2.2. Surface engineering of UPSN and radiolabeling.

Minor tweaking of the synthetic precursors, i.e. substitution of 0.1 mol % PEG₅₀₀-silane by NH₂-PPO₃₅₀-silane conferred surface functional amine groups on UPSN, for further conjugation of radiometal chelators (CHX) and dyes, for in vivo studies. Aminated UPSN was conjugated to either deferroxamine (DFO) or 2-S-(4-Isothiocyanatobenzyl)-1,4,7-triazacyclononane-1,4,7-triacetic acid (NOTA), following previously reported amine-isothiocyanate chemistry.[17] TEM images indicated no change in morphology. (Figure 1C and Supplementary figure S1C) DLS measurements indicated uniform, well-dispersed populations for both UPSN-DFO (14.78 ± 2.78; PdI: 0.146) and UPSN-NOTA (12.76 ± 2.40; PdI: 0.19) and negligible change in surface charge. (Figure 1D–E) Subsequently, UPSN-DFO was radiolabeled with long-lived radioisotope, zirconium-89 (⁸⁹Zr; t_1/2 = 78.4 h) for long-term assessment of UPSN biodistribution, while UPSN-NOTA was labeled with short-lived copper-64 (⁶⁴Cu; t_1/2 = 12.7 h) for tumor tropism studies, following previously optimized protocols.[17, 18] As seen in Figure 1G and ​and1H,1H, both ⁶⁴Cu-NOTA-UPSN and ⁸⁹Zr-DFO-UPSN demonstrated high radiochemical yields (> 85 %) within 2 h of incubation, and final products were isolated with high radiochemical purity. Serum stability studies were performed with radio-TLC, and indicated excellent fidelity of the isotope, > 62 % and 40 % intact radioactivity, 2 and 14 days post-incubation for ⁶⁴Cu-NOTA-UPSN and ⁸⁹Zr-DFO-UPSN, respectively. (Supplementary figure S3). The gradual loss of isotopes from the nanoconstructs may be attributed to both detachment from the chelator, as well as dissolution of the nanoparticles (previously shown in Supplementary figure S2).

2.3. Pharmacokinetics of ⁶⁴Cu-NOTA-UPSN and ⁸⁹Zr-DFO-UPSN.

Whole-body PET imaging was employed to gain greater information about the key components of UPSN PK, including biodistribution, stability, and clearance. ⁶⁴Cu-NOTA-UPSNs were administered systemically in healthy, non-tumor-bearing female Balb/c mice, with concurrent imaging using the following protocol: real-time dynamic PET scan up to 1 h post-injection (p.i.), followed by serial static scans at 2, 7, 18, 48 and 72 h p.i. (Supplementary figure S4A) ⁶⁴Cu-NOTA-UPSNs demonstrated prolonged systemic circulation, with 32.8 ± 0.1 %ID·g⁻¹ plasma concentration at 10 min p.i., decreasing slowly over time thereafter. (Supplementary figure S4B) A two-compartment PK model with an initial distribution phase (t_1/2,α ≈ 1.5 h) and a terminal elimination phase (t_1/2,β ≈ 16 h) best described the observed systemic concentration kinetics of ⁶⁴Cu-NOTA-UPSN; area under the curve (AUC_0−∞) was found to be 590.6 %ID·g⁻¹·h. (see Figure 4F and Methods for details) Region-of-interest (ROI) analysis of major organs indicated reasonable exposure to UPSNs and significant clearance within 72 h p.i.. These in vivo findings were confirmed via terminal PET scans followed by ex vivo gamma counting of radioactivity in major tissues. (Supplementary figure S4C)

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Figure 4.

In vivo ROI quantification and ex vivo biodistribution study.

(A) Tumor accumulation efficiency of ⁶⁴Cu-NOTA-UPSN in 4T1 and MDA-MB 231 tumors. Comparison of (B) Area-under-the-curve (AUC) for major organs and tumors, (C) tumor-to-blood ratio, (D) tumor-to-liver ratio, and (E) tumor-to-muscle ratios, between the two groups. (F) Plasma concentration kinetics of ⁶⁴Cu-NOTA-UPSN (red circles) and corresponding bi-exponential fit from a two-compartment PK model (blue curve) to evaluate plasma half-lives of ⁶⁴Cu-NOTA-UPSN: distribution t_1/2,α ≈ 1.5 h and elimination t_1/2,β ≈ 16 h. (G) Ex vivo biodistribution profiles of the two groups, 72 h p.i. (n = 4). *p < 0.05, **p < 0.01, ***p < 0.001, ****p < 0.0001, ns = non-significant (p > 0.05).

Moreover, ⁶⁴Cu-NOTA-UPSN demonstrated excellent ability for high-resolution sentinel lymph node mapping upon intradermal injection. Progressive delineation of the popliteal, sciatic, lumbar, renal, and pancreatic lymph nodes (LNs) was possible on longitudinal PET scans from 30 min p.i. up to 48 h p.i. (Supplementary figure S5A) ⁶⁴Cu-NOTA-UPSNs demonstrated maximum homing into the popliteal LNs with ~30 %ID·g⁻¹ at 30 min p.i. and prolonged retention with ~10 %ID·g⁻¹ still present at 48 h p.i. (Supplementary figure S5C) Ex vivo assessment with the gamma counter at the end of the 48 h time-point corroborated the results from in vivo ROI analysis. (Supplementary figure S5D) Overall, the results demonstrate that ⁶⁴Cu-NOTA-UPSNs could serve as excellent contrast agents for sensitive, precise, and prolonged delineation of sentinel lymph nodes, and hence for indicating the extent of metastatic spread of primary tumors.

To further investigate the long-term behavior, ⁸⁹Zr-DFO-UPSN was i.v. injected into healthy non-tumor-bearing Balb/c mice, and in vivo kinetics were monitored for a period of 2 weeks. Serial maximum intensity projection (MIP) images are shown in Figure 2A. Long-circulating ⁸⁹Zr-DFO-UPSN showed plasma concentration (40.1 ± 3.9 %ID·g⁻¹ at 1 h p.i.), which decreased gradually over time with an elimination half-life of ≈ 31 h, as estimated by a one-compartment PK model (see Supplementary figure S6D and Methods for details), giving an AUC_0−∞ of 1758.2 %ID·g⁻¹·h. Metabolic studies performed in parallel indicated that UPSNs cleared primarily through the hepatobiliary pathway; with 35.2 ± 5.2 %ID of UPSNs excreted in the feces by day 10. (Figure 2E and Supplementary figure S6A) DLS measurements indicated that ~8 % (by number) of UPSNs demonstrated HD below the renal threshold of ~8 nm (Figure 1D), possibly contributing to partial clearance from the renal pathway (typically faster than hepatic route). ⁸⁹Zr-DFO-UPSNs demonstrated almost complete clearance from the body with only 2.34 ± 0.15 %ID being retained 2 weeks p.i., indicated by almost background level of radioactivity on the terminal PET scan (Figure 2A,​,F)F) After an initial hepatic accumulation of 15.5 ± 2.9 %ID·g⁻¹ at 1 h p.i., ⁸⁹Zr-DFO-UPSNs cleared gradually, reducing to 5.7 ± 1.6 %ID·g⁻¹ at day 14 p.i. (Figure 2B) Similarly, accumulation of ⁸⁹Zr-DFO-UPSNs in the spleen reduced from 10.3 ± 2.7 to 7.2 ± 2.2 %ID·g⁻¹. AUCs for liver and spleen compartments were found to be 2362.95 and 2820.9 %ID·g⁻¹·h, respectively. (Supplementary Table S1) Of note, ⁸⁹Zr signal remained conspicuously absent from the bones up to almost a week p.i. and only appears marginally in the joints thereafter, indicating the superior radioastability of ⁸⁹Zr-DFO-UPSNs (non-chelated ⁸⁹Zr is an osteophile).[19] (Figure 2A–B) Release of the free isotope and its osteal accumulation could be possibly attributed to the dissolution and excretion of the UPSNs, in accordance with the observed in vitro serum stability data (Supplementary figure S3B–C). Uptake in the muscle remained low (< 1 %ID·g⁻¹) throughout the observation period. (Figure 2B)

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Figure 2.

Long-term biodistribution of ⁸⁹Zr-DFO-UPSN.

(A) Maximum intensity projections (MIP) from longitudinal PET scanning of healthy Balb/c mice, i.v. injected with ⁸⁹Zr-DFO-UPSN. (B) Time-activity curves (TAC) for major organs obtained from in vivo region-of-interest (ROI) analysis. (C) Schematic of semi-mechanistic mathematical model as developed for UPSNs. Liver and spleen are further sub-compartmentalized into vascular (red), extravascular (blue), and phagocytic (green) compartments. Red arrows depict plasma flow; blue arrows indicate lymph flow; yellow arrows indicate excretion (solid: macrophage; dotted: hepatobiliary); and green and white arrows depict transvascular flow and phagocytic uptake, respectively. (D) TAC obtained from fitting the model to the data. (E) Cumulative hepatic clearance of ⁸⁹Zr-DFO-UPSN over a period of 2 weeks. (F) Whole body residual radioactivity (%ID) retained in the mice over two weeks. (G) Sub-compartment activity kinetics for liver and spleen as predicted by the model. (H) Phagocytic uptake rate constant (k_phag) and muscle reflection constant (σ_m) estimated from least squares regression of the model to the data. Data represents mean ± SD (n = 4).

Unlike our previous modeling approaches to study tissue disposition kinetics[20] and tumor delivery efficacy[21–25] of NPs, here we developed a multi-compartment, semi-mechanistic model, which is a reduced physiologically based pharmacokinetic (PBPK) model[26], comprising a systemic blood pool, RES (i.e. liver and spleen), muscle, and a facultative tumor compartment (applicable for tumor-bearing groups only), which represent the dominant distribution sites of the UPSNs in vivo, connected in an anatomical fashion via plasma (red arrows) and lymph (blue arrows) flow. (Figure 2C and Supplementary figure S7) In traditional PK modeling, organs are modeled as well-stirred, black-box like compartments with homogenous, time-dependent exposure to administered drugs.[20] This approximation often leads to a limited understanding of the pharmacological behavior of the administered agent, thus resulting in partial or heterogeneous responses in the clinic. This issue is especially relevant in the case of modeling the uptake of nanoformulations by the RES organs, where resident macrophages (Kupffer cells and splenic macrophages) respond differently to NPs than to small molecules. The model employed in this study incorporates mechanisms pertinent to NP-cellular interactions by compartmentalizing each organ into physiologically relevant sub-compartments (Methods and Supplementary Information S1 for details).

We began by fitting the PBPK model to the time-course PET imaging data for different ROIs (Figure 2D) and estimated the parameters (Figure 2H, Supplementary Table S7) including k_phag (0.01 h⁻¹), σ_m (0.98), and f (895), k_phag represents the time-averaged phagocytic uptake rate constant of hepatic and splenic sinusoidal macrophages, and an estimated value of 0.01 h⁻¹ suggests a timescale of 100 h for the phagocytic process, which indicates a relatively slow macrophage-driven sequestration of the UPSNs with respect to comparable particles reported in the literature [27]; σ_m is the reflection coefficient of muscle microvasculature, and a value ~1 indicates very high resistance to the transvascular extravasation of UPSNs, primarily due to the small size (~5 nm) of vessel wall pores in the muscle tissue. [28] The f parameter is a ratio of plasma to lymph flow rates (see Methods); a value of 895 indicates that the convective extravasation of UPSNs via lymph is slower than the lymph flow itself (a typical physiological value for f is ≤ 500).[29] This disparity between UPSN extravasation rate and lymph flow rate is possibly because of interactions of UPSNs with intravascular components or endothelial cells, causing reduced transvascular flow of UPSNs. Moreover, model predictions of UPSN mass kinetics from the model show strong correlation with experimental data (Pearson correlation coefficient R = 0.99; Supplementary figure S6C), thereby validating the mechanistic basis of the model.

The calibrated model was then employed to investigate the RES disposition kinetics of UPSNs as shown in Figure 2G. Model simulations of UPSN mass kinetics in the RES sub-compartments indicate the dominant role of hepatic phagocytes followed by splenic phagocytes in governing the retention of NPs in the RES. The time-activity curves (TACs) generated for various sub-compartments in liver yielded AUC_0–340h values of 505.3, 1551.9, and 1272.5 %ID·h for the vascular, extravascular, and phagocytic sub-compartments, respectively. For the spleen, the AUC_0–340h values for vascular, extravascular, and phagocytic sub-compartments were 47.4, 16.7, and 119.5 %ID·h, respectively. (Supplementary Table S2)

2.4. In vivo passive tumor targeting with ⁶⁴Cu-NOTA-UPSN.

To investigate whether the prolonged circulation and initial escape from the RES can be translated to improved accumulation at the intended tumor site, tumor disposition kinetics of UPSNs were tested in murine TNBC model. Heterogeneity in the EPR effect has been well-documented, and is known to be influenced by both vascular bed and surrounding stroma, as well as tumor type, size, and other physiological and environmental factors.[30] To explore how such heterogeneities affect the tumor-tropic transport of UPSNs, systematic in vivo studies were performed in two TNBC models, 4T1 (rapidly growing syngeneic model with pronounced microvasculature) and MDA-MB 231 (slow growing, human xenografts with diminished microvascular network). Tumors were implanted in age-matched mice and used when they reached 5–8 mm in diameter (10 days for 4T1 and 21 days for MDA-MB 231 tumors).

⁶⁴Cu-NOTA-UPSNs were systemically administered into tumor-bearing mice, followed by serial PET scanning up to 48 h p.i. (Figure 3A) Dominant signal from the heart for up to 16 h p.i. indicated that UPSNs were largely confined to the blood pool and cleared slowly over time. (Figure 3B–C) AUC_0–48h values of 792.08 and 536.33 %ID·g⁻¹·h were measured in 4T1 and MDA-MB 231 tumor-bearing mice, respectively. (Supplementary figure S8B and S11C) UPSNs remained in the blood pool at the end of the 48 h observation period, with 8.3 ± 1.6 and 6.1 ± 1.6 %ID·g⁻¹ in 4T1 and MDA-MB 231 groups, respectively (Figure 3B–C). RES uptake was consistent with that seen with ⁸⁹Zr-DFO-UPSN, showing an initial hepatic signal of 18.6 ±3.5 (4T1) and 12.8 ± 2.5 %ID·g⁻¹ (MDA-MB 231) at 1 h p.i. that decreased constantly to final values of 9.9 ± 0.8 and 7.6 ± 3.6 %ID·g⁻¹, respectively at 48 h p.i. (Figure 3A–C) Spleen was the second major organ of clearance, with 8.7 ± 1.4 and 3.8 ± 1.5 %ID·g⁻¹, respectively for 4T1 and MDA-MB 231 models. (Figure 3B–C). TACs for individual animals in each cohort are presented in Supplementary figure S8A and S11B and indicate uniform trends across all experimental animals.

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Figure 3.

Differential tumor uptake of ⁶⁴Cu-NOTA-UPSN in different TNBC models.

(A) Whole body MIP from longitudinal PET scans of 4T1 (top panel) and MDA-MB 231 (lower panel) tumor-bearing mice after i.v. injection of ⁶⁴Cu-NOTA-UPSN. Green arrows indicate the tumors. TACs obtained from in vivo ROI analysis of (B) 4T1 and (C) MDA-MB 231 tumor-bearing mice. (D, E) TACs derived from modeling of the observed data. Data represents mean ± SD (n = 4).

Owing to significant differences in their microvascular architectures and stromal composition, both 4T1 and MDA-MB 231 demonstrated different permeability and retention of ⁶⁴Cu-NOTA-UPSN. Representative MIPs (Figure 3A and Supplementary figure S11A) at earlier time-points indicated comparable tumor uptake of the UPSNs at 1 h p.i. with 4.4 ± 0.4 and 2.6 ± 0.8 %ID·g⁻¹ in the 4T1 and MDA-MB 231 groups, respectively. However, the passive accumulation of UPSNs at the 4T1 tumor site increased progressively over the next 48 h, reaching a maximum of 17.7 ± 1.4 %ID·g⁻¹ (Figure 4A), greater than any other passively-targeted nanoformulation reported to date.[3] Comparison with off-target organs (i.e., muscle and liver) indicated excellent tumor-to-background ratios and high contrast capability of ⁶⁴Cu-NOTA-UPSN (Figure 4C–E). As the UPSNs were cleared from the body over 48 h, the tumor-to-liver ratio increased exponentially (from 0.23 ± 0.07 at 1 h p.i. to 1.8 ± 0.02 at 48 h p.i.).(Figure 4D) Despite a favorable PK profile, accumulation of ⁶⁴Cu-NOTA-UPSN in the MDA-MB 231 tumors increased only marginally up to 16 h p.i. to a maximum value of 3.9 ± 0.4 %ID·g⁻¹, reducing thereafter to 2.8 ± 0.3 %ID·g⁻¹ at 48 h p.i. Comparison with off-target tissues (i.e., muscle and liver), yielded modest ratios of 6.91 ± 2.12 and 0.5 ± 0.12 at 48 h p.i. (Figure 4D–E) To eliminate the concern that this variation in tumor uptake resulted from a difference in their blood pool activities (Supplementary figure S14A), the ratio of UPSN accumulation in the two tumor types (T_4T1/T_MDA-MB231), as well as plasma (B_4T1/B_{MDA-MB 231}), was calculated at all time-points. As seen clearly in Supplementary figure S14B, B_4T1/B_{MDA-MB 231} ratio of 1.45 ± 0.01 at 1 h p.i. (when UPSNs are in circulation), yielded a corresponding T_4T1/T_MDA-MB231 ratio of 1.40 ± 0.14. However, by 48 h p.i., the T_4T1/T_MDA-MB231 ratio increases exponentially while B_4T1/B_{MDA-MB 231} ratio tends to 1, indicating that high accumulation of UPSNs in 4T1 indeed originated from tumor-specific effects.

Tumor permeability of ⁶⁴Cu-NOTA-UPSN, defined as ratio of NP uptake in tumor and in the blood, was found to be higher for 4T1 than that for MDA-MB 231 at all time-points except the initial scan at 1 h. (Figure 4D) This is consistent with the distribution half-life of ⁶⁴Cu-NOTA-UPSN (~1.5 h; Figure 4F), where the NPs begin to interact with the tumor vasculature, and extravasation is limited. With each longitudinal scan, as ⁶⁴Cu-NOTA-UPSNs reach a steady-state, the differences in vascular permeability between the two models become more pronounced, leading to significant differences in tumor accumulation and retention. Consequently, ⁶⁴Cu-NOTA-UPSN dose exposure to the two TNBC subtypes differed significantly, indicated by the AUC_0–48h for 4T1 (730.75 ± 115.56 %ID·g⁻¹·h), which was nearly 5 times higher than that for MDA-MB 231 (158.17 ± 14.71 %ID·g⁻¹·h). The results were further confirmed with ex vivo gamma counting (Figure 4G).

To further characterize the tumor microvascular transport differences between 4T1 and MDA-MB 231 tumors, we fitted the model to the PET data. (Figure 3D–E, Supplementary figure S9 and S12) The k_phag and σ_m parameter values estimated from the healthy cohort were used as constants in the tumor compartment-bearing model in order to estimate the k_in and k_out parameters, representing the inflow and outflow rate constants of ⁶⁴Cu-NOTA-UPSN in the tumor compartment. The k_in and k_out parameter values for 4T1 are greater than that for MDA-MB 231 (P value < 0.05); this suggests improved vasculature for 4T1, thereby allowing increased passage of NPs through the tumor and thus potentially enhanced retention. (Supllementary Table S3–S5). In terms of the RES tissue disposition, there was comparable accumulation of UPSNs in both tumor-bearing cohorts, indicating that the differences in tumor accumulation are not a result of the difference in RES uptake (Supplementary figure S9 and S12, Tables S2, S6). The strong correlation between model predictions and experimental data of UPSN mass kinetics further validated the findings (Supplementary figure S10 and S13). Of note, the sub-compartment kinetics of ⁶⁴Cu-NOTA-UPSN in liver and spleen obtained from tumor-bearing mice matched with the healthy mice. (Supplementary figure S15 and Table S2) The phagocytic compartments of liver and spleen were exposed to the least cumulative ⁶⁴Cu-NOTA-UPSN doses up to day 2 p.i., compared to vascular and extravascular sub-compartments, indicating an initial resistance to uptake by the resident phagocytes. (Supplementary table S2)

Overall, the selective tumor accumulation of UPSNs, coupled with rapid clearance from the body, can be harnessed in future studies for intrinsically targeted therapeutic delivery. Furthermore, the observations from our analysis show strong indications towards the promising application of radioisotope labeled UPSNs as a companion contrast agent for patient stratification, treatment planning, and non-invasive prediction of therapies relying on nanomaterials, and macromolecular biologics, as well as prediction and monitoring of vascular effects of anti-angiogenic therapies.

Surface modification of UPSNs.

UPSNs were surface modified with radioisotope chelators (CHX); 2-S-(4-Isothiocyanatobenzyl)-1,4,7-triazacyclononane-1,4,7-triacetic acid (p-SCN-Bn-NOTA; Macrocyclics Inc, Dallas, TX) or deferroxamine (p-SCN-Bn-DFO, Macrocyclics Inc, Dallas, TX) or fluorescent dye, fluorescein isothiocyanate (FITC) for further in vitro and in vivo studies, following procedures described previously.[17] Briefly, aqueous solution of UPSN-NH₂ was reacted with CHX-SCN or FITC-SCN in a 1:10 molar ratio. The pH of the solution was tuned to 8–9 and the reaction was carried out at room temperature with vigorous stirring for 2 h. As-synthesized UPSN-CHX or UPSN-FITC were purified on PD-10 columns (GE Healthcare) with PBS as the mobile phase to remove unreacted molecules.

Characterization of UPSNs.

As-synthesized UPSN and UPSN-CHX were characterized using transmission electron microscopy (TEM) on FEI Tecnai TF30 at an acceleration voltage of 300 kV. Images were processed and particle diameter and pore sizes were measured using ImageJ software. Hydrodynamic diameters and surface charge were measured using dynamic light scattering (DLS, Malvern Zetasizer Nano ZS). Nitrogen adsorption-desorption isotherms were measured at 77 K on a Quantachrome Nova 4000e system. The samples were freeze-dried for 48 h and surface area was determined using the BET method. Pore size distribution data was collected by the Barrett-Joyner-Halenda (BJH) method of the desorption branch of the isotherm. Fourier transmission infrared spectroscopy measurements were carried out on a Bruker Equinox 55/S FT–IR Spectrophotometer.

Synthesis of Radiolabeled

UPSNs.⁸⁹Zr-oxalate and ⁶⁴CuCl₂ were produced in an onsite cyclotron (GE PETrace) at the University of Wisconsin-Madison cyclotron facility.[17, 19] 2 nmol of UPSN-DFO was reacted with 74 MBq ⁸⁹Zr-oxalate for 2 h, in the presence of 0.1 M HEPES buffer, at pH 7–8 (adjusted using 2 M Na₂CO₃), 37 °C. ⁶⁴Cu-labeled UPSNs were similarly produced by reacting 2 nmol of UPSN-NOTA with 74 MBq of ⁶⁴CuCl_{2 in} 0.1 M sodium acetate buffer. The pH was tuned to 5.5 and reaction allowed to proceed for 1 h at 37 °C. Both ⁸⁹Zr-DFO-UPSN and ⁶⁴Cu-NOTA-UPSN were purified on PD-10 columns. Time-dependent radiochemical yields were determined via instant thin layer chromatography (radio-TLC) using 50 mM EDTA as the mobile phase. Serum stability study was carried out by incubating the radiolabeled UPSNs in 1x mouse serum over 48 h. Aliquots were drawn as regular intervals and spun at 300 kDa centrifugal filters. Radioactivity in retentate and filtrate fractions was estimated to calculate the radiochemical stability.

in vivo static and dynamic PET and ex vivo biodistribution studies.

For all in vivo PET imaging studies, scans were performed on a microPET/microCT Inveon rodent model scanner (Siemens Medical Solutions USA, Inc.). For long-term evaluation of UPSNs in vivo, healthy female Balb/c mice (n=3) were i.v. injected with 9.25 MBq of ⁸⁹Zr-DFO-UPSN, and a 60 min dynamic scan was acquired and framed into 6 frames of 10 min each, followed by serial static PET scans up to 72 h p.i.

In a separate study, tumor-bearing mice (n=4) were injected with ~ 7.4 MBq of ⁶⁴Cu-NOTA-UPSN via the tail vein and PET imaging was performed 1, 6, 24 and 48 h p.i. Image reconstruction and region-of-interest (ROI) analyses were performed on company software Inveon Research Workplace (IRW) following standard protocols, as described before.[10] All data was decay corrected and converted to activity concentration, and percentage of injected dose per gram of tissue (%ID·g⁻¹). After the final PET scans, all mice were euthanized, and their organs and tumors were harvested, wet-weighed and counted on Wizard² gamma counter (PerkinElmer). Organ radioactivity was presented as %ID·g⁻¹ after dose calibration and radioactivity decay correction.

In vivo clearance using metabolic cages.

To quantitatively evaluate the metabolic clearance profile of ⁸⁹Zr-DFO-UPSN, healthy mice (n = 3) were injected with 9.25 MBq of ⁸⁹Zr-DFO-UPSN. The mice were housed individually in metabolic cages and feces were collected at specific time-points p.i. Radioactivity in the feces were counted on Wizard² gamma counter (PerkinElmer), decay corrected and presented as percentage injected dose (%ID). The mice were PET scanned periodically to monitor the changes in whole body retention of i.v. injected ⁸⁹Zr-DFO-UPSN with time. Images were reconstructed and analyzed as described before and data is presented as %ID.

Pharmacokinetic modeling.

Empirical PK modeling[34] was employed to estimate relevant PK parameters (systemic half-life t_1/2 and AUCs) of UPSNs in healthy mice from the systemic concentration kinetics data. Based on the observations, a one-compartment PK model (Eq. (1)) was used for ⁸⁹Zr-DFO-UPSN and a two-compartment PK model (Eq. (2)) for ⁶⁴Cu-NOTA-UPSN. The following mono-exponential equation is the analytical solution of a one-compartment PK model:

Where C_b is the concentration of NPs in systemic blood; C₀ is the systemic concentration of NPs at time t = 0; and k is the phenomenological first order elimination rate constant of UPSNs used to calculate t_1/2 = ln(2)/k.

The following bi-exponential equation is the analytical solution of a two-compartment PK model:

where, C₁ and C₂ are the intercepts of the back-extrapolated initial distribution phase and terminal excretion phase, respectively, with slopes k₁ and k₂ on a semi-logarithmic scale used to calculate distribution (t_1/2,α = ln(2)/k₁) and elimination(t_1/2,β = ln(2)/k₂) half-lives, respectively. Further, the trapezoidal numerical integration method was used to estimate the AUCs of the TACs. Analysis was performed in MATLAB R2018a.

Semi-mechanistic mathematical modeling.

Our mathematical model, based on simplification of currently available physiologically based pharmacokinetic (PBPK)[26], is formulated as a system of ordinary differential equations (ODEs) accounting for the transport and cellular interactions of NPs, to describe NP radioactivity kinetics (surrogate for NP mass kinetics) in the various compartments and sub-compartments. A representative system of ODEs for a general compartment i containing all the three sub-compartments (e.g., spleen and liver) is (see Supplementary figure S7):

Vascular sub-compartment

Extravascular sub-compartment

Phagocytic sub-compartment

where, N_v,i, N_e,i, and N_p,i represent the mass of NPs in the vascular, extravascular, and phagocytic sub-compartments, respectively; N_p is the mass of NPs in the systemic blood pool (plasma compartment) and V_p is the volume of the plasma compartment; V_v,i and V_e,i represent the volume of the vascular and extravascular sub-compartments, respectively.

As represented by Equation (3), NPs entering from the plasma compartment into the vascular sub-compartment, via arterial plasma flow rate Q_i, either undergo convective transvascular extravasation to enter the extravascular space following the lymph flow rate L_i, or are phagocytized according to the phenomenological, time-averaged, first order uptake rate constant k_phag. Transvascular flow of NPs is limited by the impedance of the vessel walls, which is described as the reflection coefficient σ_i and is typically a function of NP to vessel wall pore size ratio and NP charge.[33] The remaining NPs exit the vascular space to rejoin the plasma compartment via the venous plasma flow rate Q_i − L_i. As described in Equation (4), the NPs that enter the extravascular space are either excreted via bile (only in liver and spleen), which is produced at a rate B, or exit the extravascular sub-compartment via lymph to recycle to the plasma compartment. Finally, NPs sequestered by phagocytes (Equation (5)) are eventually excreted following a phenomenological first order rate constant k_ex. The complete system of equations of the model is given in SI and was solved numerically as an initial value problem in MATLAB R2018a using the non-stiff ODE solver ‘ode45’.

Model parameterization.

Compartment and sub-compartment volumes, plasma flow rates, and excretion rates were known a priori from published literature. (Table S7)[2, 29] Due to extreme disparity in the literature, the lymph flow rates were assumed to be a fraction of plasma flow rates, $L_i=\frac{Q_i}{f}$, where f > 1, and was estimated by non-linear regression of the model to the experimental data. The other unknown parameters k_phag and σ_M were estimated by fitting the data from the healthy cohort, and the values thus obtained were used as constants for the tumor-bearing cohorts. Given that hepatic and splenic sinusoids have vessel wall fenestrations that are much larger[28] than the UPSNs being studied, we therefore fixed σ_L and σ_S (the reflection coefficients for liver and spleen) at zero for all cohorts assuming negligible resistance to transvascular flow. In the tumor bearing groups, in addition to f, the k_in and k_out parameters were estimated by non-linear regression.

Immunohistochemical (IHC) staining and immunofluorescence (IF) microscopy.

For immunohistochemical studies, 4T1 and MDA-MB 231 tumor-bearing mice were euthanized once the tumors reached 6 mm in diameter. The tumors were excised and immediately soaked in 4 % paraformaldehyde (4 % PF) at room temperature overnight with gentle shaking. Following this, the tumors were washed repeatedly in ethanol, followed by PBS, and transferred for paraffin embedding and sectioning, using standard protocols. Standard procedures were employed for hematoxylin and eosin (H&E), CD31, α-SMA and Col I staining.[35] High resolution whole tissue images were taken at 40x magnification on an EVOS™ FL Auto Imaging System. Brightfield images were taken from atleast 10 fields of view on Nikon Eclipse Ti microscope. CD31 stained sections were used to manually count the number of blood vessels in the tumor periphery and tumor center. Blood vessels with large obvious lumen and those with small or negligible lumens were used to determine vascular density. Images were analyzed on FIJI software to determine intensity, area fraction and blood vessel area. Lumen diameters were calculated as geometric mean from 4 measurements taken per blood vessel.

For fluorescence microscopy, FITC-modified UPSNs (UPSN-FITC) were i.v. injected into 4T1 and MDA-MB 231 tumor-bearing mice. Tumors, liver and spleen were excised from mice 24 h p.i., mounted in Tissue-Tek O.C.T and frozen immediately. Tissues were sectioned at a thickness of 7 μm, soaked in cold acetone for 10 min, followed by blocking with goat serum for 1 h. Human anti-mouse CD31 antibody was added and incubated at 4 °C overnight. After washing twice with PBS, goat-anti human-cy3 secondary antibody was added and incubated for 1 h. Excess antibody was washed away by PBS washing. Stained sections were mounted with DAPI containing Gold-anti-fade mounting medium. Confocal images were obtained on Nikon A1 Confocal imaging system and analyzed on Nikon Elements Analysis software.

This work was supported by the University of Wisconsin – Madison and the National Institutes of Health P30CA014520, and the Brazilian Science without Borders Program SwB-CNPq. This research has also been supported in part by the National Science Foundation Grant DMS-1716737, the National Institutes of Health (NIH) Grants 1U01CA196403, 1U01CA213759, 1R01CA226537, 1R01CA222007, and U54CA210181.