The key challenge in designing anatomically adaptive loops is to find reversibly stretchable coil conductors, which have equal or only slightly worse properties than the used standard (flat) wire with respect to electrical conductivity.

For typical metallic wire, stretching results in irreversible plastic deformation beyond a few percent of elongation. A certain reversibility of a change in length can be achieved by mounting a wire with a certain length reserve (e.g., meandered style) on an elastic material. In addition, this material should be “MR silent,” which means that there is no contribution to the MR signal from this material. To restore the original state after stretching, the wire has to allow enough elasticity and ideally should mechanically behave like a spring. Standard highly conductive materials like copper, silver, gold, aluminum were too pliable for this task. Materials like iron or steel would fulfill the strength requirement, but they are ferromagnetic, and therefore not suitable for MRI. An option in between would be austenitic steel, which is not ferromagnetic and would provide enough strength, but has low conductivity. We developed several mechanical concepts, published in a filed patent [33]. One of the most promising approaches thereof is the partly-stretchable-loop—concept (see Figures 2A,C–F) used in this work.

Four different reversibly stretchable materials were investigated (see Table 2) and used for the construction of stretchable double-loops (see Figure 2A). The loops were realized with a stretchable area of length x and a width of 100 mm (z-direction) (see Figure 1A). The stretchable double-loops with loop sizes according to Table 1 were compared to four standard double-loops (see Figure 2B) as reference.

The double-loop arrays with rectangular loops were manufactured on FR-4 (fiberglass cloth with a flame-resistant epoxy resin) using the simplified circuitry illustrated in Figure 1C.

The reference loops and the fixed parts of the partly-stretchable loops were made of 6 mm wide adhesive copper tape with a copper thickness of 70 μm. Thin or very narrow copper traces increase the loops resistance thus lowering the Q value, while a wider or thicker copper trace may cause eddy current heating, B₁-distortions and/or self-shielding [14]. 16-awg thick tin-plated copper wire bridges were used to overlap at the cross sections of each loop, minimizing capacitance between the two loop traces. Segmenting capacitors were used to provide a homogeneous current distribution over the loop, reduce the E-fields induced into the sample load through voltage splitting between the capacitors, reduce the stray fields caused by the split voltages which influence the load dependence of the resonance frequency and finally reduce capacitive coupling as well as parasitic capacitance between loop and sample. Each loop was tuned to the resonance frequency of 63.6 MHz (1.5T) using a torso-shaped phantom with a main body (blue: per 1,000 mL Bayol-oil and 0.011 g MACROLEX blue) and an outer compartment (clear: per 1,000 g H₂O dist.: 1.25 g NiSO₄ × 6H₂O, 5g NaCl) (see Figure 1D).

The stretchable double-loops were mounted on a 3D laser-sintered (ObjetEden500V, Stratasys, Rechovot, Israel) frame (see Figures 1B,D), which allows the stretching of the loop material in discrete steps of 5 mm in x-direction (the stretching in y-direction is also performed, as the frame is attached to the phantom's surface). The overlap between two loops is constant and provides optimal overlap decoupling for a stretching of 15% (x = 75 mm).

Bench and MRI measurements were performed with 0, 10, 20, and 30% stretching (see Table 1). The stretch area x is fixed to start at 60 mm. The geometrical properties are calculated with Equation 5 and 6, which result from an array design of a 18-channel adaptive knee array with 3 rows of 6 rectangular loop elements (see Table 1 line 1).

Stretching of the adaptive loops changes the loop's inductance and resistance and is therefore expected to cause a shift in the resonance frequency. Therefore, the partly-stretchable loops were tuned and matched to the Larmor frequency at 1.5 Tesla (63.6 MHz) at the center between the maximum and minimum length of the stretchable areas corresponding to a stretching of 15% with x = 75 mm). The four reference double-loops were individually tuned to and matched. Capacitor values for all built double-loops can be seen in Figure 12.

The inductance of each loop is estimated from the total capacitance and the resonance frequency. The coil resistance is estimated from the measured Q-factor. Q-values for each loop were measured at a distance of 20 mm with an S21 measurement on the network analyzer (E5071C, Keysight Technologies, Santa Rosa, CA, USA) using a double-loop probe with −75 dB decoupling. To estimate the effect of stretching on inter-element coupling, the coupling coefficient k was measured using the two-mode-frequencies method:

with fin-phase =12πC*(L-M) and fanti-phase =12πC*(L+M) [34, 35]. The upper frequency and the lower frequency mode are measured on the network analyzer, with an S21 measurement, assuming that the resonant frequencies f ₀ are identical for both loops, as well as the capacitance and the inductance values for both loops are the same. The center-to-center distance for rectangular loops to achieve optimal inductive decoupling is 0.9 d [6], but due to the stretching of elements, the decoupling between elements changes. Residual coupling was suppressed by pre-amplifier decoupling. Active detuning using an LC parallel circuit was implemented to detune the loop during transmit, and baluns, reducing common mode currents on the shield of the coaxial cables, were added and tuned to the Larmor frequency.

The experimental setup (see Figure 1D) was placed in the MRI and with every stretchable double-loop configuration and the corresponding reference double-loop noise and signal data was acquired one after another. For every configuration, 2 measurements were performed: per stretched position (4 stretch-points, see Table 1, column 1) signal and noise data was acquired with the reference and the stretchable double loops.

SNR images were generated from signal- and noise datasets, acquired on a Siemens MAGNETOM Aera 1.5 Tesla MRI scanner with software platform Syngo MR E11 (Siemens Healthcare GmbH, Erlangen, Germany). To obtain the SNR images, a standard spin-echo sequence (TE = 15 ms, TR = 300 ms, FoV = 300 mm, TA = 1:20 min, slice thickness = 5 mm, acq. matrix = 256 × 256, voxel = 1.2 × 1.2 mm, bandwidth = 130 Hz/pixel) with a 90° and a 180° RF pulse was applied. For the noise measurement, the RF excitation pulse was set to zero, whereas for the signal measurement the RF excitation was set automatically. The acquired data were exported and then reconstructed offline MATLAB (MATLAB, The Mathworks, Natick, MA, USA).

SNR was calculated using the Sum-of-Squares (SoS) method ideal for high input SNR [36] and the Maximum Available (MA) method [15].

SNR_SoS values as calculated in Equation 8, are equal to the SNR for optimal combining with unknown coil sensitivities. The MA method describes optimal coil combination, were sensitivities are known. By multiplying the pixel value in each coil with the complex conjugate of the coil sensitivity for that channel, summing over all channels, and dividing this sum with the sum of the squared coil sensitivity in all channels, an optimal noise decorrelated (noise pre-whitened) combination method is used. Any phase added by the coil itself is removed and the signal is summed up. This method is also known as B₁-weighted coil combination [6].

Based on the results of the material test, the best performing material was used for further investigation. A preliminary study of the knee geometry (100 mm up/down the knee center) on 25 patients from Europe and U.S.A. showed a diameter range of 102–169 mm for European knees and 110–211 mm for U.S. knees. Standard coils like the 15-channel Tx/Rx knee coil by QED (Quality Electrodynamics, Mayfield village, Ohio, USA) have a limited inner diameter of 173 mm and field of View (FoV) in z-direction of around 200 mm. This diameter limitation makes the knee a good object to demonstrate the performance of a one-size-fits-all adaptive coil array approach.

To investigate the potential SNR improvement, a 6-channel receive-only array for 1.5 Tesla was developed. It consists of 4 adaptive channels (see Figure 3C) and a rigid 2-channel bottom part (see Figure 3B). As reference, a rigid 4-channel reference array (see Figure 3A) with an inner diameter of 180 mm, the size comparable to a single-row of a commercial 15ch knee coil (Quality Electrodynamics, Mayfield, OH, USA) was constructed, which could also be attached to the rigid 2-channel bottom part. The setup is mounted on a baseplate of the 15-channel knee coil, which is attachable to the patient table (see Figure 3A). The four adaptive channels can be attached to three different sized shells with grooves to fit the feed boards, similar to the phantoms (see Figure 4A). Geometrical decoupling was pre-adjusted during construction and is maintained with the bottom part for both arrays.

Three differently sized phantoms with 140 mm (size S, 2.4 l), 160 mm (size M, 3.2 l), and 180 mm (size L, 4.1 l) diameter each filled with per 1,000 g H₂O dist.: 1.25 g N iSO₄ × 6H₂O, 5 g NaCl were used for MR imaging. All housing parts including the three phantoms, were 3D laser sintered using the (ObjetEden500V, Stratasys 500V, Rechovot, Israel). The experimental setup can be seen in Figure 4B.

All loops were tuned and matched to 63.6 MHz and 50 Ω. The adaptive loops were adjusted at a stretching of 13.34%, which equals the diameter of the phantom size M. Decoupling was <18 dB, pre-amplifier decoupling >20 dB, and matching <20 dB. The stretchable areas of the adaptive array were made of 6 mm wide Amotape® Conduct Elast. #45792. The same properties as evaluated during the material test, were measured again for the knee array in the presence of the other loops, while inductively decoupled.

Finally, SNR was measured for the three phantom sizes using the adaptive and the reference array using the same spin-echo sequence as for the material tests. The smallest configuration of the adaptive array was used to acquire signal and noise images of the phantom size S (140 mm). The 2nd configuration was used to image phantoms S and M and the largest configuration was used to image all three knee phantoms (see Figure 4B). The acquired data were exported and reconstructed offline (MATLAB, The Mathworks, Natick, MA, USA).

The goal of the material tests was to identify a suitable material fulfilling the needs of an adaptive coil array. The CuBe2 Strain Springs were found to introduce a too high inductance and were, therefore, not further evaluated.

All tested materials were sufficiently stretchable to cover the envisioned element size. Bench measurement results for the rigid double-loop array and the three stretchable double-loop arrays are summarized in Figure 5 and show the dependence of the following parameters on the amount of stretching: Q_loaded (Figure 5A), Q_unloaded (Figure 5B), Q_ratio (Figure 5C), coupling coefficient k (Figure 5D), shift in resonance frequency (Figure 5E), inductive decoupling (Figure 5F), pre-amplifier decoupling (Figure 5G), matching (Figure 5H), coil+sample resistance (loaded) (Figure 5I), and unloaded coil resistance (Figure 5J). All coils showed a shift in resonance frequency of about−125 kHz per mm elongation by stretching (see Figure 5E). Amotape® #45792 showed consistently highest Q-ratio, best inductive and preamplifier decoupling. The loops with Amotape® #45792 showed coupling coefficients and coil resistance values in the unloaded and loaded cases which lie between the values of the other materials. All measured parameters of the stretchable loops were compared to rigid loops with equivalent sizes. Complete measurement data is listed in the Figure 11.

The results of SNR measurements in the MR scanner are shown in Figure 6. In most cases and on average, the stretchable loops with Amotape® #45792 showed the least loss in SNR (8/9% in 20/60 mm depth, respectively) as compared to the rigid double coil array.

For the adaptive knee array also Amotape® #45792 was used. The measured shift in resonance frequencies for the 4 stretchable loops within the adaptive array when stretched from a knee diameter of 140 to 180 mm, ranged from 66.39 to 61.23 MHz. This corresponds to a stretching of up to 26.68% from the original array size, the stretchable lengths × change from 60.1 to 91.5 mm. The overall size of an adaptive loop varies between 90.6 × 60 mm (un-stretched) and 122 × 60 mm (fully stretched). This resulted in a frequency shift of 164 kHz per mm elongation, which is comparable to the 128 kHz per mm as measured during the material tests for Amotape® #45792.

Q-ratios for all loops of both the rigid reference and the adaptive knee array were larger than 2, and therefore in sample noise dominance. The unloaded coil resistances R_{Coil, unloaded} of the individual antenna elements for the 180 mm knee phantom ranged from 0.84 to 1.39 Ω (reference array) and from 0.99 to 2.13 Ω (adaptive array). R_{Coil, loaded} for the same phantom size ranged from 2.38 to 3.67 Ω (reference array) and 2.51 to 4.79 Ω (adaptive array).

The coupling factor k^*Q_loaded between the loops of the reference array ranged from 0.048 to 0.125 and from 0.14 to 1.27 for the adaptive array. For the adaptive array this is higher than expected, which can be explained by the higher number of channels and their closer positioning as compared to the setting with 2 loops during the material tests, i.e., each loop was not only influenced by the direct neighbor, but also by all others.

Inductive decoupling ranged between 16.7 and 26.9 dB for the reference array and between 36.8 and 13.9 dB for the adaptive array. The best decoupling in the adaptive array was achieved at maximum stretching, as expected from the results of the material tests.

(Matching) ranged from −43.0 to −18.1 dB for the reference array. The adaptive array adjusted for the size M phantom was matched between −23.4 and −16.7 dB. At minimum and maximum stretching of the adaptive array loops, matching was completely off between −1.6 to −2.4 dB. Same results were achieved with the pre-amplifier decoupling. The reference array showed reasonable pre-amplifier decoupling values of 22.0 to 29.8 dB, whereas the loops of the adaptive array, from minimal to maximal stretching of the individual elements, ranged from 12.6 to 26.69 dB. Adjusted to the size M phantom, pre-amplifier decoupling for the adaptive array ranged from 19.6 to 26.5 dB, and is comparable to the values of the reference array.

Figure 7 illustrates the SNR images acquired with the reference and the adaptive array using the three different phantom sizes. SNR values were measured in single voxels in the middle transverse slice at three different depths from the surface, relative to the knee phantom size used. In a direct comparison between the adaptive and the reference array using phantom size L, the SNR of the adaptive array was worse at 20 mm below the knee phantoms surface (from the top), compared to the reference array. The SNR values in the center are just slightly worse for the adaptive array. When using smaller phantom sizes, the adaptive array, tuned and matched to phantom size M, achieves equal SNR values at the phantom center and much higher SNR values especially below the surfaces of the phantoms. Noise correlation is not exceeding 0.4 in any configuration of the reference or the adaptive array (see Figure 10).

In Figure 8 one can see the SNR comparison between the arrays using the three different knee phantoms. Comparing at phantom size L, it is evident that the adaptive array stretched to sizes S, M and L (but always tuned and matched for array size M and phantom size M) performs worse (−10 to −40%) than the reference array (tuned and matched for array size L and phantom size L). However, as expected due to the closer fit to the sample, an SNR gain of 29% (array size M, phantom size S), 40% (array size M, phantom size M), or 100% (array size S, phantom size S) was observed in the voxel near the adaptive part of the arrays. SNR in the center of the phantoms was approximately equal to the rigid array, and a consistent 5–10% SNR gain was found for the voxels near the rigid bottom part.

Figure 9 shows sagittal in vivo MR images of the knee center using the adaptive array, displayed as uncombined single channel images, and the combined image. The imaged knee had a very small diameter of 100 mm at the center, even smaller than the smallest size configuration of the adaptive array (130 mm), therefore, the optimal fit of the adaptive array was not reached.

BG and EL declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. RR and SZ declare to be employee of Siemens Healthcare GmbH, Erlangen, Germany.