## 4 Discussion
Accurate personalized dosimetry based on the characteristics of the patient's specific lung tissue is crucial. Therefore, dosimetric tools such as direct \(MC\) simulations or dedicated VSV kernel approaches are of paramount importance. Lung dosimetry poses unique challenges due to the extreme density heterogeneities of lung tissue and the high penetration range of beta particles in this environment. Therefore, \(MC\) simulation should be regarded as the gold standard for lung-based dosimetry in radioembolization. The simulation times demonstrated in this work are already compatible with clinical practice. However, increasing the availability of new \(MC\) codes that enable fast simulations without compromising accuracy would further support the feasibility of adopting the \(MC\) approach as standard practice. The concept of \"fast\" should not be linked to a simplified physical model (e.g., local deposition of decay electrons), but rather to hardware-wise optimization strategies, such as parallel computing on GPU cards [14; 38; 39], or the implementation of variance reduction techniques (VRT). While VRT can offer a straightforward and efficient means to reduce computational time, the choice of technique is constrained by the simulation code being used. Moreover, these techniques require careful testing through trial simulations to ensure that the \(MC\) code operates correctly both with and without VRT and to optimize the VRT parameters accordingly. A recent study [40] also tested the feasibility of using fast semi-MC approaches based on quantitative PET images. These approaches simplify the transport simulation code by individually analyzing the interacting components in tissues and calculating the energy deposited in each voxel according to the patient's attenuation for photon interactions while assuming purely local absorption for electrons. Although faster and more realistic than a full local deposition calculation, the assumption of local electron absorption presents significant limitations, particularly for low-density, heterogeneous tissues like the lungs, as has been extensively discussed. More advanced approaches for performing rapid calculations of absorbed dose distribution as alternatives to _MC_ simulation include deep-learning-based methodologies, which are being explored for their reliability and speed. For example, convolutional neural networks can predict _AD_ distributions using morphological information from CT scans and activity biodistribution from PET or SPECT scans [41; 42]. Additionally, other approaches aim to predict the distribution of treatment microspheres based on pre-treatment \({}^{99\text{m}}\)Tc-MAA SPECT/CT scans, which can then be used to estimate the _AD_ distribution [36]. The discussed results suggest that the _MC_ approach is necessary in heterogeneous tissues of highly variable density, such as lungs. This need is already recognized in various therapeutic applications, such as radioiodine therapy for iodine-avid lung metastases from differentiated thyroid carcinoma [16] and radioimmunotherapy with \({}^{131}\)I for non-Hodgkin's lymphoma [17]. In these cases, _MC_ is of paramount importance for accurately assessing tumor absorbed dose and establishing correlations between tumor regression and the average absorbed dose to healthy tissues.