BOX SPLINE BASED 3D TOMOGRAPHIC RECONSTRUCTION OF DIFFUSION PROPAGATORS FROM MRI DATA.

Area of Science:

• Medical Imaging
• Applied Mathematics
• Neuroscience

Background:

• Diffusion MRI (dMRI) enables non-invasive imaging of water diffusion in biological tissues.
• Reconstructing diffusion propagators (P(r)) provides richer microstructural information than traditional diffusion tensor imaging.
• Current methods face challenges in accurately capturing complex diffusion patterns.

Purpose of the Study:

• To introduce a tomographic approach for P(r) reconstruction using box splines.
• To leverage the mathematical properties of box splines for improved accuracy in diffusion MRI analysis.
• To demonstrate the efficacy of higher-order basis functions in P(r) reconstruction.

Main Methods:

• Utilized a box spline framework for high-order approximation of P(r) from diffusion signals.
• Exploited the closure property of box splines under the Radon transform for tomographic reconstruction.
• Applied the method to synthetic and real multi-shell diffusion-weighted MR data.

Main Results:

• The tomographic approach accurately reconstructs P(r) within a box spline framework.
• Increased accuracy of P(r) reconstruction was observed with higher-order basis functions.
• Demonstrated robustness on both synthetic and real diffusion-weighted MR datasets.

Conclusions:

• Box splines offer a powerful and mathematically sound framework for tomographic P(r) reconstruction.
• The proposed method enhances the accuracy of diffusion propagator estimation in dMRI.
• This approach has the potential to improve the characterization of neural microstructure.