Topological Data Analysis in Cardiovascular Signals: An Overview.

Topological data analysis (TDA) is a recent approach for analyzing and interpreting complex data sets based on ideas a branch of mathematics called algebraic topology. TDA has proven useful to disentangle non-trivial data structures in a broad range of data analytics problems including the study of cardiovascular signals. Here, we aim to provide an overview of the application of TDA to cardiovascular signals and its potential to enhance the understanding of cardiovascular diseases and their treatment in the form of a literature or narrative review. We first introduce the concept of TDA and its key techniques, including persistent homology, Mapper, and multidimensional scaling. We then discuss the use of TDA in analyzing various cardiovascular signals, including electrocardiography, photoplethysmography, and arterial stiffness. We also discuss the potential of TDA to improve the diagnosis and prognosis of cardiovascular diseases, as well as its limitations and challenges. Finally, we outline future directions for the use of TDA in cardiovascular signal analysis and its potential impact on clinical practice. Overall, TDA shows great promise as a powerful tool for the analysis of complex cardiovascular signals and may offer significant insights into the understanding and management of cardiovascular diseases.

𝓗1 persistent features of the resting-state connectome in healthy subjects.

The analysis of the resting-state functional connectome commonly relies on graph representations. However, the graph-based approach is restricted to pairwise interactions, not suitable to capture high-order interactions, that is, more than two regions. This work investigates the existence of cycles of synchronization emerging at the individual level in the resting-state fMRI dynamic. These cycles or loops correspond to more than three regions interacting in pairs surrounding a closed space in the resting dynamic. We devised a strategy for characterizing these loops on the fMRI resting state using persistent homology, a data analysis strategy based on topology aimed to characterize high-order connectivity features robustly. This approach describes the loops exhibited at the individual level on a population of 198 healthy controls. Results suggest that these synchronization cycles emerge robustly across different connectivity scales. In addition, these high-order features seem to be supported by a particular anatomical substrate. These topological loops constitute evidence of resting-state high-order arrangements of interaction hidden on classical pairwise models. These cycles may have implications for the synchronization mechanisms commonly described in the resting state.

Topological Data Analysis for Eye Fundus Image Quality Assessment.

The objective of this work is to perform image quality assessment (IQA) of eye fundus images in the context of digital fundoscopy with topological data analysis (TDA) and machine learning methods. Eye health remains inaccessible for a large amount of the global population. Digital tools that automize the eye exam could be used to address this issue. IQA is a fundamental step in digital fundoscopy for clinical applications; it is one of the first steps in the preprocessing stages of computer-aided diagnosis (CAD) systems using eye fundus images. Images from the EyePACS dataset were used, and quality labels from previous works in the literature were selected. Cubical complexes were used to represent the images; the grayscale version was, then, used to calculate a persistent homology on the simplex and represented with persistence diagrams. Then, 30 vectorized topological descriptors were calculated from each image and used as input to a classification algorithm. Six different algorithms were tested for this study (SVM, decision tree, k-NN, random forest, logistic regression (LoGit), MLP). LoGit was selected and used for the classification of all images, given the low computational cost it carries. Performance results on the validation subset showed a global accuracy of 0.932, precision of 0.912 for label "quality" and 0.952 for label "no quality", recall of 0.932 for label "quality" and 0.912 for label "no quality", AUC of 0.980, F1 score of 0.932, and a Matthews correlation coefficient of 0.864. This work offers evidence for the use of topological methods for the process of quality assessment of eye fundus images, where a relatively small vector of characteristics (30 in this case) can enclose enough information for an algorithm to yield classification results useful in the clinical settings of a digital fundoscopy pipeline for CAD.

Topological Data Analysis Reveals Robust Alterations in the Whole-Brain and Frontal Lobe Functional Connectomes in Attention-Deficit/Hyperactivity Disorder.

Attention-deficit/hyperactivity disorder (ADHD) is a developmental disorder characterized by difficulty to control the own behavior. Neuroimaging studies have related ADHD with the interplay of fronto-parietal attention systems with the default mode network (DMN; Castellanos and Aoki, 2016). However, some results have been inconsistent, potentially due to methodological differences in the analytical strategies when defining the brain functional network, i.e., the functional connectivity threshold and/or the brain parcellation scheme. Here, we make use of topological data analysis (TDA) to explore the brain connectome as a function of the filtration value (i.e., the connectivity threshold), instead of using a static connectivity threshold. Specifically, we characterized the transition from all nodes being isolated to being connected into a single component as a function of the filtration value. We explored the utility of such a method to identify differences between 81 children with ADHD (45 male, age: 7.26-17.61 years old) and 96 typically developing children (TDC; 59 male, age: 7.17-17.96 years old), using a public dataset of resting state (rs)fMRI in human subjects. Results were highly congruent when using four different brain segmentations (atlases), and exhibited significant differences for the brain topology of children with ADHD, both at the whole-brain network and the functional subnetwork levels, particularly involving the frontal lobe and the DMN. Therefore, this is a solid approach that complements connectomics-related methods and may contribute to identify the neurophysio-pathology of ADHD.