## 1 Introduction  
Liver cancer is the sixth most commonly diagnosed cancer and the third leading cause of cancer-related death worldwide [1]. Trans-arterial radioembolization (TARE) via intrahepatic administration of Yttrium-90 (\({}^{90}\)Y-loaded microspheres (MS)) is a minimally invasive therapy that has been used for many years for the treatment of hepatocellular carcinoma (HCC) and liver metastases from other malignancies. \({}^{90}\)Y is a nearly pure \(\beta^{-}\) emitter with an average energy of 0.927 MeV and a half-life of 2.67 days. Over 99% of the time, \({}^{90}\)Y decays via \(\beta^{-}\) emission to the ground state of zirconium-90 (\({}^{90}\)Zr). A small fraction of the radionuclide (about 0.01%) decays to the excited 0\({}^{+}\) state of \({}^{90}\)Zr, which subsequently decays to the ground state via internal conversion, internal pair production, or two-photon de-excitation [2, 3]. The maximum range of \(\beta^{-}\) radiation in soft tissue, based on the continuous slowing down approximation (CSDA), is about 11 mm [2, 3]. This radiation causes damage to tumor cells via cytotoxic effects induced by radiolytically generated reactive species. The administration of \({}^{90}\)Y-labeled microspheres is preceded by appropriate embolization of the vascular bed performed by the interventional radiologist to optimize the targeting and deposition of radioactivity in the tumor while sparing as much hepatic parenchyma as possible and minimizing pulmonary and gastrointestinal shunting. The most common devices are resin MS (SIR-Spheres(r), Sirtex Medical Limited Australia, Sydney, Australia) [4] and glass MS (TheraSphere(r), Boston Scientific Corporation, Marlborough, MA, USA) [5]. Radioembolization (RE) is preceded by diagnostic liver angiography, combined with an intra-arterial injection of 99 mTc-macroaggregated albumin (MAA) at the treatment site, followed by scintigraphic imaging. This process is used to perform arterial mapping, identify patients with contraindications to treatment, and target the tumors. The prescribed absorbed dose to tumor lesions varies depending on the patient-specific scenario and the microsphere device. It is typically around 100-120 Gy for glass microspheres and over 180 Gy for resin microspheres [4; 5; 6; 7; 8]. The main contraindications are the presence of gastrointestinal shunting and lung shunting, which result in an absorbed dose to the lungs of more than 30 Gy [2; 3]. The use of TARE as a neoadjuvant approach to hepatic lobectomy [9] or as a bridge to transplantation [10] is gaining interest in the clinical landscape of liver diseases. Personalized dosimetry is essential for effective patient management and achieving clinical goals. In this context, the ability to increase the administered activity is both highly desirable and attainable, provided that appropriate treatment planning, especially for estimating the absorbed dose to the lungs in the presence of a lung shunt, has been carried out. The state of the art in lung dosimetry is based on the recommendations of the American Association of Physicists in Medicine (AAPM) [2], the European Association of Nuclear Medicine (EANM) [3], and the manufacturers [4; 5]. In some cases, estimating the absorbed dose is impossible due to a lack of morphologic data, such as abdominal computed tomography (CT) scans that are truncated at the lungs or when there is no available morphological examination of the lung tissue. Under such conditions, the only option to assess the tolerability of the treatment is to compute the lung shunt fraction. This fraction must conventionally be lower than 20%, assuming a lung mass of 1 kg and an upper absorbed dose limit of 30 Gy [2; 3]. The absence of proper methodology for lung dosimetry could lead to cases of radiation-induced pneumonitis, even in unexpected lung shunting scenarios or when blindly following the manufacturer's instructions [11]. This highlights the need to establish a lung-specific dosimetry workflow.