492
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

A mathematical model for describing the metastasis of cancer in bone tissue

Pages 333-346 | Received 03 Feb 2010, Accepted 25 Oct 2010, Published online: 24 Jan 2011

References

  • American Cancer Society . 2006 . Cancer facts and figures 2006 , Atlanta (GA) : American Cancer Society .
  • American Cancer Society . 2007 . Cancer facts and figures 2007 , Atlanta (GA) : American Cancer Society .
  • American Cancer Society . 2008 . Cancer facts and figures 2008 , Atlanta (GA) : American Cancer Society .
  • Batson , OV . 1940 . The function of the vertebral veins and their role in the spread of metastasis . Ann Surg , 112 : 138 – 149 .
  • Bonewald , LF and Dallas , SL . 1994 . Role of active and latent transforming growth factor in bone formation . J Cell Biochem , 55 : 350 – 357 .
  • Brouwers , JEM , van Donkelaar , CC , Sengers , BG and Huiskes , R . 2006 . Can the growth factors PTHrP, Ihh and VEGF, together regulate the development of a long bone? . J Biomech , 39 ( 15 ) : 2774 – 2782 .
  • Butler , TP and Gullino , PM . 1975 . Quantitation of cell shedding into efferent blood of mamaria adenocarcinoma . Cancer Res , 35 ( 3 ) : 512 – 516 .
  • Cecchini , MG , Wetterwalda , A , van der Pluijmb , G and Thalmanna , G . 2005 . Molecular and biological mechanisms of bone metastasis . EAU Update Ser , 3 : 214 – 226 .
  • Cowin , SC . 2001 . Bone mechanics handbook , Boca Raton (FL) : CRC Press .
  • Clohisy , DR and Ramnaraine , ML . 1998 . Osteoclasts are required for bone tumors to grow and destroy bone . J Orthop Res , 16 ( 6 ) : 660 – 666 .
  • Clines , GA and Guise , TA . 2008 . Molecular mechanisms and treatment of bone metastasis . Expert Rev Mol Med , 10 : e7
  • Ebert , R , Zeck , S , Krug , R , Meissner-Weigl , J , Schneider , D , Seefried , L , Eulert , J and Jakob , F . 2009 . Pulse treatment with zoledronic acid causes sustained commitment of bone marrow derived mesenchymal stem cells for osteogenic differentiation . Bone , 44 : 858 – 864 .
  • Eriksen , EF , Axelrod , DW and Melsen , F . 1994 . Bone histomorphometry , New York (NY) : Raven Press .
  • Ferrer-Cañabate , J , Tovar , I and Martinez , P . 2002 . Osteoprotegerina y Sistema RANKL/RANK: el futuro del metabolismo seo? . Ann Med Int , 19 ( 8 ) : 385 – 388 .
  • Fidler , IJ . 1970 . Metastasis: quantitative analysis of distribution and fate of tumor emboli labelled with 125I-5-iodo-20-deoxyuridine . J Natl Cancer Inst , 45 ( 4 ) : 773 – 782 .
  • Franks , LM . 1953 . The spread of prostatic carcinoma to the bones . J Pathol Bacteriol , 66 ( 1 ) : 91 – 93 .
  • Freedman , H and Pinho , STR . 2009 . Stability criteria for the cure state in a cancer model with radiation treatment . Nonlinear Anal Real World Appl , 10 ( 5 ) : 2709 – 2715 .
  • Frost , HM . 1987 . Bone mass and the previous mechanostat. A proposal . Anat Rec , 219 : 1 – 9 .
  • Garbayo , AJ , Villafranca , E , De Blas , A , Tejero , A , Eslava , E , Manterola , A , Romero , P and Martnez , M . 2004 . Metastatic bone disease . Diag Treatm , 27 ( 3 ) : 137 – 154 .
  • Garzón-Alvarado , DA , Roa , MA and Cortés , CJ . 2004 . Análisis por elementos finitos del proceso de regeneración ósea , Unilibros : Universidad Nacional de Colombia .
  • 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 .
  • 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 .
  • Gupta , GP and Massague , J . 2004 . Platelets and previous term metastasis next term revisited: a novel fatty link . J Clin Invest , 114 ( 12 ) : 1961 – 1963 .
  • Hadjidakis , DJ and Androulakis , II . 2006 . Bone remodelling . Ann NY Acad Sci , 1092 : 385 – 396 .
  • Hindie , E , Zanotti-Fregonarav , P , Keller , I , Duron , F , Devaux , JY , Calzada-Nocaudie , M , Sarfati , E , Moretti , J-L , Bouchard , P and Toubert , M-E . 2007 . Bone metastases of differentiated thyroid cancer: impact of early 131I-based detection on outcome . Endocr Relat Cancer , 14 : 799 – 807 .
  • Hirbe , AC , Roelofs , AJ , Floyd , DH , Deng , H , Becker , SN , Lanigan , LG , Apicelli , AJ , Xu , Z , Prior , JL Eagleton , MC . 2009 . The bisphospanate zoledronic acid decreases tumor growth in bone in mice with defective osteoclasts . Bone , 44 : 908 – 916 .
  • Hoffman , J . 2001 . Numerical methods for engineers and scientists , New York (NY) : McGraw Hill .
  • Hofstetter , W , Felix , R and Cecchini , MG . 1996 . Principles of bone biolgy , San Diego (CA) : Academic Press .
  • Komarova , SV , Smith , RJ , Jeffrey Dixon , S , Sims , SM and Wahl , LM . 2003 . Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodelling . Bone , 33 ( 2 ) : 206 – 215 .
  • Kroll , MH . 2000 . Parathyroid hormone temporal effects on bone formation and reabsorption . Bull Math Biol , 62 : 163 – 188 .
  • Lemaire , V , Tobin , FL , Greller , LD , Cho , CR and Suva , LJ . 2004 . Modeling the interactions between osteoblast and osteoclast activities in bone remodelling . J Theoret Biol , 229 ( 3 ) : 293 – 309 .
  • Liotta , LA and Kohn , EC . 2001 . The microenvironment of the tumour-host interface . Nature , 411 : 375 – 379 .
  • Mendoza , M and Khanna , C . 2009 . Revisting the seed and soil in cancer metastasis . Int J Biochem Cell Biol , 41 : 1452 – 1462 .
  • Moroz , A , Crane , MC , Smith , G and Wimpenny , DI . 2006 . Phenomenological model of bone remodelling cycle containing osteocyte regulation loop . Biosystems , 84 ( 3 ) : 183 – 190 .
  • Moroz , A and Wimpenny , DI . 2007 . Allosteric control model of bone remodelling containing periodical modes . Biophys Chem , 127 ( 3 ) : 194 – 212 .
  • Mundy , GR . 2002 . Metastasis to bone: causes, consequences and therapeutic opportunities . Nat Rev Cancer , 2 ( 8 ) : 584 – 593 .
  • Paterson , A . 2009 . Management of cancer and bone: trials and tribulations . Bone , 44 : S51
  • Piotrowska , MJ and Angus , SD . 2009 . A quantitative cellular automaton model of in vitro multicellular spheroid tumour growth . J Theoret Biol , 258 ( 2 ) : 165 – 178 .
  • Pratap , J , Lian , JB , Javed , A , Barnes , GL , van Wijnen , AJ , Stein , JL and Stein , GS . 2006 . Regulatory roles of Runx2 in metastatic tumor and cancer cell interactions with bone . Cancer Metastasis Rev , 25 ( 4 ) : 589 – 600 .
  • Raisz , LG . 1999 . Physiology and pathophysiology of bone remodelling . Clin Chem , 45 : 1353 – 1358 .
  • Salmon , JM and Kilpatrick , SE . 2000 . Pathology of skeletal metastases . Orthop Clin North Am , 31 ( 4 ) : 537 – 544 .
  • Steeg , PS and Theodorescu , D . 2008 . Metastasis: a therapeutic target to cancer . Nat Clin Pract Oncol , 5 : 206 – 219 .
  • Tsukii , K , Shima , N , Mochizuki , S , Yamaguchi , K , Kinosaki , M , Yano , K , Shibata , O , Udagawa , N , Yasuda , H Suda , T . 1998 . Osteoclast differentiation factor mediates an essential signal for bone reabsorption induced by 1 alpha, 25-dihydroxyvitamin D3, prostaglandin E2, or parathyroid hormone in the microenvironment of bone . Biochem Biophys Res Commun , 256 ( 2 ) : 337 – 341 .
  • Varricchio , CG . 1997 . A cancer source book for nurses , Boston (MA) : Jones and Bartlett Publishers, Inc .
  • Willis , RA . 1973 . Secondary tumors of bone, the spread of tumors in the human body , London : Butterworth Co .
  • Zhou , F and Cui , S . 2009 . Bifurcations for a multidimensional free boundary problem modeling the growth of tumor cord . Nonlinear Anal Real World Appl , 10 ( 5 ) : 2990 – 3001 .

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.