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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

How do tumors grow in-vitro?

Dirk Drasdo and Stefan Höhme


In recent years extensive studies have been performed on in-vitro growing avascular tumor spheroids. Here we present computer simulations with a single-cell-based lattice-free approach and compare the results to the experimental findings for the growth kinetics of avascular tumor spheroids of Freyer and Sutherland (1985, 1986), and with monolayer cultures of Bru et. al. (1998).

Our findings suggest that initially the tumor diameter and cell population size both grow exponentially fast, followed by a linear increase of the tumor diameter which under certain conditions is accompanied by a power-law growth of the population size. The linear diameter growth is triggered by a confinement of cell proliferation on a surface layer which for (three-dimensional) tumor spheroids may mainly be a consequence of a glucose (or oxygen) lack in the tumor interior, while for (two-dimensional) monolayers mainly may result from an inhibition of cell division when the mechanical pressure on a cell inside the tumor exceeds a certain threshold value.

The consequence of cell proliferation limited to the surface is that cells at the boundary have performed much more cell divisions than those in the interior.

MSC Codes:
82C22, 92C05, 92C50
87.18.-h, 87.68.+z, 87.
individual cell-based model, monolayer cultures, tumor spheroids, growth kinetics, spatial patterns

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2002 Repository Open Access
Dirk Drasdo and Stefan Höhme

How do tumors grow in-vitro?