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Topological data analysis offers new ways to study blood vessel networks. This method quantifies complex 3D vascular structures and their changes over time, providing insights into diseases and treatments.

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Area of Science:

  • Biomedical Engineering
  • Data Science
  • Mathematical Biology

Background:

  • High-resolution 3D imaging reveals complex vascular networks with abnormal structures like twists and loops.
  • Quantifying these complex vascular features over time is crucial for understanding disease progression and treatment effects.
  • Existing methods often analyze vascular networks at a single scale, potentially missing multiscale organizational characteristics.

Purpose of the Study:

  • To introduce topological data analysis as a novel method for characterizing the geometric, spatial, and temporal organization of vascular networks.
  • To develop and apply two topological lenses for capturing multiscale features and vessel connectivity in 3D vascular data.
  • To quantify spatiotemporal variations in vascular structures, including twists, loops, and avascular regions (voids).

Main Methods:

  • Application of topological data analysis to 3D vascular network data obtained from intravital and ultramicroscopy.
  • Development of two novel topological lenses to analyze multiscale features and connectivity.
  • Quantification of structural features such as twists, loops, and voids in vascular networks.

Main Results:

  • The topological approach successfully characterized the organization of 3D vascular networks.
  • Demonstrated quantification of spatiotemporal variations in twists, loops, and avascular regions.
  • Validated and quantified known trends in tortuosity and loop dynamics in response to therapeutic antibodies.
  • Quantified the impact of radiotherapy on vascular architecture.

Conclusions:

  • Topological data analysis provides a powerful framework for analyzing complex vascular networks.
  • This method offers a multiscale perspective that surpasses single-scale analysis limitations.
  • The approach enables precise quantification of vascular changes relevant to disease and treatment, such as those induced by antibodies and radiotherapy.