Math. Model. Nat. Phenom.
Volume 7, Number 1, 2012Cancer modeling
|Page(s)||78 - 104|
|Published online||25 January 2012|
A Hybrid Model Describing Different Morphologies of Tumor Invasion Fronts
Department of Mathematics, Politecnico di Torino Corso Duca degli Abruzzi
2 Institute for Cancer Research and Treatment Strada Provinciale 142, 10060 Candiolo, Italy
⋆ Corresponding author. E-mail: email@example.com
The invasive capability is fundamental in determining the malignancy of a solid tumor. Revealing biomedical strategies that are able to partially decrease cancer invasiveness is therefore an important approach in the treatment of the disease and has given rise to multiple in vitro and in silico models. We here develop a hybrid computational framework, whose aim is to characterize the effects of the different cellular and subcellular mechanisms involved in the invasion of a malignant mass. In particular, a discrete Cellular Potts Model is used to represent the population of cancer cells at the mesoscopic scale, while a continuous approach of reaction-diffusion equations is employed to describe the evolution of microscopic variables, as the nutrients and the proteins present in the microenvironment and the matrix degrading enzymes secreted by the tumor. The behavior of each cell is then determined by a balance of forces, such as homotypic (cell-cell) and heterotypic (cell-matrix) adhesions and haptotaxis, and is mediated by the internal state of the individual, i.e. its motility. The resulting composite model quantifies the influence of changes in the mechanisms involved in tumor invasion and, more interestingly, puts in evidence possible therapeutic approaches, that are potentially effective in decreasing the malignancy of the disease, such as the alteration in the adhesive properties of the cells, the inhibition in their ability to remodel and the disruption of the haptotactic movement. We also extend the simulation framework by including cell proliferation which, following experimental evidence, is regulated by the intracellular level of growth factors. Interestingly, in spite of the increment in cellular density, the depth of invasion is not significantly increased, as one could have expected.
Mathematics Subject Classification: 97M60
Key words: cellular potts model / tumor invasion matrix / metalloproteinases
© EDP Sciences, 2012
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