We study solid tumor growth in the nonlinear
regime using a new formulation of classical
models. The tumor evolution is described by
by a reduced set of two new dimensionless parameters
and is qualitatively unaffected by the number
of space dimensions. One parameter describes
the relative rate of mitosis to the relaxation
mechanisms (cell-mobility and cell-to-cell adhesion).
The other describes the balance between apoptosis
(programmed cell-death) and mitosis. Both parameters
include the effect of vascularization.
Our analysis and simulations reveal that the new
dimensionless parameters uniquely divide tumor growth
into three regimes associated with increasing degrees
of vascularization. We demonstrate that critical conditions
exist for which the tumor evolves to non-trivial
dormant states or grows self-similarly. This leads
to the possibility of controlling the tumor growth
through the controlled release of tumor angiogenic
factors by restricting the volume to surface area
ratio.
Away from these critical conditions, evolution may
be unstable leading to invasive fingering into the
external tissues and nonlinear simulations demonstrate
the occurence of topological transitions such
as the capture of healthy tissue by the tumor.
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