On the choice of the phase difference increment in radiofrequency-spoiled gradient-echo magnetic resonance imaging of liquids with consideration of diffusion

Abstract

In magnetic resonance imaging, the radiofrequency-spoiled gradient-echo method aims for fast acquisition of T1-weighted images. The spoiling mechanism is driven by the radiofrequency phase difference increment. In clinical (in-vivo) imaging, the phase difference increments of 50°, 115.4°, 117° and 150° are in standard use. In this work, we examine how accurate these increments guarantee T1-weighting also in free liquids, in particular with different diffusion coefficients. The non-standard phase difference increment 169°, which was shown to improve T1 quantification methods, is considered as well. Signal simulations were performed with the extended phase-graph with diffusion concept; experiments were performed on different liquid phantoms (water with contrast medium, silicone oil). In the simulations, a parameter space consisting of relaxation times, diffusion coefficient, sequence repetition time, flip angle and image resolution was examined. The resulting efficiency of radiofrequency spoiling was quantified by the average deviation of the simulated signal-vs-flipangle curve from the ideal curve. It was found that ideal spoiling is generally better approximated with a phase difference increment of 169° compared to the other examined values. From the four commonly used values, 115.4° is recommended, in particular when the influence of diffusion is low. For clinical in-vivo imaging parameters, all examined values of the phase difference increments offer a good approximation of ideal spoiling as expected. In conclusion, radiofrequency spoiling in free liquids can be improved by using a phase difference increment of 169°.

Fig 1. Simulated RF-spoiled signals for T1/TR = T2/TR = 20, α = 30°, no diffusion.

(A) Signals S⁺ and S^- in dependency of the RF phase difference increment ψ. (B) Location of the four ψ-values used in practice (ψ = 50°, ψ = 115.4°, ψ = 117°, ψ = 150°) and ψ = 169°. (C) Signal S⁺ and the Ernst curve (ideal spoiling) in dependency of the flip angle (α = 30° as used in A and B is indicated).

Fig 2. Illustration of contrast varying with ψ.

H₂O+Gd Phantom (top row) and the silicone phantom (bottom row) imaged with different ψ-values (columns) but otherwise identical imaging parameters (TR = 20 ms, α = 60°). Different ψ-values result in different contrast.

Fig 3. Measurements (markers) and simulations (solid lines) of the RF-spoiled Signal S⁺.

(A) Silicone oil phantom with T1 = 1290 ms, T2 = 399 ms, TR = 20 ms, D = 0.0055 ∙ 10^-3 mm²/s. All curves deviate remarkably from the ideal spoiling case (Ernst curve, black line). (B) H₂O+CuSO₄ phantom with T1 = 540 ms, T2 = 340 ms, TR = 20 ms, D = 1.93 ∙ 10^-3 mm²/s. Dashed lines are the simulated curves without diffusion to highlight the impact of diffusion.

Fig 4. ε-Values according to Eq. 6.

The parameter ε quantifies the deviation of the RF-spoiled signal S⁺(α) from ideal spoiling, here for variation of T1/TR and T2/TR (TR = 20 ms) and the selected values for ψ (rows) and diffusion coefficient D (columns). The colors represent log₁₀(ε). Note also the logarithmic scaling of the colorbar. Relaxation times and diffusion coefficient for the silicone oil phantom (marker x, representing the curves in Fig 3A), grey matter at 3 Tesla (marker o) and the H₂O+CuSO₄ phantom (marker + , representing the curves in Fig 3B) are indicated.

Fig 5. ε-Values as for

Fig 4. Here with TR = 50 ms.

Fig 6. Numerical simulation of spoiling quality (ε-values) in dependence of image resolution and repetition time TR.

The voxel size on the x-axis label refers to readout direction. Top row: TR = 20 ms, bottom row: TR = 50 ms. (A)+(D): silicone oil phantom, (B)+(E): grey matter at 3T, (C)+(F): H₂O+CuSO₄ phantom.