Homogenization of a carcinogenesis model with different scalings with the homogenization parameter

Isabell Graf; Malte A. Peter

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 2, page 163-184
  • ISSN: 0862-7959

Abstract

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In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell. The diffusion on the endoplasmic reticulum, modeled as a Riemannian manifold, is described by the Laplace-Beltrami operator. For the binding process to the surface of the endoplasmic reticulum, different scalings with powers of the homogenization parameter are considered. This leads to three qualitatively different models in the homogenization limit.

How to cite

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Graf, Isabell, and Peter, Malte A.. "Homogenization of a carcinogenesis model with different scalings with the homogenization parameter." Mathematica Bohemica 139.2 (2014): 163-184. <http://eudml.org/doc/261919>.

@article{Graf2014,
abstract = {In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell. The diffusion on the endoplasmic reticulum, modeled as a Riemannian manifold, is described by the Laplace-Beltrami operator. For the binding process to the surface of the endoplasmic reticulum, different scalings with powers of the homogenization parameter are considered. This leads to three qualitatively different models in the homogenization limit.},
author = {Graf, Isabell, Peter, Malte A.},
journal = {Mathematica Bohemica},
keywords = {periodic homogenization; two-scale convergence; carcinogenesis; reaction-diffusion system; surface diffusion; periodic homogenization; two-scale convergence; carcinogenesis; reaction-diffusion system; surface diffusion},
language = {eng},
number = {2},
pages = {163-184},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homogenization of a carcinogenesis model with different scalings with the homogenization parameter},
url = {http://eudml.org/doc/261919},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Graf, Isabell
AU - Peter, Malte A.
TI - Homogenization of a carcinogenesis model with different scalings with the homogenization parameter
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 2
SP - 163
EP - 184
AB - In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell. The diffusion on the endoplasmic reticulum, modeled as a Riemannian manifold, is described by the Laplace-Beltrami operator. For the binding process to the surface of the endoplasmic reticulum, different scalings with powers of the homogenization parameter are considered. This leads to three qualitatively different models in the homogenization limit.
LA - eng
KW - periodic homogenization; two-scale convergence; carcinogenesis; reaction-diffusion system; surface diffusion; periodic homogenization; two-scale convergence; carcinogenesis; reaction-diffusion system; surface diffusion
UR - http://eudml.org/doc/261919
ER -

References

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