When May a Nonuniform Distribution of 131I Be Considered Uniform? An Experimental Basis for Multicellular Dosimetry

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* Prasad V.S.V. Neti
* Roger W. Howell

## Abstract

To varying degrees, radiopharmaceuticals are distributed nonuniformly in tissue. At a macroscopic level, the radiopharmaceutical may appear to be uniformly distributed throughout the tissue. However, on closer inspection, not all cells in the tissue may be labeled with the radiopharmaceutical. Furthermore, the radioactivity in the cells may be localized only in certain compartments within the cell. This work uses a cell culture model to examine the impact of nonuniformities at the multicellular level on the lethal effects of 131I. **Methods:** A 3-dimensional tissue culture model was used to investigate the biologic effects of nonuniform distributions of 131I in a large population of mammalian cells. Chinese hamster V79 cells were labeled with 131I-iododeoxyuridine (131IdU), mixed with unlabeled cells, and multicellular clusters (4 × 106 cells) were formed by gentle centrifugation. Thus, the labeled cells were randomly located in the cluster to achieve a uniform distribution of radioactivity at the macroscopic level, yet nonuniform at the multicellular level. The clusters were assembled as described and then maintained at 10.5°C for 72 h to allow 131I decays to accumulate. The clusters were then dismantled and the cells were plated for colony formation. **Results:** When 100% of the cells were labeled, the surviving fraction of cells in the cluster was exponentially dependent on the cluster activity down to 0.1% survival. In contrast, when 10% of the cells were labeled, it was observed that the survival fraction begins to saturate at about 1% survival. Absorbed-dose estimates reveal that the mean lethal cluster dose is 4.5, 5.7, and 6.4 Gy for 100%, 10%, and 1% labeling, respectively. **Conclusion:** These data indicate that when the distribution of 131I is uniform at the macroscopic level, but nonuniform at the multicellular level, the mean absorbed dose to a tissue element may not be a suitable quantity for use in predicting biologic effect. Rather, cellular and multicellular dosimetry approaches may be necessary to predict the biologic effects of incorporated 131I.

*   131I
*   iododeoxyuridine
*   dosimetry
*   multicellular cluster
*   V79 cells
*   survival

Radionuclides that undergo β-decay are widely used in biomedical research and in medical procedures. Furthermore, they are often encountered in environmental accidents such as the Chernobyl incident. The β-emitter 131I is perhaps one of the most widely recognized radionuclides in this category because of its carcinogenic hazard to the thyroid in the case of accidental exposures and its potent therapeutic efficacy against thyroid cancer when used in the form Na131I. The mean energy of the principal β-particles emitted by 131I is 191 keV (1) with a corresponding mean range in water of about 400 μm (2). Therefore, when this radionuclide is localized within a cell, the β-particles emitted typically irradiate target cells about 30–40 cell diameters distant. Accordingly, the impact of the limited range of the 131I β-particles has stirred considerable debate regarding the biologic consequences of nonuniform distributions of this radionuclide in tissue.

Early discussions on the dosimetric and biologic implications of nonuniform distributions of 131I began soon after its introduction to medicine (3–5). Issues concerning nonuniform distributions of β-emitters continue to be of considerable interest and debate even at present (6,7). Over the years, numerous theoretical models have been developed to explore the dosimetric implications of nonuniform distributions of 131I both from the standpoint of radiation protection as well as radiation therapy (8–18). The experimental basis for such theoretical calculations has largely been autoradiographic data (3,4,19–21). Recent calculations have melded nonuniform dose distributions with dose-response modeling to arrive at predictions of biologic responses to nonuniform distributions of 131I (22).

Although there has been extensive theoretical modeling of the dosimetry and biologic response to nonuniform distributions of 131I, little of this modeling was based on measurements of biologic responses to distributions of 131I where the nonuniform distribution of the radionuclide was controlled and known with precision (7). Kwok et al. (23) and Langmuir et al. (24) used multicellular spheroids to investigate the effects of 131I-labeled monoclonal antibodies. However, the spheroid model largely restricted the radioactivity to the periphery of the cluster, thus making it possible to only study the effects of a spherical shell distribution. In this work, the lethal effects of nonuniform distributions of 131I are studied using an in vitro multicellular cluster model wherein the variables affecting distribution of radioactivity can be tightly controlled. This has been accomplished by assembling multicellular clusters containing 4 × 106 cells wherein 1%, 10%, or 100% of the cells are radiolabeled. This tight control over the distribution of radioactivity allows one to maintain what appears to be a uniform distribution at a macroscopic level, while altering the nonuniform distribution at the multicellular level. This permits a well-controlled investigation of the biologic consequences of nonuniform activity distributions of 131I at the multicellular level.

## MATERIALS AND METHODS

### Radiochemical and Quantification of Radioactivity

131I as Na131I was obtained from Perkin Elmer Life Sciences in 0.1N NaOH (13.6 GBq/mL). Radiolabeled iododeoxyuridine (131IdU) was synthesized and purified by high-performance liquid chromatography in our laboratory according to procedures previously reported (25). The 131I activity was quantified with a Canberra HpGe well detector (364.5-keV photopeak, photopeak efficiency = 0.33, yield = 0.812) or a Packard automatic γ-counter equipped with a 3 in. (7.62 cm) sodium iodide well crystal (overall efficiency = 0.78 in the energy window 260–470 keV). The radionuclide 131I undergoes β-decay with a physical half-life of 8.04 d.

### Cell Line

Chinese hamster V79 lung fibroblasts were used in this study, with clonogenic survival serving as the biologic endpoint. The different minimum essential media (MEMA, MEMB, and wash MEMA) and culturing conditions were described in detail in a previous publication (26). The plating efficiency was typically about 60%. All media and supplements used in this study were from Life Technologies. Cells were maintained in Falcon (Becton Dickinson) 225-cm2 sterile tissue culture flasks at 37°C in a humidified atmosphere with 95% air/5% CO2 and subcultured twice weekly or as required on reaching 80%–90% confluence. The cell line was tested to be free of mycoplasma.

### Assembly of Multicellular Clusters

Multicellular clusters containing nonuniform distributions of 131I were assembled according to protocols described in detail elsewhere (26–28). Briefly, V79 cells growing as monolayers in 225-cm2 Falcon flasks were washed with 20 mL of phosphate-buffered saline, trypsinized with 0.05% trypsin and 0.53 mmol/L ethylenediaminetetraacetic acid, and suspended at 4 × 105 or 4 × 106 cells per milliliter in calcium-free MEM with 10% heat-inactivated (57°C, 30 min) fetal calf serum, 2 mmol/L l-glutamine, 50 units/mL penicillin, and 50 μg/mL streptomycin (MEMB). Aliquots of 1 mL were placed in 2 sets of sterile 17 × 100 mm Falcon polypropylene round-bottom culture tubes (10 tubes in each set) and placed on a rocker-roller (Fisher Scientific) for 3–4 h at 37°C in an atmosphere of 95% air/5% CO2. After this conditioning period, 1 mL of MEMB containing various activities of 131IdU was added to 1 set of tubes (denoted “labeled;” range of concentrations in Table 1). To the second set of tubes, 1 mL of MEMB was added (denoted “unlabeled”). The tubes were returned to a rocker-roller at 37°C, 95% air/5% CO2. After 14 h, the cells were washed 3 times with 10 mL of wash MEMA, resuspended in 5 mL of MEMA, and passed 5 times through a 21-gauge needle. The cell concentration in each tube was determined with a calibrated Coulter model ZM cell counter (Coulter Electronics), then mixed with unlabeled cells to get 100%, 10%, or 1% radiolabeled cells in a total population of 4 × 106 cells (Table 1), and centrifuged at 2,000 rpm, 4°C for 10 min. The supernatant was decanted, the pellets were disrupted, and the entire ∼200 μL of this final cell suspension was transferred directly to a sterile 400-μL polypropylene microcentrifuge tube (Helena Plastics). The tube was washed with an additional 200 μL of MEMA and the wash was transferred to the same 400-μL polypropylene microcentrifuge tube. The 400-μL tubes were then centrifuged at 1,000 rpm for 5 min at 4°C to form clusters (4 × 106 cells; Fig. 1). The capped microcentrifuge tubes containing the clusters were placed in a perforated microcentrifuge tube rack and maintained in a refrigerator at 10.5°C. This temperature was selected because V79 cells can remain in the cluster configuration at this temperature for long periods of time (up to 72 h) without decrease in plating efficiency. This was also true for V79 cells in suspension culture (26). Therefore, the cells accumulate the preponderance of their radioactive decays while in the cluster configuration as opposed to the radiolabeling and colony-forming periods.

![FIGURE 1.](http://jnm.snmjournals.org/https://jnm.snmjournals.org/content/jnumed/44/12/2019/F1.medium.gif)

[FIGURE 1.](http://jnm.snmjournals.org/content/44/12/2019/F1)

**FIGURE 1.** 
Assembly of multicellular cluster of V79 cells wherein 10% cells were radiolabeled with 131IdU.

View this table:
[TABLE 1](http://jnm.snmjournals.org/content/44/12/2019/T1)

**TABLE 1** 
Parameters Used in Preparation of Multicellular Clusters

### Determination of Surviving Fraction of Cells in Multicellular Clusters

After 72 h at 10.5°C, the supernatant was carefully removed and the tube was vortexed to disperse the cell cluster. The cells were resuspended in MEMA, transferred to 17 × 100 mm Falcon polypropylene tubes, washed 3 times with 10 mL of wash MEMA, resuspended in 2 mL of MEMA, passed through a 21-gauge needle 5 times to disperse cells, and serially diluted in wash MEMA (four 10× dilutions), and 1 mL of the appropriate dilutions (approximately 200 cells for control tubes) were seeded in triplicate into 60 × 15 mm Falcon tissue culture dishes containing 4 mL of MEMA. The dishes were then placed in an incubator at 37°C with 95% air/5% CO2. Aliquots were taken from each tube before serial dilution and the mean radioactivity per labeled cell was determined (Table 1). The tissue culture dishes were removed from the incubator after 1 wk and the resulting colonies were washed 3 times with normal saline, washed 2 times with ethanol to fix, and finally stained with 0.05% crystal violet. The numbers of colonies were counted with a dissecting microscope at 40× magnification. A colony count of 25–250 was considered as a valid data point for each tissue culture dish. The surviving fraction compared with parallel control was determined for each radioactivity concentration used.

### Response of Multicellular Clusters to Chronic External γ-Rays

Irradiation of multicellular clusters with 137Cs γ-rays allows determination of the response of the cell population to a uniform dose of low-LET ionizing radiation. The response of the clusters to chronic external γ-rays was initially assessed in our earlier study (26). However, in that study, the lowest survival fraction achieved was only about 50% due to technical limitations of the 137Cs source used to irradiate the samples. This did not allow us to observe the shape of the survival curves at lower survival fractions, an important region of the curve for comparison with the survival curves for 131IdU. Accordingly, a styrofoam box containing a coil of Tygon tubing lining the inside walls was placed inside a JL Shepherd Mark I 137Cs irradiator (with 200× Pb attenuators) and the ends of the tubing were fed through the pass-throughs on the side of the irradiator. Cooled water was continuously circulated through the tubing using a Neslab model 115 circulator equipped with a temperature feedback probe to maintain the inside of the box at precisely 10.5°C. Once equilibrium temperature was reached, microcentrifuge tubes containing multicellular clusters prepared with 4 × 106 unlabeled cells as described above were placed in the box at different distances from the 222-TBq (6,000 Ci) 137Cs source. Two control tubes were similarly maintained at 10.5°C without radiation exposure. The cumulated absorbed dose to each tube was measured using a Thomson-Nielson miniature MOSFET dosimeter system. After 72 h of chronic irradiation, the cells were processed as described above to determine the cell survival fraction. Cumulated doses ranging from 2.4 to 52 Gy were delivered over 72 h at dose rates from about 3 to 80 cGy/h, depending on the distance from the source. After the chronic irradiation, the cells were processed as above and the survival fraction was determined compared with that of unirradiated control cells.

### Measurement of Cluster Mass

Our previous studies focused on 3H and 125I localized in the cell nucleus. These radionuclides emit very short-range radiations and therefore cellular dosimetry was most relevant. However, in the case of 131I, where the mean range of the β-particles is about 400 μm, the mean absorbed dose to the cluster is of interest. Accordingly, the cluster mass was determined to facilitate the absorbed-dose calculation. This was done carrying out all preparations described above for 10 clusters of 4 × 106 cells; however, before assembling the clusters, the cells were pooled into a single sterile 17 × 100 mm Falcon polypropylene round-bottom culture tube. The resulting 40 × 106 cells were transferred to the standard 400-μL microcentrifuge tube for making clusters and the tube was then gently centrifuged at 1,000 rpm for 5 min. The resulting pellet of 40 × 106 cells was then placed in an incubator at 10.5°C. After 72 h, the supernatant was carefully aspirated using a Pasteur pipet (stretched under heat to form a small bore opening) and the tube was weighed on an electronic balance (±0.1 mg). The cluster was then removed by aspiration and the tube reweighed. The cluster weight was the difference between the 2 measurements. Two clusters of 40 × 106 cells were analyzed in separate experiments with the average weight being 79 ± 1 mg. Therefore, the average cluster weight for 4 × 106 cells was 7.9 ± 0.1 mg. This approach was originally attempted to directly determine the mass of a 4 × 106 cell cluster; however, the inaccuracies associated with aspiration of the supernatant from above the small cluster and evaporation during transport to the electronic balance interfered with the accuracy of the measurements. To ensure the accuracy of the pooled approach, the weights of additional clusters of 10 × 106, 20 × 106, and 30 × 106 were also determined. In these cases, the average weights per 4 × 106 cells were 7.910, 7.960, and 7.926 mg, respectively. Therefore, these measurements also yielded the same result as the 40 × 106 cell cluster, thereby reflecting the precision of this approach.

## RESULTS

### Uptake of 131IdU in V79 Cells

Previous results have shown that the uptake of 131IdU (and 125IdU) is linear in time over the 14-h incubation period on the rocker-roller at 37°C (29,30). In addition, uptake of 131IdU (and 125IdU) is also linearly dependent on the concentration of 131IdU in the culture medium (29,30). This was observed in the present studies as well as shown in Figure 2. It may be observed that the slope of the 100% labeling case is lower (∼0.1 mBq per cell per kBq/mL) than that in the 10% and 1% cases (∼0.6 mBq per cell per kBq/mL). This may be due to the fact that 4 × 105 cells were labeled for preparation of the 10% and 1% clusters, whereas 4 × 106 cells were labeled for the 100% cluster.

![FIGURE 2.](http://jnm.snmjournals.org/https://jnm.snmjournals.org/content/jnumed/44/12/2019/F2.medium.gif)

[FIGURE 2.](http://jnm.snmjournals.org/content/44/12/2019/F2)

**FIGURE 2.** 
Dependence of cellular uptake of 131I on initial extracellular concentration of 131IdU in culture medium. Different symbols correspond to data collected during experiments involving 100% (○), 10% (□), or 1% (▵) labeling. In 100% case, 4 × 106 cells were labeled, whereas 4 × 105 cells were labeled to prepare 10% and 1% (only 4 × 104 cells were used) cases. Linear least-squares fit of data is also shown for each case: 100% (thin line), 10% (dashed line), 1% (bold line). Inset shows enlargement of 100% case.

### Response of Multicellular Clusters to 131IdU

Figure 3 shows the surviving fraction of cells in the multicellular cluster as a function of the 131I activity in the cluster when 100%, 10%, or 1% of the cells were radiolabeled. The response curve for 100% labeling is exponential over a range of 3 logarithms of kill, whereas the curve for 10% labeling appears as a 2-component exponential over the same range. Due to limitations regarding preparation of 131IdU and loading of cells with high activities, it was only possible to observe survival fractions down to about 0.05 when only 1% of the cells were labeled. The data for each labeling condition were least-squares fit to a 2-component exponential function: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} [\mathrm{SF}\ {=}\ (1\ {-}\ b)\mathrm{e}^{{-}\ A/A\_{1}}\ {+}\ b\mathrm{e}\ ^{{-}\ A/A\_{2}}] \end{document}Eq. 1 where SF is the survival fraction, *A* is the cluster activity, and *b*, *A*1, and *A*2 are the fitted parameters. For 10% labeling, the fitted parameters *b*, *A*1, and *A*2, are 0.00777 ± 0.00109, 21.7 ± 2.5 mBq per labeled cell, and 370 ± 333 mBq per labeled cell, respectively. In the case of 100% and 1% labeling, with *b* = 0, the fitted values of *A*1 are 1.71 ± 0.039 and 241 ± 12.6 mBq per labeled cell, respectively. The fitted parameters are summarized in Table 2.

![FIGURE 3.](http://jnm.snmjournals.org/https://jnm.snmjournals.org/content/jnumed/44/12/2019/F3.medium.gif)

[FIGURE 3.](http://jnm.snmjournals.org/content/44/12/2019/F3)

**FIGURE 3.** 
Survival of V79 cells in multicellular clusters as function of initial 131I activity per labeled cell. Data are shown for experiments where 100% (○), 10% (□), or 1% (▵) of cells in multicellular cluster were labeled with 131IdU. Clusters were maintained at 10.5°C for 72 h and then survival fraction was determined compared with that of cells from control clusters (0% labeled). Data from 3 independent experiments are plotted for each labeling condition. Least-squares fits of data are shown for each labeling condition.

View this table:
[TABLE 2](http://jnm.snmjournals.org/content/44/12/2019/T2)

**TABLE 2** 
Fitted Parameters for Multicellular Cluster Survival Curves

For the medium energy β-emitter 131I where cross-irradiation plays a major role in the absorbed dose to the labeled and unlabeled cells, it is instructive to plot the survival fraction as a function of cluster activity (Fig. 4). These data are also least-squares fit to Equation 1, and the resulting fitted parameters are summarized in Table 2.

![FIGURE 4.](http://jnm.snmjournals.org/https://jnm.snmjournals.org/content/jnumed/44/12/2019/F4.medium.gif)

[FIGURE 4.](http://jnm.snmjournals.org/content/44/12/2019/F4)

**FIGURE 4.** 
Survival of V79 cells in multicellular clusters as function of initial 131I activity per cluster. Data are shown for experiments where 100% (○), 10% (□), or 1% (▵) of cells in multicellular cluster were labeled with 131IdU. Clusters were maintained at 10.5°C for 72 h and then survival fraction was determined compared with that of cells from control clusters (0% labeled). Least-squares fits of data corresponding to each labeling condition are shown: 100% (thin line), 10% (dashed line), 1% (bold line).

### Response of Multicellular Clusters to External γ-Rays

Figure 5 shows the dose-response curves for multicellular clusters of V79 cells exposed to chronic 137Cs γ-rays delivered over a 72-h period. The historical response to 137Cs γ-rays is also shown for comparison (26). A least-squares fit of these data to the linear-quadratic model (SF = exp(−αD − βD2)) yielded α = 0.0487 ± 0.022 Gy−1, β = 0.00267 ± 0.00040 Gy−2. Interestingly, these values are very close to our previously reported values that were based on a fit to data corresponding to the triangles in Figure 5 that have a maximum kill of only about 50% (26). Based on these parameters, the absorbed dose of chronic 137Cs γ-rays that is required to achieve 37% survival *D*37 is 12.2 ± 2.4 Gy.

![FIGURE 5.](http://jnm.snmjournals.org/https://jnm.snmjournals.org/content/jnumed/44/12/2019/F5.medium.gif)

[FIGURE 5.](http://jnm.snmjournals.org/content/44/12/2019/F5)

**FIGURE 5.** 
Survival of V79 cells after chronic irradiation of multicellular clusters with 137Cs γ-rays. All irradiations were performed at 10.5°C over 72-h period. Data from 3 independent experiments are shown (•, ▪, ▴); ▴ represents data reported earlier (26). Additional data was acquired to define survival curve at low survival fractions and thereby allow comparison between 137Cs and 131IdU dose-response curves. Dotted curve represents least-squares fit of 137Cs data to linear quadratic model. For comparison, least-squares fits of 131IdU data (survival fraction vs. mean absorbed dose to cluster) to 2-component exponential function are also shown for 3 labeling conditions: 100% (thin line), 10% (dashed line), 1% (bold line).

## DISCUSSION

Radioiodinated pharmaceuticals are widely used in clinical medicine to diagnose and treat a variety of medical conditions. It is well known that these radiopharmaceuticals localize in different tissues in the body and that their distribution at the macroscopic and microscopic levels is nonuniform. The degree of nonuniformity can have a profound impact on the biologic response to the radiopharmaceutical. Despite these well-known facts, current internationally accepted methods for assessing risks from diagnostic nuclear medicine procedures assume that the radioactivity in organs and tissues is uniformly distributed and that the biologic response depends principally on absorbed dose, radiation type, and tissue radiosensitivity (31). Several investigators have raised important concerns regarding the assumption of uniform distribution of radioactivity and their impact on risk estimates and therapeutic response (6,22,32). However, one of the major stumbling blocks to predict the biologic response of tissues with nonuniform distributions of radioactivity has been the absence of experimental models that allow tight control over the distribution of the radioactivity (7). The present data for 131I were obtained with a 3-dimensional tissue culture model that was designed specifically to quantify the impact of nonuniform distributions of radioactivity in tissues on the biologic effect of the incorporated radionuclides (26,28). This model provides a high degree of control over the percentage of radiolabeled cells in the cluster and therefore makes an excellent model to examine the effects of nonuniform distributions of 131I.

To assess the effects of nonuniform distributions of 131I, multicellular clusters were prepared by assembling clusters with mixtures of unlabeled cells and cells radiolabeled with 131IdU. This radiochemical, a thymidine analog, is incorporated into the DNA in the cell nucleus. It was chosen for its capacity to remain within the cell nucleus without migrating to neighboring unlabeled cells (26). The survival curves in Figure 3 correspond to the cases where 100%, 10%, or 1% of the cells was labeled. In all 3 cases, the initial response is exponential with *A*1 values of 1.71, 21.7, and 241 mBq per labeled cell, respectively (Table 2). These values are essentially the activity per labeled cell required to achieve 37% survival. As expected, to achieve the same level of overall kill, one has to put substantially more radioactivity per cell as the percentage of labeled cells decreases. Interestingly, while the percentage of labeled cells changes by factors of 10 and 100, the required activity changes by factors of 12.7 and 141. These differences are likely due to the changes in activity distribution in the cluster and perhaps the nature of the radiotoxicity imparted by the radiochemical 131IdU. These points and the tailing of the curve in the case of 10% labeling will be discussed more fully in the context of Figure 4.

Virtually all radioactivity distributions in tissues are nonuniform. At some spatial level, however, the radioactivity distribution may be considered “uniform” depending on the radiation type and energy, tissue geometry, biologic endpoint, and numerous other factors. The multicellular cluster model used in this work allows one to maintain what appears to be a uniform distribution at the macroscopic level (i.e., the labeled cells are randomly distributed in the cluster) while altering the distribution of radioactivity at the multicellular level. By some standards, one may consider this distribution of 131I to be uniform because of its capacity to cross-irradiate cells that reside as much as 30–40 cell diameters distant from the labeled cell. Accordingly, the survival fraction is also plotted as a function of the total activity in the cluster in Figure 4. The mean absorbed dose to the cluster is directly related to the cluster activity. According to the MIRD schema (33), the mean absorbed dose to the cluster *D* is given by: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} [D\ {=}\ {\tilde{A}}S,] \end{document}Eq. 2 where *Ã* is the cumulated activity and *S* is the mean absorbed dose per unit cumulated activity. The cumulated activity in the cluster during the 72-h period at 10.5°C is: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} [{\tilde{A}}\ {=}\ {{\int}_{0}^{72\ \mathrm{h}}}\ A(t)dt.] \end{document}Eq. 3

The cluster activity is given by *A*(*t*) = *A*o exp(−0.693*t*/Tp), where *A*o is the initial cluster activity and Tp is the physical half-life (8.04 d). Integration of Equation 3 gives *Ã* = 2.28 × 105 *A*o s. The mean absorbed dose per unit cumulated activity *S* was calculated using the methods and computer code described by Howell et al. (12). From the Materials and Methods, the mass of the cluster of V79 cells is 7.9 ± 0.1 mg. Assuming that the cluster is a 7.9-mg sphere of water containing uniformly distributed 131I, the calculated *S* value is 2.89 × 10−9 Gy/Bq-s (12). This *S* value takes into account both particulate and photon emissions from 131I. Substitution of *Ã* and *S* into Equation 2 gives *D* = 0.66 Gy/kBq of cluster activity. The survival fraction versus the mean absorbed dose to the cluster is plotted in Figure 5 for each of the 3 labeling conditions along with the dose-response curve for chronic 137Cs γ-rays. Using the fitted parameters in Table 2, the mean cluster doses required to achieve 37% survival *D*37 for 100%, 10%, and 1% labeling are 4.5, 5.7, and 6.4 Gy, respectively (Table 3). These may be compared with the value of 12.2 Gy obtained for chronic 137Cs γ-rays, thereby suggesting that 131I β-particles may be somewhat more lethal than 137Cs 661.7-keV γ-rays. It is apparent, however, that this conclusion is substantially dependent on the survival fraction at which the comparison is made (Fig. 5).

View this table:
[TABLE 3](http://jnm.snmjournals.org/content/44/12/2019/T3)

**TABLE 3** 
Mean Lethal Doses for V79 Cells in Multicellular Cluster

In addition to the differences in the *D*37 values for chronic 137Cs γ-rays and 131IdU under different labeling conditions, the shapes of the survival curves have marked differences. The dose-response curve for chronic 137Cs γ-rays (Fig. 5) exhibits a shoulder that is typical of the response to low-LET (linear energy transfer) radiations. In contrast, the survival curve for 100% labeling is exponential over 3 logarithms of kill despite the fact that the β-particles emitted by 131I are considered to be similarly low-LET in nature. Although exponential curves are usually associated with responses to high-LET radiations such as α-particles, one must keep in mind that a nonuniform dose distribution can substantially affect the dose-response of a population of cells (22,34). Even for the case of 100% labeling, all cells in the cluster do not receive the same absorbed dose. It is well known that when β-emitters are uniformly distributed in a sphere, the dose rate at the surface of the sphere is about one half of the dose rate at the center of the sphere (35). So even under conditions of a uniform distribution of 131I (i.e., 100% labeling), the dose received by the cells in the cluster varies by a factor of 2. The variations in our cluster model may perhaps be even somewhat larger than this given that the cluster geometry (Fig. 1) is not spherical. These variations may have an impact on the shape of the survival curve. An alternate explanation is that the damage imparted by 131IdU is somewhat like high-LET damage because the decays occur within the DNA. There is evidence to support that the relative biologic effectiveness (RBE) of 131IdU compared with external photons is substantially >1 (30,36). However, there is also evidence to suggest that the radiotoxicity of 131IdU is of a low-LET nature (37–39). Therefore, it is not clear at present whether the RBE has any impact on the shape of the survival curve for 100% labeling.

Although the data for 100% labeling are indeed interesting, the survival curve observed when 10% of the cells are labeled is perhaps of more importance given that it may better reflect what may occur in vivo. In the case of 10% labeling, there is a distinct tailing of the survival curve at high cluster activities. The tail begins at approximately 1% survival. One possible reason for this is that a small subpopulation of cells (∼0.5%–1% of the cells in the cluster) receive a substantially lower dose than the remaining cells. There are several factors that could contribute to this circumstance. The geometry of the cluster is one possibility. As described in the Materials and Methods, the multicellular cluster is formed by gently centrifuging (1,000 rpm) the 4 × 106 cells in a 400-μL microcentrifuge tube. The resulting cluster roughly approximates a sphere; however, on microscopic examination with a dissecting microscope, it may be more accurately described as a paraboloid. Furthermore, the angle of the centrifuge buckets during the pellet formation causes the surface of the top of the paraboloid to be somewhat angled as opposed to flat (increasing centrifugation speed to 2,000 rpm does not change shape). This geometry could result in a relatively low cross-dose being delivered to some of the cells around the top edge of the cluster. However, arguing against this hypothesis are our earlier results for 10% labeling with 125IdU where no tail was observed (28). Regardless of the reasons for the tail, it is clear that when 10% of the cells in the cluster are labeled at random, the distribution of radioactivity is uniform from a macroscopic perspective, yet nonuniform from a multicellular level perspective. The nonuniformities at the multicellular level have a significant impact on the biologic response of the population as a whole. Accordingly, dosimetry calculations at the cellular and multicellular levels (18), coupled with dose-response modeling at the cellular level, may provide a means to resolve these issues.

The preceding discussion has focused largely on the 100% and 10% labeling cases. For 1% labeling, Figure 4 shows an exponential drop in the survival fraction down to about 5% survival. The slope of the curve is essentially the same as the case for 10% labeling as evidenced by the similar values of *A*1 obtained with the curve fits to survival versus cluster activity (Table 2). This suggests that, down to at least 5% survival, the lethal effects imparted to the cell population in the cluster by a given cluster activity are essentially the same for 1% labeling and 10% labeling. It remains to be seen what occurs beyond 5% survival in the 1% labeling case. These effects are notably different from the 100% labeling case. It should be noted that in the 1% and 10% cases, the dose-response curve is largely dictated by the response of the unlabeled cells (receive cross-dose only) because the first 10% of the kill is largely the labeled cell population (receives cross-dose and large self-dose). In contrast, the dose-response curve for the 100% case is entirely for labeled cells. Therefore, the differences in slopes in the dose-response curves suggests that the self-dose to labeled cells is slightly more lethal than the cross-dose to unlabeled cells.

## CONCLUSION

Based on our findings with a 3-dimensional multicellular tissue culture model, it may be concluded that when the distribution of 131I is uniform at the macroscopic level, but nonuniform at the multicellular level, the mean absorbed dose to a tissue element may not be a suitable quantity for use in predicting biologic effects in the cell population within the tissue element. Rather, cellular and multicellular dosimetry approaches may be necessary. The MIRD schema is capable of handling such approaches (7,40). Dose-response modeling using cellular and multicellular dosimetry approaches are currently underway in this laboratory.

The clinical implications of our findings are apparent. However, current nuclear medicine imaging technology (SPECT, PET) cannot provide information regarding distribution of radioactivity at the multicellular level. Such information can only be obtained through detailed analysis of biopsy specimens. Though it is not likely that such detailed analyses can be performed for each patient, it is possible that generalizations regarding the microscopic distribution (i.e., fraction of cells labeled) of a given radiopharmaceutical in tissue can be made based on a limited number of samples. Such information could in turn be used to predict biologic response using cellular and multicellular dosimetry approaches.

## Acknowledgments

The authors thank Tiffany Cooke for assistance in carrying out the experiments during her summer undergraduate internship program. The authors also acknowledge Venkata Lanka and the personnel in the UMDNJ Office of Radiation Safety Services for assisting with determination of absorbed dose delivered by the 137Cs irradiator and synthesis of 131IdU. Many helpful discussions with Drs. Edouard I. Azzam, Sonia M. deToledo, and Bogdan I. Gerashchenko are highly acknowledged. Finally, the use of Dr. John Bogden’s analytical balance is also appreciated. This work was supported in part by U.S. Public Health Service grant R01CA83838.

## Footnotes

*   Received Apr. 30, 2003; revision accepted Sep. 8, 2003.
    
    For correspondence contact: Roger W. Howell, PhD, Department of Radiology, MSB F-451, New Jersey Medical School, UMDNJ, 185 S. Orange Ave., Newark, NJ 07103.
    
    E-mail: rhowell{at}umdnj.edu

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