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Geometric computation of human gyrification indexes from magnetic resonance images

Authors

  • Shu Su,

    1. Department of Mathematics, The Ohio State University, Columbus, Ohio
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  • Tonya White,

    1. Department of Child and Adolescent Psychiatry, Erasmus Medical Centre, Rotterdam, Netherlands
    2. Kinder en Jeugd NeuroImaging Centrum Rotterdam, Erasmus Medical Centre, Rotterdam, Netherlands
    3. Department of Radiology, Erasmus Medical Centre, Rotterdam, Netherlands
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  • Marcus Schmidt,

    1. Department of Child and Adolescent Psychiatry, Erasmus Medical Centre, Rotterdam, Netherlands
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  • Chiu-Yen Kao,

    Corresponding author
    1. Department of Mathematics, The Ohio State University, Columbus, Ohio
    2. Mathematical Biosciences Institute, The Ohio State University, Columbus, Ohio
    3. Department of Mathematics and Computer Science, Claremont Mckenna College, Claremont, California
    • Department of Mathematics, Mathematical Biosciences Institute, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio
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  • Guillermo Sapiro

    1. Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota
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Abstract

Human brains are highly convoluted surfaces with multiple folds. To characterize the complexity of these folds and their relationship with neurological and psychiatric conditions, different techniques have been developed to quantify the folding patterns, also known as the surface complexity or gyrification of the brain. In this study, the authors propose a new geometric approach to measure the gyrification of human brains from magnetic resonance images. This approach is based on intrinsic 3D measurements that relate the local brain surface area to the corresponding area of a tightly wrapped sheet. The authors also present an adaptation of this technique in which the geodesic depth is incorporated into the gyrification computation. These gyrification measures are efficiently and accurately computed by solving geometric partial differential equations. The presentation of the geometric framework is complemented with experimental results for brain complexity in typically developing children and adolescents. Using this novel approach, the authors provide evidence for a gradual decrease in brain surface complexity throughout childhood and adolescence. These developmental differences occur earlier in the occipital lobe and move anterior as children progress into young adulthood. Hum Brain Mapp, 2013. © 2012 Wiley Periodicals, Inc.

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