Synopsis

Keywords: High-Field MRI, Relaxometry, T1ρ

A new method entitled alternating Look-Locker (aLL) for mapping of T₁ and T_1ρ is proposed. Magnetization preparation modules incorporating adiabatic full passage pulses were imbedded in a Look-Locker scheme that additionally alternates magnetization from +Z and -Z axes. MB-SWIFT was used as a readout. Analytical derivations and relevant simulations are presented. Phantom experiments and in vivo studies in the rat brain were conducted at 9.4 T. Results show that aLL allows more robust and faster acquisitions as compared to previously introduced steady–state technique, providing the possibility of simultaneous collection of T₁ and T_1ρ maps in one acquisition.

Introduction

In this study, we developed a new method focused on T₁ and T_1ρ mapping. The method is entitled alternating Look-Locker (aLL), and is based on the combination of two known approaches. First is Look-Locker method[1,2]. The second approach, proposed in [3], improves the quality of mapping due to combination of two experiments with the positive and negative initial magnetization. Here, we present the simulated and experimental data collected at 9.4T with MB-SWIFT utilized as a readout. We furthermore compare results obtained with aLL technique and SS-SWIFT method [4] in in vivo rat’s brain and Gd-DTPA phantoms used for the relaxivity analysis.

Method

The schematic of aLL method utilizing MB-SWIFT readout is illustrated in Fig.1. The LL acquisition of magnetization evolution from negative values starts after adiabatic inversion pulse. An acquisition is performed by a segmented collection of n_s image volumes during evolution of magnetization towards steady-state[5]. Each segment consists of n_v k-space readouts. During each segment, MP modules, separated by n readouts satisfying $$$n\leq{n_v}$$$, are applied. Each MP module consists of two AFP pulses, rotating magnetization by 360 degrees and providing an adiabatic T_1ρ relaxation $$$E_{mp}=exp(-T_{MP}/T_{1ρ})$$$. After the acquisition of the last segment, the Z magnetization is again fully saturated, and after T_a a similar LL acquisition is repeated without application of the inversion pulse.
There are two sets of data, collected by averaging each of n readouts, starting evolution of magnetization at negative (M_N) and positive (M_P) hemispheres:
$$\overline{M_N(i)}≈p(M_{ss}-(M_{ss}+M_s)qE_{eff}^i ).........(1a)$$
$$\overline{M_P(i)}≈p(M_{ss}-(M_{ss}-M_s)qE_{eff}^i ).........(1b)$$
where $$$M_s=M_0^*(1-E_a)$$$ and $$$ M_0^*=M_0\sin\theta$$$, M₀ is equilibrium magnetization, 𝜃 is flip angle, $$$E_a=exp(-T_a/T_1)$$$, $$$E_{eff}=exp(-T_R/T_{eff})$$$, $$$M_{ss}=M_0^*\frac{1-E_1}{1-E_{FA}E_1}\frac{1-(E_{FA}E_1)^n}{1-E_{eff}^n}$$$ is steady-state magnetization, $$$E_1=exp(-T_R/T_1)$$$ and $$$E_{FA}=\cos\theta$$$. Here the coefficient $$$p=(1+E_{MP})/2$$$ corrects for the steps during magnetization evolution created by MP modules. Another coefficient q corrects for segmented averaging of the exponential function: $$$q=T_{eff}(E_{eff}^\frac{-n}{2}-E_{eff}^\frac{n}{2})/(nT_R)$$$.
A simultaneous three-parameter fitting using Eqs.1 provides values of T_eff, M_ss and M_s and T₁ evaluated from:
$$T_1(1-E_a)\frac{1-E_{FA}E_1}{1-(E_{FA}E_1)^n}=\frac{M_sT_R}{M_{ss}(1-E_{eff}^n)}........(2)$$
Then T_1ρ is determined from
$$T_{eff}=(\frac{1}{T_1}-\frac{\ln\cos\theta}{T_R}+\frac{T_{MP}}{T_{1ρ}T_Rn})^{-1}........(3)$$
For comparison, the known SS method [4] which allows to extract T_1ρ map from M_ss acquired with different T_MP values was used.
The in vivo study was carried out with 6 Sprague-Dawley rats which were anesthetized using isoflurane for the duration of MRI in a 9.4T 31-cm horizontal-bore magnet equipped with Agilent console (Palo Alto, CA, USA) using a quadrature volume transmit/receive coil.
In both aLL and SS methods, MP modules have the same AFP pulses, namely hyperbolic secant HS4 pulses [6] (4 is the stretching factor) with time-bandwidth product R=20, length of 3ms and peak power of 2kHz. In both methods following parameters were used: T_R=4.396ms, T_MP=6ms, $$$\theta=4^\circ$$$ with FOV 24x24x30mm³, n_v=120 to 200, n=40 or 50, ns=6. Total number of readouts was N_tot=n_vm=32000 to 40000 for aLL, N_tot was generally 80000 for SS method, other than in one case for which N_tot =40000 was used to allow fair comparisons with aLL at same SNR. Total time of acquisition of the aLL method was around 45 mins. For SS method, two experiments were conducted with n_MP =0,1 with each acquisition being 8 -10 mins for each n_MP preparation block, resulting in a total scan time around 20 mins without counting the additional time needed for collecting T₁ map used by SS method to obtain T_1ρ map.
The phantom consisted of 4 plastic tubes filled with 5% weighted agar and different concentrations of gadobenate dimeglumine (Gd-DTPA, multihance, manufactured for Bracco Diagnostics). All imaging parameters were the same as in in vivo study except the total number of readouts was n_v=80, N_tot=11200.

Result

The in vivo T_1ρ maps obtained with aLL and SS methods are displayed in Fig.2. The maps obtained with aLL method’ (Fig.2a) are less noisy relative to maps collected with SS method using similar set of acquisition parameters. Regions of interest (ROI) analysis revealed similar T_1ρ mean values in ROIs among the two methods (Fig.3), however std in general were smaller for aLL technique as compared to SS method. The relaxograms of T_1ρ values within the ROIs (Fig. 4) largely overlapped among the two methods, confirming similarity of T_1ρ values. However, the relaxogram of aLL method exhibited narrower distribution in Tha and IL/PL suggesting more robust outcomes.
The 1/T_1ρ and 1/T₁ dependencies on Gd-DTPA concentration on phantom are shown in Fig.5. The 1/T_1ρ values increased linearly with concentration of Gd-DTPA [7] and both methods show similar results.

Discussion

The proposed aLL method allows simultaneous 3D T₁ and T_1ρ mapping, is faster than known steady-state method [4], and could be generalized to other rotating frame relaxation contrasts. Instead of MB-SWIFT, any other zero-TE sequences like ZTE or UTE could be utilized. The echo-based sequences like FLASH also could be utilized, but the spectrum of the resulting T_1ρ map, in this case, would be narrower and shifted to larger relaxation times. Notably, the alternating scheme introduced in the Look-Locker method allowed improving the SNR, the fitting stability and its precision. Future acceleration can be done with a view sharing, compressed sensing or/and parallel imaging techniques.

Conclusion

A new method entitled aLL has been developed. This method provides robust and efficient simultaneous T₁ and T_1ρ mapping in vivo and could be generalized for mapping of other relaxation contrasts.

Acknowledgements

This work was supported by NIH grant P41 EB027061 (Supplement)

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