H. Lee Moffitt Cancer Center & Research Institute

Mathematical modeling of tumor growth and treatment. To understand a complex multiscale nature of cancer, in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale, mathematical and computational models are needed that are capable of integrating simulataneously multiple factors influencing tumor progression. Such computational approaches give the unique opportunity of simulating various scenarios of tumor emergence and growth, as well as different protocols of chemo- and radiotherapy over a wide range of parameters values that is not always possible in the laboratory.

Individual cells based models. This modeling approach allows one to represent each normal, tumor and/or stromal cell as an individual entity with independently regulated cell life processes, such as cell metabolism, proliferation, death or motility, and individually defined changes in cell phenotype, genotype and cell shape. The individual cell based models incorporate different biological scales: from genes and proteins to cell growth and migration, to tissue turnover and the escape from tissue homeostasis, to tumor invasion of the surrounding microenvironment and metastatic collonisation of distant tissues. These models can be parametrized with experimental and clinical data and can be used to carry 2D and 3D simulations of tumor growth and treatment.

Tumor imaging. Development of novel non-invasive imaging techniques for cancer therapy, such as multivalent targeting molecules for specific cancer imaging; establishment of new prognostic and predictive biomarkes; or use of imaging as a biomarker of therapy response, are of special interest in cancer biology as they may facilitate our understanding of cancer development, its response to different microenvironmental conditions, or its reaction to chemo- and radiotheraphy.

In vitro 2D and 3D assays. The use of standard and development of new in vitro assays is especially important in our group, as the collected experimental data are necessary to build and parametrized mathematical models and then verified ro validate model predictions. We use 2D and 3D in vitro assays to determine locations and counts of cellular processes via cell nuclear staining; to identify intercellular adherent junctions and {beta}-catenin and Wnt signaling; to test cell migratory properties via a nover in vitro invasion assay; and cell proliferative heterogeneity via a coloy forming assay.

Cancer evolutionary dynamics. Evolutionary dynamics play a big role in explaining cancer progression. Inside a tumour there are all the ingredients of an ecosystem with several cell populations competing for the limited nutrients, resources and space. Two mathematical tools: Game Theory and Cellular Automata are exceedingly useful to explore how the interaction between cells and between them and the environment influence tumour progression. Since tumour cells are known to acquire a number of different phenotypes in the path from cancer initiation to malignancy, evolutionary game theory can be a powerful tool in which to study the emergence of different tumour phenotypes with increasing degrees of malignancy, the scenarios that lead to benign tumours and the effects of therapies on tumour progression dynamics.

Bio-mechanics of tumor development. The maintenance of normal tissue architecture and mechanisms leading to the initiation of tumor growth can be investigated using bio-mechanical models in which cells are fully deformable and equipped with cell membrane receptors that cells can use to sense the microenvironment and comunicate with other cells, such as the IBCell model. This apporach can be used to accurately model structures of various tissues, such as epithelial ducts, various patterns of ductal carcinoma in situ, as well as the growth of solid tumors and clonal tumor expansion. The model can be adjusted to represent distinct biomechanical properties of the tissue under consideration and to include distinct biochemical properties of the host cells.

Modeling tumor metabolism. Many different metabolites (such as oxygen, glucose or pH) that form diffusive grandients in tumor tissues and their microenvironments create adaptive landscapes that influence somatic evolution of cancers. Moreover, it has been demonstrated that tumor cells exposed to hypoxia and acidosis in a primary tumor or in-vitro have increased metastatic potential. To investigate the mechanisms involved in these adaptations and the relationship between pHe, hypoxia, and metastasis the integrated experimental/computational models are necessary, that incorporate simultaneous measurement of critical tumor parameters and cancer-specific imaging.