Introduction

At 7T MP2RAGE¹ is commonly used for 3D structural T₁-weighted imaging of the brain. It acquires two rapid gradient echoes (INV1 and INV2) collected after a common inversion pulse, which are combined in a ratio to produce an image (UNI) with maximum contrast between white matter (WM), grey matter (GM) and cerebrospinal fluid (CSF). The sequence can also be optimised to obtain UNI and clinically relevant FLuid and White Matter Suppression (FLAWS)^2-4 images within one acquisition⁵. Here, in addition to UNI and FLAWS images, we used analytical equations accounting for partial Fourier acquisitions to produce longitudinal relaxation time (T₁) and proton density (PD) maps, having developed an approach to mitigate fitting problems.

Methods

The time between two consecutive inversion pulses (MP2RAGE repetition time, MP2RAGETR¹) consists of the delay between the inversion pulse and the first GRE block (TA), the delay between two GRE blocks (TB), the delay after the second GRE block until the next inversion pulse (TC), and the two GRE blocks¹. Following the approach by Marques et al¹, the MP2RAGE steady-state signal for the longitudinal magnetization is derived as

$$m_{z,ss}=\frac{M_0\left[\left(\left((1-EA)(cos⁡(α_1)E1)^n+(1-E1)\frac{1-(cos⁡(α_1)E1)^n}{1-cos⁡(α_1)E1}\right)EB+(1-EB)\right)(cos⁡(α_2)E1)^n+(1-E1)\frac{1-(cos⁡(α_2)E1)^n}{1-cos⁡(α_2)E1}\right]EC+(1-EC)M_0}{1+eff(cos⁡(α_1)cos⁡(α_2))^n\hspace{1mm}e^{-MP2RAGETR/T_1}}$$

where EA = exp(-TA/T1), EB = exp(-TB/T1), EC = exp(-TC/T1), and E1 = exp(-TR/T1). TR here is the time between the n small angle excitations in the GRE readouts (TR≠MP2RAGETR). The inversion efficiency eff=1 was assumed. In four subjects, data were also analysed using eff=0.96. Partial Fourier of 6/8 was used in this study in the first phase-encoding (partition) direction, acquired in the innermost k-space loop resulting in a shift in the position of k-space centre within the readout, requiring modified signal equations¹:

$$\begin{align}GRE_{TI1}&=M_0\hspace{1mm}B_1^-e^{-TE/T_2^*}sin⁡(α_1)\left[\left(\frac{-eff.m_{z,ss}}{M_0}EA+(1-EA)\right)(cos⁡(α_1)E1)^\frac{n}{3}+(1-E1)\frac{1-(cos⁡(α_1)E1)^\frac{n}{3}}{1-cos⁡(α_1)E1}\right] \\
GRE_{TI2}&=M_0\hspace{1mm}B_1^-e^{-TE/T_2^*}sin⁡(α_2)\left[\frac{\frac{m_{z,ss}}{M_0}-(1-EC)}{EC(cos⁡(α_2)E1)^\frac{2n}{3}}-(1-E1)\frac{(cos⁡(α_2)E1)^\frac{-2n}{3}-1}{1-cos⁡(α_2)E1}\right]\end{align}$$

To fit T₁ and M₀ (PD), the equations above were combined as a cost function T₁=argmin|GRE_TI1/k₁–GRE_TI2/k₂| where k₁ and k₂ represent the right-hand side of the equations excluding M₀. T₁ values were initially calculated using lsqnonlin and vpasolve functions of MATLAB R2018a (www.mathworks.com). To mitigate fitting problems within some WM regions (due to the suppressed WM INV1 signal and the discontinuity of the cost function as k₁ approaches zero), an algorithm was developed. It can be summarized as: 1) a brute-force search for T₁s between 100ms and 10000ms with steps of 1ms followed by a finer search with 0.001ms steps around T₁ minimizing the cost function, 2) if step 1 returns T₁=100ms because the real minimum is missed and a) abs(INV1)>0.02 where 0.02 is an empirical value, find the maximum slope of the function and make a search around this area b) abs(INV1)≤0.02, by fitting a line to the T₁s calculated using the range (INV1-1):0.01:(INV1+1), determine the value of T₁ for INV1 signal with ~0 amplitude, 3) If steps 1-2 fail (large residual), repeat 1-2 for T₁s of 100ms to 30000ms.
To unambiguously determine the polarity of the magnetization at TI₁ due to T₁ recovery, phase information was used as below:

$$INV1_{corrected}=real\{\hspace{1mm}INV1_{magnitude}e^{i(\,INV1_{phase}-INV2_{phase})\,}\}$$

The receive field bias (B₁^-) was calculated using SPM12⁶. A smoothed flip angle (B₁⁺) map^7-9 was used to define actual flip angles achieved.
7 healthy children and 10 adults were scanned with consent using a 7T MRI scanner (MAGNETOM Terra, Siemens Healthcare, Erlangen, Germany) either with a 1TX/32-channel RX or an 8TX/32-channel RX coil used in CP mode (both Nova Medical). Scan parameters are summarized in Table 1. In each case the T₁ maps provided by the scanner were compared to T₁ fitting results. Data acquired across age groups at the same MP2RAGETR (protocols summarized in Table 1b) were compared by segmenting the 3D T₁ maps using SPM12⁶ and calculating the means and standard deviations.

Results

Fig.1 shows T₁ maps from different fitting procedures used demonstrating low frequency spatial differences between scanner T₁ maps that do not account for variable B₁⁺. Further, distributed WM voxels have an improved fit with our optimised algorithm. Fig.2 demonstrates representative images and maps from a child from the single acquisition. T₁ results acquired at different MP2RAGETRs demonstrated highly consistent T₁ values within tissue class (Fig.3). Fitting results without B₁⁺ correction (as for scanner T₁ maps) at an MP2RAGETR of 4000ms are also included (Fig.3e). In Fig.4, the T₁ results from all subjects are plotted. Using eff=0.96, WM and GM T₁ values were ~4% and ~6% larger compared to those using eff=1, respectively (data from 4 adults). Adult T₁ values were more consistent and significantly lower than children T₁s (Mann-Whitney U-test, p<0.01) despite variability in the protocol and RF coil used.

Discussion and Conclusion

Quantitative T₁ maps and PD-weighted images were produced from a single MP2RAGE acquisition designed to obtain UNI and FLAWS images simultaneously⁵. An analytical solution of the MP2RAGE signal equations was used together with B₁⁺ maps and a dedicated algorithm to derive both T₁ and unscaled PD maps. Despite the small sample size, expected WM and GM T₁ decreases with age were found^11,12. Scanner T₁ map accuracy is reduced by not corrected B₁⁺ variability^13,14. In conclusion, using an MP2RAGE sequence and a dedicated fitting algorithm, it was possible to produce T₁ and PD maps alongside UNI and FLAWS-images within a clinically feasible single acquisition in both children and adults at 7T.

Acknowledgements

The authors would like to acknowledge David Leitao for valuable discussions.

This work was supported by GOSHCC Sparks Grant V4419, King's Health Partners, Wellcome Trust Collaboration in Science grant [WT201526/Z/16/Z], and by core funding from the Wellcome/EPSRC Centre for Medical Engineering [WT203148/Z/16/Z].

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