Ian Robert Oliphant Connell^{1,2} and Ravi S Menon^{1,2}

To-date, increasing interest in adapting dipole antennae for imaging at ultra-high field strengths has spawned the design and construction of many dipole-based RF arrays. However, increased electric-field interactions between dipole-to-sample and dipole-to-dipole provide an implementation barrier due to mutual coupling and load-sensitivity. This study presents an analysis of dipole-to-dipole coupling and implements a filter design method to isolate dipole elements in a highly-conformal array designed for human brain imaging at 7 Tesla.

Multi-channel radio-frequency (RF) arrays provide individual
sensitivity profiles that when used in concert with optimized gradient and RF
waveforms can overcome transmission field (B_{1}^{+}) inhomogeneity at ultra-high field (UHF) or reduce
specific absorption rate (SAR) via B_{1}^{+} or RF shimming^{1}.
Due to a mixture of near- and far-field electromagnetic interactions occurring at
UHF, electric dipole arrays are finding increasing utility at UHF when compared
to more conventional RF loop elements^{2}. However, synthesizing dipole
arrays presents a technical challenge.

Fig. 1 presents the
input impedance (Z_{11}) calculated for a dipole in free space and next
to a conducting medium, as well as the mutual impedance (Z_{12})
between two dipoles. As demonstrated in Fig. 1, near resonance the dipole
electrically interacts with the sample. This increases the capacitive reactance
of the input impedance of the dipole element (Z_{11} in Fig. 1). Similarly,
the capacitive reactance of the mutual impedance between two dipoles (Z_{12}
in Fig. 1) is increased when compared to that of dipoles in free-space. This
increased electrical interaction between dipole-to-dipole and dipole-to-sample
occurs due to a lossy pathway in a closely-spaced high-permittivity medium.
As demonstrated in
Fig. 1, decoupling of loaded dipoles is limited by the applicability of
conventional decoupling methods for two reasons: (a) increased slope of the
mutual reactance near-resonance and (b) increased magnitude of coupling due to
both inductive and electric sources. Ideal decoupling impedance, via insertion
of an additional ladder section between dipoles, is solved for via computing
the eigenmodes of the decoupled array and is presented in Fig. 1 clearly
demonstrating the need for a resonant decoupling section.

In this study, mutual coupling is compensated for via a
general decoupling solution with ladder filters^{3}. The filters
approximate the required decoupling impedance (Fig. 1) between dipole elements.
The decoupling method is applied to a transciever array composed of conformal,
meandered dipole antennas - array elements that are not easily decoupled by
current approaches.

Coupling matrix synthesis
(CMS) designs ladder filter networks by fitting prescribed filter responses to
analytic polynomials^{3}. A CMS solution has been adapted for
implementing a conformal, meandered dipole array designed for human head
imaging at 7 Tesla. A building block of the CMS circuit design
is presented in Fig. 2a with the specific circuit utilized in this study presented
in Fig. 2b. The dipole elements compose the ladder legs of the RF array, with
matching networks inserted, transforming the input impedance of the dipole
input to power match the complex dielectric load. Additional resonant
decoupling circuits complete the band-stop PI network, and the cascaded filter
is tiled across to span the entire RF array.

The dipole array was constructed on an elliptical former (minor and major axes: 17 cm and 20.5 m, respectively) and was composed of eight resonant dipoles implemented with 32 mm wide 2 oz. copper traces, routed atop 0.79-mm-thick garolite. Dipoles were matched to 50 (via low-pass PI matching circuits utilizing two variable capacitors (1 – 30 pF, Johanson Manufacturing, NJ) and one variable inductor (25 – 34 nH, Coilcraft, IL, USA). Sleeve baluns were constructed using triaxial cable (double braid shield, 20 AWG, Belden, IN, USA), and were directly fed to the dipole matching circuit from externally mounted BNC connectors.

Due to the conformal geometry (see Fig. 3a,b), one half of the balanced form of the decoupling network could be achieved by directly soldering the parallel inductor/capacitor ladder sections between dipoles located at the top of the head (see Fig. 3b). The second half of the decoupling network was connected via coaxial cables between elements (Fig. 3a). The additional capacitive phase shift induced in the decoupling portion of the ladder was compensated for via tuning the parallel inductor/capacitor section.

**1. **Curtis, A. et. al., Slice-by-slice
RF Shimming at 7 T. MRM, 2012.

**2. ** Raaijmakers, AJ. et. al., Design of a radiative surface coil array
element at 7 T: the single-side adapted dipole antenna. MRM, 2011.

**3. ** Connell, IRO. et. al., General
Coupling Matrix Synthesis for Decoupling MRI RF Arrays. IEEE-TMI, 2016.

Impedance characteristics for a dipole located in free-space and a dipole adjacent to a conducting load. In comparison to free-space, the input impedance (Z_{11}) of the loaded dipole demonstrates clear sensitivity to the load via an increase in capacitive reactance near-resonance and reduced resistance. Similarly, mutual impedance (Z_{12}) shows an increase in capacitive reactance and slope of the reactance curve near-resonance. An increase in the slope of mutual reactance near-resonance necessitates a more complex decoupling network or ladder. Decoupling via an LC-network is demonstrated in the bottom figure, whereby elimination of mutual impedance requires a tuned LC impedance curve.

(a) Basic building block of the decoupling topology utilized by the Coupling Matrix Synthesis (CMS) procedure. The ladder topology computes a series of network transfer functions that minimize mutual impedance between individual dipoles located in the array. Both electric, magnetic and resistive components are present in the CMS procedure - a positive mutual reactance denoting primarily inductive coupling, with a negative mutual reactance denoting capacitive coupling. (b) Schematic of the decoupling circuits and equivalent circuit of the dipole elements, with LC-matching networks applied.

The final constructed dipole array. Visible in (a) are triaxial sleeve baluns, in yellow, attached to low-pass PI matching networks at the dipole inputs with one-half of the balanced decoupling network attached at the dipole input. As visible in (b), meandered features allowed for direct soldering of the second-half of the decoupling networks to the top portion of the dipoles.

Individual transmitter field profiles across a centrally-axial located slice demonstrated levels of high electromagnetic isolation required for multi-channel RF coil operation.

Parallel imaging inverse G-factor maps computed for acceleration rates up to R = 3x3.