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    Area of Science:

    • Neuroimaging
    • Biophysics
    • Medical Physics

    Background:

    • Diffusion MRI (dMRI) data provides insights into tissue microstructure via the ensemble average diffusion propagator (EAP).
    • Accurate estimation of the EAP is crucial for understanding tissue properties.
    • Existing methods face challenges in precisely capturing complex diffusion characteristics.

    Purpose of the Study:

    • To develop a novel method for estimating the EAP from dMRI data.
    • To represent the diffusion signal using directional radial basis functions in q-space.
    • To derive analytical expressions for key diffusion metrics and introduce new scalar indices.

    Main Methods:

    • Representing the diffusion signal as a linear combination of anisotropic Gaussian basis functions in q-space.
    • Deriving analytical expressions for diffusion orientation distribution function (ODF), return-to-origin probability (RTOP), and mean-squared-displacement (MSD).
    • Computing second and fourth-order moment tensors of the EAP for novel scalar indices like mean-fourth-order-displacement (MFD) and generalized kurtosis (GK).

    Main Results:

    • Explicit computation of second and fourth-order moment tensors of the EAP.
    • Introduction of novel scalar indices: MFD, generalized kurtosis (GK), q-space mean-squared-displacement (QMSD), and q-space mean-fourth-order-displacement (QMFD).
    • Validation on physical phantoms and in-vivo human brain data, demonstrating robustness across various b-values and gradient directions.

    Conclusions:

    • The proposed method offers an accurate and robust estimation of the EAP.
    • The novel scalar indices provide new insights into tissue microstructure and diffusion dynamics.
    • This approach enhances the analytical capabilities of diffusion MRI for biomedical research.