**1. Introduction**

24 12 Chapters on Nuclear Medicine

Zimmermann, M. B. and C. M. Crill "Iodine in enteral and parenteral nutrition." Best Pract

Internal radiation dosimetry has a fundamental and growing role in planning nuclear medicine therapies with radionuclides.

The principle of nuclear medicine therapy is to destroy pathologic tissues through the irradiation with the ionizing radiation emitted by properly chosen radionuclides, while preserving other organs and tissues from unnecessary exposure to the same radiation.

In order to realize this result, proper pharmaceuticals are chosen with a biodistribution targeted on target tissues, and labelled with a suitably chosen radionuclide. The choice of the best radionuclide is carried on with the aim of maximizing radiation energy deposition in the target tissue during the desired treatment time. Beta-emitters are the best choice in most cases, because beta radiation has a mean range in tissue from few millimetres to few centimetres. Also used are alpha- and Auger-emitters, for millimetre and sub-millimetre ranges.

The absorbed dose to the target tissues as well as to other organs and tissues depends from the biokinetics of the radiopharmaceutical and from the physical decay scheme of the radionuclide employed. While the physical properties of each nuclide are well known from experimental data, the biodistribution of the radiopharmaceutical within the patient's body depends on the dynamic biologic pathway that in turns is governed by the role of the molecule, by the characteristics of the patient, by the type and stage of the disease, and by the route of administration.

The distribution of radioactivity within the human body must be sampled several times post-administration, by means of planar or tomographic (SPECT or PET) imaging techniques. Tomographic techniques are rapidly substituting planar whole body imaging, since, thanks also to the accurate attenuation correction and image co-registration brought by a simultaneous CT scan, they reach a spatial resolution and an accuracy in activity quantification unprecedented.

After a general introduction on dosimetric quantities and their relationships, we focus on the dosimetric anthropomorphic models. We introduce also 3D techniques based on voxel dose factors, convolution of dose point-kernels and direct Monte Carlo computation, focusing on the contribution of Monte Carlo simulation to the development of new and more accurate dosimetric and microdosimetric models for internal dosimetry.

Internal Radiation Dosimetry: Models and Applications 27

by the target per unit cumulated activity in the source. The cumulated activity in *h* is defined as the total number of disintegrations in that organ, i.e. the integral of the activity *A*

> 0 *A = A t dt h h* ∞

> > *i*

fraction", i.e. the fraction of the energy emitted in the source volume *rh* which was absorbed

In general, if several organs accumulate the radiopharmaceutical, the overall dose to the target volume (organ or tissue) *k* is obtained by summing up all the contributions coming

( *k h ii k h h* ) ( ) /

Another usually employed quantity is the residence time, defined as the ratio between the

Even if the residence time has the physical dimensions of a time and it is often indicated with the same Greek letter, it must not be confused with the decay time of a radionuclide. In fact, while the decay time is the time necessary to reduce by 1/e = 0.37 the activity of an isolated sample, the residence time is the length of time an activity *A0* would have to reside

The estimation of the effect of the radiation absorbed dose in biological tissues can not neglect biological models accounting for the ability of tissues and cells to repair in some

The radiation damage can vary due to the different tissue properties (the "five Rs" of radiobiology: *repair*, *repopulation*, *reoxigenation, redistribution* and *intrinsic radiosensitivity*) in tumours and in healthy tissues, and due to the difference in possible irradiation regimes (type and energy of the radiation, dose rate, repetition or fractionation of treatments). In nuclear medicine therapies with radiopharmaceuticals, the radiation dose is often imparted by beta or Auger electrons, even if the role of alpha emitters as therapeutic agents

*h A <sup>τ</sup> <sup>=</sup> <sup>A</sup>*

0 *h*

∑

( )

←

*Sr r =*

*k h*

*i* is the average energy emitted per transition as *i*-th radiation,

*h i*

The definition of the *S* factor appearing in Equation 7 is:

in the target volume *rk*, and *mk* is the mass of the target.

cumulated activity in *h* and the administered activity *A*0:

**3. Radiobiological models of the radiation effects** 

degree the radiation-induced injury. (Cremonesi, 2011; Strigari, 2011)

in the volume to give that cumulated activity.

is the cumulated activity in the source organ and *S* is the average dose absorbed

( )

( ) *ii k h*

←

*Dr = A* ∑ ∑*Δ Φ rrm* <sup>←</sup> (10)

*k*

*m*

*Δ φ r r*

∫ , (8)

(9)

*<sup>i</sup>* is the "absorbed

φ

(11)

where *Ah*

where

Δ

from the various regions *h*:

is increasing again.

over the time:

We describe the application of such dosimetric approaches in the main nuclear medicine therapies such as the 131I therapy of thyroid diseases, the therapy of neuroendocrine tumours (NET) with somatostatin analogues labelled with beta- or Auger-emitters, and the palliation of painful bone metastases, focusing on dose-efficacy relationships and on the limiting of side effects to other potentially critical organs.
