A heterogeneous patient-specific model of glioblastoma multiforme tumor through an inverse problem

Abstract This paper presents a mathematical framework for the prognosis of glioblastoma brain tumor growth on a patient-specific basis, employing a heterogeneous image-driven methodology. The approach utilizes a reaction–diffusion model to capture the diffusion and proliferation dynamics of tumor cell density, integrated with an inverse problem based on partial differential equation-constrained formulation that links the model to medical images. We establish a theoretical framework that forms a robust foundation for our proposed methodology. Then a numerical algorithm is introduced to implement the framework effectively. We also validate the efficacy of our approach using synthetic tumors on a real brain magnetic resonance image. This work significantly contributes to advancing our understanding of glioma dynamics and offers a promising avenue for personalized treatments through the estimation of spatially varying parameters.