**Dosimetry for Beta-Emitter Radionuclides by Means of Monte Carlo Simulations**

Pedro Pérez1, Francesca Botta2, Guido Pedroli2 and Mauro Valente3

<sup>1</sup>*Agencia Nacional de Promoción Científica y Tecnológica Universidad Nacional de Córdoba* <sup>2</sup>*Medical Physics Department, European Institute of Oncology* <sup>3</sup>*CONICET, Universidad Nacional de Córdoba* 1,3*Argentina* <sup>2</sup>*Italy*

#### **1. Introductory framework 1. Introduction**

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Synthesis, radiolabeling, and in vivo evaluation of an 18F-labeled isatin analog for imaging caspase-3 activation in apoptosis. *Bioorg Med Chem Lett* Vol.16(No. Nowadays, there are interests as well as active investigations devoted to the study and application of radiolabeled molecules able to selectively target and irradiate tumoral cells during nuclear medicine procedures. With this kind of pharmaceuticals, spatial activity distribution with extremely non-uniform characteristics may be assessed in patients. Actually, this feature constitutes precisely the main advantage in view of maximizing the discrimination between affected and healthy tissue. The mentioned situation constitutes the main motivation for the present work. In this sense, the chapter is focused on nuclear medicine dosimetry pointing out the main features about how to implement Monte Carlo (MC) approaches to this aim.

Nowadays, from a general point of view, therapies with radiopharmaceuticals using beta-emitter radionuclides are growing significantly and very fast. Beta-emitters can be emitters of *β*<sup>−</sup> or *β*<sup>+</sup> radiation. Commonly, *β*<sup>+</sup> emitters, like 18F are used for imaging techniques, whereas *β*− are mainly used with therapeutic purposes, to deliver high dose rate on tumors. Therefore, *β*− emitters are usually those of more interest for dosimetry.

During nuclear medicine procedures, radiopharmaceutical activity distribution may be determined by means of different modalities. Nowadays it is mainly assessed using imaging techniques but otherwise it is also possible to infer it [Stabin (2008)]. This information is then incorporated in the treatment planning system in order to obtain an estimation of the dose distribution. More specifically, patient-specific dose distribution owing to alpha, beta and/or gamma emitters can be calculated starting from activity distribution by means of either direct MC simulation or analytical methods.

On the other hand, patient-specific dosimetry requires anatomical information, which shall be further considered as input for establishing mass distribution during MC computations. Patient anatomical information can be suitably extracted from typical non-invasive imaging techniques, like computed tomography (CT) or magnetic resonance imaging (MRI).

Many studies have been performed by means of MC applications in Nuclear Medicine up today, both in the imaging field, and regarding dosimetry calculations [F. Botta & Valente (2011), Zubal & Harrel (1992), H. Yoriyaz & dos Santos (2001), M. Ljungberg & Strand (2002)].

**2. Monte Carlo methods and nuclear medicine**

be similarly implement on any general purposes MC main code.

**2.2 The PENELOPE Monte Carlo code**

Radiation transport, including absorption and scattering processes are determined by the Boltzmann transport equation. However, it is hard to apply and to analytically solve Boltzmann equation within non-homogeneous media or regions consisting of complex boundaries. Actually, it is well known that Boltzmann equation can be analytically solved only in few cases consisting on oversimplified situations, that would strongly differ from real clinical situations. Therefore, numerical methods have been proposed for solving Boltzmann equation in complex situations performing full radiation transport by means of stochastic methods. The MC techniques belong to the most important group within this category. Physically, the evolution of an electron-photon shower has an intrinsic random nature, so MC methods provide a convenient alternative to deal with transport problems [Salvat (2009)]. On the MC method for radiation transport, the "life" of each particle is seen as a random sequence of free paths that end with an interaction event where the particle suffers any kind of interaction. Generally, the "interaction event" refers to any change in the particle quantum state and it can arise from the change of its movement direction, the loss of energy or the production of a secondary particles. The interaction type depends on the kind of actual particle along with the medium where it is moving by random processes because of its nature. In order to point out main characteristics about how to handle with MC codes with the aim of performing nuclear medicine dosimetry, it has been selected to work with the PENELOPE main code. The fundamental motivations for using PENELOPE relays on its suitability of electron and photon transport along with the relevant characteristic of providing open source routines (written on fortran 77 language). The general considerations described below could

Dosimetry for Beta-Emitter Radionuclides by Means of Monte Carlo Simulations 267

The PENELOPE v.2008 is a MC algorithm and computer code for the simulation of coupled electron-photon transport. The simulation algorithm is based on scattering models that combines numerical databases with analytical cross section models for the different interaction mechanisms and it is applicable to energies (kinetic energies in the case of electrons and positrons) from a few hundred *eV* to approximated 1*GeV*. Photon transport is simulated by means of the conventional detailed method. The simulation of charged particles (electron and positron) transport is performed by means of a mixed procedure. Hard interactions, with scattering angle *θ* or energy loss *W* greater than preselected cutoff values *θ<sup>c</sup>* and *Wc* , are simulated in detail. Soft interactions correspond to scattering angle and energy loss less than the corresponded cutoffs *θc*, *Wc* and these interactions are considered by means of suitable mechanisms for simulation condensation, mainly based on multiple scattering theories, like Mollier theory. The user can select the cutoff parameters quite large looking for speeding up the calculation considerably, but it should be preliminary carefully studied the ranges for each parameter that may produce non-negligible alterations in the final scores. A characteristic feature of the here presented simulation code is that the most delicate parts of the simulation are handled internally; electrons, positrons and photons are simulated by calling the same subroutines. Thus PENELOPE makes the practical simulation of electrons and positrons as simple as that of photons (although simulating a charged particle may take a longer time). One of the main advantages of the latest version of PENELOPE (PENELOPE v. 2008 package) regards the improvements for inner shells ionizations by electron and positron impact, which are described by using a numerical database of total cross-sections for K, L and M

**2.1 Monte Carlo radiation transport simulation**

Numerous Monte Carlo codes have been benchmarked and used for different purposes in radiation transport including nuclear medicine imaging and dosimetry. Some examples are MCPT code of Williamson (1988), EGS4 code (Luxton and Jozsef, 1999), GEANT4 code (Agostinelli, 2003) and MCNP4 code (DeMarco et al 2002b, Bohm et al 2003). The more recently developed PENELOPE (PENetration and Energy Loss Of Positrons and Electrons; photon simulation was introduced later) Monte Carlo code 2001 (Salvat et al 2001) uses cross-sections from the up-to-date EPDL97 dataset, and thus takes advantage of the latest improvements in cross-section libraries [R.D. Stewart & Strom (2001), A. Sánchez-Crespo & Larsson (2004)].

Although several MC codes are available allowing to transport photons and electrons in user-defined geometries, it should be mentioned that there two codes particularly useful for voxel dosimetry applications, named EGS4 and MCNP [E.B. Bolch & Watson (1999)].

As a particular and non common approach this chapter will discuss how to implement MC simulation in nuclear medicine by means of the PENELOPE code.

The proposed method along with the developed computation system allow to introduce as input data different types of images -both metabolic and anatomical- commonly used for nuclear medicine diagnostic, like CT, MRI, SPECT, gamma camera and PET. This capability arises from the incorporation of dedicated routines for reading and interpreting the "Digital Imaging and Communication in Medicine" (DICOM) information code, therefore significantly simplifying input data handling processes aimed to specific-patient absorbed dose distribution calculation. In this sense, suitable combination of metabolic and anatomical imaging techniques provides relevant information helpful when attempting reliable and accurate specific-patient dosimetry. When considering all together the mentioned potential advantages of the proposed method along with the implementation of dedicated voxelization techniques, it would be expected that it may constitute an important tool for daily treatment planning by means of MC simulations for specific-patient dosimetry assessment.

The estimation of dose from a distributed source is an important aspect of the application of labeled monoclonal antibodies to targeted radiotherapy. A major contribution to the dose arises from beta particles. The source may be described mathematically by a function giving the activity concentration at each position in the source. The dose produced at a specific site may then be calculated as the linear superposition of contributions from each volume element in the distribution treated as a point source. The dose produced by a point source of isotropic unit activity is known as dose point kernel [Prestwich WV (1985)] (DPK). Due to its significant importance and largely proved benefits and convenience for dosimetric purposes, carefully characterization of DPK has always received significant interests and efforts, therefore extended discussion will be presented about DPK calculation by means of MC techniques.

In summary, it would be desirable to assess a suitable and reliable method helpful for patient-specific treatment planning calculating full stochastic radiation transport by means of MC methods. Therefore, once the calculation system is already developed, it should be carried out careful and rigorous verifications of certain parameters which can point out the reliability of the proposed method.

In this sense, considering that the main goal of this work consists on performing dosimetry for beta-minus radiation therapy and according to the significant importance of beta DPK in nuclear medicine dosimetry, this quantity may be taken as a suitable parameter to check the feasibility of the proposed MC code. With the aim of simplifying, it is established from here that DPK will be referred as beta-DPK unless it will be explicitly specified.
