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Trajectories from Distribution-valued Functional Curves: A Unified Wasserstein Framework★.

Anuja Sharma1, Guido Gerig2

  • 1School of Computing, SCI Institute, University of Utah, Salt Lake City, UT, USA.

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This study introduces a new framework using Wasserstein distance to model temporal changes in medical image structures, like white matter tracts. It successfully detected delayed growth in a pediatric subject compared to healthy infants.

Keywords:
Diffusion-MRINeurodevelopmentSpatiotemporal regression

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Area of Science:

  • Medical imaging analysis
  • Computational neuroscience
  • Biomedical engineering

Background:

  • Evaluating temporal changes in medical images often involves analyzing parametrized functions representing anatomical structures.
  • Current methods may lack comprehensive frameworks for modeling the evolution of image properties along these structures.

Purpose of the Study:

  • To propose a novel framework for modeling temporal evolution trajectories of distribution-valued signatures derived from medical image structures.
  • To utilize the Wasserstein distance metric for a unified approach to analyzing these trajectories.

Main Methods:

  • Representing structures of interest (e.g., white matter tracts) as parametrized functions.
  • Attributing local neighborhood image property distributions to samples along these functions, creating distribution-valued signatures.
  • Formulating the regression problem as a constrained optimization problem solved via an alternating projection algorithm.
  • Employing Wasserstein-based test statistics for hypothesis testing.

Main Results:

  • The proposed framework simultaneously preserves functional curve characteristics and models temporal changes in distribution profiles.
  • The method ensures estimated distributions are valid.
  • Validation on synthetic data demonstrated the framework's efficacy.
  • Delayed growth was detected in diffusion tensor imaging (DTI) tracts of a pediatric subject compared to a healthy infant population.

Conclusions:

  • The developed framework provides a comprehensive approach to modeling temporal changes in medical image structures using distribution-valued signatures.
  • The Wasserstein distance metric offers a robust mathematical foundation for this analysis.
  • The method shows promise for identifying developmental abnormalities, such as delayed growth, in pediatric subjects.