Ellis Beld^{1}, Marinus A. Moerland^{1}, Max A. Viergever^{2}, Jan J.W. Lagendijk^{1}, and Peter R. Seevinck^{2}

Object localization by MRI artifact simulation and template matching is valuable for MRI-guided HDR brachytherapy. Simulations of the artifacts induced by an HDR brachytherapy source and titanium needle were implemented for four types of MRI sequences: spoiled gradient echo, spin echo, bSSFP and bSSFP-SPAIR. The simulated artifacts were compared to MR images acquired in a phantom study and applied for object localization. High correspondences between the simulations and MR images were found as well as only slight variations between the obtained object positions for all applied sequences. This enables object localization for clinically relevant MRI sequences which allow anatomy visualization.

*Simulations*

Simulation of the artifact for a spoiled gradient echo sequence was performed as described in[1], and implemented in Matlab. The simulations involve a forward calculation of the magnetic field perturbation^{2}, βB_{0}, based on the susceptibility distribution, and inclusion of the MRI signal equation (corresponding with the sequence) and k-space sampling. The signal equation of a spoiled gradient echo sequence for each k_{x} (with readout direction along x) was defined as^{1,3}:

$$S(k_x,y,z)=\sum_{j=1}^{N_x}\rho(x_j,y,z){\cdot}e^{i2\pi\gamma{\Delta}B_0(x_j,y,z)\cdot(TE+n{\Delta}t)}{\cdot}e^{-i2{\pi}k_xx_j},$$

where $$$k_x={\gamma}G_Rn{\Delta}t$$$, γ the gyromagnetic ratio, G_{R} the readout gradient strength ($$$G_R=\frac{1}{{\gamma}FOV_x{\Delta}t}$$$), n=-N_{x}/2…N_{x}/2-1 with N_{x} the number of spin isochromats along x and βt the sampling interval. This equation was implemented, and the other sequences were simulated by adapting the MRI signal equation. For a spin echo sequence, the spatial dephasing effect ($$$e^{i2\pi{\Delta}B_0(x_j,y,z){\cdot}TE}$$$) was excluded because of the 180° refocusing pulse:

$$S_{spin\:echo}(k_x,y,z)=\sum_{j=1}^{N_x}\rho(x_j,y,z){\cdot}e^{i2\pi{\Delta}B_0(x_j,y,z)n{\Delta}t}{\cdot}e^{-i2{\pi}k_xx_j}.$$

For bSSFP, the spin distribution, ρ(x,y,z), was replaced by the steady-state signal equation of a bSSFP sequence, M_{xy}(x,y,z):

$$S_{bSSFP}(k_x,y,z)=\sum_{j=1}^{N_x}M_{xy}(x_j,y,z){\cdot}e^{i2\pi{\Delta}B_0(x_j,y,z)\cdot(TE+n{\Delta}t)}{\cdot}e^{-i2{\pi}k_xx_j},$$

where M_{xy} is defined as^{4}:

$$M_{xy}(x,y,z)=M_x(x,y,z)+iM(x,y,z),$$

and M_{xy} is decomposed in the x and y components:

$$M_x(x,y,z)=M_0(1-E_1)\frac{\sin\alpha(1-E_2\cos\beta}{d},$$

$$M_y(x,y,z)=M_0(1-E_1)\frac{E_2\sin\alpha\cos\beta}{d},$$

where the following definitions hold:

$$E_1=e^{-TR/T_1},$$

$$E_2=e^{-TR/T_2},$$

$$d=(1-E_1\cos\alpha)(1-E_2\cos\beta)-E_2(E_1-\cos\alpha)(E_2-\cos\beta),$$

with M_{0} the equilibrium magnetization, α is the flip angle, β is the resonance offset angle and TR is the repetition time. The impact of βB_{0} is reflected in the resonance offset angle:

$$\beta=2\pi({\delta}_{CS}+\gamma{\Delta}B_0(x,y,z)){\cdot}TR-\phi_{RF},$$

where πΏ_{πΆπ} is the chemical shift and ππ
πΉ the RF phase increment in successive TRs (in this study: $$$\phi_{RF}=\pi$$$). Lastly, for SPAIR, the spins at a frequency of the SPAIR pulse were set to 0 (in this study: between -1.8 and -5.2 ppm for a SPAIR pulse with a frequency offset of 110 Hz).

**MRI acquisition **

The object, a non-active Ir Flexisource (Elekta) or a titanium needle (Ø1.9mm, Elekta), was positioned in the center of a doped water phantom. MR imaging was performed on a 1.5T MRI system (Ingenia, Philips). Two imaging approaches were distinguished: (I) fast 2D sequences for (real-time) tracking, and (II) clinically applied 3D/volumetric sequences for robust object localization and position verification. Four types of 2D MR sequences were applied (2 intersecting 2D slices): spoiled gradient echo, spin echo, bSSFP and bSSFP-SPAIR, see Table1a. Furthermore, the MRI sequences of the clinical prostate HDR brachytherapy scan protocol were applied: a 3D bSSFP-SPAIR sequence, a T2-weighted and a T1-weighted turbo spin echo sequence (both multi-slice 2D), see Table1b. Angles of 0° and 20° between source/needle and B_{0} were applied.

*Post-processing *

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2. J.G. Bouwman and C.J.G. Bakker Alias subtraction more efficient than conventional zero-padding in the Fourier-based calculation of the susceptibility induced perturbation of the magnetic field in MR Magn. Reson. Med. 2018; 68:621-630

3. F. Zijlstra, J.G. Bouwman, I Braskute, M.A. Viergever and P.R. Seevinck Fast Fourier-based simulation of off-resonance artifacts in steady-state gradient echo MRI applied to metal object localization Magn. Reson. Med. 2017; 78:2035-2041

4. M.L. Lauzon and R. Frayne Analytical characterization of RF phase-cycled balanced steady-state free procession Concepts Magn. Reson. 2017; 34A:133-143

5. C.D. Kuglin and D.C. Hines The phase correlation image alignment method Proc. IEEE Int. Conf. Cybernet. Soc. 1975; 163-165

**Table 1a.** The scan parameters of the spoiled gradient echo sequence, the spin echo sequence, the bSSFP sequence and the bSSFP-SPAIR sequence that were applied (all 2D).

**Table 1b.** The scan parameters of the 3D bSSFP sequence, the multi-slice 2D T2-weighted (T2w) spin echo sequence and the multi-slice 2D T1-weighted (T1w) spin echo sequence that were applied (as provided in the current clinical scan protocol of prostate HDR brachytherapy).