Physics – Mathematical Physics
Scientific paper
2009-06-27
Netw. Heterog. Media, 3(1):43-83, 2008
Physics
Mathematical Physics
34 pages, 18 figures
Scientific paper
10.3934/nhm.2008.3.43
In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular matrix, that occupies a spatial region close to a blood vessel whence cells get the nutrient needed for their vital functions. Growth of tumor cells takes place within a healthy host tissue, which is in turn modeled as a saturated mixture of non-proliferating cells. Interactions between these two regions are accounted for as an essential mechanism for the growth of the tumor mass. By weakening the role of the extracellular matrix, which is regarded as a rigid non-remodeling scaffold, a system of two partial differential equations is derived, describing the evolution of the cell volume ratio coupled to the dynamics of the nutrient, whose higher and lower concentration levels determine proliferation or death of tumor cells, respectively. Numerical simulations of a reference two-dimensional problem are shown and commented, and a qualitative mathematical analysis of some of its key issues is proposed.
No associations
LandOfFree
Multiphase modeling and qualitative analysis of the growth of tumor cords does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multiphase modeling and qualitative analysis of the growth of tumor cords, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multiphase modeling and qualitative analysis of the growth of tumor cords will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-306256