Determination of Beta Radiation Dose to the Thyroid Gland

Total activities due to the ingestion of I were evaluated in different compartments of the human body of patients. It has been shown that the 131 I activity in urine of patients increases when the 131 I uptake decreases which could represent a source of radiation for their relatives when they leave hospitals. A new dosimetric model based on the specific betadose concept was developed for evaluating committed equivalent doses to thyroid due to 131 I uptake by different age groups of patients. Data obtained are in good agreement with those obtained by using the ICRP model for iodine. Committed equivalent dose to the thyroid gland is influenced by the mass of thyroid, 131 I uptake and energy of the emitted beta particles. In addition, 131 I uptake was measured by using a gamma camera and committed equivalent doses to the thyroid gland of female patients from the ingestion of 131 I for the treatment of hyperthyroidism diseases were evaluated. Data obtained by using our model and the ICRP ingestion dose coefficients are in good agreement with each other.


Introduction
Radioiodine 131 I is successfully utilized in nuclear medicine for the treatment of hyperthyroidism and thyroid cancer [1]. This radioisotope emits beta minus particles used for the treatment and gamma photons used for diagnosis. Due to the short range of beta minus particles in tissue, damaging effects of beta radiation is restricted to thyroid cells. Information from the emitted gamma rays are analyzed by a gamma camera coupled to a computer and are transduced in images. 131 I is produced in nuclear reactors by bombarding natural tellurium metal ( 127 Te) by neutrons; it disintegrates by emitting βparticles with a half-life of 8.04 days to unstable xenon 131 Xe * which decays to stable xenon ( 131 Xe) by emitting gamma photons of different energies and intensities [2]. 131 I is widely used for diagnostic [3] and therapeutic [4] purposes. For many decades, radioactive iodine was orally administered to patients for the treatment of benign and malignant thyroid diseases [5][6][7][8][9]. Indeed, a major part of the administered radioiodine will concentrate in the thyroid gland; the emitted βparticles of short ranges will only damage thyroid cells without any harmful health effects to the neighboring organ tissues. However, the emitted gamma rays may cause radiation damage to other tissues of the patients and other individuals [10]. There are two types of biological effects of ionizing radiation: deterministic and stochastic effects. Deterministic effects are caused by the decrease in or loss of organ function due to cell damage or cell death. In the case of treatment of thyroid cancer or metastases, hyperthyroidism and goiter, the cell killing effect in some or all cells of the thyroid gland or in the metastases is the desired effect. Other organs should not be affected in such a way that deterministic effects will occur. Therefore beta-emitting 131 I is often the radionuclide chosen for these treatments, although the associated gamma emission exposes also other organs of the patient and other individuals. Stochastic effects are those that result from radiation-induced changes in cells that retain their ability to divide. These modified cells sometimes initiate malignant transformation of a cell, leading to the development of a malignant clone and eventually to a clinically observable cancer.
In the present work activities due 131 I were determined in different compartments of the human body of patients following the ingestion of 131 I. A new dosimetric model based on the formalism of specific beta-dose was developed and beta radiation doses due to the ingestion of 131 I by patients for the treatment of hyperthyroidism diseases were determined.

Determination of Activities Due to 131 I in Different Compartments of the Human Body
In terms of the International Commission on Radiological Protection (ICRP) biokinetic model for iodine [11] (Figure  1), one can divide the human body into the following compartments: The blood (B) The thyroid (Th) The rest of body (Rb) The urine (U) The faeces (F) Figure 1. Biokinetic model for iodine metabolism [11].
The rates of change of the total activity in the blood, thyroid, rest of body, urine and faeces at any time due to the ingestion of 131 I are respectively given by:   Total activities due to 131 I in the different compartments of the human body are obtained by solving the last differential equation system (Equations (1)-(5)) by using a Maple 8 code [12] providing that at t=0 these activities are equal to zero except that in the blood which is equal to A c (0). Indeed, for an n th compartment one has: where A c (0)=1Bq is the 131 I intake at time t=0, n a l is a constant and n l γ is a rate constant in d -1 .

A New Dosimetric Model for Evaluating Beta-Committed Equivalent Dose Due to 131 I in the Thyroid Gland of Patients
Beta-equivalent dose rate (Sv s -1 ) due to 131 I in the thyroid (Th) of a patient is given by: Where: is the total activity due to 131 I at time t in the thyroid.

I Th D Sp
is the specific beta-dose (Gy) deposited by βparticles emitted by 1Bq of 131 I in the thyroid tissue. W R is the radiation weighting factor which is equal to unity for beta-particles [13].
Where: K j is the emission percentage of a beta minus particle of index j and average energy E β emitted by 131 I [2]. R j (cm) is the range of a beta minus particle of index j and average energy E β emitted by 131 I in the thyroid tissue. k=1.6x10 -13 J MeV -1 is a conversion factor. S j (MeVcm -1 ) is the stopping power of the thyroid tissue for a beta minus particle of index j and average energy E β emitted by 131 I. R j and S j were determined by using an ESTAR code [14] and the chemical composition of thyroid given by in the ICRP Publication 89 [15] (Table 2). M Th is the mass (g) of the thyroid (Table 3) [15].
where τ is the exposure time which is equal to 50 years for adults and to 70 years for children. This committed equivalent dose could also be evaluated by using the following relationship: where h Th ( 131 I) is the ingestion dose coefficient for 131 I (SvBq -1 ) for a given 131 I uptake [1].

Total Activities Determined in Different Compartments of the Human Body of Patients from the Ingestion of 131 I
Activities due to 131 I were determined in different compartments of the human body of patients from the ingestion of 131 I by using Equation (6). Variation of the 131 I activity in blood, thyroid, rest of body and urine as functions of time are shown in figures (2)-(5) for adults, and 1year children patients for different 131 I uptakes, respectively. It is to be noted that the residence time of 131 I in the thyroid and rest of body (Figures 2(b) and 2(c)) is higher than that in blood (Figure 2(a)). This is because the transfer rates of 131 I from thyroid to the rest of body ( h b T R λ → ) and from the rest of body to faeces ( Rb F λ → ) are lower than that from blood to urine ( B U λ → ) ( Table 1). The retention function for 131 I in thyroid is higher for adult (Figures 2(b) and 3(b)) than for 1year children patients (Figures 4 (b) and 5 (b)), respectively. This is due to the fact that the transfer rate of 131 I from the thyroid to the rest of body is higher for 1year children than for adults (Table 1). One can note that when the 131 I uptake increases (from 5% to 55%, for instance) for adults (Figures 2 and 3) and 1year children (Figures 4 and 5) the 131 I activity in urine decreases. This is because B U λ → decreases when the 131 I uptake increases (Table 1 (b)). The presence of 131 I in urine of patients after lower 131 I uptake treatment could represent a source of radiation for their relatives when using common family toilets.

Beta Committed Equivalent Dose to Thyroid Due to the Ingestion of 131 I by Patients
In order to test the validity of our dosimetric model committed equivalent doses per unit intake (h Th ( 131 I)) were determined in the thyroid of various age groups of patients from the ingestion of 131 I by using Equation (9). Data obtained are shown in Table 4. Considering uncertainties on ranges and stopping powers [14], the relative uncertainty of the committed equivalent dose is estimated to be about 10%. Data obtained are in good agreement with those obtained by using the ICRP model [1]. h Th ( 131 I) is influenced by the thyroid mass and activity integral (Eq. (9)). It is to be noted from results shown in Table 4 that committed equivalent dose per unit intake to thyroid is clearly higher for children than for adults, for a given 131 I uptake. This is because the thyroid mass is predominant (Equation (9) (9)) is equal to 11.11 (Table 3), whereas the ratio of the corresponding 131 I activity integral is equal to 0.93 for an 131 I uptake of 55%. One can also note that for a given age group of patients, committed equivalent dose per unit intake to thyroid increases with the 131 I uptake.  15% (b), 25% (c), 35% (d), 45% (e) and 55% (f), by using this method and the ICRP ingestion dose coefficient [1].  Table 5. Ten days after, the thyroid 131 I uptake was measured for the seven women patients by using a gamma camera type Siemens Symbia T6. An example of thyroid scintigraphy image is given in Figure 6 for patient 1. Committed equivalent doses to thyroid (H Th ( 131 I)) from the ingestion of 131 I by the considered female patients were evaluated by using Equation (9). Data obtained are shown in Table 5. The relative uncertainty of the committed equivalent dose is estimated to be about 11%.
It is to be noted from results shown in Table 5 that: Even though patients 2 and 5 received the same 131 I activity and have practically the same thyroid mass, they show different committed equivalent doses to the thyroid gland. This is because 131 I uptake is larger for patient 5 than for patient 2. Patient 1 shows lower committed equivalent dose to thyroid than patient 2 even if patient 1 presents higher 131 I activity and 131 I uptake than patients 2. This due to the fact that patient 1 has a thyroid mass larger than patient 2. Even though patients 2 and 6 received the same 131 I activity and show practically the same 131 I uptake, committed equivalent dose to thyroid is clearly higher for patient 2 than for patient 6. This is because patient 6 has a thyroid mass larger than that of patient 2. Even though patients 3 and 4 have been administered different 131 I activities and show different 131 I uptakes and thyroid masses, they show practically identical committed equivalent doses to thyroid: there is compensation between the effects of these three parameters. Committed equivalent doses to thyroid were determined for patients 4, 5 and 7 by using our model and the ICRP ingestion dose coefficients for 131 I corresponding to the thyroid masses of these patients [1] (Table 5). Data obtained by the two methods are in good agreement with each other.

Conclusion
In this study, 131 I activity was calculated in different compartments of the body of different age groups of patients. It has been shown that the 131 I activity is influenced by the 131 I uptake and transfer rate of 131 I between the different compartments. A new dosimetric model based on the formalism of specific beta dose deposited by 1 Bq of 131 I in the thyroid tissue was developed and validated and beta radiation doses to the thyroid from the ingestion of radioiodine ( 131 I) by patients were evaluated. It is concluded that committed equivalent doses to the thyroid gland are influenced by the 131 I uptake, transfer rate of 131 I, mass of thyroid, and energy of the emitted beta minus particles. 131 I uptake was measured for female patients presenting different hyperthyroidism pathologies by using a gamma camera and the resulting committed equivalent doses were determined. The dosimetric model developed is a good tool for assessing beta radiation doses to the thyroid gland in order to evaluate the appropriate 131 I activity to be administered to patients for therapeutic and diagnostic purposes.