When designing a new MPI system, the major consideration is which data are desired.

• If for instance you only want to measure the harmonic response and relaxation behavior of SPIONs, then the bias coils aren't nearly as important and increasing the diameter the shielding bore will profoundly increase the efficiency of the drive coils at the cost of lower bias coil efficiency.

• If you want to study new SPIONs which may not saturate until 50 mT or higher, then having high-quality bias coil is critical (because the drive coil simply won't achieve that without major changes to the filter/amplifier). I would also make the bore smaller because if "magnetometry"/"ac-susceptometry" is the main operational mode, then only a few mT of drive is needed and the higher efficiency is better in the bias coil.

There are three main coils in the signal chain of this system each with an associated amplifier.

• 44 Turns (22 each half)
• ~33 mm long each half
• 115/36 AWG Litz
• ~60 mΩ, 8 μH @ 23.8 kHz

The Tx coils are designed to be low-loss at the operating frequency, and have homogeneous field production. Each one of these factors played a role in the design.

• The high(ish) frequency of the Tx coil is important for the wire selection, which we used Litz wire to keep the AC impedance as low as possible. We used about 2.1 mm diameter Litz wire.

• The homogeneity was a consideration when looking at the pairwise design of the Tx and Rx coils. The drive coil design was not explicitly optimized, rather to improve homogeneity it is clear that turns should be removed from the center. This is because in a simple short solenoid the field is highest at the isocenter. On the other hand, a Helmholtz pair design would be very homogeneous, but not practical due to spatial constraints and efficiency. Using FEMM 4.2, the design was iterated until a reasonable design was found. In the process the efficiency goal was to ensure at least 10 mT, and homogeneity remained within a few percent in the center 5 mm or so. Future work could improve this, but the gains will likely be marginal on both fronts.

The drive amplifier used is the TDA3255, a switch-mode amplifier from Texas Instruments. The switching frequency is sufficiently high (>400 kHz) such to be easily filtered out, and the benefit is a tremendous improvement in efficiency when compared to its linear amplifier counterparts.

A commercial amplifier was purchased (AIYIMA A07) but substantially modified. The modifications included

• converting it to Parallel bridge tied load (PBTL) mode.
• Removing the on-board low-pass filter, and instead using a band-pass design
• BNC input connector was added

For this amplifier, a 48V, 1A linear power supply is used, but this power supply limits the available power the system can output short bursts (50 ms or so) of ~2.5 A is feasible, but the voltage sags considerably. A large capacitor bank may be beneficial for this.

This amplifier in PBTL mode has maximal output power to a 4 Ohm load.

To match the amplifier to the load and purify the signal a filter was implemented. The design is consistent with the filter designer (part of OS-MPI TODO: Add link).

Because the load is such a low impedance, a current transformer is utilized to increase the apparent impedance as viewed from the filter. This is necessary because otherwise the impedance transformation by the capacitors alone would require impractically large values (10s of microFarads, which are not as available as smaller ones). Further the transformer gives an additional level of common-mode isolation which may help in reducing noise and interference.

See Transmit Coils for more details.

Drive current per 30 volts from the drive amplifier

Schematic of the filter. Note the drive coil is an equivalent load

• 100 Turns (50 each half)
• 12.5mm long segments
• 28/5 AWG Litz Wire
• 31 uH, 1.9 Ohms @ 23.8 kHz

Optimizing the Rx coils is a challenge still being investigated.

Some designs support using Litz wire for low impedance Rx, yet if large bundles are used this is going to result in a lower number of turns because Litz isn't spatially efficient-- This is true for the Litz wire which we had available. The premise is that Litz wire has many small strands that are individually isolated, but electrically parallelized. Because the current will only penetrate about one skin depth in the wire, the remaining copper is essentially wasted and only serves to increase losses from the nearby wires causing losses due to the proximity effect. These losses can be thought of as increased resistance, and noise is proportional to the square root of resistance, therefore Litz will have lower noise for the same cross-sectional area( thermal coil noise ). For very low-noise pre-amplifiers (<1nv/sqrt(Hz)) this is important because the coil noise can easily dominate.

Alternatively, you can use thin (~0.1mm) magnet wire and get many turns and because signal is proportional to turn count assuming the same turn locations, you increase your signal. With the high turn approach, you simultaneously increase resistance linearly (ignoring proximity/skin effect, which is a bad assumption). The SPaQ uses this approach(3). The downfall of adding too many turns is that the the inductance and parasitic elements can easily dominate the system's noise.

The inductance has two implications: first is on noise, the second is self-resonance. The noise will increase with large inductive loads because the equivalent input noise is thermal noise from the load (already discussed), preamp voltage noise, and the current noise multiplied by the impedance. At high frequencies the inductive impedance may cause that term to dominate. For example, the INA217 has about 1pA/sqrt(Hz) current noise and 1nV/sqrt(Hz) voltage noise. If the equivalent impedance of the load is over 1kOhm, then the current noise will dominate. MOSFET/JFET input preamps have very low current noise (generally), so they are popular in MPI. Self-resonance is challenging to predict, but in any situation where the inductance approaches the order of mH, it will likely be a problem within the MPI frequency range.

We used an in-house made Litz wire which consisted of 5 strands of 28 AWG wire. This allowed high turn density while simultaneously mitigating skin and proximity effects.

See Optimal Broadband Noise Matching to Inductive Sensors: Application to Magnetic Particle Imaging by B. Zheng for more details.

3. DC Biasing Coils

• TODO: UPDATE
• TODO: UPDATE
• TODO: UPDATE

These coils are very important in keeping the cost and simplicity of the system down and are essential for magnetometry and relaxometry mode. The thought behind these coils is that a 20Hz (or so) field has much different requirements than a high fidelity 25kHz signal, so why combine them? By using 20AWG magnet wire with enough turns to match it to an inexpensive audio amplifier such as the TDA7293, or the RCF IPS 700 which in our case was ~600 turns, you can get this "DC biasing" (perhaps "Near-DC" is a more fitting name?) field for much less than if we needed to maintain the high fidelity and bandwidth standards of the drive coil. Plus by doing this, you take less stress off of the drive amplifier which results in better noise/THD performance. To attenuate any noise from this coil from interfering with the Tx/Rx system, we employ a thick-walled copper tube between the biasing coils and the Tx/Rx coils.

The tube acts as a shield for high-frequency components via eddy current cancellation but doesn't substantially diminish the efficacy of the low-frequency components (though there is a phase-lag from current to field within the tube, still).

To mitigate the heating issue, we separate every two layers of this coil with spacers, the innermost layer is cooled by the copper tube which acts as a heat sink and the other layers act as "fins" that let passive (or forced) airflow to cool them off. See the rendering below. Otherwise, with that many layers, heat may build up over time between layers. The amplifier is thermally connected to the metal enclosure which acts as a large heat sink. The decision to include the "fins" or not is governed by how you anticipate using the system. They are great if you want to operate it for long time periods at high duty cycles. But for occasional use, they aren't worth it. They substantially reduce the efficiency (W/mT).

When designing the coil, be careful to consider the inductance of the coil. Using thick wire, adding enough turns to match to 8 Ohms seems attractive but the inductive impedance can easily overwhelm the resistive component. If you are using a DC-coupled amplifier, this is not an issue.

The symmetry of the coils in the bore plays a role in ensuring the fields generated due to the inevitable eddy currents are symmetric. The spatial distribution of the eddy currents is frequency-dependent, thus if you locate your gradiometer Rx coil to cancel out the drive frequency feed-through, in an asymmetric system you will not be positioned to ideally cancel out higher harmonics due to their different spatial maps. Below is a figure of a simple coil in an asymmetric copper tube at 1MHz showing an obvious asymmetry in the field with the |B| being ~5% different at each end of the solenoid (the simulation files are included in the project repository).

Figure 1: An example of the fields produced by a solenoid asymmetrically located in a copper tube. The coil geometry is arbitrary, and the frequency is 1MHz to clearly illustrate the asymmetric field pattern.

Another point is the sample holder's rigidity. The shape of the actual sample holder should, of course, be modified to accommodate whatever you are planning to scan, but keep in mind that if you include a long cantilevered beam, it may have the tendency to slowly oscillate which will impart a sinusoidal variation in your signal if the beam has not settled. Also the angle of the sample plays a role. If the sample is horizontal, so that axial direction of the coils are orthogonal to gravity, any bubbles in the phantom will tend to move around due to the magnetic forces on the nanoparticles. This will cause artifacts in the data. Having the axial direction aligned with gravity makes it so that the magnetic forces when the bias/drive coils are powered is in the same direction as gravity, so any bubbles that are present will not move.

Lastly, we have a stepper motor built in to put the same into a reliable location or get 1D sensitivity maps of our system, but it is important to utilize the "sleep" or "enable" functionality included in the motor driver so there is no substantial current going through the driver (which is quite noisy) when you are sampling. This is a general note that should be included in the many stepper motors across the imager too.

 (1) N. Panagiotopoulos, Magnetic particle imaging: Current developments and future directions, 2015
 (2) A. Malhotra, Tracking the Growth of Superparamagnetic Nanoparticles with an In-Situ Magnetic Particle Spectrometer (INSPECT)
 (3) M. Van De Loosdrecht, A novel characterization technique for superparamagnetic iron oxide nanoparticles: The superparamagnetic quantifier, compared with magnetic particle spectroscopy, 2019