Statistical and topological quantification of biomedical image features

Abstract

Non-linear laser microscopy techniques such as two photon excitation fluorescence (TPEF) and second harmonic generation (SHG) can generate high resolution images of biological samples, including live cells and tissue components such as collagen fibres. The imaging techniques give multi-component spectral information bearing chemical and structural signatures, which can be complex to disentangle in a robust, non-subjective manner. However, current image analysis techniques are manual, subjective, and rely on geometric summaries, while machine learning data-driven techniques are limited by the typically small number of training samples. We use topological data analysis (TDA) and statistical models to automatically and robustly detect biologically meaningful morphological features within these image types, equipping us with automated analysis to better understand biological and medical images. Our research can be split into developing methods for the analysis of two types of structures in images: micro-holes and fibres, using synthetic and real data sets of porous bone in mice, and collagen fibres in cartilage tissue imaged during the growth process, respectively.

Initially we developed a method for micro-hole structure analysis which uses persistent homology with cubical complexes and a signed Euclidean distance transform to derive persistence statistics for classification of TPaF and SHG images of porous bone samples from mice. This method summarises bone micro-hole structure, specifically the number, size, diversity, and crowding of micro-holes within bone tissue, for both inter and intra sample analysis [1]. Our second focus was to develop methods for fibre analysis that can be applied to the collagen fibre structures in the SHG images extracted using existing CT-FIRE software. We developed a persistent-homology based method for collagen fibre structure analysis, using a novel boundary-thickening filtration and alignment-direction thickening filtrations, and summarising the persistence diagrams using a combination of accumulated count function summaries we developed and persistence statistics. Both methods have clear results, are applicable to a wide range of applications and are interpretable in that they relate back to sample morphology.

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Identifiers

ORCID for Helen Ogden: orcid.org/0000-0001-7204-9776

ORCID for Ruben Sanchez-Garcia: orcid.org/0000-0001-6479-3028

ORCID for Sumeet Mahajan: orcid.org/0000-0001-8923-6666

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