Introduction

T₂ mapping can be employed to quantitatively study a wide range of pathologies. It is achieved by acquiring a series of T₂ weighted images and performing voxel-wise fitting. The commonly used multi-echo spin-echo method requires long scan times. Individual T₂ weighted images can be acquired with fast spin echo (FSE), and the total scan time can be reduced by collecting only a moderate number of images. However, these images with different echo times (TEs) have different point spread functions (PSFs), leading to artifacts in the T₂ map, such as blurring and edge enhancement. A correction using the average T₂ value can be performed to reduce these artifacts ¹. However, this correction method may not be effective when there is a large range of T₂ values. We propose an iterative PSF correction method that enables fast and accurate T₂ mapping.

Methods

The flow of the proposed method is illustrated in Figure 1. The average correction, or uncorrected T₂ map, and shortest TE image are used as initial guesses for T₂ and proton density ($$$\rho$$$), respectively. An optimization process is then conducted, iteratively updating the T₂ and $$$\rho$$$ maps to minimize the error between predicted images and the measured T₂ weighted images. In this study, the Bound Optimization BY Quadratic Approximation method ² was employed for the minimization. The cost function is $$cost=\sum_i\left \| \mathbf{x_{ik}}-\sum _j\rho_{jk}\hat{T}(j)\mathbf{PSF}(T_{2jk}, i))\right \|^2_2$$ where $$$\mathbf{\{x_{ik}\}}$$$ is a set of the $$$k$$$th lines from the image with $$$i$$$ different TEs. $$$\hat{T}(j)$$$ is the translation operator. $$$\rho_{jk}$$$ and $$$T_{2jk}$$$ are the proton density and transverse relaxation time at position $$$j$$$, respectively. $$$\mathbf{PSF}(T_{2jk}, i)$$$ is the PSF for a given T₂, determined by the phase encoding scheme of the $$$i$$$th image.

The method was validated by simulation, phantom and mouse brain experiments. 2D FSE T₂ mapping experiments were conducted on an oil-water phantom with 14 TEs, ranging from 13.7 ms to 823 ms (FOV 60x60 mm², voxel size 0.5x0.5 mm², 17 mins scan time). 3D FSE T₂ mapping experiments were performed on a mouse brain (10 TEs, FOV 22x22x18 mm³, voxel size 183x183x600 µm³, 2.8 hour scan time on a 1T system). The optimization time was 30 minutes for a single slice mouse brain on a 32 core CPU.

Results and Discussion

A single line from the T₂ and $$$\rho$$$ maps in the simulation results is shown in Figure 2. The signal-to-noise ratio (SNR) was 100. In Figure 2a, the uncorrected T₂ map, shown in green, exhibits significant edge enhancement, which is largely removed by the average correction in blue. However, the resulting profile appears noisier, and under-correction and over-correction occur in regions where T₂ differs from the average value, leading to residual edge enhancement and blurring. The artifacts are enhanced in the $$$\rho$$$ map after average correction, as shown in Figure 2b. The proposed method yielded results shown in red, closely matching the ideal profile in black, without noise amplification and resolution degradation.

Figure 3 displays the T₂ (first row) and $$$\rho$$$ (second row) maps from the phantom experiment using the uncorrected (1st column), average corrected (2nd column) and the proposed (3rd column) methods. The results agreed very well with the simulation. The proposed method effectively eliminated the edge enhancement observed in the uncorrected T₂ map and the average correction $$$\rho$$$ map. It also removed the apparent blurring in the uncorrected $$$\rho$$$ map and average correction T₂ map. The average correction was not particularly effective, especially at the oil-water interface. The proposed method provides the most accurate quantitative maps.

A slice of the 3D mouse brain FSE T₂ mapping results is shown in Figure 4. The optimization method (2nd column) significantly improved the contrast and resolution of the T₂ map (1st row) and $$$\rho$$$ map (2nd row). Notably, the hippocampus region is more discernible, and the CSF is more distinct in the optimized T₂ map, as highlighted in the top zoomed view. Edge enhancement of T₂ at the air-tissue interface was largely removed, as shown in the green window. The $$$\rho$$$ map shows low signal intensity around the ear, due to partial volume effect. This led to large errors in the uncorrected T₂ map, while the optimization method was more robust. Blurring in the uncorrected $$$\rho$$$ map was substantially removed, and high-resolution features became visible.

Conclusion

An optimization method for PSF correction in FSE T₂ mapping has been demonstrated. This method produces more accurate T₂ and $$$\rho$$$ maps, largely eliminating blurring and edge enhancements, thus enabling quantitative studies without the need to modify the existing FSE pulse sequence.

Acknowledgements

T. P. thanks NSERC Canada for a CGSD scholarship. D. X. thanks NSERC Canada for a Discovery Grant.