Synopsis

We propose a method to reconstruct 1-mm³ isotropic T2 maps based on multiple 2D multi-echo spin-echo (MESE) acquisitions. To compensate for the prolonged scan time due to multiple acquisitions, data were highly (10-fold) undersampled. The data was reconstructed by combining a classical super-resolution approach with an iterative model-based reconstruction. The method was tested on a phantom and four healthy volunteers. T2 values were compared against fully sampled MESE data. The proposed technique allows the assessment of T2 values in brain structures at high isotropic resolution.

Purpose

Theory

A high-resolution series of images $$$x_n$$$ (with $$$ n = 1, …, N,$$$ and $$$N$$$ the number of spin-echoes) is estimated by minimizing the difference to LR k-space $$$y_{j,n,c}$$$ with $$$S_c$$$ coil sensitivities (with $$$c = 1,…,C,$$$ and $$$C$$$ the number of coils), $$$T_j$$$ representing a rotation or translation of the FOV (with $$$j=1,…, J,$$$ and $$$J$$$ the number of LR k-spaces), ↓ downsampling operator, $$$F$$$ Fourier transform and $$$P$$$ undersampling. Subsequently, the image corresponding to the signal model $$$x_n=M_0 exp(-{t_n/T2})$$$ is calculated by fitting a mono-exponential decay onto $$$x_n$$$ (with echo-time $$$t_n$$$), intrinsically estimating $$$T2$$$ and $$$M_0$$$:

$$\operatorname*{arg\,min}_{T2, M_0,x_n} \sum_{i=1}^C \sum_{n=1}^N \sum_{j=1}^J \| PF\left\{S_c\downarrow T_jx_n\right\}-y_{j,n,c}\|^2 + \lambda_ \|x_n{-\ M}_0exp\left(-\frac{t_n}{T2}\right)\|^2 $$

where the first term ensures data-consistency of the HR image with the acquired data and the second term ensures model-consistency. To balance the two terms, a regularization parameter λ is introduced. The optimization is done iteratively by alternating between minimising data- and model-consistency (see Figure 1)

Methods

Simulations were performed on a numerical phantom⁶ to ascertain the trade-off between number of rotations and the acceleration factor. To this end, T2 maps were reconstructed from the simulated undersampled LR k-spaces for an increasing number of rotations and acceleration factors. The differences from the gold-standard T2 map were visually inspected and the root mean square error (RMSE) was calculated.

Data from a multipurpose phantom and four healthy subjects were acquired at 3T (MAGNETOM Skyra, Siemens Healthcare, Erlangen, Germany) with a 10-fold- accelerated GRAPPATINI⁷ prototype sequence (60 sagittal slices, (1x1x4) mm³ resolution, TR=5.4s, ΔTE=10ms, ETL=16). The acquisition was repeated four times with each scan rotated about the longitudinal axis at incremental steps of 45° (TA=18:04min). For comparison, 29 axial slices with 4mm thickness were acquired with a fully sampled MESE sequence. For the phantom, a single slice was acquired using a conventional single-echo SE sequence with three TEs (12,50,100 ms).

The proposed approach was compared to two other methods. The first approach is the “LR model-based + SR” reconstruction where the T2 maps were reconstructed on the individual LR orientations using model-based reconstruction followed by up-sampling to a HR grid. The second approach is the ‘SR only’ reconstruction without the model consistency term.

ROI analysis was performed on the phantom and in vivo T2 maps. T2 values from different compartments of the phantom were compared to the T2 values from fully sampled MESE and SE data. T2 values from ROIs were compared across volunteers to assess the consistency of T2 values.

Results

Numerical simulations showed that the best trade-off is 10-fold acceleration with four rotations (RMSE=7.8 ms, TA=18 mins). Five rotations and 6-fold acceleration showed the least error (RMSE=3.2 ms) but required an acquisition time of 37 minutes (Figure 2). Fourteen-fold acceleration with five rotations had an acquisition time of 14 minutes but an RMSE of 12.5 ms.

The proposed algorithm (Figure 3) showed improved resolution over LR images for both phantom and brain. Comparison between the proposed methods and the ‘SR only’ and ‘LR model-based + SR reconstruction’ showed that integrating SR and model knowledge in one cost function improves the reconstruction (Figure 4).

ROI analysis of the phantom compartments revealed that at shorter T2, the proposed method was comparable with the fully sampled MESE. However, the error increased with higher T2 values (compartments 3 and 4 showing a relative difference of 10-12%, and 15% for compartment 5). For the volunteers’ data, the values found in the brain structures were consistent across subjects (8.5-13.1ms standard deviation).

Discussion and Conclusion

Acknowledgements

References

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