On a mathematical model of bone marrow metastatic niche

  • Received: 23 November 2015 Accepted: 14 June 2016 Published: 01 January 2017
  • MSC : Primary: 35Q92; Secondary: 35R60

  • We propose a mathematical model to describe tumor cells movement towards a metastasis location into the bone marrow considering the influence of chemotaxis inhibition due to the action of a drug. The model considers the evolution of the signaling molecules CXCL-12 secreted by osteoblasts (bone cells responsible of the mineralization of the bone) and PTHrP (secreted by tumor cells) which activates osteoblast growth. The model consists of a coupled system of second order PDEs describing the evolution of CXCL-12 and PTHrP, an ODE of logistic type to model the Osteoblasts density and an extra equation for each cancer cell. We also simulate the system to illustrate the qualitative behavior of the solutions. The numerical method of resolution is also presented in detail.

    Citation: Ana Isabel Muñoz, J. Ignacio Tello. On a mathematical model of bone marrow metastatic niche[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 289-304. doi: 10.3934/mbe.2017019

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  • We propose a mathematical model to describe tumor cells movement towards a metastasis location into the bone marrow considering the influence of chemotaxis inhibition due to the action of a drug. The model considers the evolution of the signaling molecules CXCL-12 secreted by osteoblasts (bone cells responsible of the mineralization of the bone) and PTHrP (secreted by tumor cells) which activates osteoblast growth. The model consists of a coupled system of second order PDEs describing the evolution of CXCL-12 and PTHrP, an ODE of logistic type to model the Osteoblasts density and an extra equation for each cancer cell. We also simulate the system to illustrate the qualitative behavior of the solutions. The numerical method of resolution is also presented in detail.


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    [1] [ R. A. Adams, Sobolev Spaces Academic Press, New York-London, 1975.
    [2] [ A. A. Bryden,S. Islam,A. J. Freemont,J. H. Shanks,N. J. George,N. W. Clarke, Parathyroid hormone-related peptide: Expression in prostate cancer bone metastases, Prostate Cancer Prostatic Dis, 5 (2002): 59-62.
    [3] [ L. M. Calvi,G. B. Adams,K. W. Weibrecht,J. M. Weber,D. P. Olson,M. C. Knight,R. P. Martin,E. Schipani,P. Divieti,F. R. Bringhurst,L. A. Milner,H. M. Kronenberg,D. T. Scadden, Osteoblastic cells regulate the haematopoietic stem cell niche, Nature, 425 (2003): 841-846.
    [4] [ S. L. Chang, S. P. Cavnar, S. Takayama, G. D. Luker and J. J. Linderman, Cell, isoform, and environment factors shape gradients and modulate chemotaxis PLoS One 10 (2015), e0123450.
    [5] [ N. L. Coggins,D. Trakimas,S. L. Chang,A. Ehrlich,P. Ray,K. E. Luker,J. J. Linderman,G. D. Luker, CXCR7 controls competition for recruitment of β-arrestin 2 in cells expressing both CXCR4 and CXCR7, PLoS One, 9 (2014): 841-846.
    [6] [ K. Golan,O. Kollet,T. Lapidot, Dynamic cross talk between S1P and CXCL12 regulates hematopoietic stem cells migration, development and bone remodeling, Pharmaceuticals, 6 (2013): 1145-1169.
    [7] [ G. Innamorati,M. T. Valenti,F. Giovinazzo,L. Dalle Carbonare,M. Parenti,C. Bassi, Molecular approaches to target gpcrs in cancer therapy, Pharmaceuticals, 4 (2011): 567-589.
    [8] [ S. V. Komarova,R. J. Smith,S. J. Dixon,S. M. Sims,L. M. Wahlb, Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling, Bone, 33 (2003): 206-215.
    [9] [ A. J. Lilly, W. E. Johnson and C. M. Bunce, The haematopoietic stem cell niche: New insights into the mechanisms regulating haematopoietic stem cell behaviour Stem Cells International, 2011 (2011), ID 274564.
    [10] [ A. I. Muñoz, Numerical resolution of a model of tumor growth, Mathematical Medicine and Biology, 33 (2016): 1-29.
    [11] [ G. O'Boyle, I. Swidenbank, H. Marshall, C. E. Barker, J. Armstrong, S. A. White, S. P. Fricker, R. Plummer, M. Wright and P. E. Lovat, Inhibition of CXCR4/CXCL12 chemotaxis in melanoma by AMD11070, Br J Cancer., 108 (2013), 1634--1640, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3668477/
    [12] [ T. Oskarsson,E. Batlle,J. Massague, Metastatic stem cells: Sources, niches, and vital pathways, Cell Stem Cell, 14 (2014): 306-321.
    [13] [ A. A. Rose,P. M. Siegel, Emerging therapeutic targets in breast cancer bone metastasis, Future Oncol., 6 (2010): 55-74.
    [14] [ M. D. Ryser,N. Nigam,S. V. Komarova, Mathematical modeling of spatio-temporal dynamics of a single bone multicellular unit, J. of Bone and Mineral Research, 24 (2009): 860-870.
    [15] [ J. Sceneay,M. J. Smyth,A. Möller, The pre-metastatic niche: Finding common ground, Cancer Metastasis Rev., 32 (2013): 449-464.
    [16] [ Y. X. Sun,J. Wang,C. E. Shelburne,D. E. Lopatin,A. M. Chinnaiyan,M. A. Rubin,K. J. Pienta,R. S. Taichman, Expression of CXCR4 and CXCL12 (SDF-1) in human prostate cancers (PCa) in vivo, Journal of Cellular Biochemistry, 89 (2003): 462-473.
    [17] [ R. S. Taichman,C. Cooper,E. T. Keller,K. J. Pienta,N. S. Taichman,L. K. McCauley, Use of the stromal cell-derived factor-1/CXCR4 pathway in prostate cancer metastasis to bone, Cancer Research, 62 (2002): 1832-1837.
    [18] [ J. I. Tello, On a mathematical model of tumor growth based on cancer stem cells, Math. Biosc. Eng., 10 (2013): 263-278.
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