Integrative mathematical modeling of cancer invasion.

CS22-01 The life-threatening property of cancer is invasion, locally and at distant sites. Mechanistically, it is poorly understood but there is little doubt that it is a complex process regulated by the interaction of parameters from both cancer cells and tumor microenvironment. Cell parameters include cell-matrix interactions, cell-cell adhesion, cell metabolic rates, nutrient consumption, production of matrix degrading enzymes. Microenvironmental parameters or variable include concentration and organization of matrix, hypoxia, angiogenesis, inflammation, stromal cells. If indeed invasion is the outcome of interactions among all of these parameters, we have little hope of understanding it intuitively and mathematical modeling approaches apper to be a possible answer. At the Vanderbilt Integrative Cancer Biology Center (http://www.vanderbilt.edu/VICBC/), our major focus is to produce quantitative computer simulations of cancer invasion at a multiplicity of biological scales. To this end, we have developed a strong collaborative effort with Dr. Alexander R.A. Anderson, University of Dundee, and have combined the expertise of an interdisciplinary group of scientist, including experimental biologists, clinical oncologists, chemical and biological engineers, computational biologists, computer modelers, theoretical and applied mathematicians and imaging scientists. We have several strategies for data collection and modeling approaches at each of several scales, including the cellular (10 0 cells) multicellular ( 2 cells) and tissue level ( 6 -10 8 cells). For the cellular scale, simulation of a single cell moving in an extracellular matrix field is being parameterized with data from lamellipodia protrusion, cell speed, haptotaxis. Some of these data are being collected in novel bioengineered gadgets. For the multicellular scale, we have adopted the MCF10A 3-dimensional mammosphere system. Several parameters, including proliferation, apoptosis, cell-cell adhesion, are being fed into a mathematical model that simulates mammosphere morphogenesis and realistically takes into account cell mechanical properties. At the tissue level, we exploit mouse models of human cancer as well as xenogeneic tumor systems, in combination with advanced imaging techniques (MRI, microCT and PET scan) to parameterize and test simulations. Our current hybrid discrete-continuous (HDC) model, developed by Alexander R.A. Anderson, is based on deterministic partial differential equations (PDE) to represent oxygen consumption, matrix degradation and matrix-degrading enzymes. Tumor cell density is discretized, so that cells are represented by individual functions that calculate their probability of movements on a grid domain. Furthermore, a cell life-cycle flow-chart allows for phenotypes to be generated and tracked in the simulation. A striking prediction of this HDC model is that there is a strong effect of the microenvironment on the selection of invasive phenotypes. Furthermore, there is an unexpected link between microenvironment properties and the realization of the invasive phenotypes. Simulations and data supporting these conclusions will be shown.