Synopsis

Quantitative T2-MRI with has a plethora of clinical applications. Current quantitative T2-MRI techniques encode T2-information into the signal magnitude. In this work, a novel method encoding T2 information into the gradient echo signal phase is proposed. With certain RF phase, a heavily T2-weighted signal phase is created. The signal phase has a mild T1 dependence that can be corrected using a spoiled gradient echo magnitude signal. Feasibility in phantoms was demonstrated, as well as in vivo 3D T2 mapping of the abdomen. The proposed method has the potential to be developed into an accurate and robust T2 mapping technique.

Introduction

Theory

Spoiled gradient echo (SGRE) acquisition use a pseudo-random RF phase defined by the phase difference between each RF pulse:Φ(n)=n·ΔΦ (n=0, ….)⁶. A handful of ΔΦ (e.g. 117°) effectively spoil the magnitude of the transverse magnetization. Other choices lead to altered signal magnitude and phase (Figure 1).

The signal phase (θ) depends heavily on T2 and flip angle, mildly on T1 (Figure 1,2). Overall, the steady state SGRE signal with RF spoiling can be written as:

$$s(T1,T2;ΔΦ, α,TR)=M_{0}∙η(T1,T2;ΔΦ, α,TR)∙e^{i[θ(T1,T2;ΔΦ, α,TR)+θ^{'}]} [1]$$

Where M₀ is the longitudinal magnetization at thermal equilibrium. η(T1,T2; ΔΦ, α,TR) is the signal magnitude relative to M₀, θ(T1,T2; ΔΦ, α,TR) the signal phase.

Proposed method (no T1-correction): Based on θ(T1,T2; ΔΦ, α,TR) = - θ(T1,T2; -ΔΦ, α,TR) (Figure 3). θ(T1,T2; ΔΦ, α,TR) can be isolated from M0, η and θ’ by taking the phase difference of 2 SGRE signals acquired with opposing ΔΦs .

$$ θ(T1,T2; ΔΦ, α,TR)=0.5(∠s(T1,T2;ΔΦ, α,TR)- ∠s(T1,T2;-ΔΦ, α,TR)) [2]$$

Given a well-chosen ΔΦ (e.g. ΔΦ=2^o) and a large flip angle (e.g. 18 ^o), θ can be used to measure the change of T2 due to heavy T2 weighting while being only mildly influenced by flip angle and variation of T1 (Figure 3). Based on preliminary observations, an RF phase increment of ΔΦ =±2 o appears to be a good choice of phase increment for this acquisition strategy.

Proposed method (T1-corrected): To account for T1 related phase shifts, we propose a T2-phase encoding (e.g. ΔΦ =2^o, α=18^o) acquisition, accompanied by another acquisition with small flip (e.g. α=5^o) angle and conventional spoiling (e.g. ΔΦ=117^o) whose signal model is well established.

$$s_{1}=s(T1,T2;ΔΦ=2^{o}, α=18^{o},TR)=M_{0}∙η(T1,T2;ΔΦ, α,TR)∙e^{i[θ(T1,T2;ΔΦ, α,TR)+θ^{'}]} [3]$$

$$s_{2}=s(T1,T2;ΔΦ=117^{o}, α=5^{o},TR)=M_{0}∙\frac{sin(α)(1-e^{-frac{TR}{T1}})}{1-cos(α)e^{-frac{TR}{T1}}}e^{iθ^{'}} [4]$$

By taking the ratio of 2 complex signals, the magnitude contains mostly T1 information while the phase contains mostly T2 information:

$$\frac{s_{1}}{s_{2}} = \frac{η(T1,T2;ΔΦ=2^{o}, α=18^{o},TR)}{frac{sin(α)(1-e^{-frac{TR}{T1}})}{1-cos(α)e^{-frac{TR}{T1}}}} e^{i[θ(T1,T2;ΔΦ=2^{o}, α=18^{o},TR)]} [5]$$

Solving Eq.5 will yield a joint estimate of T1 and T2.

Methods

Simulation: Bloch equation simulations were performed to investigate the SGRE transverse signal magnitude and phase with respect to flip angle.

Phantom experiment: All MRI experiments were performed at 3T. The accuracy of the proposed method, was tested on a set of water phantom doped with CuSO4 and MnCl2. Two sets of 3D Single-echo SGRE acquisitions (ΔΦ = 117°, FA =5°, and ΔΦ = 2°, FA =18°) with TR=6.5ms were acquired. SE was acquired to provide a reference for T2 measurements.

In vivo experiment: To test the feasibility of spatially resolved 3D T2 mapping in the liver with water-fat separation, multi-echo SGRE acquisitions (ΔΦ = 117°, FA =5°, and ΔΦ = 2°, FA =18°) were acquired for the proposed method with TR = 6.5ms in a healthy volunteer (breath-hold liver scan). T2 map was reconstructed for water and fat respectively by performing CSE-MRI with single R2* model7 followed by the proposed method with T1-correction. An FOV of 40cm×34cm and a 20cm slab was covered (10 slices) in a 20s scan.

Results

Representative T2 maps were generated in water phantom with the proposed method (Figure 3). Excellent agreement (bias limited to less than 7ms) between T2 measurements by the proposed method and T2 measurements by spin-echo MRI was achieved when T1-correction was included as indicated by the comparison between ROI-averaged T2 values.

T2 maps over the entire abdomen were successfully calculated using single breath-hold 3D SGRE acquisition and the proposed method. (Figure 4). ROI-averaged T2 measurements in liver (28ms), spleen (66ms) and pancreas (41ms) showed qualitative agreement with literature values8 .

Discussion & Conclusion

Acknowledgements

References

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