Mathematics Colloquia and Seminars

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Description

I will present and discuss the current status of a mathematical and computer model of cancer growth under development in my research group. The motivation of this work is to identify and analyze diagnostic and treatment strategies through direct in silico simulations. Once completed, this sophisticated computer model will provide a physician with a tool that simulates the development of a tumor corresponding to a specific patient's clinical history. In particular, the efficacy of different treatment strategies will be assessed by direct simulation.

The development of a realistic computer model is now possible due to the recent advances by our group in adaptive numerical modeling and simulation techniques for complex evolving microstructures. These new techniques are capable of describing, for example, the complex shape of a solid carcinoma characterized by invasive fingering and metastasization.

The model will include all phases of growth that have been identified in the biological and biomedical literature:

1. the initial, diffusion-driven growth to a dormant multicell spheroid state, regulated by the transport of nutrient chemical species;

2. necrosis, and the formation of a core of dead tumor cells, due to the transport of growth inhibitor factors;

3. angiogenesis, or blood vessel formation in the tumor, triggered by tumor angiogenetic factors, and endothelial cell migration and proliferation in response to the growth of the multicell spheroid;

4. vascular growth of malignant carcinoma with invasive fingering and metastasization.

I will present the current status of the model, capable of simulating phases 1, 2, and 4, but not the process of angiogenesis. I will then demonstrate how the assumptions and predictions of the model have been validated and refined, for the case of avascular growth (1 and 2), by direct comparison with experimental observations of in vitro and in vivo tumor growth. I will also discuss how angiogenesis will be included in our model.