## 1 Introduction  
The use of Transarterial Radioembolization (TARE) for cancerous liver lesions is increasingly taking on the role of a curative treatment, moving beyond its traditional use as a palliative option, which has been the norm until recent times. For instance, TARE is gaining interest in the clinical landscape of liver diseases as a neoadjuvant approach to hepatic lobectomy [1] or as a bridge to transplantation [2]. In these new clinical scenarios, personalized dosimetry becomes essential to assess the tolerability of the treatment, especially in the presence of a lung shunt (LS), as the absorbed dose (AD) is the only reliable risk indicator for the preliminary assessment of the potential occurrence of tissue reactions. The complications occurring after radioembolization treatment are classified into two main categories [3,4]: post-radioembolization syndrome (PRS) and complications related to non-target deposition of the microspheres and cross-irradiation to the structures surrounding the target regions. Clinical evidence of PRS includes symptoms like nausea, fatigue, vomiting, anorexia, fever and abdominal pain, caused by internal radiation and microembolization [3]. The off-target distribution of microspheres to non-tumor tissues may result in complications like radioembolization-induced liver disease (REILD), pulmonary complications (i.e., radiation pneumonitis), and gastrointestinal (GI) tract complications. REILD [4, 5, 6] arises following normal hepatic parenchyma radiation exposure as a consequence of both the deposition of microspheres in normal parenchyma and the irradiation of surrounding structures. REILD leads to aberrations and hepatic dysfunction with the appearance of jaundice and ascites. Lung complications arise from the non-target deposition of microspheres in patients with high LS fractions. Radiation pneumonitis symptoms are dry cough, fever, and ventilatory dysfunction manifesting within 6 months after treatment, with an incidence rate of <1% [3,5,6]. The distribution of microspheres in the GI tract can occur in the case of variant anatomy and circulation, changes in flow dynamics during microsphere infusion, and microsphere reflux. Even low doses of radiation can compromise gastric acid production with consequent mucosal thinning, edema, and chronic inflammation, leading to gastroenteritis or ulceration [3,5,6]. Other side effects for the off-target deposition of microspheres are pancreatitis and cholecystitis, which could also arise from unexpected cutaneous and gallbladder embolization. In this scenario, internal dosimetry evaluation plays a crucial role in preventing complications and effectively managing the clinical outcomes of radioembolization treatment. The traditional eligibility criteria based on generic thresholds of pulmonary activity [7,8] are highly conservative, not patient-specific, and are no longer adequate, as they do not provide an appropriate level of personalization, which may lead to the exclusion of patients more easily, thereby limiting the therapeutic potential of TARE. Recently, a dosimetric study on \({}^{90}\)Y-labeled microspheres was conducted to evaluate the accuracy of conventional and simplified methods for personalized lung dosimetry, in comparison with the Monte Carlo (MC) direct radiation transport simulation technique [9]. The results demonstrated the inadequacy of simplified methods due to the high heterogeneity of lung tissue (LT) and the range of values skewed toward low tissue densities, highlighting the need for MC simulation of radiation transport. In TARE with \({}^{90}\)Y-labeled microspheres, pre-treatment dosimetry is performed using a gamma-emitting radiotracer, typically \({}^{99m}\)Tc-labeled macroaggregated albumin (\({}^{99m}\)Tc-MAA), and evaluated via single-photon emission computed tomography (SPECT) imaging [7,8]. This choice historically stems from the lack of suitable imaging channels for \({}^{90}\)Y, necessitating the use of a different radiotracer.