymptotically Exact A-Posteriori Error Estimators for Elements of Bi-Odd Degree. Chinese J. Math, and Appl. , 13 , 82 – 90 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.