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Front instabilities and invasiveness of simulated avascular tumors. (English) Zbl 1169.92030

Summary: We study the interface morphology of a 2D simulation of an avascular tumor composed of identical cells growing in an homogeneous healthy tissue matrix \((TM)\), in order to understand the origin of the morphological changes often observed during real tumor growth. We use the Glazier-Graner-Hogeweg model [J.A. Glazier and F. Graner, Phys. Rev. E 47, 2129ff (1993)], which treats tumor cells as extended, deformable objects, to study the effects of two parameters: a dimensionless diffusion-limitation parameter defined as the ratio of the tumor consumption rate to the substrate transport rate, and the tumor-TM surface tension. We model TM as a non-diffusing field, neglecting the TM pressure and haptotactic repulsion acting on a real growing tumor; thus, our model is appropriate for studying tumors with highly motile cells, e.g., gliomas.
We show that the diffusion-limitation parameter determines whether the growing tumor develops a smooth (noninvasive) or fingered (invasive) interface, and that the sensitivity of tumor morphology to tumor-TM surface tension increases with the size of the dimensionless diffusion-limitation parameter. For large diffusion-limitation parameters, we find a transition (missed in previous work) between dendritic structures, produced when tumor-TM surface tension is high, and seaweed-like structures, produced when tumor-TM surface tension is low. This observation leads to a direct analogy between the mathematics and dynamics of tumors and those observed in nonbiological directional solidification.
Our results are also consistent with the biological observation that hypoxia promotes invasive growth of tumor cells by inducing higher levels of receptors for scatter factors that weaken cell-cell adhesion and increase cell motility. These findings suggest that tumor morphology may have value in predicting the efficiency of antiangiogenic therapy in individual patients.

MSC:

92C50 Medical applications (general)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C37 Cell biology
92-08 Computational methods for problems pertaining to biology

Software:

CompuCell3D
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References:

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