Evaluation of magnetic nanoparticle samples made from biocompatible ferucarbotran by time-correlation magnetic particle imaging reconstruction method

In this study, four types of samples (including ferucarbotran), as listed in Table 1, with ferucarbotran as the base material and adjusted particle diameters were used. These samples were respectively prepared by magnetic separation, centrifugal separation, and gel filtration. The Fe concentration of each sample as well as the Resovist sample was adjusted to 28 [mg/mL]. The average diameter including the coating layer (Da) and the particle size distribution of the average diameter including the coating layer (Dv) were evaluated using a photon correlation spectrometer, the susceptibility was measured using the magnetic balance method, and the T ₂ relaxation time was evaluated using 0.47 [T] NMR equipment. The polydispersity index (PI) was evaluated using the light scattering method. A vibrating sample magnetometer (VSM) is commonly used for evaluating the magnetization properties; however, in this case, these properties were evaluated using our MPI prototype because the detection sensitivity in MPI was also evaluated. Each sample was sealed hermetically in 0.7 [cc] cylindrical containers (∅5 [mm], approximately 12 [mm] in length) made from acrylics, and a solenoid coil of 19 [mm] diameter and with 350 turns was arranged as a receiver coil on the outer circumference (Figure 2). They were installed centered on the gap (50 [mm]) of a customized Maxwell pair coil (Toyojiki Industry Co., Ltd., Niiza, Japan) with an iron core, 180 [mm] diameter, and 285 turns for each coil. An alternative magnetic field with an amplitude of approximately 65 [mT] was generated at the center of those coils by applying an alternative current with an amplitude of 12.0 [A] and frequency of 33.0 [Hz] to each coil in the same direction.

To distinguish between the magnetization components (harmonics) generated from an MNP and the primary magnetic field components applied from the outside, the induced EMF to a coil without a sample was observed previously, and it was defined as the raw flux density applied to an MNP. Then, an induced EMF was generated when an MNP was arranged, and the actual induced EMF generated from the MNP was determined from the difference between this observed signal and the above-described raw flux density. In this case, the absolute value of flux density was corrected using a gauss meter (Model 460; Lakeshore Cryotronics Inc., OH, USA).

The average particle diameter of each sample was computed by approximating the magnetization curve obtained in the abovementioned experiment with a Langevin function.

A gradient magnetic field intensity of 1.5 [T/m] at the center of a Maxwell pair coil and an alternating magnetic field intensity of 32.0 [mT] were used. The FOV was set as 40 [mm] × 40 [mm], and the matrix size was set as 21 × 21. The system function was analytically computed in each matrix point of this FOV based on the Langevin function approximated using the particle diameter of each MNP as evaluated by the abovementioned procedure.

Then, based on equations (1), (2) and (3) and Figure 1, image reconstruction was performed for the signal series that connected the induced EMF observed at the FFP scanned by each matrix point.

Both an alternative magnetic field and an FFP were generated using the abovementioned one-axis Maxwell pair coil. The coil current was supplied from a bipolar power supply (BP30-30; Heiwa Electric Co., Ltd., Kashiwa, Japan) in constant current mode, and the current wave for scanning the FFP was controlled by a function generator (AFG3252; Tektronix, Inc., OR, USA). After the induced EMF was detected using the receiver coil (diameter 19 [mm], 350 turns) and passed through the programmable filter (3628, NF Corporation, Yokohama, Japan), it was supplied to a 14-bit AD converter (M2i4031; Spectrum Systementwicklung Microelectronic GmbH, Grosshansdorf, Germany). The detected signal was sampled with a sampling frequency of 20 [kHz] and was sent to a personal computer (dc7800 MT/CT; Hewlett–Packard Co., CA, USA).

As a result of arranging each abovementioned sample at the center of the gap of a Maxwell pair coil and applying the alternative current with an amplitude of 6.0 [A] and frequency of 39.0 [Hz] in the same direction, the MNPs in each sample were subjected to an alternative magnetic field of approximately 30 [mT]. Under such device conditions, a gradient magnetic field of 1.9 [T/m] was generated by applying an offset current of 12.0 [A] simultaneously to the opposite direction of each coil, and an FFP was formed at the center of the Maxwell pair coil.

In a preliminary experiment, the electric current required to move the FFP by a unit length (this corresponds to the spatial resolution) was evaluated; based on this, the scanning of the FFP was controlled by the function generator. In addition, a ±20-mm region from the Maxwell pair coil’s center was set as the FOV, and the matrix that divides the inside of this FOV into 21 points was made into each measuring point (FFP).

To detect only the induced EMF generated from an MNP in consideration of the frequency purity of the alternative magnetic field due to the imperfection of the power supply and the coil, difference processing with the induced EMF and without a sample was carried out.

The induced EMF from the samples made with ferucarbotran as the base material to the external alternative magnetic field and the magnetization response obtained from the integration operation of EMF are shown in Figure 3 (in what follows, only the results of sample 1 (ferucarbotran) and sample 3, which show the characteristic tendency, were displayed.). In addition, the average particle diameter of each sample was evaluated by comparing the observed magnetization properties with the magnetization curve of the MNP as indicated by Langevin’s approximate expression (Figure 4). These magnetization curves were normalized by the maximum magnetization of each case. The results are summarized in Table 1.

It was estimated that the average particle diameter D of sample 1 (ferucarbotran), which has been clinically approved, was 15 [nm]. That of sample 3 was 20 [nm], which is the largest among all samples, and it was shown that sample 3 is the most suitable because a sample with large particle diameter is advantageous for MPI. Here, the difference between the obtained magnetization properties and the approximated curve reflected the variation in the particle size distribution of the MNPs in a sample, and it was suggested that the particle diameter of sample 3 was adjusted satisfactorily. This result was also supported by the evaluation results obtained by PI and D _v , shown in Table 1. Because the particle size distribution follows a logarithmic normal distribution [21], it was considered important to adjust the particle diameter in a sample uniformly in order to improve the image resolution in MPI. Moreover, the induced EMF detected from sample 3 was approximately 3 times that from ferucarbotran, indicating that sample 3 also contributes greatly to the improvement of SNR. This is based on the increase in the saturation magnetization of the MNP accompanying the increase in the particle diameter [15].

From the physical properties obtained by this evaluation, as listed in Table 1, it was confirmed that the particle diameter of MNPs was also related to the susceptibility and T ₂ relaxation time.

Next, the image reconstruction results of the numerical simulation based on the characteristics of sample 1 (ferucarbotran) and sample 3, which were chosen from among all samples as discussed above, are described. The images reconstructed by the fundamental image reconstruction method based on an imaging principle (an alternative magnetic field was applied at each FFP that was scanned for every encoded position [7]) and our proposed time-correlation method for a sample arranged at the center pixel of the FOV are shown in Figure 5. In addition, the profiles at z = 0 of these reconstruction images are shown in Figure 6. It was confirmed that the image artifact observed in the upper and lower sides of the actual MNP by the fundamental image reconstruction method was suppressed by the proposed method. However, the image resolution of the proposed method (~12 mm) was slightly degraded compared to that of the fundamental method (~8 mm) using the FWHM for sample 1. Then, it was shown that the image blurring increased. This is because theoretically, the distribution of correlation between the observed signal and the system function at every FFP position (Figure 1) was given as the image intensity with nearly two times the FWHM of the system function [22]. The PSF of this image reconstruction method was expected as an autocorrelation distribution of the system function, and it was superimposed in Figure 6 for MNPs of each particle diameter. Therefore, it is possible to newly propose the following iterative estimation of the distribution of MNPs in order to improve the image resolution [13].

Then, the candidate of the processing position is moved to the next FFP and the abovementioned process is repeated until the residual of the subtraction signal at every FFP becomes small. It is considered that a deconvolution with a system function can be carried out equivalently by such processing; therefore, the image blurring can be reduced effectively without inverse matrix operations.

An evaluation of the profile at z = 0 (Figure 6) showed that the spatial resolution of sample 3 was approximately 1.3 times better than that of sample 1. This corresponded to the fact that the spatial resolution obtained by a gradient magnetic field strength of 2.5 [T/m] for sample 1 was achieved by a gradient magnetic field strength of approximately 1.5 [T/m] for sample 3 (Figure 7). In other words, it was shown that the dependence on hardware requirements was reduced by 0.6 times under such conditions and that the spatial resolution could be improved by simply adjusting the particle diameter.

The waveform of the induced EMF obtained by scanning the FFP, the magnetization response calculated from the integration of the EMF, and the Fourier transform of this magnetization response are shown in Figure 8. Here, when the center coordinate of the FOV was set to 0, only the wave obtained by scanning the FFP at −20 [mm], 0 [mm], and 20 [mm] along the z-axis was indicated in the figure (this corresponds to the sign L20, C, and R20, respectively.). It was confirmed that the difference of the induced EMF’s waveform in an experiment appeared depending on the position of the FFP. In other words, because it would reflect that the position of the MNP was indistinguishable when the correlation with an observed signal was evaluated with a system function, the validity of our proposed method based on time-correlation information was also confirmed by experimental data. With regard to sample 1 (ferucarbotran) and sample 3, the one-dimensional images obtained using the fundamental image reconstruction method and the proposed method are shown in Figure 9. In these reconstructed images, although the precise system function should ideally be measured from the signal observed when the MNPs are arranged in a shape like a delta function at each analyzed point in the reconstructed image, the analytically calculated system function corresponding to each particle diameter at every image matrix point was used. This is because considerable time is generally required for the measurement of a system function, and our system’s operation might become unstable over such a long time. It was found that sample 3 afforded an image resolution superior to that of sample 1 through both the experimental results as well as the numerical simulation.