Assessing the Electromagnetic Fields Generated By a Radiofrequency MRI Body Coil at 64 MHz: Defeaturing Versus Accuracy

Abstract

Goal: This study aims at a systematic assessment of five computational models of a birdcage coil for magnetic resonance imaging (MRI) with respect to accuracy and computational cost.

Methods: The models were implemented using the same geometrical model and numerical algorithm, but different driving methods (i.e., coil "defeaturing"). The defeatured models were labeled as: specific (S2), generic (G32, G16), and hybrid (H16, [Formula: see text]). The accuracy of the models was evaluated using the "symmetric mean absolute percentage error" ("SMAPE"), by comparison with measurements in terms of frequency response, as well as electric ( ||→E||) and magnetic ( || →B ||) field magnitude.

Results: All the models computed the || →B || within 35% of the measurements, only the S2, G32, and H16 were able to accurately model the ||→E|| inside the phantom with a maximum SMAPE of 16%. Outside the phantom, only the S2 showed a SMAPE lower than 11%.

Conclusions: Results showed that assessing the accuracy of || →B || based only on comparison along the central longitudinal line of the coil can be misleading. Generic or hybrid coils - when properly modeling the currents along the rings/rungs - were sufficient to accurately reproduce the fields inside a phantom while a specific model was needed to accurately model ||→E|| in the space between coil and phantom.

Significance: Computational modeling of birdcage body coils is extensively used in the evaluation of radiofrequency-induced heating during MRI. Experimental validation of numerical models is needed to determine if a model is an accurate representation of a physical coil.

Fig. 1

Geometry characterization of the system (a) MITS1.5 physical coil (b) 3D view of the computational model as implemented in the software. The computational RF body coil system was modeled to match the physical coil geometry (c). During measurements a superellipse-shaped phantom (d) was placed in the bottom of the coil (e). The physical phantom was filled to a depth of 90 mm with a 2.5 g/L saline solution with a conductivity of 0.47 S/m

Fig. 2

||E⃗|| and ||B⃗|| were measured and computed both in air and in saline. In line with literature a first analysis was performed along the central longitudinal line of the coil (a). As complete domain analysis, measurements inside the phantom were performed in three coronal planes at three different saline depths of 35, 40, and 45 mm (corresponding to the absolute coordinates of y = −175 mm, −185 mm, −195 mm) (b). Measurements in the space between phantom and coil were performed in air (c) in five axial planes (i.e. z = −279 mm, −144 mm, 0 mm, 144 mm, 279 mm), and three coronal planes (i.e. y = 0 mm, 126 mm, 252 mm). For each plane the ξ index was calculated

Fig. 3

Five electrical models implemented: (a) Specific 2port (S2), (b) Generic 32port (G32), (c) Generic 16port (G16), (d) Hybrid 16port (H16) and Hybrid 16port frequency forced (H16_fr-forced). Model a) to c) were representative of a high pass body model wile model d) was representative of a low pass body model.

Fig. 4

Scattering parameters (i.e., S₁₁) of the physical coil and five computational models. The resonance frequency of the physical coil was captured only by the S2 and H16_fr-forced models. The G32, H16 and G16 showed a flat frequency response around 63.5 MHz.

Fig. 5

||E⃗|| and ||B⃗|| along the longitudinal axis z in the center of the coil (i.e., x_c = y_c = 0 mm). The figure shows the values measured in the physical coil as well as simulated. The five computational models were able to model the measured profile of ||B⃗||. Conversely, ||E⃗|| was accurately modeled only by the S2, G32 and H16. ||E⃗|| was about three-fold higher along the entire axis for the H16_fr-forced, while it was up to seven-fold higher at the measured minimum (i.e., z = −10 mm) for both the H16_fr-forced and G16. Values were normalized accordingly to equation 1.

Fig. 6

||E⃗|| and ||B⃗|| on coronal planes inside the phantom. For each plane the mean SMAPE ξ̄ value (equation 6) is reported in the histogram. In all three planes, ||E⃗|| and ||B⃗|| of the physical coil were well replicated only by the S2, G32, and H16 models, with a ξ less than 17 % for both. Conversely, models H16_fr-forced and G16 reported an ξ between 17 % and 32 % for ||B⃗|| and between 37 % and 54 % for ||E⃗||. This result exemplifies how the analysis of the central longitudinal line (Fig. 5) is not sufficient to assess how well a model replicates the magnetic field of a physical coil.

Fig. 7

||B⃗|| (top) and ||E⃗|| (bottom) maps on the central axial planes (i.e., z = 0 mm) in air for the physical coil and the three numerical model S2, G32, and H16. The ξ (SMAPE) maps (equation 5) are reported on the right side of the field maps. On the right, the calculated ξ̄ (equation 6) and the relative standard deviation are reported for the five axial and three coronal planes measured. In all the planes, ||B⃗|| of the physical coil was well replicated by the three computational models with ξ̄ always less than 11 %. In the central axial plane, only the S2 model was able to replicate the ||E⃗|| peak due to the ports position, whereas the G32 showed a uniform ||E⃗|| and the H16 model was highly affected by the multiport excitation - increasing the ξ̄ of the plane up to 45 %