## 1 Introduction
Even if \({}^{90}\)Y possesses a small channel of internal pair creation that allows positron emission tomography (PET) imaging [10], the use of \({}^{90}\)Y microspheres as a pre-treatment radiotracer, given the low branching ratio (about \(3\times 10^{-5}\) pairs/decay [10,11]), would require high activities to perform imaging acquisition with sufficient resolution to be used for dosimetric evaluation. Nevertheless, the use of \({}^{99m}\)Tc-MAA to simulate the biodistribution of therapeutic microspheres is intrinsically biased, being two different physical agents and not accurately reproducing the actual biodistribution of the treatment microspheres [12, 13, 14]. In recent years, a new therapeutic device based on poly-L-lactic acid (PLLA) micro spheres labeled with \({}^{166}\)Ho (Ho-MS) has been approved for clinical use (Quiremspheres(r), Terumo Therapeutic Interventional Oncology, Deventer, Netherlands) [15]. \({}^{166}\)Ho is a \(\beta^{-}\) emitter with a half-life of approximately 26.8 h, exhibiting multiple \(\beta\)-decay pathways. The two most probable decay channels have average energies of 0.651 MeV and 0.693 MeV, with probabilities of 49.9% and 48.8%, respectively, decaying either to the first excited state of \({}^{166}\)Er (followed by a characteristic gamma emission of approximately 81 keV) or directly to its ground state [16]. The primary advantage of Ho-MS lies in its multiple imaging-friendly properties: the intrinsic gamma emission allows for SPECT imaging, enabling pre-treatment biodistribution evaluation with a small amount of Ho-MS as a scout dose, which increases the predictive accuracy of pre-treatment dosimetry and may improve treatment precision and efficacy [17]. Additionally, the paramagnetic nature of Ho-MS enables magnetic resonance imaging (MRI), significantly enhancing the spatial resolution of the biodistribution, and potentially improving the dosimetric assessments [18]. Another promising approach is dual-isotope imaging, where both Ho-MS and \({}^{99\text{m}}\)Tc-stannous phytate are administered simultaneously, allowing for the visualization of both healthy liver tissue and lesions. However, this approach presents technological and timing challenges [19]. According to current European guidelines [8], lung dosimetry in TARE using Ho-MS is addressed through a mono-compartmental model based on the well-established MIRD schema, which evaluates the LS fraction using planar imaging of \({}^{99\text{m}}\)Tc-MAA and calculates the absorbed dose assuming a standard lung mass of 1 kg. The upper limit is set at a 30 Gy mean absorbed dose (\(\overline{AD}\)) in the lungs, associated with a 20% LS, based on this assumed lung mass. In the case of TARE with Ho-MS, investigating the accuracy of traditional, simplified approaches for lung dosimetry is also advisable, especially due to differences in the decay spectrum compared to \({}^{90}\)Y, as \({}^{166}\)Ho exhibits multiple low-energy \(\beta^{-}\) decay channels, along with more numerous and intense electron-capture (EC) decay emissions. This study aims to compare the most common dosimetric approaches for calculating the \(\overline{AD}\) in the lungs in \({}^{166}\)Ho TARE, using MC simulation as a reference. The MC simulation models direct radiation transport on a CT-based anthropomorphic voxelized phantom, with realistic lung density distributions across various LS scenarios. This work serves as Part B of a previously published paper focused on \({}^{90}\)Y TARE [9]. In the final section, comparisons are reported between the MC results for both radionuclides, along with an analysis of the equivalent dose at 2 Gy per fraction (\(EQD_{2}\)) [20] distributions for each.