Abstract
The prognosis for patients with malignant brain tumors remains poor. Consequently, a better understanding of the complex mechanisms underlying tumor progression is of key interest to design better treatment strategies. A powerful tool to test hypotheses on tumor evolution for individual patients and thus, to improve the understanding of the disease, is the mathematical modeling of tumor growth. A novel multi-scale approach for coupling our existing hybrid model for brain tumor progression on a microscopic scale with a molecular model based on ordinary differential equations (ODEs) is proposed.
Materials and Methods
The present work introduces a mathematical model describing the avascular tumor progression on a microscopic and molecular scale. More precisely, a hybrid model is used, which additionally considers the nutrient concentration described in terms of reaction-diffusion equations. The solution is computed using the finite element method (FEM) and itself influences a molecular network on the subcellular level. This network is defined by a system of ODEs whose solution reflects the tumor cell processes. The cellular automata method is used to simulate chemotactic motility and necrosis.
Results
Visual inspection of the results demonstrates the plausibility of the implemented model. The computed dynamics of cancerous cells follows the well known exponential increase in cell population during the early stage of cancer progression. For the subsequent cancer growth the model displays structures exhibiting a necrotic core, a rim of quiescent cells surrounded by dividing cells.
Discussion
We report first results for a multiscale simulation framework of brain cancer dynamics. The model depicts the expected characteristic spatial patterns. The central aspect of this work is the coupling of the cellular model including the nutrient concentration with a molecular network on the subcellular scale. Using the FEM to solve for the nutrient concentration it is possible to provide an efficient solution. The standard processes for cancerous cells are controlled by molecular reactions and protein concentrations. The model furthermore incorporates chemotaxis.
Materials and Methods
The present work introduces a mathematical model describing the avascular tumor progression on a microscopic and molecular scale. More precisely, a hybrid model is used, which additionally considers the nutrient concentration described in terms of reaction-diffusion equations. The solution is computed using the finite element method (FEM) and itself influences a molecular network on the subcellular level. This network is defined by a system of ODEs whose solution reflects the tumor cell processes. The cellular automata method is used to simulate chemotactic motility and necrosis.
Results
Visual inspection of the results demonstrates the plausibility of the implemented model. The computed dynamics of cancerous cells follows the well known exponential increase in cell population during the early stage of cancer progression. For the subsequent cancer growth the model displays structures exhibiting a necrotic core, a rim of quiescent cells surrounded by dividing cells.
Discussion
We report first results for a multiscale simulation framework of brain cancer dynamics. The model depicts the expected characteristic spatial patterns. The central aspect of this work is the coupling of the cellular model including the nutrient concentration with a molecular network on the subcellular scale. Using the FEM to solve for the nutrient concentration it is possible to provide an efficient solution. The standard processes for cancerous cells are controlled by molecular reactions and protein concentrations. The model furthermore incorporates chemotaxis.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the 9th European Conference on Computational Biology |
| Place of Publication | Gent, Belgien |
| Publication date | 2010 |
| Pages | G21 |
| Publication status | Published - 2010 |
