Rapid T1 quantification from high resolution 3D data with model-based reconstruction

Abstract

Purpose: Magnetic resonance imaging protocols for the assessment of quantitative information suffer from long acquisition times since multiple measurements in a parametric dimension are required. To facilitate the clinical applicability, accelerating the acquisition is of high importance. To this end, we propose a model-based optimization framework in conjunction with undersampling 3D radial stack-of-stars data.

Theory and methods: High resolution 3D T₁ maps are generated from subsampled data by employing model-based reconstruction combined with a regularization functional, coupling information from the spatial and parametric dimension, to exploit redundancies in the acquired parameter encodings and across parameter maps. To cope with the resulting non-linear, non-differentiable optimization problem, we propose a solution strategy based on the iteratively regularized Gauss-Newton method. The importance of 3D-spectral regularization is demonstrated by a comparison to 2D-spectral regularized results. The algorithm is validated for the variable flip angle (VFA) and inversion recovery Look-Locker (IRLL) method on numerical simulated data, MRI phantoms, and in vivo data.

Results: Evaluation of the proposed method using numerical simulations and phantom scans shows excellent quantitative agreement and image quality. T₁ maps from accelerated 3D in vivo measurements, e.g. 1.8 s/slice with the VFA method, are in high accordance with fully sampled reference reconstructions.

Conclusions: The proposed algorithm is able to recover T₁ maps with an isotropic resolution of 1 mm³ from highly undersampled radial data by exploiting structural similarities in the imaging volume and across parameter maps.

Keywords: MRI; T1 quantification; constrained reconstruction; imaging; inversion-recovery Look-Locker; model-based reconstruction; variable flip angle.

Figure 1

Numerical simulated VFA T ₁ reconstructions with 34 simulated spokes compared to a numerical reference in the top left. T ₁ values are given in milliseconds. Shown are transversal, sagittal and coronal views of the phantom with a simulated “tumor” in the white matter. The corresponding relative absolute error is given in Figure 2

Figure 2

Relative absolute error of numerical simulated VFA T ₁ reconstructions with 34 simulated spokes compared to a numerical reference in.1 Shown are transversal, sagittal and coronal views of the phantom with a simulated “tumor” in the white matter. The error is given given in percent. The numbers next to the images indicate the mean relative absolute error in the corresponding parameter maps as well as the structural similarity index

Figure 3

Comparison of 3D to 2D regularization for in vivo VFA T ₁ reconstruction from 34 acquired spokes. T ₁ maps are given in milliseconds. Visually observable differences are marked with white arrows. The corresponding relative absolute error maps are given in Supporting Information Figure S3. The skull has been masked out

Figure 4

MRI phantom T ₁ measurements using a VFA based sequence are shown in the upper part. Fully sampled reference in the top left, compared to the proposed method in the 1st row, TV regularization in the 2nd row, and L ¹‐wavelet regularization in the 3rd row. The lower part shows MRI phantom reconstructions using a IRLL based sequence. Cartesian reference in the lower left, compared to the proposed method and TV respectively L ¹‐wavelet regularization. All values are given in milliseconds. Quantitative evaluation of ROIs, marked in the reference, are given in Table 1 for VFA and Table 2 for IRLL reconstructions

Figure 5

In vivo VFA T ₁ measurements of the brain of a healthy volunteer reconstructed with the proposed method. Shown are reformatted views of the acquired volume in transversal, coronal and sagittal plane. T ₁ values given in milliseconds. Top left, fully sampled reference. From left to right and top to bottom increasing acceleration from 89 to 8 spokes per slice. Quantitative evaluation of ROIs is given in Table 3. The bottom half of the figure shows the corresponding error maps with a mask applied to the skull area.

Figure 6

2D histogram contour plot of reference T ₁ values versus accelerated acquired and reconstructed T ₁ values for increasing acceleration using the VFA method. The color map encodes ares of mutual voxel values and is transformed using an exponential scaling. Red line indicates 45^∘, corresponding to a perfect match, i.e. plotting the same data against each other. r indicates the Pearson correlation coefficient

Figure 7

In vivo IRLL measurements of the brain of a healthy volunteer. Shown is a reformatted view of the acquired volume in transversal, coronal and sagittal plane. Top left, fully sampled Cartesian reference. In the upper row T ₁ reconstructions from data acquired in 8 s/slice. The pseudo proton density M ₀ is shown in the bottom row. Quantitative evaluation of ROIs for T ₁ is given in Table 3. T ₁ map values are given in milliseconds, M ₀ intensity values in arbitrary units (a.u.)