Integrated Mathematical Oncology

Cancer is a dynamic complex multiscale system that can only truly be understood via the integration of theory and experiments. The goal of the IMO is to use such an integrated approach to better understand, predict and treat cancer.


The latest and greatest from IMO.

We are now accepting applications for the 2017 summer HIP IMO program.
HIP–IMO is a mathematical oncology centric internship program that delivers interdisciplinary team science research experiences for high school students. This mentored training program is designed for motivated aspiring scientists to help prepare them for interdisciplinary cancer research careers.
Working under the direction and guidance of IMO faculty/scientist mentors, interns are involved in activities designed to foster the development of life-long research skills.

One of major issues in clinical trials in oncology is their high failure rate, despite the fact that the trials were designed based on the data from successful equivalent preclinical studies. This is in part due to the intrinsic homogeneity of preclinical model systems and the contrasting heterogeneity of actual patient responses. Dr. Andersons lab has developed a mathematical model-driven framework, phase i (virtual/imaginary) trials, that integrates the heterogeneity of actual patient responses and preclinical studies through a cohort of virtual patients. The computational framework to implement phase i trials in cancer can readily capture observed heterogeneous clinical outcomes and predict patient survival. Importantly, phase i trials can be used to optimise future clinical trial design.


Moffitt Cancer Center's Physical Sciences - Oncology Center Receives $10.4 Million Grant to Study the Intersection of Evolution and Cancer Therapy. The Moffitt PSOC is led by three highly interactive principle investigators - Alexander Anderson, PhD, chair of the IMO; Robert J. Gillies, PhD, chair of Cancer Imaging and Metabolism; and Robert A. Gatenby, MD, chair of Radiology and a founder of this interdisciplinary effort. The PSOC focuses on evolution as the fundamental driving force of cancer development and the main reason that cancer therapy fails. A central goal of the center is to develop new strategies to prevent and treat cancer by exploiting Charles Darwin's concept of natural selection.

Our Faculty

IMO faculty consists of 6 internationally renowned cancer researchers and mathematical modelers. The focus of all IMO research groups is to apply physical, mathematical and mechanical principles to cancer biology to decipher fisrt order principles of tumor growth that can be exploited for novel cancer treatments. Department chair Sandy Anderson has co-authored the most-cited mathematical modeling of angiogensis paper and has pioneered the hybrid continuous-discrete modeling technique that combines individual-based models with continuous differential equations. The research interests in his lab are centered around the tumor microenvironment and understanding their interactions as an ecological system. David Basanta is a game theorist with expertise in evolutionary cancer dynamcis. His lab is interested in the tumor microenviroment, and evolutionary games explaining tumor progression and treatment response. Heiko Enderling is an expert on cancer stem cells and tumor dormancy, and the response of tumors to radiotherapy. His lab is interested in quantitative personalized medicine, with focus on radiation and immunotherapy. Bob Gatenby, chair of the Radiology department at Moffitt Cancer Center, has pioneered the development of spatial models of cancer invasion and is renowned for his work on tumor acidity and the Warburg effect. His lab is interested in tumor imaging, evolution, cancer as an ecosystem, and adaptive therapy. Kasia Rejniak is an fluid dynamics techniques and bio-mechanical agent-based modeling as applied to study the transition from tissue homeostasis to carcinogenesis, and to anti-cancer treatments. Her lab is interested in mechano-pharmacodynamics and tumor mechano-transduction. Jacob Scott is a radiation oncologist turned mathematical biologist who is interested in quantiative modeling of radiotherapy and genomically adapted doses as well as cancer evolotion.

Alexander Anderson


David Basanta

Associate Member

Heiko Enderling

Assistant Member

Robert Gatenby

Senior Member

Katarzyna Rejniak

Assistant Member

Jacob Scott


Research @ IMO

Translational mathematical and compuational oncology

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 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.

Modeling tumour 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.

Drug 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.

Cancer 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.

Tumor dormancy

The interactions of cancer cells with each other as well as their environment can provoke various nonlinear 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.


Find IMO faculty publications on   PubMed.


IMO training and outreach.

Annual interdisciplinary HANDS-ON workshops

IMO organizes annual hands-on interdisciplinary cross-training workshops on cutting-edge toppics in translational cancer research. Internationally renowned speakers and participants from all over the world make the intense 3-5 days a fantastic learning and research event.

IMO is pleased to host high school student internships every summer. This program gives students an opportunity to work on real life problems and become acquainted with mathematical oncology research. Interested students should contact IMO faculty to discuss availability.

In the media

Ongoing research with international reach or direct impact to our local community are often covered in press and media. If introdcutory interviews or fancy animations — a selection of IMO popular media articles and video releases are archived in our media library.