Lena Nohava1,2, Raphaela Czerny2, Michael Obermann2, Michael Pichler2, Roberta Frass-Kriegl2, Jacques Felblinger3, Jean-Christophe Ginefri1, and Elmar Laistler2
1IR4M (Imagerie par Résonance Magnétique et Multi-Modalités), UMR 8081, Université Paris-Sud/CNRS, Université Paris-Saclay, Orsay, France, 2Division MR Physics, Center for Medical Physics and Biomedical Engineering, Medical University of Vienna, Vienna, Austria, 3Université de Lorraine, Inserm, IADI, Nancy, France
Synopsis
The design of
flexible coaxial coils (CCs) based on the single-turn single-gap concept is
extended by multiple turns and multiple gaps (MTMG-CCs) to achieve a larger range
of coil diameters for a given resonance frequency. An equivalent circuit for
MTMG-CCs is presented and the resonance condition is solved numerically for
coils with diameters up to 20 cm, 1-3 turns, and 1-3 gaps. For validation of the
calculations, 27 coils with 6/9/12 cm diameters, 1-3 turns, and 1-3 gaps were built
and characterized on the bench.
Purpose
In RF coil array
development, auto-resonant structures such as transmission line resonators
(TLRs)1,2 implemented using coaxial cables3,4 exploit the advantages of flexibility, close-fitting
design, light weight, and robustness to coil overlap variations3. As
previously reported3,5, with a single turn of coaxial cable and
a single gap in outer and inner conductor, the coaxial coil diameter is
dictated by the desired resonance frequency (f0) and properties of the coaxial cable used, such as the
outer conductor diameter (d1),
the characteristic impedance (Z0), and the relative permittivity (εr) of the dielectric. Therefore,
the coil diameter cannot be chosen freely, and the resulting coil size is not
necessarily the optimum for a given clinical application.
In this work – based
on multi-turn multi-gap (MTMG) transmission line resonators6 – an extended design of coaxial coils with
more than one gap and/or cable turn (MTMG-CCs) is proposed with the goal to increase
the degrees of freedom in coaxial coil design. The design concept is studied by
numerical simulation and bench measurements using 27 different MTMG-CC configurations
made of one coaxial cable type.Methods
Design concept and resonance frequency calculation:
Tab.1 lists the design
properties of all investigated MTMG-CCs. Example layouts of coaxial coils with
either one, two or three gaps are schematically drawn in Fig.1a. The equivalent
circuit for MTMG-CCs is presented in Fig.1b. The total inductive reactance XL is approximated as the
inductance of a conductive loop of the same diameter and thickness as the outer
shield of the coaxial coil, which is proportional to the squared number of
turns (nt) of the coaxial
cable. The total capacitive reactance is obtained assuming that the coil
consists of 2ng (twice the
number of gaps) lossless open-ended coaxial stubs in series and using the
classical capacitive reactance formula of a stub. The corresponding equations
are given in Fig.1c. At resonance, the total reactance equals zero, thus the
resonance condition for an MTMG-CC can be derived.
From this, considering
the specific cable type used for coil construction (εr=2.1, d1=2.5mm,
Z0=50Ω), the resonance
frequency was calculated using MATLAB 2017b (The Mathworks, Inc., Natick, USA) for
various coaxial coil diameters (d0≤20cm)
and MTMG-CC configurations with ng=1-3
and nt=1-3.
Bench measurements:
A total of 27 MTMG-CCs
with diameters of 6, 9 and 12 cm, ng=1-3,
and nt=1-3, yielding 9
different coil configurations per diameter (Fig. 2a), were fabricated from
non-magnetic coaxial cable (K_02252_D-08, Huber+Suhner, Pfäffikon, Switzerland)
with gaps of 7mm width (Tab.1). The set of 9 MTMG-CCs with d0=12 cm is depicted in Fig.2b. At a constant distance from
the MTMG-CC, a decoupled double-loop probe7 was used to evaluate the coil’s quality factor
Q, and the resonance frequency (f0) for the unloaded and loaded
coil setup. A torso-shaped phantom (≈57x38x23cm3) with tissue equivalent
properties (σ=0.60S/m, εr=62) was used as a load.
Results and discussion
Calculation results
for the 27 investigated MTMG-CC configurations presented in Fig. 3 demonstrate
that – for a fixed coil diameter – the resonance frequency increases with the
number of gaps and decreases with the number of turns. At a given resonance
frequency, compared to a single-turn single-gap coaxial coil, using multiple
turns allows for smaller coil diameters, whereas adding gaps allows for larger coil
diameters.
Bench measurement
results including Q-factors (unloaded and loaded), Q-ratios and the f0 shift between loaded and
unloaded case are summarized in Fig.4. All Q-ratios are superior to 2, indicating
coil operation in a sample noise dominated regime. A drop in Qunloaded can be observed as
the resonance frequency increases (high ng,
low nt, small coil
diameter), which could be explained by other loss mechanisms (e.g. dielectric
losses or radiation losses) becoming dominant over resistive losses at high
frequencies.
The fabricated
MTMG-CCs have resonance frequencies ranging from 18 to 632 MHz. The maximum measured
f0 shift due to loading is
less than 3%. Simulated f0 values
for the unloaded setup deviate up to ±11.3% from measured results (Fig.3). In practice, an additional
capacitor or inductor at the coil port (between the inner conductors) can be
used for fine-tuning.Conclusion
In this work, we
present a design scheme and equivalent circuit for multi-turn multi-gap coaxial
RF coils, exhibiting outstanding mechanical flexibility. Predicted resonance
frequencies from numerical simulations sufficiently match measured results for
reliable MTMG-CC design. The use of multiple gaps and/or turns offers more
degrees of freedom compared to a single-turn single-gap coaxial coil whilst maintaining
mechanical flexibility and thus enlarges the range of clinical applications of coaxial
coils.Acknowledgements
This project was
funded by the Austrian/French FWF/ANR grant, Nr. I-3618, “BRACOIL“, and Austrian/French
OeAD WTZ grant FR 03/2018.References
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