Mathematics and computational analysis of brain structural MRI and application to psychiatric diseases

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Recently brain imaging studies using magnetic resonance imaging (MRI) were often reported in the psychiatry research. This study was aimed to apply an mathematical theory to the brain imaging study to understand the structural brain anatomy in psychiatric patients more simply and more accurately. We used differential geometry theories to segment the brain anatomical structure. Computational programs were written using differential geometry. Then we collected MRI imaging in psychiatric patients i.e. schizophrenia affective disorder and seizure. Using differential geometry method we compared intracranial volumes. However significant difference were not detected so far. By collecting MRI images and detecting the differences we can try to cutting edge of the psychiatric disorders in the future.