Incorporating relaxivities to more accurately reconstruct MR images

Abstract

Purpose To develop a mathematical model that incorporates the magnetic resonance relaxivities into the image reconstruction process in a single step. Materials and Methods In magnetic resonance imaging, the complex-valued measurements of the acquired signal at each point in frequency space are expressed as a Fourier transformation of the proton spin density weighted by Fourier encoding anomalies: T2*, T1, and a phase determined by magnetic field inhomogeneity (ΔB) according to the MR signal equation. Such anomalies alter the expected symmetry and the signal strength of the k-space observations, resulting in images distorted by image warping, blurring, and loss in image intensity. Although T1 on tissue relaxation time provides valuable quantitative information characteristics, the T1 recovery term is typically neglected by assuming a long repetition time. In this study, the linear framework presented in the work of Rowe et al., 2007, and of Nencka et al., 2009 is extended to develop a Fourier reconstruction operation in terms of a real-valued isomorphism that incorporates the effects of T2*, ΔB, and T1. This framework provides a way to precisely quantify the statistical properties of the corrected image-space data by offering a linear relationship between the observed frequency space measurements and reconstructed corrected image-space measurements. The model is illustrated both on theoretical data generated by considering T2*, T1, and/or ΔB effects, and on experimentally acquired fMRI data by focusing on the incorporation of T1. A comparison is also made between the activation statistics computed from the reconstructed data with and without the incorporation of T1 effects. Result Accounting for T1 effects in image reconstruction is shown to recover image contrast that exists prior to T1 equilibrium. The incorporation of T1 is also shown to induce negligible correlation in reconstructed images and preserve functional activations. Conclusion With the use of the proposed method, the effects of T2* and ΔB can be corrected, and T1 can be incorporated into the time series image-space data during image reconstruction in a single step. Incorporation of T1 provides improved tissue segmentation over the course of time series and therefore can improve the precision of motion correction and image registration.

A Bayesian Variable Selection Approach Yields Improved Detection of Brain Activation From Complex-Valued fMRI

“…It is clear from this plot that the estimated σ 2 v are larger for those voxels inside the brain than for those outside. These estimated values are also able to differentiate gray matter from the rest and are consistent with results in Karaman, Bruce, and Rowe (2015). In particular, the right plot in Figure 11 shares similarities with the estimated T1 map in Karaman, Bruce, and Rowe (2015).…”

“…These estimated values are also able to differentiate gray matter from the rest and are consistent with results in Karaman, Bruce, and Rowe (2015). In particular, the right plot in Figure 11 shares similarities with the estimated T1 map in Karaman, Bruce, and Rowe (2015). This is an important result given that our proposed models are able to capture a relatively sophisticated brain structure without incorporating nonlinear physically based components that would make posterior computations extremely challenging for these large dimensional data.…”

“…A more realistic simulated dataset was Figure 7, Figure 8 generated using a discrete version of the magnetic resonance (MR) signal equation after steady-state magnetization (Karaman, Bruce, and Rowe 2015). This equation is given by ( ,…”

Separation of parallel encoded complex-valued slices (SPECS) from a single complex-valued aliased coil image

“…The data was generated with eight axial slices that are 96×96 in dimension. A noiseless time series was generated for each slice with a theoretical $T_2^{\ast }$ weighted phantom similar to [33]. The initial $T_2^{\ast }$ weighted phantom has values between 0 and 1, and was generated with the echo time (TE) and effective echo spacing (EESP) used during the acquisition of the experimental data.…”

“…The phase encoding direction was oriented as posterior to anterior (bottom to top in images). In image reconstruction, images were Nyquist ghost corrected using the three navigator echoes method [34] and dynamic B0 field corrected using the TOAST single echo technique [33]. The phase images were further corrected by subtracting a local second order polynomial fit to their difference from the mean.…”