🍩 Database of Original & Non-Theoretical Uses of Topology

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  1. Quantification of the Immune Content in Neuroblastoma: Deep Learning and Topological Data Analysis in Digital Pathology (2021)

    Nicole Bussola, Bruno Papa, Ombretta Melaiu, Aurora Castellano, Doriana Fruci, Giuseppe Jurman
    Abstract We introduce here a novel machine learning (ML) framework to address the issue of the quantitative assessment of the immune content in neuroblastoma (NB) specimens. First, the EUNet, a U-Net with an EfficientNet encoder, is trained to detect lymphocytes on tissue digital slides stained with the CD3 T-cell marker. The training set consists of 3782 images extracted from an original collection of 54 whole slide images (WSIs), manually annotated for a total of 73,751 lymphocytes. Resampling strategies, data augmentation, and transfer learning approaches are adopted to warrant reproducibility and to reduce the risk of overfitting and selection bias. Topological data analysis (TDA) is then used to define activation maps from different layers of the neural network at different stages of the training process, described by persistence diagrams (PD) and Betti curves. TDA is further integrated with the uniform manifold approximation and projection (UMAP) dimensionality reduction and the hierarchical density-based spatial clustering of applications with noise (HDBSCAN) algorithm for clustering, by the deep features, the relevant subgroups and structures, across different levels of the neural network. Finally, the recent TwoNN approach is leveraged to study the variation of the intrinsic dimensionality of the U-Net model. As the main task, the proposed pipeline is employed to evaluate the density of lymphocytes over the whole tissue area of the WSIs. The model achieves good results with mean absolute error 3.1 on test set, showing significant agreement between densities estimated by our EUNet model and by trained pathologists, thus indicating the potentialities of a promising new strategy in the quantification of the immune content in NB specimens. Moreover, the UMAP algorithm unveiled interesting patterns compatible with pathological characteristics, also highlighting novel insights into the dynamics of the intrinsic dataset dimensionality at different stages of the training process. All the experiments were run on the Microsoft Azure cloud platform.

  2. Airway Pathological Heterogeneity in Asthma: Visualization of Disease Microclusters Using Topological Data Analysis (2018)

    Salman Siddiqui, Aarti Shikotra, Matthew Richardson, Emma Doran, David Choy, Alex Bell, Cary D. Austin, Jeffrey Eastham-Anderson, Beverley Hargadon, Joseph R. Arron, Andrew Wardlaw, Christopher E. Brightling, Liam G. Heaney, Peter Bradding
    Abstract Background Asthma is a complex chronic disease underpinned by pathological changes within the airway wall. How variations in structural airway pathology and cellular inflammation contribute to the expression and severity of asthma are poorly understood. Objectives Therefore we evaluated pathological heterogeneity using topological data analysis (TDA) with the aim of visualizing disease clusters and microclusters. Methods A discovery population of 202 adult patients (142 asthmatic patients and 60 healthy subjects) and an external replication population (59 patients with severe asthma) were evaluated. Pathology and gene expression were examined in bronchial biopsy samples. TDA was applied by using pathological variables alone to create pathology-driven visual networks. Results In the discovery cohort TDA identified 4 groups/networks with multiple microclusters/regions of interest that were masked by group-level statistics. Specifically, TDA group 1 consisted of a high proportion of healthy subjects, with a microcluster representing a topological continuum connecting healthy subjects to patients with mild-to-moderate asthma. Three additional TDA groups with moderate-to-severe asthma (Airway Smooth MuscleHigh, Reticular Basement MembraneHigh, and RemodelingLow groups) were identified and contained numerous microclusters with varying pathological and clinical features. Mutually exclusive TH2 and TH17 tissue gene expression signatures were identified in all pathological groups. Discovery and external replication applied to the severe asthma subgroup identified only highly similar “pathological data shapes” through analyses of persistent homology. Conclusions We have identified and replicated novel pathological phenotypes of asthma using TDA. Our methodology is applicable to other complex chronic diseases.