Cancer spread is a dynamical process occurring not only in time but also in space which,for solid tumors at least,can be modeled quantitatively by reaction and diffusion equations with a bistable behavior:tumor cell c...Cancer spread is a dynamical process occurring not only in time but also in space which,for solid tumors at least,can be modeled quantitatively by reaction and diffusion equations with a bistable behavior:tumor cell colonization happens in a portion of tissue and propagates,but in some cases the process is stopped.Such a cancer proliferation/extintion dynamics is obtained in many mathematical models as a limit of complicated interacting biological fields.In this article we present a very basic model of cancer proliferation adopting the bistable equation for a single tumor cell dynamics.The reaction-diffusion theory is numerically and analytically studied and then extended in order to take into account dispersal effects in cancer progression in analogy with ecological models based on the porous medium equation.Possible implications of this approach for explanation and prediction of tumor development on the lines of existing studies on brain cancer progression are discussed.The potential role of continuum models in connecting the two predominant interpretative theories about cancer,once formalized in appropriatemathematical terms,is discussed。展开更多
文摘Cancer spread is a dynamical process occurring not only in time but also in space which,for solid tumors at least,can be modeled quantitatively by reaction and diffusion equations with a bistable behavior:tumor cell colonization happens in a portion of tissue and propagates,but in some cases the process is stopped.Such a cancer proliferation/extintion dynamics is obtained in many mathematical models as a limit of complicated interacting biological fields.In this article we present a very basic model of cancer proliferation adopting the bistable equation for a single tumor cell dynamics.The reaction-diffusion theory is numerically and analytically studied and then extended in order to take into account dispersal effects in cancer progression in analogy with ecological models based on the porous medium equation.Possible implications of this approach for explanation and prediction of tumor development on the lines of existing studies on brain cancer progression are discussed.The potential role of continuum models in connecting the two predominant interpretative theories about cancer,once formalized in appropriatemathematical terms,is discussed。
