Bayesian estimation of changes in transverse relaxation rates.

Although the biasing of R(2)* estimates by assuming magnitude MR data to be normally distributed has been described, the effect on changes in R(2)* (DeltaR(2)), such as induced by a paramagnetic contrast agent, has not been reported. In this study, two versions of a novel Bayesian maximum a posteriori approach for estimating DeltaR(2) are described and evaluated: one that assumes normally distributed data and the other, Rice-distributed data. The approach enables the robust, voxelwise determination of the uncertainty in DeltaR(2)* estimates and provides a useful statistical framework for quantifying the probability that a pixel has been significantly enhanced. This technique was evaluated in vivo, using ultrasmall superparamagnetic iron oxide particles in orthotopic murine prostate tumors. It is shown that assuming magnitude data to be normally distributed causes DeltaR(2)* to be underestimated when signal-to-noise ratio is modest. However, the biasing effect is less than is found in R(2)* estimates, implying that the simplifying assumption of normally distributed noise is more justifiable when evaluating DeltaR(2)* compared with when evaluating precontrast R(2)* values.