## 1 Introduction  
Radioembolization (RE) is a clinical therapy for the treatment of primary or secondary hepatic tumors. The procedure is based on the administration of \({}^{90}\)Y-loaded microspheresthrough the hepatic artery, which is the major blood supplier for liver malignancies [1]. The vascular targeting makes RE extremely selective: high dose can be delivered to neoplastic areas while preserving nearby healthy tissue. Several approaches, empirical and dosimetric, have been proposed to establish the activity to be administered [2]. Due to their simplicity, empirical models have been applied for several years, but at present they are not considered as adequate for patient-specific treatments. In fact, the clinical benefit evidence of dosimetry-based approaches [3; 4; 5; 6; 7; 8; 9; 10] has led the scientific community to recognize the importance of accurate absorbed dose evaluation and to focus on the absorbed dose-biological effectiveness relationship. Different dosimetric approaches for RE have been applied throughout the years: the MIRD scheme at the organ level [11], the partition model [12], the local energy deposition method (LDM) [13; 14; 15], convolution calculations by voxel S-values [16; 17; 18; 19], and direct Monte Carlo (MC) simulations [20; 21]. Methods based on the MIRD approach at the organ level are mostly widespread due to their ease of use, but they present two main limitations: the regions of interest are considered to have homogeneous density, with uniform activity distributions. These unrealistic hypotheses can be overcome introducing the image-based 3D voxel dosimetry. Predictive patient-specific dosimetry is derived simulating the therapeutical procedure with the injection of \({}^{99\text{m}}\)Tc-macroaggregated albumin particles (\({}^{99\text{m}}\)Tc-MAA) to mimic the \({}^{90}\)Y-microspheres distribution inside the liver. The invasive procedure and the use of nonidentical particles may affect the perfect correspondence of pre vs. post-therapeutical activity distribution, depending on patient specific vascularity, type of disease, experience, and shrewdness. However, many authors [6; 9; 22; 23] have shown the good representativity of \({}^{99\text{m}}\)Tc-MAA activity distribution for treatment planning, which is verified afterwards by post \({}^{90}\)Y-PET or \({}^{90}\)Y-SPECT imaging. 3D approaches based on LDM or convolution of S-voxel values allow to account for the nonuniform activity distribution derived from the SPECT images, whereas they still assume a homogeneous density. MC simulation, unlike the previous methods, takes into account both tissue inhomogeneities and nonuniform activity distribution and is considered as the gold standard. In the last two decades, various Monte Carlo-based internal dosimetry programs or routines have been applied [24; 25; 26; 27; 28; 29]. Despite being considered the gold standard, they all differ in complexity and have not been integrated in the clinical practice yet, except in few centers for research purposes only. The main reason is that they usually require very high computer performances and calculation time, which are not compatible with the daily clinical routine. A second reason is often the lack of validation processes. This work deals with the physical validation of a novel treatment planning system (TPS) named MCID (MC Internal Dosimetry tool) [30; 31], performing Monte Carlo-based voxel dosimetry, applied to \({}^{90}\)Y-radioembolization of liver malignancies. Patient's CT and SPECT can be imported in MCID software, which creates different macros, i.e., sequences of scripted commands, for the simulation with GATE/Geant4[32; 33]. Each macro contains various settings about a specific aspect of the simulation (e.g., geometry of the system, source type, physics of the simulation etc. [33]). MCID prepares the macros using some settings defined by the user through the platform (e.g., numbers of primaries, type of radionuclide etc.) and some default settings, such as the definition of the physics of the simulation.