A Mathematical Model for Capillary Formation and Development in Tumor Angiogenesis: A Review

Chemotherapy ◽  
2005 ◽  
Vol 52 (1) ◽  
pp. 35-37 ◽  
Author(s):  
Serdal Pamuk
Keyword(s):  
Mathematical Model ◽  
Tumor Angiogenesis ◽  
Capillary Formation

scholarly journals Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Serdal Pamuk
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Tumor Angiogenesis ◽  
Cell Movement ◽  
Steady State Solution ◽  
Stability Criteria ◽  
Data Perturbation ◽  
Capillary Formation ◽  
The Stability ◽  
Perturbation Approximation

We present a mathematical model for capillary formation in tumor angiogenesis and solve it by linearizing it using an initial data perturbation method. This method is highly effective to obtain solutions of nonlinear coupled differential equations. We also provide a specific example resulting, that even a few terms of the obtained series solutions are enough to have an idea for the endothelial cell movement in a capillary. MATLAB-generated figures are provided, and the stability criteria are determined for the steady-state solution of the cell equation.

A NUMERICAL PROOF THAT CERTAIN CELLS FOLLOW THE TRAILS OF THE DIFFUSIONS OF SOME CHEMICALS IN THE EXTRACELLULAR MATRIX

2021 ◽  
pp. 2150027
Author(s):  
İREM ÇAY ◽  
SERDAL PAMUK
Keyword(s):  
Mathematical Model ◽  
Extracellular Matrix ◽  
Tumor Angiogenesis ◽  
Numerical Solutions ◽  
Extra Cellular Matrix ◽  
The Matrix ◽  
Good Agreement ◽  
Cellular Matrix

In this work, we obtain the numerical solutions of a 2D mathematical model of tumor angiogenesis originally presented in [Pamuk S, ÇAY İ, Sazci A, A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix, Math Biosci 306:32–48, 2018] to numerically prove that the certain cells, the endothelials (EC), pericytes (PC) and macrophages (MC) follow the trails of the diffusions of some chemicals in the extracellular matrix (ECM) which is, in fact, inhomogeneous. This leads to branching, the sprouting of a new neovessel from an existing vessel. Therefore, anastomosis occurs between these sprouts. In our figures we do see these branching and anastomosis, which show the fact that the cells diffuse according to the structure of the ECM. As a result, one sees that our results are in good agreement with the biological facts about the movements of certain cells in the Matrix.

scholarly journals Tumor Angiogenesis and Vascular Patterning: A Mathematical Model

PLoS ONE ◽  
2011 ◽  
Vol 6 (5) ◽  
pp. e19989 ◽  
Author(s):  
Rui D. M. Travasso ◽  
Eugenia Corvera Poiré ◽  
Mario Castro ◽  
Juan Carlos Rodrguez-Manzaneque ◽  
A. Hernández-Machado
Keyword(s):  
Mathematical Model ◽  
Tumor Angiogenesis ◽  
Vascular Patterning
Sign in / Sign up

Export Citation Format

Share Document