🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.001755s)

  1. Topological Data Analysis in Medical Imaging: Current State of the Art (2023)

    Yashbir Singh, Colleen M. Farrelly, Quincy A. Hathaway, Tim Leiner, Jaidip Jagtap, Gunnar E. Carlsson, Bradley J. Erickson
    Abstract 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.

  2. Algebraic Topology-Based Machine Learning Using MRI Predicts Outcomes in Primary Sclerosing Cholangitis (2022)

    Yashbir Singh, William A. Jons, John E. Eaton, Mette Vesterhus, Tom Karlsen, Ida Bjoerk, Andreas Abildgaard, Kristin Kaasen Jorgensen, Folseraas Trine, Derek Little, Aliya F. Gulamhusein, Kosta Petrovic, Anne Negard, Gian Marco Conte, Joseph D. Sobek, Jaidip Jagtap, Sudhakar K. Venkatesh, Gregory J. Gores, Nicholas F. LaRusso, Konstantinos N. Lazaridis, Bradley J. Erickson
    Abstract Background: Primary sclerosing cholangitis (PSC) is a chronic cholestatic liver disease that can lead to cirrhosis and hepatic decompensation. However, predicting future outcomes in patients with PSC is challenging. Our aim was to extract magnetic resonance imaging (MRI) features that predict the development of hepatic decompensation by applying algebraic topology-based machine learning (ML). Methods: We conducted a retrospective multicenter study among adults with large duct PSC who underwent MRI. A topological data analysis-inspired nonlinear framework was used to predict the risk of hepatic decompensation, which was motivated by algebraic topology theory-based ML. The topological representations (persistence images) were employed as input for classifcation to predict who developed early hepatic decompensation within one year after their baseline MRI. Results: We reviewed 590 patients; 298 were excluded due to poor image quality or inadequate liver coverage, leaving 292 potentially eligible subjects, of which 169 subjects were included in the study. We trained our model using contrast-enhanced delayed phase T1-weighted images on a single center derivation cohort consisting of 54 patients (hepatic decompensation, n = 21; no hepatic decompensation, n = 33) and a multicenter independent validation cohort of 115 individuals (hepatic decompensation, n = 31; no hepatic decompensation, n = 84). When our model was applied in the independent validation cohort, it remained predictive of early hepatic decompensation (area under the receiver operating characteristic curve = 0.84). Conclusions: Algebraic topology-based ML is a methodological approach that can predict outcomes in patients with PSC and has the potential for application in other chronic liver diseases