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

Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumour, it tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all primary brain tumours. Usually, GBMs are detected by magnetic resonance images (MRI). Among MRI, Fluid-attenuated inversion recovery (FLAIR) sequence produces high quality digital tumour representation. Fast detection and segmentation techniques are needed for overcoming subjective medical doctors (MDs) judgment. In the present investigation, we intend to demonstrate by means of numerical experiments that topological features combined with textural features can be enrolled for GBM analysis and morphological characterization on FLAIR. To this extent, we have performed three numerical experiments. In the first experiment, Topological Data Analysis (TDA) of a simplified 2D tumour growth mathematical model had allowed to understand the bio-chemical conditions that facilitate tumour growth: the higher the concentration of chemical nutrients the more virulent the process. In the second experiment topological data analysis was used for evaluating GBM temporal progression on FLAIR recorded within 90 days following treatment (e.g., chemo-radiation therapy - CRT) 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 had 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 the 97%.Comment: 22 pages; 16 figure

Separating Persistent Homology of Noise from Time Series Data Using Topological Signal Processing

We introduce a novel method for separating significant features in the sublevel set persistence diagram based on a statistics analysis of the sublevel set persistence of a noise distribution. Specifically, the statistical analysis of the sublevel set persistence of additive noise distributions are leveraged to provide a noise cutoff or confidence interval in the sublevel set persistence diagram. This analysis is done for several common noise models including Gaussian, uniform, exponential and Rayleigh distributions. We then develop a framework implementing this statistical analysis of sublevel set persistence for signals contaminated by an additive noise distribution to separate the sublevel sets associated to noise and signal. This method is computationally efficient, does not require any signal pre-filtering, is widely applicable, and has open-source software available. We demonstrate the functionality of the method with both numerically simulated examples and an experimental data set. Additionally, we provide an efficient $O(nlog(n))$ algorithm for calculating the zero-dimensional sublevel set persistence homology

Persistent entropy for separating topological features from noise in vietoris-rips complexes

Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional holes along such sequence is called the persistence barcode. k-Dimensional holes with short lifetimes are informally considered to be “topological noise”, and those with long lifetimes are considered to be “topological features” associated to the filtration. Persistent entropy is defined as the Shannon entropy of the persistence barcode of the filtration. In this paper we present new important properties of persistent entropy of Vietoris-Rips filtrations. Later, using these properties, we derive a simple method for separating topological noise from features in Vietoris-Rips filtrations.Ministerio de Economía y Competitividad MTM2015-67072-