Resonant Inductive Coupling Network for Human-Sized Magnetic Particle Imaging

TL;DR

This work tackles safe and scalable drive-field generation for human-sized Magnetic Particle Imaging by replacing traditional ferrite-based transformers with a resonant, toroidal, air-core inductive coupling network (ICN). A theory connects current gain $G$ to isolation and quality factor $Q$, and the authors optimize a D-shaped toroid cross-section, multi-layer winding, and segmentation to maximize $L_2$ at fixed $Q$, plus a DFG matching condition to balance particle signal against power consumption. Two toroidal ICNs are designed, simulated, and built for a two-channel MPI head scanner, achieving high coupling $k$, preserved linearity, and effective inter-channel decoupling with floating potentials for patient safety. The results validate the approach and provide design guidelines for safe, high-gain MPI drive chains, with potential applicability to other resonant-load contexts and multi-channel MPI implementations. This work thus advances practical, safe, high-performance drive-chain architectures toward clinical translation in MPI.

Abstract

In Magnetic Particle Imaging, a field-free region is maneuvered throughout the field of view using a time-varying magnetic field known as the drive-field. Human-sized systems operate the drive-field in the kHz range and generate it by utilizing strong currents that can rise to the kA range within a coil called the drive field generator. Matching and tuning between a power amplifier, a band-pass filter and the drive-field generator is required. Here, for reasons of safety in future human scanners, a symmetrical topology and a transformer, called inductive coupling network is used. Our primary objectives are to achieve floating potentials to ensure patient safety, attaining high linearity and high gain for the resonant transformer. We present a novel systematic approach to the design of a loss-optimized resonant toroid with a D-shaped cross section, employing segmentation to adjust the inductance-to-resistance ratio while maintaining a constant quality factor. Simultaneously, we derive a specific matching condition of a symmetric transmit-receive circuit for magnetic particle imaging. The chosen setup filters the fundamental frequency and allows simultaneous signal transmission and reception. In addition, the decoupling of multiple drive field channels is discussed and the primary side of the transformer is evaluated for maximum coupling and minimum stray field. Two prototypes were constructed, measured, decoupled, and compared to the derived theory and to method-of-moment based simulations.

Figures (7)

• Figure 1: Overview of the MPI transmit chain and the ICN. In (a), the power amplifier is connected to a ferrite-core transformer, a band-pass filter and to the primary side of the ICN. The secondary side of this transformer is part of a high-Q resonator, called HCR, that includes the DFG. Magnetic particles excited by the DFG induce signals via $L_\textup{Tx}$ and the receive signal is tapped within the symmetric HCR at $v_\textup{TxRx}$. In (b), a 4-fold segmented toroidal, D-shaped ICN is shown within a simulation setup of CONCEPT-II institut_fur_theoretische_elektrotechnik_concept-ii_2023.
• Figure 2: Segmented toroidal air-core transformer and THD simulation of iron-core saturation without hysteresis. Shown in (a) is a toroid parallelized with $N_s=12$ individual segments, of which $8$ are shown in different colors ($4$ are hidden). The primary winding also forms a toroid, here with $N_1=12$ turns, whereas each secondary segment has $N_2=13$ turns. In (b), the circular cross-section in the $xz$-plane is shown with characteristic parameters noted. On the right in (c), three sinusoidal input signals (1) are modulated by the magnetization curve in (2), which results in the output in (3) and its spectrum in (4). The magnetization curve is adopted from the "-8" iron powder core material micrometals_inc_datasheet_2007, but without hysteresis effects and modeled with a $\tanh$-function herceg_use_2020. A THD of 0.5%, typical for class-AB amplifiers, is caused by an amplitude of about 0.14 of $H_\textup{sat}$.
• Figure 3: Resonant transformer circuit diagram. A resonant transformer is shown, where an ideal transformer remains embedded in the center. The inductors are split into leakage and coupled inductances. The matching capacitor $C_\textup{m}$ resembles the filter output stage, which goes into resonance with the leakage inductance $L_{\sigma,1}=L_1(1-k)$ and $Z_\textup{prim}$ becomes real at $\omega=2\pi f_1$.
• Figure 4: Optimal D-shaped cross-section and multilayer toroids murgatroyd_optimal_1989. In (a), the optimal D-shape cross-section is shown for the fixed optimum ratio of ${r_\textup{o}}/{r_\textup{i}}=5.3$. The left toroid-half features a field intensity plot with the field profile along the $x$-axis in white (the toroid has 3 layers on the inside, simulated in CONCEPT-II institut_fur_theoretische_elektrotechnik_concept-ii_2023). Highlighted in orange in the right toroid-half is the curve obtained by a stepwise evaluation and integration of \ref{['eq:step_DC']}. In (b), two different types of winding arrangements of multi-layer toroidal inductors are shown.
• Figure 5: Inductance matching condition of DFG and ICN. A trade-off is identified at $L_2=L_\textup{Tx}$, when the receive signal is halved (-3dB), expressed by the intersection of the particle signal (blue) and the normalized signal-to-loss ratio (green). This graph demonstrates that additional power is required to avoid receive signal attenuation.