In Vitro Cytotoxicity of 211At-Astatide and 131I-Iodide to Glioma Tumor Cells Expressing the Sodium/Iodide Symporter

BASIC SCIENCE INVESTIGATIONS In Vitro Cytotoxicity of 211At-Astatide and 131I-Iodide to Glioma Tumor Cells Expressing the Sodium/Iodide Symporter

Sean Carlin, PhD; Gamal Akabani, PhD; and Michael R. Zalutsky, PhD

Department of Radiology, Duke University Medical Center, Durham, North Carolina

The sodium/iodide symporter (NIS) has been identified as an It is now well established that the accumulation of iodide attractive target for cancer therapy. The efficacy of 131I-iodide by the thyroid gland is mediated by the sodium/iodide for NIS-expressing tumor therapy may be limited by a combi- symporter (NIS), an integral membrane protein expressed nation of poor cellular retention and unfavorable physical characteristics (long physical half-life and low linear-energy-transfer on the basolateral surface of the thyrocyte. Iodide is trans- [LET] radiative emissions). On the other hand, 211At-astatide is ported across the cell membrane against a concentration also transported by NIS and offers several therapeutic advan- gradient in a sodium-dependent manner, in a process elec- tages over 131I-iodide due to its physical characteristics (short trochemically coupled to the energy-dependent Naϩ/Kϩ- ␣ half-life, high LET -particle emissions). The objective of this adenosinetriphosphatase (1). The cloning of the NIS gene study was to directly compare the radiotoxicity of both radio- has allowed investigations into the effect of plasmid- or nuclides using a NIS-transfected cultured cell model. Methods: Cytotoxicity was determined by colony-forming assays. Also, a viral-mediated NIS expression on the iodide-concentrating first-order pharmacokinetic model was used to simulate the capacity in a variety of thyroid and nonthyroid cell types closed compartmental system between the medium and cells. (2). These studies have indicated that NIS transgene expres- Experimental data were then fitted to this model and used to sion, under the control of a variety of promoters, confers estimate the transfer coefficients between medium and cells, iodide uptake capacity in a wide range of cell lines, allowing kc , and between cells and medium, km. Using the pharmacoki- m c the possibility of radioiodide therapy for many tumor types. netic model, the cumulated activity concentrations in the medium and cells were calculated. Monte Carlo transport methods However, several of these studies also report that the efflux were then used to assess absorbed doses from 131I and 211At. of iodide from NIS-transfected cells, including anaplastic Results: 211At-Astatide was significantly more cytotoxic than thyroid cells, is extremely rapid (3–6). This observation is 131I-iodide in this closed compartmental system. For 211At-as- of fundamental importance for any endoradiotherapeutic tatide, absorbed doses per unit administered activity were 54- strategy, as radiation-absorbed dose (and thus treatment to 65-fold higher than for 131I-iodide. Both NIS-expressing and control cells showed increased sensitivity to 211At over 131I, with efficacy) is a function of the cellular residence time and physical half-life (t ) of the radionuclide (7), with optimal significantly lower D0 (absorbed dose required to reduce the 1/2 Ϫ1 survival fraction to e ) and SF2 (2-Gy survival fraction) values, conditions reached when the radiologic t1/2 matches the ␣ highlighting the higher intrinsic cytotoxicity of -particles. How- biologic t1/2 (i.e., cellular retention). Dosimetric calculations ever, NIS-independent (nonspecific) binding of 211At-astatide and subsequent in vivo studies, using a murine xenograft 131 was higher than that of I-iodide, therefore, yielding a lower model, have indicated that successful treatment of low- absorbed dose ratio between NIS-transfected and -nontrans- 131 fected cells. Conclusion: Treatment of NIS-expressing cells retention NIS-expressing tumor deposits with I-iodide ϭ with 211At-astatide resulted in higher absorbed doses and in- (t1/2 8.04 d) may not possible without the administration creased cytotoxicity per unit administered activity than that of prohibitively high activities of radioiodide (8–10). In observed with 131I-iodide. These results suggest that 211At-as- addition, the effectiveness of 131I in curing micrometastatic tatide may be a promising treatment strategy for the therapy of disease decreases with tumor size, due to the relatively long NIS-expressing tumors. path length of the ␤-particle (11), resulting in an increased J Nucl Med 2003; 44:1827–1838 probability of disease recurrence. Astatine (astatide), the heaviest of the halogens, exhibits a pronounced accumulation in the thyroid gland in halide form and in the stomach (12). We have previously demon- Received Apr. 11, 2003; revision accepted Jul. 22, 2003. For correspondence or reprints contact: Michael R. Zalutsky, PhD, Depart- strated NIS-mediated accumulation of astatide, with uptake ment of Radiology, Box 3808, Duke University Medical Center, Durham, NC 27710. and efflux characteristics almost identical to those of iodide 211 E-mail: [email protected] (4). Fortunately, At has a physical t1/2 of 7.214 h, which

211AT-ASTATIDE:DOSIMETRY AND RADIOTOXICITY ¥ Carlin et al. 1827 closely matches the biologic t1/2 reported for iodide in a G-418 sulfate (0.5 mg/mL) (Gibco) in addition to the conditions variety of NIS-expressing xenograft models (9,13,14), un- described above. 131 211 like the physical t1/2 of I. In addition, the decay of At ␣ External Beam Irradiations results in the emission of -particles with a mean linear Cells were trypsinised, counted, and resuspended in sterile tubes ␮ energy transfer (LET) of 97 keV/ m. This value, represent- containing 5 mL fresh medium to a final concentration of 5 ϫ 105 ing the ionizing energy deposited by the particulate emis- cells per milliliter. Irradiations (0Ð9 Gy) were performed using a sion per unit distance, is approximately 500 times that of the 6-MV external photon beam accelerator at a dose rate of 0.5 therapeutic ␤-emitting radionuclides 90Y and 131I. Upon Gy-minϪ1 with the appropriate bolus to ensure full buildup of the interaction with DNA, this high density of ionization events radiation beam. Cells were plated for colony-forming assay in result in a high incidence of generally irreparable double- 6-well plates (growth area, 9.6 cm2) and grown at 37¡Cina5% strand DNA breaks, which accounts for the extreme radio- CO2 atmosphere for 7Ð10 d. Colonies were then stained and toxicity of this radionuclide (15). Also, the short range of counted, with colonies comprising 50 or more cells scored as 211At ␣-particles in tissue (maximum range, 70 ␮m) makes viable. such emissions more effective for the sterilization of micro- Radionuclides metastatic tumor clusters than ␤-particles. Another advan- The radionuclide 211At was produced at the Duke University tage of ␣-particle therapy is that cell survival is independent Medical Center CS-30 cyclotron via the 209Bi(␣, 2n)211At reaction of dose rate, which is of particular significance in relation to using the MIT-1 internal target system as previously described the rapid uptake and efflux kinetics of radiohalides in NIS- (12). 211At was distilled from the molten bismuth target and expressing cells lacking an organification mechanism. trapped in a cooled condenser. It was then isolated from the This article describes in vitro studies directed at evaluat- condenser by washing with approximately 1 mL phosphate-buff- ing the hypothesized cytotoxic advantages of 211At-astatide ered saline (PBS), pH 7.4. After isolation, Na2SO3 (Mallinckrodt) ϫ Ϫ4 over 131I-iodide for the treatment of NIS-expressing cells was added to a final concentration of 2 10 mol/L, to minimize the formation of higher oxidation state species. Sodium 131I-iodide lacking a halide organification mechanism. Experiments (no carrier added) was purchased from DupontÐNew England were performed using the human glioma cell line UVW, Nuclear. transfected with human NIS complementary DNA (cDNA) (called NIS6 hereafter), using the parental cell line (UVW) Pharmacokinetics as a negative control. The sensitivity of each cell line to Experiments were carried out to assess the uptake and efflux external beam irradiation was established by clonogenic pharmacokinetics of radiohalides. Cells were plated in 24-well ϫ 4 assay, allowing comparison of intrinsic radiosensitivity in plates at approximately 5 10 cells per well and allowed to both cell lines and also of the cellular sensitivity to both low attach overnight. For radionuclide uptake curves, cells were incubated for 1Ð30 min in wells with 0.5 mL PBS containing either and high LET particle-emitting radionuclides. Sensitivity of 211 131 211 131 At-astatide (100 kBq/mL) or I-iodide (50 kBq/mL). At- both cell lines to varying activity concentrations of I- astatide uptake and 131I-iodide uptake were terminated by the 211 iodide and At-astatide was also established by colony- removal of the radiohalide-containing incubation buffer, followed forming assay. A pharmacokinetic model was derived to by 3 rapid washes in ice-cold PBS. Cells were then solubilized by describe the closed compartmental system between the me- the addition of 0.5 mL lysis buffer (0.1 mol/L NaOH, 1% sodium dium and cells. Experimentally derived kinetic data were dodecyl sulfate, 2% Na2CO3) and assessed for radioactivity using then fitted to this model and used to estimate transfer an LKB 1282 ␥-counter (LKB), in dual-channel mode. For radio- coefficients between medium and cells. Using the pharma- halide efflux studies, cells were plated as described above in PBS cokinetic model, the cumulated activity concentrations in containing 211At-astatide (100 kBq/mL) and 131I-iodide (50 kBq/ the medium and cells were calculated. Monte Carlo trans- mL) for 30 min. Radioactive incubation buffer was then removed, ϫ Ϫ3 port methods were then used to assess absorbed doses from and cells were incubated in PBS containing 1 10 mol/L thiocyanate ion (SCNϪ) to inhibit the reuptake of radiohalide for 131I and 211At, which were correlated with the radionuclide the various time intervals to ensure the same conditions used in the sensitivity data, allowing the determination and comparison colony-forming assay. Cells were then solubilized in lysis buffer of radiobiologic parameters for both cell lines to each irra- and assessed for radioactivity using a ␥-counter. diation modality. To assess variation in total uptake as a function of cell density (number of cells per unit volume dc), cells were plated at various ϫ 4 ϫ 5 MATERIALS AND METHODS cell numbers between 1 10 and 5 10 per well and incubated as described above in 0.5 mL PBS containing either 211At-astatide Cell Culture (100 kBq/mL) or 131I-iodide (50 kBq/mL) for 30 min. Cells were The human glioma cell line UVW (European Collection of Cell then washed and counted for radioactivity with exact cell numbers Cultures no. 86022703) was transfected with cDNA encoding the determined with a hemocytometer. In this manner, we were able to human NIS gene to create the NIS6 cell line with a method that has estimate the uptake fraction as a function of cell density. previously been described (4). Cells were maintained in Eagle’s minimal essential medium (Gibco), supplemented with 10% fetal Cell Survival Fraction Assay bovine serum (Hyclone), penicillin/streptomycin (100 U/mL), and UVW and NIS6 cells were seeded in 24-well plates and allowed fungizone (2 mg/mL) (Gibco). Cells were cultured at 37¡Cina5% to attach for 24 h. Culture medium was then aspirated and replaced 131 211 CO2 atmosphere. Transfected cells were maintained in geneticin with fresh medium containing I-iodide (0Ð5 MBq/mL) or At-

1828 THE JOURNAL OF NUCLEAR MEDICINE ¥ Vol. 44 ¥ No. 11 ¥ November 2003 astatide (0Ð50 kBq/mL). For the cell survival fraction assay, cells total number of cells; and Vc ϭ Ncvc is the volume of all cells 3 were incubated for 30 min at 37¡Cina5%CO2 atmosphere. The (cm ); VT ϭ Vm ϩ Vc where VT is the total volume of the system 3 3 total number of cells per well was determined by hemocytometer (cm ); and Vm is the volume of the incubation medium (cm ). 0 u counting to assess the cell density dc. Cells were then given 3 rapid During uptake (u), the initial conditions are nm ϭ cte, nc ϭ 0, and 0 u u u washes in PBS, trypsinized, and plated for colony-forming assay by conservation of mass Vmnm ϭ Vmnm ϩ Ncvcnc, where dc ϭ u u as described above. After 10Ð14 d, colonies were stained and Nc/VT is the cell density and VT is the volume of the system during u u counted, with colonies comprising 50 or more cells scored as the uptake period; thus, the solutions for nm and nc are: viable. Absorbed dose calculations were then carried out to assess 0 n Ϫ͑ c uϩ m͒ the survival fraction as a function of absorbed dose and estimate u ͑ ͒ ϭ m ͓͑ u c ͒ kmvcd c kc t ϩ m͔ nm t ͑ u c ϩ m͒ dcvckm e kc 211 131 dcvckm kc the radiotoxicity of At-astatide and I-iodide. , Eq. 3 u c ͑ Ϫ ͒ c u m · 1 d v k Ϫ͑ ϩ ͒ Pharmacokinetic Model of Halide Distribution nu͑t͒ ϭ n0 c c m ͓1 Ϫ e kmvcdc kc t͔ c m ͑d uv kc ϩ km͒ Figure 1 illustrates a closed system describing the distribution c c m c of halide anion between medium and cells, and the differential where the decay-corrected fractional cell uptake F(dc) as a function equations that describe this closed system, following MichaelisÐ of cell density dc for an incubation period tu is given by:

Menten kinetics, are given by: u u c N v n ͑t ͒ d v k Ϫ͑ c uϩ m͒ ͑ ͒ ϭ c c c u ϭ c c m ͓ Ϫ kmvcd c kc tu͔ F dc 0 ͑ u c ϩ m͒ 1 e ,Eq.4 dn V d v Vmnm d cvckm kc m ϭ Ϫ max ϩ m c c ϩ dcvcnm kc ͑ Ϫ ͒ nc dt Km nm 1 dcvc 3 ϱ 3 , Eq. 1 which tends to equilibrium conditions when t ; thus, F(dc) dnc Vmax dcvc · c c ϩ m ϭ ϩ d n Ϫ km n dcvckm/(dcvckm kc ). This expression is used to estimate the values ϩ cvc m c ͑ Ϫ ͒ c c m dt Km nm 1 dcvc of km and kc by means of nonlinear regression analysis from experimental observations. The solutions during efflux (e) for ne where n is the average molar concentration of the nuclide in the m m and ne after an incubation period t and removal of the medium and medium; n is the average molar concentration in a cell (mol/L); c u c e ϭ e Ϫ1 dilution to a new cell density dc Nc/VT are: Vmax is the theoretic maximum transfer rate (mol/L s ); and Km is the MichaelisÐMenten constant for NIS in this system (mol/L); vc e 0 m e d cvcnc kc Ϫ͑kc d e ϩkm͒͑tϪt ͒ 3 n ͑t͒ ϭ ͓1 Ϫ e m cvc c u ͔ is the average volume of an adherent cell (cm ); dc ϭ Nc/VT is the m ͑ Ϫ e ͒ ͑ e c ϩ m͒ 1 d cvc d cvckm kc Ϫ3 , Eq. 5 cell density (cell cm ); and Nc is the total number of cells. We 0 c e m · n Ϫ͑ ϩ ͒͑ Ϫ ͒ have previously estimated the K for NIS in this system as 35 e͑ ͒ ϭ c ͓ m kmd cvc kc t tu ϩ c e ͔ m nc t ͑ c e ϩ m͒ kc e kmd cvc ␮mol/L with respect to iodide (4) but were unable to obtain a kmd cvc kc e 0 u similar estimate using astatide due to the absence of a stable where VT is the total volume of system during efflux; nc ϭ nc(tu) astatine isotope. However, we have previously demonstrated that is the initial molar concentration of cells; and by conservation of 0 e e astatide competes equally with iodide in this system (16) and, mass Ncvcnc ϭ Vmnm ϩ Ncvcnc any time afterwards. The activity therefore, assume that the Km value for astatide is similar to that of concentration in the medium am and in cells ac are then given as: iodide. nu ͑t͒ 0 Յ t Յ t The maximum initial molar concentrations used in our clono- a ͑t͒ ϭ 1 ϫ 10Ϫ3␭N ␳Ϫ1eϪ␭t ͭ m u 211 131 m A m e ͑ ͒ Ͼ genic studies of either At-astatide or I-iodide in the medium nm t t tu ϫ Ϫ6 ϫ Ϫ3 ␮ ,Eq.6 (6.2 10 and 8.2 10 mol/L, respectively) were several u͑ ͒ 0 Յ t Յ t · n t ͑ ͒ ϭ ϫ Ϫ3␭ ␳Ϫ1 Ϫ␭t ͭ c u orders of magnitude smaller than the Km value estimated for ac t 1 10 NA c e e͑ ͒ Ͼ nc t t tu iodide. Consequently, when nm ϽϽ Km, the above equations can be approximated as: where NA is Avogadro’s number; ␳m and ␳c are the densities of the medium and cells, respectively; and ␭ is the physical decay con- dn d v m ϭ Ϫ c ϩ m c c stant for the radionuclide in consideration. The cumulated activity kmdcvcnm kc ͑ Ϫ ͒ nc dt 1 dcvc concentration in the medium a˜ and in the cells a˜ are then given , Eq. 2 m c dnc dcvc · as: ϭ ϩ c Ϫ m kmdcvcnm kc ͑ Ϫ ͒ nc dt 1 dcvc ϭ u ϩ e a˜ m a˜ m a˜ m c ϭ ͮ,Eq.7 where km Vmax/Km is the transfer constant from the medium to a ϭ u ϩ e Ϫ1 a˜ c a˜ c a˜ c cell (s ) where the net transfer rate is given by Vmaxdcvc/Km, and m Ϫ1 u u kc is the transfer constant from a cell to the medium (s ); Nc is the where a˜m and a˜c are the cumulated activity concentration in the e e medium and a cell during uptake, respectively; and a˜m and a˜c are the corresponding cumulated activity concentrations for the me- u dium and cells during efflux, respectively. The expressions for a˜m, e u e a˜m, a˜c, and a˜c are given in Appendix A. The total cumulated activity per cell is then given as:

ϭ ͑ u ϩ e͒ q˜ c vc a˜ c a˜ c ,Eq.8

where vc is the average volume of a cell. Because this compartmental model is a closed system, the residence time of the radionuclide in the medium and cells during uptake is given by ␶u ϭ u u Ϫ1 Ϫ␭t e e e FIGURE 1. Compartmental model describing distribution of ␶m ϩ␶c ϭ␭ (1 Ϫ e u), and during efﬂux as ␶ ϭ␶m ϩ␶c ϭ Ϫ1 Ϫ1 0 0 0 NIS substrate anions between medium and cell. ␭ dcvc(1 Ϫ dcvc) ac/am, where ac is the cell activity concentra-

211AT-ASTATIDE:DOSIMETRY AND RADIOTOXICITY ¥ Carlin et al. 1829 211 tion after an incubation period tu. A glossary of the terminology Microdosimetry of At-Astatide used is given in Appendix B. Microdosimetry of 211At-astatide was carried out using an ␣-particle Monte Carlo transport code as described elsewhere (20). 131 Small-Scale Dosimetry of I-Iodide The cell nucleus was considered to be the target in these calcula- 131 Dosimetry of I-iodide was carried out using the EGS4 Monte tions. The total absorbed dose is then given as: Carlo transport code, which was estimated using the geometry ϭ c ៮ c ϩ c ៮ c utilized in the in vitro assays (17–19). The cell nucleus was D a˜ mhm z 1m q˜ chc z 1c , Eq. 10 considered to be the target in these calculations. UVW and NIS6 cells were stained using Cyto16 (Molecular Probes), which binds where D is average absorbed dose (Gy); a˜m is the total cumulated Ϫ1 c to nucleic acids. Phase-contrast and fluorescent images of cells activity in the medium (Bq s g ); hm is the average number of hits Ϫ1 Ϫ1 ៮ c were obtained and superimposed and used as a model for these from medium to cells (hits g Bq s ); z 1m is the average specific Ϫ1 calculations (Fig. 2). In these dosimetric calculations, 2 sources energy per event from medium to cells (Gy hit ); q˜c is the Ϫ1 c were identified: the medium where the activity was diluted, and the cumulated activity per cell (Bq s cell ); hc is the average number Ϫ1 Ϫ1 ៮ c attached cells themselves, which take up the activity from the of hits from cells to cells (hits Bq s ); and z 1c is the average Ϫ1 medium. The images provided the basic cell morphology that was specific energy per event from cells to cells (Gy hit ). The values c c ៮ c ៮ c used in these calculations. The nucleus of adherent cells had a for hm, hc, z 1m, and z 1c were estimated as a function of cells per unit semiellipsoid geometry. However, for simplification purposes, we area to account for cross fire among cells (data not shown). As an ϫ used a spheric model of the cell and nucleus, where the volume of example, a cylindric well (diameter, 16.5 mm) containing 1.4 5 the semiellipsoid nucleus was that of the sphere nucleus. Thus, the 10 adherent cells resulted in a surface cell density of 655 cells Ϫ2 ៮ c ៮ c c estimated average cell and nuclear diameter used in these studies mm , and the corresponding conversion factors for z 1m, z 1c, hm, c Ϫ1 Ϫ1 ϫ Ϫ9 3 were 16 and 10 ␮m, respectively. and hc were 0.224 Gy hit , 0.114 Gy hit , 4.456 10 hit cm Ϫ1 Ϫ1 Ϫ1 Ϫ1 The estimated dose conversion factor for 131I-iodide when the Bq s , and 0.407 hit Bq s , respectively. source was the medium and the target was the cells, S(m 3 c), was Ϫ Ϫ Ϫ 1.48 ϫ 10 11 GygBq 1 s 1, and the dose conversion factor when RESULTS both the source and the target were the cells, S(c 3 c), was 5.5 ϫ 10Ϫ4 Gy BqϪ1 sϪ1. These dose conversion factors were used to External Beam Radiation assess the total absorbed dose to UVW and NIS6 cells from Data obtained from the external beam radiation dose/ 131I-iodide. The total average absorbed dose to a cell is then given survival assay were fitted using the linear quadratic model as: of cell survival SF ϭ exp(Ϫ␣D Ϫ␤D2), where SF is the surviving fraction and D is the absorbed dose (Fig. 3). Using ϭ ͑ 3 ͒ ϩ ͑ 3 ͒ D a˜ mS m c q˜ cS c c , Eq. 9 the statistical analysis software SAS, we carried out the model fitting to assess the parameters ␣ and ␤. The esti- where a˜m is the cumulated activity concentration in the medium and q˜c is the average cumulated activity in a cell (Bq s). mated 2-Gy survival fraction, SF2, for UVW and NIS6 cell lines was 0.71 (0.62Ð0.83, 95% confidence interval [CI]) and 0.61 (0.53Ð0.70, 95% CI), respectively. There was no statistically significant difference for the SF2 between the 2 cell lines based on a t test with equal variances (P ϭ 0.3) (SAS).

Radionuclide Uptake and Efflux Pharmacokinetics The decay-corrected fraction of administered activity taken up by the cells after a 30-min incubation period F(dc) 211 was estimated as a function of cell density dc for At- astatide and 131I-iodide for UVW and NIS6 cell lines. Figure 4 shows the experimental data for NIS6 and UVW cell lines illustrating both specific and nonspecific cellular uptake. The uptake of 131I-iodide and 211At-astatide by NIS6 cells was approximately 60- and 27-fold higher than that of the nontransfected UVW (control), respectively. Also, the nonspecific (NIS independent) association of 211At-astatide was about 4-fold higher that that of 131I-iodide, possibly due to the presence of a higher oxidation state of astatine in the FIGURE 2. Superimposition of phase-contrast and fluores- aqueous solution (16). Using nonlinear regression analysis, c m cent images of adherent cells labeled with Cyto16 nuclear stain the transfer coefficients km and kc were derived based on the to show nuclear and cell morphology of UVW and NIS6 cell observed efflux kinetics (Fig. 4A) and the expression for lines. Colony-forming assays were performed under similar con- c F(dc) (Fig. 4B). Table 1 shows the estimated values for km ditions. Images were used to derive cellular and nuclear geom- m c etry, which subsequently was used in calculations to determine and kc for UVW and NIS6 cell lines. In each instance, km m cumulated absorbed dose. Strongly green regions identify cell was higher than kc , indicating that, in the presence of an nuclei. extracellular halide ion concentration, there is a net associ-

1830 THE JOURNAL OF NUCLEAR MEDICINE ¥ Vol. 44 ¥ No. 11 ¥ November 2003 using both 131I-iodide and 211At-astatide. An activity concentration-dependent decrease in surviving clonogens was observed after treatment of NIS6 cells with both radionuclides (Fig. 6). For both radionuclides examined, the control parental UVW cell line was less sensitive than the NIS- transfected cell line, indicating the preferential therapeutic efﬁcacy in NIS-expressing cells over control cells. The survival data were ﬁtted using a single exponential and, for the purpose of comparison, we used this model to calculate A0, which indicates the initial activity concentra-

FIGURE 3. Survival fraction of NIS6 and UVW as function of external beam radiation-absorbed dose. Points represent average of triplicate determinations and corresponding SD. External beam dose rate was 0.5 Gy minϪ1. The estimated 2-Gy SF (95% confidence interval [CI]) was 0.71 (0.62–0.83, 95% CI) and 0.61 (0.53–0.70, 95% CI) for UVW and NIS6, respectively. There was no statistically significant difference between NIS6 and UVW cells lines (P ϭ 0.296). ation of ion with the cell. The net rate of accumulation of astatide and iodide by NIS6 cells was 32.5- and 27.2-fold higher than that observed for UVW cells, respectively. We c m observed that astatide had a higher km and lower kc value than iodide with respect to UVW cells, reflecting the higher nonspecific association of astatide previously reported (16). Pharmacokinetic Model of Halide Distribution This model describes the distribution of 131I-iodide and 211At-astatide between the incubation medium and cells over time in the presence (uptake) and absence (efflux) of halide anions. For the purposes of these studies, we modeled a closed system to reproduce the incubation conditions used in the colony-forming assays. The uptake and efflux rate constants of c m the system (km and kc , respectively) were determined from the experimental data as described above. Figure 5 is a represen- tative example of the pharmacokinetics of 211At-astatide in NIS6 and UVW cells during uptake and efflux phases. This system is sensitive to cell density in the assay system (dc), as highlighted in Fig. 5B. During the efflux phase, the system reequilibrates as 211At-astatide moves from cells to medium FIGURE 4. (A) Fractional cell-associated activity (FCAA)of 211 and is then subject to reuptake (upper curve). Reduction of the At-astatide for UVW and NIS6 cell lines during efflux as function of time. Similar curves were generated using 131I-iodide cell density during the efflux phase, as occurs during plating (data not shown). Data represent means Ϯ SD from at least 2 for colony-forming assay, results in equilibration at a much triplicate determinations. (B) Fractional cell uptake F(dc) as func- lower cellular concentration (lower curve). This effect is more tion of cell density for NIS6 and UVW cell lines for incubation pronounced in NIS6 cells (Fig. 5B) than in UVW cells (Fig. period of 30 min for 131I-iodide and 211At-astatide. Data repre- 5A), as the total nonspecific cell-associated activity is many sent means of 3 determinations. Experimental data were fitted to theoretic expression for F(dc) to estimate transfer constants fold lower than NIS-mediated uptake. c m 131 km and kc shown in Table 1. Uptake of I-iodide by NIS6 cells was approximately 60-fold higher than that of UVW (nonspecific Administered Activity Concentration Versus Survival binding). Total uptake of 211At-astatide to NIS6 cells was ap- Fraction proximately 27-fold higher than that of UVW. Nonspecific bind- The effect of increasing radionuclide concentration on ing of 211At-astatide was approximately 4-fold higher than that clonogenic survival was assessed in UVW and NIS6 cells of 131I-iodide.

211AT-ASTATIDE:DOSIMETRY AND RADIOTOXICITY ¥ Carlin et al. 1831 TABLE 1 Estimated Pharmacokinetic Parameters for 131I-Iodide and 211At-Astatide for UVW and NIS6 Cell Lines

131I-Iodide 211At-Astatide c Ϫ1 m Ϫ1 c m c Ϫ1 m Ϫ1 c m km (s ) kc (s ) km/kc km (s ) kc (s ) km/kc

NIS6 1.96 ϫ 10Ϫ1 1.19 ϫ 10Ϫ3 164.7 4.79 ϫ 10Ϫ1 2.10 ϫ 10Ϫ3 228.1 UVW 7.20 ϫ 10Ϫ3 2.07 ϫ 10Ϫ3 3.5 1.47 ϫ 10Ϫ2 1.88 ϫ 10Ϫ3 7.8 NIS6 27.22 0.57 32.50 1.12 UVW

c m km ϭ transfer coefﬁcient from media to cells; kc ϭ transfer coefﬁcient from cells to media.

tions of each radionuclide required to reduce the clonogenic capacity of UVW and NIS6 cells by 1 natural logarithm Ϫ1 (e ). These values are shown in Table 2. The A0 ratio between UVW and NIS6 cells was 13.2-fold for 131I-iodide and 11.5-fold for 211At-astatide. The similarity of these values is consistent with the similar pharmacokinetics for

FIGURE 5. Calculated fractional cell-associated activity for UVW and NIS6 cell lines for 211At. Cell density during uptake was 5 ϫ 105. Cell density during efflux was reduced by factor of 1 ϫ 103 cells cmϪ3,reflecting conditions used during colony-forming assay. However, when cell density was left constant, a different efflux profile is observed as indicated in Equation 5. Uptake c period was 30 min. Calculations were based upon estimated km FIGURE 6. Survival fraction as function of activity concentra- m and kc coefficients that were derived from our experimental tion in medium for incubation period of 30 min. Survival fraction studies (Table 1). Area under the curve was calculated to assess of NIS6 and UVW for 131I (A) and for 211At (B), respectively. Data cumulated activity concentration in cells and corresponding represent means Ϯ SD of at least 3 triplicate determinations. absorbed dose. Therapeutic efficiency and toxicity ratios are given in Table 2.

1832 THE JOURNAL OF NUCLEAR MEDICINE ¥ Vol. 44 ¥ No. 11 ¥ November 2003 TABLE 2 Effect of 131I-Iodide and 211At-Astatide Administration on Clonogenic Survival of UVW and NIS6 Cell Lines

131 211 A0 I A0 At (MBq mLϪ1) (MBq mLϪ1) [131I]/[211At]

UVW 86.43 0.126 686 NIS 6.55 0.011 598 UVW 13.2 11.5 NIS6 both radionuclides in this system. Comparison of the rela- 131 tive toxicity of each radionuclide (A0 for I divided by A0 for 211At) indicates that, in terms of radioactive concentration, 211At-astatide is between 600 and 700 times more radiotoxic that 131I-iodide in this model (Table 2). The higher nonspecific association of 211At-astatide in this system may account for the variation observed in both of these ratios. The cumulated activity concentrations in the medium and cells were estimated by integrating the uptake-efflux kinetics over time as a function of cell density dc and then were used to calculate the absorbed doses for UVW and NIS6 per unit administered activity (Table 3). Correlation of Survival Fraction and Absorbed Dose Radionuclide sensitivity data from these experiments were correlated with estimates of absorbed dose. The cumulated activity concentrations were calculated by deter- mining the area under the curve (AUC) derived from the pharmacokinetic model. Absorbed doses were estimated by calculating the cumulated activity concentration in the medium and cells and using the corresponding conversion factors as described in Equations 9 and 10 for 131I-iodide FIGURE 7. Survival fraction of UVW and NIS6 cell lines as 211 131 211 function of absorbed dose from At-astatide (A) and I-iodide and At-astatide, respectively. These data, shown in Figure 211 (B). Estimated D0 of UVW and NIS6 for At-astatide was 0.27 7, demonstrate that both UVW and NIS6 cells have a greater (0.19–0.46, 95% CI) Gy and 0.28 (0.26–0.30, 95% CI) Gy, sensitivity to an equivalent absorbed dose of high LET respectively. 2-Gy SF was 6.3 ϫ 10Ϫ4 (3.1 ϫ 10Ϫ5 Ϫ 1.3 ϫ 10Ϫ2, ␣-particles (Fig. 7A) than to low LET ␤-particles (Fig. 7B). 95% CI) and 7.4 ϫ 10Ϫ4 (4.2 ϫ 10Ϫ4 Ϫ 1.3 ϫ 10Ϫ3, 95% CI), 131 Single-exponential equations were fitted to these data and respectively. D0 of UVW and NIS6 for I-iodide was 5.27 (2.5– fitted coefficients were used to derive D and 2-Gy surviv- 6.4, 95% CI) Gy and 4.31 (3.0–7.6, 95% CI) Gy, respectively, 0 and 2-Gy SF for UVW and NIS6 was 0.68 (0.02–20.4, 95% CI) ing fractions (SF2) for each cell line and radionuclide. These and 0.66 (0.35–1.22, 95% CI), respectively. data are shown in Table 4. This similarity of D0 and SF2 values between NIS6 and UVW using each treatment modality cells confirms that plasmid-mediated NIS expression does not alter the intrinsic cellular radiosensitivity in this model system. The SF2 values obtained from external beam TABLE 4 Dose Factors and 2-Gy Survival Fraction Associated with TABLE 3 131I-Iodide, 211At-Astatide, and External Beam Radiation Average Absorbed Dose per Unit Administered Activity in UVW and NIS6 Cells Lines In Vitro of 131I-Iodide and 211At-Astatide in UVW and NIS6 Cells Lines 131I 211At XRT D (Gy) SF D (Gy) SF SF 131I (Gy-mL/MBq) 211At (Gy-mL/MBq) [211At]/[131I] 0 2 0 2 2 UVW 5.27 0.68 0.27 6.3 ϫ 10Ϫ4 0.71 UVW 4.59 ϫ 10Ϫ2 3.01 65.5 NIS6 4.31 0.66 0.28 7.4 ϫ 10Ϫ4 0.61 NIS 6.64 ϫ 10Ϫ1 36.5 55.0 NIS6 14.5 12.0 UVW XRT ϭ external beam radiotherapy.

211AT-ASTATIDE:DOSIMETRY AND RADIOTOXICITY ¥ Carlin et al. 1833 radiotherapy (Fig. 3) are similar to those derived from above. The ratio of A0 values between NIS-negative (UVW) 131I-iodide treatment, which is in concordance with many and NIS-expressing (NIS6) cells (ratio 1, Table 2) was 13.2 for 131 211 previous observations. However, the SF2 values derived I-iodide and 11.5 for At-astatide (Table 2). The similarity from 211At-astatide treatment were 900- to 1,100-fold higher of these values reflects the similar pharmacokinetics of cellular (Table 4) than those from both external beam radiotherapy iodide and astatide association in this model system. The and 131I in both cell lines, reflecting the cytotoxicity of smaller therapeutic differential calculated for 211At may reflect 211At-astatide observed in this system (Table 2). Compari- the higher degree of nonspecific binding observed with aque- 211 131 son of D0 values for At-astatide and I-iodide demon- ous astatide solutions (16,21). For this study, we define the strates a 15.3- and 19.5-fold differential for UVW and NIS6, terms “specific binding” as NIS-mediated, perchlorate-sensi- respectively, highlighting the therapeutic advantage, in tive cellular uptake and “nonspecific binding” as non-NIS- terms of radiation quality, of high LET 211At ␣-particles mediated, perchlorate-insensitive cellular uptake of radioha- over low LET 131I ␤-particles. lide. Detailed examination of the properties of specific and nonspecific uptake of both 131I-iodide and 211At-astatide in this model system have previously been reported (16). Comparison DISCUSSION of A0 values for each radionuclide indicated an enhanced The transgene-mediated expression of the NIS has been sensitivity to 211At of 686-fold in UVW cells and 598-fold in demonstrated to confer iodide uptake capacity to a wide NIS6 cells compared with 131I. Similar enhancements in sen- range of cell types that would not normally concentrate sitivity (up to 1,400-fold) were observed previously when iodide (2–4). NIS gene transfer, followed by radioiodide comparing the cytotoxicity of 211At- and 131I-labeled benzyl- administration, allows the possibility of treatment of tumors guanidine compounds in neuroblastoma cells (22). These data, at many sites in a manner analogous to the highly effica- and our own observations, are in accordance with calculations cious treatment of differentiated thyroid carcinoma with that predict a 1,200-fold increase in cytotoxicity for ␣-particles radioiodide. However, the short retention time of iodide on a single cell basis (23). It should be noted that A0 values, observed in nonthyroid xenografts, combined with the rel- expressed in units of activity per unit volume (Bq mLϪ1) only 131 atively long physical t1/2 of I, results in an insufficient indicate the relative toxicity of each radionuclide under the absorbed dose for successful tumor eradication. The use of experimental conditions used for these studies. Calculation of radionuclides with similar chemical properties and more cumulated absorbed dose from each radionuclide also requires favorable physical properties, such as a higher LET and that radiologic t1/2 and system geometry be taken into account. shorter physical t1/2, should result in an increased radiation Absorbed dose calculations indicate that administration of dose and thus enhanced efficacy. 211At-astatide results in an increase (53.9- to 64.9-fold) over We have previously reported that plasmid-mediated cellular 131I-iodide in absorbed dose per administered activity concen- expression of the NIS confers the ability to accumulate 211At- tration (Table 3). astatide in addition to iodide (16). Here we describe clonogenic The rapid efflux of iodide from NIS-expressing cells survival experiments designed to directly compare the radio- lacking an organification mechanism has been observed in toxicity of 131I-iodide and 211At-astatide on a cultured cell several cell lines and rodent xenograft models (4,9,24). The model and a pharmacokinetic model, which was used to esti- biologic t1/2 of iodide in xenograft tumors is generally mate absorbed dose for each radionuclide in UVW and NIS6 longer than that observed in 2-dimensional cultured cell cell lines. To determine whether expression of the NIS protein, models, presumably due to the continual reuptake of iodide or selection of NIS-positive clones, resulted in an alteration of by the tumor. Although this has allowed effective demon- cellular radiosensitivity, a comparison of the radiation sensi- strations of the potential of NIS expression for tumor im- tivity of UVW and NIS6 cell lines was performed by exam- aging using NIS substrate molecules such as 123IϪ, 124IϪ, and 99m Ϫ ining the clonogenic survival of both cell lines in response to TcO4 (25–27), the successful sterilization of such tumors 131 external photon beam irradiation. The SF2 values obtained for with I is likely to require the administration of prohibi- both cell lines were not significantly different, 0.71 (0.62Ð0.83, tively large quantities of radioactivity (9). However, studies 95% CI) and 0.61 (0.53Ð0.70, 95% CI) for UVW and NIS6, performed using an in vivo prostate model have demon- respectively (Fig. 3), indicating that expression of NIS has no strated, given sufficiently high administered radioactivity, effect on intrinsic radiosensitivity. The effect of activity con- that nonthyroid tumor xenografts with transgene-mediated centration of both 131I-iodide and 211At-astatide on UVW and NIS expression can be successfully treated with 131I(8). NIS6 cells was determined by colony-forming assay. An ac- This demonstrates the principle that NIS-expressing tumor tivity concentration-dependent decrease in clonogenic survival deposits can be successfully targeted and treated with an was observed in both cell lines with both radionuclides (Fig. ionic radiohalide in vivo and that the therapeutic effect is 6), with NIS6 cells having increased sensitivity to each radio- dependent on delivering a sufficient radiation dose to tumor. nuclide when compared with control UVW cells. Using these ␣-Particle-emitting radionuclides have considerable po- data, values were calculated to indicate the activity concentra- tential as cytotoxic agents in the treatment of malignant tion required to cause a reduction in survival by 1 natural disease. The short range and high LET ␣-particle makes logarithm (A0), using the incubation conditions described their use particularly suited to the treatment of micrometa-

1834 THE JOURNAL OF NUCLEAR MEDICINE ¥ Vol. 44 ¥ No. 11 ¥ November 2003 static and minimal residual disease, where the radiation dose similar to that encountered in vivo, which will aid in the to tumor is normally limited by the dose delivered to sur- future design of NIS-based therapeutic strategies. rounding normal tissues. Tumor-specific targeting of ␣-par- Given the similar pharmacokinetics of 131I-iodide and ticles can result in highly focal irradiation, high tumor 211At-astatide in our model system, our observation of a absorbed doses, and minimization of surrounding normal higher absorbed dose using 211At-astatide can be explained tissue toxicity. The first clinical trial with an 211At-labeled by a combination of the higher energy ␣-particle (5.87 therapeutic antibody (antitenascin monoclonal antibody MeV) versus 131I ␤-particle emission (0.6 MeV) as well as 211 131 81C6) is currently underway, with encouraging initial ob- the shorter physical t1/2 of At (7.2 h vs. 192 h for I). servations of high radiation doses to the target area and low Similarly, a study into the potential of 188Re (in the form 188 Ϫ doses to surrounding normal tissue (28). ReO4 ) to sterilize NIS-expressing cells calculated a 4.5- The data presented in this article indicate that the admin- fold higher absorbed dose, when compared with 131I(14). istration of 211At-astatide results in a significant increase This enhancement is likely due to a combination of factors: (55- to 65.6-fold) over 131I-iodide in absorbed dose per 188Re emits ␤-particles with a higher energy than 131I (2.12 Ϫ Ϫ administered activity concentration (Table 3). However, the vs. 0.61 MeV), and ReO4 had higher tumor uptake than I nonspecific association of 211At-astatide with cells lacking in a NIS-expressing xenograft model (14). However, much NIS expression also contributes to the dose to these cells, of the increase in absorbed dose results from the compara- 188 resulting in a lower therapeutic differential than that ob- tively short physical t1/2 (16.7 h) of Re (14). These find- served with 131I-iodide at the same administered activity ings are of particular significance in relation to cell types concentration (12.0 and 14.5, respectively) (Table 3). lacking a peroxidase-based organification mechanism, as A previous study evaluating the uptake of 211At-astatide these cells generally exhibit a very short cellular retention of by NIS transgene-expressing thyroid tumor cells (21) pre- iodide (3,4), and matching of both the physical and biologic sented several observations similar to our current and pre- half-lives of the radioisotope is desirable for maximal ra- viously published data (16). Uptake and efflux kinetics of diobiologic effect. both 211At-astatide and 131I-iodide are similar in each cul- In vivo, tumor cells may show a heterogeneous expres- tured cell model system, and uptake of both radiohalides sion of NIS that can be predicted to result in a heteroge- Ϫ Ϫ was sensitive to excess perchlorate (ClO4 ) and iodide (I ) neous cumulated activity distribution with the tumor mass. concentration, demonstrating that 211At-astatide is trans- However, depending on the range of the radiations emitted ported by NIS with an efficiency approaching that of iodide. by the radionuclide used for therapy, there is a potential for Using a murine xenograft model, the intraperitoneal admin- cross fire among tumors cells. Although the range of ␣-par- istration of 211At-astatide resulted in a 14.4-fold increase in ticles is significantly shorter than that of ␤-particles, a tumor absorbed dose over that predicted for 131I-iodide, with degree of cross fire can be predicted. The proportion of cells similar biologic half-lives observed for both anions (21). receiving a highly toxic absorbed dose from 211At-astatide Although the difference in pharmacokinetics between in will therefore depend on a combination of the overall trans- vitro and in vivo models precludes a direct comparison of fection efficiency, the spatial distribution of transgene ex- absorbed dose, the conclusions of Petrich et al. (21), in pression and radionuclide within the tumor, and the degree accordance with this study, indicate that the administration of cross fire. The use of cultured cell models, such as the of 211At-astatide results in a significantly higher absorbed one described here, affords the opportunity for detailed dose to NIS-expressing cells than 131I-iodide per unit ad- analysis of these issues and may provide the basis for a ministered activity. clinical implementation of transgene-mediated radionuclide The pharmacokinetic model presented in this study de- therapy in the future. It is also important to note that there scribes the phenomenologic distribution of halide anions in are some tumor types, such as thyroid and invasive breast a closed system, which accurately describes the conditions carcinoma, that may express sufficient NIS to facilitate used in the cultured cell clonogenic assays described above. 211At-astatide therapy without the need for transgene-medi- It is also possible to use this model to analyze the pharma- ated expression. 188 Ϫ 211 cokinetics of other NIS substrate anions, such as ReO4 or The use of ionic At-astatide for the treatment of thyroid 99m Ϫ TcO4 , under similar experimental conditions. In addi- carcinoma has previously been investigated in murine xeno- tion, it can also be adapted, given appropriate experimental graft models, with high tumor uptakes reported for more observations, to predict the effect of alteration of many differentiated thyroid tumor cells, which generally retain a system parameters (e.g., level of NIS expression, heteroge- higher level of NIS expression than anaplastic thyroid tu- neous cell populations, pharmacologic inhibitors of halide mors (29–31). A study comparing the uptake of 125I-iodide efflux) on both pharmacokinetic distribution and cumulated and 211At-astatide in nude mice bearing human fetal thyroid absorbed dose. We intend to further develop this model to and human malignant thyroid xenografts observed that the examine the pharmacokinetics of NIS-mediated anion trans- human tissue accumulated both halides with similar kinet- port in a 3-dimensional cultured cell system and, in combi- ics, suggesting that 211At-astatide may be an alternative nation with biodistribution data, to develop a model describ- radionuclide to 131I-iodide for the treatment of thyroid car- ing the pharmacokinetics in a dynamic extracellular system cinoma (29). Another study examining the comparative

211AT-ASTATIDE:DOSIMETRY AND RADIOTOXICITY ¥ Carlin et al. 1835 transport of 125I-iodide and 211At-astatide using normal por- CONCLUSION cine thyrocytes in a polarized system also observed simi- The data presented in this article demonstrate that 211At- larities in the basal membrane (i.e., NIS mediated) transport astatide has potential as an alternative radionuclide to 131I- of both radiohalide anions (32). Interestingly, this study also iodide for the treatment of NIS-expressing tumor cells. The reported the perchlorate- and ouabain-insensitive basal direct comparison of 211At and 131I in this closed system membrane transport of astatide, by normal thyrocytes, sug- highlights the enhancements in absorbed dose and radiotox- gesting the possibility of another, NIS-independent astatide icity of high LET ␣-particles over low LET ␤-particle uptake mechanism in these cells. Further elucidation of this irradiation. 211At-Astatide administration results in in- transport mechanism may provide some explanation as to creased cytotoxicity (686- to 598-fold) and higher absorbed the differences in biodistribution of astatide and iodide, in doses (55- to 65.5-fold) per unit administered activity when addition to providing another means of targeting astatine to 131 compared with I-iodide. In addition, the physical t1/2 of tumor cells. 211At is closely matched to the radionuclide residence time 211 The biodistribution of systemically administered At- observed in nonthyroid tumor types, providing a further astatide, though similar to that of iodide, has several clini- therapeutic advantage over 131I. These observations imply cally relevant differences. In particular, a signiﬁcantly that some of the limitations of 131I administration for the higher uptake than iodide in both lung and spleen tissues is therapy of endogenous or transgene-mediated NIS-express- 211 observed (12,33). At present, clinical trials of At-astatide ing tumors can be overcome. The pharmacokinetic model for the treatment of thyroid carcinoma have not been initi- presented here is a valuable tool in predicting the inﬂuence ated, possibly because of concerns over radiotoxicity in on absorbed dose resulting from modulation of many ex- these tissues or due to the limited availability of the radio- perimental system parameters. Further development of this nuclide. Previous investigations have revealed that pharma- model to describe a 3-dimensional tumor within a dynamic cologic intervention may modify the level of astatide uptake environment will aid in the elucidation of the relationship in normal tissues (12), and further studies into the possible between administered radioactivity and resulting absorbed mechanisms involved in the lung and spleen retention of doses in NIS-expressing tumors with different retention astatide are currently underway. Although lung and spleen characteristics. uptake currently precludes the systemic administration of 211At-astatide, combined gene transfer/radionuclide treatment of compartmentalized tumors such as those of brain, ACKNOWLEDGMENTS bladder, and ovary may be possible with minimal involve- NIS cDNA was kindly provided by Dr. Sissy M. Jhiang ment of the systemic circulation. Further advances in the (Ohio State University, Columbus, OH). This work was understanding of the mechanisms of astatine uptake and supported by grants CA42324, CA70164, and CA91927 retention in lung and spleen will aid greatly in the clinical from the National Institutes of Health and by an AstraZen- implementation of systemic 211At-astatide therapy for tu- eca Union Internationale Contre le Cancer Translational mors with both endogenous and gene transferÐmediated Cancer Research Fellowship (American Cancer Society Be- NIS expression. ginning Investigator 11/2001).

APPENDIX A Pharmacokinetics

System description: dn d v dn d v m ϭ Ϫ c ϩ m c c c ϭ ϩ c Ϫ m c c kmdcvcnm kc ͑ Ϫ ͒ nc, kmdcnm kc ͑ Ϫ ͒ nc dt 1 dcvc dt 1 dcvc

0 The uptake solutions given conservation of mass Vmnm ϭ Vmnm ϩ Ncvcnc are: 0 u c n Ϫ͑ c uϩ m͒ ͑1 Ϫ d v ͒k Ϫ͑ c uϩ m͒ u ͑ ͒ ϭ m ͓ u c kmvcd c kc t ϩ m͔ u͑ ͒ ϭ 0 c c m ͓ Ϫ kmvcd c kc t͔ nm t ͑ u c ϩ m͒ dcvckme kc , nc t nm ͑ u c ϩ m͒ 1 e dcvckm kc dcvckm kc nu ͑t͒ 0 Յ t Յ t nu͑t͒ 0 Յ t Յ t ͑ ͒ ϭ ϫ Ϫ3␭ ␳Ϫ1 Ϫ␭tͭ m u ͑ ͒ ϭ ϫ Ϫ3␭ ␳Ϫ1 Ϫ␭tͭ c u am t 1 10 NA m e e ͑ ͒ Ͼ , ac t 1 10 NA c e e͑ ͒ Ͼ nm t t tu nc t t tu

0 u c a Ϫ͑ c uϩ m͒ Ϫ␭ ͑1 Ϫ d v ͒k Ϫ͑ c uϩ m͒ Ϫ␭ u ͑ ͒ ϭ m ͓ u c kmvcd c kc t ϩ m͔ t u͑ ͒ ϭ 0 c c m ͓ Ϫ kmvcd c kc t͔ t am t ͑ u c ϩ m͒ dcvckme kc e , ac t am ͑ u c ϩ m͒ 1 e e dcvckm kc dcvckm kc Ϫ͑ c u ϩ mϩ␭͒ Ϫ␭ c u ͑ Ϫ kmd cvc kc tu͒ m͑ Ϫ tu͒ u ϭ 0 ͫ kmdcvc 1 e ϩ kc 1 e ͬ a˜ m am ͑ c u ϩ m͒͑ c u ϩ m ϩ ␭͒ ␭͑ c u ϩ m͒ kmdcvc kc kmdcvc kc kmdcvc kc

1836 THE JOURNAL OF NUCLEAR MEDICINE ¥ Vol. 44 ¥ No. 11 ¥ November 2003 0 c u a k ͑1 Ϫ d v ͒ Ϫ͑ c u ϩ mϩ␭͒ Ϫ␭ u ϭ m m c c ͓͑ c u ϩ m͒ ϩ ␭ kmd cvc kc tu Ϫ ͑ c u ϩ m ϩ ␭͒ tu͔ a˜ c ͑ c u ϩ m͒͑ c u ϩ m ϩ ␭͒␭ kmdcvc kc e kmdcvc kc e kmdcvc kc kmdcvc kc 0 The efﬂux solutions given conservation of mass Ncvcnc ϭ Vmnm ϩ Ncvcnc are: de n0 km n0 e cvc c c Ϫ͑ c e ϩ m͒ e c m Ϫ͑ c e ϩ m͒ c e ͑ ͒ ϭ ͓ Ϫ kmd cvc kc t͔ ͑ ͒ ϭ ͓ kmd cvc kc t ϩ ͔ nm t ͑ Ϫ e ͒ ͑ e c ϩ m͒ 1 e , nc t ͑ c e ϩ m͒ kc e kmdcvc 1 dcvc dcvckm kc kmdcvc kc de a0 km a0 e cvc c c Ϫ͑ c e ϩ m͒ Ϫ␭ e c m Ϫ͑ c e ϩ m͒ c e Ϫ␭ ͑ ͒ ϭ ͓ Ϫ kmd cvc kc t͔ t ͑ ͒ ϭ ͓ kmd cvc kc t ϩ ͔ t am t ͑ Ϫ e ͒ ͑ e c ϩ m͒ 1 e e , ac t ͑ c e ϩ m͒ kc e kmdcvc e 1 dcvc dcvckm kc kmdcvc kc a0dev km a0͑␭ ϩ kc dev ͒ e ϭ c c c c e ϭ c m c c a˜ m ␭͑ Ϫ e ͒͑ e c ϩ m ϩ ␭͒ a˜ c ␭͑ e c ϩ m ϩ ␭͒ 1 dcvc dcvckm kc dcvckm kc Residence times:

c u Ϫ͑kc d u ϩkmϩ␭͒t m Ϫ␭t k d v ͑1 Ϫ e m cvc c u͒ k ͑1 Ϫ e u͒ m c c ϩ c ϩ u e ͑ c u ϩ m͒͑ c u ϩ m ϩ ␭͒ ␭͑ c u ϩ m͒ a˜ a˜ ϩ a˜ kmdcvc kc kmdcvc kc kmdcvc kc ␶ ϭ m ϭ m m ϭ m 0 0 c u m a a u c Ϫ͑k vcd ϩk ͒tu Ϫ␭tu e m m m ΄ ͑1 Ϫ d v ͒k ͑1 Ϫ e m c c ͒e d v k ΅ c c m c c c ͑ u c ϩ m͒ ␭͑ Ϫ e ͒͑ e c ϩ m ϩ ␭͒ dcvckm kc 1 dcvc dcvckm kc

c u c u m Ϫ͑kc d u ϩkmϩ␭͒t c u m Ϫ␭t k ͑1 Ϫ d v ͓͒͑k d v ϩ k ͒ ϩ ␭e m cvc c u Ϫ ͑k d v ϩ k ϩ ␭͒e u͔ m c c m c c c m c c c ϩ u e ͑ c u ϩ m͒͑ c u ϩ m ϩ ␭͒␭ a˜ a˜ ϩ a˜ kmdcvc kc kmdcvc kc ␶ ϭ c ϭ c c ϭ c 0 0 c u m a a u c Ϫ͑k d vcϩk ͒tu Ϫ␭tu c e m m ΄ ͑1 Ϫ d v ͒k ͓1 Ϫ e m c c ͔e ͑␭ ϩ k d v ͒ ΅ c c m m c c ͑ u c ϩ m͒ ␭͑ e c ϩ m ϩ ␭͒ dcvckm kc dcvckm kc

3 APPENDIX B Vc Volume of cells (cm ) 3 Glossary VT Total volume of system (cm ) u VT Total volume of system during uptake period 3 nm Average halide concentration in medium (cm ) e (mol/L) VT Total volume of system during efflux period u 3 nm Average halide concentration in medium (cm ) during uptake (mol/L) F(dc) Fractional cell uptake (unitless) e nm Average halide concentration in medium FCAA Fractional cell-associated activity (unitless) during efflux (mol/L) am Average activity concentration in medium Ϫ3 nc Average halide concentration in cells (Bq cm ) u (mol/L) a˜m Average cumulated activity concentration in u Ϫ3 nc Average halide concentration in cells during medium during uptake (Bq s cm ) e uptake (mol/L) a˜m Average cumulated activity concentration in e Ϫ3 nc Average halide concentration in cells during medium during efflux (Bq s cm ) efflux (mol/L) ac Average activity concentration in the cell Ϫ3 Vmax Theoretical maximum halide transfer rate (Bq cm ) Ϫ1 u (mol/L s ) a˜c Average cumulated activity concentration in Ϫ3 Km MichaelisÐMenten constant for NIS (mol/L) a cell during uptake (Bq s cm ) Ϫ3 e vc Average volume of a cell (cm ) a˜c Average cumulated activity concentration in Ϫ3 Ϫ dc Average cell density (cell cm ) a cell during efflux (Bq s cm 3) u Ϫ3 dc Average cell density during uptake (cell cm ) q˜c Average cumulated activity in a cell (Bq s) e Ϫ3 dc Average cell density during efflux (cell cm ) ␶u Residence time of system during uptake (s) Nc Total number of cells (cell) ␶e Residence time of system during efflux (s) Ϫ km Transfer rate between a cell to medium (s 1) u c ␶m Residence time of halide in medium during c Ϫ1 km Transfer rate between medium to a cell (s ) uptake (s) 3 Vm Volume of medium (cm )

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1838 THE JOURNAL OF NUCLEAR MEDICINE ¥ Vol. 44 ¥ No. 11 ¥ November 2003