Open AccessOn a mathematical model of bone marrow metastatic niche
Author(s) -
Ana María Muñoz Muñoz,
J. Ignacio Tello
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2017019
Subject(s) - ode , osteoblast , bone marrow , chemotaxis , niche , metastasis , microbiology and biotechnology , biology , cancer research , chemistry , computer science , cancer , immunology , medicine , mathematics , receptor , in vitro , ecology , biochemistry
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.