Synopsis

Quantitative DCE-MRI requires fast pre-contrast T₁ mapping (scan time <3 min) with matching resolution and coverage. Recent advances in imaging have substantially improved resolution and coverage of DCE-MRI but without matched improvements in the pre-contrast T₁ data. Here, we demonstrate a sparse T₁ mapping method and characterize a tradeoff between data acquisition and T₁ statistics, using a variable flip angle (VFA) approach and sparse Cartesian spiral sampling pattern, with image domain wavelet sparsity constraint. This method provides the necessary high-resolution whole-brain T₁/M₀ maps for DCE-MRI tracer kinetic analysis.

Introduction

Method

Data were acquired on a glioblastoma subject using a GE MR750 scanner with a 12-channel head coil. The vendor provided 3D spoiled gradient echo sequence was modified to include sparse undersampling. Six increasing flip angles each with 5000 TRs and a final flip angle with 20000 TRs were performed. Note that the last flip angle has a longer duration since it is used in the DCE scan and precedes the contrast injection. The flip angle increased from 1.5° to 15° logarithmically². Other settings: 5 ms TR, 1.9 ms TE, 240×240×240 mm³ FOV, 2 mm slice thickness, and 256×240×120 matrix size.

Pre-contrast T₁/M₀ mapping is performed by solving the following constrained inverse problem²:

$$p = \min_p \Vert F_u S m - d\Vert_{\ell_2}^2 + \lambda \Vert \Psi m\Vert_{\ell_1}$$

where the estimated anatomic image magnitude is

$$\Vert m\Vert = Dp = M_0\left(1-e^{-\frac{TR}{T_1}}\right)\frac{\sin{B_1\alpha}}{1-\cos{B_1\alpha}}$$

$$$p$$$ concatenates T₁ and M₀ into a vector, $$$F_u$$$ is the undersampled Fourier transform, $$$S$$$ is the coil sensitivity, $$$m$$$ is VFA images, $$$D$$$ converts T₁ and M₀ values into VFA images, $$$\Psi$$$ is a sparsifying transform (e.g., wavelet), $$$d$$$ is measured $$$k$$$-space data, and $$$\lambda$$$ is a regularization parameter. This problem is solved using POCS iterations, which alternate between thresholding wavelet coefficients and forcing data consistency. A flowchart of this workflow is shown in Figure 1.

We used wavelet transform as the spatial sparsifier as it preserves subtle features as well as denoises data. $$$\lambda$$$ was empirically chosen as 0.3 and remained constant in all experiments. To avoid model failure impacting the estimation process, we impose both non-negative and non-infinite constraints on each pixel’s T₁ and M₀ values.

We explored T₁ mapping accuracy as a function of the number of TR periods included at each flip angle. Faster acquisitions were simulated by discarding samples at each flip angle, as illustrated in Figure 2. We measure and report the error in T₁ and M₀ maps as functions of the amount of retained data.

Results

Figure 3 shows the ROI outline and difference maps for T₁, M₀, and anatomic images within the ROI. These maps were obtained by computing differences between results of (5000, 20000) setting and results of any (A, B) setting. Note that M₀ difference decreases as B decreases when A is small. In addition, there was at most 85 ms T₁ difference per pixel, and the differences in quantity of magnetization and image energy were 1.873% and 3.290% at most.

Figure 4 shows means and standard deviations of estimated T₁ in normal white matter. T₁ values were selected from the ROI in Figure 3. All results show similar mean T₁. Interestingly, increasing A or decreasing B both result in a subtle decrease in standard deviation of T₁.

Figure 5 illustrates a $$$k$$$-space error curve, a ROI T₁ absolute change curve and a ROI image increment curve. Both T₁ change and image increment became trivial after 80 iterations, while residuals in $$$k$$$-space were quite significant.

Discussion

This approach enables adequate pre-contrast T₁ estimation matched to the resolution and coverage of modern high-resolution whole-brain DCE-MRI in a reasonable scan time (<3 minutes), in stark contrast to a fully sampled VFA acquisition that would require more than 20 minutes. Despite different subsample settings, both T₁ values mean and standard deviation were stable, and no substantial bias was observed. This indicates that the proposed approach is flexible and allows a trade-off between data acquisition time and T₁ statistics.

Another important observation is significant $$$k$$$-space residuals. One possible cause is that wavelet sparsity regularization can over-smooth images. One way to compensate for these residuals is to impose TGV constraints on vascular parameters directly³, or to enforce data consistency after each iteration (used in this work).

Conclusion

Acknowledgements

References

1. Guo, Y., Lebel, R. M., Zhu, Y., Lingala, S. G., Shiroishi, M. S., Law, M. and Nayak, K. (2016), High‐resolution whole‐brain DCE‐MRI using constrained reconstruction: Prospective clinical evaluation in brain tumor patients. Med. Phys., 43: 2013-2023. doi:10.1118/1.4944736

2. Lebel, R. M., Guo, Y., Lingala, S. G., Frayne, R., Nayak, K. S. "Highly Accelerated DCE imaging with integrated T1 mapping." Proc. ISMRM 25th Scientific Sessions, Honolulu, April 2017, p138.

3. Maier O., Schoormans J., Schloegl M., et al. Rapid T1 quantification from high resolution 3D data with model‐based reconstruction. Magn Reson Med. 2018;00:1–18. https://doi.org/10.1002/mrm.27502