An innovative method based on topological data analysis is introduced for classifying EEG recordings of patients affected by epilepsy. We construct a topological space from a collection of EEGs signals using Persistent Homology; then, we analyse the space by Persistent entropy, a global topological feature, in order to classify healthy and epileptic signals. The performance of the resulting one-feature-based linear topological classifier is tested by analysing the Physionet dataset. The quality of classification is evaluated in terms of the Area Under Curve (AUC) of the receiver operating characteristic curve. It is shown that the linear topological classifier has an AUC equal to $$97.2\%$$ while the performance of a classifier based on Sample Entropy has an AUC equal to 62.0%.

Negro R, et al. Korean J Radiol. 2020 Feb;21:e68. https://doi.org/10.3348/kjr.2019.0798

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%.

Hypernetworks are based on topological simplicial complexes and generalize the concept of two-body relation to many-body relation. Furthermore, Hypernetworks provide a significant generalization of network theory, enabling the integration of relational structure, logic and analytic dynamics. A pulmonary embolism is a blockage of the main artery of the lung or one of its branches, frequently fatal. Our study uses data on 28 diagnostic features of 1427 people considered to be at risk of pulmonary embolism enrolled in the Department of Internal and Subintensive Medicine of an Italian National Hospital “Ospedali Riuniti di Ancona”. Patients arrived in the department after a first screening executed by the emergency room. The resulting neural hypernetwork correctly recognized 94 % of those developing pulmonary embolism. This is better than previous results obtained with other methods (statistical selection of features, partial least squares regression, topological data analysis in a metric space). In this work we successfully derived a new integrative approach for the analysis of partial and incomplete datasets that is based on Q-analysis with machine learning. The new approach, called Neural Hypernetwork, has been applied to a case study of pulmonary embolism diagnosis. The novelty of this method is that it does not use clinical parameters extracted by imaging analysis.