VARYING COEFFICIENT MODEL FOR MODELING DIFFUSION TENSORS ALONG WHITE MATTER TRACTS.

Area of Science:

• Neuroimaging
• Biostatistics
• Medical Image Analysis

Background:

• Diffusion tensor imaging (DTI) is crucial for mapping brain white matter structure and fiber orientation.
• DTI data are represented as 3x3 symmetric positive definite (SPD) matrices, posing unique analytical challenges.
• Existing methods may not fully capture the complex relationships between DTI metrics and covariates like age and gender.

Purpose of the Study:

• To develop a novel functional data analysis framework for modeling diffusion tensors.
• To investigate the dynamic associations between diffusion tensors and covariates (age, gender) in brain white matter.
• To identify potential gender-specific differences in neurodevelopment using DTI data.

Main Methods:

• Modeling diffusion tensors as functional data on a Riemannian manifold.
• Utilizing a statistical model with varying coefficient functions for SPD matrix-valued responses.
• Employing weighted least squares estimation and developing a global test statistic for hypothesis testing.
• Validating the model's performance using simulated data.

Main Results:

• The proposed framework effectively models diffusion tensors along fiber tracts.
• Weighted least squares estimators for varying coefficient functions were calculated using the Log-Euclidean metric.
• A global test statistic and simultaneous confidence bands were developed for hypothesis testing.
• Simulated data confirmed the finite sample performance of the estimation methods.

Conclusions:

• The developed statistical model provides a robust approach for analyzing DTI data.
• Significant gender differences in the development of diffusion tensors along the right internal capsule tract were identified.
• This framework offers valuable insights into neurodevelopmental trajectories and potential sex-based variations in brain structure.