Application of square-wave inverter in excitation system for magnetic nanoparticle tomography

Measuring the spatial distribution of magnetic markers composed of bio-functionalized magnetic nanoparticles (MNPs) represents a promising technique for medical imaging, especially for the detection of targets such as cancer cells.^1,2 In particular, magnetic particle imaging exploits the nonlinear magnetization behavior of MNPs to detect and estimate the spatial position and quantity of MNPs in a target region.^3,4

Owing to the nonlinear response of MNPs during measurement, various harmonic frequencies appear when a sufficiently large ac excitation field is applied. Magnetic particle imaging detects these harmonic signals by rapidly scanning a field-free point across the imaging field of view, and an image with high contrast and resolution can be acquired. However, a generating a field free point requires a strong gradient magnetic field (typically 1-2 T/m).⁴ Furthermore, high-speed scanning of the field free point requires a rapidly varying gradient field, which can cause adverse effects on the human body, such as peripheral nerve stimulation and tissue heating.^5,6 To prevent these problems, we have introduced an alternative imaging method called magnetic nanoparticle tomography (MNT).^7,8 MNT uses an array of multiple magnetic sensors to achieve high resolution without requiring a gradient magnetic field. The proposed imaging method inspired by magnetoencephalography acquires harmonic signals from MNPs through multiple pickup coils.

Considering the clinical use of MNT, the excitation system should generate a strong magnetic field to detect signals from distant MNPs with low concentrations to detect signals from accumulations of MNPs and inter-subject variability. In Refs. 7 and 8, a linear amplifier-type ac power source was used to generate high-quality sinusoidal excitation for MNT. Nevertheless, this source has a low efficiency and increases the cost of the system.⁹ Alternatively, we adopted a square-wave inverter to generate a large current with high power efficiency in this study.

Excitation using a class-D amplifier has been used for magnetic particle imaging, generating an excitation current with high power efficiency by using an inverter.¹⁰ Similarly, we use an H-bridge voltage source inverter (VSI) to apply square-wave voltage excitation for MNT. Square-wave excitation using common switching in inverters exhibits harmonic components in the excitation current. In particular, the third harmonic has the same frequency as the MNP signals, thus distorting these signals and degrading the imaging performance. In an H-bridge inverter, specific harmonic components can be suppressed by selecting the appropriate switching phase of the transistors.¹¹ Accordingly, we propose a method to suppress the third harmonic from the excitation current by devising the switching phase to extract the third-harmonic signal of the MNPs.

Fig. 1 shows a diagram of the excitation system for MNT. The system was almost the same as in Refs. 7 and 8, except for the inclusion of a VSI. We used a square-wave voltage to drive an excitation coil with a resonant capacitor. The quality factor of the resonant circuit was approximately 26.4. The square-wave voltage was generated by sending a gate signal to the H-bridge inverter circuit using the 24-channel digital input/output module of a data acquisition device (PXIe-6356; NI, Austin, TX, USA) and the voltage from a dc power supply (PWR801L; Kikusui, Yokohama, Japan). The sampling rate of the module was set to 1 MS/s to generate the gate signal. The current frequency was set to f₁ = 5400 Hz, as explained in Ref. 8. The excitation coil had a height of 22 mm and inner and outer diameters of 200 and 280 mm, respectively. The excitation coil had 50 turns and was made of Cu litz wire with a diameter of 0.1 mm and 784 filaments. The intensity of the magnetic fields exceeds approximately 7 mT at z = -25 mm for the current amplitude of 30 A. The z axis indicates the distance between the MNP sample and excitation coil.

An array of 16 pickup coils were located within the excitation coil. Each pickup coil has a height of 6 mm, inner and outer diameters of 2 and 8 mm, respectively, and 1200 turns. The coils were made from solid Cu wire with a diameter of 0.1 mm. When a magnetic flux of 1 pT at the third harmonic (f₃ = 16 200 Hz) passes through the pickup coil, the induced voltage reaches 2.40 nV. To eliminate the effect of the direct magnetic flux generated by the excitation coil, the sensing directions of the pickup coils were parallel to the x or y axis.

To mitigate the third harmonic component from the pickup coil, we used a system for suppressing the fundamental wave using a digital-to-analog converter with 16-bit resolution at 1 MS/s rate in the PXIe-6356 device to generate a wave that cancels cancel out the fundamental signal by the excitation magnetic field while amplifying only the harmonic component. Fig. 2 shows a schematic diagram of the amplifier circuit. A resonance capacitor was connected to the pickup coils to enhance the third harmonic and suppress noise from the inverter. The enhanced signals were amplified using a low-noise instrumentation amplifier (AD8429; Analog Devices, Norwood, MA, USA). Gain G (set to 100 in this study) was adjusted with a resistor connected to terminals R_G. An inductor was connected in series to the resistance in terminals R_G to establish a lowpass filter that prevents steep high-order harmonic signals that exceed the operating range of the amplifier. In addition, a two-pole pair band-elimination filer (SR-2BE2; NF, Yokohama, Japan) and a low-noise operational amplifier (OP1177ARZ; Texas Instruments, Dallas, TX, USA) amplified the third-harmonic component. The gain of the non-inverting amplifier was set to 11. Subsequently, the output signal was recorded using a 32-channel analog-to-digital converter (NI PXIe-4303, NI) at 24-bit resolution and 51.2 kS/s rate. Then, the third harmonic signal was extracted using the fast Fourier transform.

Fig. 3 shows the equivalent circuit of the excitation system. We adopted an H-bridge inverter with four n-channel power MOSFETs (metal-oxide-semiconductor field-effect transistors) Q₁ − Q₄ with an on-resistance of 0.55 mΩ (AUIRFS8409-7P; International Rectifier, El Segundo, CA, USA). Schottky barrier diodes (MBRB4030G; ON Semiconductor, Phoenix, AZ, USA) were connected in parallel with the MOSFETs to absorb the reverse current. R_ex and L_ex represents the internal resistance and inductance of the excitation coil, respectively, and C_R represents the resonant capacitor. Noninductive shunt resistance R_S (HF100; Newtons4th, Leicester, UK) of 1 mΩ was used to measure and analyze the spectrum of excitation current $iext$ based on the fast Fourier transform. In addition, the waveform of output voltage $vext$ was measured using a ScopeCorder DL850E device (Yokogawa, Tokyo, Japan) with a 4-channel isolation module 720254 (Yokogawa) to compare the measured and ideal waveforms.

The square wave output voltage can be controlled by adjusting the gate signals of transistors Q₁ and Q₃ (Fig. 3). The gate signals of transistors Q₂ and Q₄ have a fixed phase difference of π rad from those of transistors Q₁ and Q₃, respectively.¹¹ For phase α, Q₁ and Q₃ are turned on simultaneously, and the output voltage is zero. Fig. 4 (a) shows the transistor switching diagram and output voltage waveform when α = 0. This setting establishes the conventional generation of square-wave voltages in H-bridge VSIs. The Fourier series of the output voltage is given by

which shows the third harmonic component. Although the third-harmonic field is generated from the excitation coil, we measure third harmonic MNP signals, and the third-harmonic excitation interferes with signal acquisition.

Fig. 4 (b) shows the transistor switching diagram and the output voltage waveform for α = π/3. By applying the same analysis as above, the output voltage can be expressed as

where harmonics whose frequencies are multiples of three of the fundamental frequency are eliminated from the output voltage. Therefore, if switching is controlled properly as described above, the third harmonic of the excitation field can be effectively suppressed to preserve only the MNP signals. Furthermore, generating a waveform by shifting the switching phase by π/3 rad allows to eliminate the third harmonic of any periodic waveform. Accordingly, we apply the corresponding switching method to the H-bridge VSI for MNT.

In this study, we used Resovist (Fujifilm RI Pharma, Chiba, Japan) magnetic markers as MNP samples. The Resovist MNP sample was diluted to the desired concentration using glycerol to obtain a sample volume of 150 μl. The sample was sealed in a cylindrical cell of 6 × 5 mm.

We evaluated the third harmonic signal detection performance using the square-wave voltage excitation for phase control parameters α = 0 and π/3, that is the conventional and proposed methods, respectively. The signal of the MNP sample containing 500 μl of Fe was detected by moving the sample using two motorized stages (OSMS26-300(XY) and OSMS20-85(Z); Sigma Koki, Tokyo, Japan), as detailed in Ref. 8. The sample was scanned on the xy plane at a speed of 10 mm/s, while an ac magnetic field was generated along the z axis by the excitation coil. The resolution on the xy plane was set to 5 × 5 mm. The excitation current was set to 30 A. The distances between the MNP samples were −50 mm.

Fig. 5 shows the experimental waveforms of the output voltage and excitation current from the H-bridge VSI obtained using the DL850E device. Figs. 5(a) and (b) show the voltage and current waveforms of phase control using the conventional and proposed methods, respectively. The input dc voltage was controlled to 7.8 V for the conventional method and 9.0 V for the proposed method, such that the amplitude of the excitation current was 30 A. It shows that the square-wave voltage generated in experiment was similar to the ideal voltage shown in Fig. 4. However, the waveform is distorted due to ringing during voltage fluctuation. This distortion can be mitigated by increasing the number of decoupling capacitors connected in parallel with the power source. On the other hand, the current waveform shows a switching transient possibly caused by the slight mismatch between the resonance frequency and excitation current frequency. Therefore, the frequency of the excitation current should be adjusted to achieve an ideal waveform.

Fig. 6 shows the spectrum of excitation current i_ex(t) obtained by applying the fast Fourier transform using measurements at shunt resistance R_S. The currents in Figs. 6 (a) and (b) were generated using the output voltages shown in Figs. 5 (a) and (b) respectively. The amplitudes of the third harmonic currents were approximately 0.0741 and 0.007 37 A in Figs. 6 (a) and (b), respectively. The third harmonic is substantially reduced by applying the proposed switching method. However, it persists despite not appearing in (2) and thus can be further mitigated. The remnant of the third harmonic can be explained by the 1 MS/s sampling rate of the module generating the gate signal, which is not sufficient for the phase shift of the periodic function of 5400 Hz to accurately approximate π/3.

Fig. 7 shows the distribution maps of the third harmonic component from pickup coil 11 (see Fig. 1) obtained using the conventional and proposed methods. The amplitude of excitation current i_ex(t) was set to 30 A, and the MNP sample was placed at z = −50 mm. Fig. 7(a) shows that the peak of the signal is masked by noise, indicating a strong third harmonic in the excitation field that distorts the signal acquired from the MNP sample. The third harmonic in the excitation current degrades the map despite the temperature of the excitation coil being stabilized and the amplitude of the current being controlled to be constant. In contrast, Fig. 7(b) shows a clear signal from the MNP sample by applying the proposed method. These results indicate that the proposed method successfully mitigates third-harmonic noise while increasing the sensitivity to the third harmonic signal generated by the MNP sample. Moreover, a strong magnetic field can be generated with high power efficiency to obtain the magnetic signals of MNPs at low concentrations.

To generate high magnetic fields with high power efficiency for MNT, we apply a square-wave VSI for magnetic field excitation. In addition, to eliminate the third harmonic component in the excitation field generated by the square wave, we propose a method for generating the waveform by controlling the switching phase of the VSI transistors. Experimental results show that the third harmonic field is reduced compared with that obtained using the conventional method. In addition, the distribution of the third-harmonic signal from the MNPs is clearly acquired at a depth of 50 mm using the square-wave voltage generating excitation current of 30 A and the proposed method for harmonic suppression.

This study was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI (Grant Number JP21H01342).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.