Glioblastoma is the most aggressive primary brain cancer, with poor survival that can be largely attributed to intra-tumoural heterogeneity. While these tumours are primarily monitored via contrast-enhanced (CE) T1-weighted and T2-weighted magnetic resonance (MR) images, these standard clinical images are known to be non-specific in their correlation with tumour cell density. This lack of relationship makes it difficult to define the specific regions of interest to target for surgery and radiation. Previous efforts have shown some promise in better interpreting these images utilizing either machine learning (ML) or mechanistic modelling independently. But methods to harness the strengths of both approaches are sorely needed to make clinically actionable progress.
Here we present a novel, first-of-its-kind, hybrid model which brings together a graph-based semi-supervised machine learning approach with a mechanistic partial differential equation model of glioblastoma growth, known as the Proliferation-Invasion (PI) model, to generate predictive tumour cell density maps with high accuracy. Our ML approach bridges cell density as quantified from image-localized biopsies with texture analysis of multiparametric MR images. To incorporate the mechanistic model, the PI model is first used to generate an independent prediction of cell density which is then introduced into the ML algorithm through a Laplacian matrix, which ensures regions with similar predictions from the PI model will have similar predictions in the final model.
We have applied our proposed ML-PI model framework to 18 patients with a total of 82 image localized biopsies. Each patient’s tumour was imaged with multi-parametric MR images, including T1-weighted, CE T1-weighted, T2-weighted, dynamic contrast-enhanced (DCE) imaging, diffusion weighted imaging (DWI), and diffusion tensor imaging (DTI). In this cohort, our hybrid model was able to achieve higher accuracy in cell density prediction than either of the independent models (ML or PI) alone, with a mean accuracy prediction error of 0.084 vs 0.227 for PI alone and 0.220 for ML alone. We hope that with more verification, this tool can be used to not only guide spatially localized therapies such as surgery and radiation, but also help broadly in the interpretation of images for glioblastoma patients.