The problem of automatic quantification of brain tissue by utilizing single-valued (single echo) magnetic resonance imaging (MRI) brain scans is addressed. It is shown that this problem can be solved without classification or segmentation, a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap. The general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues. The quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture. This problem is solved by tree annealing with and without partial volume utilized, the results compared, and the sensitivity of the tree annealing algorithm to various parameters is exhibited. The actual quantification is performed by two methods: a classification-based method called Bayes quantification, and parameter estimation. Results from each method are presented for synthetic and actual data.

Statistical models of partial volume effect for systems with various types of noise or pixel value distributions are developed and probability density functions are derived. The models assume either Gaussian system sampling noise or intrinsic material variances with Gaussian or Poisson statistics. In particular, a material can be viewed as having a distinct value that has been corrupted by additive noise either before or after partial volume mixing, or the material could have nondistinct values with a Poisson distribution as might be the case in nuclear medicine images. General forms of the probability density functions are presented for the N material cases and particular forms for two- and three-material cases are derived. These models are incorporated into finite mixture densities in order to more accurately model the distribution of image pixel values. Examples are presented using simulated histograms to demonstrate the efficacy of the models for quantification. Modeling of partial volume effect is shown to be useful when one of the materials is present in images mainly as a pixel component.

The phase-mapping method of phase-contrast magnetic resonance angiography is shown to be based on an implicit assumption that the intravoxel velocity distribution is symmetric about its mean velocity. The effect of asymmetric distributions on the accuracy of quantitative average velocity measurements is determined analytically and verified experimentally. An explicit formulation is developed for the estimated average velocity in a voxel as a function of the true average velocity and the asymmetry of the distribution about the true average velocity. Worst-case distributions are determined for unidirectional and bidirectional flow, and the special case of laminar flow is also investigated. Computer simulations and phantom imaging experiments demonstrate the accuracy of the analysis. For voxels with unidirectional flow, the phase-mapping method produces accurate estimates of average velocity, while results for bidirectional flow indicate possible large errors unless the aliasing velocity is increased, which decreases the signal-to-noise ratio in the resultant velocity map image.