The PhD student will be hosted by the
laboratory J. A. Dieudonné, a joint unit CNRS-Université Côte d'Azur,and by the joint Inria team COFFEE. Le is located in the campus Valrose in Nice.
The PhD student will attend the scientific activity of the unit.
He is expected to
collaborate tightly with biologists form IPMC, as well as with colleagues from the Institut Mathématiques de Marseille.
Mathematical modeling of tumor growth has led to a wide literature, with fascinating theoretical developments as well as insight with direct clinical impact. Many models of the interactions with the immune system rely on, quit esophisticated, differential systems, but which cannot take into account the space structuration of teh quantities of interest. We wish to propose new models intended to describe time-space structuration of the tumor growth, the tumor micro-environement and its infiltration by the immune system, and then to compare numerical predictions to experimental observations. To this end, we shall use data acquired by innovative technologies developed at IPMC by means of mass cytometry.
These techniques provide information of the space repartition of several biological markers (tumor cells, immune cells, fibroblasts, proteins,...) on sections of human cutaneous carcinoma. Our ambition is to set up equations and numerical methods able to reproduce the observations and to elaborate a tool for predicting and optimizimng therapeutic stategies. Our inspiration comes th etheory of mixtures, on which we have an established backgound, and which already appeared for tumor growth modeling.
The model couples non linear convection-diffusion equations for several interacing phases, together with algebraic constaints. Mathematical analysis can provide some insights on simpified situations, in order to bring out some fundamental properties of the solutions. The numerical challenge consists in capturing the space heterogeneities of the tumor advance. A difficulty is to preserve at the discrete level the various formulations of the equations, which is an important consistency property of the scheme.
The objectives of the project are :
- To set up a system of PDEs describing the tumor growth and the immune response,
- To elaborate a numerical scheme, able to capture the salient features of these complex interactions, ment,
- To identify and calibrate the parameters in order to produce quantitatively relevant simulations,
An utlimate goal will be to contribute to the elaboration of therapeutic scenario.
To this end, we shall develop Discrete Duality Finite Volumes schemes which have certain conceptual advantages to handle the PDEs describing such complex flows.
The PhD is intended to mix up, at proportions depending on the own tastes of the applicant: modeling, analysis, numerical simulations
and data analysis.
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