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Understanding how individual cells behave inside living systems will help enable new diagnostic tools and cellular therapies. Superparamagnetic iron oxide (SPIO) particles can be used to label cells and theranostic capsules for non-invasive tracking using MRI. Contrast changes from SPIO are often subtle relative to intrinsic sources of contrast, presenting a detection challenge. Here we describe a versatile post-processing method, called Phase map cross-correlation Detection and Quantification (PDQ), that automatically identifies localized deposits of SPIO, estimating their volume magnetic susceptibility and magnetic moment. To demonstrate applicability, PDQ was used to detect and characterize SPIO-labeled magnetocapsules implanted in porcine liver and suspended in agarose gel. PDQ was also applied to mouse brains infiltrated by MPIO-labeled macrophages following traumatic brain injury (TBI); longitudinal, in vivo studies tracked individual MPIO clusters over three days, and tracked clusters were corroborated in ex vivo brain scans. Additionally, we applied PDQ to rat hearts infiltrated by MPIO-labeled macrophages in a transplant model of organ rejection. PDQ magnetic measurements were SNR-invariant for images with SNR>11. PDQ can be used with conventional gradient-echo pulse sequences, requiring no extra scan time. The method is useful for visualizing biodistribution of cells and theranostic magnetocapsules, and for measuring their relative iron content.
Superparamagnetic iron oxide (SPIO) particles are used extensively for cellular MRI due to their biocompatibility and strong contrast efficacy. SPIO particles in tissue create microscopic static magnetic field perturbations that extend 10–50 times the particle’s diameter, thereby reducing the T2 and T2* of nearby water protons (1). Resulting magnitude images often exhibit regions of hypointensity indicating SPIO accumulation. For preclinical research, a wide variety of SPIO particles have been used with different sizes, compositions, and functional surface coatings, such as peptides or antibodies for molecular epitope detection. Histologically, SPIO presence in tissue has been verified using electron microscopy, iron staining, or immunohistochemistry (2). Many cell types have been labeled by SPIO (3), either ex vivo or in situ (2). Macrophages have been shown to endocytose SPIO particles up to 1.6 μm in diameter (3). Non-phagocytic cells can also be labeled ex vivo via the use of transfection agents (4), electroporation (5), sonoporation (6), receptor-mediated binding, or receptor-mediated endocytosis (7). Numerous studies have investigated the impact of SPIO labeling on cell viability and function (8,9). Clinical translation of SPIO-based cell tracking has also been demonstrated (10).
Distinguishing SPIO-induced image hypointensity from intrinsic contrast is a common challenge when imaging these agents using T2 or T2*-weighted scans, especially if their biodistribution is not known beforehand. False positives can originate from intrinsic contrast sources, for example, from tissue interfaces, blood vessels, necrosis, hemorrhage, or low proton density. To help address this challenge, investigators have developed image acquisition methods that generate positive contrast images highlighting SPIO. These methods include, for example, differential imaging before and after agent delivery, specialized weighted contrast methods (11), spectrally-selective excitation (12–14), gradient dephasing (15,16), quantum coherence imaging (17), and ultrashort TE image subtraction (18). These techniques generate positive contrast images that complement anatomical magnitude images, but may also carry limitations. For example, several methods require foreknowledge of the magnitude of the field disturbances caused by SPIOs, and this information is used to configure scan parameters such as excitation frequency, bandwidth, selective RF pulse shape (12), echo time, slice thickness, and rephasing gradient amplitude (15). Additionally, some of these techniques demand high-end or customized hardware (18) or additional anatomical scans that result in prolonged acquisition times (12,13,15). Positive contrast methods tend to diminish the signal-to-noise ratio (SNR) per unit scan time compared to conventional magnitude images in order to reap the benefits of positive contrast. Alternatively, one can highlight SPIO by using conventional acquisition methods, followed by generation of positive-contrast images using MRI phase images. Applying high-pass filters to phase images has been shown to accentuate spatial magnetic field variations due to SPIO deposits (19,20).
Overall, positive-contrast methods for imaging SPIO assume unknown or arbitrary distributions of agent. However, if SPIO is distributed in a known geometry, this can be exploited to computationally estimate the total number of SPIO deposits, and each deposit’s volume magnetic susceptibility and iron concentration. Previously, phase images have been used to assay these quantities for macroscopic objects such as cylinders (21) or spheres (22). An in vivo study quantified iron by modeling a localized tissue injection of SPIO as a sphere (23). Other studies quantify clusters of SPIO labeled cells by measuring local signal loss (24) or proton relaxation rates (25). Analyzing magnitude signal loss around SPIO deposits generally leads to quantification results that correlate with echo time or sample orientation (23).
In this paper we describe a post-processing method, called Phase map cross-correlation Detection and Quantification (PDQ), that uses phase images to automatically identify and count spherical SPIO deposits (26) and estimate their volume magnetic susceptibility and magnetic moment. Prior work on PDQ (26) reporting on phantom and ex vivo tissue studies, demonstrated the method’s efficacy in generating positive-contrast images, and counting SPIO deposits automatically, even in low-SNR images (26). Here, we present a powerful extension of the PDQ algorithm enabling estimation of the volume magnetic susceptibility and magnetic moment of detected superparamagnetic deposits, which greatly extends the method’s quantification abilities and power to discriminate against false positives. We demonstrate the utility of the improved PDQ algorithm in several diverse MRI data sets. First, we apply PDQ to detect magnetocapsules implanted in porcine liver. Magnetocapsules are spheres of alginate crosslinked with SPIO that are permeable to metabolites but not native antibodies, thereby encapsulating and immunoisolating therapeutic cells (27). The PDQ analysis was validated in MRI phantoms containing magnetocapsules. Moreover, superconducting quantum interference device (SQUID) magnetometry was used to validate PDQ’s magnetostatic quantification abilities. Next, we applied PDQ to an in vivo mouse model of traumatic brain injury (TBI) to analyze inflammation-associated MPIO-labeled macrophage infiltration. In the TBI model, PDQ longitudinally tracked individual MPIO clusters over three days in vivo. Finally, PDQ was applied to rat hearts infiltrated by MPIO-labeled macrophages as a result of organ transplant rejection. Overall, we show that using PDQ it is feasible to detect and quantify thousands of individual MPIO-labeled cells or magnetocapsules throughout tissue volumes in an automated fashion, with significant discrimination capacity against endogenous tissue contrast.
MR images are typically reconstructed from a series of echoes acquired in k-space using a multi-dimensional Fourier transform, with each voxel in the reconstruction having a real and imaginary component. The magnitude image, given by is typically displayed, where μR and μI represent real and imaginary signal components, respectively. Phase angle information, given by = tan−1(μI/μR), is typically discarded. The phase angle in each voxel of a phase map can be simplified as
where is the measured phase angle, low–f represents low-spatial-frequency contributions to the phase angle, SPIO represents contribution from nearby SPIO, and high–f represents other, non-SPIO high-spatial-frequency contributions (e.g., material/tissue interfaces). When working with a single gradient-recalled echo (GRE) image, the phase image must first be ‘unwrapped’ to remove phase discontinuities when crossing from −π to +π over the image field of view before one can distinguish the desired SPIO component in Eq. . These −π/+π boundaries can be eliminated using unwrapping algorithms that determine the multiple of 2π that must be added or subtracted from the phase angle to obtain a discontinuity-free phase map. After unwrapping, we eliminate low– f by applying a high-pass filter to the unwrapped phase map, resulting in a phase-offset image, with each voxel represented by
The resulting phase-offset image contains only phase contributions from SPIO and other high-spatial-frequency sources. A voxel’s intensity in the phase-offset image (Δ) is proportional to that voxel’s deviation in magnetic field (ΔBZ) relative to its surrounding background material, i.e.,
where γ is the proton gyromagnetic ratio and TE is echo time. ΔBZ(r,θ) for a spherical deposit of a paramagnetic or diamagnetic substance will cause a dipolar magnetic field perturbation of the form (28)
where Δχ is the difference in magnetic susceptibility between the sphere and its surroundings, B0 is background field strength, a is the sphere radius, r is distance from its center, and θ is the angular deviation from the direction of B0. Notably, the sphere has a maximum ΔBZ (r, θ) field deviation at its poles given by
Substituting an estimated radius, a, for an SPIO deposit into Eqs.  & , allows one to calculate the deposit’s mean Δχ by sampling many of its surrounding phase-offset (Δ) values. From Δχ, one can calculate a representative, uniform magnetic susceptibility, χA, for an SPIO deposit, provided the background susceptibility (χB) is known, using:
Note that in the case of magnetocapsules, we assume SPIO is homogeneously distributed throughout each capsule’s volume.
The radius parameter, a, is measured by optical microscopy for each batch of magnetocapsules, and ranges from 230–330 μm. In the case of SPIO-labeled cells, we assume each cell is spherical and a approximates the cell radius. Since cells are sub-voxel-sized, details of the actual intracellular SPIO distribution are inconsequential for this analysis.
Common values for χB (unitless) include water at 37 °C (χ = −9.051 × 10−6) (28), agarose (χ ≈ χwater) (29), human tissues (−11.0 × 10−6 < χ < −7.0 × 10−6), liver (χ = −8.8 × 10−6), and air (χ = +0.36 × 10−6) (28). Even in tissues with severe pathological iron loading (e.g., hemochromatosis), it has been estimated that χ ≈ 0.0; thus, the most extreme natural tissue susceptibility value in organs is only a few ppm more paramagnetic than water (28).
After finding χA for an SPIO deposit, this can be used to estimate the deposit’s bulk volume magnetization using
where A is the sphere’s volume magnetization (in units A·m−1), μ0 = 4π × 10−7 T·m·A−1, and is the surrounding magnetic field strength (in T units) (30). We model each SPIO deposit as a uniform sphere with a magnetic moment given by
where A is the magnetic moment (units pA·m2) and χA is sphere susceptibility from Eq. .
Cells and magnetocapsules are predominantly water by volume. Thus, the uniform susceptibility for these deposits, χA, calculated from Eq. , represents both aqueous (χwater) and anhydrous (χan) susceptibility components. We assume that the cell or magnetocapsule is mostly water by volume and the anhydrous content (e.g., SPIO) is of negligible volume (i.e., νan νwater). We estimate the SPIO anhydrous susceptibility component (χan) by subtracting the aqueous susceptibility component (χwater) from the deposit’s measured χA value:
By removing water’s susceptibility contribution, this aqueous SPIO deposit is modeled as a negligible volume of anhydrous material uniformly distributed throughout a spherical space with radius a. The magnetic dipole moment for this rarefied anhydrous sphere (an) is calculated by substituting χan for χA in Eq. . Moreover, if the SPIO dominates χan, one can estimate iron content of the deposit using
where mFe is mass of iron, an is the magnetic moment of the SPIO deposit assuming χan, and Fe is the mass magnetization of the SPIO (units emu/g or A·m2/kg).
An overview of the PDQ algorithm is shown in Fig. 1; this flowchart shows the progression from raw k-space data to a list of quantified magnetic dipoles (i.e., SPIO deposits). First, the phase image is unwrapped in 3D, which provides more information than 2D unwrapping, improves accuracy (31), and avoids phase-unwrapping errors in the Z-stack dimension (32). The unwrapped phase data is high-pass filtered, resulting in the phase-offset image described by Eq. . The SPIO deposits are detected using templates generated from Eqs.  &  as a model function. Since many dipoles do not lie exactly on the Cartesian grid points of acquired MRI data, 27 templates are generated, representing dipoles that are offset [−0.4, 0.0, or +0.4 ] voxels from the Cartesian grid, in each of x-, y-, and z-dimensions. The search templates and the phase-offset data set are passed through a 3D normalized cross-correlation algorithm (26). This algorithm overlays each search template onto every template-sized patch in the phase offset image. The algorithm output is a set of 27 template similarity (TS) matrices, where each voxel contains a TS value between [−100%, 100%], representing the likelihood that a voxel in the phase image represents the center of a magnetic dipole (i.e., SPIO deposit). A 3D peak-finding algorithm is applied to each TS matrix to pinpoint the center of each dipole. To reduce the chance of detecting false-positive dipoles, peak locations with TS < 30% are discarded and deemed deviant from Eq.  theory, since many false-positive peaks with a TS < 30% are found in random noise. To measure Δχ for each SPIO deposit, a 3D least-squares fit is performed between the phase-offset image impression and its search template. The dipole’s uniform magnetic susceptibility, χA, is calculated from user-provided χB via Eq.  and its magnetic moment from Eq. . If the SPIO deposit’s spherical volume is predominantly water, Eq.  is used to calculate χan. If the SPIO mass magnetization (i.e., g/emu) is known, Eq.  can be used to estimate the iron content of the SPIO deposit.
PDQ was initially evaluated in a set of phantoms, each containing 103 magnetocapsules suspended in 13 mL of 2% agarose gel (~70 capsules/mL). In brief, magnetocapsules were synthesized by crosslinking alginate with poly-L-lysine and 2.5%, 5%, or 10% v/v Feridex® SPIO (11.2 mg [Fe]/ml, Berlex Laboratories, Montville, New Jersey). A coating layer of alginate was added to the surface of the initial capsules. Capsules had uniform Feridex® labeling and a diameter of 570 ± 60 μm (preparation details described elsewhere (27)).
MRI data were acquired for 12 agarose gel phantoms containing suspended 2.5%, 5%, and 10% v/v Feridex® magnetocapsules (n=3, 5, and 4, respectively). All samples were imaged using a 4.7 T, 40 cm horizontal bore Bruker AVANCE AVI scanner (Bruker BioSpin, Billerica, MA) using a 3D GRE pulse sequence with imaging parameters: TE/TR=1.2/300 ms, averages = 18, and 280μm isotropic resolution.
The accuracy of PDQ magnetic measurements in low-SNR images was also tested. One 10% v/v Feridex magnetocapsule phantom was imaged with decreasing scan times to generate images with SNR = 29, 18, 14, and 11. Addition of Gaussian noise to the data’s real and imaginary components simulated images with SNR = 4.5 and 2.5. PDQ was run on each image to count the detected magnetocapsules and calculate apparent magnetic properties.
The magnetic moment of the magnetocapsules was measured using SQUID magnetometry. Triplicate samples were prepared, each containing 100 dehydrated 10% Feridex v/v magnetocapsules. Dehydration was performed via immersion in 100% ethanol followed by desiccation under vacuum for 10 minutes. To ensure that this process did not degrade the magnetocapsules, samples were challenged with ethanol immersion for 72 hours, resulting in no noticeable loss of integrity. For magnetometry, desiccated magnetocapsules were counted (100 ± 1) and placed into an empty two-piece gelatin capsule. Each gelatin capsule sample was held in a plastic drinking straw by a small amount of quartz wool and placed into a SQUID magnetometer (Quantum Design, San Diego, CA). Measurements were made at 310 K as a function of magnetic field ranging from 0–7 T; magnetic moment values were averaged across the three samples and corrected for the diamagnetic contributions from the gelatin capsule and quartz wool.
Using a porcine model, PDQ was used to analyze 10% v/v Feridex magnetocapsules lodged in the vasculature of a porcine liver. Approximately 1.4×105 magnetocapsules were injected via portal vein into a swine using methods described elsewhere (27). On the same day as transplant the swine was sacrificed, the liver was harvested, and a 58 cm3 section was fixed in 4% paraformaldehyde for ex vivo imaging. A 3D GRE image of the liver section was acquired at 4.7 T with TE/TR=3.5/200 ms, averages = 5, and a resolution of 180×280×140μm.
PDQ was used to analyze macrophage infiltration in mouse brains following TBI induced by a controlled cortical injury (CCI). Male C57BL/6J mice (Charles River Laboratories, Wilmington, MA) aged between 11–15 weeks were anesthetized and injected with 4.5 mg [Fe]/kg of 0.9 μm-diameter microspheres containing 62% magnetite (w/w) and fluorescein-5-isothiocyanate dye cross-linked within polystyrene/divinylbenzene (Bangs Laboratories, Fishers, IN). These MPIO particles are endocytosed by circulating monocytes and macrophages, thereby labeling these cells in situ (33). Control mice received no MPIO injection or CCI. Between 24–48 hours after MPIO injection a CCI was delivered as previously described (34). Mice were imaged 24 and 96 hours post-TBI using a 7 T, 21 cm horizontal bore Bruker AVANCE AV3 system using a standard 3D GRE pulse sequence with parameters: TE/TR = 7/100 ms, averages = 4, and a resolution of 58×79×79 μm. After the final in vivo session mice were perfused, fixed with 4% paraformaldehyde, and the brains excised. 3D volume images were acquired in the fixed brains using an 11.7 T, 89-mm vertical bore Bruker AVANCE micro-imaging system with parameters: TE/TR=6/500 ms, averages=4, and 58×39×39 μm resolution.
PDQ investigated MPIO-labeled macrophages infiltrating cardiac tissue in a working-heart model of chronic cardiac rejection. In this model, the heart and lung from a PVG.1U rat are transplanted en bloc into the abdomen of a PVG.R8 rat, where the experimental details are described elsewhere (35). One day before transplant, or 1–5 weeks after transplant, each of the 27 transplant recipients was injected i.v. with 4.5 mg [Fe] per rat of 0.9 μm-diameter MPIO (Bangs). At different time points after transplantation (2–26 weeks), rats were sacrificed, perfused, and the intact heart tissues were fixed in 4% paraformaldehyde. Hearts were imaged at 11.7 T using a standard 3D GRE pulse sequence with parameters TE/TR = 8/500 ms, averages = 2, and an isotropic resolution of 40 μm. All animal experiments throughout this methods section were approved by the Carnegie Mellon Institutional Animal Care and Use Committees (IACUC), or the Johns Hopkins IACUC, and animals received care in compliance with the National Institute of Health Guide for the Care and Use of Laboratory Animals.
An overview of the PDQ algorithm is displayed in Fig. 1, and the details are described below. First, PDQ reconstructed the raw k-space data into magnitude and phase images, where unwrapping of the 3D phase data was performed using PRELUDE (32). Phase-unwrapped data were imported into MATLAB (The MathWorks, Inc., Natick, MA) and high-pass filtered with a kernel designed to exclude the lowest 10% of frequencies, which is the smallest percentage of frequencies that must be removed in order to eliminate large-scale magnetic inhomogeneity, as described by Eq. . As described above, Eqs.  &  were used to generate 27 templates, sized 7×7×7 voxels, with each template representing dipoles shifted [−0.4, 0.0, or +0.4 ] voxels in x-, y-, and z-dimensions. 3D normalized cross-correlation was applied between each of the 27 templates and the high-passed phase data, resulting in 27 similarity matrices. A 3D peak detection algorithm was applied to the non-shifted similarity matrix to pinpoint each dipole’s location. To account for dipole shifts off the Cartesian grid, each dipole was assigned its maximum TS value from the 27 shifted similarity matrices, and peaks with TS ≤ 30% were discarded.
Δχ for SPIO deposits with TS ≥ 70% was measured using a 3D least-squares fit between the phase-impression in the high-passed phase image and a dipole template. The 70% TS threshold is used since PDQ was found to underestimate magnetic moments by >15% when applied to dipoles with TS < 70%, (see Results). The dipole’s χA was calculated from user-provided χB using Eq.  and its magnetic moment from Eq. . For each SPIO deposit, we calculated χan using Eq. , an using Eq. , and Fe using Eq. . The final result of the PDQ process is a list of high-confidence SPIO deposit locations and their magnetic and iron measurements.
PDQ analyzed the experimental datasets assuming the following χB parameters: Magnetocapsules in agarose χB = −9.05×10−6 (28,29), magnetocapsules in liver χB = −8.8×10−6 (28), and macrophages in mouse brain and rat heart χB = χwater = −9.05×10−6 (28). The PDQ radius parameter for macrophage was assumed to be a ≈ 8.5μm (36).
Figure 2a shows a magnitude and phase image of an agarose phantom containing a uniform distribution of magnetocapsules. Table 1 lists the PDQ calculated magnetic measurements derived from this data. Note that the 2.5% magnetocapsules are diamagnetic overall, due to their low SPIO content. Figure 3 shows a plot of the anhydrous magnetic moment (an) calculated from Eqs.  &  versus template similarity for ~2,000, 10% v/v Feridex magnetocapsules. Notably, the measured magnetic moment of the magnetocapsule is correlated to its template similarity (TS) value. Figure 4 shows estimated magnetic moments for ~4,000 magnetocapsules with a TS ≥ 70%. Across all magnetocapsules, iron content estimated using Eq.  ranged from 15–125 ng. These iron estimates assume a saturation magnetization for Feridex of 68 emu/g [Fe] (37,38).
The PDQ-derived magnetocapsule magnetic moment was compared to values obtained from direct SQUID magnetometry measurements. Figure 5 shows the mean magnetic moment for 300 magnetocapsules as a function of applied magnetic field. As expected, above 3 T the magnetite in the magnetocapsules shows saturation. The mean magnetic moment, 8,100 ± 200 pA·m2, was used to estimate the saturation magnetization of Feridex in units emu/g [Fe]; we substituted this value into Eq.  along with the Feridex iron concentration (11.2 mg [Fe]/ml) and the magnetocapsule radius (298 μm). The result gives a saturation magnetization of 65 ± 13 emu/g [Fe], in agreement with published magnetite magnetization values between 68–130 emu/g [Fe] (37,38). From PDQ, the magnetocapsule anhydrous magnetic moment was calculated to be 8,300 pA·m2 when the TS value is extrapolated to 100%, which agrees with the SQUID-measured value (8,100 ± 200 pA·m2). At TS=50%, PDQ appears to underestimate the magnetic moment by 27% of the SQUID-measured value, whereas for TS ≥ 70%, PDQ underestimates the value by only 15%. We note that no similar accuracy trend with decreasing TS was found for sub-voxel-sized SPIO deposits in labeled cells (below), possibly implying that the magnetic moment underestimates are due to aspherical variations in magnetocapsule shape and partial magnetocapsule alignment along B0 (see Fig. 3, inlay).
The PDQ magnetic measurement accuracy in low-SNR images was also tested using the 10% v/v Feridex magnetocapsule phantom. Table 2 lists the results of this test. For SNR > 11, magnetic susceptibility and moment measurements were stable and equivalent to the reference scan (SNR = 30). Magnetic measurements remain largely independent of noise levels since sampling 343 voxels surrounding each dipole deemphasizes noise error contributions. For SNR ≤ 4.5, magnetic measurements were erroneous (Table 2), even when averaged over 200–600 magnetocapsules. Also, the fraction of magnetocapsules detected decreased as SNR decreased, with 71% detected for SNR = 4.5 and 25% detected for SNR = 2.5. Previously, PDQ detection accuracy was analyzed for low-SNR 2-dimensional images and exhibited accuracy comparable to that found in this 3-dimensional analysis (26).
PDQ was used to detect and analyze 10% v/v Feridex magnetocapsules implanted in vivo in the porcine liver via intraportal infusion. A portion of the resected liver was imaged, and PDQ detected ~700 isolated magnetocapsules in a 58 cm3 sample (12 isolated capsules/cm3). Figure 2b shows representative magnitude and phase images of the liver lobe. We observed that numerous magnetocapsules clustered within the liver blood vessels with a curvilinear distribution. PDQ assigned low TS values to these strings of magnetocapsules, often excluding them from magnetic measurement, since the magnetic impression due to abutting magnetocapsules is dissimilar to that for an isolated sphere of SPIO. Histological analyses of similar porcine livers with portal vein injections of large numbers of magnetocapsules showed qualitatively similar results (27).
PDQ was used to analyze mouse brains (n=27) following TBI to detect MPIO in inflammation-associated macrophages that infiltrated lesioned areas. Macrophages migrate and accumulate both near the site of injury and elsewhere in the brain following TBI, and recruit other immune cells. We previously reported immunohistological validation of this TBI model, and these data are presented elsewhere (34). The histology shows that the F4/80+ macrophages contain a variable number of 0.9 μm-diameter MPIO particles (34). Control TBI mice with no injected MPIO had no dipole patterns present in the brain volume. Figures 2c-d show ex vivo and in vivo magnitude and phase images of mouse brains, and Table 1 lists the magnetic measurement results.
Figure 6 shows the estimated magnetic moment for all macrophages detected in brains scanned ex vivo. Magnetic moments ranged from 0.2–2.7 pA·m2, corresponding to an estimated iron content of 3–38 pg, assuming MPIO particles have a saturation magnetization of 68 emu/g [Fe] (37,38). This range of iron content is comparable to published values of ex vivo labeled macrophage, where rat or human macrophages incubated in media containing 0.9 μm or 1.6 μm-diameter MPIO internalize between 27–39 pg of iron (3,39). The wide distribution of magnetic moments shown in Figure 6 for these MPIO-labeled cells is presumably due to different numbers of internalized MPIO particles. Iron content can be used to estimate the number of MPIO particles within these cells, since each 0.9 μm-diameter MPIO particle contains on average ~0.47 pg [Fe] (62% magnetite w/w). This implies that PDQ detected macrophages labeled with as few as ~6 MPIO particles and as many as ~76 MPIO particles. Also, there appears to be an inverse relationship between magnetic moment and the number of macrophages. Macrophages containing no or only a few particles have weak magnetic moments (<0.2 pA·m2) and were not detected by the PDQ analysis.
PDQ was also able to detect and measure magnetic moments of MPIO-labeled macrophages in vivo in the TBI model. Comparing the same cohort of brains scanned in vivo and ex vivo (i.e., fixed), approximately 75% of labeled macrophages were detected in vivo. The in vivo scans were acquired with lower resolution and SNR than in the excised brains. In vivo, macrophages with low magnetic moments went undetected, and thus the average magnetic moment measured in vivo was greater than ex vivo (Table 1). When in vivo isotropic resolution was reduced further, from 63 μm to 100 μm, only 25% of labeled cells were detected, relative to ex vivo. Figure 7 shows co-registrated images of a comparable slice acquired in vivo (Fig. 7a) and ex vivo (Fig. 7b); the slice contains two prominent MPIO clusters, presumed to be concentrated within macrophages or macrophage clusters, while comparable slices from a wild-type mouse brain shows no similar signal voids. In vivo, the measured magnetic moments of these deposits where 1.1 and 1.2 pA·m2 (top to bottom, respectively), while ex vivo PDQ measured 0.7 and 1.0 pA·m2 for the same deposits. We note that this small discrepancy may be due to different background tissue susceptibilities between the live and fixed tissues. Figure 7c shows a second mouse brain imaged 24 and 96 hours following MPIO injection. Both images show a cell or cell cluster in the same anatomical location, with a magnetic moment of 2.5 and 2.4 pA·m2 at 24 and 96 hours, respectively, while a comparable slice from a wild-type mouse exhibits no dipole patterns in its phase image.
PDQ investigated SPIO-labeled macrophages infiltrating cardiac tissue in a heterotopic working heart transplant model of chronic cardiac rejection. Macrophages are observed to migrate and accumulate in regions of solid organ rejection, often performing secretory and phagocytic functions (2,3,33). In this experiment, macrophages were labeled in situ with 0.9 μm-diameter MPIO following i.v. injection. We previously reported immunohistological validation of the rat chronic heart rejection model (35) and showed that ED1+ macrophages contain a variable number of 0.9 μm-diameter MPIO particles (35). Figure 2e shows magnitude and phase images of macrophage-infiltrated heart tissue, where the corresponding PDQ’s magnetic measurements are listed in Table 1. The mean (n=27) magnetic moment of MPIO-labeled macrophages in heart tissue was approximately equal to that measured for macrophages in mouse brains following TBI (see above). Both models label macrophages through i.v. injection of 0.9 μm-diameter MPIO.
In this paper we present a post-processing method that uses phase MR images to automatically identify and count spherical SPIO deposits and estimate their volume magnetic susceptibility and magnetic moment. The PDQ algorithm can automatically scan, detect and quantify individual MPIO-labeled cells, cell clusters or therapeutic magnetocapsules in tissue volumes, with significant discrimination capacity. Moreover, the PDQ algorithm provides an estimation of the volume magnetic susceptibility and magnetic moment of these detected paramagnetic deposits, which may enable greater discrimination against false positives. The utility of the PDQ algorithm is demonstrated in several diverse MRI data sets, acquired in animal models of therapeutic magnetocapsule engraftment, TBI, and organ transplant rejection, both in fixed tissues and in vivo.
There are a several sources of error in PDQ’s magnetic measurements. First, phase unwrapping can assign an incorrect multiple of 2π to a pixel, especially if phase is spatially undersampled (i.e., two adjacent pixels have an actual phase difference greater than π) (31). The unwrapping algorithm used has an error rate of 0.4% when SNR = 2.5 (32), but SNR < 2.5 is common at the center of dipoles, where signal-free pixels contain random phase values (23). To mitigate this effect, one may weigh or mask out pixels with SNR < 2.5 to deemphasize these in the PDQ analysis (23), or acquire phase maps using multi-echo GRE pulse sequences that replace phase unwrapping with ‘temporal unwrapping.’ Second, there is often imprecise knowledge of the background χ-values among different tissues. This fact was acknowledged in comparing magnetic moment values of the same paramagnetic deposit acquired in vivo versus in fixed tissue in the TBI model (Fig. 7); fixed, perfused brain specimens have the blood removed and undergo dehydration in the fixation process that may alter χ. Finally, in order for PDQ’s dipole counts to be comparable across different datasets, each must be acquired at similar resolution and SNR. Datasets with low resolution and/or SNR may have many dipoles omitted from final counts, due to thresholding of the TS parameter; in the analysis presented, dipoles with TS<30% were ignored.
If labeled cells or magnetocapsules are very close or touching, PDQ will detect these as a single entity yielding an aggregate magnetic susceptibility and moment. If cells or magnetocapsules are further apart, but within each other’s template-sized region, their phase image profiles overlap, and TS values will tend to decline. A possible extension of the algorithm could measure the magnetic properties of neighboring dipoles simultaneously. One can model dipoles as vertices (νV) in a graph G = (V, E), with edges (e= (ν1, ν2) E ) representing dipole pairs that share the same 7×7×7 voxel space. Then, for each connected subgraph of G, one would perform a least squares fit to account for all dipoles in that subgraph.
When considering neighboring magnetic dipoles, one may also consider how each neighboring field changes the effective B0 experienced at the other location. Calculations using Eq.  show that this effect is very small for adjacent magnetocapsules (ΔB0 = ~16ppm) and for adjacent MPIO-labeled cells (ΔB0 = ~190 ppm). Other materials and SPIO configurations may have a larger effect requiring appropriate correction.
SPIO deposits change the precession frequency of surrounding protons, distorting the phase image along its readout dimension. If scan parameters are not configured to minimize this effect, SPIO deposits will not exhibit the expected geometry for detection and measurement (e.g., Eq. ). Specifically, a proton spin experiencing a magnetic field deviation of ΔBZ exhibits a spatial shift in the readout dimension in a phase image of amount (28)
where Δp is the distance the proton is shifted in pixels, Nx is the number of pixels in the readout dimension, ΔBZ is magnetic field deviation from B0 (T), FOVx represents readout field of view (m), Gx represents readout gradient amplitude (T/m), γ represents proton gyromagnetic ratio (Hz/T), and BW represents readout bandwidth (Hz/T). Equation  teaches that the spatial shift artifact is minimized by increasing bandwidth, which also reduces image SNR. Equations  &  can be used to calculate the minimum BW required to avoid image distortion.
To optimally acquire an image for PDQ analysis, SPIO deposits should be localized and punctate in appearance, since we assume they are spheres or ideal points. If PDQ is used on 2D images, slice thickness should be chosen so that each dipole’s magnetic perturbation in the phase image is significant relative to image noise levels.
The echo time, TE, should be sufficiently long to allow for dephasing around SPIO deposits to occur, but not so long that SNR declines substantially. When dipoles are in highly heterogeneous backgrounds, dual-echo GRE scans may enable more accurate measurements than single-echo GRE scans (23). In samples where SPIO deposits reside within homogenous tissue backgrounds (e.g., brain, liver) a single TE gradient-echo image is sufficient.
Template sizes should be larger than 3×3×3 voxels, so that no dipoles are found in random noise. The template should be sized so that voxels on its periphery have a phase offset of greater magnitude than phase image noise. Oversized templates may start to overlap neighboring dipoles. Users must set a template similarity (TS) threshold above 30%, as lower thresholds generally detect dipoles in random noise. PDQ underestimates magnetic measurements when applied to SPIO deposits with different orientations or slightly aspherical geometries. Therefore to maximize magnetic measurement accuracy, one should measure dipoles with the highest TS values available for a particular dataset, or modify the templates generated by Eq.  to reflect non-spherical geometries.
PDQ detects single cells or cell clusters in vivo, measuring magnetic moments as low as 0.8 pA·m2 (~12 pg [Fe]) at 7 Tesla. Previously, single macrophages were detected when labeled with 100 pg [Fe] at clinical field strengths as low as 1.5 Tesla (39). Magnetic measurements provided by PDQ, in addition to location data, may provide more certainty when identifying labeled cells at different time points in longitudinal studies. For in vivo PDQ, sufficient resolution is critical, as an SPIO deposit’s magnetic field rapidly attenuates with distance from its center (~1/r3). In vivo imaging also presents challenges including movement from breathing and cardiac function, as well as cellular motion. Many cells may migrate during multi-hour scans, confounding PDQ. For example, multipotent neuroblasts can move 100 μm/hour in vivo (40). Problems can be avoided by performing sufficiently short scans so cells move no more than one voxel.
Tracking of single cells by PDQ should be increasingly feasible through motion correction, cell-registration methods, increased magnetic field strengths, and development of sensitive hardware and contrast agents. In vivo cell tracking studies may potentially be used to detect the arrival of immune cells at sites of disease, define optimal cell populations and delivery methods in the emerging field of cellular therapeutics, and understand basic biological phenomena in vivo. For example, in cardiac tissue undergoing immune rejection, macrophage numbers reflect different stages of rejection (33) and can be used to titrate dosage and monitor the efficacy of immunosuppressive therapy (2). Magnetic moment measurement can also be used for theranostic magnetocapsule applications to assay magnetocapsule integrity (i.e., intact versus ruptured), which can be an important predictor of encapsulated pancreatic islet survival (27), for example. Moreover, labeling capsules with different iron contents may allow for unambiguous magnetic moment signatures enabling, for example, identification of multiple encapsulated therapeutic cell types, or transplants occurring at different times.
Superparamagnetic MRI contrast agents are increasingly being used to label cells and theranostic vehicles for in vivo imaging applications. This study addresses an urgent need in this emerging field which is the analysis and quantification of the resulting MR images. The PDQ algorithm detects localized SPIO deposits, and measures their magnetic moment, which is a quantity that can be used to improve detection specificity. PDQ is capable of detecting single cells and cell clusters in vivo, and provides reliable magnetic measurements. PDQ requires no additional scan time or special pulse sequences, and requires only a few user-set parameters. PDQ may have future applications for monitoring therapies, measuring cellular iron content, and observing cell behaviors.
We acknowledge support from the National Institutes of Health (grants R01-EB005740, R01-CA134633, R01-EB003453, R01-HL081349, and RO1-EB007825). The Pittsburgh NMR Center for Biomedical Research is supported by P41-EB001977.