Amani Remmo*a,
Frank Wiekhorst
a,
Olaf Kosch
a,
Stefan Lyer
b,
Harald Unterweger
b,
Harald Kratz
c and
Norbert Löwa
a
aPhysikalisch-Technische Bundesanstalt Berlin, Metrology for Magnetic Nanoparticles, Abbestr. 2-12, 10587 Berlin, Germany. E-mail: amani.remmo@ptb.de
bDepartment of Otorhinolaryngology, Head and Neck Surgery, Section of Experimental Oncology and Nanomedicine (SEON), Professorship for AI-Controlled Nanomaterials, Universitätsklinikum Erlangen, Erlangen, Germany
cCharité-Universitätsmedizin Berlin, Clinic for Radiology, Charitéplatz 1, 10117 Berlin, Germany
First published on 24th May 2023
Magnetic particle imaging (MPI) is an imaging modality to quantitatively determine the three-dimensional distribution of magnetic nanoparticles (MNPs) administered as a tracer into a biological system. Magnetic particle spectroscopy (MPS) is the zero-dimensional MPI counterpart without spatial coding but with much higher sensitivity. Generally, MPS is employed to qualitatively evaluate the MPI capability of tracer systems from the measured specific harmonic spectra. Here, we investigated the correlation of three characteristic MPS parameters with the achievable MPI resolution from a recently introduced procedure based on a two-voxel-analysis of data taken from the system function acquisition that is mandatory in Lissajous scanning MPI. We evaluated nine different tracer systems and determined their MPI capability and resolution from MPS measurements and compared the results with MPI phantom measurements.
There are two main MPI reconstruction techniques: f-space and x-space.8,9 The x-space MPI (magnetic insight) is simpler but requires the exact location of the field-free point at each time point for image generation.8 In contrast, the f-space MPI (Bruker) needs the complex calibration and reconstruction of the tracer distribution. To evaluate the MPI performance of tracers, x-space MPI (where no inversion step or deconvolution is required for image generation) uses MPS devices that record a point-spread function of which peak width and height are used to estimate how much a given MNP distribution appears spatially enlarged (“smeared into neighbouring voxels”).8 However, this does not include the benefit of an inversion step or deconvolution within x-space or f-space MPI. By the inversion step of f-space MPI the smearing is reduced.10 However, it makes the result more sensitive to noise.
For the f-space MPI, there are several methods to evaluate the MPI performance of tracers. One is to use, resolution phantoms, see Fig. 1. A prerequisite for the reconstruction of the tracer distribution in resolution phantoms is the time-consuming acquisition (typically one day acquisition time) of a so-called system function (SF). This type of calibration is mandatory for the MPI reconstruction since each tracer system has its own specific magnetic response when exposed to the AC excitation fields.8,11 To this end, the SF contains numerous calibration scans that are performed using a point-like reference sample of the tracer type intended for the investigation, which is positioned by a robot at a series of defined positions within the field-of-view (FoV). The impact of the tracer type on the MPI image quality can be seen in Fig. 1 on the yellow marked diagonal elements (tracer type is identical for phantom measurement and SF acquisition). Each of the two different iron oxide multi-core tracers possesses an individual MPI tracer performance. Where the spiral filled with Synomag-D can be resolved very precisely (upper left panel of Fig. 1), the spiral containing SPION-citrate tracer (central panel) exhibits a slightly reduced resolution. The importance of the correct SF is displayed at the off-diagonal panels of Fig. 1. Here, a SF of a different tracer type at the same iron concentration has been used for the image reconstruction, deliberately. In all cases, the image quality is heavily distorted so that nearly no geometry details of the spiral are resolved.
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Fig. 1 MPI image reconstructions of the resolution (spiral) phantom using different tracer – SF combinations. Two tracer types SYN (left column, Synomag-D, details of the tracers are summarized in Table 1, see Section 2.1) and SPI (right column, SPION-citrate) have been measured in water (top row) in the spiral phantom. The temperature was kept constant at 20 °C during the measurements and the positioning of the phantoms filled with liquid tracer was done using the animal support (rat bed). The position varied by several millimeters. The reconstructions were carried out with each of the two SFs that were acquired using a reference sample of 4 μL at an iron concentration c(Fe) = 45 mmol L−1 (total iron amount of 10 μg) over a regular grid of 25 × 25 × 13 voxels (single voxel size 1 mm3), so that one SF recording took about 9 h. |
This demonstrates that the MPI image quality is crucially depending on the tracer type and that the selection of a suitable SF for image reconstruction plays an important role for the resolution and quality of MPI images.
Another, much more effective way to assess the tracer performance can be achieved by using magnetic particle spectrometers (MPS), i.e., detecting the dynamic non-linear magnetic susceptibility waiving any spatial resolution. These technically simpler MPS devices are easier and faster (measurement takes a few seconds) to operate, less expensive and more sensitive.3 Usually the MPS parameters and A5/A3 are used to evaluate the tracer performance.12 On the one hand, such simplified considerations of parameters do not give any information about Néel or Brownian relaxation of the parameters under given measurement parameters. Néel and Brownian signal contributions depends on both particle and measurement parameters.13,14 Especially, the Brownian contribution generally will be impacted by the presence of binding states (changing the mobility of the particles). On the other hand, usually a wideband harmonic response should be incorporated to evaluate the tracer performance.
and A5/A3 just give a first hint but the higher harmonics (required for f-space reconstruction) are even more important – especially in case that you are interested in image details. Taking only the lower harmonics (such as A3 and A5) would result in a blurred blob in the reconstructed image in cases where higher harmonics are not present. Here we additionally considered the number of harmonics Ak with amplitudes above the limit of detection (LOD) kA>LOD of the MPS device to evaluate the MPS signal in relation to the noise and to consider the dependence of the inversion step on the noise. The duration of the SF acquisition depends on the repetition time that is different for 2D or 3D imaging, on the use of focus fields to move (enlarge) the FOV, and on the number of averages. Since the acquisition of a SF for a single tracer system takes about 9 h (see Fig. 1), prior prediction of tracer behaviour in MPI using MPS would be beneficial.
Besides magnetic parameters obtained by MPS, physical parameters such as the total (hydrodynamic) size and size distribution have been correlated with MPI performance.6,15 These parameters are often relevant in specific MPI applications, e.g., for imaging of vessel flows where small and stable MNP are preferable.16–18 In addition, the total size of a tracer becomes relevant when it is changing due to aggregate formation.17,19 The thereby increased magnetic (dipole–dipole) interactions between the particles in an aggregate lead to a strong decrease of the signal from a tracer.19
In this work we investigated the capability of MPS to obtain reliable, quantitative values for resolution and detection limits of a tracer system without the need of time-consuming MPI acquisition of SFs. For nine different tracer systems, we first correlated characteristic MPS parameters as well as the hydrodynamic diameter and size distribution extracted from dynamic light scattering (DLS) to the resolution r obtained by the recently introduced two-voxel-analysis of MPI SFs.20 To demonstrate the performance of our analysis we compared the results with phantom measurements of a spiral phantom developed for MPI resolution measurements.21
Sample name | ID | Product information | MPS | MPI | DLS | |||
---|---|---|---|---|---|---|---|---|
A5/A3 (%) | kA>LOD | r (mm) | dhyd (nm) | PDI | ||||
a Given are the sample name, the ID used as abbreviation in graphs and text together with the name of the supplier and the coating of the tracer. Furthermore, the hydrodynamic diameter dhyd (z-average), polydispersity index (PDI) obtained by DLS and characteristic MPS parameters ![]() |
||||||||
Ferucarbotran | FER | Meito Sangyo | 4.1(1) | 30.525(3) | 73 | 2.8 | 59.42(2) | 0.2(4) |
LOT: DDM128N/S1-007 surface: carboxy dextran | ||||||||
Perimag | PER | Micromod Partikeltechnologie GmbH | 8.4(2) | 30.862(2) | 75 | 2.24 | 139.4(1) | 0.22(1) |
LOT: 05216102-02 surface: plain | ||||||||
Synomag | SYN | Micromod Partikeltechnologie GmbH | 17.6(4) | 32.073(2) | 97 | 1.87 | 45.8(7) | 0.05(2) |
LOT: 01517104-04 surface: dextran-plain | ||||||||
SHP30-10 | SHP | Ocean Nanotech | 5.3(1) | 14.25(3) | 39 | 3.92 | 70.5(7) | 0.14(1) |
LOT: 17318SHP surface: carboxylic acid | ||||||||
HK111 | HK1 | Charité-Experimental Radiology | 8.3(2) | 26.325(5) | 91 | 2.13 | 57.6(2) | 0.12(3) |
LOT: HK2015 surface: carboxy methyl dextran | ||||||||
BNF-Dextran | BNF | Micromod Partikeltechnologie GmbH | 0.0344(7) | 10(2) | 11 | 4.53 | 130.3(5) | 0.13(5) |
LOT: 1131684-01 surface: dextran | ||||||||
La32-BSA | LA3 | Universitätsklinikum Erlangen | 2.32(5) | 20.55(3) | 33 | 4.59 | 75(1) | 0.17(1) |
LOT: SEONLA32-BSA1 surface: Lauric acid | ||||||||
Spion citrat | SPI | Universitätsklinikum Erlangen | 1.93(4) | 19.39(4) | 35 | 4.56 | 50.3(9) | 0.28(1) |
LOT: SEONC16 surface: citrate | ||||||||
Resovist® | RES | Bayer HealthCare | 4.8(1) | 26.096(9) | 71 | 2.71 | 58.3(1) | 0.29(5) |
LOT: 21![]() |
The limit of detection (LOD) of the MPS was determined according to the guidance of the International Union of Pure and Applied Chemistry (IUPAC): LOD (Ak) = μ + 3σ of ten empty-sample-holder (background) measurements. For , the uncertainty was performed with the uncertainty contributions of the iron concentration c, the amplitude A3, and the volume V.23 The relative uncertainty for c and V was assumed to be 1.5%. A relative uncertainty of 1.5% was assumed for c and V. For the concentration independent A5/A3, only the noise contributions were considered. The MPS noise of A5 and A3 was determined using 20 blank measurements by calculating the standard deviation from the 20 individual measurements. The uncertainty for kA>LOD was estimated geometrically as ±2.
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The of the investigated tracers varied between
for SYN and
for BNF. Note, that
of the MPI gold standard RES was 4.8 A m2 kg−1 (Fe). This demonstrates the broad variation of the dynamic responses of potential MPI tracer systems and the excellent sensitivity and huge dynamic range (about five orders of magnitude) of the MPS device.
Only information-carrying harmonics above the noise level should be used for image reconstruction in MPI. Therefore, it is generally expected that the flatter the decay of the amplitudes Ak in the measured MPS spectrum of a tracer, the better the spatial resolution after MPI image reconstruction. The slope of the odd harmonics (in MPS spectra even harmonic have zero amplitude due to the symmetry of the magnetization curve and in the absence of any offset field) is parametrized by the A5/A3 value as a first order estimation. Although for high MPI resolution in f-space MPI, a wideband harmonic response is mandatory, a high A5/A3 value is often associated with high resolution in MPI. MPI spectra contain even and odd harmonics and more complex patterns due to the three slightly different excitation frequencies and the gradient (offset) fields used for spatial encoding (see 2.4). Corresponding to the value, the A5/A3 value of the tested tracers also varied between A5/A3 = 32.1% for SYN and A5/A3 = 10% for BNF. The A5/A3 of the well known RES sample was 26.1%.
Next, we further analysed the number of amplitudes Ak above the limit of detection (LOD) kA>LOD of the MPS system as another parameter to describe the MPI performance of a tracer. Fig. 2 shows MPS spectra at Bex = 12 mT for the three tracers SYN, SHP and BNF (obtained at an iron concentration c(Fe) = 45 mmol L−1) together with the LOD (black line) for each harmonic starting at about 3 × 10−12 A m2 that was determined as the mean +3 times the standard deviation of ten background measurements at the same excitation field.
An “ideal” reaction of a tracer exposed to the oscillating magnetic excitation fields used in MPI or MPS would be the immediate switching of the magnetization towards its saturation value MS even at the smallest field amplitude, which is mathematically described by a step function centered at the origin B = 0 with an amplitude ±MS.28
For a step function, the harmonics Ak of the Fourier transform can be expressed analytically by
Ak = 4MS/(πk) | (1) |
Next, we evaluated the relation between MPI resolution r obtained from the two-voxel-analysis for each tracer and the three characteristic MPS parameters (, A5/A3 and kA>LOD), see Fig. 3. For all tracer systems a resolution r in the range 1.5 mm to 5 mm was found with SYN exhibiting the best resolution r = 1.9 mm. The determining factor for the best achievable resolution r is mainly the number of frequency components (FC) of signal ū above the noise floor that can be used in the reconstruction. The number and the strength especially of the FC at higher frequencies depends on the tracer while the noise floor is influenced by the MPI. The lower end of the resolution (here 4–5 mm) depends on the size of the FoV and the pattern that exhibit the lower FC in the SF over the FoV. A much lower resolution is obtained for the tracers La3, SPI, BNF with 4.59 mm, 4.56 mm, and 4.53 mm, respectively. It should be emphasized that these tracers have not been developed as MPI tracer systems. The obtained values from MPS were then correlated with the MPI resolution parameter r to estimate the prediction capability of the parameters for MPI performance (see Fig. 3). By linear regression (black lines) the correlation coefficients R2 = 0.65, 0.71, and 0.93 were determined for
, A5/A3, and kA>LOD, respectively. Thus, the MPS parameter kA>LOD enables a reliable prediction of achievable resolution r in MPI measurements, for the chosen MPS and MPI scanner setups parameters (see 2.3 and 2.4). Assuming a linear relation between kA>LOD and r with kA>LOD = 141(9) − 25(3) × r [in mm], r can be parametrized as
r = (141 − kA>LOD)/25 | (2) |
In addition, the size distribution (the values of dhyd and PDI as obtained by DLS, see Table 1) was correlated to the resolution r. Only a poor correlation was found for the nine tracer systems (R2 = 0.04 for dhyd and 0.001 for PDI). A precise relation between structure and size distribution of a tracer and the resulting resolution needs extensive and accurate characterization and should be further investigated. Very promising approaches for structural analyses are separation techniques that have already been described in ref. 12 and 31.
To demonstrate that we can predict the tracer MPI resolution of a tracer from the MPS parameter kA>LOD we performed spiral phantom measurements (with a complete SF acquisition) for the tracer systems SYN and SHP, from which the resolution r for the MPI application was determined according to ref. 21, see Fig. 4.
The resolution of the spiral phantom rs can be estimated in the image reconstruction from the minimum distance above which neighboring segments of the spiral channel are melding with each other so that the inner part (and the gap) of the spiral is no longer visible. From the MPI image reconstruction of the spiral a resolution rs = 1.57 mm for SYN and rs = 3.52 mm for SHP phantom was extracted. This is in very good agreement with r = 1.87 mm for SYN and r = 3.92 mm for SHP.
This journal is © The Royal Society of Chemistry 2023 |