Details
| Original language | English |
|---|---|
| Pages (from-to) | 25-48 |
| Number of pages | 24 |
| Journal | European Journal of Applied Mathematics |
| Volume | 24 |
| Issue number | 1 |
| Publication status | Published - Feb 2013 |
Abstract
In this paper we consider a two-phase model describing the growth of avascular solid tumors when taking into account the effects of cell-to-cell adhesion and taxis due to nutrient. The tumor is surrounded by healthy tissue which is the source of nutrient for tumor cells. In a three-dimensional context, we prove that the mathematical formulation corresponds to a well-posed problem, and find radially symmetric steady-state solutions of the problem. They appear in the regime where the rate of cell apoptosis to cell proliferation is less than the far field nutrient concentration. Furthermore, we study the stability properties of those radially symmetric equilibria and find, depending on the biophysical parameters involved in the problem, both stable and unstable regimes for tumor growth.
Keywords
- Classical solution, Radially symmetric stationary solution, Stability, Taxis, Tumor growth
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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In: European Journal of Applied Mathematics, Vol. 24, No. 1, 02.2013, p. 25-48.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Analysis of a two-phase model describing the growth of solid tumors
AU - Escher, Joachim
AU - Matioc, Anxa Aoichita
PY - 2013/2
Y1 - 2013/2
N2 - In this paper we consider a two-phase model describing the growth of avascular solid tumors when taking into account the effects of cell-to-cell adhesion and taxis due to nutrient. The tumor is surrounded by healthy tissue which is the source of nutrient for tumor cells. In a three-dimensional context, we prove that the mathematical formulation corresponds to a well-posed problem, and find radially symmetric steady-state solutions of the problem. They appear in the regime where the rate of cell apoptosis to cell proliferation is less than the far field nutrient concentration. Furthermore, we study the stability properties of those radially symmetric equilibria and find, depending on the biophysical parameters involved in the problem, both stable and unstable regimes for tumor growth.
AB - In this paper we consider a two-phase model describing the growth of avascular solid tumors when taking into account the effects of cell-to-cell adhesion and taxis due to nutrient. The tumor is surrounded by healthy tissue which is the source of nutrient for tumor cells. In a three-dimensional context, we prove that the mathematical formulation corresponds to a well-posed problem, and find radially symmetric steady-state solutions of the problem. They appear in the regime where the rate of cell apoptosis to cell proliferation is less than the far field nutrient concentration. Furthermore, we study the stability properties of those radially symmetric equilibria and find, depending on the biophysical parameters involved in the problem, both stable and unstable regimes for tumor growth.
KW - Classical solution
KW - Radially symmetric stationary solution
KW - Stability
KW - Taxis
KW - Tumor growth
UR - http://www.scopus.com/inward/record.url?scp=84871266536&partnerID=8YFLogxK
U2 - 10.1017/S0956792512000290
DO - 10.1017/S0956792512000290
M3 - Article
AN - SCOPUS:84871266536
VL - 24
SP - 25
EP - 48
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
SN - 0956-7925
IS - 1
ER -