Effects of vascularization on lymphocyte/tumor cell dynamics: Qualitative features |
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Institution: | Department of Mathematics and Statistics, Old Dominion University Norfolk, VA 23529, U.S.A. |
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Abstract: | By adapting a pre-existing model to include the effects of Vascularization within a tumor or multicell spheroid, a predator-prey system describing the cell populations of a solid tumor and reactive lymphocytes is formulated. The paper serves as a review of the minimal deterministic approach to tumor-host immune system interactions while examining, in a qualitative manner, the modifications to the dynamics induced by a simple representation of the vascularized tumor. In addition, the possibility of limit-cycle behavior is studied by regarding each of six parameters present in the model as a bifurcation parameter. Thus, in principle, well-defined and periodic oscillations in both lymphocyte and tumor cell populations may occur under appropriate circumstances; whether or not such oscillations are sustainable by the host, and their stability, amplitude and period depend on aquisition of more quantitative information concerning the relevant parameter ranges. |
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