A mathematical model of epiphyseal development: hypothesis on the cartilage canals growth

References

• Abad , V , Meyers , JL , Weise , M , Gafni , RI , Barnes , KM , Nilsson , O , Bacher , JD and Baron , J . 2002 . The role of the resting zone in growth plate chondrogenesis . Endocrinology , 143 ( 5 ) : 1851 – 1857 .
   PubMedGoogle Scholar
• Álvarez , J , Costales , L , López-Muñiz , A and López , JM . 2005 . Chondrocytes are released as viable cells during cartilage resorption associated with the formation of intrachondral canals in the rat tibial epiphysis . Cell Tissue Res , 320 ( 3 ) : 501 – 507 .
   PubMedGoogle Scholar
• Álvarez , J , Costales , L , Serra , R , Balbín , M and López , J . 2005 . Expression patterns of matrix metalloproteinases and vascular endothelial growth factor during epiphyseal ossification . J Bone Min Res , 20 ( 6 ) : 1011 – 1021 .
   PubMedGoogle Scholar
• Blumer , MJ , Longato , S and Fritsch , H . 2008 . Structure, formation and role of cartilage canals in the developing bone . Ann Anat , 190 ( 4 ) : 305 – 315 .
   PubMed Web of Science ®Google Scholar
• Blumer , M , Longato , S , Richter , E , Pérez , MT , Konakci , KZ and Fritsch , H . 2005 . The role of cartilage canals in endochondral and perichondral bone formation: are there similarities between these two processes? . J Anat , 206 ( 4 ) : 359 – 372 .
   PubMed Web of Science ®Google Scholar
• Blumer , MJ , Schwarzer , C , Pérez , MT , Zeynep , K , Konakci , KZ and Fritsch , H . 2006 . Identification and location of bone-forming cells within cartilage canals on their course into the secondary ossification centre . J Anat , 208 ( 6 ) : 695 – 707 .
   PubMedGoogle Scholar
• Burkus , JK , Ganey , TM and Ogden , JA . 1993 . Development of the cartilage canals and the secondary center of ossification in the distal chondroepiphysis of the prenatal human femur . YJBM , 66 : 193 – 202 .
   PubMed Web of Science ®Google Scholar
• Byers , PD , Path , FRC and Brown , RA . 2006 . Cell columns in articular cartilage physes questioned: a review . Osteoarthritis Cartilage , 14 : 3 – 12 .
   PubMed Web of Science ®Google Scholar
• Carter , DR and Wong , M . 2003 . Modelling cartilage mechanobiology . Phil Trans R Soc Lond , 358 : 1461 – 1471 .
   PubMed Web of Science ®Google Scholar
• Garzón-Alvarado , DA , García-Aznar , JM and Doblaré , M . 2009a . Appearance and location of secondary ossification centres may be explained by a reaction-diffusion mechanism . Comput Biol Med , 39 ( 6 ) : 554 – 561 .
   PubMed Web of Science ®Google Scholar
• Garzón-Alvarado , DA , García-Aznar , JM and Doblaré , M . 2009b . A reaction-diffusion model for long bones growth . Biomech Model Mechanobiol , 8 ( 5 ) : 381 – 395 .
   PubMed Web of Science ®Google Scholar
• Garzón-Alvarado , DA , Roa , MA and Ramírez , AM . 2008 . Factores que influyen en el crecimiento endocondral: experimentos y modelos . Rev Cubana Ortop Traumatol , 49 ( 1 ) : 55 – 67 .
   Google Scholar
• Geris , L , Gerisch , A , Sloten , JV , Weiner , R and Oosterwyck , HV . 2008 . Angiogenesis in bone fracture healing: a bioregulatory model . J Theor Biol , 251 ( 1 ) : 137 – 158 .
   PubMed Web of Science ®Google Scholar
• Herrero , MA and López , JM . 2005 . Bone formation: biological aspects and modelling problems . J Theor Med , 6 ( 1 ) : 41 – 55 .
   Google Scholar
• Kugler , JH , Tomlinson , A , Wagstaff , A and Ward , SM . 1979 . The role of cartilage canals in the formation of secondary centres of ossification . J Anat , 129 ( 3 ) : 493 – 506 .
   PubMedGoogle Scholar
• Provot , S and Schipani , E . 2005 . Molecular mechanisms of endochondral bone development . BBRC , 328 ( 3 ) : 658 – 665 .
   PubMed Web of Science ®Google Scholar
• Roach , HI , Baker , JE and Clarke , NM . 1998 . Initiation of the bony epiphysis in long bones: chronology of interactions between the vascular system and the chondrocytes . J Bone Min Res , 13 ( 6 ) : 950 – 961 .
   PubMedGoogle Scholar
• Rivas , R and Shapiro , F . 2002 . Structural stages in the development of the long bones and epiphyses a study in the new zealand white rabbit . JBJS , 84-A ( 1 ) : 85 – 100 .
   Google Scholar
• School Of Chemical Engineering [SCE] . 2005 . Design, interfaces, rheology and processes laboratory. Teaching module interfacial phenomena: enhanced Oil recovery , Mérida, Venezuela : Andes University .
   Google Scholar
• Shapiro , F . 2008 . Bone development and its relation to fracture repair: the role of mesenchymal osteoblasts and surface osteoblasts . Eur Cell Mater , 15 : 53 – 76 .
   PubMed Web of Science ®Google Scholar
• Shefelbine , SJ and Carter , DR . 2004 . Mechanobiological predictions of growth front morphology in developmental hip dysplasia . J Orthop Res , 22 ( 2 ) : 346 – 352 .
   PubMed Web of Science ®Google Scholar
• Stevens , S , Beaupré , G and Carter , DR . 1999 . Computer model of endochondral growth and ossification in long bones: biological and mechanobiological influences . J Orthop Res , 17 ( 5 ) : 646 – 653 .
   PubMedGoogle Scholar
• Stockwell , RA . 1979 . “ Chapter 5: chondrocyte nutrition, cartilage boundaries and permeability ” . In Biology of cartilage cells , Edited by: Hall , BK . 124 – 175 . Cambridge : Cambridge University Press .
   Google Scholar
• Sundaramurthy , S and Mao , JJ . 2006 . Modulation of endochondral development of the distal femoral condyle by mechanical loading . J Orthop Res , 24 ( 2 ) : 229 – 241 .
   PubMed Web of Science ®Google Scholar
• Tovar A. 2004. Bone remodeling as a hybrid cellular automaton optimization process [Ph.D. thesis]. [Notre Dame (IN)]: University of Notre Dame
   Google Scholar
• Ward , DP , Murray , AT and Phinn , SR . 2000 . A stochastically constrained cellular model of urban growth . Comput Environ Urban , 24 ( 6 ) : 539 – 558 .
   Google Scholar
• Ytrehus , B , Carlson , CS and Ekman , S . 2007 . Etiology and pathogenesis of osteochondrosis . Vet Pathol , 44 ( 4 ) : 429 – 448 .
   PubMedGoogle Scholar