Topological data analysis in biomedicine: A review

Skaf, Yara; Laubenbacher, Reinhard

doi:10.1016/j.jbi.2022.104082

Cited by 59 publications

(39 citation statements)

References 103 publications

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“…Of note, the TDA Applications Library [17] catalogs hundreds of compelling applications of TDA in various fields. For a comprehensive survey of TDA methods in biomedicine, see the survey [41].…”

Section: Tda In Computer Visionmentioning

confidence: 99%

Topology-Aware Focal Loss for 3D Image Segmentation

Demir

Massaad

Kızıltan

2023

Preprint

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The efficacy of segmentation algorithms is frequently compromised by topological errors like overlapping regions, disrupted connections, and voids. To tackle this problem, we introduce a novel loss function, namely Topology-Aware Focal Loss (TAFL), that incorporates the conventional Focal Loss with a topological constraint term based on the Wasserstein distance between the ground truth and predicted segmentation masks' persistence diagrams. By enforcing identical topology as the ground truth, the topological constraint can effectively resolve topological errors, while Focal Loss tackles class imbalance. We begin by constructing persistence diagrams from filtered cubical complexes of the ground truth and predicted segmentation masks. We subsequently utilize the Sinkhorn-Knopp algorithm to determine the optimal transport plan between the two persistence diagrams. The resultant transport plan minimizes the cost of transporting mass from one distribution to the other and provides a mapping between the points in the two persistence diagrams. We then compute the Wasserstein distance based on this travel plan to measure the topological dissimilarity between the ground truth and predicted masks. We evaluate our approach by training a 3D U-Net with the MICCAI Brain Tumor Segmentation (BraTS) challenge validation dataset, which requires accurate segmentation of 3D MRI scans that integrate various modalities for the precise identification and tracking of malignant brain tumors. Then, we demonstrate that the quality of segmentation performance is enhanced by regularizing the focal loss through the addition of a topological constraint as a penalty term.

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Section: Tda In Computer Visionmentioning

confidence: 99%

Topology-Aware Focal Loss for 3D Image Segmentation

Demir

Massaad

Kızıltan

2023

Preprint

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“…8−10 For the latest work on TDA for biomedical applications, we refer the reader to Singh et al (2023) and Skaf and Laubenbacher (2022). 8,11 TDA is based on topology, which is the mathematical study of shape. In fields such as biology and medicine, much information can be obtained from looking at the shape of objects, which can lead to an increase in understanding.…”

Section: ■ Mass Spectrometry Imagingmentioning

confidence: 99%

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

Derwae,

Nijs,

Geysels

et al. 2023

Anal. Chem.

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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.

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“…Over the last few years, rapid advancements in artificial intelligence and deep learning, in particular, have resulted in a surge of publications in medical image analysis fields. Establishing innovative, effective diagnostic support tools could improve disease detection, such that physicians can make more accurate diagnostic decisions to quickly treat patients [ 1 , 2 ]. Physical exam findings, laboratory testing, and expert-driven interpretation of ultrasonography, computed tomography (CT), and magnetic resonance imaging (MRI) are used in clinical practice for detecting a variety of conditions.…”

Section: Introductionmentioning

confidence: 99%

“…TDA solves the issues of dimensionality (the large number of predictors relative to the number of patients from whom data was collected) and metric mismatches (such as the aforementioned unit of measurement). In a coordinate-free approach (where metrics are not needed or used), this branch of data science defines the dataset structure as shapes; these shapes are created by connecting pieces of point data or loops within the dataset, profiling the data as point clouds with a notion of distance or similarity [ 1 – 4 ]. Datasets collected on the same biological systems using different technological platforms can thus be directly compared.…”

Section: Introductionmentioning

confidence: 99%

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

Singh

Farrelly²,

Hathaway

et al. 2023

Insights Imaging

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Machine learning, and especially deep learning, is rapidly gaining acceptance and clinical usage in a wide range of image analysis applications and is regarded as providing high performance in detecting anatomical structures and identification and classification of patterns of disease in medical images. However, there are many roadblocks to the widespread implementation of machine learning in clinical image analysis, including differences in data capture leading to different measurements, high dimensionality of imaging and other medical data, and the black-box nature of machine learning, with a lack of insight into relevant features. Techniques such as radiomics have been used in traditional machine learning approaches to model the mathematical relationships between adjacent pixels in an image and provide an explainable framework for clinicians and researchers. Newer paradigms, such as topological data analysis (TDA), have recently been adopted to design and develop innovative image analysis schemes that go beyond the abilities of pixel-to-pixel comparisons. TDA can automatically construct filtrations of topological shapes of image texture through a technique known as persistent homology (PH); these features can then be fed into machine learning models that provide explainable outputs and can distinguish different image classes in a computationally more efficient way, when compared to other currently used methods. The aim of this review is to introduce PH and its variants and to review TDA’s recent successes in medical imaging studies.

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Topological data analysis in biomedicine: A review

Cited by 59 publications

References 103 publications

Topology-Aware Focal Loss for 3D Image Segmentation

Topology-Aware Focal Loss for 3D Image Segmentation

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

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

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