INTRODUCTION In recent years, imaging of magnetic nanoparticles (MNPs) has attracted attention as a new diagnostic imaging technique for the imaging of certain targets, such as cancer cells [1]. We previously proposed an MNP imaging method, “magnetic nanoparticle tomography” (MNT), that uses multiple magnetic sensors [2], [3]. In the previous study, an inverse problem analysis was performed to estimate the position of MNPs using the non-negative least squares method (NNLS), which is often used for magnetic particle imaging (MPI). The NNLS method achieves high sensitivity and spatial resolution. However, due to the existence of measurement noise and high sensitivity of NNLS, some MNPs are incorrectly estimated, that is, some artefacts appear. In this study, we apply the minimum variance spatial filter (MV-SF), which is often used in magnetoencephalography (MEG) inverse problem analysis [4], to reduce the artefacts. METHODS The experimental setup is presented in Fig. 1. The Resovist MNP sample was arranged in a sinusoidal magnetic field, which was generated using an excitation coil. The third harmonic magnetic field from MNPs was detected using 16 detection coils. To improve the sensitivity, a cancelation circuit for the fundamental magnetic field was employed. The two-dimensional concentration map of the MNP sample was subsequently obtained by the application of the MV-SF. The distance between the MNP sample and the imaging system (excitation coil and detection coils) was set from 25 mm to 40 mm at intervals of 5 mm. We used two samples with different concentrations of 100 µg-Fe and 500 µg-Fe and estimated the positions for each of them. RESULTS The result of the reconstructed map when the MNP sample was set at are shown in Fig. 2. The white circle in the figure represents the actual sample position. Fig. 2 (a) depicts the result for a sample containing 500 µg-Fe. This result reveals that a sharp signal peak position is observed in the vicinity of the sample position. Fig. 2 (b) exhibits the result for a sample containing 100 µg-Fe. This result indicates that the error between a sharp signal peak position and the actual sample position is within 10 mm. No artefacts appear in both results, contrary to the results using NNLS [3]. From these results, we can conclude that MV-SF is useful for reducing the artefact and estimating the positions of MNPs in magnetic nanoparticle tomography. ACKNOWLEDGMENTS This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Young Scientists [grant number JP19K14996], and by a research grant from the Mazda Foundation.

**References:**

[1] T. Knopp and T. M. Buzug, “Magnetic Particle Imaging—An Introduction to Imaging Principles and Scanner Instrumentation,” Springer, 2012. [2] T. Sasayama, T. Yoshida, K. Enpuku, “Two-Dimensional Magnetic Nanoparticle Imaging Using Multiple Magnetic Sensors Based on Amplitude Modulation,” Journal of Magnetism and Magnetic Materials, Vol. 505, 2020, Art. no. 166765. [3]T. Sasayama, N. Okamura, and T. Yoshida, “Sensitivity Improvement of Magnetic Nanoparticle Imaging by Compensation with Digital-to-Analog Converter,” IEEE Trans. Magn. In press. DOI: 10.1109/TMAG.2020.3014375. [4] K. Sekihara and S. S. Nagarajan, “Adaptive Spatial Filters for Electromagnetic Brain Imaging,” New York, USA: Springer-Verlag, 2008.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d77d396ce684c3b306bcd9bb12e3471f.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/c12c936808039c93bb5834187a35adca.jpg)

 Inverse Problem Analysis in Magnetic Nanoparticle Tomography with Minimum Variance Spatial Filter

The imaging of magnetic nanoparticle (MNP) distributions is a promising biomedical imaging technique for detecting cancers [1]. A method is magnetic nanoparticle tomography (MNT), in which multiple magnetic sensors are used to detect the harmonic signal of MNPs [2] [3]. In our previous study [2] [3], a linear amplifier power supply with low power efficiency was used to generate the excitation magnetic field. In this study, a square-wave inverter was alternatively used to provide high efficiency. However, the third harmonic excitation field was generated by the general square-wave inverter excitation, degrading the imaging performance. Therefore, we developed a method to suppress the third harmonic by shifting the switching phase of the inverter. The experimental setup is shown in Fig. 1. A full-bridge inverter was used to generate a square excitation voltage. Generally, a square-wave voltage was generated by shifting the switching phase of the left- and right-arms by 180°. The square voltage generated using this method contained the third harmonic. We developed a method to suppress the third harmonic by shifting the switching phase by 120°. In this case, the third harmonic does not appear theoretically. The Resovist MNP sample (500 mg-Fe / 150 mg) was arranged and magnetized by an alternating-current magnetic field in the Z-axis using an excitation coil. The sample moved on the x-y plane, and the third harmonic signal of the MNPs was obtained using 16 detection coils. The distance between the excitation coil and the sample was set to 35 mm. Figs. 2(a) and (b) show the third harmonic signal distribution from MNPs using 180° and 120° shifts, respectively, detected by a detection coil. The signal from the MNPs was masked by the excitation field noise (Fig. 2(a)). In contrast, the peak and trough were visible. The results show that the proposed method increases the feasibility of MNT using a square wave inverter excitation. This study was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI (Grant Number JP21H01342).

![](https://assets.underline.io/uploads/markdown_image/1/image/777fa0726302b15db535960bf43377e8.jpg)

Fig.1. Experimental setup

![](https://assets.underline.io/uploads/markdown_image/1/image/885c75975b872192e473feafc18347b4.jpg)

Fig. 2. Third harmonic signal distributions of MNPs using (a) 180° and (b) 120° shifts (The cross mark indicates the position of a detection coil.)

Square-Wave Inverter Excitation for Magnetic Nanoparticle Tomography

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Inverse Problem Analysis in Magnetic Nanoparticle Tomography with Minimum Variance Spatial Filter

Square-Wave Inverter Excitation for Magnetic Nanoparticle Tomography

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