A personalized mathematical tool for neuro-oncology: A clinical case study

This work evaluates the predictive ability of a novel personalized computational tool for simulating the growth of brain tumours using the neuroimaging data collected during one clinical case study. The mathematical model consists of an evolutionary fourth-order partial differential equation with degenerate motility, in which the spreading dynamics of the multiphase tumour is coupled with a parabolic equation determining the diffusing oxygen within the brain.

The model also includes a reaction term describing the effects of radiotherapy, that is simulated in accordance with the clinical schedule. We collect Magnetic Resonance (MRI) and Diffusion Tensor (DTI) imaging data for one patient at given times of key clinical interest, from the first diagnosis of a giant glioblastoma to its surgical removal and the subsequent radiation therapies. These neuroimaging data allow reconstructing the patient-specific brain geometry in a finite element virtual environment, that is used for simulating the tumour recurrence pattern after the surgical resection. In particular, we characterize the different brain tissues and the tumour location from MRI data, whilst we extrapolate the heterogeneous nutrient diffusion parameters and cellular motility from DTI data.

The numerical results of the simulated tumour are found in good qualitative and quantitative agreement with the volume and the boundaries observed in MRI. Moreover, the simulations point out a consistent regression of the tumour mass in correspondence to the application of radiotherapy, with an average growth rate which is of the same order as the one calculated from the neuroimaging data.

Remarkably, our results display the highest Jaccard index of the tumour region reported in the biomathematical literature. In conclusion, this work represents an important proof-of-concept of the ability of this mathematical framework to predict the tumour recurrence and its response to therapies in a patient-specific manner.