Generalized parameter estimation in multi-echo gradient-echo-based chemical species separation

Abstract

To develop a generalized formulation for multi-echo gradient-echo-based chemical species separation for all MR signal models described by a weighted sum of complex exponentials with phases linear in the echo time. Constraints between estimation parameters in the signal model were abstracted into a matrix formulation of a generic parameter gradient. The signal model gradient was used in a parameter estimation algorithm and the Fisher information matrix. The general formulation was tested in numerical simulations and against literature and in vivo results. The proposed gradient-based parameter estimation and experimental design framework is universally applicable over the whole class of signal models using the matrix abstraction of the signal model-specific parameter constraints as input. Several previous results in magnetic-field mapping and water-fat imaging with different models could successfully be replicated with the same framework and only different input matrices. A framework for generalized parameter estimation in multi-echo gradient-echo MR signal models of multiple chemical species was developed and validated and its software version is freely available online.

Keywords: Cramér-Rao lower bound; Parameter estimation; fatty acid composition; noise analysis; variable projection method (VARPRO); water-fat imaging.