Introduction

In the last decade, interest in multiparametric estimation has increased judging from the growing number of studies published on simultaneous relaxometry mapping¹. Relaxometry parameters such as T1 and T2* have been demonstrated to be versatile biomarkers for the investigation of stroke, multiple sclerosis, to study the pathogenesis and the evolution of several neurodegenerative diseases, as well as for tumour identification and characterisation^2,3. However, it is well known that T1 mapping can not transcend knowledge of the excitation field B1, whose inhomogeneities could hinder accuracy in T1 estimation, especially at high magnetic field⁴.
Among the proposed sequences for B1 mapping, Actual Flip angle Imaging (AFI)⁵ stands out to be a low-SAR⁶ 3D gradient-echo based sequence that implements two repetition times (TR₂ = n·TR₁, n>1) to sample each k-space line in different steady states. As part of TR₂ is generally unused and hosts relaxation-induced signal decay, this could be sampled via multi gradient-echo readout without any time penalty. Here, we propose the Relaxation Alternate Mapping of Spoiled Echo Signals sequence (RAMSES) for simultaneous T1, T2*, B1, and net magnetisation (M0) mapping following the Variable flip angle with Actual Flip angle Imaging (VAFI)⁷ approach, which requires an AFI and at least a spoiled gradient echo (SPGR) image.

Methods

RAMSES was developed as a 3D RF-spoiled SPGR-based sequence – the respective pulse diagram is reported in Figure 1 – and tested at 4.7 T and 7 T with an MRI preclinical scanner (MR Solutions, Guildford, UK).
Simulations: we performed sequence simulations via Extended Phase Graph model⁸ in order to define the RF spoiling increment to be used for TR₁ = 20 ms, n = 4, T1 $$$\in$$$ [0.5, 4.5] s, T2 $$$\in$$$ [0.1, 1] s, D $$$\in$$$ [0, 0.002] mm²/s, flip angle α = 60°. RF phase for the j-th pulse was incremented as φ_j = φ_j-1 + jφ₀.
Test samples: gelatin phantom and Gd-DOTA water solutions (Dotarem, Guerbet, Villepinte, FR). Ground truth values were estimated based on MRI data acquisition using a 22-points Inversion Recovery (TR = 10 s, TI $$$\in$$$ [0.075, 3.5] s) and a multi-echo gradient-echo (MGE) with bipolar readout (TR = 20 ms, α = 60°, TE₁ = 2.19 ms, ΔTE = 1.24 ms, 6 echoes). RAMSES data were acquired with matrix size = [128$$$\times$$$128$$$\times$$$64], FOV = (40$$$\times$$$40$$$\times$$$40) mm³, TR₁ = 20 ms, n = 4, TE = 2.19 ms, ΔTE = 1.24 ms, 5 echoes, read direction only spoiling gradient areas for TR₁ and TR₂ = 327.1/1414.7 mT·ms/m.
SPGR images were acquired with the same parameters, with α = [5,14,24]°, for a total of M = 3 volumes. T1, B1 and M0 were estimated voxel-wise by fitting the first two echo signals of RAMSES (S_R1, S_R2) and the SPGR images (S_S). Steady state signal model for these were:
$$ S_{R 1,2} = M_0 \sin(\kappa\alpha) \cdot \frac{1-E_{2,1}+(1-E_{1,2})E_{2,1}\cos(\kappa\alpha)}{1-E_1E_2\cos^2(\kappa\alpha)} \, , \, S_{S} = M_0 \sin(\kappa\alpha) \cdot \frac{1-E_1}{1-E_1\cos(\kappa\alpha)} $$
with κ representing the flip angle scaling factor, E_1,2 = exp(-TR_1,2/T1) and assuming TE<<T2*. The residual sum of squares was minimised in a bounded condition using the L-BFGS-B algorithm⁹:
$$ RSS = \sum_{i=1}^2 \Big( S_{Ri} - \hat{S}_{Ri} \Big)^2 + \sum_{j=1}^{M} \Big( S_{S,j} - \hat{S}_{S,j} \Big)^2 $$ where $$$\mathrm{S}$$$ and $$$\mathrm{\hat{S}}$$$ represent the voxel-wise model and observed signal intensity, respectively. T2* was computed by fitting S_Ri with i=[2,5] against an exponential decay.

Results

RF spoiling characteristics for RAMSES follow the behavior of AFI sequence, so we chose the RF spoiling characteristic increment φ₀ = 56.5°, which both minimises the median and the range of the absolute distance between the simulated signal and the ideally spoiled steady state signal for S_R1 (see Figure 2).
Full 3D RAMSES volumes with three additional SPGR volumes were acquired with a total acquisition time of 22 minutes with no additional time with respect to VAFI method. Mean and standard error for T1 and T2* estimates from RAMSES on phantoms are reported in Figure 3 and compared to IR and MGE values, respectively. T1 values show a small underestimation with respect to the ground truth values (relative difference lower than 10% - its higher value for the 125 mM sample is likely due to the T2*>>TE assumption of RAMSES, here violated), RAMSES mean and standard errors for T2* are comparable to ground truth MGE values. Independent fitting of the 3 SPGR volumes with no B1 information resulted in biased (>30%) and noisy (standard deviation > 1.2s) T1 estimates.

Discussion

RAMSES allows accurate and precise estimation of both T1 and T2* for a range of values at high magnetic field where B1 inhomogeneities can result in variations of the flip angle amplitude exceeding 40% of the nominal value. Spoiling characteristics need to be carefully taken into consideration to avoid ghost artifacts and biases from the ideal steady state, which may arise when a completely spoiled regime is not reached. Further correction of T1 values based on the computed T2* values could be integrated. Also, validation of the RAMSES protocol for in-vivo imaging is needed.

Conclusion

We propose RAMSES, a new 3D gradient-echo based sequence for quantitative relaxometry mapping which, in combination with at least one SPGR is able to provide accurate T1, T2*, B1, and M0 maps.

Acknowledgements

This research was funded by the B-Q MINDED EU H2020 project under grant agreement No.764513.

References

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