Radon-220 diffusion from 224Ra-labeled calcium carbonate microparticles: Some implications for radiotherapeutic use

Alpha-particle emitting radionuclides continue to be the subject of medical research because of their high energy and short range of action that facilitate effective cancer therapies. Radium-224 (224Ra) is one such candidate that has been considered for use in combating micrometastatic disease. In our prior studies, a suspension of 224Ra-labeled calcium carbonate (CaCO3) microparticles was designed as a local therapy for disseminated cancers in the peritoneal cavity. The progenies of 224Ra, of which radon-220 (220Rn) is the first, together contribute three of the four alpha particles in the decay chain. The proximity of the progenies to the delivery site at the time of decay of the 224Ra-CaCO3 microparticles can impact its therapeutic efficacy. In this study, we show that the diffusion of 220Rn was reduced in labeled CaCO3 suspensions as compared with cationic 224Ra solutions, both in air and liquid volumes. Furthermore, free-floating lead-212 (212Pb), which is generated from released 220Rn, had the potential to be re-adsorbed onto CaCO3 microparticles. Under conditions mimicking an in vivo environment, more than 70% of the 212Pb was adsorbed onto the CaCO3 at microparticle concentrations above 1 mg/mL. Further, the diffusion of 220Rn seemed to occur whether the microparticles were labeled by the surface adsorption of 224Ra or if the 224Ra was incorporated into the bulk of the microparticles. The therapeutic benefit of differently labeled 224Ra-CaCO3 microparticles after intraperitoneal administration was similar when examined in mice bearing intraperitoneal ovarian cancer xenografts. In conclusion, both the release of 220Rn and re-adsorption of 212Pb are features that have implications for the radiotherapeutic use of 224Ra-labeled CaCO3 microparticles. The release of 220Rn through diffusion may extend the effective range of alpha-particle dose deposition, and the re-adsorption of the longer lived 212Pb onto the CaCO3 microparticles may enhance the retention of this nuclide in the peritoneal cavity.


Introduction
Cancer therapy with radionuclides has been the recipient of increased interest, and several beta-and alpha-particle emitter-based therapeutic radiopharmaceuticals have either been a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 approved or are undergoing clinical investigation [1][2][3][4][5][6][7]. The radionuclides that are used include the beta emitters 89 Sr, 90 Y, 131 I, 153 Sm, 177 Lu and beta-emitting 212 Pb, which generates alpha-emitting progenies, as well as the alpha emitters 211 At, 213 Bi, 223 Ra, 225 Ac, 224 Ra and 227 Th. In general, long-range, low linear energy transfer (LET) beta emitters are believed to be more suitable for the treatment of larger tumors than short-range, high-LET alpha emitters, which are considered to be more effective for the treatment of micrometastases and single-cell diseases [8].
From a logistical point of view, 224 Ra has a convenient half-life of 3.63 days [9,10]. It decays via several radioactive progenies, producing four alpha particles and two beta particles (Table 1 and Fig 1). Recently, it has been subject of preclinical [11][12][13][14][15] and clinical [16][17][18] research for its potential use in antitumor agents. While the properties related to high-LET radiobiology [19] make 224 Ra a potent cytotoxic agent, there are some concerns regarding the fate of its progenies in vivo as daughter nuclides can distribute differently than a parent because of differing biological affinities. For the brachytherapy application called diffusing alpha-emitters radiation therapy (DaRT) in which 224 Ra-loaded wires are implanted into solid tumors, the distribution of progenies both within the tumor and in normal tissues have been examined [13,20]. The release of progenies from one such 224 Ra source has been shown to have a therapeutic effect in a region of 5-7 mm in diameter. Table 1. Details of the nuclear decay data for 224 Ra and its daughters indicating x-and γ-lines with 1% or higher abundance and divided into two columns: one for energies in the 60-110 keV detection window and the second for energies above 110 keV.

Nuclide
Half life Daughter nuclide x-and γ-lines, keV (Abundance) All data were taken from the Decay Data Evaluation Project [10]. To compare the x-ray and gamma incidences between the radionuclides at equilibrium in the decay series, the branching factor (see Fig 1) for 212 Bi, 212 Po and 208 Tl must be considered.
https://doi.org/10.1371/journal.pone.0248133.t001 We have previously described the use of a suspension of calcium carbonate (CaCO 3 ) microparticles as carriers for 224 Ra and its progenies [21]. This novel application is designed to treat disseminated micrometastatic cancers, such as peritoneal carcinomatosis following intraperitoneal (IP) administration. Radium-224 adsorbed on CaCO 3 microparticles has demonstrated antitumor activity against ovarian cancer xenografts in the peritoneal cavity of mice [11,15]. Because of the multiple alpha-emitting daughters of 224 Ra, it is important to investigate the interaction of these progenies with the carrier compound. For example, 212 Pb, the progeny of 224 Ra with the longest half-life in the decay chain (10.64 h [9,10] , Fig 1), may reach systemic circulation if it is prematurely released from the CaCO 3 microparticles. A release of 212 Pb from the carrier compound can influence the dose delivered to the target area and hence reduce the therapeutic effect of the product. Therefore, the behavior of the noble gas 220 Rn, the immediate daughter of 224 Ra and the grandparent of 212 Pb in the decay chain, is of particular interest. Because it is gaseous, 220 Rn may diffuse away from the CaCO 3 microparticles and mediate a re-localization of the radioactivity.

PLOS ONE
In this study, we explored some fundamental product properties related to the two critical progenies, 220 Rn and 212 Pb, when CaCO 3 microparticles are used as a carrier compound for 224 Ra. The diffusion of 220 Rn from the microparticles was investigated in both air and liquid phases. The fate of 212 Pb subsequent to its release due to the diffusion of 220 Rn was also studied under conditions mimicking an in vivo environment. Further, CaCO 3 microparticles labeled with 224 Ra through either surface adsorption or inclusion into the bulk of the microparticles were hypothesized to impact 220 Rn diffusion and thus evaluated for their therapeutic effect in mice following the IP inoculation of the human ovarian cancer cell line ES-2.

Extraction of 224 Ra
The 224 Ra-labeled CaCO 3 microparticles were prepared by two different procedures: (1) the adsorption of 224 Ra onto the surfaces of pre-manufactured CaCO 3 microparticles and (2) the incorporation of 224 Ra into the bulk during CaCO 3 microparticle production.
The CaCO 3 microparticles that were subsequently used for surface labeling with 224 Ra were prepared by a spontaneous precipitation process. In short, equal volumes of 0.33 M CaCl 2 (Merck) and 0.33 M Na 2 CO 3 (Merck or VWR International, Radnor, PA, USA) were mixed either by magnetic or overhead stirring. The microparticles were collected by centrifugation, subsequently dried in an oven for 1 h at 180˚C and stored as a dried powder. In addition, a batch of CaCO 3 microparticles was purchased from PlasmaChem GmbH (Berlin, Germany). In some experiments, the additive polyacrylic acid (PAA, average M w~2 50 000, 35% wt. in H 2 O, Sigma-Aldrich) was used to coat the CaCO 3 microparticle surface at a ratio of 1.3 μL PAA solution per microparticle mg and added towards the end of the microparticle crystallization process. All types of microparticles had a mainly spherical geometry with volume-based median diameters ranging from 3-7 μm when representative batches were measured by laser diffraction (Mastersizer 3000, Malvern Instruments Ltd, Worcestershire, UK). Two microparticle batches, produced with and without PAA coating respectively, were also analyzed for visualization of crystal shape and surface morphology with scanning electron microscopy (SEM) performed at Particle Analytical (Hørsholm, Denmark) with a Leica Stereoscan 360. The results are presented in S1 Table. For the surface radiolabeling, the microparticles were washed three times with water and two times with 0.1 M Na 2 SO 4 (Merck) before dispersion in either 0.9% NaCl or a sucrose solution (composed of 94 mg/mL sucrose from Sigma-Aldrich, St. Louis, MO, USA and 2 mg/mL Na 2 SO 4 ) as previously described [21]. Subsequently, 224 Ra solution was added along with 0.004-0.3 w/w% Ba 2+ and 0.3-0.6 w/w% SO 4 2− relative to the amount of CaCO 3 . Microparticle suspensions were placed under orbital rotation for 1.5 h (HulaMixer, Invitrogen, Thermo Fisher Scientific, Waltham, MA, USA) during the radiolabeling process. The inclusion-labeled CaCO 3 microparticles were prepared by rapidly mixing equal volumes of 0.33 or 1 M CaCl 2 solution containing 224 Ra at the target radioactivity level and 0.004-0.3 w/w% Ba 2+ (relative to CaCO 3 ) with 0.33 or 1 M Na 2 CO 3 solution containing 0-0.7 w/w% SO 4 2-(relative to CaCO 3 ) with magnetic stirring or vortexing for 1-3 min. Also for inclusion-labeled microparticles, surface coating was applied in some experiments by addition of PAA towards the end of the crystallization process. The mass amount of the CaCO 3 microparticles produced was determined by assuming the quantitative yield of the precipitation process.
For both radiolabeling procedures, excess radiolabeling solution was removed prior to the CaCO 3 microparticles being washed twice with 0.9% saline, sucrose solution or water to remove any 224 Ra not bound to the particles.
Non-radioactive CaCO 3 microparticles were also prepared for some experiments through a mock labeling process following the same protocol as for surface-labeling but without the addition of 224 Ra.

Radioactivity measurements
Gamma-ray spectroscopy was performed using a Hidex Automatic Gamma Counter (Hidex, Turku, Finland) equipped with a 3-inch diameter NaI crystal. The detector was shielded from background radiation with a lead shield a minimum of 55 mm thick (80 mm on the conveyor side). The counts per minute (CPM) was registered to the 60-110 or 65-345 keV detection window. As can be seen in Table 1, the most abundant x and gamma radiation in these energy ranges originate from 212 Pb. For the analyses of the radioactive samples, it was therefore assumed that the CPM in these detection windows originated only from the 212 Pb as the contribution from the other nuclides in the series was considered minimal. The activity of the 212 Pb was determined directly from the CPM in the 60-110 keV window [23], whereas the 224 Ra activity was determined indirectly based on counts in the 65-345 keV window when the transient equilibrium between the 224 Ra and 212 Pb had been established. Transient equilibrium can be assumed > 2 days after the initial 212 Pb measurement when the sample vial is left sealed. The data used for the 220 Rn activity determination were acquired with sources at secular equilibrium (> 6 h after separation and > 1 day from radiolabeling/transfer to a new container) so that decay correction to a common reference time was achieved using the half-life of 212 Pb. The limit of quantification (LOQ) was set to equal the average CPM plus 10 times the standard deviation of the measurements of a series of blank samples. When the measured CPM for a sample was below the LOQ value, the CPM was set as equal to the LOQ to produce a theoretical maximum value.

Release of 220 Rn from open 224 Ra sources
The release of 220 Rn from open 224 Ra sources was evaluated with the two different experimental setups as visualized in Fig 2. The first setup (Fig 2A) aimed at investigating the release of 220 Rn through the air from a 224 Ra source. Two μL 224 RaCl 2 or 25 μg 224 Ra-CaCO 3 microparticles in 2 μL of water suspension were applied on the surface of a small paper strip (1 × 1.5 cm, absorbent bench paper) attached to a syringe needle that had previously been inserted through the silicone septum of a 3 mL glass v-vial (Supelco Analytical, Merck) screw cap. A low sample volume was used for the liquid to be immediately absorbed by the paper and evaporate. In this way, potential release of 224 Ra from the microparticles to the surrounding liquid could be disregarded. Subsequently, the screw cap with the radioactive sample was carefully inserted into the v-vial while avoiding contact between the paper strip and the interior surfaces of the v-vial before the cap was tightened. After approximately 24 h, the paper strip and needle were placed into two separate vials (sample P and N). The cap was put back onto the empty original vial (V) and the radioactivity in the now three vials was measured (time = t 1 ). The total 224 Ra activity applied on the paper strip (A Ra ) at time of assembly (t 0 ) was assumed to equal the decay corrected sum of the activities in samples P, N and V: where EF Ra is the efficiency factor (CPM/Bq) for the 65-345 keV window, λ = ln 2/t ½ and Δt 1 = t 1 −t 0 . The amount of 220 Rn release into air was estimated by the measured 212 Pb activity in the empty original vial (V) divided by the theoretical maximum 212 Pb activity generated through 220 Rn decay (A Pb ) at the time of measurement (t 1 ): where EF Pb is the efficiency factor (CPM/Bq) for the 60-110 keV window [23] and A Pb;t 1 was calculated using the Bateman equation: Although 212 Pb was present in the samples applied to the paper strip, none of this had the ability to translocalize from the paper strip to the inner surfaces of the vial, and it can therefore be disregarded in the calculations above. Two additional measurements on subsequent days were performed to ensure that there was no 224 Ra contamination in the original vial (V). The second experimental setup ( Fig 2B) sought to investigate the release of 220 Rn from solutions containing 224 Ra. Distinct volumes from 5 to 1000 μL of either free cationic 224 Ra 2+ in solution (diluted in 0.9% NaCl or water) or a suspension of 4.3 mg surface-labeled PAA-coated CaCO 3 microparticles in water were added to 1.5 mL Eppendorf tubes with the lids removed. Each sample tube (S) was inserted into a 5 mL Eppendorf tube (O1) and the lid closed. After 1 day, the outer tube was opened, the inner sample tube transferred to a new 5 mL Eppendorf tube (O2) and the radioactivity in both tubes was measured. The amount of 220 Rn release from the liquid into the air was estimated by the measured 212 Pb activity in the empty outer tube (O1) divided by the total activity: The procedure was repeated after 3 and 7 days. The trapping efficiency of the 220 Rn in the Eppendorf tubes was verified in a separate experiment and found to be more than 99.8%. In this experiment, a sample containing approximately 50 kBq 224 Ra in a 1.5 mL Eppendorf tube was contained in a sealed zip lock plastic bag for 1 or 7 days before the radioactivity in the plastic bag was measured without the Eppendorf tube inside. Potential release of 224 Ra to the solution was not taken into account because previous experiments showed that the retention of 224 Ra on surface-labeled CaCO 3 microparticles was above 97% in vitro [21].

Adsorption of 212 Pb onto CaCO 3 microparticles
To investigate the chemical fate of 212 Pb subsequent to its release caused by 220 Rn gas diffusion, a set of experiments was conducted to examine whether the 212 Pb could be re-adsorbed onto the CaCO 3 microparticles.
In a pilot experiment, duplicate samples of 5 mg surface-labeled CaCO 3 microparticles in 0.4 mL sucrose solution were added to a dialysis device (Slide-A-Lyzer MINI Dialysis Device, 0.5 mL format, 20 kDa MWCO, Thermo Fisher Scientific). The device was placed into a conical 15 mL centrifuge tube pre-filled with a suspension of 50 mg non-radioactive CaCO 3 microparticles in 14 mL Dulbecco's PBS (pH 7, Gibco, Fisher Scientific), and the tube was then capped with a screw lid. The tube was gently shaken at 150 rpm using a table orbital shaker for 24 h at room temperature before the dialysis device was removed and the tube centrifuged to collect the microparticles in the external solution. The radioactivity levels in the dialysis device (A D ), the supernatant of the external solution (A S ) and the pelleted microparticles from the 15 mL tube (A P ) were measured. The percentage of released 212 Pb during the 24 h was estimated as follows: The percentage of the released 212 Pb activity that was adsorbed onto the CaCO 3 particles was estimated as: The dependency of the adsorption of 212 Pb on the CaCO 3 microparticle concentration was examined in further experiments with a more simplified setup. In this case, 212 Pb was used directly and not as in the previous experiments where the source of 212 Pb was the great-grandparent nuclide 224 Ra. Samples of non-radioactive CaCO 3 microparticles in 75% Dulbecco's PBS and 25% fetal bovine serum solution (pH 7.5-8.5) with concentrations ranging from 0.1-50 mg/mL were prepared in 1.5 or 5 mL Eppendorf tubes. Equal activities of 212 Pb were added to each sample before stirring with orbital motion at 450 rpm using an Eppendorf C thermomixer or at 30 rpm using a HulaMixer at 37˚C. After 45-95 min, the samples were centrifuged to separate the microparticles from the solution. The radioactivity levels in the supernatant (A S ) and the pelleted microparticles (A P ) were measured, and the percentage of 212 Pb activity that had adsorbed onto the originally non-radioactive CaCO 3 microparticles was determined as described above.
The 212 Pb was produced and separated from the 224 Ra via 220 Rn emanation [24] using a single chamber diffusion system [23]. A few μL of 224 RaCl 2 solution were distributed on quartz wool (ProQuarz, Mainz, Germany) that was fixed on the inside of the screw cap of a 100 mL glass flask (Simax-Kavalierglass, Prague, Czech Republic). The sealed flask was left inverted overnight in a fume hood for the 220 Rn to be released through the air inside the vial. The 220 Rn would then decay into 212 Pb and become deposited on the interior walls of the container. After 20 to 28 h, the cap with the 224 Ra source was carefully removed, avoiding the 224 Ra contamination of the vial. The 212 Pb was subsequently retrieved by washing the glass walls with 1 M HCl solution.

Therapeutic effect of surface-and inclusion-labeled 224 Ra-CaCO 3 microparticles in mice
Female athymic nude mice (Hsd:Athymic Nude-Foxn1 nu , bred at the Department of Comparative Medicine, The Norwegian Radium Hospital, Oslo University Hospital, Oslo, Norway) of 4-6 weeks of age at the start of the experiment were used. The animals were maintained under pathogen-free conditions with food and water supplied ad libitum and monitored for changes in body weight, behavior, posture and appearance throughout the study. All procedures involving animals were approved by the Norwegian Food Safety Authority (permit ID 7274) and performed in compliance with regulations set by the same authority and EU Directive 2010/63/EU on the protection of animals used for scientific purposes.
Human ovarian epithelial carcinoma cell line ES-2 (American Type Culture Collection, Wesel, Germany) was cultured in McCoy's 5A medium (Gibco, Fisher Scientific) supplemented with 10% fetal bovine serum (Gibco, Fisher Scientific) and 1% penicillin/streptomycin (Gibco, Fisher Scientific) at 37˚C in a humid atmosphere with 5% CO 2. The cells were harvested with TrypLE Express solution (Gibco, Fisher Scientific), suspended in cold RPMI 1640 growth medium (Gibco, Fisher Scientific) and kept on ice until inoculation.
The therapeutic effects of four different variants of 224 Ra-CaCO 3 microparticles were investigated: both surface-and inclusion-labeled microparticles each with and without PAA coating. A total of 40 mice were randomized to the experimental groups and inoculated IP with 1 × 10 6 ES-2 cells. One day later, the mice were given the different treatments as shown in Table 2. All the animals that were treated with 224 Ra-CaCO 3 microparticles received a single IP injection of 0.29-0.52 mL to achieve the same radioactivity dose based on their body weight. The control animals received 0.9% NaCl (0.4 mL) or 5 mg CaCO 3 microparticles (0.4 mL) dispersed in sucrose solution.
Therapeutic effect was evaluated by the time it took to reach the pre-determined humane endpoints, which were defined as rapid body weight loss (> 10% within one week), ascites build-up that severely impaired mobility and/or cachexia. Mice were euthanized by cervical dislocation when they reached the predetermined endpoint and necropsied for gross pathological examination.

Statistical analysis
All statistical analyses were performed in GraphPad Prism (version 8.2.1, GraphPad Software, La Jolla, CA, USA) using a significance level of 0.05. The release of 220 Rn from different 224 Ra sources was analyzed by Kruskal-Wallis test using the Dunn method to correct for multiple comparisons. Survival curves were compared pairwise by log-rank tests and the Holm-Sidak method to adjust the p-values for multiple comparisons.

Release of 220 Rn to air from open 224 Ra sources
The release of 220 Rn to air from open 224 Ra microsources was measured indirectly through the amount of daughter 212 Pb that had re-localized. Radium-224, either in the form of free cation or as surface-or inclusion-labeled CaCO 3 microparticles, was applied on a paper strip fixed on a needle suspended in a glass vial (Fig 2A). The percentage of 220 Rn release was estimated by dividing the 212 Pb activity detected in the outer vial with the theoretical maximum amount of 212 Pb generated from 220 Rn decay. The results displayed in Fig 3 show higher 220 Rn release from 224 Ra as a free cation than as 224 Ra-labeled CaCO 3 microparticles, although the difference was not significant (Kruskal-Wallis, p � 0.0512). No evident difference was seen between the different 224 Ra-labeling methods of the CaCO 3 microparticles (p � 0.9999).

Ra-labeling method PAA coating Activity dose (kBq/kg bodyweight) CaCO 3 mass dose (mg per mouse) No. of mice
0.9% NaCl n/a n/a n/a n/a 7 The emanation of 220 Rn was also evaluated for open liquid sources of 224 Ra (Fig 2B). Different volumes of free 224 Ra or surface-labeled PAA-coated CaCO 3 microparticles were added to a tube without a cap that was contained inside a larger closed tube. After approximately 1 day, the ratio of 212 Pb activity detected in the outer vial to the total 212 Pb activity was used to indicate the 220 Rn release from the open liquid sources. The results show that the 220 Rn release was at least 4 times lower when the 224 Ra was adsorbed onto the microparticles as compared with as a dissolved cation, which is in line with the findings from the first experimental setup. The re-localization of 212 Pb due to 220 Rn diffusion also appears to be dependent on the liquid volume of the sample, with higher 220 Rn release at lower volumes (Fig 4). The release at low volumes may be underestimated because of the 212 Pb activity deposited on the inner tube wall (Fig 2B). The experiment was repeated on days 3 and 7, yielding similar results for the volume dependency (S1 Fig), which indicates that a steady state was obtained after 1 day.

Adsorption of the 220 Rn daughter 212 Pb on CaCO 3 microparticles
In order to investigate whether the 212 Pb released from the surface-labeled 224 Ra-CaCO 3 microparticles could re-adsorb onto the microparticles, both the percentage of the 212 Pb activity released from the dialysis unit to the outer solution and the percentage of the 212 Pb adsorbed onto the originally non-radioactive microparticles were measured. Of the approximately 6% 212 Pb that had crossed the dialysis barrier, 75% was found to have re-associated with the CaCO 3 microparticles.
Subsequent experiments showed that the degree of 212 Pb adsorption was high even at relatively low CaCO 3 microparticle concentrations (Fig 5). Adsorption decreased at CaCO 3 microparticle concentrations below 1 mg/mL, whereas between 1 and 50 mg/mL, it appeared to reach a plateau with adsorption of approximately 70-80%.

Therapeutic effect of surface-and inclusion-labeled 224 Ra-CaCO 3 microparticles in mice
A single IP injection of 224 Ra-CaCO 3 microparticles significantly improved survival as compared with both the saline and non-radioactive CaCO 3 microparticle groups (p � 0.023), regardless of the different radiolabeling methods and PAA coating (Fig 6). The control groups had no survivors beyond day 17, whereas all mice were alive at this time in the different 224 Ra-CaCO 3 microparticle groups. No statistically significant difference was found between the surface-and inclusion-labeled products (p � 0.1868), although the survival curves indicate that treatment with the inclusion-labeled 224 Ra-CaCO 3 microparticles with a PAA coating had a slightly inferior effect as compared with the other 224 Ra-labeled microparticle treatments. The survival curves of the saline control group and the group receiving PAA-CaCO 3 microparticles overlap, showing that the microparticle carrier itself had no effect in this cancer model.

Discussion
The current study demonstrates that there is a significant diffusion of 220 Rn from 224 Ra-CaCO 3 microparticles. Radon emanation from mineral grains is assumed to be governed by  alpha recoil because diffusion through the solid matrix can be considered negligible [25,26]. When 220 Rn is generated by alpha decay of 224 Ra (Fig 1), the atom acquires a kinetic energy of approximately 100 keV [27] resulting in a recoil range below 50 nm in most solids [28]. Hence, 220 Rn can only escape from the CaCO 3 microparticles if the 224 Ra atom upon decay is located closer than the recoil distance to either the outer surface of the microparticle or the surface of an internal pore connected to the outer surface, such that radon can subsequently diffuse through the pore volume and out from the microparticle.
The degree of 220 Rn diffusion seemed to be relatively independent of the radiolabeling method, that is, whether 224 Ra was adsorbed onto the surfaces or incorporated into the bulk of the microparticles during CaCO 3 precipitation. Based on the established theory for radon emanation from mineral grains, this may be explained by a porous structure of these CaCO 3 microparticles that allows 220 Rn to escape. SEM images presented in S1 Table indicate a degree of porosity of CaCO 3 microparticles, both with and without PAA coating. This is also in line with literature, where CaCO 3 microparticles synthesized by a similar procedure were shown to be highly porous, as approximately 40% of the volume of the microparticles was estimated to be internal pores [29]. The comparable 220 Rn release from the differently 224 Ra-labeled CaCO 3 microparticles is further corroborated by a relatively high radon diffusion coefficient in limestone [30], a mineral mostly composed of various crystal forms of CaCO 3 . The average distance 220 Rn can travel is dependent upon half-life (55.8 s, Fig 1) and the diffusion coefficient of the material the radon atoms traverse. Typically, the mean diffusion range is estimated to be a few hundred micrometers in water and centimeters in air ( Table 3). The estimated mean distance of 5.2 mm that 220 Rn can travel in limestone is thus approximately 1000 times greater than the median diameter of the CaCO 3 microparticles examined (range from 3 to 7 μm, S1 Table) and indicate low attenuation of radon diffusion within the microparticles.
The high diffusion coefficient of radon in limestone also implies that diffusion rates should be similar from 224 Ra-CaCO 3 microparticles and cationic 224 Ra. However, both the air and liquid phase studies demonstrated that the diffusion of 220 Rn was reduced when 224 Ra was bound to microparticles as compared with free 224 Ra. One explanation for this difference may be that release of 220 Rn through alpha recoil into a pore space also can lead to embedding of the radon atom into an adjacent grain [26]. If the residual kinetic energy of the recoiling radon atom is sufficient to traverse the internal pore diameter of the microparticles, the result can be a retrapping of 220 Rn in the solid microparticle matrix. The probability of implantation of recoiling radon atoms will be higher if pores are filled with air compared to water and is also dependent on the pore size [34].
All variants of the 224 Ra-CaCO 3 microparticles significantly extended the survival of the mice with IP tumors, but a correlation between the effect and the parameters that were varied was not clear. One treatment, inclusion-labeled 224 Ra-CaCO 3 microparticles with a PAA coating, seemed to be slightly less effective. Because of some variations in the 224 Ra-labeling yield, the activity dose was not directly comparable in the four different 224 Ra-CaCO 3 microparticle groups. The highest activity dose (474 kBq/kg) was administered to the mice receiving inclusion-labeled 224 Ra-CaCO 3 microparticles with a PAA coating. Therefore, this does not explain why this variant of the 224 Ra-CaCO 3 microparticles appeared less effective and may instead indicate a potential reduction of 220 Rn diffusion from the microparticles caused by the polymer surface coating. The surface-labeled PAA-coated variant would on the other hand not be affected by this, because surface labeling was performed after the microparticles were coated with the polymer and not prior to, as was the case for the inclusion-labeled. The surfacelabeled 224 Ra-CaCO 3 microparticles were given at an activity dose approximately twice as high (350 kBq/kg) as the analog with the PAA coating (138 kBq/kg) and the inclusion-labeled without (179 kBq/kg). Previous studies in the same tumor model showed prolonged survival with increasing administered activity [11,15]; however, the difference was not statistically significant between activity doses of 150 and kBq/kg [11]. Free 224 Ra was not used as a control in mice due to rapid translocalization from the peritoneal cavity [21] which resulted in inferior therapeutic efficacy compared to 224 Ra-CaCO 3 microparticles, even at 25% higher radioactivity dose [15]. The release of 220 Rn from CaCO 3 microparticles affects the microdistribution of the alpha particles from the 224 Ra series. The distance 220 Rn can travel subsequent to its escape from the microparticles can be estimated by its mean diffusion length (Table 3). In the case of using the 224 Ra-CaCO 3 microparticles as a treatment for IP cancer when the intent is to irradiate liquid volumes and serosal surfaces in the peritoneal cavity harboring micrometastases, the diffusion distance in water is probably the most relevant to consider. The additional distance 220 Rn atoms can travel in water because of recoil energy is estimated to be only 0.09 μm [28], which is significantly shorter than the 300-400 μm 220 Rn on average diffuses in the same material and was therefore disregarded. As illustrated in Fig 7,220 Rn diffusion can result in an increase in the irradiated volume from 224 Ra-CaCO 3 microparticles. The maximum distance an alpha particle can travel in water is less than one third of the mean diffusion length of 220 Rn in the same medium. Thus, the irradiated volume can be increased by a factor of 27 through 220 Rn diffusion. This indicates that the alpha-particle related microdosimetry of 224 Ra-labeled microparticles may be significantly different from that of microparticles labeled with single-step decaying alpha-emitting radionuclides. If only alpha-particle radiation is considered significant for the biological activity of 224 Ra-CaCO 3 microparticles, then three out of four alpha particles are produced by 220 Rn and its progenies. Depending on the degree of radon diffusion from the microparticles, a significant fraction of the therapeutic radiation dose can be delivered beyond the alpha-particle range from a microparticle. Thus, the emanation of 220 Rn could be of benefit both for extending the effective alpha-particle range and in terms of radiation "dose smoothening" as the microparticles may not be perfectly distributed in the treated cavity. The brachytherapy application DaRT also exploits the daughter nuclides of 224 Ra for extending the effective alpha-particle range. Through modeling, it has been shown that a point source of 224 Ra (with approximately 100 kBq) placed in a solid tumor with approximately 40% of the radon being released results in therapeutic alpha-particle dose levels over a distance of 4-7 mm in diameter [20]. This distance is also in line with preclinical studies in which necrotic regions of 5-7 mm in diameter have been observed after the placement of a single 224 Ra wire into squamous cell carcinoma tumors in mice [13].
The diffusion of 220 Rn from CaCO 3 microparticles also raises questions about the fate of the subsequent progenies. The immediate daughter of 220 Rn, 216 Po, has a half-life of only 0.15 s and will decay essentially in the same location as the mother nuclide. However, the subsequent progeny, 212 Pb, has a sufficiently long half-life to allow it to be transported further away from the parent nuclide and even redistribute from the peritoneal cavity. Approximately 30% of the energy released from alpha particles in the 224 Ra decay chain originate from progenies of 212 Pb. Hence, a significant fraction of the therapeutic radiation dose can be lost if this radionuclide decays away from the target area. This is the case in the DaRT application, where a considerable fraction of 212 Pb (assumed to be between 30 and 50% [20,35]) leaves the tumor via systemic circulation and redistributes to distant organs and tissues. With this in mind, a particularly interesting feature of 224 Ra-CaCO 3 microparticles is their ability to adsorb the free-floating 212 Pb generated following 220 Rn escape from the microparticles. The data from liquid phase studies indicate that the adsorption of 212 Pb onto the microparticles occurs to a significant degree, even under conditions mimicking an in vivo environment. The adsorption was also high over a wide range of microparticle concentrations, indicating that this phenomenon can also occur in the clinical treatment setting.
An understanding of which factors that impact the therapeutic effect is important when developing a new radiopharmaceutical. For the surface-labeled 224 Ra-CaCO 3 microparticles we have previously shown that the antitumor activity was dependent on the administered activity [11,15]. In addition, the results supported a positive correlation between therapeutic effect and specific activity, defined as the ratio of activity to mass dose of CaCO 3 , and a negative correlation between specific activity and degree of 224 Ra retention on the microparticles in vivo [15], altogether indicating that the therapeutic effect is not solely dependent on the total activity dose. The results presented in the current study suggest that 220 Rn diffusion from the microparticles and re-adsorption of 212 Pb may play a role. Further investigations are needed to elucidate the relationship between these different factors.

Conclusion
The 220 Rn diffusion from 224 Ra-labeled CaCO 3 microparticles is significant yet reduced as compared with the release from cationic 224 Ra. Furthermore, the diffusion of 220 Rn from microparticles seem to be independent on whether the microparticles were labeled by the surface adsorption of 224 Ra or if the 224 Ra was incorporated into the bulk of the microparticles. There is a significant adsorption of 212 Pb, the 220 Rn daughter with the longest half-life, onto CaCO 3 microparticles even at microparticle concentrations of a few mg/mL. Thus, the release of 220 Rn and re-adsorption of 212 Pb are features that may have implications for the radiotherapeutic use of 224 Ra-labeled CaCO 3 microparticles. The diffusion of 220 Rn up to a few hundred micrometers can extend the effective range of the inherent short-range alpha particles and may cause a "dose-smoothening effect" to counteract potential heterogeneous distribution of microparticles in the treated cavity, while the re-adsorption of 212 Pb onto the CaCO 3 microparticles can contribute to enhancing the retention of 212 Pb in the target area.