Towards Personalized Diagnosis of Glioblastoma in Fluid-Attenuated Inversion Recovery (FLAIR) by Topological Interpretable Machine Learning

Matteo Rucco,Lorenzo Falsetti,Giovanna Viticchi

doi:10.3390/math8050770

Abstract

Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumor, which tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all primary brain tumors. Usually, GBMs are detected by magnetic resonance images (MRI). Among MRI, a fluid-attenuated inversion recovery (FLAIR) sequence produces high quality digital tumor representation. Fast computer-aided detection and segmentation techniques are needed for overcoming subjective medical doctors (MDs) judgment. This study has three main novelties for demonstrating the role of topological features as new set of radiomics features which can be used as pillars of a personalized diagnostic systems of GBM analysis from FLAIR. For the first time topological data analysis is used for analyzing GBM from three complementary perspectives—tumor growth at cell level, temporal evolution of GBM in follow-up period and eventually GBM detection. The second novelty is represented by the definition of a new Shannon-like topological entropy, the so-called Generator Entropy. The third novelty is the combination of topological and textural features for training automatic interpretable machine learning. These novelties are demonstrated by three numerical experiments. Topological Data Analysis of a simplified 2D tumor growth mathematical model had allowed to understand the bio-chemical conditions that facilitate tumor growth—the higher the concentration of chemical nutrients the more virulent the process. Topological data analysis was used for evaluating GBM temporal progression on FLAIR recorded within 90 days following treatment completion and at progression. The experiment had confirmed that persistent entropy is a viable statistics for monitoring GBM evolution during the follow-up period. In the third experiment we developed a novel methodology based on topological and textural features and automatic interpretable machine learning for automatic GBM classification on FLAIR. The algorithm reached a classification accuracy up to 97%.

Highlights

Gliomas are the most common primary brain tumors, originating from glial cells
Topological data analysis is a reliable approach to shedding light on glioblastoma multiforme (GBM) characteristics, as has been demonstrated by the three numerical experiments described in this paper
For the sake of precision, the main limitation of our work is due to that persistent homology can be computed only over one proximity parameter at a time and it does not allow us to study how the topology of the simplicial complexes changes along two or multiple directions

Summary

Introduction

Gliomas are the most common primary brain tumors, originating from glial cells. We can differentiate between benign tumors, with, in some cases, a long life expectancy, and malignant forms. GBM are characterized by a diffuse and infiltrative growth pattern, as invasive glioma cells often migrate along myelinated white matter (WM) fiber tracts. This is a major cause of their appalling prognosis—tumor cells invade, displace, and possibly destroy WM. Persistent holes are more likely to represent true features of the underlying space, rather than artifacts of sampling (noise), or due to particular choices of parameters. In order to compute persistent homology, we need a distance function on the underlying space. This can be obtained constructing a filtration on a simplicial complex, which is a nested sequence of increasing subcomplexes.

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Conclusion