Determination of concentrations by time domain fitting of proton NMR echo signals using prior knowledge

A fast and flexible time domain iterative fitting procedure that can be used to fit free induction decays as well as echo-like signals is described. Damping constants of the first and second part of the echo do not have to be identical. Prior knowledge can be used to diminish the number of parameters to be fitted, which results in an improved accuracy. It is shown how prior knowledge is mathematically incorporated in the Gauss-Newton method. From proton NMR measurements of model solutions actual prior knowledge is extracted. With this knowledge relative concentrations are determined from a mixture of metabolites. The fitted results agree with the true values within the margins of the noise. After some minor changes the same prior knowledge was successfully used to analyze a series of in vivo rat brain measurements.