Integrated Mathematical Oncology Research

Translational Mathematical and Computational Oncology


Mathematical Modeling of Tumor Growth

Mathematical Modeling Of Tumor Growth And Treatment

To understand a complex multi-scale 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 simultaneously 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.

Tumor ImagingTumor 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 biomarkers; 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 micro-environmental conditions, or its reaction to chemo- and radiotherapy.

Cancer Evolutionary DynamicsCancer Evolutionary Dynamics

Evolutionary dynamics play a big role in explaining cancer progression. Inside a tumor 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 tumor progression. Since tumor 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 tumor phenotypes with increasing degrees of malignancy, the scenarios that lead to benign tumors and the effects of therapies on tumor progression dynamics.

Modeling Tumour MicroenvironmentModeling Tumor Microenvironment

Interactions between tumor cells and the surrounding tissue, both the immediate microenvironment (cell-cell or cell-matrix interactions) and the extended microenvironment (e.g. vascular bed, stroma) are thought to play crucial roles in both tumor progression and suppression. Mathematical models, such as HDC, are ideally suited to examine the key role of the microenvironment as a selective force in the growth and evolution of cancer. Moreover, mathematical modeling can be used to link the wealth of gene expression data that currently exist with the phenotypes that create the tumor, thus creating a cell centered bridge between genetic change and clinical outcome.

Cancer Stem CellsCancer Stem Cells

Tumors are heterogeneous populations composed of different cells types: stem cells with the capacity for self-renewal and more differentiated cells lacking such ability. The overall growth behavior of a developing neoplasm is determined largely by the combined kinetic interactions of these cells. By tracking the fate of individual cancer cells using agent-based methods in silico, one can apply basic rules for cell proliferation, migration and cell death to show how these kinetic parameters interact to control, and perhaps dictate defining spatial and temporal tumor growth dynamics in tumor development.

Individual Cells Based ModelsIndividual 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 colonization 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.

In Vitro 2D and 3D AssaysIn 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 colony forming assay.

Bio-Mechanics of Tumor DevelopmentBio-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 are used by the cells to sense cues from the microenvironment and to communicate with other cells, such as the IBCell model. This approach can be used to accurately model structures of various tissues, such as epithelial ducts, various patterns of ductal carcinoma in situ, stratified epithelia of the skin, 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.

Drug Interstitial TransportDrug Interstitial Transport

Many different metabolites (such as oxygen, glucose or pH), as well as anti-cancer chemotherapeutic agents and biomarkers form diffusive gradients in tumor tissues and their microenvironments and create adaptive landscapes that influence tumor growth and response to treatments. Using a mechano-pharmacodynamics model (microPD) we can investigate the mechanisms involved in the interstitial transport and extracellular distributions of drug and metabolite molecules, as well as complex kinetics and effective scheduling of multi-drug therapies.

Tumor DormancyTumor Dormancy

The interactions of cancer cells with each other as well as their environment can provoke various non-linear growth kinetics in the emerging tumor. An intrinsic dormant state and environmentally induced dormancy are inevitable early tumor progression bottlenecks within a range of biologically realistic cell kinetic parameters. In certain conditions, cell kinetics can combine to enable escape to tumor progression.