Topological data analysis in medical imaging: current state of the art

Visualizing radiological data bias through persistence images

Persistence images, derived from topological data analysis, emerge as a powerful tool for visualizing and mitigating biases in radiological data interpretation and AI model development. This technique transforms complex topological features into stable, interpretable representations, offering unique insights into medical imaging data structure. By providing intuitive visualizations, persistence images enable the identification of subtle structural differences and potential biases in data acquisition, interpretation, and AI model training. Persistence images can also facilitate stratified sampling, matching statistics, and noise filtration, enhancing the accuracy and equity of radiological analysis. Despite challenges in computational complexity and workflow integration, persistence images show promise in developing more accurate, equitable, and trustworthy AI systems in radiology, potentially improving patient outcomes and personalized healthcare delivery.

Mitigating bias in radiology: The promise of topological data analysis and simplicial complexes

Topological Data Analysis (TDA) and simplicial complexes offer a novel approach to address biases in AI-assisted radiology. By capturing complex structures, n-way interactions, and geometric relationships in medical images, TDA enhances feature extraction, improves representation robustness, and increases interpretability. This mathematical framework has the potential to significantly improve the accuracy and fairness of radiological assessments, paving the way for more equitable patient care.

Persistence landscapes: Charting a path to unbiased radiological interpretation

Persistence landscapes, a sophisticated tool from topological data analysis, offer a promising approach to address biases in radiological interpretation and AI model development. By transforming complex topological features into statistically analyzable functions, they enable robust comparisons between populations and datasets. Persistence landscapes excel in noise filtration, fusion bias mitigation, and enhancing machine learning models. Despite challenges in computation and integration, they show potential to improve the accuracy and equity of radiological analysis, particularly in multi-modal imaging and AI-assisted interpretation.

Persistence barcodes: A novel approach to reducing bias in radiological analysis

Persistence barcodes emerge as a promising tool in radiological analysis, offering a novel approach to reduce bias and uncover hidden patterns in medical imaging. By leveraging topological data analysis, this technique provides a robust, multi-scale perspective on image features, potentially overcoming limitations in traditional methods and Graph Neural Networks. While challenges in interpretation and implementation remain, persistence barcodes show significant potential for improving diagnostic accuracy, standardization, and ultimately, patient outcomes in the evolving field of radiology.

Dual structure-aware image filterings for semi-supervised medical image segmentation

Semi-supervised image segmentation has attracted great attention recently. The key is how to leverage unlabeled images in the training process. Most methods maintain consistent predictions of the unlabeled images under variations (e.g., adding noise/perturbations, or creating alternative versions) in the image and/or model level. In most image-level variation, medical images often have prior structure information, which has not been well explored. In this paper, we propose novel dual structure-aware image filterings (DSAIF) as the image-level variations for semi-supervised medical image segmentation. Motivated by connected filtering that simplifies image via filtering in structure-aware tree-based image representation, we resort to the dual contrast invariant Max-tree and Min-tree representation. Specifically, we propose a novel connected filtering that removes topologically equivalent nodes (i.e. connected components) having no siblings in the Max/Min-tree. This results in two filtered images preserving topologically critical structure. Applying the proposed DSAIF to mutually supervised networks decreases the consensus of their erroneous predictions on unlabeled images. This helps to alleviate the confirmation bias issue of overfitting to noisy pseudo labels of unlabeled images, and thus effectively improves the segmentation performance. Extensive experimental results on three benchmark datasets demonstrate that the proposed method significantly/consistently outperforms some state-of-the-art methods. The source codes will be publicly available.

Scoping Review: Methods and Applications of Spatial Transcriptomics in Tumor Research

Spatial transcriptomics (ST) examines gene expression within its spatial context on tissue, linking morphology and function. Advances in ST resolution and throughput have led to an increase in scientific interest, notably in cancer research. This scoping study reviews the challenges and practical applications of ST, summarizing current methods, trends, and data analysis techniques for ST in neoplasm research. We analyzed 41 articles published by the end of 2023 alongside public data repositories. The findings indicate cancer biology is an important focus of ST research, with a rising number of studies each year. Visium (10x Genomics, Pleasanton, CA, USA) is the leading ST platform, and SCTransform from Seurat R library is the preferred method for data normalization and integration. Many studies incorporate additional data types like single-cell sequencing and immunohistochemistry. Common ST applications include discovering the composition and function of tumor tissues in the context of their heterogeneity, characterizing the tumor microenvironment, or identifying interactions between cells, including spatial patterns of expression and co-occurrence. However, nearly half of the studies lacked comprehensive data processing protocols, hindering their reproducibility. By recommending greater transparency in sharing analysis methods and adapting single-cell analysis techniques with caution, this review aims to improve the reproducibility and reliability of future studies in cancer research.

Dissecting glial scar formation by spatial point pattern and topological data analysis

Glial scar formation represents a fundamental response to central nervous system (CNS) injuries. It is mainly characterized by a well-defined spatial rearrangement of reactive astrocytes and microglia. The mechanisms underlying glial scar formation have been extensively studied, yet quantitative descriptors of the spatial arrangement of reactive glial cells remain limited. Here, we present a novel approach using point pattern analysis (PPA) and topological data analysis (TDA) to quantify spatial patterns of reactive glial cells after experimental ischemic stroke in mice. We provide open and reproducible tools using R and Julia to quantify spatial intensity, cell covariance and conditional distribution, cell-to-cell interactions, and short/long-scale arrangement, which collectively disentangle the arrangement patterns of the glial scar. This approach unravels a substantial divergence in the distribution of GFAP+ and IBA1+ cells after injury that conventional analysis methods cannot fully characterize. PPA and TDA are valuable tools for studying the complex spatial arrangement of reactive glia and other nervous cells following CNS injuries and have potential applications for evaluating glial-targeted restorative therapies.

Beyond pixels: Graph filtration learning unveils new dimensions in hepatocellular carcinoma imaging

This editorial explores the emerging role of Graph Filtration Learning (GFL) in revolutionizing Hepatocellular carcinoma (HCC) imaging analysis. As traditional pixel-based methods reach their limits, GFL offers a novel approach to capture complex topological features in medical images. By representing imaging data as graphs and leveraging persistent homology, GFL unveils new dimensions of information that were previously inaccessible. This paradigm shift holds promise for enhancing HCC diagnosis, treatment planning, and prognostication. We discuss the principles of GFL, its potential applications in HCC imaging, and the challenges in translating this innovative technique into clinical practice.

Advancing Precision Medicine: Algebraic Topology and Differential Geometry in Radiology and Computational Pathology

Precision medicine aims to provide personalized care based on individual patient characteristics, rather than guideline-directed therapies for groups of diseases or patient demographics. Images-both radiology- and pathology-derived-are a major source of information on presence, type, and status of disease. Exploring the mathematical relationship of pixels in medical imaging ("radiomics") and cellular-scale structures in digital pathology slides ("pathomics") offers powerful tools for extracting both qualitative and, increasingly, quantitative data. These analytical approaches, however, may be significantly enhanced by applying additional methods arising from fields of mathematics such as differential geometry and algebraic topology that remain underexplored in this context. Geometry's strength lies in its ability to provide precise local measurements, such as curvature, that can be crucial for identifying abnormalities at multiple spatial levels. These measurements can augment the quantitative features extracted in conventional radiomics, leading to more nuanced diagnostics. By contrast, topology serves as a robust shape descriptor, capturing essential features such as connected components and holes. The field of topological data analysis was initially founded to explore the shape of data, with functional network connectivity in the brain being a prominent example. Increasingly, its tools are now being used to explore organizational patterns of physical structures in medical images and digitized pathology slides. By leveraging tools from both differential geometry and algebraic topology, researchers and clinicians may be able to obtain a more comprehensive, multi-layered understanding of medical images and contribute to precision medicine's armamentarium.

Prediction of nanocomposite properties and process optimization using persistent homology and machine learning

Physical property prediction and synthesis process optimization are key targets in material informatics. In this study, we propose a machine learning approach that utilizes ridge regression to predict the oxygen permeability at fuel cell electrode surfaces and determine the optimal process temperature. These predictions are based on a persistence diagram derived from tomographic images captured using transmission electron microscopy (TEM). Through machine learning analysis of the complex structures present in the Pt/CeO2 nanocomposites, we discovered that l2 regularization considering diverse structural elements is more appropriate than l1 regularization (sparse modeling). Notably, our model successfully captured the activation energy of oxygen permeability, a phenomenon that could not be solely explained by the geometric feature of the Betti numbers, as demonstrated in a previous study. The correspondence between the ridge regression coefficient and persistence diagram revealed the formation process of the local and three-dimensional structures of CeO2 and their contributions to pre-exponential factor and activation energies. This analysis facilitated the determination of the annealing temperature required to achieve the optimal structure and accurately predict the physical properties.

A novel multi-task machine learning classifier for rare disease patterning using cardiac strain imaging data

To provide accurate predictions, current machine learning-based solutions require large, manually labeled training datasets. We implement persistent homology (PH), a topological tool for studying the pattern of data, to analyze echocardiography-based strain data and differentiate between rare diseases like constrictive pericarditis (CP) and restrictive cardiomyopathy (RCM). Patient population (retrospectively registered) included those presenting with heart failure due to CP (n = 51), RCM (n = 47), and patients without heart failure symptoms (n = 53). Longitudinal, radial, and circumferential strains/strain rates for left ventricular segments were processed into topological feature vectors using Machine learning PH workflow. In differentiating CP and RCM, the PH workflow model had a ROC AUC of 0.94 (Sensitivity = 92%, Specificity = 81%), compared with the GLS model AUC of 0.69 (Sensitivity = 65%, Specificity = 66%). In differentiating between all three conditions, the PH workflow model had an AUC of 0.83 (Sensitivity = 68%, Specificity = 84%), compared with the GLS model AUC of 0.68 (Sensitivity = 52% and Specificity = 76%). By employing persistent homology to differentiate the "pattern" of cardiac deformations, our machine-learning approach provides reasonable accuracy when evaluating small datasets and aids in understanding and visualizing patterns of cardiac imaging data in clinically challenging disease states.

Topological Deep Learning: A New Dimension in Gastroenterology for Metabolic Dysfunction-Associated Fatty Liver

Topological deep learning (TDL) introduces a novel approach to enhancing diagnostic and monitoring processes for metabolic dysfunction-associated fatty liver disease (MAFLD), a condition that is increasingly prevalent globally and a leading cause of liver transplantation. This editorial explores the integration of topology, a branch of mathematics focused on spatial properties preserved under continuous transformations, with deep learning models to improve the accuracy and efficacy of MAFLD diagnosis and staging from medical imaging. TDL's ability to recognize complex patterns in imaging data that traditional methods might miss can lead to earlier and more precise detection, personalized treatment, and potentially better patient outcomes. Challenges remain, particularly regarding the computational demands and the interpretability of TDL outputs, which necessitate further research and development for clinical application. The potential of TDL to transform the gastroenterological landscape marks a significant step toward the incorporation of advanced mathematical methodologies in medical practice.

A Framework for Interpretability in Machine Learning for Medical Imaging

Interpretability for machine learning models in medical imaging (MLMI) is an important direction of research. However, there is a general sense of murkiness in what interpretability means. Why does the need for interpretability in MLMI arise? What goals does one actually seek to address when interpretability is needed? To answer these questions, we identify a need to formalize the goals and elements of interpretability in MLMI. By reasoning about real-world tasks and goals common in both medical image analysis and its intersection with machine learning, we identify five core elements of interpretability: localization, visual recognizability, physical attribution, model transparency, and actionability. From this, we arrive at a framework for interpretability in MLMI, which serves as a step-by-step guide to approaching interpretability in this context. Overall, this paper formalizes interpretability needs in the context of medical imaging, and our applied perspective clarifies concrete MLMI-specific goals and considerations in order to guide method design and improve real-world usage. Our goal is to provide practical and didactic information for model designers and practitioners, inspire developers of models in the medical imaging field to reason more deeply about what interpretability is achieving, and suggest future directions of interpretability research.

Imaging-based deep learning in kidney diseases: recent progress and future prospects

Kidney diseases result from various causes, which can generally be divided into neoplastic and non-neoplastic diseases. Deep learning based on medical imaging is an established methodology for further data mining and an evolving field of expertise, which provides the possibility for precise management of kidney diseases. Recently, imaging-based deep learning has been widely applied to many clinical scenarios of kidney diseases including organ segmentation, lesion detection, differential diagnosis, surgical planning, and prognosis prediction, which can provide support for disease diagnosis and management. In this review, we will introduce the basic methodology of imaging-based deep learning and its recent clinical applications in neoplastic and non-neoplastic kidney diseases. Additionally, we further discuss its current challenges and future prospects and conclude that achieving data balance, addressing heterogeneity, and managing data size remain challenges for imaging-based deep learning. Meanwhile, the interpretability of algorithms, ethical risks, and barriers of bias assessment are also issues that require consideration in future development. We hope to provide urologists, nephrologists, and radiologists with clear ideas about imaging-based deep learning and reveal its great potential in clinical practice.Critical relevance statement The wide clinical applications of imaging-based deep learning in kidney diseases can help doctors to diagnose, treat, and manage patients with neoplastic or non-neoplastic renal diseases.Key points• Imaging-based deep learning is widely applied to neoplastic and non-neoplastic renal diseases.• Imaging-based deep learning improves the accuracy of the delineation, diagnosis, and evaluation of kidney diseases.• The small dataset, various lesion sizes, and so on are still challenges for deep learning.

Novel dimensionality reduction method, Taelcore, enhances lung transplantation risk prediction

In this work, we present a new approach to predict the risk of acute cellular rejection (ACR) after lung transplantation by using machine learning algorithms, such as Multilayer Perceptron (MLP) or Autoencoder (AE), and combining them with topological data analysis (TDA) tools. Our proposed method, named topological autoencoder with best linear combination for optimal reduction of embeddings (Taelcore), effectively reduces the dimensionality of high-dimensional datasets and yields better results compared to other models. We validate the effectiveness of Taelcore in reducing the prediction error rate on four datasets. Furthermore, we demonstrate that Taelcore's topological improvements have a positive effect on the majority of the machine learning algorithms used. By providing a new way to diagnose patients and detect complications early, this work contributes to improved clinical outcomes in lung transplantation.

The Value of Topological Radiomics Analysis in Predicting Malignant Risk of Pulmonary Ground-Glass Nodules: A Multi-Center Study

BACKGROUND

Early detection and accurate differentiation of malignant ground-glass nodules (GGNs) in lung CT scans are crucial for the effective treatment of lung adenocarcinoma. However, existing imaging diagnostic methods often struggle to distinguish between benign and malignant GGNs in the early stages. This study aims to predict the malignancy risk of GGNs observed in lung CT scans by applying two radiomics methods: topological data analysis and texture analysis.

METHODS

A retrospective analysis was conducted on 3223 patients from two centers between January 2018 and June2023. The dataset was divided into training, testing, and validation sets to ensure robust model development and validation. We developed topological features applied to GGNs using radiomics analysis based on homology. This innovative approach emphasizes the integration of topological information, capturing complex geometric and spatial relationships within GGNs. By combining machine learning and deep learning algorithms, we established a predictive model that integrates clinical parameters, previous radiomics features, and topological radiomics features.

RESULTS

Incorporating topological radiomics into our model significantly enhanced the ability to distinguish between benign and malignant GGNs. The topological radiomics model achieved areas under the curve (AUC) of 0.85 and 0.862 in two independent validation sets, outperforming previous radiomics models. Furthermore, this model demonstrated higher sensitivity compared to models based solely on clinical parameters, with sensitivities of 80.7% in validation set 1 and 82.3% in validation set 2. The most comprehensive model, which combined clinical parameters, previous radiomics features, and topological radiomics features, achieved the highest AUC value of 0.879 across all datasets.

CONCLUSION

This study validates the potential of topological radiomics in improving the predictive performance for distinguishing between benign and malignant GGNs. By integrating topological features with previous radiomics and clinical parameters, our comprehensive model provides a more accurate and reliable basis for developing treatment strategies for patients with GGNs.

Predictors of Pathological Gastroesophageal Reflux among Emirati Patients with Reflux Symptoms Who Undergo Wireless pH Monitoring

Background: Diagnosis of gastroesophageal reflux disease (GERD) relies on recognizing symptoms of reflux and mucosal changes during esophagogastroduodenoscopy. The desired response to acid suppression therapy is reliable resolution of GERD symptoms; however, these are not always reliable, hence the need for pH testing in unclear cases. Our objective was to identify potential predictors of a high DeMeester score among patients with potential GERD symptoms to identify patients most likely to have pathological GERD. Methods: We conducted a retrospective case-control study on patients who underwent wireless pH monitoring from January 2020 to April 2022. Cases were patients with a high DeMeester score (more than 14.7), indicating pathological reflux, and controls were those without. We collected clinical and demographic data, including age, sex, body mass index (BMI), smoking status, non-steroidal anti-inflammatory drugs (NSAIDs) use, and presence of atypical symptoms. Results: 86 patients were enrolled in the study. 46 patients with high DeMeester scores were considered cases, and 40 patients with DeMeester scores less than 14.7 were considered controls. Esophagitis (grade A) was found in 41.1% of the cases and in 22.5% of the control group. In our study, age of more than 50 years compared with age of 20-29 years and being overweight appeared to be predictors of true pathological reflux among patients with reflux symptoms who underwent wireless pH monitoring. Conclusion: Age above 50 years compared with age between 20-29 years and being overweight appeared to be predictors of true pathological reflux among patients with reflux symptoms who underwent wireless oesophageal pH monitoring. The presence of oesophagitis was approximately four times more likely to be associated with true pathological reflux.

Spatiochemical Characterization of the Pancreas Using Mass Spectrometry Imaging and Topological Data Analysis

Mass Spectrometry Imaging (MSI) is a technique used to identify the spatial distribution of molecules in tissues. An MSI experiment results in large amounts of high dimensional data, so efficient computational methods are needed to analyze the output. Topological Data Analysis (TDA) has proven to be effective in all kinds of applications. TDA focuses on the topology of the data in high dimensional space. Looking at the shape in a high dimensional data set can lead to new or different insights. In this work, we investigate the use of Mapper, a form of TDA, applied on MSI data. Mapper is used to find data clusters inside two healthy mouse pancreas data sets. The results are compared to previous work using UMAP for MSI data analysis on the same data sets. This work finds that the proposed technique discovers the same clusters in the data as UMAP and is also able to uncover new clusters, such as an additional ring structure inside the pancreatic islets and a better defined cluster containing blood vessels. The technique can be used for a large variety of data types and sizes and can be optimized for specific applications. It is also computationally similar to UMAP for clustering. Mapper is a very interesting method, especially its use in biomedical applications.