A statistical method for determining the proportions of gray matter, white matter, and CSF using computed tomography

The brain may be considered as a collection of volume elements (voxels) containing unknown proportions of gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF). If one assumes that (1) the attenuation coefficients for voxels with the same proportions of GM, WM, and CSF follow a Gaussian distribution whose mean is a weighted average of the mean attenuation coefficients of pure GM, WM, and CSF and (2) the voxel-to-voxel variation in proportion follows a Dirichlet probability distribution, then the overall proportions of GM, WM, and CSF can be calculated by optimizing the parameters of a compound Dirichlet-Gaussian distribution. This approach permits a quantitative analysis of the compartmental composition of the brain and may be useful in the evaluation of patients with cerebral edema, hydrocephalus, and leukoencephalopathy.