Kerker Effect in Ultrahigh-Field Magnetic Resonance Imaging

Ultrahigh-field (UHF) magnetic resonance imaging (MRI) systems are getting a lot of attention as they ensure high intrinsic signal-to-noise ratio resulting in higher spatial and temporal resolutions as well as better contrast. This promises improved clinical results with regard to morphological as well as functional and metabolic capabilities. Traditionally, MRI relies on volume coils (birdcage) able to deliver a homogeneous radio frequency field exciting the nuclei magnetic spin. However, this strategy is hindered at UHF because of the rf field inhomogeneities yielded by the increased Larmor frequency. A standard approach consists of inserting passive dielectric elements within the volume coil in order to locally enhance the rf field and mitigate these inhomogeneities. However, the lack of control over their electromagnetic properties prevents the development of optimal solutions. Here, a single meta-atom is used to achieve efficient and tunable rf field control in UHF MRI. We demonstrate theoretically and experimentally a full overlap between the electric dipolar and magnetic dipolar resonances of the meta-atom. This interaction is precisely tuned to reach the so-called Kerker scattering conditions when illuminated in the near field by a birdcage coil. At these conditions, a strong enhancement or suppression of the rf field is achieved in the vicinity of the meta-atom within the MRI volume coil.

Popular Summary

Magnetic resonance imaging (MRI) scanners have become one of the most efficient diagnostic tools available to physicians. Over time, their magnetic field strength has been steadily increased, yielding huge improvements in spatial and temporal resolution as well as image contrast. However, this strategy decreases the wavelength of the radio-frequency excitation field. This becomes problematic once the rf wavelength becomes comparable to the human body size, leading to major losses in contrast or shadowing on the images. Here, we use electromagnetic metamaterials to tailor the rf field inside the MRI coils, which could lead to faster and more precise imaging.

Metamaterials are composite materials whose effective properties mimic a homogeneous material that is not available in nature. Given the ability to fine-tune their electric and magnetic properties, this makes metamaterials ideal for controlling the rf field. We design a single “meta-atom,” based on a set of four hybridized metallic wires, and show that it can redistribute the rf field in a commercial MRI coil. The meta-atom can either enhance the local rf field by a factor of 3 or shield overexposed body areas from the rf radiation.

Our device is not optimized for imaging, but rather it is a proof of concept for controlling the rf field. Metallic metamaterials do not degrade with time, and they are cost effective and very easy to manufacture, making them excellent candidates for improving MRI scans in the near future.

Figure 1

7 T sagittal MR images of a human brain slice obtained with various acquisition sequences: (a) Flip-angle ($\mathrm{FA}\propto B_1^{+}$) map acquired using the actual flip-angle imaging sequence (color bar in degree). (b) T1-weighted magnetization-prepared rapid gradient echo sequence. (c) T2-weighted turbo spin echo sequence. Those images have been acquired with a birdcage coil for excitation and a 32-loops phased array for reception. Notice (a) the large $B_1^{+}$ field heterogeneity over the head (dispersion of $\sim 30\%$). When FA is too far from the target, as is the case here in the cerebellum (white arrows), it leads to loss in contrast (b) or even worse to shadowing (c) depending on the acquisition strategy.

Figure 2

(a) Sketch of the HMA configuration. Four metallic wires oriented along $z$ are placed at the four corners of a rectangle of sides $d_1=1.5\mathrm{cm}$ and $d_2=2\mathrm{cm}$. A fifth wire is used as a source located at a distance $S$ large compared to the wavelength at 297.2 MHz. Such a configuration allows us to study the response of the HMA with a plane wave excitation. All wires have a diameter of 2 mm. (b) Radiated power from the HMA (solid red line) as a function of the wire length (excitation frequency 297.2 MHz is kept constant) is compared with the power radiated by a single wire (dashed black line) of the same varying length. The inset shows the phase of the current within the four wires of the HMA. This is evidence of the hybridization mechanism leading to a broad dipolar electric resonance and a sharp magnetic dipolar resonance. (c) Radiated power from the HMA on a narrow window (solid red line). Dashed black line and solid thin blue line show the isolated contributions of the two resonances excited in the HMA. The two insets show the radiation pattern of the magnetic dipolar resonance and the electric dipolar resonance. (d) Far-field radiation pattern at the two Kerker conditions (HMA lengths denoted above). The first one presents a reduction of the forward scattered field while a cancellation of the backward scattered field is observed at the second position.

Figure 3

(a) Sketch of the considered geometry for the insertion of the HMA inside a birdcage model. The birdcage is composed of 16 legs on a 26-cm-diameter cylinder. The legs are 28 cm long and the HMA is located at $S=2.5\mathrm{cm}$ from the first leg. Red circle denotes the ROI for the $B_1^{+}$ enhancement plot. (b) $B_1^{+}$ amplitude calculated in a quadrature driven empty birdcage. (c) $B_1^{+}$ enhancement in the ROI with respect to the empty birdcage in function of the HMA length. The solid red line corresponds to the HMA and the blue dashed line corresponds to the single wire case. (d) Calculated $B_1^{+}$ amplitude maps with the HMA for three lengths of interest shown in (c), respectively, 47.5, 49.6, and 49.8 cm.

Figure 4

(a) Schematic view of experimental configuration inside the 7 T MRI: birdcage coil (dark gray), HMA (4 blue rods), and oil phantom ${\epsilon }_r=3.4$ (light gray). (b),(c) Pictures of the experimental setup, positioning of the HMA in the birdcage coil and into the MRI scanner. (d) Average flip-angle magnitude in the ROI [red circle in (a)] as a function of the HMA length. The dashed line indicates the reference value (without HMA). (e) Top: Normalized axial $B_1^{+}$ maps measured for two lengths of interest, namely, 49 and 49.5 cm. Each corresponds to the Kerker conditions with an enhancement or cancellation of the $B_1^{+}$ field close to the HMA. Bottom: Normalized field maps obtained from the theoretical calculations for the two Kerker conditions. HMA length from left to right at the calculated Kerker conditions (49.6 and 49.8 cm, respectively). A circular mask is applied to reproduce the phantom dimensions.

Figure 5

(a) Schematic view of experimental configuration inside the 7 T MRI: birdcage coil (dark gray), HMA (4 blue rods), and phantom (yellow). (b),(c) Measured $B_1^{+}$ maps (in $\mu \mathrm{T}/\mathrm{V}$) of the gel spherical phantom (${\epsilon }_r=74.2$, $\sigma =0.87\mathrm{S}/\mathrm{m}$) (b) without HMA and (c) for various HMA lengths: (I) 46.5 cm and (II) 49.5 cm. (d) Average $B_1^{+}$ magnitude in the three color-marked ROIs (a) as a function of the HMA length. The black solid line corresponds to the whole phantom. The green solid line corresponds to the central region of the phantom (1.85 cm radius). The red solid line corresponds to the right-hand region of the phantom (1.5 cm radius). The horizontal dotted lines indicate the reference value (without HMA) for each ROI. The three vertical arrows denote the three lengths of interest depicted above.

Figure 6

(a)–(c) Left: Schematic view of the experimental configurations inside the 7 T MRI: birdcage legs in gray circles, specific anthropomorphic mannequin (SAM) in yellow, positioning of the ${\mathrm{BaTiO}}_3$ pad in blue (b) and HMA in red dots (c). The horizontal dotted line shows the imaging plane. Right: Measured $B_1^{+}$ coronal maps (in $\mu \mathrm{T}$) of the SAM phantom: (a) with SAM only, (b) in the presence of a ${\mathrm{BaTiO}}_3$ pad on the right-hand side, and (c) replacing the pad with a 42-cm-long HMA. HMA is located 2 cm away from the phantom.

Figure 7

SNR measurement with and without HMA on SAM phantom. (a) Proton density weighted (PDW) coronal image with birdcage and (b) with 42-cm-long HMA inserted (metamaterial along the right-hand side of the phantom). Local enhancement can be visually identified by the white arrow along the HMA. (c) Corrected SNR maps (arbitrary units) obtained with the birdcage alone and (d) in presence of HMA. (e) Calculated SNR enhancement map in percentage. It confirms a strong SNR enhancement close to the HMA but also a slight improvement on a relatively large part of the phantom volume.