3D small-scale dosimetry and tumor control of 225Ac radiopharmaceuticals for prostate cancer

Radiopharmaceutical therapy using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upalpha$$\end{document}α-emitting \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{225}$$\end{document}225Ac is an emerging treatment for patients with advanced metastatic cancers. Measurement of the spatial dose distribution in organs and tumors is needed to inform treatment dose prescription and reduce off-target toxicity, at not only organ but also sub-organ scales. Digital autoradiography with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upalpha$$\end{document}α-sensitive detection devices can measure radioactivity distributions at 20–40 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu {\hbox {m}}$$\end{document}μm resolution, but anatomical characterization is typically limited to 2D. We collected digital autoradiographs across whole tissues to generate 3D dose volumes and used them to evaluate the simultaneous tumor control and regional kidney dosimetry of a novel therapeutic radiopharmaceutical for prostate cancer, [225Ac]Ac-Macropa-PEG4-YS5, in mice. 22Rv1 xenograft-bearing mice treated with 18.5 kBq of [225Ac]Ac-Macropa-PEG4-YS5 were sacrificed at 24 h and 168 h post-injection for quantitative \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upalpha$$\end{document}α-particle digital autoradiography and hematoxylin and eosin staining. Gamma-ray spectroscopy of biodistribution data was used to determine temporal dynamics and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{213}$$\end{document}213Bi redistribution. Tumor control probability and sub-kidney dosimetry were assessed. Heterogeneous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{225}$$\end{document}225Ac spatial distribution was observed in both tumors and kidneys. Tumor control was maintained despite heterogeneity if cold spots coincided with necrotic regions. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{225}$$\end{document}225Ac dose-rate was highest in the cortex and renal vasculature. Extrapolation of tumor control suggested that kidney absorbed dose could be reduced by 41% while maintaining 90% TCP. The 3D dosimetry methods described allow for whole tumor and organ dose measurements following \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{225}$$\end{document}225Ac radiopharmaceutical therapy, which correlate to tumor control and toxicity outcomes.


Experimental design
Immunocompromised Nu/nu mice (5-6 weeks old, Strain: 002019, Jackson Laboratories) were used for subcutaneous xenografts.Each mouse was subcutaneously inoculated with 2.5 million 22Rv1 cells mixed with Matrigel (Corning, #354230) in a 1:1 ratio.Tumor growth was monitored for 21 days until the tumors reached a volume of 0.4-0.6 cc.All animals for prostate cancer models used in our studies were male mice.22Rv1 xenograft-bearing mice received an intravenous injection of 18.5 kBq of [ 225 Ac]Ac-Macropa-PEG 4 -YS5 via the tail vein and were sacrificed at two time points: 24 h post-injection (p.i.) and 168 h (7 d) postinjection. 225Ac was in equilibrium at the time of injection.Euthanization was performed with a high dose of isoflurane (5% for 10 min), followed by cervical dislocation.Blood, tumors, kidneys, and other selected organs were collected for biodistribution (BioD: NaI automatic gamma counter, Hidex), and only tumors and kidneys were subjected for autoradiography (iQID: ionizing-radiation quantum imaging detector, QScint Imaging Solutions, LLC).Consecutive tissue slices were stained with hematoxylin and eosin (H&E) using a standard protocol.Antibody conjugation, 225 Ac radiolabeling, and [ 225 Ac]Ac-Macropa-PEG 4 -YS5 synthesis followed the procedure described previously 17 .
In total, four cohorts of identically prepared mice are described in this study: animals for DAR method comparison ( N = 4 ), animals for 3D DAR ( N = 4 ), animals for BioD-based 213 Bi corrections ( N = 8 ), and animals in a 7-d BioD study to determine the time-dose-rate curves for [ 225 Ac]Ac-Macropa-PEG 4 -YS5 in the mice ( N = 17).

iQID digital autoradiography imaging
An ionizing-radiation quantum imaging detector (iQID) camera DAR device (QScint Imaging Solutions, LLC) was used to obtain high-resolution (voxel size 39 µm × 39 µm × 210 µm ) images of the instantaneous spatial distribution of α-particle emissions in tissues at the start of the acquisition.The iQID camera can be used at 10-40 µm effective voxel size.In this study, a larger stage (80 mm diameter) was used to increase the number of tissue samples that could be measured simultaneously, with the trade-off of increasing the effective voxel size.
After sacrifice, tissue samples were prepared in an Optimum Cutting Temperature (OCT) medium, sliced using a cryotome to 10 µm thickness, and mounted on the iQID camera for imaging.The iQID camera uses a disposable α-sensitive scintillator (ZnS:Ag film EJ-440; Eljen Technology) and light-amplifying optical compo- nents to image scintillation light onto a 2448 × 2048 px CMOS camera with a CMOSIS CMV4000 CMOS sensor (Grasshopper© 3, FLIR Integrated Imaging).Activity images are obtained from single-particle event maps using the ROI segmentation and registration procedures as published in our open-source Python toolkit 19 , then decaycorrected to the time of sacrifice.An additional correction factor for the device frame-rate (1.09) was derived for 225 Ac due to the rapid decay of progeny 217 At ( t 1/2 = 32 ms ), which occurs on the order of the iQID frame rate (25 FPS = 40 ms/frame) (see Supplement).
As in previous work with 211 At 19 , 10 7 α-particle primaries were generated in Monte Carlo framework GATE v9.0 20 to simulate the decay of 225 Ac.Alpha-particle emissions from the 225 Ac decay chain were simulated in a 181µm cube of 1-µm water voxels using the emstandard_opt3 physics list and 10 nm range cuts.The energies and branching ratios of the alpha-particle primaries were provided by the Lund/LBNL Nuclear Data Search ( 225 Ac: 25%, 221 Fr: 25%, 217 At: 25%, 213 Bi: 0.52%, 213 Po: 24.48%) 21 .Progeny were assumed to be in secular equilibrium, since iQID measurements were taken long enough after sacrifice for free 213 Bi to decay significantly (> 5 h).Only the alpha particles were generated as primaries.The kernel was averaged radially and binned to the voxel size of the iQID image stack (XY: 39 µ m; Z: 10 µm).

iQID calibration
The quantitative accuracy of 225 Ac measurements using iQID was calibrated using droplet samples of known radioactivity.Solutions of 185 Bq/µ L were prepared and serially diluted by factors of two down to 5.78 Bq/µ L with small volumes reserved at each dilution.2-µ L droplets of each concentration were prepared ( N = 3 per concentration), counted in a Hidex NaI(Tl) automatic gamma counter (60 s, 175-250 keV and 385-490 keV windows with Gaussian and linear background fits), pipetted onto ZnS:Ag scintillator paper, and evaporated in a fume hood at room temperature, leaving circular samples of 370, 185, 92. 5, 46.25, 23.13, and 11.56 Bq as calculated from the stock dilution. 225Ac was provided as a dissolved chloride salt in water, and therefore it does not vaporize at room temperature during the procedure.The swatch was measured in iQID at 25 FPS for 24 h.For activities below 46.25 Bq, the mean spatial pileup loss was 23.8% ± 0.7% , yielding an absolute efficiency of 38% when including 50% geometric efficiency.Although greater saturation occurred at higher activities, these are beyond the range of tissue measurements in this study.The complete calibration results are shown in Supplementary Fig. S4.

2D to 3D DAR
DAR-based αRP dosimetry conventionally requires a series of around 10 consecutive slices to be imaged per dose-rate measurement 15,22 .The co-registered activity volume is used for dose-point kernel (DPK) convolution or Monte Carlo (MC) simulation.If one assumes that neighboring slices are nearly identical since the slice thickness is small (10 µm ), absorbed dose-rate can be estimated with only one slice by digitally duplicating the measured slice to generate the DPK convolution input volume 19 .To validate the technique ("cloning method") for [ 225 Ac]Ac-Macropa-PEG 4 -YS5 in a mouse model, ten consecutive slices ( 10 × 10 µm = 100 µm total) from each mouse kidney and tumor were cut, imaged, and digitally re-registered ( N = 4 mice).The dose rate of the central slice was compared between the sequential and cloning methods.
To assess 3D dose volumes, mice were identically prepared ( N = 4 ), but instead single tissue slices were extracted at 200 µm intervals from kidneys and tumors to yield 3D volumes of 20-30 slices per tissue (voxel size 39 µm × 39 µm × 210 µm ).Spatial dose rates were estimated in each slice using the cloning method and DPK convolution.This procedure will be referred to as 3D digital autoradiography (3D DAR) and produces 3D digital autoradiographs (3D DARs).At 200 µm sampling rate in a 5-mm diameter tissue, the cloning method reduces the slices that must be prepared for 3D DAR from 250 to 25. 3D DAR figures were rendered with 3D Slicer, an open-source image analysis software package 23 .

Tumor control probability
Tumor control probability (TCP) is a statistical predictor of treatment efficacy based on whether tumor cells survive the treatment, where TCP = 1 indicates that all malignant cells die.We use the formalism reviewed by Spoormans et al 10 , where TCP in a heterogeneous DAR is the product of voxel control probabilities (VCPs).The VCP nomenclature is discussed further in the Supplement.A voxel i containing n i cells is assumed to contain uniform dose D i , and the surviving fraction S is based on the linear quadratic (LQ) probability model: The above simplification is reasonable for 225 Ac RPs, which mainly deliver dose through high-LET α-particle emissions for which the radiosensitivity parameter α >> β .We used α = 1.8 Gy −1 , based on an in vitro survival assay with [ 225 Ac]Ac-Macropa-PEG 4 -YS5 (Supplementary Fig. S1) 17 . (1) Vol:.( 1234567890 24 .We assumed secular equilibrium between 225 Ac (t 1/2 = 9.9d ) and 221 Fr ( t 1/2 = 4.8min ), but not between 225 Ac and 213 Bi ( t 1/2 = 45.6 min ), since measurements occurred > 30 min after sacrifice.Derivations and some nuances are discussed in the Supplement.A measurement at time t post-sacrifice provided A a (t) and A b (t) , the respective 225 Ac and 213 Bi activities, which were related to A a (0) and A b (0) at the instant of sacrifice ( t = 0 ) by: All measurements corresponded to animals sacrificed at the same time post-injection.Equation ( 2) is equivalent to A b (t)/A a (t) = 1 is the condition that describes secular equilibrium between 225 Ac and 213 Bi at any time t.For tissues with A b (t)/A a (t) > 1 (Fig. S2), the difference between the total activities at sacrifice, A b (0) − A a (0) , was the quantity of free 213 Bi present at that moment (e.g.due to redistribution from other tissues).

Gamma-ray spectroscopy
Gamma-ray emissions from organs and tumors were counted in a Hidex NaI(Tl) automatic gamma counter between 0.5 and 3 h post-sacrifice, allowing 60 s active counting time per tissue.Net counts were recorded in energy windows corresponding to 221 Fr (168-268 keV) and 213 Bi (370-510 keV), using a least-squares Gaussian distribution with linear background to correct for ambient background ( 213 Bi) and down-scatter ( 221 Fr) in each energy window (Supplementary Fig. S2).Counts were corrected by their respective branching ratios, decay times, and energy-dependent detector efficiencies, determined by a known-activity detector calibration using the same procedures.

Macro-to-micro dosimetry
The temporal evolution of activity was estimated using macroscopic gamma-counting measurements and a macro-to-micro approach 25 .The absorbed dose value in each DAR voxel was extrapolated by scaling the doserate curve measured within whole tumors and kidneys by a factor c based on the mean dose-rate of the DAR measurement at one time-point (24 h or 168 h p.i.), assuming that the activity does not significantly redistribute over time.The dose-rate curve was modelled with time-dependent BioD from 1 d, 2 d, 4 d, and 7 d p.i. ( N = 17).
Energy from the 225 Ac decay chain was assumed to deposit entirely within the tumor (which showed A b (t)/A a (t) = 1 within uncertainties), but in kidneys, we separated 225 Ac contributions from free 213 Bi and its products.Resulting dose-rates were fit to bi-exponential curves using least-squares optimization.We extracted extrapolation factors c 24h and c 168h , where D was the total integrated dose under the time-rate curve (TRC) to six half-lives, and Ḋ24h (for example) was the dose-rate measured at 24 h p.i by BioD.iQID dose-rate DARs from 24 h p.i. were scaled by c 24h to obtain the voxel distribution of total absorbed dose D i , and similarly for 168 h p.i. DARs by c 168h .

Histological staining
Tissue slices consecutive with each sample series (sequential-method validation mice) or with each tissue slice (3D DAR mice) were stained with hematoxylin and eosin (H&E) using a standard protocol.Images were acquired with Octopus-Versa Slide Scanner (Leica).

Tumors
Cell nuclei in tumor H&E images were segmented using a custom ImageJ-Fiji macro based on watershed segmentation and the Analyze Particles function (Supplementary Fig. S3).These cell nuclei maps and iQID images were initially co-registered using automated rigid-body transformations with mean-squared-error intensity comparison, as described previously 19 , but more precise registration was needed to match n i cells in a voxel to dose D i to calculate TCP.After the initial rigid-body registration, the two images were manually aligned with affine transformations using Bigwarp 26 , a landmark-based deformation tool in ImageJ-Fiji 27 .To minimize interpolation errors, the DAR was treated as the reference image where possible.When DARs were transformed, the sum of pixel values was preserved using a scaling factor according to the difference before and after transformation.External edges of the tissue were preferred as landmarks to avoid biasing co-registration of internal structures receiving dose.
Tissue slices from both modalities (iQID and H&E) sometimes contained damaged or folded sections from the cryosectioning procedure.Identifiable damage was masked out of the TCP calculations, but the difference in total tissue extent sometimes hindered the registration.If a visibly adequate co-registration could not be achieved, the slice was omitted from analysis.To reduce the sensitivity of the calculation to registration error, we applied a 5 px × 5 px erosion mask to the edge of the contour outlining n i > 0 pixels.
(2) www.nature.com/scientificreports/Kidneys Kidney H&E images were manually segmented into four regions: cortex; the combined inner and outer stripes of medulla (ISOM/OSOM); the combined inner medulla and papilla (IM/Pa); and the combined vasculature and renal pelvis (V/Pe), using the reference histology images provided by NIH's National Toxicology Program 28 .We reduced the uncertainty in segmentation by combining the outer and inner stripes of medulla into one segment, and defined the boundary with the cortex as the presence or absence of glomerules.Similarly, we did not distinguish where the inner medulla and papilla ended or began and masked them as one segment.Automated rigid-body transformations were sufficient for approximate alignment of the sub-organ regions when registering anatomical masks with 3D DARs.We evaluated our DAR-based sub-organ dosimetry results from 24 h p.i. next to a regional S-value dosimetry model developed by Vargas et al. 14 .This model takes the total activity as measured by BioD and distributes it according to the relative activity ratios in each compartment.We calculated this ratio using DARs from across the whole kidney volume and applied the published S-value calculations according to the procedure described by the authors.Since we did not separate the ISOM and OSOM, or the IM from the papilla, these segments were combined and their S-values averaged.Vasculature was assigned to the compartment within which it was found for this analysis, since it was not segmented in the reference.

Statistical analysis
Results reported as x ± σ describe the mean value x and one standard deviation σ .Results of the form x (x 1 , x 2 ) show asymmetric uncertainties, where x 1 is the lower bound and x 2 is the upper bound propagated from dose calculations.For sub-organ dosimetry using H&E stains, damage to the kidneys during cryotome slicing resulted in only N = 1 mouse per time point, for which x and σ are calculated using contralateral samples (left and right kidneys).

Results
All mentions of dose refer to absorbed dose (Gy), with no radiation weighting or relative biological effectiveness factor.

2D to 3D DAR
Figure 1A-B shows an example comparison between the absorbed-dose-rate DAR calculated using the sequential and cloning methods for a 24 h p.i. tumour.Across subjects (kidneys and tumors at both time points), the cloning method calculated the mean dose-rate of the sequential method with an accuracy of 4.1% ± 3.7% (Fig. 1C).Gross features were captured, but the approximation was noisier and over-or under-emphasized high-activity regions.We assessed the spatial accuracy with γ analysis, a difference-and distance-based metric for similarity between two dose distributions that is used to evaluate clinical external-beam radiation therapy plans 29,30 .97% ± 3% of dose-rate pixels in kidneys were accurately calculated ( γ < 1 ), using a tolerance of 10% within three pixels (117 µm ) and local normalization (Fig. 1D).Higher discrepancy was observed in tumors ( γ < 1 : 87% ± 6% ), which reflects the fact that heterogeneities between slices are not preserved when using the cloning method approximation.

Bi spectroscopy
BioD results from 24 h p.i. are shown in Fig. 2A ( N = 4 ).The ratio A b (t)/A a (t) was compared to unity at t = 1h post-sacrifice (first bar in each 4-bar set) to determine deviation from secular equilibrium in tissues.In kidneys, A b /A a = 6.1 ± 0.3 > 1 indicated substantial free redistributed 213 Bi.Blood measurements were deficient in 213 Bi (A b /A a = 0.62 ± 0.01 < 1 ), which suggests that 213 Bi was cleared from blood through the kidneys.Tumors were in secular equilibrium ( 0.97 ± 0.04 ).At 168 h p.i., A b /A a for tumor, kidney, and blood was 1.06 ± 0.04 , 5.30 ± 0.56 , and 1.03 ± 0.10 , respectively.Both early and late time points showed tumors in secular equilibrium between 225 Ac and 213 Bi, while kidneys collected redistributed 213 Bi.Lowered levels of 213 Bi in the blood at the early time point had equilibrated by the late time point.
The decay of A b (t)/A a (t) in kidneys post-sacrifice followed Eq. ( 2) with a goodness-of-fit coefficient of determination r 2 = 0.996 ( N = 4 mice, 60 s active counting per tissue).The decreasing signal in the kidneys was used to measure the free 213 Bi using Eqs.( 2) and (3).A b (0)/A a (0) was calculated from Eqs. ( 2) and (3) for 24 h p.i. mice as 14.7 ± 0.2 and 14.0 ± 1.2 , respectively, which agree within 1σ .Agreement was also observed at 168 h p.i. ( 17.1 ± 1.8 and 15.6 ± 2.4 ).In both cases, the more precise result was used for subsequent analyses.Greater uncertainties for the experimental fit at 168 h p.i. are attributable to the lower overall activities remaining in the system and a poorer exponential fit due to an oversight in the 168 h p.i. data that resulted in a narrower time window for the measurements (only 8 min between mice).

Single-time-point dosimetry
Figure 2B shows time-dose-rate curves (TRCs) using the approach illustrated in Fig. 2A to separate kidney absorbed dose contributions into 225 Ac and free 213 Bi components.No 213 Bi data from 24 h p.i. were available from this cohort due to a 7-h delay in measurement.The 24 h p.i. data shown were extrapolated from the measured 225 Ac activity A a and the calculated correction factor A b (0)/A a (0).
The dominant uncertainty in the TRCs was the variable uptake between animal subjects, shown as 1σ error bars around the mean absorbed dose rate.Individual subject data points are shown instead of the mean dose rates themselves.We calculated the total absorbed dose for each TRC as the integrated area, with uncertainties as the dose from upper-and lower-bound curves defined by modulating the fitting parameters by ±1σ .Table 1 summarizes the calculated doses and conversion factors c for each TRC with bound-based uncertainties.
Use of the extrapolation factor assumes that the intra-organ and intra-tumor spatial activity do not change over time.Figure 2C shows representative DARs for kidneys and tumors at 24 h and 168 h post-injection.The ratio between mean absorbed dose-rates in each renal compartment (cortex, ISOM/OSOM, IM/papilla, and V/ Pe) was (1, 0.50, 0.88, 1.19) at 24 h p.i., and (1, 0.60, 0.83, 1.06) at 168 h p.i., indicating that similar compartmental distribution was preserved.In tumors, both time-points exhibited morphology-dependent activity distribution with low dose in the necrotic core, but higher tumor saturation was observed at 168 h post-injection.

3D kidney dosimetry
The mean kidney absorbed dose from 18.5 kBq [ 225 Ac]Ac-Macropa-PEG 4 -YS5 was 6.4 (4.6, 8.9) Gy and 7.5 ± 2.2 Gy from DAR and BioD, respectively (Table 2).75% (73%, 78%) (DAR) and 78 ± 7 % (BioD) of the total mean dose was due to the decay of free 213 Bi, where the 213 Bi correction to iQID DARs was provided by the A b (0)/A a (0) ratio.The spatial distribution of free 213 Bi was not obtained from these DARs, which were imaged several days post-sacrifice.The reported mean values of the two modalities differed by 15% and agree within 1σ of BioD statistical uncertainties.Figure 3A illustrates an example H&E stained slice, the anatomically segmented regions (cortex, ISOM/ OSOM, IM/papilla, and V/Pe), and the corresponding iQID DAR.All 23 slices from a 24 h p.i. kidney were combined to create the 3D DAR and co-registered 3D anatomical model in Fig. 3B.Dose-rate volume histograms (DrVHs) from each anatomical compartment are shown in Fig. 3C.Average 225 Ac dose-rate in the renal cortex doubled that in the medulla at 24 h p.i. (16.6 ± 0.1 mGy/h vs. 8.2 ± 0.1 mGy/h) and was 67% higher at 168 h p.i. (4.24 ± 0.04 mGy/h vs. 2.53 ± 0.07 mGy/h).The inner medulla and papilla mean dose-rate was similar to that in the cortex (13%, 18% less for respective time-points).Blood vessels and the renal pelvis collected comparatively high amounts of 225 Ac at the two time points (20 ± 1 mGy/h, 4 ± 1 mGy/h).These results show high 225 Ac concentrations at key transport locations: blood vessels, cortex, and the renal pelvis.Intact antibody-based radiopharmaceutical compounds such as [ 225 Ac]Ac-Macropa-PEG 4 -YS5 may be too large for filtration and thus stagnate in the glomeruli or remain in the blood.
The iQID DAR and regional S-value methods agreed within uncertainties for cortex and ISOM/OSOM regions (Fig. 3D).However, the S-value calculation indicated an IM/Pa dose rate exceeding 5 times that of the DAR method (bar extends beyond figure limits).The BioD mean dose rate (23.1 ± 3.6 mGy/h), which assumed full energy deposition of all decay products within the tissue, was naturally uniform and higher than the iQID and S-value estimates, except for the IM/Pa (Fig. 3D).

Tumor dosimetry and TCP
Tumors received an average of 50.8 ± 4.1 Gy (DAR) and 57.4 ± 18.5 Gy (BioD) between the two modalities (2.8 ± 0.2 Gy/kBq or 3.1 ± 1.0 Gy/kBq: Table 2).Figure 4A-D summarizes tumor dosimetry and the TCP calculation process for a 24 h p.i. tumor, including the 3D DAR (Fig. 4A), example registered iQID and cell density images from H&E (Fig. 4B), TCP values for individual slices (Fig. 4C), and DrVHs for individual slices and the total volume for an example 24 h p.i. tumor (Fig. 4D).This analysis was conducted for N = 3 mice (labelled M9,  Despite heterogeneous dose distribution and cold spots, high tumor control is attained in mouse M9 because low-dose regions correspond to the necrotic core of the tissue with few cell nuclei (Fig. 4B).Between the two 24 h p.i. mice, lower mean dose (17% less) and heterogeneous uptake of the radiopharmaceutical in non-necrotic regions resulted in decreased TCP.The red dashed circle in the 3D DAR (Fig. 4E) indicates a region of reduced uptake in one lobe of the tumor.Figure 4F shows a representative gray-scale DAR with low slice-TCP (0.00), with voxels with VCP i < 0.95 indicated in red.Fig. 4G shows the same for a low-TCP slice from 7 d post-injection.
The mean slice-TCP and kidney dose were estimated for a range of injected activities (IA) from 0 to 18.5 kBq, assuming that dose scales linearly with IA and maintains the same organ and sub-organ spatial distribution Table 2. Absorbed dose comparisons between modalities and tissues using single-point dosimetry.*Dose due to α-particles from redistributed free 213 Bi and its associated progeny 213 Po.For DAR, separation of 213 Bi (and 213 Po) dose is based on A b (0)/A a (0) ratio calculated in the 213 Bi spectroscopy section.Significant redistribution was not observed to tumors (Fig. 2A) (Fig. 4A).We then calculated a predictive de-escalation scheme using the highest TCP tumor (M9, Fig. 4B).In this simple model, a reduced IA of 10.9 kBq maintained a TCP of 0.9 with a 41% reduction in kidney dose.75% www.nature.com/scientificreports/IA reduction (4.625 kBq) was predicted to yield non-controlled tumors (TCP = 0 ).To test this, one additional mouse was prepared and analyzed with 4.625 kBq IA.We observed sparse radiopharmaceutical uptake, in comparison to the 18.5 kBq cohort, and TCP was calculated as zero for all slices in agreement with the model (Fig. 5B-C).This calculation is consistent with a previous therapy and survival study with [ 225 Ac]Ac-Macropa-PEG 4 -YS5 in mice, which found that 4.625 IA treatment extended survival and inhibited tumor growth for 41 days compared to saline, followed by tumor regrowth 17 .Subjects M10 and M11 did not reach 0.9 TCP and were not evaluated for de-escalation.

Discussion
Microdosimetry and small-scale dosimetry are crucial to understanding the biological effect and treatment strategy of α-particle radiopharmaceuticals by linking spatial absorbed dose distribution to tumor kill or organ toxicity 8,31,32 .In this work, we have demonstrated how three staples of pre-clinical RP studies-gamma-ray biodistribution, immunohistological stains, and digital autoradiography-may be combined to assess tumor control probability and produce DrVHs of anatomical compartments.To our knowledge, this is the first study to generate and analyze 3D-DAR in entire organs and tumors, and to calculate voxel-based TCP for experimental 225 Ac α RP measurements simultaneously with sub-organ kidney dosimetry.Since tumor dose from radiotherapeutics is limited by the tolerance of normal tissues, it is necessary and natural that small-scale tumor and organ dosimetry should be evaluated concurrently.
The study is mainly limited by the fact that no direct-comparison survival-and-treatment study of [ 225 Ac] Ac-Macropa-PEG 4 -YS5 was conducted at the 18.5 kBq IA level, and therefore we cannot draw final conclusions about the treatment outcome and toxicity.However, results from 4.625 kBq treatments are available and can provide some insight to our results 17 .The 4.625 kBq [ 225 Ac]Ac-Macropa-PEG 4 -YS5 treatment extended survival and inhibited tumor growth for 41 days compared to saline, but tumors ultimately regrew.This is consistent with our simple predictive model and the added 4.625 kBq mouse assessed with the DAR-TCP method.For sub-organ dosimetry, we found that [ 225 Ac]Ac-Macropa-PEG 4 -YS5 was predominantly in the cortex, vasculature, and pelvis-adjacent structures.This agrees with the survival study, which observed mild to moderate renal toxicity and histopathological reduction and atrophy of the cortical glomerules and tubules.The simple de-escalation scheme was calculated for only one mouse with high TCP ( > 0.9 ), since de-escalation is not a goal for sub-controlled tumors.Therefore, we can only treat this method as a proof of concept.With the DAR-TCP and sub-organ methodological framework established, future treatment studies can both utilize and validate the method by calculating TCP in cohorts treated at several injected activity levels and identifying potential correlation to disease progression and mortality.Exploration of these methods is increasingly relevant given the positive outcomes reported by clinical de-escalation trials 33 .
We found several important nuances when using VCP-product TCP as a metric for αRP treatment efficacy.In this framework, if every 10-µm slice has a high TCP = 0.95 , where TCP = 1 is complete tumor control, then the cumulative 3D TCP of a 5-mm tumor would be (0.95) 50 = 0.08 .Given the tumor inhibition observed in treatment studies, we suspect that the mean TCP per slice may better reflect the treatment efficacy 17 .The TCP metric is conservative, formulated based on the probability of 100% cell kill, and thus does not necessarily capture meaningful outcomes such as prolonged survival, as we found with our comparison to the 4.625 kBq study.Additionally, we used conservative assumptions to estimate the radiosensitivity parameter α (see Supplement), so the actual biological impact and tumor control are likely to be higher than predicted when correcting for binding saturation, sterilized cells, well geometry, and dose delivered by recoiling nuclei.We have not considered hypoxia, variable radiosensitivity, or repopulation and repair 10 .
An inherent drawback of ex vivo DAR and BioD studies is that the animal must be sacrificed to conduct a measurement, precluding monitoring of the same animal over time and demanding costly increases in sample size to minimize inter-subject variability.Moreover, the treatment cannot be adjusted on a subject-specific basis unless tissue biopsies are obtained.In this study, we utilized the minimum number of mice feasible to obtain a representative data set, resulting in large uncertainties attributable to single-point pharmacokinetics and the resulting inter-subject variability (Fig. 2B).These challenges are characteristic of the macro-to-micro dosimetry approach.Although the animal cohort was small, each tissue or tumor was assessed over 20-30 independent slices to evaluate intra-subject variability and the benefit of a 3D DAR approach.Fig. 4C and the 3D DAR panels in the Supplement demonstrate that a single 2D slice might not include structural or dose-distribution features present elsewhere in the 3D volume.
An in vivo study of the α RP characterizing the continuous pharmacokinetics over time within subjects, if one can be achieved given the low administered activities, could improve the precision of the macro-tomicro approach.Our group is working to develop ultra-high-sensitivity gamma-ray imaging techniques for α RPT 12,[34][35][36] .In vivo PET and SPECT imaging surrogates for 225 Ac RPs are also under investigation in our group and elsewhere 17,37 .An imaging surrogate is a chemically similar diagnostic radiopharmaceutical that may be injected at higher activities to obtain a tracer distribution correlated with the αRP kinetics at millimeter or sub- millimeter resolution (e.g., replacement of 225 Ac with 133 La or 134 Ce/ 134 La for PET, or 226 Ac for SPECT).This spatial resolution may be sufficient to observe gross sub-organ features such as renal cortex-medulla separation, with the advantage of monitoring the same subject over time.The utility of surrogate imaging techniques is limited by the chemical similarity of the surrogate to the therapeutic isotope, the complication of dosimetry (requiring studies to correlate imaging biokinetics to therapeutic absorbed dose), and the lack of information provided by the surrogate about the distribution of recoil progeny.These imaging strategies are complementary to the methods described here, and can be used for in vivo imaging and ultimately for applications in clinical dosimetry 31,38 .
This work complements the study by Mellhammar et al, who used a MC-simulation DAR-TCP approach with 177 Lu-PSMA-617 extrapolated to [ 225 Ac]Ac-PSMA-617 13 .We demonstrated experimentally that, as the authors simulated, low tumor penetration reduces TCP for the same IA level.Our approach differed in that quantitative single-particle DARs of the α-emitting RP were measured, instead of using a relative-intensity β-particle DAR as a proxy for the spatial distribution of α-particles.We also used 3D DAR for TCP (improving statistical count and morphological assessment), included concurrent sub-organ kidney dosimetry, and accounted for both biological and physical clearance with an experimental TAC curve for the macro-to-micro conversion.
These voxel-TCP approaches may help estimate the biological outcome of doses in de-escalation studies.Although tumor dose is heterogeneous in Fig. 4B, the low-dose region corresponds to the necrotic core of the tissue with few cell nuclei, resulting in high tumor control.Conversely, de-escalation reduces tumor penetration and increases RP sparsity, affecting tumor management, as shown in Fig. 5C.DAR-based studies can explore these effects during drug development.Although we demonstrated the concept for de-escalation analysis in Fig. 5, a rigorous de-escalation model would require more refined uncertainty analysis and a larger cohort, as described above.
For 225 Ac RPT, off-target toxicity rather than cytotoxic efficacy may be the current challenge limiting routine clinical use.The high tumor control observed here was accompanied by 350-400 mGy/kBq (6.4-7.5 Gy) absorbed dose to kidneys.Gamma-ray spectroscopy suggested that this was largely attributable to redistributed 213 Bi.Inclusion of a biological weighting factor such as relative biological effectiveness (RBE) or radiation weighting ( w R ) representing the double-strand breaks from α-particles could bring the 6.4-7.5 Gy α-particle dose above the 15 Gy threshold associated with nepropathy in external-beam radiation therapy 39 .Since our spectroscopy approach only predicts the total activity correction and not the sub-organ spatial distribution of free 213 Bi, earlytime DAR or other separation techniques 40 might reveal different critical sub-structures than those we identified.
We characterized the cloning method performance to evaluate the assumption in DAR dosimetry that adjacent slices are functionally identical.The method is accurate within 10% for mean dose-rates, but differences between slices do affect spatial dose distribution in tumors ( 87% ± 6% γ-passing rate).Still, the approximation procedure allowed the rapid collection of 3D DARs, which revealed spatial variation in [ 225 Ac]Ac-Macropa-PEG 4 -YS5 dose within tissues.The identical-slices assumption thus appears suitable, and perhaps necessary, to generate 3D DARs for sub-organ anatomical dosimetry, but stochastic cellular microdosimetry would require a high-resolution, multi-slice source volume for accurate results.We speculate that this method only holds because of the "small-scale" (not truly microdosimetric) nature of the analysis.If a higher-resolution iQID setting or device were used, such that individual kidney tubules or glomeruli were identifiable, then the assumption that adjacent slices are replicates of each other is unlikely to be true.

Conclusion
We developed a method for 3D digital autoradiography (3D DAR) and combined it with advanced gamma-ray spectroscopy and histological segmentation to conduct small-scale dosimetry in murine studies of α-emitting [ 225 Ac]Ac-Macropa-PEG 4 -YS5.Tumor control and 3D sub-organ kidney absorbed dose distributions were evaluated at the voxel level (39 µm × 39 µm × 210 µm ).These methods provide an important framework to assess treatment outcomes and organ risk for 225 Ac radiopharmaceutical studies.

Figure 2 .
Figure 2. Temporal studies of [ 225 Ac]Ac-Macropa-PEG 4 -YS5 in 22Rv1 xenograft-bearing mice.(A) 213Bi correction example using gamma-ray spectroscopy for 24 h p.i. mice (subjects M5-M8).Activity ratios of the two 225 Ac daughters demonstrates clearance of free 213 Bi in the blood through the kidneys ( N = 4 ).The decay of the A b (t)/A a (t) ratio following sacrifice follows Eq. (2) despite variable uptake between subjects. (B) Time- dose-rate curves (18.5 kBq, N = 17 ), with contributions from free 213 Bi and 225 Ac in kidneys separated.(C) Representative DARs from kidneys and tumors at two time points.

Fig. 5 .
Fig. 5. De-escalation predictive calculation.(A) Calculation of mean-slice TCP for a range of injected activities.(B) In subject M9, de-escalation calculation suggests that kidney dose may be reduced by 41% while maintaining 90% TCP.For 4.625 kBq I.A., the model predicts 0% TCP.(C) Slice from 4.625 kBq I.A. experiment, showing gray-scale DAR dose-rate with underdosed voxels ( < 0.95 VCP) indicated.The calculated TCP of 0% is consistent with the model's prediction.

225 Ac decay chain Redistribution
) of free213Bi was measured with time-sensitive gamma-counting ( 213 Bi correction cohort: N = 4 at each of 24 h and 168 h p.i.), similar to Seoane et al

Table 1 .
Absorbed dose calculations and correction factors from integration of BioD dose-rate curves (Fig.2B).