Single-Sided Magnetic Particle Imaging Device with Field-Free-Line Geometry for in-vivo Imaging Applications

Abstract

Magnetic Particle Imaging (MPI) has shown great promise to surpass existing in vivo imaging modalities in some clinical applications. However, one of the challenges to MPI being translated into clinical practice has been the ability to scale up the selection field coils to surround a human body while being able to generate and drive a sufficiently strong magnetic field gradient. These requirements impose safety concerns as well as prohibitively high-power consumption in devices with large cylindrical volume. Therefore, we consider an alternative approach such as a single-sided topology, in which all the hardware is located on one side of the imaging volume accommodating larger subjects. Moreover, different from the previously implemented field-free point single-sided scanners, we realized a field-free line geometry providing, in principle, factor of ten higher signal and benefiting from a more robust back-projection image reconstruction technique. In this work, we present and characterize a first prototype of a single-sided MPI device with field-free-line geometry suited for in-vivo imaging of small animals as well as regions of interest in humans.

I. Introduction

Magnetic Particle Imaging (MPI) is a new biomedical imaging modality designed to image the distribution of superparamagnetic iron oxide nanoparticles (SPIOn) with high temporal and spatial resolutions [1]. An MPI scanner typically consists of three types of coils based on its purpose: (1) to generate a static magnetic gradient selection field, (2) to excite the tracer consisting of iron-oxide nanoparticles, (3) to receive the nonlinear magnetization response from the nanoparticles. The selection field has to have a field-free region: a field-free point (FFP) [2] or a field-free line (FFL) [3]. Scanners with the FFP geometries typically consist of a fewer number of coils to generate the required field configuration and do not require physical rotation of the hardware or a subject. However, the FFL geometry provides signals that are factor of ten higher and benefits from a more robust image reconstruction technique similar to CT image reconstruction [3]. Thus, FFL scanners may be beneficial for the future clinical applications.

The main challenge of MPI to be used on humans is scaling up all the coils to provide sufficient imaging volume. Alternatively, a small scanner with single-sided hardware configuration could provide a small imaging volume for the local imaging of specific body parts. A single-sided MPI scanner [4], [5] could be an essential technology to translate the MPI modality into the human domain. This will enable diagnosis of specific pathologies, such as cancer [6] and allow safer biopsy of sentinel lymph node [7], [8].

The single-sided device has all the hardware on one side of the imaging volume [4]; therefore, such a device can be used equally well on small animals and humans for multidimensional diagnostic imaging and as a magnetic particle spectrometer (MPS) [9]. Recent developments in MPI include 2D and 3D imaging utilizing an FFP single-sided device [10], [11]. To benefit from the FFL geometry, we previously proposed a single-sided all electromagnet [12] and a hybrid permanent-electromagnet [13] designs for coil configurations.

Here, we present a first prototype of the asymmetric MPI scanner built with fewer number of coils and capable of spatial encoding a 2D volume of interest. This single-sided scanner is capable of generating 1.3 T/m magnetic field gradient providing in-plane image at a penetration depth of 2–3 cm, which is sufficient for imaging small animals and future translation into clinical applications.

II. Material and Methods

This section describes the hardware realization of the single-sided FFL device.

A. Field generator coils

The theory of the FFL formation in such a single-sided device is described in [12]. Different from the original single-sided proposal consisting of five coils, in this prototype device, we incorporated three elongated electromagnetic coils, which is the minimum number of coils required to encode the image. Figure 1(a) shows the complete coil structure in the enclosure with the embedded temperature and water pressure sensors. The coil system is designed to hold current densities of up to 10 A/mm² and incorporates water cooling to address power dissipation both due to coil losses and eddy currents in the coil structure. The coil assembly in the enclosure was manufactured by Resonance Research, Inc. (Billerica, MA).

Fig. 1.

(a) Single-sided FFL device assembly; (b) selection-drive structure model composed of three coils: selection-shift and drive coils on top and in the bottom respectively; (c) the coils’ assembly showing the top set of the coils.

The overall device’s dimensions are 40 cm long, 18 cm wide, and 12 cm high. The coil’s implementation is shown in Fig. 1(c). Each of the top electromagnetic coils is 30 cm long with a 5.5:1 aspect ratio and consists of 8 pancake-like elements with N = 26 windings of rectangular-shaped copper wire of 1 mm cross-section, which are connected in parallel to the corresponding terminals of the coils. The bottom coil (see Fig. 1(b)) consists of 6 pancake-like elements with the same dimensions as the top coils. Each of the pancake elements has transverse epoxy stripes in the bottom creating multiple slits through the conductor’s volume for water cooling. The measured electric properties of the top and bottom coils are: dc resistances of 124 mOhm and 119 mOhm and inductances of 396 μH and 377 μH at 1 kHz, respectively.

The coil’s model diagram is shown in Fig. 1(b). The top two coils are used to create a stationary selection gradient magnetic field in the form of a FFL, as well as to shift the FFL along the x-axis by altering the relative current in the coils. These coils are separated by 11 mm from each other and located 4 mm from the surface of the device. The bottom coil, located in the middle of the device 5 mm deep under the top coils, is primarily used to generate the drive field for the excitation of SPIOn as well as to shift the FFL along z-axis.

The magnetic field measurements are performed using Magsys HGM09s gaussmeter (Germany) with the transverse hall probe mounted on a custom-made 3D robot. For the respective field mapping we applied dc current of <10 A to the coils from the regulated current supplies. In addition, we tested the device performance with the dc current of up to 40 A and utilized an active cooling with de-ionized water. The maximum magnetic fields at the surface in the iso-plane are measured to be 0.62 mT/A from the top coils and 0.2 mT/A from the bottom coil.

B. Signal chain

The MPI scanner’s operating signal chain that we utilized for the experimental validation tests is shown in Fig. 2. The main purpose of the MPI signal chain is to generate low noise ac magnetic field by the drive coil to excite an SPIOn sample on the surface of the scanner and simultaneously measure the nonlinear magnetization response of the SPIOn by detecting the signal at higher harmonics of the excitation frequency.

Fig. 2.

Signal chain block diagram: DAC - digital-to-analogue converter, PA - power amplifier, LPF - low pass filter with 3rd harmonic tuning, BSF - band stop filter, LNA - low noise amplifier, ADC - analog-to-digital converter.

In our experimental SPIOn detection validation tests the excitation waveform at f₁ = 23 kHz was generated by the National Instrument DAC (NI USB-6363, National Instruments Corp.) with MATLAB (MathWorks) GUI console. The AC drive current is provided by AE Techron 7224 power amplifier (Elkhart, IN). The small magnetization response from the SPIOn is overlapped in time with the high-power excitation field. Thus, it is important to reject the drive frequency component at the receiving chain and ensure the drive waveform is purely sinusoidal. For the latter task we implemented a high-power 4^th order low-pass filter (LPF) [14], which together with the drive coil resonates at 23 kHz and attenuates 3^rd harmonic up to 50 dB with respect to the transmission peak.

In the preliminary magnetic particle detection experiment, a point-source bulb phantom of 18 μL undiluted (5.5 mg/mL) VivoTrax SPIOn (Magnetic Insight, Alameda, CA) with the single core size of 6 nm was used corresponding to 100 μg of iron. To detect the signal from the SPIOn we utilized a surface receive coil (Rx). The Rx coil is wound with two layers of Litz wire (22 AWG, 40/38) with 15 mm inner and 45 mm outer diameters and has 30 turns. Such coil has in-plane sensitivity range of 30 mm in diameter with the plateau reached at about 10 mm height. In order to reject the direct feedthrough of the main and high order components of the field from the drive chain the Rx coil is shifted by 34 mm off axis from the drive coil and centered at B_z,drive=0. In addition, the Rx coil is connected to a band-stop filter (BSP). The 3^rd order Butterworth BSP was designed to reject the drive frequency with up to 50 dB attenuation and tuned with L_Rx = 29 μH inductance to transmit the signal at the 3^rd harmonic f₃ = 69 kHz. After the BSF the signal is amplified by a low-noise preamplifier (LNP), Stanford Research Systems SR560 (Sunnyvale, CA), with $4nV/\sqrt{Hz}$ input noise performance. The time series MPI signal from the receive chain is digitized by the DAC and recorded through MATLAB GUI. Note, the selection gradient, which is normally required for the image encoding, was not applied during the SPIOn detection sensitivity studies. In addition, the receive chain described here detects only the 3^rd harmonic of the MPI signal, which simplifies the filtering requirements, however, limiting the signal power by not utilizing the higher harmonics.

III. Theory

The static selection magnetic field is created by a pair of the top selection coils with currents I₁ = I₂ as shown in Fig. 1(b). The magnetic field in the vicinity of the FFL can be expressed as

$${\mathbf{\text{B}}}^s(x,y,z)=\mathbf{\text{Gr}}=\left[\begin{array}{ccc}{G}_{xx}& 0& 0\\ 0& 0& 0\\ 0& 0& G_{zz}\end{array}\right]\left[\begin{array}{l}x\hfill \\ y\hfill \\ z\hfill \end{array}\right].$$ (1)

Here, G_xx = −G_zz = G is the gradient of the magnetic field so the FFL is formed along y-axis and the selection field is equivalent to a quadrupole field: ${\mathbf{\text{B}}}^s(x,z)=Gx\widehat{\mathbf{\text{x}}}-Gz\widehat{\mathbf{\text{z}}}$.

The theory of formation of the FFL from the pair of selection coils with thin infinite conductors is described in [12]. That work provides an analytical expression for the magnetic field in the symmetry x=0 plane, height of the FFL, and the maximum gradient of the magnetic field.

The field from the bottom drive coil is expressed as

$${\mathbf{\text{B}}}^d(x,y,z,t)=B_z^d(x,z,t)\widehat{\mathbf{\text{z}}}+{\mathbf{\text{B}}}_{\mathit{\text{offset}}}(x,z),$$ (2)

where $B_z^d(x,z,t)=B^d(x,z)\text{ sin}\left(2\pi f_{1}t\right)$ is the excitation ac field and B_offset is the offset dc field that can alter the static height of the FFL. Adapting the theory in [12] we can obtain an expression for the vertical shift h_FFL(α) of the FFL for I_1,2 = I due to the offset field B_offset:

$$h_{FFL}(\alpha )=sb\sqrt{\frac{1-1/b-\alpha }{b-1+\alpha }},$$ (3)

where α = ηI_offset/I is the scaled current ratio between the drive ηI_offset and the selection coils I; s is the size of the coil’s core; b is the geometrical factor representing the ratio between the distances of the center of each coil’s conductor from the iso-center. So the static height is given by the coil’s geometry: $h_{FFL}(0)=s\sqrt{b}$.

Thus the total magnetic field generated by all the coils is given by

$$\mathbf{\text{B}}(x,y,z,t)={\mathbf{\text{B}}}^s(x,z)+{\mathbf{\text{B}}}_{\mathit{\text{offset}}}(x,z)+B_z^d(x,z,t)\widehat{\mathbf{\text{z}}}.$$ (4)

For the dynamical operation, where the coordinate r_FFL of the FFL has to be shifted along x-axis, the superposition of the fields from the selection coils with I₁ ≠ I₂ forms the FFL at x ≠ 0 and in general at an altered height. The trajectory r_FFL in zx-plane represents an arc and needs a correction for flattening by applying I_offset according to Eq.3.

In MPI the response to the total magnetic field B(x, y, z, t) from the distribution of SPIOn c(x, y, z) is described by the nonlinear magnetization function according to the Langevin model:

$$\mathbf{\text{M}}(x,y,z,t)=c(x,y,z)m_s\mathcal{L}(\beta \Vert \mathbf{\text{B}}(x,y,z,t)\Vert ))\frac{\mathbf{\text{B}}}{\Vert \mathbf{\text{B}}\Vert },$$ (5)

where $\mathcal{L}$ is the Langevin function; β = m_s/k_BT with m_s is the saturation magnetic moment of the SPIOn, T is temperature, and k_B is Boltzmann’s constant.

The oscillating magnetization induces a voltage in the receive coil, which according to the reciprocity principle can be written as

$$u(t)=-{\int }_V{\mathbf{\text{B}}}_1(x,y,z)\frac{\partial }{\partial t}\mathbf{\text{M}}(x,y,z,t)dxdydz,$$ (6)

where B₁(x, y, z) is the receive coil’s sensitivity vector profile given by the magnetic field in the Rx coil generated by the unit current. The voltage signal is expanded in series with harmonics of f₁ and the 3^rd harmonic amplitude is detected.

IV. Results

A. Simulations

First, the coil structure design was verified by carrying out the magnetic field simulations using the boundary Integral Methods of Radia package [15] interfaced with Mathematica (Wolfram).

The simulated magnetic field from the selection coils for the reference current I_1,2 = I = 5 A, is shown in Fig. 3, where the |B| field contour plots in zy-, xy- and zx- planes are shown in Fig. 3(a–c), respectively. According to the simulations the static FFL is formed in the iso-center x = 0 between two selection coils at height z = 17 mm above the surface of the scanner. The contour plots show that the FFL is sufficiently straight over 4 cm of length along the y direction. From the simulated magnetic field we obtained the magnetic field gradient to be G = 13 mT/m/A so for the projected current I = 100 A it becomes G = 1.3 T/m.

Fig. 3.

The magnetic field simulations (a-c) and measurements (d-f): (a,d) zy-, (b,e) xy- and (c,f) zx- planes showing the FFL formed at (x, z) = (0, 17) mm. Here the currents are I₁ = I₂ = 5 A.

B. Experimental measurements

To validate the device’s performance we carried out the experimental measurements of the field in various operating regimes.

First, we compared the fields in a static regime, where I_1,2 = I = 5 A. The corresponding magnetic field from the selection coils is shown in Fig. 3, where the |B| field contour plots in zy-, xy- and zx- planes are shown in Fig. 3(d–f), respectively. Overall, the measured fields match well the simulations (Fig. 3(a–c)) validating the design. Some discrepancies in the scale of the field may be attributed to the coil’s modeling approximation. The measured static height of the FFL above the device surface is h₀ = 17 mm ± 0.5 mm. From the measured magnetic field we also obtained the magnetic field gradient to be G = 12.5 mT/m/A, which for I = 100 A gives G = 1.25 T/m.

C. Spatial encoding

In MPI, image encoding is provided by deterministically shifting the coordinates of the FFL r_FFL(t) in a plane. To investigate such dynamical performance of the device we looked into the trajectories of the FFL along z and x directions. The corresponding trajectories are presented in Fig. 4.

Fig. 4.

Measured trajectories r_FFL: (a) height shift h_FFL vs. drive offset current I_offset/I_avg; (b) FFL transverse shift x_FFL for I_offset = 0; (c) offset current I_drive/I_avg as a function of shift current (I₁ − I₂)/I_avg required to flatten transverse trajectory; (d) flattened x_FFL trajectory of (b) at fixed height h = 12.5 mm with the applied I_offset(x) from (c). Here, the solid lines represent the corresponding polynomial fits, dashed line is the theory curve, the error bars of ±0.5 mm represent the spatial dimensions of the magnetic probe.

The vertical trajectory h_FFL(x = 0) can be dynamically controlled by adding the offset current I_offset to the drive coil as described by Eq.3. Figure 4(a) shows the corresponding height change per normalized current I_offset/I_avg, where I_avg = (I₁ + I₂)/2. Thus the linear fit provides the vertical shift of 10.7 mm per unit of the normalized I_offset. The theory curve from Eq.3 provides the analytical trajectory with the geometrical factors: s = 10 mm, b = 2.8, η = 0.6, which give the static height of h₀ = 16.7 mm. The FFL height adjustment is important for the depth encoding of the imaging volume.

In order to provide an image encoding in the plane parallel to the surface of the scanner the device should be capable of shifting the FFL along x direction. Overlapping sequential transverse shift with the subject rotation around z-axis of 0°−180° would enable implementation of a backprojection image reconstruction algorithm in a similar fashion to computer tomography technique [16].

In these studies, the transverse shift was realized by manually altering the currents in the selection coils ΔI = I₁ – I₂ = 0 − 7.5 A. The resulted measured transverse trajectory x_FFL(z) is shown in Fig. 4(b), where the fit gives the parabolic trajectory −Ax² + h₀ with A – fitting parameter. Since the reconstruction technique relies on a flat FFL trajectory in xy-plane we devised a correction algorithm. Using the linear and parabolic fits from Fig. 4(a) and (b), respectively, we obtained the relation for the normalized offset current in the drive coil as a function of ΔI/I_avg as shown by the fit in Fig. 4(c) to flatten the transverse trajectory. The corrected trajectory of the FFL with the linear fit x_FFL(z = h) is shown in Fig. 4(d). Here, we chose to flatten the trajectory by lowering the height of the middle points bringing the operating imaging plane to h = 12.5 mm. The results imply that our prototype is capable of providing a 4 cm × 4 cm field of view in xy-plane. By supplying additional constant dc bias current to the drive coil the operating plane can be altered according to Fig. 4(a) thus providing a volume encoding.

D. SPIOn detection experiment

The experimental arrangements showing the Rx coil and the sample placed on top of the surface coil and the experimental data are shown in Fig. 5. The phantom was placed in a holder in the iso-axis at the height of 1 cm above the surface (see Fig. 5). The drive coil was driven at a carrier frequency of f₀ = 23 kHz and a current amplitude of I = 14.2 A providing a 2.8 mT drive field, which was pulsed with 1.2% duty cycle. The time series 3^rd harmonic data with and without the sample show SNR=30, implying the achieved sensitivity of the device at these operating parameters of 10 μg of iron.

Fig. 5.

Experimental setup and the 3^rd harmonic signal from the undiluted point sample of VivoTrax with 100 μg iron content showing SNR=30.

V. Discussion

The preliminary data suggest that the described single-sided device is capable of encoding a 2D FOV. In order to perform imaging in 2D, we will implement xy-plane electronically controlled shifting and height adjustment of the FFL and combine it with the mechanical rotation of the imaging subject. In principle, the trajectory z_FFL(x(t)) can be realized in time at the rate of ω according to the expressions:

$$I_1=I_0(1+\epsilon \text{ cos}(\omega t)),I_2=I_0(1-\epsilon \text{ cos}(\omega t)),$$

where I₀ is the maximum current amplitude that defines the gradient of the field, and ε is a modulation factor, that defines the spatial encoding range covered by the FFL translation. While the next-generation scanner will have mechanically rotated coils, for simplicity, in this prototype we will incorporate a subject turntable with a diameter of D = 18 cm to overlap with the surface of the scanner and allow placement of phantoms and rodents. The rotation of the turntable will be governed by a software-controlled stepper motor. For in-plane image encoding, we will utilize a filtered back-projection reconstruction technique. For example, to image a 4 cm-size 2D phantom with up to 2 mm resolution, 41 shifts of FFL at each rotation angle with the total of 72 projections will be acquired for 0°−180° total rotation with a rotation rate of up to ~ 100 rpm, which gives the estimated image acquisition time of ~ 10 s.

Our demonstrator device is capable of reaching clinically relevant sensitivities required for the applications ranged from angiography to cancer detection. For example, to estimate the clinically relevant sensitivity, consider the average human injected dose (ID) of ~ 400 mg (Fe), the lower bound of a passive uptake of the SPIOn by the tumor of ~ 1 (%ID)/g [17], then, for the average tumor mass of 1.2 mg per 1 mm³ voxel [18], the targeted sensitivity is 4.8 μg (Fe). With the additional modifications in the signal chain and incorporation of the surface gradiometer Rx coils, we expect to reach the the targeted sensitivity.

VI. Conclusions

We presented a first prototype of a single-sided MPI scanner with the FFL geometry that consists of all the three coils in a unilateral configuration. The measurements of the magnetic fields agree well with the simulations. We further validated our MPI device by demonstrating magnetic particle signal detection using a point-source phantom. Further work with this prototype device aims to boost the detection sensitivity and incorporate rotational subject platform to allow carrying out in-vivo studies with rodents. Future work includes developing a fully functional multidimensional scanner on a rotational platform based on this single-sided geometry, which will serve as a clinical prototype MPI scanner.