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Glioblastoma multiforme (GBM) is a fast-growing and highly invasive braintumour, it tends to occur in adults between the ages of 45 and 70 and itaccounts for 52 percent of all primary brain tumours. Usually, GBMs aredetected by magnetic resonance images (MRI). Among MRI, Fluid-attenuatedinversion recovery (FLAIR) sequence produces high quality digital tumourrepresentation. Fast detection and segmentation techniques are needed forovercoming subjective medical doctors (MDs) judgment. In the presentinvestigation, we intend to demonstrate by means of numerical experiments thattopological features combined with textural features can be enrolled for GBManalysis and morphological characterization on FLAIR. To this extent, we haveperformed three numerical experiments. In the first experiment, TopologicalData Analysis (TDA) of a simplified 2D tumour growth mathematical model hadallowed to understand the bio-chemical conditions that facilitate tumourgrowth: the higher the concentration of chemical nutrients the more virulentthe process. In the second experiment topological data analysis was used forevaluating GBM temporal progression on FLAIR recorded within 90 days followingtreatment (e.g., chemo-radiation therapy - CRT) completion and at progression.The experiment had confirmed that persistent entropy is a viable statistics formonitoring GBM evolution during the follow-up period. In the third experimentwe had developed a novel methodology based on topological and textural featuresand automatic interpretable machine learning for automatic GBM classificationon FLAIR. The algorithm reached a classification accuracy up to the 97%.

Towards personalized diagnosis of Glioblastoma in Fluid-attenuated inversion recovery (FLAIR) by topological interpretable machine learning