Temporal phase correction of multiple echo T2 magnetic resonance images

Abstract

Typically, magnetic resonance imaging (MRI) analysis is performed on magnitude data, and multiple echo T 2 data consist of numerous images of the same slice taken with different echo spacing, giving voxel-wise temporal sampling of the noise as the signals decay according to T 2 relaxation. Magnitude T 2 decay data has Rician distributed noise which is characterized by a change in the noise distribution from Gaussian, through a transitional region, to Rayleigh as the signal to noise ratio decreases with increasing echo time. Non-Gaussian noise distributions may produce errors in the commonly applied non-negative least squares (NNLS) algorithm that is used to assess multiple echo decays for compartmentalized water environments through the creation of T 2 distributions. Typically, Gaussian noise is sought by performing spatial-based phase correction on the MRI data; however, these methods cannot capitalize on the temporal information available from multiple echo T 2 acquisitions. Here we describe a temporal phase correction (TPC) algorithm that utilizes the temporal noise information available in multiple echo T 2 acquisitions to put the relevant decay information in the Real portion of the decay data and leave only noise in the Imaginary portion. We apply this TPC algorithm to create real-valued multiple echo T 2 data from human subjects measured at 1.5 T. We show that applying TPC causes changes in the T 2 distribution estimates; notably the possible resolution of separate extracellular and intracellular water environments, and the disappearance of the commonly labeled cerebrospinal fluid peak, which might be an artefact observed in many previously published multiple echo T 2 analyses.

New approach to phase correction in multi-echoT2relaxometry

“…This results in a nonlinear problem; however, when the phase changes linearly with time, the ML estimator can be efficiently implemented using the Fast Fourier Transform (FFT). This case is of special interest, as linear phase variations were observed in the in vivo data used both in this paper and in [16].…”

“…A few suggestions on how to solve this sub-optimality problem are available in the literature [14,15], where the authors apply maximum likelihood (ML) methods, taking the Rice distribution into account; however, these approaches are nonlinear and rather involved, which complicates the implementation and can lead to convergence problems. To make the problem more tractable, many algorithms for T 2 estimation are based on minimizing the LS criterion; however, it has been suggested that LS-based approaches can lead to tissue mischaracterization caused by the Rician noise [16]. Another approach, that was applied in [17], estimates the signal decay and the noise properties from the magnitude images, and uses this information to transform the magnitude data into a Gaussian signal that can be used for T 2 estimation.…”

“…A method for temporal phase correction (TPC) has been proposed in [16], where the phase of the signal in an arbitrary voxel is fitted by two fourth-order polynomials using weighted LS. The estimated phase is then removed from the data, effectively projecting the signal onto the real axis.…”

“…However, the TPC method does not make the best use of the data, and can be both simplified and generalized. Moreover, no simulations were performed in [16] to show the statistical performance of TPC. In the following, our aim is to statistically improve upon the method in [16], generalize it to any linearly parameterized phase function, and extend it to multi-coil data.…”

QuantitativeT2: interactive quantitative T2 MRI witnessed in mouse glioblastoma

“…Therefore, N was set to 96 and echoes 97 to 128 were not used to avoid analysis artifacts that can be caused by the Rician noise floor. 28 In addition, M ¼ 120 logarithmically spaced T2 bins ranging from 8.25 ms (1.5× shortest echo time) to 1056 ms (2× longest echo time) were used to model the T2 decay in each voxel. The T2 − s j combinations for every voxel were stored independently as T2 distributions, and also summed together to create a T2 distribution histogram for the entire MR slice.…”