Topological Data Analysis for Self-organization of Biological Tissues

Jiménez, Manuel García; Rucco, Matteo; Vicente‐Munuera, Pablo; Gómez-Gálvez, Pedro; Escudero, Luis

doi:10.1007/978-3-319-59108-7_18

Cited by 9 publications

(6 citation statements)

References 16 publications

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“…We have found the work in [8] extremely useful as a first approach, and this paper can be seen, partially, as a continuation of it. Independently, a similar approach was presented in the conference paper [18]. In this case, persistent entropy was used instead of polynomial variables.…”

Section: Previous Topological Data Analysis Approachesmentioning

confidence: 99%

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Stable Topological Summaries for Analyzing the Organization of Cells in a Packed Tissue

2021

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We use topological data analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify the lifetime of homology classes (persistent homology) along different filtrations (increasing nested sequences of simplicial complexes) that are built from the regions representing the cells in the tissue. We use a complete and well-grounded set of numerical variables over those persistence barcodes, also known as topological summaries. A novel combination of normalization methods for both the set of input segmented images and the produced barcodes allows for the proven stability results for those variables with respect to small changes in the input, as well as invariance to image scale. Our study provides new insights to this problem, such as a possible novel indicator for the development of the drosophila wing disc tissue or the importance of centroids’ distribution to differentiate some tissues from their CVT-path counterpart (a mathematical model of epithelia based on Voronoi diagrams). We also show how the use of topological summaries may improve the classification accuracy of epithelial images using a Random Forest algorithm.

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Section: Previous Topological Data Analysis Approachesmentioning

confidence: 99%

“…This paper can be seen as a continuation of the conference papers [18,20], where the experiments have been extended and improved, adding more variables and combining different filtrations. In addition, an exhaustive theoretical analysis is presented to avoid the bias present in those preliminary studies.…”

Section: Previous Topological Data Analysis Approachesmentioning

confidence: 99%

Stable Topological Summaries for Analyzing the Organization of Cells in a Packed Tissue

2021

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“…TDA has been used in different domains-biology, manufacturing, medicine and others [28]. Topological entropy, namely Persistent Entropy, is equipped with suitable mathematical properties, that permits to describe complex systems [29] and it has been applied in different experiments, for example, the analysis of biological images [30] and the analysis of medical signals [31].…”

Section: Topological Data Analysis For Radiomics and Tumor Growth Analysismentioning

confidence: 99%

Towards Personalized Diagnosis of Glioblastoma in Fluid-Attenuated Inversion Recovery (FLAIR) by Topological Interpretable Machine Learning

2020

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Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumor, which tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all primary brain tumors. Usually, GBMs are detected by magnetic resonance images (MRI). Among MRI, a fluid-attenuated inversion recovery (FLAIR) sequence produces high quality digital tumor representation. Fast computer-aided detection and segmentation techniques are needed for overcoming subjective medical doctors (MDs) judgment. This study has three main novelties for demonstrating the role of topological features as new set of radiomics features which can be used as pillars of a personalized diagnostic systems of GBM analysis from FLAIR. For the first time topological data analysis is used for analyzing GBM from three complementary perspectives—tumor growth at cell level, temporal evolution of GBM in follow-up period and eventually GBM detection. The second novelty is represented by the definition of a new Shannon-like topological entropy, the so-called Generator Entropy. The third novelty is the combination of topological and textural features for training automatic interpretable machine learning. These novelties are demonstrated by three numerical experiments. Topological Data Analysis of a simplified 2D tumor growth mathematical model had allowed to understand the bio-chemical conditions that facilitate tumor growth—the higher the concentration of chemical nutrients the more virulent the process. Topological data analysis was used for evaluating GBM temporal progression on FLAIR recorded within 90 days following treatment completion and at progression. The experiment had confirmed that persistent entropy is a viable statistics for monitoring GBM evolution during the follow-up period. In the third experiment we developed a novel methodology based on topological and textural features and automatic interpretable machine learning for automatic GBM classification on FLAIR. The algorithm reached a classification accuracy up to 97%.

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“…PE is a tool, equipped with suitable mathematical properties, that permits to describe complex systems [2] and it has been applied in different experiments, e.g. the analysis of biological images [22] and the analysis of medical signals [40]. Usually, temporal logics are used for specifying properties and labeled transition systems are the basic semantic structures on which the model is defined.…”

Section: Definition 21 (Persistent Entropy)mentioning

confidence: 99%

Topological Run-time Monitoring for Complex Systems

Rucco,

Tesei,

Merelli

2019

Preprint

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In this paper we introduce a new data-driven run-time monitoring system for analysing the behaviour of time evolving complex systems. The monitor controls the evolution of the whole system but it is mined from the data produced by its single interacting components. Relevant behavioural changes happening at the component level and that are responsible for global system evolution are captured by the monitor. Topological Data Analysis is used for shaping and analysing the data for mining an automaton mimicking the global system dynamics, the so-called Persistent Entropy Automaton (PEA). A slight augmented PEA, the monitor, can be used to run current or past executions of the system to mine temporal invariants, for instance through statistical reasoning. Such invariants can be formulated as properties of a temporal logic, e.g. bounded LTL, that can be run-time model-checked. We have performed a feasibility assessment of the PEA and the associated monitoring system by analysing a simulated biological complex system, namely the human immune system. The application of the monitor to simulated traces reveals temporal properties that should be satisfied in order to reach immunization memory.

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Topological Data Analysis for Self-organization of Biological Tissues

Cited by 9 publications

References 16 publications

Stable Topological Summaries for Analyzing the Organization of Cells in a Packed Tissue

Stable Topological Summaries for Analyzing the Organization of Cells in a Packed Tissue

Towards Personalized Diagnosis of Glioblastoma in Fluid-Attenuated Inversion Recovery (FLAIR) by Topological Interpretable Machine Learning

Topological Run-time Monitoring for Complex Systems

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