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A procedure for estimating the joint probability density function (pdf) of T 1 , T 2 and proton spin density (P D ) for gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) in the brain is presented. The pdf's have numerous applications, including the study of tissue parameter variability in pathology and across populations. The procedure requires a multispectral, spin echo magnetic resonance imaging (MRI) data set of the brain. It consists of five automated steps: (i) preprocess the data to remove extracranial tissue using a sequence of image processing operators; (ii) estimate T 1 , T 2 and P D by fitting the preprocessed data to an imaging equation; (iii) perform a fuzzy c-means clustering on the same preprocessed data to obtain a spatial map representing the membership value of the three tissue classes at each pixel location; (iv) reject estimates which are not from pure tissue or have poor fits in the parameter estimation, and classify the remaining estimates as either GM, WM or CSF; (v) compute statistics on the classified estimates to obtain a probability mass function and a Gaussian joint pdf of the tissue parameters for each tissue class. Some preliminary results are shown comparing computed pdf's of young, elderly and Alzheimer's subjects. Two brief examples applying the joint pdf's to pulse sequence optimization and generation of computational phantoms are also provided.
Pham et al. (Mon,) studied this question.