MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Cell-based models of avascular tumor growth

Dirk Drasdo, Sabine Dormann, Stefan Höhme and Andreas Deutsch


Two models for in-vitro avascular tumor growth are discussed which are complementary with respect to the growth stages they model. One of the models is a single-cell-based off-lattice model (in three dimensions), the other is a lattice approach (in two dimensions).

The off-lattice approach operates in an early tumor growth stage where no growth-limitation due to a lack of nutrient occurs, whereas the lattice approach focuses on a later stage where nutrients are already lacking inside the tumor such that a necrotic core is formed.

Chemicals released by dying cells at the later stage induce a cell migration toward the necrotic core which eventually is found to limit further growth. By combining the results of both models a potential qualitative scenario of avascular tumor growth is discussed.

MSC Codes:
68Q80, 82C22, 92C50
avascular tumors, iindividual-based models, off-lattice, cellular automata

Related publications

2004 Repository Open Access
Dirk Drasdo, S. Dormann, Stefan Höhme and Andreas Deutsch

Cell-based models of avascular tumor growth

In: Function and regulation of cellular systems / Andreas Deutsch (ed.)
Basel : Birkhäuser, 2004. - pp. 367-378
(Mathematics and biosciences in interaction)