Modeling glioblastoma with cell-cell and cell-substrate interactions
by
Mathilde Badoual
Laboratoire IMNC, 15 rue Georges Clemenceau, bat 104, 91406 Orsay Cedex, France
Coauthors: Christophe Deroulers (Laboratoire IMNC) Marine Aubert (Laboratoire IMNC) Basile Grammaticos (Laboratoire IMNC)

Glioblastoma are malignant tumors associated with a very poor prognosis, due to the capacity of individual glioma cells to

invade surrounding normal brain tissue, far from the tumor focal area. This infiltration results in the inability to completely

resect this tumor and is responsible for the almost inevitable recurrence after treatment.

Cell-cell (homotype) as well as cell-substrate (heterotype) interactions are key events in the migration process.

We have developed a cellular automaton where the strength of each type of interaction is ajustable, to describe the migration of glioma cells [1,2].

From this automaton, we were able to derive a macroscopic equation of diffusion, where the diffusion coefficient is original compared

to other classical models[3]. First, it is nonlinear as it depends on the cell density. Second, it depends on the two parameters measuring the strength of homotype and heterotype interactions.

Here, we use this nonlinear diffusion coefficient in a diffusion-proliferation equation to model the

growth of glioblastoma. We define two cell populations, characterized by different homotype and heterotype interaction parameters

and a proliferation rate that depends on the strength of heterotype interactions. First, we study the interplay between cell-cell and cell-matrix interactions during cell migration in vitro on different substrates, and we reproduce some experimental results [4].

We also compare the effects of classical treatments (surgery, radiotherapy) for different values of homotype and heterotype interaction parameters and we show that inhibing heterotype (or increasing homotype) interactions (by inhibiting gap-junctions or intergrins for example) in the margin of an operated tumor could have a clinical interest, by reducing the chances of recurrence.

[1] Aubert M, Badoual M, Fereol S, Christov C and Grammaticos B, 2006, A cellular automaton model for the migration of glioma cells, Phys. Biol. 3 93.

[2] Aubert M, Badoual M, Christov C and Grammaticos B, 2008, A model for glioma cell migration on collagen and astrocytes, J. R. Soc. Interface, 5,75-83.

[3] Tracqui P, Cruywagen GC, Woodward DE, Bartoo GT, Murray JD and Alvord EC Jr, A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth, Cell Prolif, 1995, 28, 17-31.

[4] Giese A, Loo MA, Tran N, Haskett D, Coons SW, Berens ME, 1996, Dichotomy of astrocytoma migration and proliferation, Int. J. Cancer 67, 275-282.

Date received: May 15, 2008