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 (
90Y-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.
90Y is a nearly pure β
− emitter with an average energy of 0.927 MeV and a half-life of 2.67 days. Over 99% of the time,
90Y decays via β
− emission to the ground state of zirconium-90 (
90Zr). A small fraction of the radionuclide (about 0.01%) decays to the excited 0
+ state of
90Zr, which subsequently decays to the ground state via internal conversion, internal pair production, or two-photon de-excitation [
2,
3]. The maximum range of β
− 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
90Y-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
®, Sirtex Medical Limited Australia, Sydney, Australia) [
4] and glass MS (TheraSphere
®, Boston Scientific Corporation, Marlborough, MA, USA) [
5]. Radioembolization (RE) is preceded by diagnostic liver angiography, combined with an intra-arterial injection of
99mTc-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.
In tissues with densities similar to soft tissue and with unmarked tissue heterogeneities, approximate calculation methodologies have achieved excellent results, even when compared to Monte Carlo (MC) simulations on patients [
12,
13,
14,
15]. In contexts where tissue heterogeneities are significant, especially with low-density tissues, the physical conditions of radiation transport make the applicability of methods other than direct
MC simulations questionable, necessitating further evaluation. In clinical contexts beyond RE, such as the treatment of iodine-avid metastases from differentiated thyroid carcinoma or Hodgkin’s lymphoma in the lung with radioiodine [
16,
17], the fundamental role of accurate
MC simulation in internal dosimetry and its impact on treatment success have been evaluated. This suggests that a similar evaluation may be necessary for dosimetry in RE, particularly in cases with significant pulmonary shunts.
This study aims to evaluate the most commonly used dosimetric approaches in RE for estimating the absorbed dose to the lungs. This evaluation will be conducted using an anthropomorphic CT-derived voxelized phantom with various lung shunt fraction cases, and the results will be compared with MC simulations of direct radiation transport.
4. Discussion
Using a standard desktop computer with
primaries and no variance reduction techniques,
MC simulations on the Reference phantom took about 6 days each. The relative uncertainties affecting
AD values (reported in
Table 1) ranged from 1 to 3% for
LS ≥ 10%. Given these benefits, the
MC calculation method could be adapted for clinical applications with relatively minimal effort, especially when compared to the 2–3 days at most required for inverse planning in EBRT.
The validation of the presented results is supported by previously published work that internally validated the GATE code for soft tissue with controlled tissue heterogeneities. This prior research demonstrated good agreement between the
MC AD distributions and those obtained using the MIRD and VSV method with a soft-tissue kernel [
12]. Additionally, a second validation step was performed on homogeneous lung tissue with an
LS of 20%. This step demonstrated the internal consistency of the
MC simulation results in comparison to the VSV method using a lung tissue kernel (see
Section 3.2). A more extensive validation to assess the reliability of the
MC simulation for strongly heterogeneous lung tissue would involve comparing different
MC codes. However, such an evaluation was beyond the scope of the present work.
Comparisons between the VSV kernels in
Figure 2 highlight the specific properties of radiation transport in lung tissue compared to ST. In the lungs, the
AD increases considerably for any given source-target distance relative to ST, as does the radiation penetration in the medium. The most abrupt slope change in the lung VSV trend occurs at approximately 38 mm. This is well-correlated with the maximum penetration of the
90Y emitted beta radiation in the lung, whose maximum CSDA range is approximately 38.6 mm [
31] for the β
− end-point energy of
90Y; beyond that distance, the only contributions to the absorbed dose are due to bremsstrahlung radiation. Data scattering increases with the source-target distance. This is due to growing statistical uncertainty, as fewer and fewer interaction events are recorded when approaching and exceeding the maximum penetration range of beta radiation.
The use of the lung kernel on the entire patient’s activity map equates to the assumption that all the patient’s tissues have the same composition as the lung. For these reasons, cross-irradiation from the liver to the lungs due to the activity retained in the liver resulted in values three times higher than those obtained by
MC simulation. Therefore, when using VSV kernels, it is crucial to apply activity map cropping for approximated
AD calculations in scenarios where organs with highly differing densities are contiguous. This approach is particularly important for estimating the
AD to tissues with lower densities. Some new approaches [
32] have been proposed, introducing a convolution approach using mixed kernels for regions defined as soft tissue or lungs. These approaches report good agreement with reference
MC simulations on patient data.
Comparisons of the “classical” dosimetric approaches (MIRD, LED, and VSVs with soft-tissue kernel) with reference MC simulations show unacceptable underestimation of the lungs’ . The MIRD and LED methodologies inherently assume a direct proportionality between the and the LS. However, the contribution of cross-irradiation from the hepatic region, as indicated by the MC simulations, varies depending on the activity in the liver. This results in RD ranging from − to − for SVOX_ST and from to for LED. When using the MIRD approach with a lung mass of 1 kg instead of the personalized mass, the relative differences compared to using the personalized mass are about , worsening the RD with respect to the reference data. The largest discrepancies arise from using the SVOX methodology with the ST VSV kernel, resulting in about RD. This is mainly due to the higher density of the soft tissue used in the VSV calculations compared to the lung density, not counterbalanced by the increase in energy deposition, leading to lower AD values.
Conversely, lower differences relative to MC are observed with the SVOX methodology when local density corrections are applied or with the LED approach (which inherently accounts for local density variations). Notably, after applying local density corrections, the corrected SVOX data (named SVOX_L) become almost identical to the LED data. This is due to the limited penetration range of the 90Y emitted radiation in ST, compared to the voxel size or spatial resolution. In this work, activity maps were modeled without imaging data, so the nominal spatial resolution is determined by the voxel size (2.21 mm). However, the abrupt decrease in the S-value means that contributions to the target voxels from distant voxels are negligible, and the main dosimetric contributions are coming from the nearest neighbors. Therefore, for 90Y, using the ST VSV kernel for convolution calculations with local density corrections intrinsically approximates LED conditions.
Moreover, the initial evidence of the inaccuracy of post-convolution local density corrections is highlighted by the VSV comparison. When considerable radiation transport occurs, as expected for lung tissue, a reliable
AD correction would require correction factors that vary with the source-target distance for each contribution to the target voxel. These issues cannot be addressed with a single correction factor based on a density ratio, as clearly demonstrated by the VSV kernel comparison. This corrective method was initially proposed for correcting voxel
AD for slight density variations and small penetration ranges (as seen in ST). However, it has been well established that local density correction only accounts for the fluency correction of primary particles without affecting the contribution of secondary particles to the
[
15]. Therefore, this correction becomes increasingly imprecise with greater radiation penetration ranges and larger density variations in the medium.
The use of a lung VSV kernel yielded the results reported in
Figure 5. The
RD obtained using a VSV kernel specifically calculated for a lung medium density of
(ICRU lung tissue [
21,
22,
28]) varied between −
and −
compared to the reference
MC simulation. Although the relative difference shows a slight improvement over the data obtained with the ST kernel, the agreement with the
MC reference data remains poor. Despite the VSVs being calculated using a medium density considerably closer to the Reference phantom’s mean lung density (
), the significant discrepancy cannot be easily attributed to the density differences between the Reference phantom and the ICRU mean lung density.
A global density correction based on the average density of resulted in a still high RD (from − to −). Even with local density corrections, the RD remained unacceptable (varying from − to −).
Since the computed using the lung VSV kernel was in good agreement with the reference data for a homogeneous lung medium and provided activity map cropping, the observed differences should be correlated with the significant tissue heterogeneities of the lungs. If this is the case, an MC simulation of the reference phantom with uniform density lungs (corresponding to the mean density value of the phantom’s lungs) should result in a smaller compared to an MC simulation on the same phantom with heterogeneous lung density and the same mean density. Indeed, the RD between the two simulations under the stated density conditions resulted in approximately −, clearly indicating that:
Radiation transport is strongly influenced by the tissue heterogeneities of the lungs, which substantially affect the absorbed dose.
A lung tissue with a uniform density corresponding to the average density of the case under study is not an accurate descriptor of the real tissue.
Lung density variations in this phantom range from 0 to 1.06 g/cm³, with a positively skewed distribution. A heterogeneous density pattern is generally observed in bone tissue. However, in that case, the density distribution is shifted towards a higher value, resulting in local energy deposition. This contrasts with lung tissue, for which the MC simulations of radiation transport are essential to achieve an accurate description of energy deposition.
The choice of this reference phantom is not representative of the entire population but is intended to address the physical nature of the problem under discussion. Density distribution varies significantly with age, individual conditions, and comorbidities [
28]. Therefore, it is crucial to evaluate on a case-by-case basis the differences that arise from using different computational approaches in a realistic case. To maintain accuracy, it is essential to use a
MC radiation transport approach tailored to the specific density distribution being treated.
Two studies [
13,
14] have investigated the role of lung density in the dosimetric evaluation of
LS in radioembolization using different dosimetric approaches. Capotosti et al. [
14] conducted a two-step study comparing the performance of a fast-MC Graphic Processing Unit (GPU)-driven code versus the VSV method using a soft-tissue kernel. This comparison was performed on a reference lung–liver phantom to simulate a 10%
LS environment and was also applied to data from 24 patients. In this study, the
MC showed an approximate RD of −
for the VSV
compared to the
MC on the reference phantom. Additionally, the VSV method resulted in a global overestimation of the
of lungs in the patients’ dataset, which is consistent with the findings of our study. Mikell et al. [
13] conducted a general analysis of lung
for the homolateral lung using patient data. They compared
MC simulations performed with the Electron Gamma Shower of the National Research Council of Canada (EGSnrc) against classical approaches, including LED and the VSV approach with a soft-tissue kernel. Their analysis included comparisons with and without local density corrections. In this study, the VSV approach showed a −
RD with respect to MC, while the VSV approach corrected for local density and LED reported a 20% and 17%
RD, respectively, with a global underestimation of the
MC for the first method and a global overestimation of the
for the last two. This latter result contrasts with our analysis, which showed a global overestimation of the
for the same dosimetric approaches across all
LS conditions in our reference phantom. This difference may be attributed to variations in patient geometry modeling in the EGSnrc simulation, such as differences in voxel density definitions and the poor image resolution of the post-therapy activity images obtained by
90Y bremsstrahlung SPECT/CT.
Unlike previously published papers, this work included all commonly used dosimetric approaches for lung dosimetry in radioembolization and compared them with an MC simulation using a reference phantom representing the same complexity as real patients but with known lung composition and density. Additionally, our study introduces an optimized alternative method for comparison: VSV with lung tissue kernel.
Regarding the potential clinical impact of this work,
Table 6 illustrates that the primary factor determining
AD in the lungs is the activity present in the lungs themselves. For the case considered, to avoid exceeding the dose limit of 30 Gy, the lung activity should be limited to approximately 260 MBq. This translates to the maximum safely administrable activity, based on the variable
LS considered, ranging from 2.54 to 0.65 GBq. These results highlight the unreliability of current safety limits for treatment, whether they are based on calculating the lung dose using the single-compartment MIRD model [
2,
3], the 20%
LS limit [
2,
4], or the MLA of approximately 600 MBq [
3,
5]. It is also worth noting that in cases of lobar or highly selective treatments, the results presented offer considerable flexibility, potentially making it feasible to treat patients with high levels of
LS. Nonetheless, we must acknowledge that this study does not tackle the formidable challenge of accurately predicting
LS and the biodistribution of microspheres through pre-treatment imaging for
90Y RE.
Lung dosimetry is a major issue in RE and remains a topic of ongoing debate. Increasingly, studies [
33] are highlighting the need for more patient-specific approaches, emphasizing how the highly heterogeneous nature of lung can negatively impact approximated dosimetric calculation and thereby underscore the necessity for a personalized calculation approach. For instance, a recent review [
34], which provides a general discussion of the state of the art regarding lung dosimetric limits in radioembolization, found that using a standard lung mass of 1 kg leads to a general overestimation of lung mass by an average of 20%. The use of
MC simulations for radiation transport allows to account for the patient-specific tissue description. This was demonstrated by Auditore et al. [
35] in a detailed dosimetric study on a patient who exhibited a post-treatment unexpected accumulation of microspheres in a specific area of the lungs, analyzing the correlation between the inflammatory state and the absorbed dose in that particular region.
Currently, no accurate alternatives to direct
MC simulations exist for lung dosimetry of patients undergoing radioembolization, and no guidelines have been established to assess the role and need for more accurate approaches. The latest European guidelines on radioembolization [
3] clearly state that lung absorbed dose assessments must be performed using the mono-compartmental MIRD model. This model relies on available patient information, such as average lung density or the amount of activity in the lungs measured by planar or tomoscintigraphic scans. It is also noteworthy that there are no precise methodologies based on patient imaging in the clinical context to predict microsphere biodistribution in the lungs and
LS for
90Y RE, due to intrinsic differences between radiotracers (e.g.,
99mTc-MAA vs.
90Y microspheres). However, new deep-learning-based methodologies are currently under development to predict post-treatment microsphere distribution in the lungs [
36].
The role of radioembolization in the clinical landscape is evolving beyond its initial palliative intent to become a potential curative approach [
9,
10,
37]. This shift is exemplified by radiation segmentectomy for early-stage HCC, which has proven to be a viable alternative in specific cases where surgery or simple ablation is contraindicated or impossible. For intermediate and advanced HCC, radioembolization has demonstrated effectiveness in downstaging to resection (e.g., for central liver lesions) or transplantation. Various studies have reported better outcomes with radioembolization compared to alternative approaches, such as chemoembolization. Even patients with severe conditions such as portal vein thrombosis can undergo radioembolization as a bridge to transplantation, provided careful case selection is performed. This broad application landscape can be further expanded through personalized precision dosimetry, which enables the use of specific activity prescriptions and the delivery of high doses to the lesions. However, this introduces potential risks in managing patients with
LS, which must be carefully addressed. 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
99mTc-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
131I 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.