Sofia Chavez^{1}

B1+ field inhomogeneity is a major source of errors in quantitative mapping. The accuracy of B1 maps, depicting the effects of B1+ inhomogeneity on the flip angle, is thus critical. However, there is no gold standard B1 mapping method in vivo so absolute accuracy is difficult to determine. In this work, we propose steps that exploit known B1 effects in a small phantom to obtain absolute accuracy estimates in vivo. Two B1 mapping methods are required, but neither need be accurate. We demonstrate the proposed assessment by obtaining stability and absolute accuracy measurements of the Method of Slopes B1 maps.

At main field (B0) strengths of ≥3T, the
transmit radiofrequency (RF) field, B1^{+}, is inhomogeneous, giving rise to local flip angle (α)
variations. B1^{+} inhomogeneity is a major source of error in quantitative
parametric mapping methods^{1-5}. The accuracy of B1 maps, which commonly depict the ratio of local to nominal α, is thus critical. Several
methods are proposed for B1 mapping, relying on different acquisition sequences and mathematical models of the signal dependence on α and other MR parameters^{6-10}. By acquiring the signal at least twice, with varying parameters, these methods extract α algebraically.
The accuracy and stability of B1 maps depend primarily, on how well the model predicts the signal. The robustness of B1 maps can be assessed via simulations^{11} and mathematical error propagation^{12}, but these approaches do not consider how well the model predicts signal behaviour in vivo. To better assess the stability in vivo,
repeat experiments can be performed^{13}. However, due to the lack of a gold
standard B1 map in vivo, accuracy is usually measured *relatively*,
i.e., by how much one method varies with respect to another, reference technique. There is no consensus on the reference, thus assessing the accuracy of B1 maps is somewhat arbitrary.

The Method of Slopes (MoS)^{14} has been proposed as a simple 3D
method that yields B1 maps (B1_{MoS}) using an extrapolation to signal null, i.e., exploiting the linearity of the spoiled gradient echo (SPGR) signal vs α relationship as the
signal approaches the null point (α=180°). Here, we measure stability and
*absolute *accuracy of B1_{MoS} maps. In doing so, we propose a set of systematic
steps that can be used to assess B1 mapping accuracy in an *absolute *sense, by-passing the lack of gold standard.

To determine the accuracy of the B1_{MoS} maps,
we use a small phantom (relative to the RF wavelength) with flat signal profile and B1=1 expected within. We also rely on any other B1 mapping method. The key is that it does not need to be accurate because we use ratios as follows.

Experiments were performed at 3T (MR750, GE
Healthcare) with a receive-only headcoil. The phantom consists of an aqueous MnCl_{2} solution, with physiological T2 and T1, in small (*dia*=5cm) and big (*dia*=9cm) beakers. The phantom and six volunteers were scanned in compliance with the institutional REB. For B1_{MoS}, two full volume 3D SPGR sagittal scans (TR=50ms, (4mm)^{3 }) were acquired: S3(α=130°) and S4(α=150°)^{14}. A second B1 map was obtained using the stock Bloch-Siegert (BS)^{10} sequence (B1_{BS}): α =15°, 5mm×(4mm)^{2 }.

Estimates of absolute B1 error were computed using the small beaker data: δB1=B1_{measured}/B1_{true}=AVE(B1)_{small}/1 for both methods. The ratio was then computed: ψ_{small}=δB1_{MoS}/δB1_{BS}. Similarly, ψ_{big}=AVE(B1_{MoS})_{big}/AVE(B1_{BS})_{big }and ψ_{brain}=AVE(B1_{MoS})_{brain}/AVE(B1_{BS})_{brain }were computed for validation (Fig.1). AVE values were taken in regions-of-interest (ROIs) avoiding edges. B1 maps were scaled by ξ=1/δB1 to obtain accurate maps.

Poor RF spoiling can compromise the SPGR signal. Thus, stability and accuracy of B1_{MoS} was tested on the phantom and two volunteers, at various RF seed (φ) values: 50°, 115.4°, 92.4°. S3 and S4 were acquired
three times for each φ, yielding temporal AVE and STD. Nine possible (S3,S4) pairs were used to compute nine
B1 maps at each φ. ROIs were used to extract average values in the beakers while voxelwise computations, preserving spatial information, were used in vivo.

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14. Chavez S, Stanisz GJ. A novel method for simultaneous 3D B1 and T1 mapping: the method of slopes (MoS). Nmr in Biomedicine 2012;25(9).

Fig.1 Flow Chart for Measurement of B1 Accuracy. Measurementes are acquired with a receive-only headcoil. The flat profile with B1≈1 in a small phantom is exploited to extract absolute accuracy of B1 maps in vivo, depsite the lack of in vivo gold standard. Any two B1 mapping methods are required: B1a and B1b. If one of the two methods does not yield a flat profile in the small phantom and changes to the phantom are not successful, and/or ψ_{brain }≠ ψ_{small }for the two methods, one method may not be accurate enough in vivo so another method may be required.

Fig.2 Plots of signal stability measurements in the phantom. Values are taken as averages in ROI within small and big beakers. Multiple measurements of S3 and S4 are superimposed and difficult to distinguish due to the high stability at a given φ. Average values vary with φ but the resulting nine B1 values do not differ significantly (STD(B1)<0.3%). In particular, B1≈1 in the small beaker (AVE(B1)<0.2%), for all φ. Despite the small effect of φ, we choose φ=115.4° for accuracy tests since it seems most stable and AVE(B1) is closest to B1=1.

Fig.3 Results for accuracy tests in the phantom. The ROI placements are shown in (a). Both B1 maps are relatively flat in the small beaker as can see in the profiles in (b). B1_{BS} maps over-estimate B1 relative to B1_{MoS}. Because δB1_{MoS}=1, B1 is scaled (by ξ=1/δB1_{BS}) only for B1_{BS} . The resulting B1 maps (B1_{MoS} and B1_{BS} scaled) are in close agreement as shown by profiles.

Fig.4 Results of B1_{MoS} stability tests in vivo. AVE(B1) and CV(B1) maps across three repeats are shown in (a). AVE(B1) vary slightly across φ, moslty around edges. In the data shown, CV(B1) maps exhibit larger values for a given φ which differs per subject: φ=50° (subj#1) and φ=92.4° (subj#3). However, Subject #1 was scanned again and φ=115.4° gave highest CV values (data not shown) so it is not consistent within subject. Despite this variability, CV(B1) are <2% in most brain regions. Percentage AVE(B1) differences shown in (b) reveal that the largest contribution comes from the instabilities.

Fig.5 Results of B1_{MoS} accuracy tests in vivo. A sample ROI is shown in (a). Resulting B1 maps and B1_{BS} scaled (by 1/δB1_{MoS})_{ } are shown in (b) for subj#1 (ψ_{brain}=0.894) and subj#3 (ψ_{brain}=0.8475) (lowest value). Profiles of B1 maps are shown in (c), demonstrating good agreement between B1_{MoS} and B1_{BS} scaled (since ψ_{brain }≈ψ_{small} , even for subj#3 ), despite some obvious residual brain structure in B1_{BS} maps. (d) shows that ψ_{brain }values, plotted in blue in with AVE( ψ_{brain}) ± SD(ψ_{brain}) given by the black bars, agree with ψ_{small }and ψ_{big}, shown in red.