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A diffuse interface model for tumour growth with applications to neuro-oncology

Dr. Abramo Agosti, Politecnico di Milano

Sala conferenze IMATI-CNR, Pavia - Martedì 17 Aprile 2018 h.16:15

Abstract. In this talk I will describe a diffuse-interface model based on mixture theory recently used to model tumor growth, and in particular to model the patient-specific evolution of a highly malignant brain tumour, the glioblastoma multiforme (GBM).
Using thermodynamic principles, a Cahn-Hilliard type equation with degenerate mobility is obtained, in which the spreading dynamics of the multiphase tumour is coupled through a growth term with a parabolic equation describing a nutrient species dynamics.

A single-well potential of Lennard-Jones type is used in the model to describe the cell-cell mechanical interactions.
As a consequence, the degeneracy set of the mobility and the singularity set of the potential do not coincide. This feature introduces a nontrivial difference with respect to the Cahn-Hilliard equations with a double-well potential analyzed in the literature.

I will show some analytical results for simplified versions of the model, together with different finite element approximations of the problem which preserve the analytical properties of the continuous solutions.

By comparing the observed in-vitro evolution of a culture of glioblastoma cells to the growth and coarsening dynamics described by the model, I will prove the effectiveness of using a single-well potential to describe the GBM cells interaction.

The tumor growth model is finally fed by clinical neuroimaging data that provide the anatomical and  microstructural characteristics of a patient brain.
I will show the predictions of numerical simulations and the comparison with the clinical data for a case test study, observing a good accordance with the data and highlighting the ground-breaking potential of the model for delivering accurate patient-specific predictions.

This work has been conducted in collaboration with Pasquale Ciarletta, Maurizio Grasselli, Paola F.
Antonietti, Marco Verani, Chiara Giverso, Elena Faggiano and Aymeric Stamm.

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Dipartimento di Matematica ''F. Casorati''

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