Soraya Gavazzi^{1}, Cornelis AT van den Berg^{1,2}, Alessandro Sbrizzi^{2}, Mick Bennis^{3}, Lukas JA Stalpers^{3}, Jan JW Lagendijk^{1}, Hans Crezee^{3}, and Astrid LHMW van Lier^{1}

The feasibility of permittivity imaging relies on high precision of the underlying $$$\it{B_1^+}$$$ amplitude maps. We tested AFI, Bloch-Siegert and DREAM $$$\it{B_1^+}$$$ mapping techniques on a pelvic-sized phantom at 3T, comparing their SNR in $$$\it{B_1^+}$$$ maps and (resulting) permittivity precision. Our results indicated that the DREAM-based permittivity map was the most sensitive to sequence-related systematic errors. The commonly-used AFI technique, instead, was the least precise method. We also found that Bloch-Siegert is generally best suited for permittivity mapping compared to the other two methods, due to its higher $$$\it{B_1^+}$$$ precision and accuracy.

A pelvic-sized, two-compartment phantom^{6} was used to test the three $$$\it{B_1^+}$$$ mapping techniques. Phantom properties resembled human pelvis properties. All MR scans were 3D acquisitions performed on a clinical 3T scanner (Ingenia, Philips Healthcare, Netherlands), using a 28-channel body array for reception. For all 3 techniques an equal (clinically acceptable) scan time of ~5:30 minutes was strived for. See *Table1* for $$$\it{B_1^+}$$$ mapping sequence settings and phantom properties.

Permittivity images were reconstructed using a noise-robust kernel for Laplacian operation^{1}. The transceive phase assumption^{1} was employed and a spin echo sequence (TE/TR = 5.2/1200 ms) was used for transceive phase mapping^{7}.

For each compartment and each technique, SNR values of $$$\it{B_1^+}$$$ amplitude ($$$\it{SNR_{B_1^+}}$$$, Eq 1, *Fig.2*) were calculated. The uncertainty in $$$\it{B_1^+}$$$ (i.e. $$$\it{\Delta B_1^+}$$$) was retrieved by applying sequence-specific error propagation on the SNR of the original images $$$\it{S_1}$$$ and $$$\it{S_2}$$$ (Eq 3,5,7). SNR maps of the images were obtained with Kellman’s method^{8}. Moreover, the uncertainty in the permittivity $$$\Delta\varepsilon_r$$$ was calculated as the standard deviation (SD) of $$$\varepsilon_r$$$ in boundary-free regions inside both compartments.

*Figure3 *displays $$$\it{B_1^+}$$$ and $$$\it{SNR_{B_1^+}}$$$ distributions in the phantom obtained with the three methods. A low value for $$$\it{SNR_{B_1^+}}$$$ in the inner sphere was found for all techniques, with the lowest value for AFI. In terms of $$$\it{SNR_{B_1^+}}$$$, in the outer compartment BS outperformed DREAM and AFI, which shared similar values. The sequence-based permittivity images showed that noise and systematic errors hampered the reconstruction in AFI and DREAM. BS-based $$$\varepsilon_r$$$-map, instead, provided the predicted permittivity distribution (as quantified in *Fig.4*), including anti-symmetric transceive phase assumption errors in the outer compartment^{6}.

In *Figure5* the relationship between $$$\it{SNR_{B_1^+}}$$$ and $$$\Delta\varepsilon_r$$$ is demonstrated experimentally for both compartments, along with Lee's theoretical model^{2}. In the inner high-$$$\varepsilon_r$$$ sphere, DREAM and BS had comparable $$$\it{SNR_{B_1^+}}$$$ leading to $$$\Delta\varepsilon_r$$$ $$$\approx$$$40 units (75% of true $$$\varepsilon_r$$$). Nonetheless, a higher increase in $$$\it{SNR_{B_1^+}}$$$ was found in the outer low-$$$\varepsilon_r$$$ compartment for BS, where $$$\Delta\varepsilon_r$$$ reduced to 20 units (55% of true $$$\varepsilon_r$$$).

Our results showed that BS is best suited for EPT purposes and that AFI was the least precise method. BS and DREAM shared similar precision performances (as is evident in the high-$$$\varepsilon_r$$$/$$$T_1$$$ compartment); nonetheless, the higher flip angle of BS in relation to short $$$T_1$$$ of the outer compartment (Table1) led to a higher $$$\it{SNR_{B_1^+}}$$$ than in DREAM (with settings chosen as recommended(9)).

Although the higher $$$\it{SNR_{B_1^+}}$$$, BS $$$\Delta\varepsilon_r$$$ was still relatively large compared to the true $$$\varepsilon_r$$$.

BS-based average permittivity was close to the true value in both compartments (*Fig.4*), unlike AFI and DREAM, where mean $$$\varepsilon_r$$$-values might have been affected by the higher degree of $$$\it{B_1^+}$$$ imprecision. Not only $$$\it{B_1^+}$$$ precision, but also sequence-derived inaccuracies and the transceive-phase assumption bias correct permittivity retrieval. White arrows in DREAM-based $$$\varepsilon_r$$$-map in *Figure3*, for instance, evidently point to errors deriving from the $$$\it{B_1^+}$$$ map itself rather than boundary errors (verified using simulations, results not shown).

Moreover, such sources of error possibly influence the calculated $$$\Delta\varepsilon_r$$$. This might also explain the little discrepancy between experimental data and Lee’s model (e.g. in inner compartment for AFI and DREAM, *Fig.5*). However, we found good agreement between measurements and the theoretical model (which was limited to the noise only) for this specific kernel ($$$K_{vL}$$$).

We have explored the capabilities of AFI, Bloch-Siegert and DREAM sequences in terms of $$$ \it{SNR_{B_1^+}}$$$ at 3T on a heterogeneous pelvic-sized phantom in order to estimate their impact on permittivity precision. Furthermore, we have validated experimentally Lee’s theory. We have identified the BS technique to be the best $$$ \it{B_1^+}$$$ mapping candidate for EPT, for its high precision and accuracy.

Analogous results can be expected* in vivo*, since our phantom properties were in the range of dielectric and relaxation properties of the human pelvis.

Overall, extremely precise and accurate $$$ \it{B_1^+}$$$ maps are needed for permittivity quantification with conventional EPT; however, other
reconstruction methods, e.g. CSI-EPT^{10}, might enable accurate permittivity estimation already with clinically achievable $$$\it{SNR_{B_1^+}}$$$.

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9. Nehrke K et al. Volumetric B_{1}^{+} mapping of the brain at 7T using DREAM.
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10. Balidemaj E et al. CSI-EPT: A Contrast Source Inversion Approach for Improved MRI-Based Electric Properties Tomography. IEEE Trans Med Imaging. 2015;34(9):1788–96.

11. Voigt T et al. Patient-individual local SAR determination: *In vivo* measurements and numerical validation. Magn Reson Med. 2012;68(4):1117–26.

*Table 1*. Settings for each $$$\it{B_1^+}$$$ mapping method: AFI, DREAM and Bloch-Siegert (BS) and phantom properties. 3D scans were acquired for all methods. Receiver non-uniformity was corrected by enabling CLEAR^{11}. DREAM was set based on the recommended parameters in ref9.

The phantom consisted of an elliptical cylinder with an inner sphere. Its length was 40 cm.

The dielectric properties were validated at 128 MHz with a dielectric probe (85070E, Agilent Technologies).

$$$T_1$$$ and $$$T_2$$$ values were average values taken from $$$T_1$$$ and $$$T_2$$$ maps measured with a vendor-specific mix-TSE sequence, single slice, isotropic voxel size = 5 mm^{3}.

*Figure 2*. Equation 1 defines the $$$\it{SNR_{B_1^+}}$$$, Eqs 2,4,6 illustrate the formulas to retrieve transmit sensitivity $$$\it{B_1^+}$$$ for all methods from the combination of the original signals $$$S_1$$$ and $$$S_2$$$. Eqs 3,5,7 represent the uncertainty in $$$\it{B_1^+}$$$, $$$\it{\Delta B_1^+}$$$, for each method, and were calculated with the law of error propagation ($$$\Delta \it{B_1^+}$$$ = $$$\sqrt{(\frac{\partial \it{B_1^+}}{\partial \it{S_1}})^2 \cdot \eta_1^2 + (\frac{\partial \it{B_1^+}}{\partial \it{S_2}})^2 \cdot \eta_2^2}$$$). Note that $$$\eta_i$$$ = $$$\frac{S_i}{SNR_i}$$$ is the noise level in the image $$$S_i$$$ and $$$\Delta\theta_i$$$ = $$$\frac{1}{SNR_i}$$$ is the uncertainty in the phase image $$$\theta_i$$$, for $$$\it{i}$$$ = 1,2.

*Figure 3*. $$$\it{B_1^+}$$$ maps (first row), normalized to the average value of central slice, $$$\it{SNR_ {B_1^+}}$$$ maps (second row) and permittivity, $$$\varepsilon_r$$$, maps (third row), for AFI (first column), Bloch-Siegert (BS, second column) and DREAM (third column). All the colorbars are in arbitrary units.

The white arrows in DREAM-based permittivity point to sequence-related artefacts, which are not mere boundary errors: the $$$\it{thick}$$$ $$$\it{arrow}$$$ points to the large rim around the phantom. This effect was found also in MR-simulated DREAM-$$$\varepsilon_r$$$-map (not shown). The $$$\it{thin}$$$ $$$\it{arrow}$$$ points to the stripe-like artefact in the inner sphere (also visible in the $$$\it{B_1^+}$$$ map).