Traveling wave MR [1] is a promising method for large field-of-view imaging at ultrahigh fields, which uses relatively small and simple RF transmit/receive devices (or antennas). Due to the far distance between the antenna and imaging subjects, however, a major issue currently faced in traveling wave MR is low transmit efficiency and limited signal-to-noise ratio (SNR). In previous work [2], it was found that the SNR in traveling wave MRI can be significantly improved by using a free resonator positioned close to the imaging sample. It is worth noting that the free resonator has no physical connection with transmit path or receive path, which is different from the local receive-only array [3]. In this study, we aim to validate this finding in simulation. Besides the receive performance, we also comparatively evaluate the transmit performance (transmit efficiency and E fields).

The free loop can be seen as an inductively coupled resonator, of which the induced current forms a secondary magnetic field. Therefore the total magnetic field H can be expressed as: H=H⁰+H^’, where H⁰ is the original magnetic field of traveling-wave antenna and H^’ is the secondary magnetic field of the free loop, as shown in Fig. 1.

Numerical studies were performed by using a full-wave FEM-based simulator (ANSYS HFSS, Canonsburg, PA, USA). A cylindrical copper shield was used as the waveguide (O.D. 63 cm and length 160 cm). A patch antenna was placed at one end of the bore as RF source. It was used as a transmitter/receiver, and was matched to 50 ohm and tuned to 298 MHz, the Larmor frequency at 7T. A cylindrical water phantom (length 10 cm, diameter 5 cm, σ=0.59 S/m and ε_r=78) was placed ~80 cm away from the patch antenna, i.e., at the center of the bore. A free loop (dimension 3.8 cm Χ 5 cm) with 4 distributed capacitors was placed about 1 cm above the phantom. Values of all capacitors were obtained by a RF and 3-D co-simulation method [4]. As a comparison, we also simulated the traditional travelling wave without using free resonators.

Fig. 2A shows the H-field vector in the MRI bore. It is clear that the magnetic flux goes through the loop and induces obvious current along the loop conductors. The local B₁ field (both B₁⁺ and B₁^-) showed a 20-fold increase when the free loop was used (Fig. 2B). Since the loop was placed quite close to the sample, the total magnetic field H was dominated by H^’, which can also been seen from B₁ pattern.

Figs. 2C and 2D show the E-field and B₁⁺/E distributions. Although the E-field is increased at some areas when using free resonator, the ratio of B₁⁺ field to E-field is still increased obviously. Fig. 2E shows the normalized SNR on the phantom (central transverse slice), with averaged SNRs in dotted-line squares marked in red or white colors. The SNR was calculated by: signal/noise [5], where signal equals to $$sin(V|B_1^+|\gamma\tau)|B_1^-|^*$$ and noise equals to $$\sqrt{\int_{volume}\sigma|E|^{2}dv}$$. With the help of the free loop, SNR on the phantom has a 16-fold gain (56.8 VS 3.6) at near area and 3-fold gain at far area (9.7 VS 3.5). This result is also consistent with previous MR imaging experimental results [2].

Based on the present analysis, the single free resonator can be extended to a multi-channel array or birdcage coil as long as the induced current exists. To validate this assumption, we simulated a simple 2-channel loop array in traveling wave. Fig. 3 shows the simulation results of H-field vector, B₁ field and E-filed of the 2-channel array.The simulation results show that SNR and transmit efficiency in traveling wave can be well improved by using free local resonators. This improvement can be attributed to the secondary magnetic field caused by induced current of the free resonator. For simplicity, we only use a linearly polarized patch antenna in present analysis. In this case, the free loop should be positioned to ensure the magnetic flux goes thought it. It is also noted that the transmission efficiency and SNR were improved with a significant compromising of B₁ homogeneity. This might be overcome by using the multi-element array or volume birdcage coil. It is of interest to note that, the use of free resonators in traveling wave might be a quite simple and efficient method in wireless RF coil design at ultrahigh fields.