Modelling and simulation of anisotropic growth in brain tumours through poroelasticity: A study of ventricular compression and therapeutic protocols

Malignant brain tumours represent a significant medical challenge due to their aggressive nature and unpredictable locations. The growth of a brain tumour can result in a mass effect, causing compression and displacement of the surrounding healthy brain tissue and possibly leading to severe neurological complications. In this paper, we propose a multiphase mechanical model for brain tumour growth that quantifies deformations and solid stresses caused by the expanding tumour mass and incorporates anisotropic growth influenced by brain fibres. We employ a sharp interface model to simulate localised, noninvasive solid brain tumours, which are those responsible for substantial mechanical impact on the surrounding healthy tissue. By using patient-specific imaging data, we create realistic three-dimensional brain geometries and accurately represent ventricular shapes, to evaluate how the growing mass may compress and deform the cerebral ventricles. Another relevant feature of our model is the ability to simulate therapeutic protocols, facilitating the evaluation of treatment efficacy and guiding the development of personalized therapies for individual patients. Overall, our model allows to make a step towards a deeper analysis of the complex interactions between brain tumours and their environment, with a particular focus on the impact of a growing cancer on healthy tissue, ventricular compression, and therapeutic treatment.