Calibrating variable flip angle (VFA)-based T1 maps: when and why a simple scaling factor is justified
Sofia Chavez1

1CAMH, Toronto, ON, Canada


Variable Flip Angle (VFA)-based T1 maps are known to be prone to errors deriving from B1 errors (inaccurate knowledge of flip angles) and poor signal spoiling. In general, in vivo T1VFA values tend to overestimate T1 values obtained using a gold standard inversion recovery method :T1IR. Calibrating T1VFA with T1IR has been proposed but it requires knowledge of the exact relationship between these. This work models the contribution of B1 errors and poor spoiling to T1VFA errors and via simulations, the conditions for T1VFA/T1IR= constant (i.e. simple scaling) are derived. Experiments on phantoms and in vivo are used for validation.


T1 brain maps, essential for probing brain microstructure, are difficult to produce accurately in vivo. Thus, a variety of T1 mapping methods are currently used1-9, leading to a lack of consensus of T1 values and a need to calibrate across methods7. A gold standard inversion recovery based T1 map (T1IR)8 is often used to validate and assess the accuracy of T1 maps. In particular, the variable-flip-angle (VFA) method, using a spoiled-gradient-echo (SPGR) sequence, has been shown to produce T1VFA that overestimate T1 values in vivo, relative to T1IR7. The main sources of T1VFA map errors are the errors in B1 maps (depicting the ratio of local to nominal α) and poor RF spoiling7,9-12. To correct for T1VFA errors, a calibration with respect to T1IR has been suggested although the exact form has not been given7. While it is tempting to use a simple scaling factor, this has not yet been justified, i.e., the conditions required for this have not been described. Thus, this constitutes the main goal of this work.


A simple scaling factor, ξ, can correctly calibrate a T1VFA map only if the relationship between T1VFA and T1IR is constant, or equally, the T1VFA error, δT1VFA, is constant: δT1VFA=T1VFA/T1IR =1/ξ. Here, a two-point VFA method is used to compute T1VFA from SPGR signals: S11) and S22) where Si=S0(1-E1)sin(B1·αi)/(1-E1cos(B1·αi)), for E1=exp(-TR/T1), B1=(αi)locali and S0=equilibrium signal. Simulations are used to model the effects of B1 errors and RF spoiling errors on T1VFA as follows.

Most B1 mapping methods produce approximately constant brain B1 error13-15: δB1=B1measured/B1true. Furthermore, the relationship δT1VFA vs δB1 is approximately independent of (B1,T1), over a range of relevant brain values (B1:0.8-1.3; T1:800-2000ms)4,16, but noise (low SNR) can compromise this16. Thus, given sufficient SNR, δB1 produces a constant brain δT1VFA and, in the absence of poor spoiling, a simple scaling factor: ξ=1/δT1VFA can be used to calibrate T1VFA maps.

Poor RF spoiling, resulting from poor RF seed, φ, selection or challenging parameters (e.g.,α>20°), can produce banding/ghosting artifacts and signal instabilities/bias12,17,18. Isochromat simulations have been used to propose φ values10,11,12,17,18, optimizing either signal accuracy or stability, but the models fail to predict the signal in vivo7,11. Thus, we take a different, novel approach. We assume that φ is chosen to obtain stable but biased signal with error: δS i=(Si)meas/Si. Using (α12)=(3°,14°), we can assume δS1≈1 and simulate the effects of δS2 on δT1VFA .Using the SPGR signal equation, step-wise values of δS2=0.9:0.05:1.1 are used to compute T1VFA(S1,(S2)meas) and δT1VFA vs δB1 curves are traced out for relevant (B1,T1), at each step. The curves for δS2≠1 in Fig.1a show the simultaneous effect of δB1 and poor spoiling on δT1VFA. To a good approximation, these curves are independent of (B1,T1), as long as SNR is sufficient (Fig.1b). Thus, for a simple scaling factor to be justified, we propose the following conditions: SNR(S1)≥15, constant δB1, stable (S1,S2) with δS1=1 and constant δS2.

To test these conditions, experiments were performed at 3T (MR750, GE Healthcare) with a receive-only headcoil. A phantom (consisting of an aqueous MnCl2 solution in two beakers) and six volunteers were scanned in compliance with the institutional REB. (S1,S2) were acquired from full volume, 3D FSPGR sagittal scans: (1mm)3, ASSET=2, TR=10.7ms6. Repeat phantom measurements (3X) were obtained at several seed values around φ=50° (proposed for stability)11 and φ=115.4° (GE default). Three volunteers were also scanned thrice at φ=50° and 115.4°, and once at other φ values. Signal ratios across φ (i.e., normalizations) were used to test for biases. In vivo, B1MoS maps were produced using the Method of Slopes6 for T1VFA computations. Single slice, four-point T1IR were also produced8 per subject yielding ξ=T1IR/T1VFA , using white matter (WM) T1 values.


Fig.2 shows repeated phantom measurement results. Data points represent average values over regions-of-interest (ROIs) shown in (a). CV =(STD/AVE)·100% maps show signal instabilities. Signal biases are tested using ratios/normalizations. Fig.3 shows in vivo results from signal stability and bias experiments at φ=50° and 115.4°. Fig.4 shows in vivo bias tests for other φ. ROIs are used to obtain signal instability/bias per φ, per tissue type. Fig.5 shows δT1VFA assessments in vivo.

Discussion and Conclusion

Phantom signal averaged in ROIs changes with φ>115.4° but remains temporally stable; poor spoiling causes local increased instability and nonuniform δS2 (shown in CV maps and normalized S2 images). In vivo S1 and S2 (for φ=50°) give stable signal with δS1=1 and constant whole brain δS2. Using these acquisitions and B1MoS, we demonstrated that the conditions for simple scaling were met, thus yielding consistent δT1VFA for all volunteers: AVE(δT1VFA)±STD(δT1VFA)=1.328±0.022, and ξ=1/AVE(δT1VFA)=0.753.


No acknowledgement found.


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Fig.1 Simulated plots describing the relationships between δB1, δS2 and δT1VFA. (a) shows that for all relevant (B1,T1) values, the δT1VFA vs δB1 curves are still relatively consistent given a constant |δS2|>0 (small spread of same-coloured curves) so to a good approximation, we expect constant δT1VFA for constant values of δB1 and δS2. (b) shows the effect on the curves when Gaussian distributed noise with standard deviation=σ=S1/SNR, is added to S1 and S2. The independence of the curves on (B1,T1) values is compromised by noise as shown by the increased spread of equal-coloured curves for SNR=15 and 8.

Fig.2 Results from repeated measurements in the phantom. Signal from each scan is averaged within the central slice ROIs shown in (a). Temporal average (AVE) and standard deviation (STD) are plotted in (a) across φ. Temporal STD of average signal within an ROI varies little across φ: it is not a good measure of poor spoiling. Signal bias is large for φ=119°-121° as expected 10. In (b), sample images: AVE, CV and Ratio of AVE (normalized to φ=50.2°), show that poor spoiling can lead to signal instability (increased CV) and nonuniform signal bias (Ratio of AVE) (at φ=119° and 121°).

Fig.3 Sample stability results for one volunteer. (a) shows AVE and STD maps for repeat measurements at φ=50° and 115.4°. To measure the effect over the whole brain, STD values were summed per slice. Slice-wise STD are plotted in (b). Whole brain total(STD) was used to score the seed values. For S1, both values are stable. For S2, φ=50° is more stable (smaller score). The same results were obtained on the other two subjects. (c) shows that the Ratio of AVE(S2) across φ gives Gaussian distributed values centered around 1, suggesting δS2 is constant and equal for both φ values.

Fig.4 Results of signal bias measurements on one volunteer. (a) shows normalized S2 images for all φ. The images are single S2 measurements normalized by the temporal AVE(S2) obtained at either φ=50° (top) or φ=115.4°(bottom). Histograms of whole brain normalized S2 values (black lines) are shown with Gaussian fits (red) and peak values. Images for φtested < 118.0° look uniform. Histograms show constant whole brain δS2, to within experimental error, with small bias variations given by shifting peaks. (b) shows that for φtested < 118.0°, S1 and S2 are stable and consistent within structure. Results were similar for other volunteers.

Fig.5 Results for obtaining the scaling factor in vivo. T1 maps for two volunteers are shown. Optimal φ=50° was used (better stability of S2) for the FSPGR scans. Histograms for T1VFA (whole brain) and T1IR (single slice) are superimposed and WM peaks are identified. T1VFA errors can be computed as: δT1VFA=T1VFA(WM)/T1IR(WM). δT1VFA was computed for all subjects and very close agreement was obtained: AVE(δT1VFA) ± STD(δT1VFA) = 1.328±0.022. This yielded: ξ=1/AVE(δT1VFA)=1/1.328=0.753. Histograms and images of T1VFA scaled (i.e., ξ·T1VFA) show very good agreement with T1IR values and thus validate the simple scaling factor calibration for this data.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)