The goal of this cross-disciplinary project is to produce mathematical models and simulation software that describe quantitatively the process of cancer invasion and encapsulate the knowledge derived from a wide range of experimental observations into a correlative and predictive tool, available to all researchers. Cancer invasion is thought to involve a number of cellular parameters (including altered rates of cell proliferation, apoptosis, migration, adhesion, metabolism, and mutation), as well as microenvironmental parameters (including extracellular matrix composition, angiogenesis, inflammation, and proteases). From a mathematical point of view, some of these parameters are continuous and some discrete Therefore, our primary approach is based on a hybrid model in which both continuum deterministic and discrete stochastic parameters and variables are integrated. Because of its hybrid nature, the model can be directly linked to experimental measurements of those cellular and microenvironmental parameters recognized by cancer biologists as important in cancer invasion. Predictions based on the hybrid models will be visualized by software that implements computer simulations of invasion. These models and the associated simulations will be the basis for generating hypotheses that will be tested in vitro, in two-dimensional (2D) and three-dimensional (3D) cancer cell culture systems, as well as in vivo, in xenograft and genetic mouse models for human cancers. Experimental validation will be used to both refine and improve the mathematical models and simulation programs in an iterative fashion and provide new input parameters for the models. Initially, we will model invasion parameters at a level of complexity that does not hinder mathematical and experimental feasibility, but that already provides a realistic representation of cancer invasion. As we progress, we will be able to introduce increasing levels of complexity, since the model is open to incorporation of parameters and experimental data from several scales, e.g., the macro-scale (tissue), micro-scale (cells), subcellular, and molecular scales. The long-term goal is to produce a comprehensive, quantitative description of the major mechanisms underlying cancer invasion. This description, and the associated computer simulations, should enable a rational approach for accurate diagnostic staging and therapeutic targeting of the invasion/metastasis step of cancer progression.
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