**2. Biodistribution modeling**

Physical and temporal variability of the iodine −131 activity distributions in tissue constitute what is commonly called bio distribution models. The models are based on what is known in mathematics as compartmental modeling. For the sake of radiation dose calculations scientist may use different models to estimate the activity present in the patient body and the fraction of the radioactivity released from his or her body using simple two compartment model. More rigorous models also exist, having more than five compartments.

Biodistribution experiments are also published and new ones are still being published it is a dynamic field of research. The same apply for different radiopharmaceuticals. Organs Residence time is one important factors being measured while developing a bio distribution experiments leading to the proposal of a new bio distribution model.

Factors altering such models are very important to be aware of, because the alteration in the bio distribution will directly impact the radiation dose calculations and therefore the safety of the patients undergoing radioiodine therapy. To the best of our knowledge there are no general agreement on the methods or standards applied when reporting bio distribution studies. Therefore we will attempt to summarize the ones in the literature.

#### **2.1 Biokinetic data**

Biokinetic data are variables that describe the bio distribution space time functions. Among the most common of these variables are: the uptake fraction by the organ example the thyroid, the excreted fraction as (urine or feces), the biological halflife or time in a specific organ or body tissues like blood, thyroid, and intestine for example. The fractions are mostly given as % and the time are often given in days most of the times in the case of radioactive iodine. Biokinetic data for radioactive iodine are reported in ICRP-30 [1].

#### **2.2 Radionuclide delivery system**

Radionuclide delivery systems are now as antibodies, nanoparticles both inorganic and organic and finally as Microspheres.

In this reference good information is given on targeted radionuclide therapy for the thyroid cancer treatment. Parallelism is shown between preclinical animal models in rats and mice versus humans [2].

Translation of the experimental findings and research results is an issue that warrants the attention of the researcher; in this case the range of radiation in tissues and the organ sizes needs to be considered. Also the difference among the metabolism and metabolism rate models used directly affects the biodistribution in the animal or the human under study.

#### **2.3 Compartmental biological modeling**

Compartmental models are used for internal radioisotope ingestions or injections dosimetry since the seventies. We are referring to the ICRP publication 30 published in 1979. In that documents several compartmental models are proposed, we focus on the model proposed for iodine metabolism in humans.

*Recent Advances in Biodistribution, Preclinical and Clinical Applications of Radiolabelled Iodine DOI: http://dx.doi.org/10.5772/intechopen.99113*

In order to apply the model a set of differential equations has to be solved simultaneously to obtain the biodistribution of iodine in human body. The equations can be solved numerically using algorithm included in software like Mathematica or Matlab.

Biokinetic models parameters are taken for healthy individuals. In order to apply the models to cancer patients for example, the metabolic data has to be customized to represent their actual metabolism status. Currently, scientists are recommending the use of personalized radiopharmaceutical therapy where each therapeutic procedures is planned based on the individual patient data and not using the generic data from reports like ICRP and others.

The following 4 differential equations are for the model in **Figure 1**:

$$\mathbf{dq}\_1 \wedge \mathbf{dt} = -\left(\mathcal{X}\_{\mathrm{p}} + \mathcal{X}\_{\mathrm{i}\mathrm{z}}\right) \mathbf{q}\_1 \tag{1}$$

**Figure 1.** *Five compartments human body biokinetic model of iodine as per ICRP-30 report.*

$$\mathbf{dq}\_{\rm z} \wedge \mathbf{dt} = \mathcal{J}\_{\rm z2} \mathbf{q}\_{\rm z} - \left(\mathcal{J}\_{\rm p} + \mathcal{J}\_{\rm z5} + \mathcal{J}\_{\rm z3}\right) \mathbf{q}\_{\rm z} + \mathcal{J}\_{\rm 42} \mathbf{q}\_{\rm 4} \tag{2}$$

$$\mathbf{d}\mathbf{q}\_{3} \wedge \mathbf{d}\mathbf{t} = \mathbb{A}\_{\mathbf{z}3}\mathbf{q}\_{\mathbf{z}} - \left(\mathbb{A}\_{\mathbf{p}} + \mathbb{A}\_{\mathbf{3}4}\right)\mathbf{q}\_{3} \tag{3}$$

$$\mathbf{d}\mathbf{q}\_4 \wedge \mathbf{d}\mathbf{t} = \mathcal{Z}\_{34}\mathbf{q}\_3 - \left(\mathcal{Z}\_{\mathbf{p}} + \mathcal{Z}\_{4\mathbf{z}} + \mathcal{Z}\_{4\mathbf{5}}\right)\mathbf{q}\_4 \tag{4}$$

This five compartment model is the one proposed by the −30 to represent the biokinetic model of iodine in healthy individuals.

After solving the system of simultaneous four differential equations above the solution yield the following.

$$\mathbf{T\_{1/2}}\left(\text{thy}\right) = \mathbf{80}\,\mathbf{d}, \mathbf{T\_{1/2}}\left(\text{Body Fluid}\right) = \mathbf{0.25}\,\mathbf{d}, \mathbf{i\_{z\_3}}\left(\text{thy}\right) = \mathbf{90}\,\mathbf{\%}, \mathbf{i\_{z\_5}}\left(\text{excrection}\right) = \mathbf{\%}\mathbf{0\%}.$$

These results are for the healthy individuals, solving the same system for thyroid cancer patients yields the following [3, 4]:

T thy d,T Body Fluid d,i thy %,i excretion %. 1 2/ / ( ) = 0.66 1 2 ( ) = 0.52 <sup>23</sup> ( ) = 12 <sup>25</sup> ( ) = 88

We can see that there is a significant difference in the values obtained. Where the importance of personalized dose estimates, the analysis of the results dictates the importance to take into account the pathology of the patients and his thyroid disease status and diagnosis before interpreting the results of any biokinetic experiment or data analysis.

#### **2.4 Biodistribution studies and biokinetic models**

The radiopharmaceutical kinetic data often known as Biodistribution is a function of space and time. Imaging the whole body or specific region using planar scintillation Gamma camera can be used to obtain the necessary data for the study. The accuracy of this method is better when the radiopharmaceutical is localized in a specific area of the body or organ and this region do not overlap with other uptake area in the planar projection.

A region of interest (ROI) is determined in order to estimate the absolute amount of radioactivity in the organ. Modern Gamma cameras provide capability to delineate ROI of nay shape and to perform statistical analysis on the pixels inside the ROI to obtain the number of counts per pixel inside the ROI and the count rate.

Sequential imaging as a function of time postadministration of the radiopharmaceutical provides the time dependence of activity (time-activity curve) [5]. In this reference a full description of the imaging based method using planar gamma camera, SPECT and PET are described in great details.

Clinical and preclinical imaging protocols are published by different groups of scientists worldwide. Imaging is the key part of the bio distribution data acquisition experiment and constitutes the primary data for the model that will be proposed based on the results obtained during the experiment.

Imaging acquisition at different times after oral administration of a known activity of I-131 1100 MBq is the most common used with human subjects. Using a clinical gamma camera scanned data form the organs of interest, example the

stomach using an region of interest (ROI) is converted to counts per pixel per sec. Will be acquired and data will be extracted for further analysis.

### **2.5 Image- based, patient- specific dosimetry**

Such technique will allow the distribution of the agent in tumors and normal organs to be quantified [6]. Dosimetry as implemented in RPT may be thought of as the ability to perform the equivalent of a pharmacodynamic study in treated patients in real time [7]. When patient dosimetry is performed it allow prediction of treatment success based on reported results in the literature, it is then possible to calculate both normal tissue and tumor doses.

Organ uptake, Reminder of body uptake, Assumed waste. Derivation of the biological half –life values in different organs: they are theoretical estimations of the time-dependent quantity of I-131 in various compartments.

In Ref. [7] the authors have found that estimated biological half-life's obtained via the biokinetic model of radioiodine for thyroid cancer patients was found to strongly deviate from those recommended by Eckerman's suggestion for healthy male.

## **2.6 Organs residence times**

By definition lambda is given by:

$$\mathcal{A} = \operatorname{Ln}\left(\mathbf{2}\right) / \operatorname{T}\_{\mathrm{1}/\mathrm{2}}\tag{5}$$

Where T1/2 is the half-life. it could be the biological (Tb), physical (Tp) or effective (Teff) half-life depending on the application.

Knowing that:

$$\mathbf{1}/\mathbf{T}\_{\rm eff} = \mathbf{1}/\mathbf{T}\_{\rm b} + \mathbf{1}/\mathbf{T}\_{\rm p} \tag{6}$$

The biological half-life of radiopharmaceuticals is organ dependents. We will observe dissimilar values for different organs.

Time integrated activity coefficients (TIAC) are known also as organs residence times. They are proportional to the radiation absorbed dose by the organ or body tissue.

The radiopharmaceutical effective half-life is different for each organ in the body. And they are dependent of the biodistribution or the individual organ uptake fraction of the total injected activity. The same applies to the tumor tissues targeted by the radiopharmaceutical therapy; in our case here it is the remaining of the post ablation thyroid tissues treated using I-131.

## **3. Radioactive iodine treatment for thyroid cancer patients**

In many medical applications involving the administration of iodine-131 (131I) in the form of iodide (I− ), most of the dose is delivered to the thyroid gland [3].

To reliably estimate the thyroid absorbed dose, the following data are required: the thyroid gland size (i.e. mass), the fractional uptake of 131I by the thyroid, the spatial distribution of 131I within the thyroid, and the length of time 131I is retained

in the thyroid before it is released back to blood, distributed in other organs and tissues, and excreted from the body [4, 8–10].

Estimation of absorbed dose to non-thyroid tissues likewise requires knowledge of the time course of activity in each organ. Such data are rarely available, however, and therefore dose calculations are generally based on reference models. The MIRD and ICRP have published metabolic models and have calculated absorbed doses per unit intake for many nuclides and radioactive pharmaceuticals. Given the activity taken into the body, one can use such models and make reasonable calculations for average organ doses. When normal retention and excretion pathways are altered, the baseline models need to be modified, and the resulting organ dose estimates are subject to larger errors.

Even if the uptake of iodine is very specific to thyroid tissue, side effects from off-target accumulation are common. Frequent short-term side effects after 131I therapy of patients with differentiated thyroid cancer are gastrointestinal symptoms, pain or swelling in the neck or salivary glands, while frequent late effects are functional problems with salivary glands [11–15].

The hypothalamus-pituitary-thyroid (HPT) axis is an example of an endocrine feedback loop that is known to have a circadian rhythm [16].

Patients with chronic renal failure exhibited significant salivary gland, oral, nasal, and gastric activity 1 week after radioiodine administration [17].

#### **3.1 Sodium/iodide symporter (NIS)**

Active iodide (I<sup>−</sup> ) transport in both the thyroid and some extra-thyroidal tissues is mediated by the Na+ /I− symporter (NIS).

The cDNA encoding NIS was isolated in 1996, marking a major breakthrough in thyroid research that led to the subsequent characterization of NIS at the molecular level. Functional NIS is found in several extra-thyroidal tissues, such as the salivary glands, stomach, and lactating breast, as well as in primary and metastatic breast cancers. The latter findings have raised the possibility that NIS-mediated 131I− treatment may be effective in breast cancer. One of the most remarkable properties of NIS is that it transports different substrates with different stoichiometries**.** TSH is the primary regulator of NIS in the thyroid at both the transcriptional and posttranscriptional levels. At the molecular level, excess I− may have a deleterious effect on the thyroid by modifying NIS mRNA stability and increasing the production of reactive oxygen species. Thyroidal NIS function is also regulated by direct cross talk between NIS and a K+ channel [18].

#### **3.2 Future perspective and applications**

In the last two decades, NIS has become an important player in the use and optimization of gene therapy owing to its capacity as a reporter and as a therapeutic gene*.* NIS could be introduced into virtually any cell or tissue for imaging and/or therapeutic purposes. NIS is becoming the counterpart for human studies of green fluorescent protein and luciferase, which have been used extensively in cells and other organisms.

NIS expression and activity correlate with cell viability because only living cells can accumulate I−. NIS also offers higher detection sensitivity, because it actively transports its substrates rather than simply binding a substrate stoichiometrically. Moreover, NIS can translocate a variety of substrates, which can be detected using different systems, such as gamma cameras, PET, and SPECT (single-photon emission computed tomography) combined with computed tomography (CT) [18]*.*

*Recent Advances in Biodistribution, Preclinical and Clinical Applications of Radiolabelled Iodine DOI: http://dx.doi.org/10.5772/intechopen.99113*
