|
|
||||||||
Basic Science Investigations |
Department of Radiology, Duke University Medical Center, Durham, North Carolina
| ABSTRACT |
|---|
|
|
|---|
-particle emissions). The objective of this study was to directly compare the radiotoxicity of both radionuclides using a NIS-transfected cultured cell model. Methods: Cytotoxicity was determined by colony-forming assays. Also, a first-order pharmacokinetic model was used to simulate the closed compartmental system between the medium and cells. Experimental data were then fitted to this model and used to estimate the transfer coefficients between medium and cells, kmc, and between cells and medium, kcm. Using the pharmacokinetic model, the cumulated activity concentrations in the medium and cells were calculated. Monte Carlo transport methods were then used to assess absorbed doses from 131I and 211At. Results: 211At-Astatide was significantly more cytotoxic than 131I-iodide in this closed compartmental system. For 211At-astatide, absorbed doses per unit administered activity were 54- to 65-fold higher than for 131I-iodide. Both NIS-expressing and control cells showed increased sensitivity to 211At over 131I, with significantly lower D0 (absorbed dose required to reduce the survival fraction to e-1) and SF2 (2-Gy survival fraction) values, highlighting the higher intrinsic cytotoxicity of
-particles. However, NIS-independent (nonspecific) binding of 211At-astatide was higher than that of 131I-iodide, therefore, yielding a lower absorbed dose ratio between NIS-transfected and -nontransfected cells. Conclusion: Treatment of NIS-expressing cells with 211At-astatide resulted in higher absorbed doses and increased cytotoxicity per unit administered activity than that observed with 131I-iodide. These results suggest that 211At-astatide may be a promising treatment strategy for the therapy of NIS-expressing tumors. | INTRODUCTION |
|---|
|
|
|---|
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 demonstrated NIS-mediated accumulation of astatide, with uptake and efflux characteristics almost identical to those of iodide (4). Fortunately, 211At has a physical t1/2 of 7.214 h, which closely matches the biologic t1/2 reported for iodide in a variety of NIS-expressing xenograft models (9,13,14), unlike the physical t1/2 of 131I. In addition, the decay of 211At results in the emission of
-particles with a mean linear energy transfer (LET) of 97 keV/µm. This value, representing the ionizing energy deposited by the particulate emission per unit distance, is approximately 500 times that of the therapeutic ß-emitting radionuclides 90Y and 131I. Upon interaction with DNA, this high density of ionization events result in a high incidence of generally irreparable double-strand DNA breaks, which accounts for the extreme radiotoxicity of this radionuclide (15). Also, the short range of 211At
-particles in tissue (maximum range, 70 µm) makes such emissions more effective for the sterilization of micrometastatic tumor clusters than ß-particles. Another advantage of
-particle therapy is that cell survival is independent of dose rate, which is of particular significance in relation to the rapid uptake and efflux kinetics of radiohalides in NIS-expressing cells lacking an organification mechanism.
This article describes in vitro studies directed at evaluating the hypothesized cytotoxic advantages of 211At-astatide over 131I-iodide for the treatment of NIS-expressing cells lacking a halide organification mechanism. Experiments were performed using the human glioma cell line UVW, transfected with human NIS complementary DNA (cDNA) (called NIS6 hereafter), using the parental cell line (UVW) as a negative control. The sensitivity of each cell line to external beam irradiation was established by clonogenic assay, allowing comparison of intrinsic radiosensitivity in both cell lines and also of the cellular sensitivity to both low and high LET particle-emitting radionuclides. Sensitivity of both cell lines to varying activity concentrations of 131I-iodide and 211At-astatide was also established by colony-forming assay. A pharmacokinetic model was derived to describe the closed compartmental system between the medium and cells. Experimentally derived kinetic data were then fitted to this model and used to estimate transfer coefficients between medium and cells. Using the pharmacokinetic model, the cumulated activity concentrations in the medium and cells were calculated. Monte Carlo transport methods were then used to assess absorbed doses from 131I and 211At, which were correlated with the radionuclide sensitivity data, allowing the determination and comparison of radiobiologic parameters for both cell lines to each irradiation modality.
| MATERIALS AND METHODS |
|---|
|
|
|---|
External Beam Irradiations
Cells were trypsinised, counted, and resuspended in sterile tubes containing 5 mL fresh medium to a final concentration of 5 x 105 cells per milliliter. Irradiations (09 Gy) were performed using a 6-MV external photon beam accelerator at a dose rate of 0.5 Gy-min-1 with the appropriate bolus to ensure full buildup of the radiation beam. Cells were plated for colony-forming assay in 6-well plates (growth area, 9.6 cm2) and grown at 37°C in a 5% CO2 atmosphere for 710 d. Colonies were then stained and counted, with colonies comprising 50 or more cells scored as viable.
Radionuclides
The radionuclide 211At was produced at the Duke University Medical Center CS-30 cyclotron via the 209Bi(
, 2n)211At reaction using the MIT-1 internal target system as previously described (12). 211At was distilled from the molten bismuth target and trapped in a cooled condenser. It was then isolated from the condenser by washing with approximately 1 mL phosphate-buffered saline (PBS), pH 7.4. After isolation, Na2SO3 (Mallinckrodt) was added to a final concentration of 2 x 10-4 mol/L, to minimize the formation of higher oxidation state species. Sodium 131I-iodide (no carrier added) was purchased from DupontNew England Nuclear.
Pharmacokinetics
Experiments were carried out to assess the uptake and efflux pharmacokinetics of radiohalides. Cells were plated in 24-well plates at approximately 5 x 104 cells per well and allowed to attach overnight. For radionuclide uptake curves, cells were incubated for 130 min in wells with 0.5 mL PBS containing either 211At-astatide (100 kBq/mL) or 131I-iodide (50 kBq/mL). 211At-astatide uptake and 131I-iodide uptake were terminated by the removal of the radiohalide-containing incubation buffer, followed by 3 rapid washes in ice-cold PBS. Cells were then solubilized by the addition of 0.5 mL lysis buffer (0.1 mol/L NaOH, 1% sodium dodecyl sulfate, 2% Na2CO3) and assessed for radioactivity using an LKB 1282
-counter (LKB), in dual-channel mode. For radiohalide efflux studies, cells were plated as described above in PBS containing 211At-astatide (100 kBq/mL) and 131I-iodide (50 kBq/mL) for 30 min. Radioactive incubation buffer was then removed, and cells were incubated in PBS containing 1 x 10-3 mol/L thiocyanate ion (SCN-) to inhibit the reuptake of radiohalide for the various time intervals to ensure the same conditions used in the colony-forming assay. Cells were then solubilized in lysis buffer and assessed for radioactivity using a
-counter.
To assess variation in total uptake as a function of cell density (number of cells per unit volume dc), cells were plated at various cell numbers between 1 x 104 and 5 x 105 per well and incubated as described above in 0.5 mL PBS containing either 211At-astatide (100 kBq/mL) or 131I-iodide (50 kBq/mL) for 30 min. Cells were then washed and counted for radioactivity with exact cell numbers determined with a hemocytometer. In this manner, we were able to estimate the uptake fraction as a function of cell density.
Cell Survival Fraction Assay
UVW and NIS6 cells were seeded in 24-well plates and allowed to attach for 24 h. Culture medium was then aspirated and replaced with fresh medium containing 131I-iodide (05 MBq/mL) or 211At-astatide (050 kBq/mL). For the cell survival fraction assay, cells were incubated for 30 min at 37°C in a 5% CO2 atmosphere. The total number of cells per well was determined by hemocytometer counting to assess the cell density dc. Cells were then given 3 rapid washes in PBS, trypsinized, and plated for colony-forming assay as described above. After 1014 d, colonies were stained and counted, with colonies comprising 50 or more cells scored as viable. Absorbed dose calculations were then carried out to assess the survival fraction as a function of absorbed dose and estimate the radiotoxicity of 211At-astatide and 131I-iodide.
Pharmacokinetic Model of Halide Distribution
Figure 1 illustrates a closed system describing the distribution of halide anion between medium and cells, and the differential equations that describe this closed system, following MichaelisMenten kinetics, are given by:
![]() | (Eq. 1) |
|
![]() | (Eq. 2) |
![]() | (Eq. 3) |
![]() | (Eq. 4) |
thus, F(dc)
dcvckmc/(dcvckmc + kcm). This expression is used to estimate the values of kmc and kcm by means of nonlinear regression analysis from experimental observations. The solutions during efflux (e) for nme and nce after an incubation period tu and removal of the medium and dilution to a new cell density dce = Nc/VTe are:
![]() | (Eq. 5) |
![]() | (Eq. 6) |
m and
c are the densities of the medium and cells, respectively; and
is the physical decay constant for the radionuclide in consideration. The cumulated activity concentration in the medium ãm and in the cells ãc are then given as:
![]() | (Eq. 7) |
![]() | (Eq. 8) |
u =
mu +
cu =
-1(1 - e-
tu), and during efflux as
e =
me +
ce =
-1dcvc(1 - dcvc)-1ac0/am0, where ac0 is the cell activity concentration after an incubation period tu. A glossary of the terminology used is given in Appendix B.
Small-Scale Dosimetry of 131I-Iodide
Dosimetry of 131I-iodide was carried out using the EGS4 Monte Carlo transport code, which was estimated using the geometry utilized in the in vitro assays (1719). The cell nucleus was considered to be the target in these calculations. UVW and NIS6 cells were stained using Cyto16 (Molecular Probes), which binds to nucleic acids. Phase-contrast and fluorescent images of cells were obtained and superimposed and used as a model for these calculations (Fig. 2). In these dosimetric calculations, 2 sources were identified: the medium where the activity was diluted, and the attached cells themselves, which take up the activity from the medium. The images provided the basic cell morphology that was used in these calculations. The nucleus of adherent cells had a semiellipsoid geometry. However, for simplification purposes, we used a spheric model of the cell and nucleus, where the volume of the semiellipsoid nucleus was that of the sphere nucleus. Thus, the estimated average cell and nuclear diameter used in these studies were 16 and 10 µm, respectively.
|
c), was 1.48 x 10-11 Gy g Bq-1 s-1, and the dose conversion factor when both the source and the target were the cells, S(c
c), was 5.5 x 10-4 Gy Bq-1 s-1. These dose conversion factors were used to assess the total absorbed dose to UVW and NIS6 cells from 131I-iodide. The total average absorbed dose to a cell is then given as:
![]() | (Eq. 9) |
c is the average cumulated activity in a cell (Bq s).
Microdosimetry of 211At-Astatide
Microdosimetry of 211At-astatide was carried out using an
-particle Monte Carlo transport code as described elsewhere (20). The cell nucleus was considered to be the target in these calculations. The total absorbed dose is then given as:
![]() | (Eq. 10) |
1mc is the average specific energy per event from medium to cells (Gy hit-1);
c is the cumulated activity per cell (Bq s cell-1); hcc is the average number of hits from cells to cells (hits Bq-1 s-1); and
1cc is the average specific energy per event from cells to cells (Gy hit-1). The values for hmc, hcc,
1mc, and
1cc were estimated as a function of cells per unit area to account for cross fire among cells (data not shown). As an example, a cylindric well (diameter, 16.5 mm) containing 1.4 x 105 adherent cells resulted in a surface cell density of 655 cells mm-2, and the corresponding conversion factors for
1mc,
1cc, hmc, and hcc were 0.224 Gy hit-1, 0.114 Gy hit-1, 4.456 x 10-9 hit cm3 Bq-1 s-1, and 0.407 hit Bq-1 s-1, respectively. | RESULTS |
|---|
|
|
|---|
D - ßD2), where SF is the surviving fraction and D is the absorbed dose (Fig. 3). Using the statistical analysis software SAS, we carried out the model fitting to assess the parameters
and ß. The estimated 2-Gy survival fraction, SF2, for UVW and NIS6 cell lines was 0.71 (0.620.83, 95% confidence interval [CI]) and 0.61 (0.530.70, 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 = 0.3) (SAS).
|
|
|
|
|
|
|
-particles (Fig. 7A) than to low LET ß-particles (Fig. 7B).
|
-particles over low LET 131I ß-particles.
|
| DISCUSSION |
|---|
|
|
|---|
We have previously reported that plasmid-mediated cellular expression of the NIS confers the ability to accumulate 211At-astatide in addition to iodide (16). Here we describe clonogenic survival experiments designed to directly compare the radiotoxicity of 131I-iodide and 211At-astatide on a cultured cell model and a pharmacokinetic model, which was used to estimate absorbed dose for each radionuclide in UVW and NIS6 cell lines. To determine whether expression of the NIS protein, or selection of NIS-positive clones, resulted in an alteration of cellular radiosensitivity, a comparison of the radiation sensitivity of UVW and NIS6 cell lines was performed by examining the clonogenic survival of both cell lines in response to external photon beam irradiation. The SF2 values obtained for both cell lines were not significantly different, 0.71 (0.620.83, 95% CI) and 0.61 (0.530.70, 95% CI) for UVW and NIS6, respectively (Fig. 3), indicating that expression of NIS has no effect on intrinsic radiosensitivity. The effect of activity concentration of both 131I-iodide and 211At-astatide on UVW and NIS6 cells was determined by colony-forming assay. An activity concentration-dependent decrease in clonogenic survival was observed in both cell lines with both radionuclides (Fig. 6), with NIS6 cells having increased sensitivity to each radionuclide when compared with control UVW cells. Using these data, values were calculated to indicate the activity concentration required to cause a reduction in survival by 1 natural logarithm (A0), using the incubation conditions described above. The ratio of A0 values between NIS-negative (UVW) and NIS-expressing (NIS6) cells (ratio 1, Table 2) was 13.2 for 131I-iodide and 11.5 for 211At-astatide (Table 2). The similarity of these values reflects the similar pharmacokinetics of cellular iodide and astatide association in this model system. The smaller therapeutic differential calculated for 211At may reflect the higher degree of nonspecific binding observed with aqueous astatide solutions (16,21). For this study, we define the terms
specific binding
as NIS-mediated, perchlorate-sensitive cellular uptake and
nonspecific binding
as non-NIS-mediated, perchlorate-insensitive cellular uptake of radiohalide. 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 of A0 values for each radionuclide indicated an enhanced sensitivity to 211At of 686-fold in UVW cells and 598-fold in NIS6 cells compared with 131I. Similar enhancements in sensitivity (up to 1,400-fold) were observed previously when comparing the cytotoxicity of 211At- and 131I-labeled benzylguanidine compounds in neuroblastoma cells (22). These data, and our own observations, are in accordance with calculations that predict a 1,200-fold increase in cytotoxicity for
-particles on a single cell basis (23). It should be noted that A0 values, expressed in units of activity per unit volume (Bq mL-1) only indicate the relative toxicity of each radionuclide under the experimental conditions used for these studies. Calculation of cumulated absorbed dose from each radionuclide also requires that radiologic t1/2 and system geometry be taken into account. Absorbed dose calculations indicate that administration of 211At-astatide results in an increase (53.9- to 64.9-fold) over 131I-iodide in absorbed dose per administered activity concentration (Table 3).
The rapid efflux of iodide from NIS-expressing cells lacking an organification mechanism has been observed in several cell lines and rodent xenograft models (4,9,24). The biologic t1/2 of iodide in xenograft tumors is generally longer than that observed in 2-dimensional cultured cell models, presumably due to the continual reuptake of iodide by the tumor. Although this has allowed effective demonstrations of the potential of NIS expression for tumor imaging using NIS substrate molecules such as 123I-, 124I-, and 99mTcO4- (2527), the successful sterilization of such tumors with 131I is likely to require the administration of prohibitively large quantities of radioactivity (9). However, studies performed using an in vivo prostate model have demonstrated, given sufficiently high administered radioactivity, that nonthyroid tumor xenografts with transgene-mediated NIS expression can be successfully treated with 131I (8). This demonstrates the principle that NIS-expressing tumor deposits can be successfully targeted and treated with an ionic radiohalide in vivo and that the therapeutic effect is dependent on delivering a sufficient radiation dose to tumor.
-Particle-emitting radionuclides have considerable potential as cytotoxic agents in the treatment of malignant disease. The short range and high LET
-particle makes their use particularly suited to the treatment of micrometastatic and minimal residual disease, where the radiation dose to tumor is normally limited by the dose delivered to surrounding normal tissues. Tumor-specific targeting of
-particles can result in highly focal irradiation, high tumor absorbed doses, and minimization of surrounding normal tissue toxicity. The first clinical trial with an 211At-labeled therapeutic antibody (antitenascin monoclonal antibody 81C6) is currently underway, with encouraging initial observations of high radiation doses to the target area and low doses to surrounding normal tissue (28).
The data presented in this article indicate that the administration of 211At-astatide results in a significant increase (55- to 65.6-fold) over 131I-iodide in absorbed dose per administered activity concentration (Table 3). However, the nonspecific association of 211At-astatide with cells lacking NIS expression also contributes to the dose to these cells, resulting in a lower therapeutic differential than that observed with 131I-iodide at the same administered activity concentration (12.0 and 14.5, respectively) (Table 3).
A previous study evaluating the uptake of 211At-astatide by NIS transgene-expressing thyroid tumor cells (21) presented several observations similar to our current and previously published data (16). Uptake and efflux kinetics of both 211At-astatide and 131I-iodide are similar in each cultured cell model system, and uptake of both radiohalides was sensitive to excess perchlorate (ClO4-) and iodide (I-) concentration, demonstrating that 211At-astatide is transported by NIS with an efficiency approaching that of iodide. Using a murine xenograft model, the intraperitoneal administration of 211At-astatide resulted in a 14.4-fold increase in tumor absorbed dose over that predicted for 131I-iodide, with similar biologic half-lives observed for both anions (21). Although the difference in pharmacokinetics between in vitro and in vivo models precludes a direct comparison of absorbed dose, the conclusions of Petrich et al. (21), in accordance with this study, indicate that the administration of 211At-astatide results in a significantly higher absorbed dose to NIS-expressing cells than 131I-iodide per unit administered activity.
The pharmacokinetic model presented in this study describes the phenomenologic distribution of halide anions in a closed system, which accurately describes the conditions used in the cultured cell clonogenic assays described above. It is also possible to use this model to analyze the pharmacokinetics of other NIS substrate anions, such as 188ReO4- or 99mTcO4-, under similar experimental conditions. In addition, it can also be adapted, given appropriate experimental observations, to predict the effect of alteration of many system parameters (e.g., level of NIS expression, heterogeneous cell populations, pharmacologic inhibitors of halide efflux) on both pharmacokinetic distribution and cumulated absorbed dose. We intend to further develop this model to examine the pharmacokinetics of NIS-mediated anion transport in a 3-dimensional cultured cell system and, in combination with biodistribution data, to develop a model describing the pharmacokinetics in a dynamic extracellular system similar to that encountered in vivo, which will aid in the future design of NIS-based therapeutic strategies.
Given the similar pharmacokinetics of 131I-iodide and 211At-astatide in our model system, our observation of a higher absorbed dose using 211At-astatide can be explained by a combination of the higher energy
-particle (5.87 MeV) versus 131I ß-particle emission (0.6 MeV) as well as the shorter physical t1/2 of 211At (7.2 h vs. 192 h for 131I). Similarly, a study into the potential of 188Re (in the form 188ReO4-) to sterilize NIS-expressing cells calculated a 4.5-fold higher absorbed dose, when compared with 131I (14). This enhancement is likely due to a combination of factors: 188Re emits ß-particles with a higher energy than 131I (2.12 vs. 0.61 MeV), and ReO4- had higher tumor uptake than I- in a NIS-expressing xenograft model (14). However, much of the increase in absorbed dose results from the comparatively short physical t1/2 (16.7 h) of 188Re (14). These findings are of particular significance in relation to cell types lacking a peroxidase-based organification mechanism, as these cells generally exhibit a very short cellular retention of iodide (3,4), and matching of both the physical and biologic half-lives of the radioisotope is desirable for maximal radiobiologic effect.
In vivo, tumor cells may show a heterogeneous expression of NIS that can be predicted to result in a heterogeneous cumulated activity distribution with the tumor mass. However, depending on the range of the radiations emitted by the radionuclide used for therapy, there is a potential for cross fire among tumors cells. Although the range of
-particles is significantly shorter than that of ß-particles, a degree of cross fire can be predicted. The proportion of cells receiving a highly toxic absorbed dose from 211At-astatide will therefore depend on a combination of the overall transfection efficiency, the spatial distribution of transgene expression and radionuclide within the tumor, and the degree of cross fire. The use of cultured cell models, such as the one described here, affords the opportunity for detailed analysis of these issues and may provide the basis for a clinical implementation of transgene-mediated radionuclide therapy in the future. It is also important to note that there are some tumor types, such as thyroid and invasive breast carcinoma, that may express sufficient NIS to facilitate 211At-astatide therapy without the need for transgene-mediated expression.
The use of ionic 211At-astatide for the treatment of thyroid carcinoma has previously been investigated in murine xenograft models, with high tumor uptakes reported for more differentiated thyroid tumor cells, which generally retain a higher level of NIS expression than anaplastic thyroid tumors (2931). A study comparing the uptake of 125I-iodide and 211At-astatide in nude mice bearing human fetal thyroid and human malignant thyroid xenografts observed that the human tissue accumulated both halides with similar kinetics, suggesting that 211At-astatide may be an alternative radionuclide to 131I-iodide for the treatment of thyroid carcinoma (29). Another study examining the comparative transport of 125I-iodide and 211At-astatide using normal porcine thyrocytes in a polarized system also observed similarities in the basal membrane (i.e., NIS mediated) transport of both radiohalide anions (32). Interestingly, this study also reported the perchlorate- and ouabain-insensitive basal membrane transport of astatide, by normal thyrocytes, suggesting the possibility of another, NIS-independent astatide uptake mechanism in these cells. Further elucidation of this transport mechanism may provide some explanation as to the differences in biodistribution of astatide and iodide, in addition to providing another means of targeting astatine to tumor cells.
The biodistribution of systemically administered 211At-astatide, though similar to that of iodide, has several clinically relevant differences. In particular, a significantly higher uptake than iodide in both lung and spleen tissues is observed (12,33). At present, clinical trials of 211At-astatide for the treatment of thyroid carcinoma have not been initiated, possibly because of concerns over radiotoxicity in these tissues or due to the limited availability of the radionuclide. Previous investigations have revealed that pharmacologic intervention may modify the level of astatide uptake in normal tissues (12), and further studies into the possible mechanisms involved in the lung and spleen retention of astatide are currently underway. Although lung and spleen uptake currently precludes the systemic administration of 211At-astatide, combined gene transfer/radionuclide treatment of compartmentalized tumors such as those of brain, bladder, and ovary may be possible with minimal involvement of the systemic circulation. Further advances in the understanding of the mechanisms of astatine uptake and retention in lung and spleen will aid greatly in the clinical implementation of systemic 211At-astatide therapy for tumors with both endogenous and gene transfermediated NIS expression.
| CONCLUSION |
|---|
|
|
|---|
-particles over low LET ß-particle irradiation. 211At-Astatide administration results in increased cytotoxicity (686- to 598-fold) and higher absorbed doses (55- to 65.5-fold) per unit administered activity when compared with 131I-iodide. In addition, the physical t1/2 of 211At is closely matched to the radionuclide residence time observed in nonthyroid tumor types, providing a further therapeutic advantage over 131I. These observations imply that some of the limitations of 131I administration for the therapy of endogenous or transgene-mediated NIS-expressing tumors can be overcome. The pharmacokinetic model presented here is a valuable tool in predicting the influence on absorbed dose resulting from modulation of many experimental system parameters. Further development of this model to describe a 3-dimensional tumor within a dynamic environment will aid in the elucidation of the relationship between administered radioactivity and resulting absorbed doses in NIS-expressing tumors with different retention characteristics. | APPENDIX A |
|---|
|
|
|---|
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
| APPENDIX B |
|---|
|
|
|---|
nmu Average halide concentration in medium during uptake (mol/L)
nme Average halide concentration in medium during efflux (mol/L)
nc Average halide concentration in cells (mol/L)
ncu Average halide concentration in cells during uptake (mol/L)
nce Average halide concentration in cells during efflux (mol/L)
Vmax Theoretical maximum halide transfer rate (mol/L s-1)
Km MichaelisMenten constant for NIS (mol/L)
vc Average volume of a cell (cm-3)
dc Average cell density (cell cm-3)
dcu Average cell density during uptake (cell cm-3)
dce Average cell density during efflux (cell cm-3)
Nc Total number of cells (cell)
kcm Transfer rate between a cell to medium (s-1)
kmc Transfer rate between medium to a cell (s-1)
Vm Volume of medium (cm3)
Vc Volume of cells (cm3)
VT Total volume of system (cm3)
VTu Total volume of system during uptake period (cm3)
VTe Total volume of system during efflux period (cm3)
F(dc) Fractional cell uptake (unitless)
FCAA Fractional cell-associated activity (unitless)
am Average activity concentration in medium (Bq cm-3)
ãmu Average cumulated activity concentration in medium during uptake (Bq s cm-3)
ãme Average cumulated activity concentration in medium during efflux (Bq s cm-3)
ac Average activity concentration in the cell (Bq cm-3)
ãcu Average cumulated activity concentration in a cell during uptake (Bq s cm-3)
ãce Average cumulated activity concentration in a cell during efflux (Bq s cm-3)
c Average cumulated activity in a cell (Bq s)
u Residence time of system during uptake (s)
e Residence time of system during efflux (s)
mu Residence time of halide in medium during uptake (s)
cu Residence time of halide in cells during uptake (s)
me Residence time of halide in medium during efflux (s)
ce Residence time of halide in cells during efflux (s)
D Average absorbed dose (Gy)
S(m
c) Dose conversion factor from medium (source) to cells (target) (Gy g Bq-1 s-1)
S(c
c) Dose conversion factor from cells (source) to cells (target) (Gy g Bq-1 s-1)
hmc Average number of hits from medium (source) to a cell (target) (hit)
hcc Average number of hits from cells (source) to a cell (target) (hit)
1mc Specific energy per event from medium (source) to a cell (target) (Gy hit-1)
1cc Specific energy per event from cells (source) to a cell (target) (Gy hit-1)
SF Survival fraction (unitless)
SF2 2-Gy survival fraction (unitless)
Physical decay constant of radionuclide (s-1)
D0 Absorbed dose required to reduce survival fraction to e-1 (Gy)
A0 Activity concentration required to reduce survival fraction to e-1 (MBq cm-3)
| ACKNOWLEDGMENTS |
|---|
| FOOTNOTES |
|---|
For correspondence or reprints contact: Michael R. Zalutsky, PhD, Department of Radiology, Box 3808, Duke University Medical Center, Durham, NC 27710.
E-mail: zalut001{at}mc.duke.edu
| REFERENCES |
|---|
|
|
|---|
-particle-emitting targeted radiotherapeutics using histological images. J Nucl Med. 2003;44:792805.