Applications of the likelihood function for dynamic contrast enhanced MRI

Motivation: Least squares can provide biased and inefficient estimations of pharmokinetic parameters in certain circumstances. Goal(s): To develop a more efficient method to extract pharmokinetic parameters as well as the limit on the precision of those parameters. Approach: The likelihood function for multi-channel receive dynamic contrast enhanced MRI was used to develop a method to extract pharmokinetic parameters. Results: The proposed maximum likelihood estimator method has substantially less bias than the typical least squares method. For the input parameters investigated the maximum likelihood estimated pharmacokinetic parameters had standard deviations within 10% or less of their fundamental lower bound. Impact: The developed tool provides nearly efficient pharmokinetic estimations, thereby providing an improved method over the standard least squares approach, as well as demonstrating the limited utlility of future machine learning and other methods attempting to solve this problem.