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Dosimetric dependencies on target geometry and size in radioiodine therapy for differentiated thyroid cancer

  • Joachim N. Nilsson
    Correspondence
    Corresponding author at: Department of Molecular Medicine and Surgery, Karolinska Institutet, 17176 Stockholm, Sweden.
    Affiliations
    Department of Molecular Medicine and Surgery, Karolinska Institutet, Stockholm, Sweden

    Department of Medical Radiation Physics and Nuclear Medicine, Karolinska University Hospital, Stockholm, Sweden
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  • Jonathan Siikanen
    Affiliations
    Department of Medical Radiation Physics and Nuclear Medicine, Karolinska University Hospital, Stockholm, Sweden

    Department of Oncology-Pathology, Karolinska Institutet, Stockholm, Sweden
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  • Catharina Ihre Lundgren
    Affiliations
    Department of Molecular Medicine and Surgery, Karolinska Institutet, Stockholm, Sweden

    Department of Breast, Endocrine Tumours and Sarcoma, Karolinska University Hospital, Stockholm, Sweden
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  • Oscar Ardenfors
    Affiliations
    Department of Medical Radiation Physics and Nuclear Medicine, Karolinska University Hospital, Stockholm, Sweden

    Department of Oncology-Pathology, Karolinska Institutet, Stockholm, Sweden
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Open AccessPublished:May 31, 2022DOI:https://doi.org/10.1016/j.ejmp.2022.05.010

      Highlights

      • Impact of non-spherical target geometry on energy deposition.
      • Both size and geometry can impact treatment, for small and eccentric targets.
      • Dosimetric aspects on metastases in thyroid cancer.

      Abstract

      Purpose Radioiodine therapy is used in most disease stages for differentiated thyroid cancer. Its success depends on several factors, such as lesion size, completeness of surgery, extent of metastasis and tumoural iodine avidity. We aimed to investigate the importance of non-spherical geometries and size of metastases and thyroid remnants for the absorbed dose delivered. Methods Absorbed doses and energy depositions from homogeneously distributed iodine-131 in clinically relevant geometries and sizes were calculated using Monte Carlo simulations with MCNP6. A total of 162 volumes with different sizes and geometries corresponding to spheres, and prolate or oblate spheroids were simulated. Results Oblate and prolate spheroids had worse radiation coverage compared to spheres for equal masses, up to a difference of 38% for the most eccentric oblate spheroids and smallest masses simulated (a micrometastasis of mass 0.005 g). The differences in coverage could be explained by different volume - to - surface - area ratios of the spheroids. The impact of size alone caused up to 71% lower absorbed doses per decay in a spherical target mass of 0.005 g compared to 50 g. Conclusions While the iodine avidity, and therefore the total amount of decays, is the predominant contributing factor to absorbed dose in radioiodine therapy, eccentric spheroids and small target sizes can receive substantially lower absorbed doses from the same administration of radioiodine.

      Keywords

      Introduction

      Differentiated thyroid cancer is treated with surgical removal of one or both lobes of the thyroid gland. Based on the histopathological and clinical staging of the disease, radioiodine therapy is used for all but the smallest tumours, for which surgery remains the only treatment.
      Depending on disease stage, the approach and dosage of radioiodine therapy varies. For radically removed tumours without, or with only microscopic spread disease, the treatment aims to ablate any remnant of the thyroid gland with a lower activity of radioiodine after surgery to enable efficient follow-up [
      • Schlumberger M.
      • Catargi B.
      • Borget I.
      • Deandreis D.
      • Zerdoud S.
      • Bridji B.
      • et al.
      Strategies of radioiodine ablation in patients with low-risk thyroid cancer.
      ]. In patients with large locally invasive tumours or lymph node metastases, radioiodine can be given in larger amounts as adjuvant therapy to treat any unknown residual or metastatic disease (including micrometastases of diameters <2 mm). For gross residual tumour or manifest metastatic disease, repeated high activity radioiodine treatments are used for disease control and curative intent, given that the metastatic lesions concentrate iodine [
      • Haugen B.R.
      • Alexander E.K.
      • Bible K.C.
      • Doherty G.M.
      • Mandel S.J.
      • Nikiforov Y.E.
      • et al.
      2015 American thyroid association management guidelines for adult patients with thyroid nodules and differentiated thyroid cancer: the American thyroid association guidelines task force on thyroid nodules and differentiated thyroid cancer.
      ,
      • Luster M.
      • Clarke S.E.
      • Dietlein M.
      • Lassmann M.
      • Lind P.
      • Oyen W.J.G.
      • et al.
      Guidelines for radioiodine therapy of differentiated thyroid cancer.
      ]. This means that radioiodine treatment is a therapeutic option for both very small and large lesions, that can differ in geometry due to their anatomical surroundings.
      The ability of thyroid cancer tissue to concentrate and retain iodine is summarised in the concept of iodine avidity. In the individual patient, the tumoural iodine avidity is usually unknown when choosing therapeutic activity after surgery. Methods to estimate avidity have been previously established for gross metastatic disease using SPECT imaging with iodine-131, and for PET imaging with iodine-124 [
      • Freudenberg L.S.
      • Jentzen W.
      • Petrich T.
      • Frömke C.
      • Marlowe R.J.
      • Heusner T.
      • et al.
      Lesion dose in differentiated thyroid carcinoma metastases after rhTSH or thyroid hormone withdrawal: 124I PET/CT dosimetric comparisons.
      ,
      • Sgouros G.
      • et al.
      Patient-specific dosimetry for 131I thyroid cancer therapy using 124I PET and 3-dimensional-internal dosimetry (3D-ID) software.
      ,
      • Mínguez P.
      • Flux G.
      • Genollá J.
      • Delgado A.
      • Rodeño E.
      • Sjögreen Gleisner K.
      Whole-remnant and maximum-voxel SPECT/CT dosimetry in 131 I-NaI treatments of differentiated thyroid cancer: SPECT/CT dosimetry 131 I-NaI differentiated thyroid cancer.
      ]. However, the accuracy and feasibility of such methods diminishes as the size of the target decreases. For example, the spatial resolution of clinically available nuclear imaging systems (SPECT) of around 10 mm for iodine-131 severely limits accurate imaging of smaller targets [
      • Erdi Y.E.
      Limits of tumor detectability in nuclear medicine and PET.
      ,
      • Dewaraja Y.K.
      • Ljungberg M.
      • Green A.J.
      • Zanzonico P.B.
      • Frey E.C.
      • Bolch W.E.
      • et al.
      MIRD Pamphlet No. 24: guidelines for quantitative 131I SPECT in dosimetry applications.
      ]. The accuracy in image-based dosimetry is further hampered by the lack of complex geometries employed when using the Medical Internal Radiation Dose (MIRD) scheme [
      • Watson E.E.
      • Stabin M.G.
      • Siegel J.A.
      MIRD formulation.
      ]. The MIRD methodology continues to evolve in order to accommodate more realistic calculations, for example, in different surroundings and tumour sizes [
      • Olguin E.
      • President B.
      • Ghaly M.
      • Frey E.
      • Sgouros G.
      • Bolch W.E.
      Specific absorbed fractions and radionuclide S-values for tumors of varying size and composition.
      ]. However, the impact of non-spherical geometries is often not considered in its use for tumour dosimetry. This in part explains the limited clinical use of image dosimetry in the treatment of thyroid cancer [
      • Sjögreen Gleisner K.
      • Spezi E.
      • Solny P.
      • Gabina P.M.
      • Cicone F.
      • Stokke C.
      • et al.
      Variations in the practice of molecular radiotherapy and implementation of dosimetry: results from a European survey.
      ]. Instead, standardised amounts of iodine activity guided by clinical and pathological staging (TNM-staging [
      • Amin M.B.
      • Greene F.L.
      • Edge S.B.
      • Compton C.C.
      • Gershenwald J.E.
      • Brookland R.K.
      • et al.
      The Eighth Edition AJCC cancer staging manual: continuing to build a bridge from a population-based to a more “personalized” approach to cancer staging: the Eighth Edition AJCC cancer staging manual.
      ]) are widely used today, taking neither avidity, size nor geometry into consideration.
      This work was performed to study the radiation coverage in a range of clinically occuring geometries and sizes. Analysis of absorbed doses and energy deposition was performed, and data is presented on the impact of both target size and geometry.

      Methods

      Simulations

      Monte Carlo simulations were performed using the Monte Carlo N-particle 6 (MCNP6) code [
      • Goorley T.
      • James M.
      • Booth T.
      • Brown F.
      • Bull J.
      • Cox L.J.
      • et al.
      Initial MCNP6 release overview.
      ]. The simulations were performed to calculate energy deposition and absorbed doses for a range of sizes and geometries. A series of spheroidal geometries of liquid water were simulated with homogeneously dispersed iodine-131 radiation sources, surrounded by liquid water without any radiation sources, allowing backscatter. The geometrical shapes were chosen to approximate relevant clinical targets, such as lymph node metastases, thyroid remnants and thin segments of unresectable tumour tissue. All shapes and sizes were discussed and selected in collaboration with a thyroid surgeon (with 30 years clinical experience). The sphere was intended to model a lymph node metastasis and thyroid remnant growing in a deformable (soft tissue) surrounding. To model tumours and metastases growing in a constricted surrounding, or onto other structures, prolate and oblate spheroids were chosen. The simulated spheres had radii ranging between 1 and 50 mm, in 18 steps (of 1 mm steps from 1 mm to 10 mm, after which 5 mm steps were used) corresponding to scaled shapes with masses between 4.2 mg and 520 g. Sizes of spherical mass equivalents of 2 mm (size threshold for cervical lymph node micrometastases [
      • Randolph G.W.
      • Duh Q.-Y.
      • Heller K.S.
      • LiVolsi V.A.
      • Mandel S.J.
      • Steward D.L.
      • et al.
      The prognostic significance of nodal metastases from papillary thyroid carcinoma can be stratified based on the size and number of metastatic lymph nodes, as well as the presence of extranodal extension.
      ]) and 20 mm (size threshold for pT2 stage [
      • Amin M.B.
      • Greene F.L.
      • Edge S.B.
      • Compton C.C.
      • Gershenwald J.E.
      • Brookland R.K.
      • et al.
      The Eighth Edition AJCC cancer staging manual: continuing to build a bridge from a population-based to a more “personalized” approach to cancer staging: the Eighth Edition AJCC cancer staging manual.
      ]) diameter were encompassed in order to provide commonly encountered thyroid remnant, tumour and metastasis sizes. Sizes up to 100 mm diameter spheres were simulated to study the largest clinically occurring tumours. By varying the radii of one or two of the dimensions with axis proportions 1:16, 1:8, 1:4, 1:2, and 1:1, a total of 162 volumes were generated. This means that the shortest perpendicular axis of the smallest spheroid was 0.125 mm across, equivalent to the width of some 25 thyroid follicular cells. An illustration of the simulated geometrical shapes are shown in Fig. 1.
      Figure thumbnail gr1
      Fig. 1The simulated source geometries of oblate spheroids (upper left grid) and prolate spheroids (bottom right grid) with corresponding axis ratios. Spheres were included in both grids for illustration. Each geometry was simulated in eighteen different size scales.
      A pulse height *f8 tally (MCNP6 nomenclature) was used to score the energy deposition per starting particle. The length between resampling of the beta particles was on average 20 µm and the energy cut-off was 1 keV, corresponding to an electron range in liquid water of about 30 nm, which is a small fraction of the diameter of a thyroid follicular cell [
      • Pimblott S.M.
      • Siebbeles L.D.A.
      Energy loss by non-relativistic electrons and positrons in liquid water.
      ]. The energy deposition was separately simulated for beta, gamma, x-ray, Auger and internal conversion electrons using decay and energy distribution data adopted from ICRP Publication 107 [
      • Eckerman K.
      • Endo A.
      ICRP Publication 107. Nuclear decay data for dosimetric calculations.
      ].
      The total energy deposition per decay was calculated by summarizing the contributions from each radiation type multiplied with the corresponding yield per decay. The absorbed doses per decay were consequently calculated using the mass of each corresponding volume. Also, the contribution from each emission type to the total energy deposition was calculated. The energy deposition data were in some cases linearly interpolated in order to be able to report values for exactly the same masses for all spheroids and spheres.
      Additionally, the corresponding volume-to-surface-area (V/A) ratios for all sizes and geometries were analysed. This was done to explore any underlying dependencies that could better explain differences between geometric shapes. The surface area of the spheroids were calculated using Thomsen's approximative formula for general ellipsoids [

      Thomsen K, Michon G. Surface area of an ellipsoid. Numericana, n.d. https://www.numericana.com/answer/ellipsoid.htm#thomsen (accessed Feb. 12, 2022).

      ].

      Results

      The results show that for mass 0.005 g (2.1 mm diameter sphere, just above the 2 mm threshold for micrometastases), 99.6%, 72.3% and 72.5% of the energy from Auger electron, conversion electron and beta particle emissions was deposited in the target tissue. Less than 1% of the total energy from gamma and x-ray photons was deposited in the 0.005 g sphere. For a target sphere of mass 4.2 g (20 mm diameter sphere, threshold for pT2 stage), 97.6% of the beta particle kinetic energy was deposited within the target. Gamma and x-ray contributions increased for larger sizes, but only contributed to a small fraction of the total energy deposition even for large spheres. In the largest simulated sphere of 524 g (100 mm diameter), 20% of the deposited energy originates from gamma and x-rays combined, as illustrated in Fig. 2a. The contributions of Auger electrons and x-rays were below 0.5% of the total energy deposition for all sizes simulated.
      Figure thumbnail gr2
      Fig. 2a) Absolute energy deposition contributions per decay in a target sphere for all studied emissions. b) Total energy deposition to the lower range of simulated masses for spheres and for some prolate and oblate spheroids. For the masses shown, beta emissions were the dominant contributor to energy deposition.
      The energy deposition in the target for oblate and prolate spheroids was lower than in a sphere for the same mass, as seen in Fig. 2b.
      The absorbed dose coverage for spheres becomes more complete as the mass increases, with 71% higher absorbed dose per decay at 50 g compared to 0.005 g.
      The dependence of source geometry on absorbed dose is illustrated in Table 1, where normalised absorbed doses for a given time-integrated activity coefficient were calculated for different geometries while keeping the mass constant. The co-dependence of geometry and size is highlighted in the results for prolate and oblate spheroids. For target masses above 1 g, the difference was less than 12%. For a target mass of 0.005 g, the difference can amount to 38% between a perfect sphere and oblate spheroids with a 1:16 axis ratio. Oblate geometries had worse radiation coverage than prolate geometries for a given mass.
      Table 1Normalised absorbed doses for different spheroids and spheres. Varying axis ratios horizontally, and different target masses vertically. Values are normalised to the absorbed dose to a sphere of the same mass.
      Axis ratio
      OblateSphereProlate
      Mass (g)1:161:81:41:21:11:21:41:81:16
      0.0050.620.770.840.931.000.940.890.810.68
      0.010.690.810.940.971.000.980.920.830.74
      0.050.750.860.940.991.000.990.930.880.82
      0.10.810.910.960.991.000.990.950.900.87
      0.50.850.930.970.991.000.990.980.950.93
      1.00.880.940.981.001.001.000.980.970.94
      5.00.920.950.981.001.001.000.980.970.95
      100.930.960.981.001.001.000.990.980.96
      The dependence of energy deposition on geometry was analysed with respect to the V/A ratio, and the results are shown in Fig. 3. Fig. 3a shows the inherent mathematical relationship between the V/A ratio and mass for each geometry. The overall energy deposition is shown in Fig. 3b. Since the corresponding mass for the shapes increases with the V/A ratio, the increased energy deposition is expected. However, the energy depositions were very similar for all shapes for lower V/A ratios, but diverged as the ratio increased. For beta, Auger and internal conversion electron emissions, the differences in energy deposition between spheroidal geometries was completely explained by the V/A ratio of the target, as shown in Fig. 3c (only beta shown). The divergence in Fig. 3b was only evident for substantial gamma and x-ray contributions to the total energy deposition, i.e. at higher V/A ratios; the divergence for gamma is more clearly shown in Fig. 3d. Oblate spheroids have the lowest V/A ratios for a given mass of all the simulated geometries, followed by prolate spheroids; this appears to explain their relatively lower energy deposition per decay seen in Fig. 2b.
      Figure thumbnail gr3
      Fig. 3a) Relation between the V/A ratio and mass for the studied geometries. b) Overall energy deposition per decay for spheres and prolate and oblate spheroids for a range of V/A ratios. c) Energy deposition from beta particles per decay for a range of V/A ratios (similar agreement was observed for internal conversion and Auger electrons). d) Energy deposition for gamma emissions for a range of V/A ratios (similar behaviour was found for x-rays). The oblate and prolate spheroids absorb higher proportions of gamma energy for a given V/A ratio, as they have larger masses for a given V/A ratio.

      Discussion

      The results of our simulations clarify for which target shapes and sizes radioiodine treatments are impacted by geometrical factors. The factors can be important for dosimetry of micrometastases and thin layers of tumour or thyroid remnant tissue.
      In adjuvant treatment, where metastases of very small sizes are the most common target, the incomplete coverage of beta particles can be substantial. This limits treatment efficacy, as micrometastases have to be assumed present in many clinical cases. The simulations are also based on homogeneous distribution of iodine-131 in the geometric shapes, something rarely seen clinically, where iodine-concentrating tumour structures may be present in some parts of a tumour but not others [
      • Eszlinger M.
      • Khalil M.
      • Gillmor A.H.
      • Huang H.
      • Stewardson P.
      • McIntyre J.B.
      • et al.
      Histology-based molecular profiling improves mutation detection for advanced thyroid cancer.
      ]. As currently available SPECT and PET systems cannot resolve lesions below a few millimetres, the direct implementation of the current results for all patients may be limited. However, the results in this work could be useful when treating patients with unresectable tumour growing onto the trachea (thin tumour segments), or miliary lung metastases (multiple small nodules). The presence of such targets are often known from perioperative inspection or sub-millimetre resolved CT-scans, and the clinician is not reliant on nuclear imaging systems with limited resolution. The target geometry and size can then be taken into account in adapting treatment, for example with an increase in administered activity. In larger lesions with heterogeneous iodine accumulation, the range of beta particles can instead be beneficial; regions with lower uptake may be irradiated from neighbouring tissue with higher uptake of iodine. The radiation bystander effect may also have an impact in the case of heterogeneous uptake, and mediate some effect onto low-uptake regions [
      • Mukherjee S.
      • Chakraborty A.
      Radiation-induced bystander phenomenon: insight and implications in radiotherapy.
      ]. Geometric shapes in this work were chosen as regular shapes with resemblance of what can be encountered in clinical practice. The spheroidal approximation of irregular target shapes still somewhat limits the extrapolation of results to the clinical setting.
      The geometric shape of the target can similarly to size have an effect on absorbed doses delivered. The difference between a perfect sphere and the most eccentric oblate spheroids was found to only be substantial (more than 10% difference compared to a sphere) in masses below 1 g. Oblate spheroids had worse energy deposition per decay than had prolate spheroids, owing to the larger surface area for a given mass. It could be argued that metastases of small sizes are less likely to have severely restricted space, and are therefore unlikely to form the most eccentric spheroid shapes studied in this work.
      The impact of geometry in radioiodine treatment has been studied before. Previous work has been performed on spheres in the context of radioiodine treatment of micrometastases, where electron tracks for iodine-131 and iodine-123 were compared [
      • Li W.B.
      • et al.
      Track structures and dose distributions from decays of (131)I and (125)I in and around water spheres simulating micrometastases of differentiated thyroid cancer.
      ]. Different geometrical shapes has been studied in relation to thyroid remnant ablation, in a work that briefly discusses calculative errors in assuming absorbed fractions of 1 for beta particles in targets of varied geometries, including one spheroid shape [
      • Grosev D.
      • Loncarić S.
      • Huić D.
      • Dodig D.
      Geometric models in dosimetry of thyroid remnant mass.
      ]. However, the current work has expanded the analysis with detailed data on spheroids, which to the authors' knowledge has not been published before.
      While the absorbed dose contribution from internal conversion electrons was approximately 5% for all sizes and geometries, Auger electrons contributed to less than 0.5%, as can be seen in Fig. 2a. It should be noted that the linear energy transfer of such emissions is higher than for high energy beta particles and gamma rays. Auger electrons can therefore have a higher therapeutic impact near the radiation source than indicated by the raw percentage contribution to the absorbed dose [
      • Ku A.
      • Facca V.J.
      • Cai Z.
      • Reilly R.M.
      Auger electrons for cancer therapy – A review.
      ,
      • Pirovano G.
      • Wilson T.C.
      • Reiner T.
      Auger: the future of precision medicine.
      ]. While the continuous-slowing-down-approximation may cause relatively large errors on small scales for especially low energy Auger electrons, the low yield of Auger electrons in iodine-131 and the average resampling distance in this work of 20 µm limits this effect in the studied target size range [
      • Bousis C.
      • Emfietzoglou D.
      • Nikjoo H.
      Calculations of absorbed fractions in small water spheres for low-energy monoenergetic electrons and the Auger-emitting radionuclides (123)Ι and (125)Ι.
      ].
      The V/A ratio studied here has previously been discussed as a useful parameter in the context of internal dosimetry [
      • Romanchikova M.
      • Flux G.
      • Partridge M.
      Impact of surface area-to-volume ratio on S-value.
      ]. In this work it was shown that for spherical or spheroidal shapes, the energy deposition was almost equal for widely different shapes, given equal V/A ratios. It may therefore be a useful complementary parameter to mass when comparing different geometrical shapes.
      The results on size and geometry should be considered together with the impact of iodine avidity. Our data suggests geometry and size can make up to a three-fold difference (for the smallest, most eccentric oblate targets) in absorbed dose per decay. Previously published data by Schlesinger et al. [
      • Schlesinger T.
      • Flower M.A.
      • McCready V.R.
      Radiation dose assessments in radioiodine (131I) therapy. 1. The necessity for in vivo quantitation and dosimetry in the treatment of carcinoma of the thyroid.
      ] highlighted the dosimetric importance of iodine avidity relative to target size to achieve adequate absorbed doses for successful treatment. Avidity has been shown to vary more than a hundred-fold pre-therapeutically between different patients, and is linked to mutations in BRAF and the TERT-promoter [
      • Nilsson J.N.
      • Siikanen J.
      • Hedman C.
      • Juhlin C.C.
      • Ihre Lundgren C.
      Pre-therapeutic measurements of iodine avidity in papillary and poorly differentiated thyroid cancer reveal associations with thyroglobulin expression, histological variants and Ki-67 index.
      ,
      • Liu J.
      • Liu R.
      • Shen X.
      • Zhu G.
      • Li B.
      • Xing M.
      The genetic duet of BRAF V600E and TERT promoter mutations robustly predicts loss of radioiodine avidity in recurrent papillary thyroid cancer.
      ,
      • Yang X.
      • Li J.
      • Li X.
      • Liang Z.
      • Gao W.
      • Liang J.
      • et al.
      TERT promoter mutation predicts radioiodine-refractory character in distant metastatic differentiated thyroid cancer.
      ]. Absorbed doses above 40–80 Gy to a metastatic lesion are associated with a high success rate, and 50–300 Gy has been associated with successful thyroid remnant ablation [
      • Maxon H.R.
      • Thomas S.R.
      • Hertzberg V.S.
      • Kereiakes J.G.
      • Chen I.-W.
      • Sperling M.I.
      • et al.
      Relation between effective radiation dose and outcome of radioiodine therapy for thyroid cancer.
      ,
      • Wierts R.
      • Brans B.
      • Havekes B.
      • Kemerink G.J.
      • Halders S.G.
      • Schaper N.N.
      • et al.
      Dose-response relationship in differentiated thyroid cancer patients undergoing radioiodine treatment assessed by means of 124I PET/CT.
      ,
      • Flux G.D.
      • Haq M.
      • Chittenden S.J.
      • Buckley S.
      • Hindorf C.
      • Newbold K.
      • et al.
      A dose-effect correlation for radioiodine ablation in differentiated thyroid cancer.
      ]. Such absorbed doses would be impossible in a completely non-avid target. Furthermore, in the clinical setting, iodine avidity is temporarily increased, potentially more than tenfold, through potent stimulation by increased serum levels of thyroid stimulating hormone [
      • Castro M.R.
      • Bergert E.R.
      • Goellner J.R.
      • Hay I.D.
      • Morris J.C.
      Immunohistochemical analysis of sodium iodide symporter expression in metastatic differentiated thyroid cancer: correlation with radioiodine uptake.
      ,
      • Kogai T.
      • Brent G.A.
      The sodium iodide symporter (NIS): regulation and approaches to targeting for cancer therapeutics.
      ]. Iodine uptake can also be increased by having patients follow a low-iodine diet prior to treatment, which effect may approach a two-fold increase compared to normal diet [
      • Sawka A.M.
      • Ibrahim-Zada I.
      • Galacgac P.
      • Tsang R.W.
      • Brierley J.D.
      • Ezzat S.
      • et al.
      Dietary iodine restriction in preparation for radioactive iodine treatment or scanning in well-differentiated thyroid cancer: a systematic review.
      ].
      In conclusion, our results establish that while the most important factor in radioiodine treatment success is high iodine avidity, the geometry and size of the target can have a substantial impact, mainly for very small and compressed targets.

      Data Availability

      The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

      Declaration of Competing Interest

      The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

      References

        • Schlumberger M.
        • Catargi B.
        • Borget I.
        • Deandreis D.
        • Zerdoud S.
        • Bridji B.
        • et al.
        Strategies of radioiodine ablation in patients with low-risk thyroid cancer.
        N Engl J Med. 2012; 366: 1663-1673
        • Haugen B.R.
        • Alexander E.K.
        • Bible K.C.
        • Doherty G.M.
        • Mandel S.J.
        • Nikiforov Y.E.
        • et al.
        2015 American thyroid association management guidelines for adult patients with thyroid nodules and differentiated thyroid cancer: the American thyroid association guidelines task force on thyroid nodules and differentiated thyroid cancer.
        Thyroid. 2016; 26: 1-133
        • Luster M.
        • Clarke S.E.
        • Dietlein M.
        • Lassmann M.
        • Lind P.
        • Oyen W.J.G.
        • et al.
        Guidelines for radioiodine therapy of differentiated thyroid cancer.
        Eur J Nucl Med Mol Imaging. 2008; 35: 1941-1959
        • Freudenberg L.S.
        • Jentzen W.
        • Petrich T.
        • Frömke C.
        • Marlowe R.J.
        • Heusner T.
        • et al.
        Lesion dose in differentiated thyroid carcinoma metastases after rhTSH or thyroid hormone withdrawal: 124I PET/CT dosimetric comparisons.
        Eur J Nucl Med Mol Imaging. 2010; 37: 2267-2276
        • Sgouros G.
        • et al.
        Patient-specific dosimetry for 131I thyroid cancer therapy using 124I PET and 3-dimensional-internal dosimetry (3D-ID) software.
        J Nucl Med. Aug. 2004; 45: 1366-1372
        • Mínguez P.
        • Flux G.
        • Genollá J.
        • Delgado A.
        • Rodeño E.
        • Sjögreen Gleisner K.
        Whole-remnant and maximum-voxel SPECT/CT dosimetry in 131 I-NaI treatments of differentiated thyroid cancer: SPECT/CT dosimetry 131 I-NaI differentiated thyroid cancer.
        Med Phys. 2016; 43: 5279-5287
        • Erdi Y.E.
        Limits of tumor detectability in nuclear medicine and PET.
        Mol Imaging Radionucl Ther. 2012; 21: 23-28https://doi.org/10.4274/Mirt.138
        • Dewaraja Y.K.
        • Ljungberg M.
        • Green A.J.
        • Zanzonico P.B.
        • Frey E.C.
        • Bolch W.E.
        • et al.
        MIRD Pamphlet No. 24: guidelines for quantitative 131I SPECT in dosimetry applications.
        J Nucl Med. 2013; 54: 2182-2188
        • Watson E.E.
        • Stabin M.G.
        • Siegel J.A.
        MIRD formulation.
        Med Phys. 1993; 20: 511-514https://doi.org/10.1118/1.597046
        • Olguin E.
        • President B.
        • Ghaly M.
        • Frey E.
        • Sgouros G.
        • Bolch W.E.
        Specific absorbed fractions and radionuclide S-values for tumors of varying size and composition.
        Phys Med Biol. 2020; 65235015https://doi.org/10.1088/1361-6560/abbc7e
        • Sjögreen Gleisner K.
        • Spezi E.
        • Solny P.
        • Gabina P.M.
        • Cicone F.
        • Stokke C.
        • et al.
        Variations in the practice of molecular radiotherapy and implementation of dosimetry: results from a European survey.
        EJNMMI Phys. 2017; 4
        • Amin M.B.
        • Greene F.L.
        • Edge S.B.
        • Compton C.C.
        • Gershenwald J.E.
        • Brookland R.K.
        • et al.
        The Eighth Edition AJCC cancer staging manual: continuing to build a bridge from a population-based to a more “personalized” approach to cancer staging: the Eighth Edition AJCC cancer staging manual.
        CA Cancer J Clin. 2017; 67: 93-99
        • Goorley T.
        • James M.
        • Booth T.
        • Brown F.
        • Bull J.
        • Cox L.J.
        • et al.
        Initial MCNP6 release overview.
        Nucl Technol. 2012; 180: 298-315
        • Randolph G.W.
        • Duh Q.-Y.
        • Heller K.S.
        • LiVolsi V.A.
        • Mandel S.J.
        • Steward D.L.
        • et al.
        The prognostic significance of nodal metastases from papillary thyroid carcinoma can be stratified based on the size and number of metastatic lymph nodes, as well as the presence of extranodal extension.
        Thyroid. 2012; 22: 1144-1152
        • Pimblott S.M.
        • Siebbeles L.D.A.
        Energy loss by non-relativistic electrons and positrons in liquid water.
        Nucl Instrum Methods Phys Res, Sect B. 2002; 194: 237-250https://doi.org/10.1016/S0168-583X(02)00693-6
        • Eckerman K.
        • Endo A.
        ICRP Publication 107. Nuclear decay data for dosimetric calculations.
        Ann ICRP. 2008; 38: 7-96https://doi.org/10.1016/j.icrp.2008.10.004
      1. Thomsen K, Michon G. Surface area of an ellipsoid. Numericana, n.d. https://www.numericana.com/answer/ellipsoid.htm#thomsen (accessed Feb. 12, 2022).

        • Eszlinger M.
        • Khalil M.
        • Gillmor A.H.
        • Huang H.
        • Stewardson P.
        • McIntyre J.B.
        • et al.
        Histology-based molecular profiling improves mutation detection for advanced thyroid cancer.
        Genes Chromosomes Cancer. 2021; 60: 531-545
        • Mukherjee S.
        • Chakraborty A.
        Radiation-induced bystander phenomenon: insight and implications in radiotherapy.
        Int J Radiat Biol. 2019; 95: 243-263https://doi.org/10.1080/09553002.2019.1547440
        • Li W.B.
        • et al.
        Track structures and dose distributions from decays of (131)I and (125)I in and around water spheres simulating micrometastases of differentiated thyroid cancer.
        Radiat Res. 2001; 156: 419-429https://doi.org/10.1667/0033-7587(2001)156[0419:tsaddf]2.0.co;2
        • Grosev D.
        • Loncarić S.
        • Huić D.
        • Dodig D.
        Geometric models in dosimetry of thyroid remnant mass.
        Nuklearmedizin. 2008; 47: 120-126
        • Ku A.
        • Facca V.J.
        • Cai Z.
        • Reilly R.M.
        Auger electrons for cancer therapy – A review.
        EJNMMI radiopharm chem. 2019; 4: 27https://doi.org/10.1186/s41181-019-0075-2
        • Pirovano G.
        • Wilson T.C.
        • Reiner T.
        Auger: the future of precision medicine.
        Nucl Med Biol. 2021; 96–97: 50-53https://doi.org/10.1016/j.nucmedbio.2021.03.002
        • Bousis C.
        • Emfietzoglou D.
        • Nikjoo H.
        Calculations of absorbed fractions in small water spheres for low-energy monoenergetic electrons and the Auger-emitting radionuclides (123)Ι and (125)Ι.
        Int J Radiat Biol. 2012; 88: 916-921https://doi.org/10.3109/09553002.2012.666003
        • Romanchikova M.
        • Flux G.
        • Partridge M.
        Impact of surface area-to-volume ratio on S-value.
        J Nucl Med. 2009; 50: 1868
        • Schlesinger T.
        • Flower M.A.
        • McCready V.R.
        Radiation dose assessments in radioiodine (131I) therapy. 1. The necessity for in vivo quantitation and dosimetry in the treatment of carcinoma of the thyroid.
        Radiother Oncol. 1989; 14: 35-41https://doi.org/10.1016/0167-8140(89)90006-6
        • Nilsson J.N.
        • Siikanen J.
        • Hedman C.
        • Juhlin C.C.
        • Ihre Lundgren C.
        Pre-therapeutic measurements of iodine avidity in papillary and poorly differentiated thyroid cancer reveal associations with thyroglobulin expression, histological variants and Ki-67 index.
        Cancers (Basel). 2021; 13: 3627https://doi.org/10.3390/cancers13143627
        • Liu J.
        • Liu R.
        • Shen X.
        • Zhu G.
        • Li B.
        • Xing M.
        The genetic duet of BRAF V600E and TERT promoter mutations robustly predicts loss of radioiodine avidity in recurrent papillary thyroid cancer.
        J Nucl Med. 2020; 61: 177-182https://doi.org/10.2967/jnumed.119.227652
        • Yang X.
        • Li J.
        • Li X.
        • Liang Z.
        • Gao W.
        • Liang J.
        • et al.
        TERT promoter mutation predicts radioiodine-refractory character in distant metastatic differentiated thyroid cancer.
        J Nucl Med. 2017; 58: 258-265
        • Maxon H.R.
        • Thomas S.R.
        • Hertzberg V.S.
        • Kereiakes J.G.
        • Chen I.-W.
        • Sperling M.I.
        • et al.
        Relation between effective radiation dose and outcome of radioiodine therapy for thyroid cancer.
        N Engl J Med. 1983; 309: 937-941
        • Wierts R.
        • Brans B.
        • Havekes B.
        • Kemerink G.J.
        • Halders S.G.
        • Schaper N.N.
        • et al.
        Dose-response relationship in differentiated thyroid cancer patients undergoing radioiodine treatment assessed by means of 124I PET/CT.
        J Nucl Med. 2016; 57: 1027-1032
        • Flux G.D.
        • Haq M.
        • Chittenden S.J.
        • Buckley S.
        • Hindorf C.
        • Newbold K.
        • et al.
        A dose-effect correlation for radioiodine ablation in differentiated thyroid cancer.
        Eur J Nucl Med Mol Imaging. 2010; 37: 270-275
        • Castro M.R.
        • Bergert E.R.
        • Goellner J.R.
        • Hay I.D.
        • Morris J.C.
        Immunohistochemical analysis of sodium iodide symporter expression in metastatic differentiated thyroid cancer: correlation with radioiodine uptake.
        J Clin Endocrinol Metab. 2001; 86: 5627-5632https://doi.org/10.1210/jcem.86.11.8048
        • Kogai T.
        • Brent G.A.
        The sodium iodide symporter (NIS): regulation and approaches to targeting for cancer therapeutics.
        Pharmacol Ther. 2012; 135: 355-370https://doi.org/10.1016/j.pharmthera.2012.06.007
        • Sawka A.M.
        • Ibrahim-Zada I.
        • Galacgac P.
        • Tsang R.W.
        • Brierley J.D.
        • Ezzat S.
        • et al.
        Dietary iodine restriction in preparation for radioactive iodine treatment or scanning in well-differentiated thyroid cancer: a systematic review.
        Thyroid. 2010; 20: 1129-1138