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Computer Methods in Biomechanics and Biomedical Engineering Volume 15, 2012 - Issue 11
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Original Articles

Comparative analysis of numerical integration schemes of density equation for a computational model of bone remodelling

D. A. Garzón-Alvarado Group of Mathematical Modeling and Numerical Methods GNUM-UN, National University of Colombia, Bogotá, Colombia; Department of Mechanical and Mechatronics Engineering, National University of Colombia, Bogotá, ColombiaCorrespondence[email protected]
&
D. Linero Department of Civil and Agricultural Engineering, National University of Colombia, Bogotá, Colombia
Pages 1189-1196 | Received 31 Aug 2010, Accepted 03 May 2011, Published online: 01 Aug 2011

References

  • Beaupre , G , Orr , T and Carter , DR . 1990 . An approach for time dependent bone modeling and remodeling – theoretical development . J Orthopedic Res , 8 : 651 – 661 .
  • Chen , G , Pettet , G , Pearcy , M and McElwain , DLS . 2007 . Comparison of two numerical approaches for bone remodelling . Med Eng Phys , 29 : 134 – 139 .
  • Cowin , SC . 1986 . Wolffs law of trabecular architecture at remodeling equilibrium . J Biomech Eng , 108 : 83 – 88 .
  • Cowin , S . 2001 . Bone mechanics handbook , 2nd ed , Boca Raton, FL : CRC Press .
  • Cowin , SC and Hegedus , DH . 1976 . Bone remodeling I: a theory of adaptive elasticity . J Elast , 6 : 313 – 326 .
  • Cowin , SC and Nachlinger , RR . 1978 . Bone remodeling III: uniqueness and stability in adaptive elasticity theory . J Elast , 8 : 285 – 295 .
  • Fernández , JR , García-Aznar , JM , Martínez , R and Viao , JM . 2010 . Numerical analysis of a strain-adaptive bone remodelling problem . Comput Methods Appl Mech Eng , 199 : 1549 – 1557 .
  • Frost , HM . 1964a . The laws of bone structure , Springfield, IL : Charles C. Thomas .
  • Frost , HM . 1964b . Mathematical elements of lamellar bone remodeling , Springfield, IL : Charles C. Thomas .
  • Frost , HM . 1987 . Vital biomechanics. Proposed general concepts for skeletal adaptations to mechanical usage . Calcif Tissue Int , 42 : 145 – 156 .
  • Ganong , WF . 2006 . Fisiología médica , 20th ed , México : Manual Modern .
  • Hegedus , DH and Cowin , SC . 1976 . Bone remodeling II: small strain adaptive elasticity . J Elast , 6 : 337 – 352 .
  • Hoffma , JD . 1992 . Numerical methods for engineers and scientists , 2nd ed , New York : McGraw-Hill .
  • Jacobs , CR , Levenston , ME , Beaupré , GS , Simó , JC and Carter , DR . 1995 . Numerical instabilities in bone remodeling simulations: the advantages of a node-based finite element approach . J Biomech , 28 : 449 – 459 .
  • Jacobs , C , Simo , JC , Beaupré , GS and Carter , DR . 1997 . Adaptative bone remodeling incorporating simultaneous density and anisotropy considerations , Oxford : Butterworth-Heinemann .
  • Kummer , BKF . 1972 . “ Biomechanics of bone mechanical properties, functional structure, functional adaptation ” . In Biomechanics: its foundation and objectives , Edited by: Fung , YC , Perrone , N and Anliker , M . 237 – 271 . Englewood Cliffs, NJ : Prentice Hall .
  • Nackenhorst , U . 1997 . Numerical simulation of stress stimulated bone remodeling . Tech Mech , 17 ( 1 ) : 31 – 40 .
  • Oñate , E . 2009 . Structural analysis with the finite element method. Linear statics: volume 1: basis and solids , Barcelona, Espaa : Springer .
  • Pauwels , F . 1965 . Gesammelte abhandlungen zur funktionelen anatomie des bewegungsapparates , Berlin : Springer .
  • Weinans , H , Huiskes , R and Grootenboer . 1992 . The behavior of adaptive bone remodeling simulation models . J Biomech , 25 ( 12 ) : 1425 – 1441 .
  • Wolff , J . 1892 . Das gesetz der transformation der knochen , Berlin : Hirschwald .

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