arXiv subjects

Francesca Ballatore

Publications and source records attributed to Francesca Ballatore.

2 recordsLinked to original sources

arXiv2025

From Brain Scans to Therapy Response: PDE Modelling of Immunotherapy for Glioblastoma

Glioblastoma Multiforme (GBM) is a highly aggressive brain tumour with limited therapeutic options and poor prognosis. This study presents a mathematical framework to investigate the efficacy of immunotherapy strategies based on cytotoxic T-lymphocyte (CTL) infusion. The model couples tumour and immune dynamics through a system of partial differential equations (PDEs), incorporating cell proliferation, diffusion, and chemotactic migration in response to TGF-$\beta$, a tumour-secreted signalling molecule. A reduced ordinary differential equation (ODE) model is first analysed to derive threshold conditions for tumour eradication, identifying critical infusion levels consistent with clinical data. Numerical bifurcation analysis explores the impact of parameter variations. The full PDE model is solved using the finite element method on simplified 2D domains, followed by sensitivity analyses to quantify parameter influence on tumour mass and volume. The model is then applied to a realistic 3D brain geometry reconstructed from patient-specific MRI and DTI data, accounting for anatomical anisotropy and tissue heterogeneity. Therapeutic scenarios are simulated with spatially localised lymphocyte infusion. Results highlight spatial variations in tumour growth and treatment response, with infusion intensity and tumour location critically influencing therapeutic outcomes. These findings emphasise the importance of personalised, spatially informed modelling in optimising immunotherapy protocols for GBM.

q-bio.PE↗

arXiv2025

A phenotype-structured reaction-diffusion model of avascular glioma growth

We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into account anisotropic cell movement and oxygen diffusion related to structural anisotropy of the brain's extracellular environment. In this model, phenotypic heterogeneity of tumour cells is captured by a continuous phenotype-structuring variable, the value of which evolves due to phenotypic changes. We first analyse a one-dimensional version of the model and formally show, through a Hopf-Cole transformation, that it admits, in appropriate asymptotic regimes, phenotypically heterogeneous travelling wave solutions, wherein the locally prevailing cell phenotype varies across the wave due to the presence of oxygen gradients. This provides a mathematical formalisation for the emergence of intratumour phenotypic heterogeneity driven by differences in oxygen availability across the tumour. We then report on the results of both 1D simulations, which corroborate the results of formal asymptotic analyses, and 2D simulations, which also demonstrate the impact of anisotropy in cell movement and oxygen diffusion on tumour growth and on the phenotypic composition of the tumour edge. These results are complemented with additional results of 3D simulations, which are carried out on the geometry of the brain by using a hybrid finite difference-finite element method and integrating patient-specific magnetic resonance imaging data with diffusion tensor imaging data.

q-bio.PE↗