Abstract
We evaluated the effects on the absorbed dose to thyroid follicular cells of selfabsorption of ^{131}I radiation (specifically, βrays) in the follicular colloid. Methods: Thyroid follicles were modeled as colloidfilled spheres, containing a uniform concentration of ^{131}I and surrounded by a concentric monolayer of cells. Assuming close packing of identical follicles, we used Monte Carlo simulation to assess the absorbed dose to follicular cells. Results: Because of βray selfabsorption in colloidal spheres with radii larger than 50 μm, the absorbed dose to follicular cells is less than the average thyroid absorbed dose. Conclusion: For the same thyroid mass, radioiodine thyroid uptake, and effective halflife, patients with follicles with colloidal sphere radii of 100, 200, 300, and 400 μm should be administered 9%, 15%, 21%, and 30% more ^{131}I, respectively, than patients with colloidal sphere radii of less than 50 μm, to yield the same absorbed dose to follicular cells.
Radioiodine (^{131}Iiodide) therapy is generally the treatment of choice for uncomplicated Graves disease in adults. The ideal goal is to destroy or otherwise affect enough thyroid tissue to produce euthyroidism. Despite efforts to assess clinically the target absorbed dose by accounting for the gland size and radioiodine kinetics, the success of radioiodine therapy remains largely unpredictable (1,2).
The current methods define the whole thyroid as the target organ, although the biologic effects are primarily due to irradiation of thyroid follicular cells. The current article presents evidence that a ^{131}I absorbed dose to thyroid follicular cells differs from the mean thyroid absorbed dose and that such differences increase with increasing sizes of thyroid follicles.
MATERIALS AND METHODS
Systemically administered iodide is captured by the thyroid and organified and appears in the follicular colloid within minutes of administration, as demonstrated by autoradiographic studies in rats (3). In contrast, the biologic halflife of thyroidal iodine is quite long, varying from 15 to 60 d and yielding an effective halflife of 5–7 d for ^{131}I. This means that most ^{131}I decays occur within the colloid, that is, extracellularly.
In the current analysis, we considered only the βradiation of ^{131}I. The contribution of γradiation to total average gland absorbed dose (average thyroid absorbed dose from both γradiation and βparticles of ^{131}I) increases with the gland size and depends on the gland shape; for a 20g gland, it is 6% (Appendix). This component is not negligible and should be taken into account. However, because of the relatively long mean free path of γrays, compared with particle ranges, the absorbed energy distribution of γrays is expected to be uniform across the thyroid volume (i.e., insensitive to thyroid microarchitecture).
The βradiation–absorbed dose to thyroid follicular cells, D_{cell}, is due to βparticles emanating from their own colloid (the selfdose [D_{self}]) and from βparticles coming from the colloid of neighboring follicles (the crossdose [D_{cross}]):Eq. 1We assumed that a thyroid is composed of identical follicles. E_{0} denotes the total energy of all βparticles emerging from the ^{131}I distributed uniformly in the colloid of the thyroid follicles. Then D_{self} equals the energy absorbed in follicular cells originating from their own colloid E_{self} divided by the mass of follicular cells m_{cells}:Eq. 2Because of somewhat irregular arrangements of follicles, one cannot assume a regular geometric model of follicular packing. Such an irregular arrangement of follicles leads to the assumption that all radiation energy emanating from the follicles, E_{0} − E_{coll} − E_{self}, is uniformly absorbed over the thyroid mass, m_{thy}, where E_{coll} is the radiation energy selfabsorbed within the colloid. This yields the following equation for the nonself, or cross, absorbed dose, D_{cross}:Eq. 3Combining Equations 1–3 yields the total follicular cell–absorbed dose:Eq. 4Assuming that all energy of βparticles and secondary radiation are totally absorbed in the thyroid (Appendix), E_{0}/m_{thy} is the average dose to thyroid tissue, assessed on the basis of the administered activity and measured thyroid uptake, mass, and effective halflife.
For clarity, we defined the dimensionless quantity, the relative absorbed dose to follicular cells, , as the ratio of D_{cell} to the average thyroid dose, E_{0}/m_{thy}:Eq. 5Multiplying the administered activity determined to deliver a prescribed mean absorbed dose to the thyroid by the quantity 1/ , termed the activity correction factor, yields the administered activity that would deliver the same prescribed dose specifically to follicular cells.
, the first term on the right side of Equation 5, is the relative selfabsorbed dose to follicular cells:Eq. 6which equals the selfabsorbed fraction of the follicular cells weighed by thyroid–to–follicular cell mass ratio. The relative crossabsorbed dose to follicular cells is simply the fraction of total energy of βparticles that leaves the original follicles:Eq. 7
Finally, the ratio of the relative selfabsorbed and crossabsorbed doses to follicular cells equals the ratio of the respective absolute absorbed doses:Eq. 8To calculate the relative absorbed dose to follicular cells and its self and crosscomponents, one should assess the fractions of total energy selfabsorbed in the colloid and in the follicular cells and the thyroidtofollicular cell mass ratio.
We used the Monte Carlo code EGS5 (4) to calculate the selfabsorbed fractions E_{coll}/E_{0} and E_{self}/E_{0}. The input model of the thyroid follicle was a unitdensity water sphere, comprising a spheric shell of cells and a concentric inner sphere filled with uniform concentration of ^{131}I. The initial electron energies were sampled from the ^{131}I βspectrum as calculated by Simpkin and Mackie (5). The emissions of discrete electrons were simulated as well. The numbers of simulated electron histories were always sufficiently large that the statistical uncertainties (errors) were less than 1%. Electrons and photons were followed until their energy reached the transport cutoff values, which were both set equal to 1 keV. Below this cutoff, the energy was deposited locally. Secondary particles were followed if their initial energy was greater than 1 keV. The calculations were performed for radii of colloid spheres ranging from 10 to 400 μm and follicular cell thicknesses of 5, 10, and 15 μm.
The thyroid–to–follicular cell mass ratio was calculated assuming that 90% of thyroid tissue is composed of follicles (6). Denoting by r the radius of colloid sphere and by h the thickness of epithelial cell layer, this ratio is:Eq. 9
RESULTS
The selfabsorbed fraction in colloid spheres ranges from several percentage points for small radii (i.e., up to 50 μm) to 45% for large radii (i.e., 400 μm). The relative absorbed dose to follicular cells ranges from about 1, in the case of colloid radii below 50 μm, to about 0.77 for a 400μm radius. The follicular cell thickness had minor effects (Table 1).
In terms of the practical useful activity correction factor, 1/, patients having colloid spheres with radii of 100, 200, 300, and 400 μm should be given 9%, 15%, 21%, and 30% more ^{131}I activity than that administered to patients with colloidal spheres of radii of less than 50 μm.
DISCUSSION
The motivation for this work was our clinical results on the cohort of patients with Graves disease treated with radioiodine. The patients with a normoechogenic gland with a planned average thyroid dose of 200 Gy (ablative dose) had comparable outcomes to patients with a hypoechogenic gland with planned average thyroid doses of only 100–120 Gy (nonablative doses).
Within the thyroid, the majority of ultrasound reflections occur at interfaces between follicular cells and colloid. Thyroid glands, which are hypercellular (i.e., have relatively little colloid), have fewer reflective surfaces and thus are hypoechogenic, whereas normoechogenic (or hyperechogenic) patterns are seen in glands with normal (or high) colloidal content (i.e., with normalsize [or large] follicles and relatively small cellular volume) (7,8). Although at presentation the hyperactive glands are almost always hypoechogenic (7), antithyroid medication occasionally normalizes follicular structure. Consequently, patients who had prior antithyroid therapy present with a wide spectrum of echogenicities (9,10). In normal thyroids, follicular radii range from 100 to 500 μm, and untreated hyperactive glands are characterized by cell hypertrophy and hyperplasia and small, almostemptied colloidal spaces due to accelerated hormone turnover (11). In practice, because of variable antithyroid drug–induced involution of thyroid tissue, a wide range of follicle sizes is expected. Thus, our clinical results (10) seem reasonable in terms of more radiation being “wasted” in the larger follicles of normoechogenic glands than in the smaller follicles of hypoechogenic glands.
However, the results of this simulation only partly explain our clinical results (10). Although the effect of the substantial fraction of radiation energy absorbed within large colloid spheres on diminishing the ^{131}I radiation dose to thyroid follicular cells is significant, it is not as large as might be anticipated. To explain these results, one should consider the components of the relative absorbed dose to follicular cells. The colloid selfabsorption diminishes the relative crossabsorbed dose to follicular cells, which depends solely on the fraction of radiation energy emerging from each follicle (Eq. 7). However, this effect is balanced to some extent by the opposing effect on the relative selfabsorbed dose to follicular cells: the larger the colloid sphere, the lesser the fraction of follicular cells in thyroid mass and the greater the selfabsorbed dose (Eq. 7). For small follicles, the crossabsorbed dose is several times larger than is the selfabsorbed dose. However, as the follicle size and colloidal selfabsorption increase, the relative contribution of crossabsorbed dose rapidly diminishes to about only 2 times the selfabsorbed dose in the case of a 400μm radius of follicular colloid.
The generalization of the current model, allowing for the distribution of follicle sizes in a thyroid, is also possible. The assumption of identical follicles was used only in Monte Carlo estimations of the selfabsorbed fractions E_{coll}/E_{0} and E_{self}/E_{0}; Equations 1–9, however, also hold in cases of nonuniform follicular sizes. Given the distribution of follicle sizes, the fractions of radiation energy selfabsorbed in colloid and follicular cells can be estimated from the current results, assuming uniform concentration of radioiodine in all colloidal spheres.
The histologic data on the thyroid follicular sizes describe the distribution of the sizes of crosssections of irregularly packed follicles in random cut planes. These data underestimate the actual follicular sizes, which can be assessed only in the follicular equatorial planes. In addition, the use of punch biopsies instead of surgical specimens (7,8) has never been evaluated, and one cannot exclude the possibility that pooling the punched tissue through a narrow metal cylinder selectively draws the subpopulation of smaller follicles. Data on the actual sizes of thyroid follicles are currently incomplete. In any case, the current study demonstrates that the thyroid microstructure may be at least partially responsible for more favorable clinical responses of hypoechogenic thyroids, with smaller colloidal spaces and therefore lower intracolloidal selfabsorption of ^{131}I βradiation. However, the possible effects on follicular cell response of patienttopatient differences in intrinsic radiosensitivity certainly cannot be ignored.
We used 2 assumptions in assessing the relative absorbed dose to follicular cells: the spatially uniform absorption of radiation emanating from the follicles (the fraction not selfabsorbed in colloid and follicular cells) and close packing of the follicles, regardless of their size. The latter is suggested by micrographs of normal and hyperactive thyroid tissue showing that, although varying in size, follicles are always closely packed (11), with the assumption that follicles comprise 90% of the mass of the thyroid likewise based on animal data (6). The assumption of uniform distribution of crossabsorbed dose means that radiation emanating from a given follicle is not preferentially absorbed in any of the 3 thyroid compartments, colloid or follicular cells, or interfollicular spaces. Although the assumption may not be perfectly realistic in all patients, it agrees with partly irregular, close packing of follicles and avoids the need for a geometric model of follicular packing in assessing crossdose.
Insight into follicular structure could also prove useful in ablative radioiodine therapies (toxic nodular goiter, metastases of differentiated thyroid carcinoma), at least as a prognostic factor. The predominance of the follicular cell crossdose over the selfdose is specific for βradiation of ^{131}I. In the case of Auger emitters, such as ^{125}I, the opposite would be true, because the dose is largely confined to the follicle in which the electrons are emitted.
CONCLUSION
The characteristic histologic structure of thyroid tissue, organized in follicles, and the hormone kinetics, effectively segregating radioiodine in follicular lumen, affect the distribution of radiationabsorbed dose between the follicular cells and other gland structures, even in the case of the relatively longrange βemitter ^{131}I. This may require a patientspecific approach to radioimmunotherapy of Graves disease. Methods to assess the variable thyroid histology in clinical settings should be addressed.
APPENDIX
Relative Contributions and Absorbed Fractions of γ and βRadiations of ^{131}I Uniformly Distributed in a Typical Thyroid Lobe
A typical thyroid lobe was modeled as a rotational ellipsoid with semiaxes a = b = 1.0 cm and c = 2.5 cm (volume, 10.5 cm^{3}), filled with a uniform activity concentration of ^{131}I. For calculation of photon selfabsorbed fractions ϕ_{γ} (E_{i}), we used the Monte Carlo code EGS5 (4). All relevant photon emissions of ^{131}I, as listed at the National Nuclear Data Center Web site (12), were considered. According to the MIRD schema (13), the photon component of the lobular S value (mean absorbed dose per unit cumulated activity, that is, per 1 decay) due to ^{131}I selfirradiation is:where Δ_{i} = n_{i} E_{i} is the product of emission probability (n_{i}) and energy (E_{i}) of photon emissions, and m = 10.5 × 10^{−3} kg. Summing across the relevant γemissions:The γradiation selfabsorbed fraction is the average photon energy absorbed per decay of ^{131}I, m × S_{γ}, divided by the intensity weighted mean photon energy, which gives:A similar approach was used to calculate the βcomponent of the selfirradiation lobular (i.e., lobe to lobe) S factor due to ^{131}I:where _{β}(E) is the selfabsorbed fraction of the βparticle of energy E, and the integration was performed over the continuous ^{131}I βspectrum and included summation over the discrete emissions of electrons. The initial values for the ^{131}I βenergy spectrum were sampled according to the method of Simpkin and Mackie (5). For βradiation, the EGS5 code yields directly the selfabsorbed fraction (average electron energy absorbed per decay of ^{131}I, m × S_{β}, divided by the mean electron energy), as previously described by Grosev et al. (14), yielding:Because the mean electron energy calculated from the βspectrum is 190 keV, one obtains:Thus, for a typical thyroid lobe with uniformly distributed ^{131}I, the selfirradiation S value is:The percentage contribution of γradiation to total lobe dose is:
Considering the whole organ, one could take into account the cross–γradiation of the contralateral lobe, which we omit here for simplicity.
Thus, the underestimation error of ignoring the γcomponent to the average thyroid dose from ^{131}I selfirradiation and the overestimation error of ignoring the partial penetration of βradiation to some extent cancel out. For a typical thyroid lobe, the total error is an underestimation of about 3.4%.
Acknowledgments
This research was partially funded by grants 21600000216 and 02309828873064 from the Croatian Ministry of Science, Technology and Sports.
Footnotes

COPYRIGHT © 2008 by the Society of Nuclear Medicine, Inc.
References
 Received for publication April 28, 2008.
 Accepted for publication August 27, 2008.