A scanner for imaging magnetic particles in planar samples was developed using the planar frequency mixing magnetic detection technique. The magnetic intermodulation product response from the nonlinear nonhysteretic magnetization of the particles is recorded upon a two-frequency excitation. It can be used to take 2D images of thin biological samples.
The setup of a planar Frequency Mixing Magnetic Detection (p-FMMD) scanner for performing Magnetic Particles Imaging (MPI) of flat samples is presented. It consists of two magnetic measurement heads on both sides of the sample mounted on the legs of a u-shaped support. The sample is locally exposed to a magnetic excitation field consisting of two distinct frequencies, a stronger component at about 77 kHz and a weaker field at 61 Hz. The nonlinear magnetization characteristics of superparamagnetic particles give rise to the generation of intermodulation products. A selected sum-frequency component of the high and low frequency magnetic field incident on the magnetically nonlinear particles is recorded by a demodulation electronics. In contrast to a conventional MPI scanner, p-FMMD does not require the application of a strong magnetic field to the whole sample because mixing of the two frequencies occurs locally. Thus, the lateral dimensions of the sample are just limited by the scanning range and the supports. However, the sample height determines the spatial resolution. In the current setup it is limited to 2 mm. As examples, we present two 20 mm × 25 mm p-FMMD images acquired from samples with 1 µm diameter maghemite particles in silanol matrix and with 50 nm magnetite particles in aminosilane matrix. The results show that the novel MPI scanner can be applied for analysis of thin biological samples and for medical diagnostic purposes.
Magnetic nanoparticles (MNP) have found widespread applications in molecular biology and in medicine, i.e., for manipulation of biomolecules and single cells1, for selectively labeling target entities for detection,2, 3 for chromatin modulation,4 and for mRNA isolation and cancer treatment.5 Due to their superparamagnetic properties, they are especially useful for medical imaging. They can serve, for instance, as contrast agents or tracers for Magnetic Resonance Imaging (MRI) or for susceptibility imaging using Superconducting Quantum Interference Device (SQUID) detectors. 2, 6 The superparamagnetic nanoparticles yield a good contrast to the different tissues of the human body which are dia- or paramagnetic.7 Thus, the particles can conveniently be used to acquire medical images of human body parts with relatively good spatial resolution and sensitivity.8
The Magnetic Particle Imaging (MPI) technique introduced by Gleich and Weizenecker9 makes use of the nonlinearity of the particle's magnetization. At zero or weak magnetic field bias, the response of MNP to an ac excitation of frequency f is strong due to their large susceptibility. In particular, the particle's nonlinear magnetization gives rise to the generation of harmonics n·f, with n = 2, 3, 4 … At high magnetic field bias, the harmonic response becomes weak because the particles are magnetically saturated. In the MPI technique, the sample is completely magnetized except for a field-free line (FFL) or a field-free point (FFP). Only particles situated close to this line or point will contribute to the nonlinear response of the sample. With the movement of a FFP and employment of suitable receiver coils, Gleich and Weizenecker acquired MPI images with a spatial resolution of 1 mm.
In order to obtain information on the spatial distribution of MNP, two methods are usually employed, the mechanical movement of the sensor with respect to the sample, or movement of the FFL/FFP by means of electromagnets.2, 3 In the latter case, image reconstruction techniques like harmonic-space MPI3 or X-space MPI10, 11, 12 are required. The spatial resolution of MPI is determined by the convolution properties of excitation and detection coils as well as by the characteristics of the magnetic field gradient. This allows image reconstruction algorithms to obtain an improved resolution over the native resolution, which is determined by size and distance of the pickup coils as well as by the magnetic field distribution governed by Maxwell's equations.
A MPI scanner is usually comprised of a strong magnet for magnetizing the whole sample, a controllable coil system for steering a FFL or FFP across the sample, a high frequency excitation coil system, and a detection coil system for picking up the nonlinear response from the sample. The FFL/FFP is continuously moved through the sample volume while the harmonic response from this unsaturated sample region is recorded. In order to avoid the problem of fitting the specimen into the scanner, a single-sided MPI scanner has been demonstrated by Gräfe et al.13, however at the expense of reduced performance. Best results are obtained if the sample is surrounded by the magnets and coils. Because the sample has to be fully magnetized except for the FFL/FFP region, the technique requires relatively large and strong magnets with water cooling, leading to a rather bulky and heavy MPI system.
Our approach is based on frequency mixing at the non-linear magnetization curve of superparamagnetic particles.14 When super-paramagnets are exposed to magnetic fields at two distinct frequencies (f1 and f2), sum frequencies representing a linear combination m·f1 + n·f2 (with integer numbers m, n) are generated. It was shown that the appearance of these components is highly specific to the nonlinearity of the magnetization curve of the particles.15 In other words, when the MNP sample is simultaneously exposed to a driving magnetic field at frequency f2 and a probing field at frequency f1, the particles generate a response field at frequency f1 + 2·f2. This sum frequency would not be existent without the magnetically nonlinear sample, therefore the specificity is extremely high. We called this method "frequency mixing magnetic detection" (FMMD). It has been experimentally verified that the technique yields a dynamic range of more than four orders of magnitude in particle concentration.14
In contrast to typical MPI instrumentation, the planar frequency mixing magnetic detection (p-FMMD) approach does not require to magnetize the sample close to saturation because the generation of the sum frequency component f1 + 2·f2 is maximum at zero static bias field.14 Therefore, the need for strong and bulky magnets is alleviated. In fact, the outer dimensions of the measurement head are only 77 mm × 68 mm × 29 mm. For comparison, MPI setups are typically meter-sized.7 The drawback, however, is that the technique is restricted to planar samples with a maximum thickness of 2 mm in the current setup. The sample has to be scanned relatively to the two-sided measurement head. A re-construction allowing for thicker samples is possible, but has to be traded in for a loss of spatial resolution.
Based on this FMMD technique, we present a special type of MPI detector for planar samples, the so-called "planar frequency mixing magnetic detection" (p-FMMD) scanner. The principle has been recently published.17 In this work, we focus on the methodology of the technique and present protocols how to set up such a scanner and how to perform scans. It has been shown that MPI can be applied for medical diagnostic purposes such as cardiovascular or cancer imaging.16, 18, 19 Therefore we believe that the new MPI scanner can be used for a broad range of potential applications, e.g., for measuring magnetic particle distribution in tissue slices.
1. Design a Planar FMMD Measurement Head
Figure 1. Schematic drawing of the p-FMMD set-up. Two measurement heads are electronically connected to each other. The sample is placed in the space between the heads. Detection coils (+) measure the sample signal, counter-wound detection coils (-) serve as reference to cancel out the direct field from the high frequency excitation coils. Amp – preamplifier, x – mixer, LPF – low pass filter, DAQ – data acquisition. Please click here to view a larger version of this figure.
2. Construct the Measurement Head
Figure 2. Technical drawing and photo of p-FMMD head. Cross-sections along a vertical plane (top left) and a horizontal plane (bottom left) are shown as well as a photograph of the opened measurement head before coil winding. 1 – Aluminum support, 2 – coil former for detection coils, 3 – threaded coil former for excitation coils which can be moved up/down by rotation, 4 – sample support plates, 5 – aluminum lids, 6 – sample stopper support, 7 – stopper in x direction, 8 – stopper in y direction. 6 – 8 are removed for scanning. The size of the p-FMMD head is 77 mm × 68 mm × 29 mm. Please click here to view a larger version of this figure.
3. Set up Measurement Electronics
4. Set up 2D Scanner
5. Prepare Sample
6. Perform 2D FMMD Scan
Figure 3. Photo of p-FMMD measurement setup. The sample is affixed with adhesive tape on the plastic carrier moved by the motor stage (left). Then the sample is scanned in the p-FMMD head (right). Please click here to view a larger version of this figure.
Figure 4. Graphical User Interface of the scanning software. The scan parameters are entered here. The measurement is started by pressing the red button.
7. Image Processing
Figure 5a shows the calculated sensitivity distribution of the inner double-differential detection coil as a function of the coordinates x and y in the sample plane. It was calculated in an inverse approach by determining the superposition of the magnetic fields at all points (x, y) in the central plane generated by all four detection coils. In reverse, this determines the detection coil's sensitivity to a magnetic moment at each of these points. The calculation was performed by approximating the coils as long coils of negligible height. Thus, the sensitivity distribution depicted in Figure 5a represents the sensitivity map in the scanning plane, the so-called point spread function (PSF). In a similar fashion, Figure 5b shows the sensitivity as a function of the axial coordinate z and the radial coordinate r (r2 = x2 + y2), thus giving a vertical mapping of the sensitivity in the slit of the measurement head. The origin x = 0 and y = 0 is located exactly in the center of the detection coil. The spacing between the centers of the upper and lower detection coil is 2 mm. The coil parameters are listed in Table 1. Figure 5c shows the result of an experimental scan over the string-type line sample prepared according to protocol 5.2. For comparison, a sensitivity trace was calculated by numerically integrating the point spread function depicted in Figure 5a over a 2 mm wide ideal line. The agreement is good, except that the negative shoulders in the calculated signal are not observed experimentally. In the simulation, these negative parts originate from the negative contributions from the reference coils which are more in the far-field regime than the detection coils next to the sample. We believe the negative contribution is overestimated in simulation because the coils are approximated with negligible height of windings.
Figure 5. Performance of the measurement head. Calculated sensitivity distribution of the measurement head (a) as a function of the planar coordinates x and y for z = 0, (b) as a function of the axial coordinate z and the radial coordinate r. The sensitivity is given relatively to the center between the upper and lower detection coil at x = 0, y = 0 and r = 0. (c) Comparison of measured and simulated sensitivity. Please click here to view a larger version of this figure.
We calculated the physical detection limit of the coil at measurement frequency f1 = 76.56 kHz with respect to magnetic moments at the center of the measurement head. For the calculation, the parameters of the inner coil were taken as listed in Table 1, assuming a filling factor (i.e., the copper fraction in the windings cross section) of KF = 0.5. We obtained a magnetic moment sensitivity of m0/√f = 1.8·10-14 Am2/√Hz. For 1 sec measurement time, this amounts to a resolvable minimum magnetic moment of m0 = 7.3·10-14 Am2. This value is comparable than the detection limit that can be obtained with a standard 8 mm diameter measurement head.14
Figure 6a shows the signal intensity as a function of the concentration of magnetic beads solution. The scanning speed was 1.0 cm/min. The concentration of the paper pellets prepared according to protocol 5.2 was varied from 0.04 to 25.0 mg/ml. The error bars denote the standard deviation of the FMMD measurement. The results showed a strong correlation between the concentration of magnetic beads and the signal from the detector. The coefficient of determination R2 of the linear regression was evaluated as 0.98. Figure 6b shows the measured relationship between the speed of the scanning stage and the signal intensity measured with the 5 mg/ml paper pellet sample according to protocol 5.3. It was found that higher signals can be obtained at lower speed.
Figure 6. Calibration. Normalized calibration curve of (a) the p-FMMD measurement using different concentrations of magnetic beads. As samples, paper pellets with 2.0 mm diameter were prepared using a biopsy punch, soaked in magnetic particle solution of different concentrations (see protocol 5.3). The measurement head passed the paper pellets with different concentrations of MP. The speed of the stage was adjusted to 1.0 mm/sec. (b) Signal intensity as function of the speed of the XY stage for the 5.0 mg/ml paper pellet sample. Please click here to view a larger version of this figure.
Figure 7 shows a photograph of membrane-type samples prepared according to protocol 5.4 and the reconstructed p-FMMD image obtained from it. The picture area as well as the scanning area are both 20 mm × 25 mm. The comparison of the p-FMMD scan with the optical image of the sample clearly demonstrates the feasibility to use the p-FMMD as MPI scanner. However, the p-FMMD scans are somewhat broader than the real objects. This broadening can be mainly attributed to the sensitivity profile of the measurement head. As shown in Figure 5a, the measurement of a magnetic particle distribution is broadened by this distribution even to ±2.0 mm from the center of the measurement heads.
Figure 7. 2D FMMD scan. (a) Photograph of the string type sample. The sample was prepared using a nitrocellulose Membrane soaked with 1 µm diameter maghemite particle solution SiMAG-Silanol see protocol 5.4. (b) Reconstructed MPI image, size 20 mm × 25 mm. The sample is continuously scanned in y direction and consecutively stepped in x direction by 4 mm. Please click here to view a larger version of this figure.
A second sample was prepared, consisting of two microtubes filled with different magnetic particle concentration, as described in protocol 5.5. Figure 8 shows a photograph of the sample and the reconstructed p-FMMD image, both with a size of 20 mm × 25 mm. This example demonstrates that concentrations differing by a factor of 20 can be well imaged with clearly discernible image features.
Figure 8. 2D FMMD scan. (a) Photograph of two microtubes of 10 µl volume with different sample concentrations of fluid MAG-Amine, see protocol 5.5. (b) Reconstructed MPI image, size 20 mm × 25 mm. The sample is continuously scanned in y direction and consecutively stepped in x direction by 4 mm. Please click here to view a larger version of this figure.
Coil dimensions | Windings | Coil below sample | Coil above sample | ||||||
Coil | R1 [mm]a | W [mm]b | H [mm]c | No. of windings | Wire-Ø [mm] | R [Ω]d | L [mH]e | R [Ω]d | L [mH]e |
Measurement | 1.0 | 4.0 | 1.7 | 2 × 600 | 0.08 | 47.67 | 0.95 | 47.66 | 0.95 |
Excitation | 3.8 | 8.5 | 1.0 | 476 | 0.10 | 29.90 | 1.56 | 29.70 | 1.45 |
Driver | 5.0 | 8.5 | 5.0 | 2,000 | 0.12 | 190.75 | 36.90 | 141.28 | 37.90 |
aR1 is the inner radius of the coil. The average radius is R1+H/2, the outer radius is R1+H. | |||||||||
bW is the width of the coil, i.e., the cross section of the windings. | |||||||||
cH is the height of the coil windings. | |||||||||
dR denotes the Ohmic resistance at DC. In case of the measurement coils, it is the series resistance of both coils. | |||||||||
eL denotes the inductance, measured with an inductance meter at 1 kHz. |
Table 1. Coil Parameters. Dimensions and windings of the coils of the measurement head.
The measurement technique utilizes the nonlinearity of the magnetization curve of the superparamagnetic particles. The two-sided measurement head simultaneously applies two magnetic excitation fields of different frequency to the sample, a low frequency (f2) component to drive the particles into magnetic saturation and a high frequency (f1) probe field to measure the nonlinear magnetic response. In particular, both harmonics of the incident fields, m·f1 and n·f2, and sum frequencies, m·f1 + n·f2 (with integer numbers m, n), are generated. These intermodulation products are detected by the differentially wound pickup coil. The reference coils do not pick up these signals because they are located far away from the sample. They serve for suppression of the directly induced high frequency excitation which would otherwise saturate the preamplifier. Thus, the tiny sum-frequency signal due to the presence of super-paramagnetic materials becomes measurable and quantifiable. In the readout electronics, only the intermodulation product at sum frequency f1 + 2·f2 is demodulated because it is the strongest nonlinear component which is present without static bias field. It was shown that this technique allows fast processing and a very large dynamic detection range. Details of the FMMD principle and the readout electronics are described in detail in Ref. 10.
The measurement results shown in Figure 6 reveal that the p-FMMD signal depends on the speed of the scanning stage and on the concentration of the magnetic particles. Consequently, spatial resolution and detection limit of the technique are also speed- and concentration-dependent. We attribute this finding to the signal reduction of the low pass filter at the output of the two-stage lock-in detection of the readout electronics. Previous research on MPI also showed that the spatial resolution is dependent on the parameters speed of gradient strength, particle diameter, volume of the magnetic core and mechanical speed of the stage.20 Our findings are consistent with these results.
Our 2D scanning method differs considerably from the conventional MPI technique based on generating a Field Free Point (FFP) or Field Free Line (FFL), even though the detection principle based on the non-linear signal from superparamagnets is similar.3, 21 Although conventional MPI has advantages over the new p-FMMD technique, such as the simultaneous 3D analysis without mechanical movement of sample or system7, the new MPI scanner does not need big magnets to generate a strong field. We believe that both the conventional MPI scanner and the p-FMMD scanner have their specific advantages. The advantage of the p-FMMD scanner is its simplicity and its small dimensions. There is no need for employing large gradient coils and no need for cooling coils. The sample size in x and y direction are not limited by the technique, just by the scanner and the support. However, the technique is only applicable to sufficiently thin samples that fit between the detection coils. It requires movement of the sample relatively to the measurement head, whereas standard MPI utilizes electrically controlled scanning of the FFL/FFP without sample movement.
MPI is a relatively new technique that has a variety of potential applications in many scientific and industrial fields. It has been shown that its spatial resolution is comparable with that of other medical imaging modalities. In this study, we introduced a new technique called p-FMMD to perform MPI of planar samples. Compared to other MPI scanners, it does not require the generation of a FFL or FFP. No strong magnetic field or field gradient is needed. We believe that the p-FMMD technique will become an alternative method in the field of MPI. Potential application areas include the analysis of biological tissue sections for diagnostic purposes. With a re-design to accommodate thicker samples, non-invasive studies of larger objects and small animals will become feasible.
The authors have nothing to disclose.
This work was supported by the ICT R&D program of MSIP/IITP, Republic of Korea (Grant No: B0132-15-1001, Development of Next Imaging System).
Magnetic particles "SiMAG Silanol" | Chemicell (http://www.chemicell.com) | 1101-5 | Aqueous dispersion of magnetic silica particles, Maghemite, dia. 1 µm |
Magnetic nanoparticles "fluidMAG-Amine" | Chemicell (http://www.chemicell.com) | 4121-5 | Aqueous dispersion of magnetic nanoparticles, Magnetite, dia. 50 nm |
Microtube 10 µl | Hirschmann Laborgeräte (http://www.hirschmann-laborgeraete.de/?sc_lang=en) | volume 10 µl, outer diameter 400 µm, length 40 mm | |
Nitrocellulose Membrane Biodyne B | Thermo Scientific (http://www.thermoscientific.com) | 77016 | Biodyne B Nylon Membrane, 0.45 µm, 8 cm x 12 cm |
DDS chip AD9834 | Analog Devices (http://www.analog.com) | AD9834 | 20 mW Power, 2.3 V to 5.5 V, 75 MHz Complete DDS |
Operational Amplifier AD829 | Analog Devices (http://www.analog.com) | AD829 | High Speed, Low Noise Video Op Amp |
Analog Multiplier MPY634 | Texas Instruments (http://www.ti.com) | MPY634 | Wide Bandwidth Precision Analog Multiplier |
High-Speed Buffer BUF634 | Texas Instruments (http://www.ti.com) | BUF634 | 250mA High-Speed Buffer |
Operational Amplifier OPA627 | Texas Instruments (http://www.ti.com) | OPA627 | Precision High-Speed Difet(R) Operational Amplifiers |
Operational Amplifier TL072 | Texas Instruments (http://www.ti.com) | TL072 | Dual Low-Noise JFET-Input General-Purpose Operational Amplifier |
Lock-In Amplifier SR830 | Stanford Instruments (http://www.thinksrs.com) | SR830 | 100 kHz DSP lock-in amplifier |
XYZ motorized stage | Sciencetown, Incheon, Korea (http://mkmsll.en.ec21.com/) | ||
Cleanroom wiper | Seoul Semitech Co (http://www.seoulsemi.com) | CF-909 | dimension 2.0 mm × 18 mm |