Topology- and Graph-Informed Imaging Informatics

Accurate segmentation of liver vessels is crucial for medical applications due to its pivotal role in diagnosing liver diseases, planning surgical interventions, and assessing treatment effectiveness. In this paper, we present a new dataset for liver vessel separation and propose two novel plug-and-play modules integrated into deep learning frameworks for liver vessel segmentation. The first module, termed as the skeleton tracking module, addresses the issue of segmentation fragmentation by effectively tracking the vessel skeletons. The second module, the graph attention module, is introduced for vessel separation. We demonstrate the effectiveness of our proposed approach through comprehensive experiments, showcasing significant improvements in segmentation accuracy. The dataset is publicly available, fostering research and development. https://​github.​com/​oneway-phil/​SKTS-GAT/​tree/​main.

Image segmentation is a complex task that aims to simultaneously satisfy various quality criteria. In this context, topology is being increasingly considered. Guaranteeing correct topological properties is indeed crucial for objects presenting challenging shapes. Designing topology-aware metrics is then relevant, both for assessing the quality of segmentation results and for designing losses involved in learning procedures. In this article, we introduce ccDice (connected component Dice), a topological metric that generalises the popular Dice score. By contrast to Dice, that acts at the scale of pixels, ccDice acts at the scale of connected components of the compared objects, leading to a topological assessment of their relative structure and embedding. ccDice is a simple, explainable, normalized and low-computational topological metric. We provide a formal definition of ccDice, an algorithmic scheme for computing it, and we assess its behaviour by comparison to other usual topological metrics. Code is available on GitHub: https://​github.​com/​PierreRouge/​ccDice.

Microscopic examination of slides prepared from tissue samples is the primary tool for detecting and classifying cancerous lesions, a process that is time-consuming and requires the expertise of experienced pathologists. Recent advances in deep learning methods hold significant potential to enhance medical diagnostics and treatment planning by improving accuracy, reproducibility, and speed, thereby reducing clinicians’ workloads and turnaround times. However, the necessity for vast amounts of labeled data to train these models remains a major obstacle to the development of effective clinical decision support systems.

In this paper, we propose the integration of topological deep learning methods to enhance the accuracy and robustness of existing histopathological image analysis models. Topological data analysis (TDA) offers a unique approach by extracting essential information through the evaluation of topological patterns across different color channels. While deep learning methods capture local information from images, TDA features provide complementary global features. Our experiments on publicly available histopathological datasets demonstrate that the inclusion of topological features significantly improves the differentiation of tumor types in ovarian and breast cancers.

Recent advances in molecular and genetic research have identified a diverse range of brain tumor sub-types, shedding light on differences in their molecular mechanisms, heterogeneity, and origins. The present study performs whole-brain connectome analysis using diffusion-weighted images. To achieve this, both graph theory and persistent homology-a prominent approach in topological data analysis are employed in order to quantify changes in the structural connectivity of the whole-brain connectome in subjects with brain tumors. Probabilistic tractography is used to map the number of streamlines connecting 84 distinct brain regions, as delineated by the Desikan-Killiany atlas from FreeSurfer. These streamline mappings form the connectome matrix, on which persistent homology based analysis and graph theoretical analysis are executed to evaluate the discriminatory power between tumor sub-types that include meningioma and glioma. A detailed statistical analysis is conducted on persistent homology-derived topological features and graphical features to identify the brain regions where differences between study groups are statistically significant (\(p<0.05\)). For classification purpose, graph-based local features are utilized, achieving a highest accuracy of 88%. In classifying tumor sub-types, an accuracy of 80% is attained. The findings obtained from this study underscore the potential of persistent homology and graph theoretical analysis of the whole-brain connectome in detecting alterations in structural connectivity patterns specific to different types of brain tumors.

Segmentation models achieved expert-level performance in a large variety of medical applications. However, their robustness to rotations is rarely discussed and can be crucial for clinical use with the risk of discarding subtle but diagnostically relevant anatomical structures. In medical images, complex structures appear in a wide range of positions and rotations, requiring rotation robustness. In this work, we investigate the robustness to rotations of a standard 3D nnU-Net in the context of two segmentation tasks: the hippocampus in MRI and the pulmonary airway system in CT. In addition, we introduce a 3D Locally Rotation Invariant (LRI) operator based on the bispectrum to achieve high robustness to input rotations. It is compared to a standard nnU-Net, a nnU-Net with extended rotational data augmentation and XEdgeConv, a state-of-the-art approach for RI. While all models performed similarly in terms of Dice score for right-angle rotations, the Bispectral U-Net outperformed other designs in the context of finer and more realistic rotations. Furthermore, the Bispectral U-Net and the XEdgeConv were more stable w.r.t. input rotation, i.e. the predictions are significantly more consistent across input rotations. Important inconsistencies of the nnU-Net were observed for lung airway segmentation, suggesting potential risks of using the model in clinical routine.

Accurate segmentation of vascular networks is essential for computer-aided tools designed to address cardiovascular diseases. Despite more than thirty years of research, it remains a challenge to obtain vascular segmentation results that preserve the connectivity of the underlying vascular network. Yet connectivity is one of the key features of these tools. In this work, we propose a post-processing algorithm aiming to reconnect vascular structures that have been disconnected by a segmentation algorithm. Connectivity being a complex property to model explicitly, we propose to learn this geometric feature either through synthetic data or annotations of the application of interest. The resulting post-processing model can be used on the output of any supervised or unsupervised vascular segmentation algorithm. We show that this post-processing effectively restores the connectivity of vascular networks both in 2D and 3D images, leading to improved overall segmentation results.

Accurate skeleton segmentation of the entire anteroposterior bone scintigrams of the human body is essential for diagnosing bone metastases. However, conventional methods lack a loss design incorporating prior anatomical information, leading to segmentation failures, particularly when dealing with the irregular shapes of organs or high concentrations of positive accumulation. Cases where diagnostic support systems present anatomically abnormal findings may shatter the confidence of doctors and their reliability in these systems. In this paper, we propose a novel multi-factor component tree loss function to resolve the topological issues in segmentation failures. The proposed loss function, computed based on the component trees, comprises two factors: image maxima vanishment and reconnection. We aim to discard the false positive connected components (FPCCs) and reconnect the disconnected true positive connected components (TPCCs) for each bone. Experiments conducted on a private bone scintigrams dataset show that our proposed method outperforms state-of-the-art approaches in dice similarity coefficient (DSC) while efficiently addressing topological issues at a low computational cost. Code is available at https://​github.​com/​MultiCTree/​MultiCTree.

Topological Data Analysis (TDA) represents a pioneering methodology for revealing intricate structures within complex datasets. This study introduces a novel framework for leveraging the Mapper algorithm in neuroimaging studies. The proposed framework involves mapping new independent test samples onto a pre-constructed train graph, thereby harnessing embedded topological features to derive novel insights about test data. Validation of the framework employs a neuroimaging dataset sourced from the Human Connectome Project (HCP), encompassing white matter brain features, and includes practical applications for predicting categorical and continuous outcomes. The results validate the framework efficacy in transferring knowledge from train data to predict unseen samples, underscoring its potential across diverse neuroimaging applications.

This research highlights the potential of the Mapper-based TDA framework in neuroimaging, paving the way for its application across diverse neuroscience domains to extract clinically relevant features, improve predictive accuracy, and enhance patient treatment strategies. By discerning intricate patterns within high-dimensional patient data, this approach enables precise diagnostics and personalized treatment strategies, contributing to more accurate disease profiling and optimizing therapeutic interventions in personalized medicine.

Functional dyspepsia (FD) is a complex condition identified by chronic indigestion without an obvious organic cause, characterized by diverse abdominal symptoms. Recent studies employing resting-state functional magnetic resonance imaging (rs-fMRI) have investigated gut-brain interactions in FD. These studies report altered functional connectivity patterns that are associated with the severity of the disease. The investigation of resting-state functional connectivity patterns involves defining connectivity nodes for subsequent graph-theory analyses, thus emphasizing the importance of brain parcellation. While traditional methods employ predefined brain atlases, fMRI-driven parcellation offers a more specific approach able to extract functionally homogeneous regions. In this study, we applied the Topological Data Analysis (TDA) tool of Mapper algorithm to rs-fMRI data to develop a whole-brain TDA-driven fMRI parcellation pipeline. This functional parcellation, applied in a group of healthy controls (HC), provides a reference for comparing network properties between HC and FD groups. We propose that the TDA Mapper is able to recover structure in rs-fMRI data, showing that topological complexes embedded in fMRI data could be identified and explored using this tool. Based on the brain network thus derived, we highlight the potential of applying graph analysis on rs-fMRI data to assess topological properties of brain connectivity, showing significant differences between groups in the functional parcel located in the frontal pole for nodal strength and degree.

White matter hyperintensities (WMH) are a hallmark of cerebrovascular disease and multiple sclerosis. Automated WMH segmentation methods enable quantitative analysis via estimation of total lesion load, spatial distribution of lesions, and number of lesions (i.e., number of connected components after thresholding), all of which are correlated with patient outcomes. While the two former measures can generally be estimated robustly, the number of lesions is highly sensitive to noise and segmentation mistakes – even when small connected components are eroded or disregarded. In this article, we present P-Count, an algebraic WMH counting tool based on persistent homology that accounts for the topological features of WM lesions in a robust manner. Using computational geometry, P-Count takes the persistence of connected components into consideration, effectively filtering out the noisy WMH positives, resulting in a more accurate and robust count of true lesions. We validated P-Count on the ISBI2015 longitudinal lesion segmentation dataset, where it produces significantly more accurate results than direct thresholding. Our code will be made publicly available upon acceptance.

The success of machine learning algorithms heavily relies on the quality of samples and the accuracy of their corresponding labels. However, building and maintaining large, high-quality datasets is an enormous task. This is especially true for biomedical data and for meta-sets that are compiled from smaller ones, as variations in image quality, labeling, reports, and archiving can lead to errors, inconsistencies, and repeated samples. Here, we show that the uniform manifold approximation and projection (UMAP) algorithm can find these anomalies essentially by forming independent clusters that are distinct from the main (“good”) data but similar to other points with the same error type. As a representative example, we apply UMAP to discover outliers in the publicly available ChestX-ray14, CheXpert, and MURA datasets. While the results are archival and retrospective and focus on radiological images, the graph-based methods work for any data type and will prove equally beneficial for curation at the time of dataset creation.

Fluorescence Imitating Brightfield Imaging (FIBI) represents an innovative approach in microscopy, providing real-time, non-destructive imaging of tissue without the need for the preparation of thin sections mounted on glass slides. The non-destructive nature of the technology permits tissue preservation for downstream analysis, which makes FIBI a promising alternative to traditional hematoxylin and eosin (H&E) staining in histopathology. Previous research has shown that FIBI can identify morphological features with similar or, in some cases, higher quality compared with H&E images. To comprehensively quantify the advantages and limitations of FIBI in tissue visualization, we propose a novel framework for characterizing the topological difference of FIBI and H&E slide pairs. Experiments are performed on slide pairs of FIBI and H&E imaging of the same tissue area. The proposed approach shows that FIBI can make morphological structures, like vessels, more salient and holds great promise as a complementary technique to H&E, offering novel insights into tissue architecture and potentially improving histopathological diagnostic accuracy.

Traditional Topological Data Analysis (TDA) methods, such as Persistent Homology (PH), rely on distance measures (e.g., cross-correlation, partial correlation, coherence, and partial coherence) that are symmetric by definition. While useful for studying topological patterns in functional brain connectivity, the main limitation of these methods is their inability to capture the directional dynamics - which are crucial for understanding effective brain connectivity. We propose the Causality-Based Topological Ranking (CBTR) method, which integrates Causal Inference (CI) to assess effective brain connectivity with Hodge Decomposition (HD) to rank brain regions based on their mutual influence. Our simulations confirm that the CBTR method accurately and consistently identifies hierarchical structures in multivariate time series data. Moreover, this method effectively identifies brain regions showing the most significant interaction changes with other regions during seizures using electroencephalogram (EEG) data. These results provide novel insights into the brain’s hierarchical organization and illuminate the impact of seizures on its dynamics.