Project abstract

Tumor evolution is a very complex process, involving many different phenomena, which occur at different scales. From the modelling point of view there are three natural scales of interest: the sub-cellular scale, the cellular scale and the macroscopic scale.

The main objective of the project is to organise human capital, activities, structures, management in common to develop mathematical models, algorithms, and computer software for the simulation of multiscale modeling in cancer.

The successful development of the project requires a synergy of research efforts and knowledge of mathematics, biology, medicine, computer science, chemistry, and physics. In addition, it requires the development of different phases referring to the modelling process: phenomenological observation, mathematical modelling, mathematical methods, simulation, prediction, experiments, model validation and refinement. The development of all this requires an interdisciplinary approach.

Objectives 

1. Developing the whole modeling process from phenomenological observation to simulation and validation, through the design of mathematical models and their qualitative and quantitative study, in order to simulate tumour evolution within the full range of scales: from sub-cellular to macroscopic.
2. Linking all above approaches, in order to gain deeper insight into the dynamics of tumour growth.
3. Developing predictive, quantitative mathematical models which can be used by clinicians in the fight against cancer as a support to experimental research.
4. Modeling the action of specific therapies to combat cancer, e.g. control of angiogenic phenomena, activation of the immune response, application of chemotherapeutical actions.
5. Developing computational schemes and simulation tools for the benefit of users active in immunology, cell biology, and medicine who are not necessarily expert in mathematics or computer sciences. The design of specific simulation tools can be a very useful bridge between applied mathematicians and bioscientists and can help reducing lab experiments and optimising otherwise frustrating therapies.

Developing mathematical models at all the scales implies making use of a wide variety of theoretical tools from a range of branches of mathematical sciences (e.g. cellular automata, individual-based models, kinetic theory, stochastic processes, system theory, compartmental models, continuum mechanics, multiphase flows) and developing different mathematical tools to obtain both qualitative and quantitative results. Of course, the modeling of physical phenomena should be developed at the pertinent scale, but with the ability of models to shift from one scale to the other.

The objective of the project is to link models developed by specialists participating in the project and to incorporate information obtained from studies at other scales, thus forming a network of mathematical models.

The links can be of two types: in “series” and in “parallel” In the former case, the output obtained using a particular model can be used as input parameters for another model at a different scale. For instance, a sub-cellular model for the cell-cycle could help to better estimate reproduction rates for the dynamics of cell populations, which can then be used in a cellular model. Eventually, the study of the project will consist of a sub-model for each level, which can be used for simulations and predictions or for studies being performed in parallel with laboratory experiments. These sub-models are vertically interlinked with each other by their input and output data, consistently with the project objective. In the latter case, information deriving from different types of mathematical models are compared. For instance, in the process of angiogenesis the mechanism of aggregation of endothelial cells can be described using a fluid-dynamic model, but useful insight can be obtained developing kinetic models, or cell-based models, or using cellular automata. From the mathematical point of view, it is possible to relate the models above through suitable limit procedures, so that one can check the correspondence between the models operating at different scales. This is particularly relevant for dealing with anti-angiogenic therapies which work at a sub-cellular level to influence cell proliferation, migration or organisation.