# Feasibility Study of UTE-Image-based SAR Estimation Without B1 mapping at 3T

Zhongzheng He, Guillaume Paillart, Julien Lamy, Freddy Odille, Paulo Loureiro de Sousa

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Zhongzheng He, Guillaume Paillart, Julien Lamy, Freddy Odille, Paulo Loureiro de Sousa. Feasibility Study of UTE-Image-based SAR Estimation Without B1 mapping at 3T. 2026 ISMRM-ISMRT Annual Meeting and Exhibition, May 2026, Cape Town, South Africa. hal-05493766

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# Feasibility Study of UTE-Image-based SAR Estimation Without B1 mapping at 3T

**Primary:** Physics & Engineering - Safety ) **Secondary:** Contrast Mechanisms - Electromagnetic Tissue Properties ) **Digital Poster** · 60 min | Safety · Tuesday, May 12 at 04:00 PM ) **Keywords:** ELECTRICAL CONDUCTIVITY SAR EPT LOCAL SAR ULTRA-SHORT ECHO TIME (UTE)

**Zhongzheng He** (1), **Guillaume Paillard**2, **Julien Lamy**1, **Freddy Odille**2, **Paulo Loureiro de Sousa**1

¹ICube, CNRS, Université de Strasbourg, Strasbourg, France

²IADI U1254, INSERM and Université de Lorraine, Nancy, France

Presenting Author: Zhongzheng He (zhongzheng.he@unistra.fr)

## Impact

This work introduces a rapid UTE-based SAR estimation method that eliminates explicit $|B_1^+|$ mapping, demonstrating strong potential for efficient subject-specific RF safety monitoring from a single short acquisition and paving the way toward clinically practical, image-based SAR assessment at 3T.

## Synopsis

**Motivation:** Conventional image-based SAR estimation methods rely on separate $|B_1^+|$ mapping and transceive phase acquisition, increasing scan time and limiting clinical feasibility.

**Goals:** To develop a rapid, subject-specific SAR estimation approach using UTE imaging without explicit $|B_1^+|$ mapping.

**Approach:** We formulated a novel SAR expression based on the UTE signal's proportionality to $B_1^+ B_1^-$, combined with segmentation-based MRI-natural-contrast $I_0$ estimation for tissue-dependent scaling. Validation through simulations (noiseless/SNR=30) and in vivo 3T data demonstrated feasibility.

**Results:** The UTE-based method achieved comparable accuracy to $B_1^+$-based SAR (~30% overestimation vs ground truth), reduced scan time to ~5 min, and demonstrated strong potential for clinical integration.

## Introduction

Local Specific Absorption Rate (SAR) estimation is essential for MRI safety. While numerical simulations face limitations in inaccessible RF coil characteristics and inter-subject variability ¹, current image-based methods using Electrical Properties Tomography (EPT) require separate $|B_1^+|$ and phase acquisitions, prolonging scan times ²⁻⁵. UTE sequences offer an efficient alternative, which is proportional to $I_0 B_1^+ B_1^-$ enabling simultaneous conductivity and permittivity mapping from a single acquisition ⁶,⁷. We propose a novel UTE-image-based SAR method that eliminates explicit $|B_1^+|$ mapping by estimating native contrast $I_0$ via segmentation. Numerical simulations and 3T in vivo experiments demonstrate this method's promising potential for clinical implementation compared to conventional $B_1^+$-based SAR approaches.

## Theory

SAR is defined from the electric field:

$$ SAR = \frac{\sigma |\mathbf{E}|^2}{2\rho_m} $$

Since direct $\mathbf{E}$ measurement is unavailable, we use $\mathbf{E} = \frac{1}{\mu_0\kappa} \nabla \times \mathbf{B}$ with $\kappa = \sigma + i\omega\epsilon_0\epsilon_r$ to express SAR via magnetic field $\mathbf{B}$.

Defining circularly polarized components $B_1^+ = \frac{B_x+iB_y}{2}$ and $B_1^- = \frac{B_x-iB_y}{2}$, and assuming $\nabla B_z \approx 0$, the curl simplifies to:

$$ \nabla \times \mathbf{B} \approx \begin{bmatrix} -\frac{\partial B_y}{\partial z} \\ \frac{\partial B_x}{\partial z} \\ \frac{\partial B_y}{\partial x} - \frac{\partial B_x}{\partial y} \end{bmatrix}, \quad \mathbf{B} = \begin{bmatrix} B_1^+ + B_1^- \\ -i(B_1^+ - B_1^-) \\ B_z \end{bmatrix} $$

SAR estimation requires assumptions (as only $|B_1^+|$ and $\phi_{tr}$ are measurable) about the unknown $B_1^-$ in addition to the transceive phase assumption ($\phi^+ \approx \phi_{tr}/2$).

1. $B_1^-$-excluded SAR$^{2,3,8}$: Neglecting $B_1^-$ entirely yields:

$$ SAR_{B_1^- = 0} = \frac{\sigma}{2\rho_m |\mu_0\kappa|^2} \left( 2 \left| \frac{\partial B_1^+}{\partial z} \right|^2 + \left| \frac{\partial B_1^+}{\partial x} - i \frac{\partial B_1^+}{\partial y} \right|^2 \right) $$

This causes a major SAR underestimation, requiring a correction factor of 1.79-3.08$^{4,9}$.

2. $B_1^+$-based SAR: Based on left-right symmetry assumptions in the imaging center$^{10}$, including symmetric field magnitudes ($|B_1^+(x, y, z)| \approx |B_1^-(x, y, z)|$) and corresponding gradient patterns (opposite along x, equal along y and z):
$$ \text{SAR}_{B_1^+} = \frac{2\sigma}{\rho_m |\mu_0 \kappa|^2} \left( \left| \frac{\partial B_1^+}{\partial z} \right|^2 + \left| \frac{\partial B_1^+}{\partial x} - i \frac{\partial B_1^+}{\partial y} \right|^2 \right) $$

3. **Q-Based SAR** (see Fig.1): Using $Q = B_1^+ B_1^-$ and assuming $B_1^+ \approx B_1^- \approx \sqrt{Q}$, the SAR$_{B_1^+}$ become:

$$ \text{SAR}_Q = \frac{\sigma}{2\rho_m |\mu_0 \kappa|^2} \frac{|\nabla Q|^2}{|Q|} $$

4. **UTE-based SAR**: Assuming the MRI natural contrast $I_0$ is slowly varying ($\nabla I_0 \approx 0$), we substitute $Q = S_{\text{UTE}}/I_0$ from the UTE signal equation into the Q-based formulation:

$$ \text{SAR}_{\text{UTE}} = \frac{\sigma}{2\rho_m |\mu_0 \kappa|^2} \frac{|\nabla S_{\text{UTE}}|^2}{I_0 |S_{\text{UTE}}|} $$

## Methods

* **$I_0$ Estimation** (Fig.2): $I_0$ was modeled from UTE signals (neglecting T2-decay) as $I_0 = \lambda \cdot \rho_0 \cdot f(T_1)$. A proton density map $\rho_0$ was derived from literature values 11,12, and a T1-weighting map $f(T_1)$ was computed using UTE parameters (FA=3°, TE/TR = 50 $\mu$s/3.6ms) at 3T. The scale factor $\lambda$ was obtained by normalizing $|S_{\text{UTE}}|$ to a reference $|Q_{\text{ref}}|$.

* **In silico brain data** were from ADEPT database 13 at 128 MHz (Sim4Life, 1W RF power, 1mm-isotropic). The synthetic UTE signal was derived as $S_{\text{UTE}} = \rho_0 f(T_1) B_1^+ B_1^-$ then normalized to 1, with $|Q_{\text{ref}}| = |0.12 \mu T|^2$. Ground truth, $B_1^-$-excluded, $B_1^+$-, Q-and UTE-based SAR were reconstrcuted across two SNR conditions (noiseless/SNR=30). Gradient calculation employed segmentation-based second-order-polynomial-fitting cube-shaped kernels (3³ for noiseless and 11³ for SNR=30), followed by 3x3x3 median filtering.

* **In vivo brain data** were acquired on a 3T Siemens Vida scanner using a transmit body coil and 20-channel receive array with adaptive coil combination to minimize $|B_1^+ - B_1^-|$. UTE images (4min11s, 1.2mm-isotropic) were coregistered with satTFL-B1 mapping (1.2mmx1.2mmx7.5mm) and 1mm-isotropic-MPRAGE. Both $|Q|$ and $|B_1^+|$ were normalized to match simulation references. $B_1^-$-excluded, $B_1^+$- and UTE-based SAR were reconstructed using the same kernel sizes as the simulation of SNR=30. EPs included: ex vivo simulation values and in vivo EPT-derived from UqEPT toolbox 14.

## Results

The proposed UTE-based SAR method demonstrated consistent performance across noise levels in simulations (Figs.3,4 ▼), closely matching the spatial distributions of $B_1^+$-and Q-based methods. All three methods showed ~30% overestimation compared to ground truth but accurately identified hotspot locations, while $B_1^-$-excluded SAR underestimated by at least 50%.

In vivo experiments (Fig.5) revealed 10-20% overestimation by the UTE method compared to $B_1^+$-based approaches, primarily in regions where $\sqrt{|Q|} \approx |B_1^+|$ failed, particularly near ventricles and CSF boundaries.

## Discussion

This novel method, based on $B_1^+ \approx B_1^-$ with $I_0$ scaling, eliminates explicit $|B_1^+|$ mapping and enables ~5-minute subject-specific SAR estimation. While showing clinical potential, further refinement through advanced coil combination or calibration is needed for clinical deployment.

## Acknowledgements

The study was funded by ANR-21-CE19-0040 (ELECTRA project). We thank Thomas Benkert (PhD, Application Development, Siemens Healthcare, Erlangen, Germany) for providing the UTE sequence. We thank Thierry G. Meerbothe (Department of Radiotherapy, Division of Imaging and Oncology, University Medical Center Utrecht, Utrecht, The Netherlands) for providing the silico brain data.

## References

1. Thomas M. Fiedler, Mark E. Ladd, and Andreas K. Bitz. "SAR Simulations & Safety". In: NeuroImage 168 (Mar.2018), pp. 33–58. issn: 10538119. doi: 10.1016/j.neuroimage.2017.03.035. C&R

2. U. Katscher et al. "Determination of Electric Conductivity and Local SAR Via B1 Mapping". In: IEEE Transactions on Medical Imaging 28.9 (Sept. 2009), pp. 1365–1374. issn: 0278-0062, 1558-254X. doi:10.1109/TMI.2009.2015757.

3. T. Voigt et al. "Patient-individual local SAR determination: In vivo measurements and numerical validation". In: Magnetic Resonance in Medicine 68.4 (Oct. 1, 2012). Publisher: John Wiley & Sons, Ltd, pp. 1117–1126. issn: 0740-3194. doi: 10.1002/mrm.23322. C&R

4. Jessica A. Martinez et al. "Feasibility Study of Subject-specific, Brain Specific-absorption-rate Maps Retrieved from MRI Data". In: Magnetic Resonance in Medicine (May 24, 2025), mrm.30547. issn: 0740-3194, 1522-2594. doi: 10.1002/mrm.30547. C&R

5. Jiaen Liu et al. "Electrical Properties Tomography Based on $\$B \{ (1) \}\$ Maps in MRI: Principles, Applications, and Challenges". In: IEEE Transactions on Biomedical Engineering 64.11 (Nov.2017), pp. 2515–2530. issn: 0018-9294, 1558-2531. doi: 10.1109/TBME.2017.2725140.

6. Seung-Kyun Lee et al. "Tissue Electrical Property Mapping from Zero Echo-Time Magnetic Resonance Imaging". In: IEEE transactions on medical imaging 34.2 (Feb.
Figures and Tables

Q-based SAR. Using $Q = B_1^2 B_2^2 = M_c^2$ where $M = M^+ M^-$ and $\Phi = \phi^+ + \phi^-$, and assuming $B_1^2 = B_2^2 = \psi Q$, the spatial derivatives in SAR$_{xy}$ become:

• Longitudinal Derivatives:

$$
\frac{\partial B_z}{\partial z} = \frac{\partial}{\partial z} \left( \sqrt{M_c} e^{i\phi} \right) \\
= e^{i\phi} \frac{1}{2\sqrt{M_c}} \left[ \frac{\partial M_c}{\partial z} + \frac{\sqrt{M_c}}{2} \frac{\partial \phi}{\partial z} \right]
$$

$$
\left| \frac{\partial B_z}{\partial z} \right| = \left| \frac{1}{4M_c} \left( \frac{\partial M_c}{\partial z} \right)^2 + \frac{M_c}{4} \left( \frac{\partial \phi}{\partial z} \right)^2 \right|
$$

• Transverse Derivatives:

$$
D = \frac{\partial B_z}{\partial z} - \frac{\partial \phi}{\partial z} \\
= e^{i\phi/2} \left[ \frac{1}{2\sqrt{M_c}} \left( \frac{\partial M_c}{\partial z} \right)^2 + \frac{\sqrt{M_c}}{2} \left( \frac{\partial \phi}{\partial z} \right)^2 \right]
$$

The magnitude squared expands to:

$$
|D|^2 = \frac{1}{4M_c} \left| \frac{\partial M_c}{\partial z} \right|^2 + \frac{M_c}{4} \left| \frac{\partial \phi}{\partial z} \right|^2 \\
+ \frac{1}{2} \left[ \left( \frac{\partial M_c}{\partial z} \right) \left( \frac{\partial \phi}{\partial z} \right) - \left( \frac{\partial M_c}{\partial z} \right) \left( \frac{\partial \phi}{\partial z} \right)^2 \right]
$$

The cross term is the scalar cross product (VM × VQ). It becomes negligible under a specific physical condition observed in our simulations: the spatial gradients of the magnitude and phase are approximately anti-parallel, i.e. VQ × VM = -VM × VM. Substituting this relation into the cross term VM × VQ = VM × (-VM) = 0 demonstrates its vanishing contribution. This anti-parallel gradient condition physically corresponds to the magnitude and phase exhibiting opposing quadratic spatial dependencies in a homosotropic region, justifying the isolation.

Combining both contributions:

$$
\begin{align*}
\mathrm{SAR}_{Q} &= \frac{\partial \phi}{\partial M_c} \left[ \frac{1}{2\sqrt{M_c}} \left( \frac{\partial M_c}{\partial z} \right)^2 + \frac{M_c}{4} \left| \frac{\partial \phi}{\partial z} \right|^2 \right] \\
&= \frac{\partial \phi}{\partial M_c} \left[ \frac{\left| \frac{\partial M_c}{\partial z} \right|^2}{M_c} + M_c \left| \frac{\partial \phi}{\partial z} \right|^2 \right]
\end{align*}
$$

Recognizing $|\nabla Q|^2 = |VM|^2 + M_c^2|VQ|^2$ yields the compact form:

$$
\mathrm{SAR}_{Q}=-\frac{\sigma}{2 \pi \mu_{\mathrm{m}} \mu_{\mathrm{p}}} \left|\nabla Q^{2} \right| / \nabla Q
$$

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<caption>**Figure 1:** Q-based SAR Formula Derivation ($Q=B_1^2+B_1^1-$).</caption>
<figure><img src="image_3.png" /></figure>

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**Figure 2:** Estimation of the MRI Natural Contrast ($I_0$) from UTE Magnitude Signal (neglecting T2 decay), which is proportional to proton density ($\rho_0$) and T1-weighting ($f(T_1)$). The scale factor ($\lambda$) is derived by normalizing the UTE magnitude signal ($|S_{\text{UTE}}|$) to a reference value ($|Q_{\text{ref}}|$) averaged over a transversal central slice (e.g., $|11.74 \mu T|^2$ for standard RF pulse).

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**Figure 3:** Simulation Results at SNR=$\infty$ with 1W RF Power. Local SAR and 10g-SAR distributions across different estimation methods, compared against the ground truth E-field-based SAR. Violin plots show the SAR distribution with median values, and normalized mean absolute error (nmae) quantifies the accuracy of each method.
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<figure><img src="image_9.png" /><figcaption>**Figure 4:** Simulation Results at SNR=30 with 1W RF Power. Local SAR and 10g-SAR distributions across different estimation methods, compared against the ground truth E-field-based SAR. Violin plots show the SAR distribution with median values, and normalized mean absolute error (nmae) quantifies the accuracy of each method.</figcaption></figure>

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<caption>**Figure 5:** In vivo Results of $B_{1}^{1}$-$^{ excluded, $B_{1}^{1}$+}$-and UTE-based SAR Estimation, normalized to 1W RF power, with ex vivo (matching the simulation case) and in vivo EP values derived from the UTE-image-based EPT reconstruction with cubic kernel sizes of $15^{3}$ for Savitzky-Golay fitting and $21^{3}$ for post-processing ($\sigma = [0.61, 0.82, 1.31]$ S/m and $\epsilon = [62, 52, 34]$ for WM, GM, and CSF, respectively). Violin plots show the SAR distribution with median values.</caption>