🍩 Database of Original & Non-Theoretical Uses of Topology

(found 21 matches in 0.004714s)

  1. Imaging-Based Representation and Stratification of Intra-Tumor Heterogeneity via Tree-Edit Distance (2022)

    Lara Cavinato, Matteo Pegoraro, Alessandra Ragni, Francesca Ieva
    Abstract Personalized medicine is the future of medical practice. In oncology, tumor heterogeneity assessment represents a pivotal step for effective treatment planning and prognosis prediction. Despite new procedures for DNA sequencing and analysis, non-invasive methods for tumor characterization are needed to impact on daily routine. On purpose, imaging texture analysis is rapidly scaling, holding the promise to surrogate histopathological assessment of tumor lesions. In this work, we propose a tree-based representation strategy for describing intra-tumor heterogeneity of patients affected by metastatic cancer. We leverage radiomics information extracted from PET/CT imaging and we provide an exhaustive and easily readable summary of the disease spreading. We exploit this novel patient representation to perform cancer subtyping according to hierarchical clustering technique. To this purpose, a new heterogeneity-based distance between trees is defined and applied to a case study of prostate cancer. Clusters interpretation is explored in terms of concordance with severity status, tumor burden and biological characteristics. Results are promising, as the proposed method outperforms current literature approaches. Ultimately, the proposed method draws a general analysis framework that would allow to extract knowledge from daily acquired imaging data of patients and provide insights for effective treatment planning.

  2. Persistent Homology for Breast Tumor Classification Using Mammogram Scans (2022)

    Aras Asaad, Dashti Ali, Taban Majeed, Rasber Rashid
    Abstract An Important tool in the field topological data analysis is known as persistent Homology (PH) which is used to encode abstract representation of the homology of data at different resolutions in the form of persistence diagram (PD). In this work we build more than one PD representation of a single image based on a landmark selection method, known as local binary patterns, that encode different types of local textures from images. We employed different PD vectorizations using persistence landscapes, persistence images, persistence binning (Betti Curve) and statistics. We tested the effectiveness of proposed landmark based PH on two publicly available breast abnormality detection datasets using mammogram scans. Sensitivity of landmark based PH obtained is over 90% in both datasets for the detection of abnormal breast scans. Finally, experimental results give new insights on using different types of PD vectorizations which help in utilising PH in conjunction with machine learning classifiers.

  3. Genomics Data Analysis via Spectral Shape and Topology (2022)

    Erik J. Amézquita, Farzana Nasrin, Kathleen M. Storey, Masato Yoshizawa
    Abstract Mapper, a topological algorithm, is frequently used as an exploratory tool to build a graphical representation of data. This representation can help to gain a better understanding of the intrinsic shape of high-dimensional genomic data and to retain information that may be lost using standard dimension-reduction algorithms. We propose a novel workflow to process and analyze RNA-seq data from tumor and healthy subjects integrating Mapper and differential gene expression. Precisely, we show that a Gaussian mixture approximation method can be used to produce graphical structures that successfully separate tumor and healthy subjects, and produce two subgroups of tumor subjects. A further analysis using DESeq2, a popular tool for the detection of differentially expressed genes, shows that these two subgroups of tumor cells bear two distinct gene regulations, suggesting two discrete paths for forming lung cancer, which could not be highlighted by other popular clustering methods, including t-SNE. Although Mapper shows promise in analyzing high-dimensional data, building tools to statistically analyze Mapper graphical structures is limited in the existing literature. In this paper, we develop a scoring method using heat kernel signatures that provides an empirical setting for statistical inferences such as hypothesis testing, sensitivity analysis, and correlation analysis.

  4. Topological Data Analysis Distinguishes Parameter Regimes in the Anderson-Chaplain Model of Angiogenesis (2021)

    John T. Nardini, Bernadette J. Stolz, Kevin B. Flores, Heather A. Harrington, Helen M. Byrne
    Abstract Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound healing, and contributes to many diseases including cancer and rheumatoid arthritis. The structure of the resulting vessel networks determines their ability to deliver nutrients and remove waste products from biological tissues. Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data. Specifically, we propose a topological data analysis (TDA) pipeline for systematic analysis of the model. TDA is a vibrant and relatively new field of computational mathematics for studying the shape of data. We compute topological and standard descriptors of model simulations generated by different parameter values. We show that TDA of model simulation data stratifies parameter space into regions with similar vessel morphology. The methodologies proposed here are widely applicable to other synthetic and experimental data including wound healing, development, and plant biology.

  5. The Shape of Cancer Relapse: Topological Data Analysis Predicts Recurrence in Paediatric Acute Lymphoblastic Leukaemia (2021)

    Salvador Chulián, Bernadette J. Stolz, Álvaro Martínez-Rubio, Cristina Blázquez Goñi, Juan F. Rodríguez Gutiérrez, Teresa Caballero Velázquez, Águeda Molinos Quintana, Manuel Ramírez Orellana, Ana Castillo Robleda, José Luis Fuster Soler, Alfredo Minguela Puras, María Victoria Martínez Sánchez, María Rosa, Víctor M. Pérez-García, Helen Byrne
    Abstract Acute Lymphoblastic Leukaemia (ALL) is the most frequent paediatric cancer. Modern therapies have improved survival rates, but approximately 15-20 % of patients relapse. At present, patients’ risk of relapse are assessed by projecting high-dimensional flow cytometry data onto a subset of biomarkers and manually estimating the shape of this reduced data. Here, we apply methods from topological data analysis (TDA), which quantify shape in data via features such as connected components and loops, to pre-treatment ALL datasets with known outcomes. We combine these fully unsupervised analyses with machine learning to identify features in the pre-treatment data that are prognostic for risk of relapse. We find significant topological differences between relapsing and non-relapsing patients and confirm the predictive power of CD10, CD20, CD38, and CD45. Further, we are able to use the TDA descriptors to predict patients who relapsed. We propose three prognostic pipelines that readily extend to other haematological malignancies. Teaser Topology reveals features in flow cytometry data which predict relapse of patients with acute lymphoblastic leukemia

  6. Classification of Skin Lesions by Topological Data Analysis Alongside With Neural Network (2020)

    Naiereh Elyasi, Mehdi Hosseini Moghadam
    Abstract In this paper we use TDA mapper alongside with deep convolutional neural networks in the classification of 7 major skin diseases. First we apply kepler mapper with neural network as one of its filter steps to classify the dataset HAM10000. Mapper visualizes the classification result by a simplicial complex, where neural network can not do this alone, but as a filter step neural network helps to classify data better. Furthermore we apply TDA mapper and persistent homology to understand the weights of layers of mobilenet network in different training epochs of HAM10000. Also we use persistent diagrams to visualize the results of analysis of layers of mobilenet network.

  7. Identification of Relevant Genetic Alterations in Cancer Using Topological Data Analysis (2020)

    Raúl Rabadán, Yamina Mohamedi, Udi Rubin, Tim Chu, Adam N. Alghalith, Oliver Elliott, Luis Arnés, Santiago Cal, Álvaro J. Obaya, Arnold J. Levine, Pablo G. Cámara
    Abstract Large-scale cancer genomic studies enable the systematic identification of mutations that lead to the genesis and progression of tumors, uncovering the underlying molecular mechanisms and potential therapies. While some such mutations are recurrently found in many tumors, many others exist solely within a few samples, precluding detection by conventional recurrence-based statistical approaches. Integrated analysis of somatic mutations and RNA expression data across 12 tumor types reveals that mutations of cancer genes are usually accompanied by substantial changes in expression. We use topological data analysis to leverage this observation and uncover 38 elusive candidate cancer-associated genes, including inactivating mutations of the metalloproteinase ADAMTS12 in lung adenocarcinoma. We show that ADAMTS12−/− mice have a five-fold increase in the susceptibility to develop lung tumors, confirming the role of ADAMTS12 as a tumor suppressor gene. Our results demonstrate that data integration through topological techniques can increase our ability to identify previously unreported cancer-related alterations., Rare cancer mutations are often missed using recurrence-based statistical approaches, but are usually accompanied by changes in expression. Here the authors leverage this information to uncover several elusive candidate cancer-associated genes using topological data analysis.

  8. Prediction in Cancer Genomics Using Topological Signatures and Machine Learning (2020)

    Georgina Gonzalez, Arina Ushakova, Radmila Sazdanovic, Javier Arsuaga
    Abstract Copy Number Aberrations, gains and losses of genomic regions, are a hallmark of cancer and can be experimentally detected using microarray comparative genomic hybridization (aCGH). In previous works, we developed a topology based method to analyze aCGH data whose output are regions of the genome where copy number is altered in patients with a predetermined cancer phenotype. We call this method Topological Analysis of array CGH (TAaCGH). Here we combine TAaCGH with machine learning techniques to build classifiers using copy number aberrations. We chose logistic regression on two different binary phenotypes related to breast cancer to illustrate this approach. The first case consists of patients with over-expression of the ERBB2 gene. Over-expression of ERBB2 is commonly regulated by a copy number gain in chromosome arm 17q. TAaCGH found the region 17q11-q22 associated with the phenotype and using logistic regression we reduced this region to 17q12-q21.31 correctly classifying 78% of the ERBB2 positive individuals (sensitivity) in a validation data set. We also analyzed over-expression in Estrogen Receptor (ER), a second phenotype commonly observed in breast cancer patients and found that the region 5p14.3-12 together with six full arms were associated with the phenotype. Our method identified 4p, 6p and 16q as the strongest predictors correctly classifying 76% of ER positives in our validation data set. However, for this set there was a significant increase in the false positive rate (specificity). We suggest that topological and machine learning methods can be combined for prediction of phenotypes using genetic data.

  14. Persistent Homology Index as a Robust Quantitative Measure of Immunohistochemical Scoring (2017)

    Akihiro Takiyama, Takashi Teramoto, Hiroaki Suzuki, Katsushige Yamashiro, Shinya Tanaka
    Abstract Immunohistochemical data (IHC) plays an important role in clinical practice, and is typically gathered in a semi-quantitative fashion that relies on some degree of visual scoring. However, visual scoring by a pathologist is inherently subjective and manifests both intra-observer and inter-observer variability. In this study, we introduce a novel computer-aided quantification methodology for immunohistochemical scoring that uses the algebraic concept of persistent homology. Using 8 bit grayscale image data derived from 90 specimens of invasive ductal carcinoma of the breast, stained for the replicative marker Ki-67, we computed homology classes. These were then compared to nuclear grades and the Ki-67 labeling indices obtained by visual scoring. Three metrics for IHC staining were newly defined: Persistent Homology Index (PHI), center coordinates of positive and negative groups, and the sum of squares within groups (WSS). This study demonstrates that PHI, a novel index for immunohistochemical labeling using persistent homology, can produce highly similar data to that generated by a pathologist using visual evaluation. The potential benefits associated with our novel technology include both improved quantification and reproducibility. Since our method reflects cellularity and nuclear atypia, it carries a greater quantity of biologic data compared to conventional evaluation using Ki-67.

  15. Topological Data Analysis for Discovery in Preclinical Spinal Cord Injury and Traumatic Brain Injury (2015)

    Jessica L. Nielson, Jesse Paquette, Aiwen W. Liu, Cristian F. Guandique, C. Amy Tovar, Tomoo Inoue, Karen-Amanda Irvine, John C. Gensel, Jennifer Kloke, Tanya C. Petrossian, Pek Y. Lum, Gunnar E. Carlsson, Geoffrey T. Manley, Wise Young, Michael S. Beattie, Jacqueline C. Bresnahan, Adam R. Ferguson
    Abstract Data-driven discovery in complex neurological disorders has potential to extract meaningful knowledge from large, heterogeneous datasets. Here the authors apply topological data analysis to assess therapeutic effects in preclinical traumatic brain injury and spinal cord injury research studies.

  16. Identification of Copy Number Aberrations in Breast Cancer Subtypes Using Persistence Topology (2015)

    Javier Arsuaga, Tyler Borrman, Raymond Cavalcante, Georgina Gonzalez, Catherine Park
    Abstract DNA copy number aberrations (CNAs) are of biological and medical interest because they help identify regulatory mechanisms underlying tumor initiation and evolution. Identification of tumor-driving CNAs (driver CNAs) however remains a challenging task, because they are frequently hidden by CNAs that are the product of random events that take place during tumor evolution. Experimental detection of CNAs is commonly accomplished through array comparative genomic hybridization (aCGH) assays followed by supervised and/or unsupervised statistical methods that combine the segmented profiles of all patients to identify driver CNAs. Here, we extend a previously-presented supervised algorithm for the identification of CNAs that is based on a topological representation of the data. Our method associates a two-dimensional (2D) point cloud with each aCGH profile and generates a sequence of simplicial complexes, mathematical objects that generalize the concept of a graph. This representation of the data permits segmenting the data at different resolutions and identifying CNAs by interrogating the topological properties of these simplicial complexes. We tested our approach on a published dataset with the goal of identifying specific breast cancer CNAs associated with specific molecular subtypes. Identification of CNAs associated with each subtype was performed by analyzing each subtype separately from the others and by taking the rest of the subtypes as the control. Our results found a new amplification in 11q at the location of the progesterone receptor in the Luminal A subtype. Aberrations in the Luminal B subtype were found only upon removal of the basal-like subtype from the control set. Under those conditions, all regions found in the original publication, except for 17q, were confirmed; all aberrations, except those in chromosome arms 8q and 12q were confirmed in the basal-like subtype. These two chromosome arms, however, were detected only upon removal of three patients with exceedingly large copy number values. More importantly, we detected 10 and 21 additional regions in the Luminal B and basal-like subtypes, respectively. Most of the additional regions were either validated on an independent dataset and/or using GISTIC. Furthermore, we found three new CNAs in the basal-like subtype: a combination of gains and losses in 1p, a gain in 2p and a loss in 14q. Based on these results, we suggest that topological approaches that incorporate multiresolution analyses and that interrogate topological properties of the data can help in the identification of copy number changes in cancer.

  18. Topological Descriptors of Histology Images (2014)

    Nikhil Singh, Heather D. Couture, J. S. Marron, Charles Perou, Marc Niethammer
    Abstract The purpose of this study is to investigate architectural characteristics of cell arrangements in breast cancer histology images. We propose the use of topological data analysis to summarize the geometric information inherent in tumor cell arrangements. Our goal is to use this information as signatures that encode robust summaries of cell arrangements in tumor tissue as captured through histology images. In particular, using ideas from algebraic topology we construct topological descriptors based on cell nucleus segmentations such as persistency charts and Betti sequences. We assess their performance on the task of discriminating the breast cancer subtypes Basal, Luminal A, Luminal B and HER2. We demonstrate that the topological features contain useful complementary information to image-appearance based features that can improve discriminatory performance of classifiers.

  19. Extracting Insights From the Shape of Complex Data Using Topology (2013)

    P. Y. Lum, G. Singh, A. Lehman, T. Ishkanov, M. Vejdemo-Johansson, M. Alagappan, J. Carlsson, G. Carlsson
    Abstract This paper applies topological methods to study complex high dimensional data sets by extracting shapes (patterns) and obtaining insights about them. Our method combines the best features of existing standard methodologies such as principal component and cluster analyses to provide a geometric representation of complex data sets. Through this hybrid method, we often find subgroups in data sets that traditional methodologies fail to find. Our method also permits the analysis of individual data sets as well as the analysis of relationships between related data sets. We illustrate the use of our method by applying it to three very different kinds of data, namely gene expression from breast tumors, voting data from the United States House of Representatives and player performance data from the NBA, in each case finding stratifications of the data which are more refined than those produced by standard methods.

  20. Topological Analysis of Gene Expression Arrays Identifies High Risk Molecular Subtypes in Breast Cancer (2012)

    Javier Arsuaga, Nils A. Baas, Daniel DeWoskin, Hideaki Mizuno, Aleksandr Pankov, Catherine Park
    Abstract Genomic technologies measure thousands of molecular signals with the goal of understanding complex biological processes. In cancer these molecular signals have been used to characterize disease subtypes, signaling pathways and to identify subsets of patients with specific prognosis. However molecular signals for any disease type are so vast and complex that novel mathematical approaches are required for further analyses. Persistent and computational homology provide a new method for these analyses. In our previous work we presented a new homology-based supervised classification method to identify copy number aberrations from comparative genomic hybridization arrays. In this work we first propose a theoretical framework for our classification method and second we extend our analysis to gene expression data. We analyze a published breast cancer data set and find that that our method can distinguish most, but not all, different breast cancer subtypes. This result suggests that specific relationships between genes, captured by our algorithm, help distinguish between breast cancer subtypes. We propose that topological methods can be used for the classification and clustering of gene expression profiles.

  21. Topology Based Data Analysis Identifies a Subgroup of Breast Cancers With a Unique Mutational Profile and Excellent Survival (2011)

    Monica Nicolau, Arnold J. Levine, Gunnar Carlsson
    Abstract High-throughput biological data, whether generated as sequencing, transcriptional microarrays, proteomic, or other means, continues to require analytic methods that address its high dimensional aspects. Because the computational part of data analysis ultimately identifies shape characteristics in the organization of data sets, the mathematics of shape recognition in high dimensions continues to be a crucial part of data analysis. This article introduces a method that extracts information from high-throughput microarray data and, by using topology, provides greater depth of information than current analytic techniques. The method, termed Progression Analysis of Disease (PAD), first identifies robust aspects of cluster analysis, then goes deeper to find a multitude of biologically meaningful shape characteristics in these data. Additionally, because PAD incorporates a visualization tool, it provides a simple picture or graph that can be used to further explore these data. Although PAD can be applied to a wide range of high-throughput data types, it is used here as an example to analyze breast cancer transcriptional data. This identified a unique subgroup of Estrogen Receptor-positive (ER+) breast cancers that express high levels of c-MYB and low levels of innate inflammatory genes. These patients exhibit 100% survival and no metastasis. No supervised step beyond distinction between tumor and healthy patients was used to identify this subtype. The group has a clear and distinct, statistically significant molecular signature, it highlights coherent biology but is invisible to cluster methods, and does not fit into the accepted classification of Luminal A/B, Normal-like subtypes of ER+ breast cancers. We denote the group as c-MYB+ breast cancer.