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Volumn 2011, Issue , 2011, Pages

Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells

Author keywords

[No Author keywords available]

Indexed keywords

CELLS; CYTOLOGY; MICROGRIDS; TUMORS;

EID: 79952947931     PISSN: 1748670X     EISSN: 17486718     Source Type: Journal    
DOI: 10.1155/2011/452320     Document Type: Article
Times cited : (24)

References (49)
  • 1
    • 79952952992 scopus 로고    scopus 로고
    • World Health Organization Statistical Information System January
    • World Health Organization Statistical Information System, WHO database of mortality andburden estimates. January 2010, http://www3.who.int/whosis/mort
    • (2010) WHO Database of Mortality and Burden Estimates
  • 2
    • 79952975685 scopus 로고    scopus 로고
    • UN Database of Population Projections, January
    • UN Database of Population Projections,. January 2010, http://esa.un.org/unpp
    • (2010)
  • 3
    • 33750078422 scopus 로고    scopus 로고
    • Modelling the response of vascular tumours to chemotherapy: A multiscale approach
    • DOI 10.1142/S0218202506001522, PII S0218202506001522
    • Byrne H. M., Owen M. R., Alarcon T., Murphy J., Maini P. K., Modelling the response of vascular tumours to chemotherapy: a multiscale approach Mathematical Models and Methods in Applied Sciences 2006 16 1 1219 1241 (Pubitemid 44576651)
    • (2006) Mathematical Models and Methods in Applied Sciences , vol.16 , Issue.SUPPL. 1 , pp. 1219-1241
    • Byrne, H.M.1    Owen, M.R.2    Alarcon, T.3    Murphy, J.4    Maini, P.K.5
  • 4
    • 38849187163 scopus 로고    scopus 로고
    • Metamodeling tumor-immune system interaction, tumor evasion and immunotherapy
    • d'Onofrio A., Metamodeling tumor-immune system interaction, tumor evasion and immunotherapy Mathematical and Computer Modelling 2008 47 5-6 614 637
    • (2008) Mathematical and Computer Modelling , vol.47 , Issue.56 , pp. 614-637
    • D'Onofrio, A.1
  • 6
    • 0035501748 scopus 로고    scopus 로고
    • An analysis of a mathematical model of trophoblast invasion
    • DOI 10.1016/S0893-9659(01)00079-9, PII S0893965901000799
    • Byrne H. M., Chaplain M. A. J., Pettet G. J., McElwain D. L. S., An analysis of a mathematical model of trophoblast invasion Applied Mathematics Letters 2001 14 8 1005 1010 (Pubitemid 33676854)
    • (2001) Applied Mathematics Letters , vol.14 , Issue.8 , pp. 1005-1010
    • Byrne, H.M.1    Chaplain, M.A.J.2    Pettet, G.J.3    McElwain, D.L.S.4
  • 9
    • 30344453406 scopus 로고    scopus 로고
    • On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis
    • DOI 10.1016/j.ijnonlinmec.2005.07.006, PII S0020746205000922
    • Bellomo N., Bellouquid A., On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis International Journal of Non-Linear Mechanics 2006 41 2 281 293 (Pubitemid 43061445)
    • (2006) International Journal of Non-Linear Mechanics , vol.41 , Issue.2 , pp. 281-293
    • Bellomo, N.1    Bellouquid, A.2
  • 10
    • 33747088162 scopus 로고    scopus 로고
    • Tumor-immune system interaction: Modeling the tumor-stimulated proliferation of effectors and immunotherapy
    • DOI 10.1142/S0218202506001571, PII S0218202506001571
    • D'Onofrio A., Tumor-immune system interaction: modeling the tumor-stimulated proliferation of effectors and immunotherapy Mathematical Models and Methods in Applied Sciences 2006 16 8 1375 1401 (Pubitemid 44221742)
    • (2006) Mathematical Models and Methods in Applied Sciences , vol.16 , Issue.8 , pp. 1375-1401
    • D'Onofrio, A.1
  • 13
    • 0021079540 scopus 로고
    • Tumor invasion and the extracellular matrix
    • Liotta L. A., Rao C. N., Barsky S. H., Tumor invasion and the extracellular matrix Laboratory Investigation 1983 49 6 636 649 (Pubitemid 14220329)
    • (1983) Laboratory Investigation , vol.49 , Issue.6 , pp. 636-649
    • Liotta, L.A.1    Rao, C.N.2    Barsky, S.H.3
  • 16
    • 0036192302 scopus 로고    scopus 로고
    • Differential experimental micrometastasis to lung, liver, and bone with lacZ-tagged CWR22R prostate carcinoma cells
    • DOI 10.1023/A:1013833111207
    • Holleran J. L., Miller C. J., Edgehouse N. L., Pretlow T. P., Culp L. A., Differential experimental micrometastasis to lung, liver, and bone with lacZ-tagged CWR22R prostate carcinoma cells Clinical and Experimental Metastasis 2002 19 1 17 24 (Pubitemid 34208350)
    • (2002) Clinical and Experimental Metastasis , vol.19 , Issue.1 , pp. 17-24
    • Holleran, J.L.1    Miller, C.J.2    Edgehouse, N.L.3    Pretlow, T.P.4    Culp, L.A.5
  • 18
    • 16644400591 scopus 로고    scopus 로고
    • Mathematical modeling of tumor-induced angiogenesis
    • DOI 10.1007/s00285-003-0262-2
    • Mantzaris N. V., Webb S., Othmer H. G., Mathematical modeling of tumor-induced angiogenesis Journal of Mathematical Biology 2004 49 2 111 187 (Pubitemid 40882678)
    • (2004) Journal of Mathematical Biology , vol.49 , Issue.2 , pp. 111-187
    • Mantzaris, N.V.1    Webb, S.2    Othmer, H.G.3
  • 19
    • 0029683949 scopus 로고    scopus 로고
    • Biology of metastasis and its clinical implications: Renal-cell cancer
    • Ulchaker J. C., Klein E. A., Biology of metastasis and its clinical implications: renal-cell cancer World Journal of Urology 1996 14 3 175 181 (Pubitemid 126775159)
    • (1996) World Journal of Urology , vol.14 , Issue.3 , pp. 175-181
    • Ulchaker, J.C.1    Klein, E.A.2
  • 20
    • 0042378367 scopus 로고    scopus 로고
    • An introduction to lymphocyte and viral dynamics: The power and limitations of mathematical analysis
    • DOI 10.1098/rspb.2003.2386
    • Asquith B., Bangham C. R. M., An introduction to lymphocyte and viral dynamics: The power and limitations of mathematical analysis Proceedings of the Royal Society B 2003 270 1525 1651 1657 (Pubitemid 37041284)
    • (2003) Proceedings of the Royal Society B: Biological Sciences , vol.270 , Issue.1525 , pp. 1651-1657
    • Asquith, B.1    Bangham, C.R.M.2
  • 21
    • 0034254401 scopus 로고    scopus 로고
    • Modelling and mathematical problems related to tumor evolution and its interaction with the immune system
    • DOI 10.1016/S0895-7177(00)00143-6, PII S0895717700001436
    • Bellomo N., Preziosi L., Modelling and mathematical problems related to tumor evolution and its interaction with the immune system Mathematical and Computer Modelling 2000 32 3-4 413 452 (Pubitemid 30610360)
    • (2000) Mathematical and Computer Modelling , vol.32 , Issue.3-4 , pp. 413-452
    • Bellomo, N.1    Preziosi, L.2
  • 23
    • 0037560902 scopus 로고    scopus 로고
    • Modelling and simulation of tumour development, treatmentand control
    • Bellomo N., De Angelis E., Modelling and simulation of tumour development, treatmentand control Mathematical and Computer Modelling 2003 37 11
    • (2003) Mathematical and Computer Modelling , vol.37 , Issue.11
    • Bellomo, N.1    De Angelis, E.2
  • 24
    • 26844581605 scopus 로고    scopus 로고
    • Modelling complex systems in molecular biology and tumordynamics and control
    • Bellomo N., De Angelis E., Modelling complex systems in molecular biology and tumordynamics and control Mathematical and Computer Modelling 2005 41 10
    • (2005) Mathematical and Computer Modelling , vol.41 , Issue.10
    • Bellomo, N.1    De Angelis, E.2
  • 28
    • 0028882787 scopus 로고
    • Models of tumor-host interaction as competing populations: Implications for tumor biology and treatment
    • Gatenby R. A., Models of tumor-host interaction as competing populations: implications for tumor biology and treatment Journal of Theoretical Biology 1995 176 4 447 455
    • (1995) Journal of Theoretical Biology , vol.176 , Issue.4 , pp. 447-455
    • Gatenby, R.A.1
  • 29
    • 0029751950 scopus 로고    scopus 로고
    • A reaction-diffusion model of cancer invasion
    • Gatenby R. A., Gawlinski E. T., A reaction-diffusion model of cancer invasion Cancer Research 1996 56 24 5745 5753 (Pubitemid 26422183)
    • (1996) Cancer Research , vol.56 , Issue.24 , pp. 5745-5753
    • Gatenby, R.A.1    Gawlinski, E.T.2
  • 30
    • 79952915251 scopus 로고    scopus 로고
    • A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion
    • Anderson A. R. A., A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion Mathematical Medicine and Biology 2005 16 1219 1242
    • (2005) Mathematical Medicine and Biology , vol.16 , pp. 1219-1242
    • Anderson, A.R.A.1
  • 33
    • 0042009645 scopus 로고    scopus 로고
    • Measuring progress against cancer in Europe: Has the 15% decline targeted for 2000 come about?
    • DOI 10.1093/annonc/mdg353
    • Boyle P., d'Onofrio A., Maisonneuve P., Severi G., Robertson C., Tubiana M., Veronesi U., Measuring progress against cancer in Europe: has the 15 decline targeted for 2000 come about? Annals of Oncology 2003 14 8 1312 1325 (Pubitemid 37039061)
    • (2003) Annals of Oncology , vol.14 , Issue.8 , pp. 1312-1325
    • Boyle, P.1    D'Onofrio, A.2    Maisonneuve, P.3    Severi, G.4    Robertson, C.5    Tubiana, M.6    Veronesi, U.7
  • 35
    • 27644463491 scopus 로고    scopus 로고
    • Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system
    • DOI 10.1142/S0218202505000947
    • Chaplain M. A. J., Lolas G., Mathematical modelling of cancer cell invasion of tissue: the role of the urokinase plasminogen activation system Mathematical Models and Methods in Applied Sciences 2005 15 11 1685 1734 (Pubitemid 41551043)
    • (2005) Mathematical Models and Methods in Applied Sciences , vol.15 , Issue.11 , pp. 1685-1734
    • Chaplain, M.A.J.1    Lolas, G.2
  • 36
    • 85182867322 scopus 로고    scopus 로고
    • Mathematical modelling of cancer invasion of tissue: Dynamic heterogeneity
    • Chaplain M. A. J., Lolas G., Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity Networks and Heterogeneous Media 2006 1 3 399 439
    • (2006) Networks and Heterogeneous Media , vol.1 , Issue.3 , pp. 399-439
    • Chaplain, M.A.J.1    Lolas, G.2
  • 39
    • 0002670122 scopus 로고    scopus 로고
    • A mathematical model of vascular tumour growth and invasion
    • Orme M. E., Chaplain M. A. J., A mathematical model of vascular tumour growth and invasion Mathematical and Computer Modelling 1996 23 10 43 60 (Pubitemid 126656514)
    • (1996) Mathematical and Computer Modelling , vol.23 , Issue.10 , pp. 43-60
    • Orme, M.E.1    Chaplain, M.A.J.2
  • 40
    • 0032767250 scopus 로고    scopus 로고
    • Extracellular matrix concentration exerts selection pressure on invasive cells
    • DOI 10.1016/S0959-8049(99)00125-2, PII S0959804999001252
    • Perumpanani A. J., Byrne H. M., Extracellular matrix concentration exerts selection pressure on invasive cells European Journal of Cancer 1999 35 8 1274 1280 (Pubitemid 29359190)
    • (1999) European Journal of Cancer , vol.35 , Issue.8 , pp. 1274-1280
    • Perumpanani, A.J.1    Byrne, H.M.2
  • 41
    • 0030407429 scopus 로고    scopus 로고
    • Biological inferences from a mathematical model for malignant invasion
    • Perumpanani A. J., Sherratt J. A., Norbury J., Byrne H. M., Biological inferences from a mathematical model for malignant invasion Invasion and Metastasis 1996 16 4-5 209 221 (Pubitemid 27399787)
    • (1996) Invasion and Metastasis , vol.16 , Issue.4-5 , pp. 209-221
    • Perumpanani, A.J.1    Sherratt, J.A.2    Norbury, J.3    Byrne, H.M.4
  • 43
    • 0039440566 scopus 로고    scopus 로고
    • A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion
    • PII S0167278998002723
    • Perumpanani A. J., Sherratt J. A., Norbury J., Byrne H. M., A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion Physica D 1999 126 3-4 145 159 (Pubitemid 129496521)
    • (1999) Physica D: Nonlinear Phenomena , vol.126 , Issue.3-4 , pp. 145-159
    • Perumpanani, A.J.1    Sherratt, J.A.2    Norbury, J.3    Byrne, H.M.4
  • 45
    • 0037105740 scopus 로고    scopus 로고
    • Alterations in gene expression profiles during prostate cancer progression: Functional correlations to tumorigenicity and down-regulation of selenoprotein-P in mouse and human tumors
    • Calvo A., Xiao N., Kang J., Best C. J. M., Leiva I., Emmert-Buck M. R., Jorcyk C., Green J. E., Alterations in gene expression profiles during prostate cancer progression: functional correlations to tumorigenicity and down-regulation of selenoprotein-P in mouse and human tumors Cancer Research 2002 62 18 5325 5335 (Pubitemid 35024609)
    • (2002) Cancer Research , vol.62 , Issue.18 , pp. 5325-5335
    • Calvo, A.1    Xiao, N.2    Kang, J.3    Best, C.J.M.4    Leiva, I.5    Emmert-Buck, M.R.6    Jorcyk, C.7    Green, J.E.8
  • 46
    • 0025336879 scopus 로고
    • The receptor for urokinase type plasminogen activator polarizes expression of the protease to the leading edge of migrating monocytes and promotes degradation of enzyme inhibitor complexes
    • Estreicher A., Muhlhauser J., Carpentier J. -L., Orci L., Vassalli J. -D., The receptor for urokinase type plasminogen activator polarizes expression of the protease to the leading edge of migrating monocytes and promotes degradation of enzyme inhibitor complexes Journal of Cell Biology 1990 111 2 783 792
    • (1990) Journal of Cell Biology , vol.111 , Issue.2 , pp. 783-792
    • Estreicher, A.1    Muhlhauser, J.2    Carpentier, J.-L.3    Orci, L.4    Vassalli, J.-D.5
  • 49
    • 27644503155 scopus 로고    scopus 로고
    • Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours
    • DOI 10.1142/S0218202505000935
    • Lachowicz M., Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours Mathematical Models and Methods in Applied Sciences 2005 15 11 1667 1683 (Pubitemid 41551042)
    • (2005) Mathematical Models and Methods in Applied Sciences , vol.15 , Issue.11 , pp. 1667-1683
    • Lachowicz, M.1


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