Imperfect spoiling in variable flip angle T1 mapping at 7T: Quantifying and minimizing impact

Abstract

Purpose: The variable flip angle (VFA) approach to T₁ mapping assumes perfectly spoiled transverse magnetisation at the end of each repetition time (TR). Despite radiofrequency (RF) and gradient spoiling, this condition is rarely met, leading to erroneous T₁ estimates ( $T_1^{\text{app}}$ ). Theoretical corrections can be applied but make assumptions about tissue properties, for example, a global T₂ time. Here, we investigate the effect of imperfect spoiling at 7T and the interaction between the RF and gradient spoiling conditions, additionally accounting for diffusion. We provide guidance on the optimal approach to maximise the accuracy of the T₁ estimate in the context of 3D multi-echo acquisitions.

Methods: The impact of the spoiling regime was investigated through numerical simulations, phantom and invivo experiments.

Results: The predicted dependence of $T_1^{\text{app}}$ on tissue properties, system settings, and spoiling conditions was observed in both phantom and in vivo experiments. Diffusion effects modulated the dependence of $T_1^{\text{app}}$ on both $B_1^{+}$ efficiency and T₂ times.

Conclusion: Error in $T_1^{\text{app}}$ can be minimized by using an RF spoiling increment and gradient spoiler moment combination that minimizes T₂ -dependence and safeguards image quality. Although the diffusion effect was comparatively small at 7T, correction factors accounting for this effect are recommended.

Keywords: 7T; EPG; MPM; T1 mapping; VFA; imperfect spoiling.

FIGURE 1

Numerical simulations, for each spoiling condition, of ${\mathrm{T}}_1^{\text{app}}$ error (ε) in two specific cases: T₁ = 1.5 s, D = 0.8 µm²/ms, T₂ = 45 ms, and ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}$ = 100% (A); T₁ = 1 s, D = 1 µm²/ms, T₂ = 35 ms, and ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}$ = 160% (B). Sensitivity of ${\mathrm{T}}_1^{\text{app}}$ to ${\mathrm{B}}_1^{+}$ efficiency (C), the true T₂ time (D‐E), the true T₁ time (F‐G), and the diffusion coefficient (H‐I). The sensitivity to T₁, T₂, and D are computed in two conditions: ${\mathrm{B}}_1^{+}$ efficiency of 100% (D‐F‐H) or 160% (E‐G‐I)

FIGURE 2

Residual errors after applying imperfect spoiling correction parameters derived with T₂ = 45 ms and D = 0.8 µm²/ms to ${\mathrm{T}}_1^{\text{app}}$. ${\mathrm{T}}_1^{\text{app}}$ was estimated from data simulated with a true T₁ time of 1.5 s, and a true T₂ time ranging from 35 to 55 ms for nPi = 2π (dashed lines) or 6π (solid lines). Each row corresponds to a different ${\mathrm{B}}_1^{+}$ efficiency, ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}$, ranging from 40 to 160%. The error is minimized when the T₂ used to estimate the correction parameters matches the true T₂ (ie, 45 ms). Dashed vertical lines indicate the RF spoiling increments used in the in vivo acquisitions (ie, 50°, 117°, 120°,and 144°)

FIGURE 3

${\mathrm{T}}_1^{\text{app}}$ (A,B,F,G) and corrected T₁ (C,D,E,H,I,J) in the phantom with ${\varphi }_0\in {\left[50,117,120,144\right]}^{\circ }$, as a function of the ${\mathrm{B}}_1^{+}$ efficiency, ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}$. Dephasing across a voxel of 2π (A‐E) and 6π (F‐J) per TR are shown. A,F, Numerical simulations. Fixed parameters are: T₁ = 950 ms, T₂ = 80 ms, D = 1.7 µm²/ms. B‐E,G‐J, Acquisitions. Corrected T₁ with correction factors from set 1 (C,H), set 2 (D,I), and set 3 (E,J) from Table 1A

FIGURE 4

In vivo${\mathrm{T}}_1^{\text{app}}$, obtained with ${\varphi }_0\in {\left[50,117,120,144\right]}^{\circ }$, as a function of the ${\mathrm{B}}_1^{+}$ efficiency, ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}$. Dephasing across a voxel of 2π (A,B) and 6π (C,D) per TR are shown. A,C, Numerical simulations. Fixed parameters are: T₁ = 1250 ms, T₂ = 45 ms, D = 0.8 µm²/ms. B,D, Acquisitions, and linear fitting for illustration purposes. The number of voxels included in each bin is depicted by the shaded background of each graph for each ϕ₀

FIGURE 5

In vivo${\mathrm{T}}_1^{\text{app}}$, obtained with ${\varphi }_0\in {\left[50,117,120,144\right]}^{\circ }$, as a function of T₂. Dephasing across a voxel of 2π (A‐D) and 6π (E‐H) per TR are shown. Original (×1) (A,C,E,G) and high (×1.6) (B,D,F,H) transmitter reference voltage are shown. A,B,E,F, Numerical simulations. Fixed parameters are: T₁ = 1250 ms, D = 0.8 µm²/ms, ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}=70\text{\%}$, and 130% as measured in the transmit field map in the slice of interest. C,D,G,H, Acquisitions, and linear fitting for illustration purposes. The number of voxels included in each bin is depicted by the shaded background of each graph for each ϕ₀

FIGURE 6

A, Axial view from T₁ maps obtained with nominal ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}$ (ie, no reference voltage manipulation) and nPi = 2π (columns 1, 3, and 5) or 6π (columns 2, 4, and 6) for each RF spoiling increment (rows). These are presented before (ie, ${\mathrm{T}}_1^{\text{app}}$, columns 1 and 2) and after correction for imperfect spoiling using a fixed D of 0.8 µm²/ms and a T₂ of either 35 ms (columns 3 and 4) or 55 ms (columns 5 and 6). Black and green boxes highlight areas particularly affected by changing nPi or applying correction factors. B, Maps of σ _row, the voxel‐wise SD of T₁ across conditions for a given RF spoiling increment (ie, along rows in (A)). C, Maps of σ_col, the voxel‐wise SD of T₁ across RF spoiling increments for a given condition (ie, along columns in (A))

FIGURE 7

Histograms of the estimated T₁ times for WM and GM without (ie, ${\mathrm{T}}_1^{\text{app}}$) and with correction for imperfect spoiling. Five sets of correction factors were computed based on different T₂ times and diffusion coefficients and applied separately. Only those voxels with ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}$ between 95% and 105% (measured with no reference voltage manipulation) were included in the analysis

FIGURE 8

A, Sagittal view of T₁‐weighted images acquired with rectangular or elliptical k‐space sampling using different spoiling conditions. The images have been windowed to highlight background signal. B, The same sagittal slice and an axial slice are shown windowed to visualize the brain. The turquoise line in the axial view indicates the sagittal position while the red line on the sagittal view indicates the axial position. The two phase‐encoding directions (lines and partitions) are indicated in the sagittal view. C, Numerical simulations of the impact of partial voluming on the phase of the signal across lines and partitions (rectangular sampling case, all partitions are acquired before incrementing the line) for each RF spoiling increment

FIGURE 9

Numerical simulations without (BPF = 0, dashed line) and with (BPF = 0.117, solid line) a bound pool fraction leading to MT. The exchange rate from the free to the bound pool was 4.3 s⁻¹, and thermal equilibrium was assumed. The BPF was 0.117 and the diffusion coefficient was 0.8 µm²/ms. A, ${\mathrm{T}}_1^{\text{app}}$ for ϕ ₀ from 1 to 180°, T₂ = 45 ms, T₁ = 1.25 s (for both pools), and ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}$ of 100%. The total dephasing per TR was set to 6π. B‐C, ${\mathrm{T}}_1^{\text{app}}$ as a function of ${\mathrm{f}}_{{\mathrm{B}}_1^{+}}$ and T₂ time, respectively, for ϕ ₀ = 50°, 117°, 120°, and 144°