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Simulating complex tumor dynamics from avascular to vascular growth using a general level-set method. (English) Zbl 1100.92029
Summary: A comprehensive continuum model of solid tumor evolution and development is investigated in detail numerically, both under the assumption of spherical symmetry and for arbitrary two-dimensional growth. The level set approach is used to obtain solutions for a recently developed multi-cell transport model formulated as a moving boundary problem for the evolution of the tumor. The model represents both the avascular and the vascular phase of growth, and is able to simulate when the transition occurs; progressive formation of a necrotic core and a rim structure in the tumor during the avascular phase are also captured. In terms of transport processes, the interaction of the tumor with the surrounding tissue is realistically incorporated.
The two-dimensional simulation results are presented for different initial configurations. The computational framework, based on a Cartesian mesh/narrow band level-set method, can be applied to similar models that require the solution of coupled advection-diffusion equations with a moving boundary inside a fixed domain. The solution algorithm is designed so that extension to three-dimensional simulations is straightforward.

92C50 Medical applications (general)
35K57 Reaction-diffusion equations
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
65C20 Probabilistic models, generic numerical methods in probability and statistics
92C37 Cell biology
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