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Advances in imaging techniques enable high resolution 3D visualisation ofvascular networks over time and reveal abnormal structural features such astwists and loops, and their quantification is an active area of research. Herewe showcase how topological data analysis (TDA), the mathematical field thatstudies `shape' of data, can characterise the geometric, spatial and temporalorganisation of vascular networks. We propose two topological lenses to studyvasculature, which capture inherent multi-scale features and vesselconnectivity, and surpass the single scale analysis of existing methods. Weanalyse images collected using intravital and ultramicroscopy modalities andquantify spatio-temporal variation of twists, loops, and avascular regions(voids) in 3D vascular networks. This topological approach validates andquantifies known qualitative trends such as dynamic changes in tortuosity andloops in response to antibodies that modulate vessel sprouting; furthermore, itquantifies the effect of radiotherapy on vessel architecture.

Multiscale Topology Characterises Dynamic Tumour Vascular Networks