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    We developed a new statistical framework, functional nonlinear mixed effects modeling (FNMEM), to analyze brain development over time. This method helps understand brain growth patterns and their links to conditions like autism.

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    Area of Science:

    • Neuroimaging
    • Statistical Modeling
    • Developmental Neuroscience

    Background:

    • Large-scale longitudinal brain image data present challenges for modeling complex spatial-temporal patterns.
    • Understanding nonlinear growth trajectories is crucial for diagnosing and tracking neurodevelopmental and neurodegenerative disorders.

    Purpose of the Study:

    • To introduce a novel functional nonlinear mixed effects modeling (FNMEM) framework for analyzing nonlinear spatial-temporal brain growth.
    • To quantify individual developmental trajectories and their association with covariates.
    • To provide statistical tools for analyzing growth patterns and their clinical relevance.

    Main Methods:

    • Developed a functional nonlinear mixed effects modeling (FNMEM) framework.
    • Implemented an efficient estimation method for nonlinear growth functions and spatial-temporal covariance operators.
    • Proposed a global test and simultaneous confidence bands for specific growth patterns.
    • Utilized Monte Carlo simulations to validate the method's performance.

    Main Results:

    • The FNMEM framework effectively models nonlinear spatial-temporal brain growth patterns.
    • Individual trajectories and their associations with covariates are explicitly quantified.
    • The proposed estimation and testing procedures demonstrate good finite-sample performance in simulations.
    • Applied FNMEM to analyze white-matter fiber skeleton dynamics in autism research.

    Conclusions:

    • FNMEM offers a robust approach for analyzing complex brain development from longitudinal imaging data.
    • The framework can reveal critical insights into the spatial-temporal dynamics of brain structure and function.
    • FNMEM has the potential to aid in understanding developmental trajectories across various neuropsychiatric and neurodegenerative disorders.