Nanoparticle drug delivery holds significant promise for cancer and other diseases by enabling temporally and spatially controlled delivery of therapeutics with reduced systemic toxicity (Luo 2023). However, efficient transport and accumulation at the target site remain the primary obstacles limiting its clinical impact (Coelho et al 2010). Most systemically administered nanoparticles are sequestered by the mononuclear phagocyte system and eventually accumulate in the liver and spleen (Ngo et al 2022), while only a small portion reach target regions, such as small tumors. In this context, meta-analyses have shown that a median of only 0.7% of the injected dose (ID) reaches solid tumors, largely independent of nanoparticle size, shape, composition, or surface chemistry (Wilhelm et al 2016, Cheng et al 2020, Chen et al 2023). Importantly, these same meta-analyses reveal a gap in systematic, quantitative evaluation of nanoparticle biodistribution dynamics: only a small fraction of studies report quantitative biodistribution data at three or more time points (Chen et al 2023). This highlights the need for improved tools and methodologies to rigorously assess and overcome barriers to effective nanomedicine delivery.

Non-invasive quantitative imaging techniques are powerful tools for evaluating nanoparticle biodistribution dynamics. Both magnetic resonance imaging (MRI) and nuclear imaging, such as positron emission tomography (PET) and single-photon emission computed tomography (SPECT), allow for longitudinal studies in vivo but have significant drawbacks in studying nanoparticle biodistribution quantitatively. MRI contrast is indirect, arising from magnetic nanoparticle (MNP) or gadolinium-based agents that modulate water proton relaxation times, producing T2 or T1 contrast, respectively (Estelrich et al 2015). The technique might not be entirely quantitative due to this modulation also depending on tissue contrast (Lind et al 2017) and requires the use of specific acquisition sequences or analysis techniques (Hoopes et al 2012, Lind et al 2017). Although PET/SPECT offer high sensitivity and quantitative capability, they rely on short-lived radiolabels produced in cyclotron facilities (Skotland et al 2022) and assume stable label-nanoparticle coupling. Any radiolabel dissociation leads to off-target uptake, such that the measured biodistribution reflects the radioisotope rather than the true in vivo fate of the MNPs (Chakravarty et al 2017). Fluorescence imaging is a simple and widely available alternative but is greatly affected by tissue-dependent attenuation (Liu et al 2012) and signal distortion due to quenching, dequenching and saturation of the fluorophores used that hinder quantification (Meng et al 2018).

Magnetic particle imaging (MPI) is an emerging imaging modality that leverages the unique magnetic response of engineered MNPs to generate the image. It relies on a strong selection gradient magnetic field to generate regions of MNP saturation, and a small field-free region (FFR) where the MNP can respond to a weaker uniform alternating magnetic field. This response generates a signal in the MPI receive coils, while MNPs outside the FFR do not (Knopp and Buzug 2012). To generate an image, the FFR is scanned across the field of view (FOV), and the result is a map of signal intensity, which is directly proportional to the mass of MNP in a particular location. Most importantly, MPI does not display tissue attenuation and is quantitative in nature, so it can be used to produce MNP biodistribution maps non-invasively in vivo and throughout timepoints. Its attributes of negligible tissue attenuation and background signal, linear quantitative behavior, lack of ionizing radiation, and high sensitivity make MPI a promising modality for the evaluation of nanoparticle biodistribution. However, MPI resolution is currently in the order of 1–2 mm, similar to PET/SPECT, making it challenging to discern nearby signals within a FOV (Fink et al 2023, Fernando et al 2024). This poses challenges when applying MPI for in vivo studies, especially in small animals like mice.

Recent articles on MPI signal identification, separation and quantification have pointed out a phenomenon known as ‘shine-through’ or ‘spillover’ that must be accounted for to improve accuracy and reliability of quantitative MPI (Sehl et al 2024, Shakeri-Zadeh et al 2025). This phenomenon, which is also prevalent in MRI (Gatidis et al 2015, Perri et al 2015, Duran et al 2014) and nuclear imaging (Abdul-Fatah et al 2009, Kolb et al 2015, den Toom et al 2020), refers to the leakage of signal from adjacent areas within a region of interest (ROI), which significantly affects in vivo quantification of target sites adjacent to vasculature in early timepoints or adjacent to large accumulation organs like the liver for longer timepoints after systemic administration of the tracer (Shakeri-Zadeh et al 2025). Shakeri-Zadeh and coauthors analyzed the spillover effect on MPI images in controlled phantoms, where they calculated the total signal for fiducials at different distances from more-concentrated targets. They further evaluated spillover in vivo in a live mouse subjected to three consecutive systemic tracer administrations through a tail catheter at 40 min intervals, leading to saturated liver/spleen macrophage uptake. They prepared two fiducials with different amounts of tracer and placed them in different positions with respect to the accumulated signal, yielding an unintended signal increment in the fiducials due to spillover from the liver/spleen. While these authors studied signal increment due to spillover in terms of signal and acknowledge that it would result in overquantification, they do not transform signal values into mass, nor do they suggest a strategy to counteract the spillover. Rather, they affirm that appropriate calibration and optimization can preserve MPI’s quantitative accuracy, and that the MPI community needs to develop methods to account for and further reduce spillover effects.

Anatomically correct phantoms serve as valuable tools in preclinical research, allowing for the simulation of imaging conditions without the need for live animal experimentation (Wegner et al 2023), advancing the 3R principles promoting the ethical use of animals in scientific research (MacArthur Clark 2017). Furthermore, these phantoms can be produced via additive manufacturing, providing accurate anatomical structures while reducing the cost of tooling (Wegner et al 2023). Our group previously reported the design and use of a 3D-printed mouse phantom to investigate the impact of magnetic tracer accumulation in the liver on MPI sensitivity in brain and breast tumor models (Sarna et al 2022). That 3D-printed phantom was developed using computer aided design (CAD) techniques to extract the mouse anatomy from the Digimouse 3D whole body mouse atlas surface tessellation data (Dogdas et al 2007). In this article (Sarna et al 2022) the authors reported quantification of signal in the brain and breast tumor insert in the presence of a liver cavity filled with 10 and 200 gFe, respectively. They discussed difficulties that arise due to the presence of the liver signal, such as identifying and thresholding signals in the ROI, as well as their impact on the MPI limit of detection. However, their study did not systematically evaluate the effect of liver signal when varying the distance with respect to the target site nor did they propose strategies to improve quantification accuracy.

In this work we report a new design for the 3D-printed mouse phantom that consists of a fillable liver cavity, ports to place capillaries in the brain and lung regions, and a hind-flank cavity. We acquired images of the phantom emulating situations where high liver uptake coexists with low MNP accumulation in target regions. We considered scenarios representative of different tumors: (i) small, internal and far from the liver; (ii) superficial, spatially extended and far from the liver; and (iii) localized near the liver, where spillover is expected to be most severe. We tested quantification using different segmentation approaches, such as threshold-based and constant volume spherical segments and we developed a subtraction strategy to mitigate liver-induced spillover.

2.1. Materials

For the synthesis of the MNPs, an iron(III) oleate precursor was prepared in lab from iron(III) acetylacetonate (98% pure) purchased from TCI American and oleic acid (90% technical grade) purchased from Sigma-Aldrich. Other materials involved in the synthesis and washing procedures were oleyl alcohol (80%–85% technical grade), hexane (98.5%, certified ACS), toluene (99.5%, certified ACS), ethanol (200 proof), and tetrahydrofuran (THF, 99.8% for HPLC) purchased from Thermo Fisher Scientific.

For the coating of the MNPs, the coating polymer molecule was synthesized using methoxy polyethylene glycol with MW of 5kDa purchased from JenKem USA, 3,4-Dihydroxy-L-phenylalanine (98%), N-Hydroxysuccinimide, and chloroform were purchased from Sigma-Aldrich. Sodium nitrite was purchased from Fisher Scientific and N,N’-Dicyclohexylcarbodiimide was purchased from Thermo Fisher Scientific.

For the iron quantification in the MNP stock, nitric acid (67%–70%, for ultra trace elemental analysis) and hydroxylamine hydrochloride (99%) were purchased from Thermo Fisher Scientific and 1,10-phenanthroline monohydrate (99.5%, ACS certified) was purchased from Sigma-Aldrich.

For 3D printing, Clear V4 Resin was purchased from Formlabs Inc. and isopropanol (99.9% for HPLC) from Thermo Fisher Scientific.

2.2. MNP synthesis

The MNP cores were synthesized through an esterification process described in Velazquez-Albino et al (2026). Particularly, 13 ml of oleyl alcohol were added to a 100 ml three-neck flask, placed in a heating mantle, and mixed using a magnetic stir bar and plate. The reactor’s left neck was connected to a Schlenk line, and the middle neck had a rubber septum holding a thermocouple used to monitor the temperature throughout. A glass stopper was added to the right neck of the reactor before starting a vacuum treatment for 1 h while heating to 140 C. After the vacuum treatment, the reactor was purged with Argon. Then, the reactor was wrapped in insulation before heating to the reaction temperature of 320 C. After reaching the aforementioned temperature, the iron oleate was dripped from the middle neck of the reactor at 0.16 ml min using a syringe pump. MNP crude was washed prior to polymer coating using a solvent/anti-solvent wash procedure with magnetic separation in a Halbach array. Specifically, 1 ml of the crude from the reaction mixture was added to a 15 ml centrifuge tube with 0.3 ml of hexane and 1 ml of ethanol. The solution was vortexed and placed in a Halbach array for 10 min. Following, the supernatant was decanted and the MNPs were resuspended into 1 ml of hexane along with 1 l of oleic acid. The solution was sonicated for 1 min before ethanol was added and the mixture was placed back in the Halbach array. This was repeated one time further and the final solution was resuspended in THF.

MNPs were imaged using a FEI Talos F200i S/TEM at 200 kV. Washed MNP solution was dropped onto a 200-mesh carbon-coated copper grid. Images were analyzed using MATLAB code to determine the diameter of over 1000 particles to generate a diameter histogram. A representative transmission electron microscopy image of the synthesized particles can be seen in figure S1(A) in the supplementary material, along with the histogram in figure S1(B). Their average diameter is 19 nm.

2.3. MNP coating

Polymer coating of the MNPs was carried out using a ligand exchange method. Therein, oleic-acid stabilized iron oxide nanoparticles were coated with an in-lab synthesized polyethylene glycol-based polymer possessing a 6-nitro-L-3,4-dihydroxyphenylalanine as an anchor group (nDPEG). The nDPEG ligand was synthesized as reported in the literature with slight modification (Napolitano et al 1992, Amstad et al 2009). Due to its high affinity towards the iron oxide MNPs surface, the nDPEG ligand conjugated to the particles, enhancing their colloidal stability. For this purpose, 4 mg of oleic-acid stabilized MNPs in 0.4 ml toluene was added to a solution of 22 mg of nDPEG in 4.6 ml toluene prepared by heating at 100 C in a 15 ml Pyrex tube. After probe sonication (750 W, 35% amplitude, 1 min), the particle solution placed on a heating block at 100 C for 24 h. Next, after cooling down the solution, 15 ml of diethyl ether were added, and the nDPEG-coated MNPs were magnetically separated using a Halbach array. After, the MNPs are redispersed in 4 ml of THF with probe sonication (750 W, 35% amplitude, 1 min) and purified by repeatedly washing with diethyl ether and separating using the Halbach array. Finally, the nDPEG-coated MNPs were dispersed in deionized (DI) water and further purified by passing the solution through a Miltenyi magnetic column.

2.4. Iron quantification

The iron concentration for the nDPEG-coated MNP stock was determined through the 1,10- phenanthroline assay, following a similar procedure to the one reported in the standard (ASTM Committee E15 on Industrial and Speciality 2004). In particular, 10 l of MNP solution in DI water were digested in 70% nitric acid overnight in a heating block at 100 C, in triplicate. Following digestion, 10 l of each replicate was placed in a quartz plate and liquid was evaporated in a heating block at 115 C. The quartz plate was placed in the Opentrons OT-2 Liquid Handler to complete the assay, where 46 l of DI water was added to each replicate well, followed by 30 l of hydroxylamine solution. An hour after hydroxylamine addition, the liquid handler added 49 l of sodium acetate solution and 75 l of 1,10-phenanthroline, for a total of 200 l of liquid in each well. Simultaneously, reference samples with known iron masses were prepared and underwent the same procedure in the robot. The plate is removed from the robot and placed in the Spectramax-M5 Plate Reader, and the end-point absorbance is measured at 508 nm. Concentrations for each nDPEG-coated MNP aliquot were determined by relating the absorbance to that of the reference samples.

2.5. MPI performance

To determine the coated MNP performance in MPI, we used a MOMENTUM MPI Scanner (Magnetic Insight, Alameda, CA, USA) in the Relax mode and fitted it to a Langevin derivative model to determine the signal intensity and full-width-at-half-maximum (FWHM), relating to the sensitivity and resolution of the MNPs, respectively. A 10 l aliquot of MNP solution was loaded in a microcentrifuge tube and scanned in this mode. The results can be seen in figure S1(C) of the supplementary material. The signal intensity obtained from the fits was 141 mgFe and the FWHM 8.5 mT.

2.6. 3D-printed phantom design

This study utilized existing CAD files (Sarna et al 2022) of the Digimouse 3D whole body mouse atlas reported by Dogdas et al (2007) to facilitate the creation of a custom mouse phantom in OnShape (OnShape, Inc.). The initial design leveraged CAD techniques to generate 3D-printable models of the mouse anatomy using surface tessellation data. The original body and organ CAD geometries were reused and independently modified in this work to create a new phantom design. The external mouse body was segmented into head, torso, and hindquarter components using two transverse planes and the Split tool. Alignment pegs and corresponding holes were added using extruded circular sketches to enable repeatable assembly and positioning within the animal bed.

The liver cavity was created by subtracting the anatomical liver geometry from the torso segment. Fill ports and air vents were added using Extrude-Remove operations to allow the cavity to be filled with tracer solution while permitting air to escape during filling. In contrast, the brain and lung regions are represented by cylindrical capillary channels created using Extrude-Remove operations. These channels were positioned through the centers of the corresponding anatomical structures to provide anatomically accurate horizontal placement of capillary tube samples. A capillary filling guide was also designed to ensure consistent vertical positioning of the tracer sample.

Two hindquarter designs were developed. The first consisted solely of the hindquarter segment and was used for brain and lung imaging studies. The second incorporated a removable flank tumor insert. The tumor insert was designed as a spherical cavity enclosed within a solid body and included fill ports and air vents for tracer loading. To ensure repeatable positioning, a cross-shaped alignment feature was added to the insert using the Extrude tool, and a corresponding cavity with a small clearance tolerance was removed from the hindquarter segment using Extrude-Remove. All models described can be found in the data repository associated with this article or in the lab’s GitHub repository.

2.7. 3D print processing

All CAD files were exported as STLs from OnShape and formatted for printing using PreForm (Formlabs Inc.). Each model was 3D printed with a Form 3 stereolithography printer (Formlabs Inc.) using Clear V4 resin with a layer size of 0.100 mm for the bed and 0.050 mm for the models. During the 3D-print processing procedure, which consists of soaking prints in an isopropanol bath and curing the resin, all cavities were manually cleared of resin. Cavities with narrow openings, such as the liver and flank tumor cavities, pose difficulties in resin removal. This leads to inconsistencies in the true volumes of each model. To address this, the resulting models were characterized by filling the cavities with DI water and measuring the mass of the model before and after filling. The average difference in mass resulted in average loaded mass, which directly correlates to the average volume as the density of water is 1 g ml. These average volume measurements were later utilized in dilution calculations. We obtained an average flank volume of 65 l with a standard deviation of 3 l and an average liver cavity of 830.5 l with a standard deviation of 0.4 l.

The resin is diamagnetic, with a susceptibility close to that of water (Sangal et al 2023) and scans of 3D printed parts devoid of MPI tracer confirm that there is no additional signal relative to empty bore scans. Once excess resin was removed, the 3D prints were cured in a FormCure for 15 min at 60 C. Following the processing, each model was scanned in the MOMENTUM MPI Scanner (Magnetic Insight, Alameda, CA, USA) in 2D High Sensitivity (3.0 T m gradient strength) to ensure no magnetic contamination on the prints.

2.8. Cavity and capillary filling

A single dilution at 0.12 mgFe ml was prepared for filling the liver part, allowing for the filling of the 830.5 l cavity with 100 gFe. The dilution was placed into the model with a 1000 l pipette and special attention was put into eliminating air bubbles through the air vent by gently tapping the model against the preparation surface. Once filled, a ball of putty (Chā-Seal, Kimble) was gently pressed on the fill port and air vent to seal the model and prevent leaks.

For the brain and lung samples, a serial dilution of a 0.98 mgF ml stock was prepared with gradually decreasing iron masses ranging from 2.5 to 0.05 gFe. Capillary tubes with internal diameters of 0.8 mm were filled with around 2.5 l of each dilution using a 2.5 l pipette. Each sample’s position was adjusted using the 3D-printed capillary filling guide displayed in figure S2 in the supplementary material to ensure the sample was contained inside the phantom once placed into the corresponding capillary hole. All the capillaries were sealed on both ends with Chā-Seal and the sample position verified again using the capillary filling guide in case movement was promoted by the sealing process.

The flank tumor samples were prepared through the serial dilution of a 0.038 mgFe ml stock. The final samples had gradually decreasing iron masses ranging from 2.5 to 0.05 gFe in 65 l of DI water. The model was filled with a 100 l pipette, tapped to remove air bubbles and sealed with Chā-Seal in fill port and air vent. The initial concentrations of each serial dilution were calculated so we could fill the highest test mass capillary or cavity without diluting.

Reference curve samples were created with varying masses with each volume sample having its own respective reference curve due to previous reports stating that quantification accuracy depends on matching reference and sample volumes (Zammataro et al 2025). The 2.5 l sample (brain and lung) reference curve consisted of eight samples with iron masses 0, 0.05, 0.1, 0.25, 0.5, 1, 1.75 and 2.5 gFe in 2.5 l filled capillary tubes. The 65 l flank tumor reference curve also consisted of eight samples with iron masses 0, 0.05, 0.1, 0.25, 0.5, 1, 1.75 and 2.5 gFe in 65 l flank cavities.

All ROI and reference samples were prepared the day of imaging to ensure the correct concentration.

2.9. Image acquisition

3D MPI scans were obtained on the MOMENTUM MPI Scanner (Magnetic Insight, Alameda, CA, USA) in standard mode (5.7 T m gradient strength) for all sample configurations. The 3D scans were acquired utilizing 35 projections in the 6 (), 6 () and 12 () cm full FOV, with a 0.3 cm offset in the direction, to encompass the entire phantom. After each 3D MPI scans, computed tomography (CT) scans were collected on an IVIS Spectrum CT (Perkin Elmer), maintaining phantom position consistent.

In particular, the phantom was imaged with gradually decreasing iron mass in each ROI (brain, flank and lung) and a liver cavity filled with 100 gFe (what we call ‘subject scans’). The BR2 and LU2 holes were used to place the capillaries into for the brain and lung dataset, correspondingly. Also, a phantom with an empty ROI and just the liver cavity filled was imaged each day of the study (‘reference scan’). The reference samples and an image registration dataset were imaged in the same conditions. The registration dataset consisted of a 3D MPI and a CT scan of four fiducials with MNP solution in 1:1 DI water and Omnipaque CT contrast agent (GE HealthCare) taped into the bed (two in the and two in the direction). The time for MPI acquisition was 50 min for each 3D scan.

2.10. Image analysis

The analysis of all MPI scans was conducted using 3D Slicer (Slicer 5.8.1), an open-source software for medical image analysis (Kikinis et al 2013, BWH and 3D Slicer contributors), complemented by Python scripts. The MPI data acquired consisted of 35 projections obtained through an X-space direct reconstruction and the application of a manufacturer-implemented equalization filter (Lu et al 2013). Reconstructed volumes were obtained from the scanner’s implementation of filtered back-projection with default parameters and no additional filtering or post-processing was applied. The data was analyzed as 3D volumes (filtered back projection reconstruction from the 35 projections) or 2D volumes by taking just the center projection of the 3D scan (17th projection). Linear transformations were performed to the MPI and CT volumes to display the data in the correct coordinate system.

Slicer’s Landmark Registration Tool was used to obtain the registration matrices for the study. The process consisted in colocalizing the four fiducials in the CT scan from the registration dataset with their signal in the corresponding MPI images (both as 3D and 2D volumes).

A Python script to segment and quantify signals from the MPI phantom data was created. The script was run in Slicer’s Python console. An overview of the analysis pipeline done with the script can be seen in figure S3 in the supplementary material. The input is a comma-separated value table, detailing each MPI scan label (i.e. ROI and iron mass) and path, as well as the corresponding CT scan path for that configuration. The script prompts the user for the desired analysis mode (3D or 2D MPI volume) and registers the MPI volume with its CT scan by applying the corresponding registration matrix. It creates a mouse contour segment from the high-pass thresholding of the phantom-mouse body from the CT, as well as a liver segmentation from the MPI volume by searching for the maximum signal () in the liver region and thresholding all the voxels with values from 0.5 to (0.5Max Threshold). These two segments provide a spatial reference when displayed with the MPI scan.

To obtain segmentations of the ROIs being considered (i.e. brain, flank or lung), the user is prompted to enclose the ROI region with an interactive-boundary box and a search for the maximum value is performed inside the box. In this article we explore different segmentation approaches for the ROI signals: 0.5Max Threshold (Threshold), CV and constant volume with subtraction (CVS). Once segmented, the total signal for the ROI is calculated as the , where is the number of voxels and is the average signal in the segment.

To convert total signal to quantified iron mass of the ROI, the same segmentation approach is used to segment the reference samples with known iron mass and their nominal iron mass vs Total Signal is fitted with the linear regression , obtaining and . This conversion equation is then used to transform any total signal to quantified iron mass. Note that we use reference samples with volumes similar to that of the ROI we want to quantify. For example, to obtain conversion equations for brain and lung, we obtain and for capillary reference samples while for flank we used 65 l cavities as reference samples. Figure S4 in the supplementary material shows the nominal iron mass vs. total signal for the reference samples for all methods used to segment and table S1 has the fit parameters and , as well as the value for the data.

3.1. 3D-printed phantom design

Anatomically-correct mouse phantoms with multiple fillable cavities enable the emulation of biologically-relevant scenarios

The phantom design is based on previous models and its design is described in section 2.6. The anatomical structure of the mouse is divided into three parts: the head, the torso, and the hindquarters. This division was achieved using two transverse sections across the mouse. To improve ease of use, and allow interchangeability of parts, the phantom parts were designed to be connected using friction-fitting pegs, enabling the phantom to be handled as a unified object while retaining the modularity of its components.

The head portion design includes two cylindrical cavities across the y axis each with a diameter of 1.9 mm. These cavities house tracer filled capillary tubes (0.8 mm inner 1.6 mm outer diameter) to represent the two hemispheres of the brain. The left hemisphere is labeled BR1, and the right is labeled BR2 (see figures 1(A)–(C)).

Figure 1. Additive manufacturing of mice phantoms enables the systematic study of biomedically relevant scenarios and consistent tracer positioning. (A) Solid and (B) transparent top views of the 3D-printed mouse phantom depicting regions of interest. (C) Side view of the transparent phantom illustrating locations for MNP tracer insertion. (D) Photograph of the 3D-printed phantom filled with a MNP solution containing 100 gFe in the liver, 2.5 gFe in the flank and two capillaries with 2.5