## 1 Introduction  
Hepatocellular Carcinoma (HCC) is one of the major causes of cancer-related deaths in the world [1]. Furthermore, liver cancer is the fourth most prevalent cause of cancer-related death, and the sixth most commonly diagnosed cancer [2]. Based on annual projections, the accumulated death caused by liver cancer will be more than one million by the year 2030, according to World Health Organization predictions [3]. However, in many countries, HCC morbidity and mortality are on the rise [4]. Currently, systemic drug treatments for HCC are limited, and side effects are prevalent [5]. There is a strong need to find other effective HCC treatment methods. The portal vein supplies most blood to normal liver tissue, whereas the hepatic artery supplies blood to most liver malignant tumours. As a result, locogenized therapies such as transarterial radioembolization (TARE) can be delivered preferentially in the arteries supporting tumours, resulting in particle deposition selectively in the tumour while avoiding detrimental side effects on healthy liver tissue [6]. Although radionuclides are increasingly used in nuclear medicine for both therapeutic and diagnostic purposes, precise patient-specific dosimetry is still not routinely conducted in clinical practice [7]. However, treatment planning for radioembolization of HCC might be challenging, because the amount of radiation that may be delivered to a tumour is restricted by the absorbed dose of organs at risk (OARs), which must be below the tolerable dose limit. Various MC codes can be used to simulate radiation transport over any media, providing precise dose estimation. The MC program based on the GEometry ANd Tracking 4 (Geant4) simulation toolkit has been developed for medical radiation dosimetry applications [8]. Geant4 Application for Tomographic Emission (GATE) is one MC simulation software for nuclear medical imaging based on the Geant4 code used for nuclear imaging devices [9]. In gamma camera imaging, the acquisition energy window is centred around the photopeak to detect most primary photons. A well-established therapy option for hepatic radioembolization is the radioisotope, \({}^{90}\)Y, which provides beta radiation for therapy with the possibility of post-treatment imaging by bremsstrahlung radiation but with significantly poor quality [10], as the spectrum of bremsstrahlung radiation is both complicated and continuous; one of the most challenging topics in nuclear medicine is selecting acquisition energy windows [11]. Macroaggregated albumin (MAA) labelled with technetium-99m (\({}^{99}\)Tc) is currently employed as a radioactive tracer for planning \({}^{90}\)Y microsphere radioembolization therapy. It is critical to include this post-treatment imaging radioactive tracer in order to estimate the in vivo effects of \({}^{90}\)Y radiation [12]. Numerous theranostic (therapy and diagnostic) radioisotopes such as Samarium-153 (\({}^{153}\)Sm), Holmium-166 (\({}^{166}\)Ho), Lutetium-177 (\({}^{177}\)Lu), and Rhenium-188 (\({}^{188}\)Re) have been proposed as \({}^{90}\)Y alternatives for radioembolization of HCC [13].\({}^{159}\)Gd has also been proposed for theranostic applications, however, has not been fully explored, especially in radioembolization of HCC. The \({}^{159}\)Gd radioisotope has a physical half-life of 18.48 h and emits \(\beta\) particles with energy of 970.5 keV, making it suitable for HCC therapeutic purposes. The \({}^{159}\)Gd gamma spectrum has two photopeaks (58 keV and 363.54 keV) [14], enabling the dose distribution of \({}^{159}\)Gd to be detected by a gamma camera and SPECT during TARE therapeutic administration for HCC. Furthermore, it is a highly paramagnetic element, useful in imaging via MRI.