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

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.