Dosimetric impact of physics libraries for electronic brachytherapy Monte Carlo studies

Abstract

Background

Low‐energy x‐ray beams used in electronic brachytherapy (eBT) present significant dosimetric challenges due to their high depth‐dose gradients, the dependence of detector response on materials, and the lack of standardized dose‐to‐water references. These challenges have driven the need for Monte Carlo (MC) simulations to ensure accurate dosimetry. However, discrepancies in the physics models used by different MC systems have raised concerns about their dosimetric consistency, particularly in modeling bremsstrahlung interactions.

Purpose

To assess the dosimetric impact of using different physics approaches in three state‐of‐the‐art MC systems for eBT, focusing on the disagreements observed when different MC methods are used to evaluate bremsstrahlung interactions.

Methods

The MC studies of the Axxent S700, the Esteya, and the INTRABEAM eBT systems were performed using two EGSnrc applications (egs_brachy and egs_kerma), TOPAS, and PENELOPE‐2018 (PEN18). The fluence spectra and depth doses were compared for simplified x‐ray tube models, which maintain the target mode (transmission or reflection), the target material and thickness, and the surface applicators’ source‐to‐surface distance. An extra simulation was made to evaluate the utility of the simplified models as proxies in predicting the most important characteristics of an accurate applicator's simulation (detailed model of INTRABEAM's 30 mm surface applicator). The EGSnrc applications and PEN18 utilized their default bremsstrahlung angular emission approaches. TOPAS used two physics lists: g4em‐livermore (TOPAS_liv) and g4em‐penelope (TOPAS_pen).

Results

The most significant differences between MC codes were observed for the transmission target mode. The bremsstrahlung component of the fluence spectra differed by about 15% on average, comparing PEN18, EGSnrc applications, and TOPAS_liv, with PEN18's fluences consistently lower. EGSnrc and PEN18 agreed within 3% for their characteristic spectrum components. However, PEN18's characteristic lines overreached TOPAS_liv’s by 40%. Those spectral characteristics generated depth dose differences, where PEN18, on average, scored 9% lower than EGSnrc and TOPAS_liv. Considering TOPAS_pen in the transmission mode, PEN18's fluence spectrum presented a lower bremsstrahlung (5%) but a higher characteristic component (10%); these spectral differences compensated, generating depth dose differences within 1% average. In the reflection target mode, EGSnrc and PEN18 agreed within 4% for the bremsstrahlung and characteristic components of the fluence spectra. With TOPAS_pen in the reflection mode, PEN18 presents 12% lower fluences in the bremsstrahlung component but 6% higher characteristic lines. This spectral behavior diminished the depth dose differences up to 3%.

Conclusion

This work found considerable disagreements between three state‐of‐the‐art MC systems commonly used in medical applications when simulating bremsstrahlung in eBT. The differences arose when the bremsstrahlung angular distribution and the atomic relaxation processes in the target became relevant. More theoretical and experimental studies are necessary to evaluate the impact of these differences on related calculations.

1. INTRODUCTION

Low‐energy x‐ray beams (< 70 kVp) gained the attention of the scientific and clinical community due to their use in electronic high‐dose‐rate brachytherapy (eBT), as reflected in several reports. ¹ , ² , ³ , ⁴ , ⁵ However, their high depth‐dose gradient (between 7% and 40% per mm), ⁶ , ⁷ the marked detector response dependence on the construction materials, ⁸ the hardening effect with depth, ⁵ and the lack of dose‐to‐water standards ⁹ impose significant challenges on low‐energy bremsstrahlung beams dosimetry. In addition, there is a recognized need to develop model‐based dose calculation algorithms (MBDCA), ¹⁰ which has encouraged the AAPM/GEC‐ESTRO/ABS/ABG Working Group on Model‐Based Dose Calculation Algorithms (WGMBDCA) in Brachytherapy to create clinical test cases to help in the commissioning of treatment planning systems (TPS). ¹¹ Finally, besides MBDCAs, the determination of TG‐43 parameters for eBT applicators is also underway. ¹² , ¹³

The challenges inherent to eBT beams generate an extensive reliance on Monte Carlo (MC) simulations to derive relevant dosimetric quantities. However, MC methods have documented limitations for this range of energies. Increased Type B uncertainties associated with different implementations of photoelectric modeling have been reported in the literature, ¹⁴ , ¹⁵ and such differences increase when incorporating bremsstrahlung modeling. ¹⁶ The latter is attributed to different approaches in calculating the angular distribution of the emitted photons, where the agreement among bremsstrahlung models depends on the photon's emission angle. ¹⁶

AAPM/GEC‐ESTRO Task Group 253 (TG‐253) on surface brachytherapy has included three eBT systems in its report, whose x‐ray tubes (XRT) present two configurations depending on the photon emission angle: transmission (clinical beam in the direction of the electrons) and reflection (clinical beam opposite to the electrons’ direction) modes. ¹ This work aims to evaluate the effect of different physics approaches on MC dosimetric studies of eBT devices, using three state‐of‐the‐art MC systems commonly used in medical applications.

2. MATERIAL AND METHOD

2.1. eBT systems

This work considered simplified models of the Axxent S700 (Elekta Brachytherapy, Veenendaal, the Netherlands), the Esteya eBT (Elekta Brachytherapy, Veenendaal, the Netherlands), and the INTRABEAM (Carl Zeiss Meditec, Inc., Oberkochen, Germany) XRTs. The simplification included the target thickness and composition, the target mode (transmission or reflection), electron energy, and the source‐to‐surface distance (SSD), neglecting everything else (see Figures S1, S2, and S3 in Supplemental Material and Figure 1). This work will adopt the following abbreviation regarding simplified models: Tr‐Au (transmission mode with a thin gold target, i.e., INTRABEAM), Tr‐W (transmission mode with a thin tungsten target, i.e., Axxent), and Rf‐W (reflection mode with a thick tungsten target, i.e., Esteya) (Table 1).

FIGURE 1.

(a) Detailed model of the INTRABEAM's 30 mm surface applicator. (b) Simplified model of the INTRABEAM's x‐ray tube (Tr‐Au).

TABLE 1.

Details of the simplified x‐ray tube (XRT) models.

eBT system	XRT mode	Electron energy (keV)	Target material	Target thickness (mm)	SSD (mm)
Axxent (Tr‐W)	Transmission	50	Tungsten	0.001	20
Esteya (Rf‐W)	Reflection	69.5	Tungsten	2	60
INTRABEAM (Tr‐Au)	Transmission	50	Gold	0.001	18

The targets are slabs of material (2 mm × 2 mm cross‐section) with thicknesses listed.

A detailed model of the INTRABEAM's 30 mm diameter surface applicator was simulated for comparisons with its simplified model. This version (see Figure 1) comprises a realistic XRT, a flattening filter, and the electron deflection pattern. The details of this geometry are proprietary information, although the XRT's specifications are similar (not identical) to those reported elsewhere. ¹⁷ , ¹⁸

2.2. MC simulations

For the simplified simulations, absorbed depth dose (collisional kerma approximation, see Table 2 for specifics) and fluence spectra were scored in a (20 cm) ³ water phantom. The depth dose was tallied in a 1D array of (0.5 mm) ³ voxels aligned with the beam axis up to 5 cm depth. In the detailed model case, the absorbed dose was scored in a 3D array of (0.5 mm) ³ voxels running from −3 cm to 3 cm in x and y directions and 5 cm in z (depth; total ∼ 1.5 × 10⁶ voxels). The fluence spectra were tallied in the first voxel of the array (phantom surface) in intervals of 0.1 keV for the simplified simulations. Photons and electrons were tracked down to 1 keV. Photon transport was enabled in all materials, while electrons were transported only in the target or in a volume enclosing the target, as in the case of EGSnrc for the simplified models (see Table 2). All materials followed the NIST specifications ¹⁹ except for water, which used the latest ICRU‐90 updates. ¹⁴

TABLE 2.

Summary of the main characteristics of the Monte Carlo simulations used in this work.

Item	PENELOPE	EGSnrc	TOPAS
Code	PENELOPE‐2018, 20 penEasy v. 2019‐09‐21. 21	EGSnrc 2021 22 applications: egs_brachy 23 and egs_kerma. 24	TOPAS 3.8 based on Geant4 10.07.p03. 26 , 46
Validation	Previously validated. 47 , 48	egs_brachy: previously validated. 23 , 49 egs_kerma: used as reference for Penelope and egs_brachy comparisons. 15	Previously validated. 27 , 50
Timing	On average, 3.4 × 1010 histories 280 h (CPU time) per simulation, averaging 289 hist/s per process (120 parallel processes).	egs_brachy: 1 × 1010 histories are considered, taking an average of 320 h (CPU) time, averaging 174 hist/s per process (using 50 parallel processes). egs_kerma: Sub 0.1 % statistics with 4 × 1010 primary histories at 9500 hist/s for about 1200 h per simulation on 1600 cores.	For each model, 2 × 1011 initial histories. About 20 h per simulation in nodes of 40 or 64 cores running in multithread mode.
Source description	X‐ray sources. Transmission target mode: electron beam of 50 keV, impinging in a thin target (1 µm thickness approx.) of gold or tungsten. Reflection target mode: 69.5 keV electrons, impinging in a thick tungsten target (2 mm).
Cross–sections	Photoelectric is calculated with PHOTACS. 51 Rayleigh and Compton scatterings use non‐relativistic perturbation theory 52 , 53 , 54 , 55 and a relativistic impulse approximation, 56 respectively. Electron impact ionization according to Bote and Salvat. 38 The atomic relaxation transition probabilities are calculated according to EADL. 40 The x‐ray energies from K to L vacancies are obtained from Deslattes et al., 41 and the energies of those coming from M‐shells are according to the Bearden dataset. 42 The bremsstrahlung scaled function is interpolated from tables using Seltzer and Berger's data. 28 The angular emission distribution is obtained from an analytic fit 57 of the “shape function” calculated by Kissel et al. 31	XCOM photon cross–section database and MCDF‐XCOM photon cross‐section database 15 , 51 , 58 ; Rayleigh scattering, bound Compton scattering, triplet production, and electron impact ionization 22 ; Atomic relaxation using the EADL transition probabilities 40 ; Bremsstrahlung and Pair Production cross section databases 22 ; Pair production angular sampling. 59	Livermore includes photo‐electric effect, Compton scattering, Rayleigh scattering, gamma conversion, bremsstrahlung, ionization, and atomic de‐excitation module for fluorescence and Auger electron emission using the EPDL97, EPICS2014, EEDL, and EADL data libraries. 40 , 55 , 60 Binding energies from Scofield. 61 Electromagnetic physics of PENELOPE‐2008. 62 Photoelectric is calculated with EPDL. 55 Rayleigh and Compton scattering, atomic relaxation and bremsstrahlung are the same as described in PENELOPE‐2018.
Transport parameters	Analog step‐by‐step simulation. Photon cutoff = 1 keV Electron cutoff = 1 keV in the target, not transported elsewhere.	egs_brachy: Photon cutoff = 1 keV Electron cutoff: 1 keV cutoff in a volume of 1 cm3 centered at the target; no electron transport elsewhere. egs_kerma: 1 keV cutoff for photons and electrons. Electron impact ionization = EII‐penelope or EII‐IK Brems cross sections = NRC. Bound Compton scattering = On Rayleigh scattering = On Bremsstrahlung angular sampling = KM	Lowest electron energy = 1 keV EM range min = 1 keV EM range max = 500 MeV Production cut lower edge = 1 keV Production cut high edge = 30 MeV Cut for electron = 10 cm (water and air) and 10 nm (tungsten foil) Cut for gamma = 2.302 mm (air) and 10 nm (water and tungsten foil) Bremsstrahlung. photoelectric fluorescence, auger, auger cascade, deexcitation ignore cut = True
Variance reduction	Interaction forcing for electrons: bremsstrahlung and inner‐shell ionization at the target. Interaction forcing for photons: Compton and photoelectric in the water phantom. 20	egs_brachy: track‐length estimation is used for dose (kerma approximation), fluence, and energy spectrum calculations. 23 , 63 Bremsstrahlung cross‐section enhancement with uniform splitting enhancement and splitting factor. 23 , 64 egs_kerma: exponential track‐length estimator and uniform bremsstrahlung splitting. 24	Track‐length estimator for dose scoring (kerma approximation). Secondary biasing and directional splitting
Scored quantities	Absorbed dose (collision kerma approximation) and fluence spectra.
Statistical uncertainties	History‐by‐history. Averaged differences with Type A uncertainties 1% (k = 2)
Post‐processing	None

2.3. MC systems

Three state‐of‐the‐art MC systems were used in this study: PENELOPE 2018 (PEN18) ²⁰ along with penEasy, ²¹ a FORTRAN main steering program that allows the use of the PEN18 capabilities; EGSnrc ²² through two applications: egs_brachy ²³ and egs_kerma ²⁴ (two different teams worked with egs_brachy, while a separate team worked with egs_kerma); Geant4, ²⁵ steered by TOPAS, ²⁶ a toolkit that wraps and extends the general‐purpose MC code Geant4. ²⁷

2.4. Photoelectric library

A previous work described the effect of using different photoelectric cross‐sections in low‐energy photon beams (DHFS vs. MCDF). ¹⁵ DHFS stands for the Dirac–Hartree–Fock–Slater self‐consistent potential approach. This approximation considers a single electron in a central potential, interacting with a photon without considering the electrons' influence in other orbitals. MCDF corresponds to the multi‐configuration Dirac‐Fock method, a more elaborate atomic model involving a non‐local potential, different for each sub‐shell. For the work presented herein, PENELOPE and EGSnrc applications used the MCDF photoelectric library, while TOPAS utilized DHFS. An extra simulation was performed using PEN18 with the DHFS to assess the effect of the photoelectric library in this specific case. Finally, all MC systems used in this work allow the use of different variance reduction tools (i.e., particle splitting and interaction forcing, among others); please refer to Table 2 for more details.

2.5. Bremsstrahlung cross‐sections

Bremsstrahlung simulations require knowledge of cross sections differential in photon energy (scaled function) and emission angle (shape function). According to their documentation, these MC systems use the scaled function published by Seltzer and Berger (1986). ²⁸ egs_brachy and egs_kerma used the NRC option, which is similar to the NIST dataset (i.e., Seltzer and Berger [1986]) but replaced the electron‐electron part with exact calculations in the first Born approximation. ²⁹

Although they used almost the same dataset for the scaled function, they all differ in the shape function approximation. PEN18 uses an analytic fit of the data calculated by Bremss, ³⁰ a FORTRAN code using the same theoretical approach as Kissel et al. (1983), ²⁰ , ³¹ hereafter called KQP, which consists of a relativistic partial‐wave approach. The EGSnrc applications calculate the double differential cross‐sections of the electron nucleus bremsstrahlung process, relying on two plane‐wave first Born approximations, classified by Koch and Motz (1959) ³² as 2BN (without screening correction) and 2BS (with screening correction, extreme‐relativistic and small angles approach). Due to the different drawbacks presented by both approaches, EGSnrc implemented an intermediate solution, KM, which includes the 2BS formula corrected by 2BN's angle‐dependent leading term. ¹⁶ , ³³ Finally, TOPAS's simulations included two physics lists, g4em‐penelope (TOPAS_pen) and g4em‐livermore (TOPAS_liv). TOPAS_pen used KQP, while TOPAS_liv utilized 2BN. Generally, the KQP approach is considered the benchmark option in experimental and theoretical research. ¹⁶ , ³⁰ , ³⁴ , ³⁵ Therefore, all the comparisons were performed against PEN18. This choice is not intended as a recommendation but rather as the selection of a reference to present the data clearly and consistently. Such selection relies only on the preferences of other authors (when it comes to benchmarking) in the absence of sufficient data for further considerations. The reader can find a detailed description of the physics (including the shape functions) involved in all MC systems elsewhere. ¹⁶ , ²⁰ , ²⁹ , ³⁶ , ³⁷

2.6. Electron impact ionization (inner shell ionization) and atomic relaxation

The electron impact ionization (EII) or inner shell ionization by electrons creates low‐energy secondary particles such as fluorescent (characteristic) x‐rays, Auger, and Coster‐Kroning electrons, leading the atom to its ground state (atomic relaxation or atomic de‐excitation). These particles will deposit most of their energy near the phantom surface. In this regard, PEN18 uses two approximations to calculate the EII: the plane‐wave first Born approximation (PWBA) and the distorted‐wave Born approximation (DWBA), using a method described by Bote and Salvat (2008). ³⁸ Briefly, PEN18 chooses between the two approaches depending on the projectile's kinetic energy relative to the ionization energy, U_i. In this way, PEN18 uses DWBA to calculate the ionization in orbitals K, L, M, and N for kinetic energies from ∼ U_i to 16U_i. Then, PEN18 uses PWBA multiplied by an empirical energy‐dependent scaling factor, which tends to the unity at high energies when this approximation is considered reliable (30U_i, approximately). ²⁰ , ³⁸ egs_brachy was set to use the exact implementation as PEN18 (EII‐penelope), except that EGSnrc only considered orbitals K‐shell and L‐subshells. ²² Additionally to EII‐penelope, egs_kerma was set to use another EII model, which only uses PWBA (EII‐IK). Finally, TOPAS_liv obtains its cross‐sections by interpolation of the Evaluated Electron Data Library (EEDL), ³⁹ while TOPAS_pen uses the theory of a previous PENELOPE version described in Salvat (2001). ³⁶

On the atomic relaxation side, PEN18 obtains the transition probabilities from the Evaluated Atomic Data Library (EADL), ⁴⁰ where the energies of the x‐rays emitted from K‐shell and L‐subshells, and M‐shells vacancies are taken from Deslattes et al. (2003) and Bearden (1967), respectively. ²⁰ , ⁴¹ , ⁴² If some transition is not included in the last dataset, PEN18 takes the x‐rays energies directly from the EADL library. ²⁰ TOPAS_liv, and TOPAS_pen use the EADL library for transition probabilities and x‐ray energies. ³⁶ In the case of EGSnrc, transition probabilities for atomic shells with binding energy above 1 keV are taken by default from the EADL library. ²⁹ , ⁴³ The shell binding energies are consistently selected based on the photon cross‐section compilations requested (EPDL or XCOM), in this case, from the XCOM library. ⁴⁴

2.7. Comparisons performed

Depth doses and fluence spectra were compared in the following cases:

1. Detailed model of the INTRABEAM 30 mm diameter applicator simulated with egs_brachy (KM), TOPAS_pen (KQP), and TOPAS_liv (2BN), with PEN18 (KQP) as reference. A dose profile comparison (phantom surface) was also included.

2. Tr‐W, Rf‐W, and Tr‐Au simulated with PEN18 (KQP), egs_brachy (KM), TOPAS_pen (KQP), and TOPAS_liv (2BN). The bremsstrahlung and characteristic components of the fluence spectra were analyzed separately.

3. Tr‐W and Tr‐Au simulated with PEN18 using the DHFS and MCDF photoelectric libraries.

4. Tr‐Au system simulated by egs_kerma, using (scaled function + shape function + electron impact ionization) NRC + KM + EII‐penelope and NRC + KM + EII‐IK. The bremsstrahlung and characteristic components of the fluence spectra were analyzed separately.

The differences in depth dose and fluence spectra were reported as [1 – D_MCsys(z) / D_PEN18(z)] and [1 – Φ_MCsys(E) / Φ_PEN18(E)], respectively. Here, D_MCsys(z) and Φ_MCsys(E) denote the absorbed dose calculated at depth z and the fluence differential in energy E, respectively, simulated by TOPAS or EGSnrc. In the spectral case, the average value is calculated according to Σ [Φ_PEN18(E)—Φ_MCsys(E)] / ΣΦ_PEN18(E). Finally, this work presented the differences in “absolute” units (i.e., Gy/histories). The readers can quickly normalize the data at the preferred depth using the information uploaded as Supplemental Material. The reader can find the RECORDS ⁴⁵ summary of the simulations in Table 2.

3. RESULTS

3.1. Detailed eBT model

Figure 2 shows a dosimetric comparison between egs_brachy and PEN18 for simulations of the detailed model of the INTRABEAM's 30 mm diameter surface applicator (shown in Figure 1). A marked difference between the egs_brachy and PEN18 curves can be appreciated: the average difference is −7% (σ = 2.2%) over the 3D scoring voxel array (see Figure S6 in Supplemental Material), which is larger than Type A uncertainties. The depth dose curve presents an average difference of −9.3 ± 0.1%. TOPAS_liv delivers ‐8.0% (σ = 2.9%) and −10.0 ± 0.3%, while TOPAS_pen agrees within 1.7% (σ = 1.3%) and 1.1 ± 0.3%, considering the 3D scoring voxel array and depth dose, respectively.

FIGURE 2.

Dosimetric comparison between egs_brachy (KM) and PEN18 (KQP) simulating the detailed INTRABEAM's 30 mm diameter surface applicator model. (a) Depth dose comparison. (b) Profile comparison at the phantom surface. The dashed curves represent the differences between MC systems (shaded areas show the Type A uncertainties, k = 2).

3.2. Simplified setups

The simplified setup comparisons are summarized in Table 3. egs_brachy (KM) and TOPAS_liv (2BN) delivered weighted average differences compared to PEN18 (KQP) between −10% and −15% when the bremsstrahlung component of the fluence spectra (excluding characteristic lines) was compared for the transmission mode (Axxent and INTRABEAM eBT, see Figure 3). The comparison with TOPAS_pen and PEN18 (both using KQP) returns lower differences around ‐5% on average (see Figure 3). In the case of egs_brachy, the differences diminished for the reflection mode up to 4% (see Figure 4). However, TOPAS_pen in reflection target mode has similar bremsstrahlung differences as the transmission targets. Considering only the characteristic lines, egs_brachy performed akin to PEN18 (lower than 3% difference). On the other hand, TOPAS delivered higher disagreements with PEN18, averaging 9% and 39% differences for TOPAS_pen and TOPAS_liv, respectively.

TABLE 3.

Average differences between egs_brachy and TOPAS relative to PEN18.

MC system	Quantity	Item	Rf‐W (%)	Tr‐W (%)	Tr‐Au (%)
egs_brachy (KM)	Fluence spectrum	Full	1.8 (5)	−6.5 (2)	−7.9 (5)
		Bremss.	4.0 (6)	−10.5 (2)	−15.6 (7)
		Lines	−1.1 (7)	−0.7 (3)	2.8 (8)
	Depth dose	–	2.7 (3)	−8.9 (2)	−9.8 (4)
TOPASpen (KQP)	Fluence spectrum	Full	−4.4 (3)	2.7 (1)	−1.0 (6)
		Bremss.	−12.0 (4)	−3.9 (2)	−6.3 (8)
		Lines	5.7 (4)	12.7 (2)	7.8 (9)
	Depth dose	–	−3.1 (3)	0.1 (2)	0.7 (5)
TOPASliv (2BN)	Fluence spectrum	Full	–	6.7 (1)	–
		Bremss.	–	−14.1 (2)	–
		Lines	–	38.6 (1)	–
	Depth dose	–	–	−9.6 (2)	–

For data calculated using TOPAS, two physics lists are considered: G4em‐livermore (TOPAS_liv) and g4em‐penelope (TOPAS_pen) (see section 2.5). The fluence results are divided into the full spectrum (Full), and the bremsstrahlung (Bremss) and characteristic lines (Lines) components. Type A uncertainty (k = 2) is in parentheses, corresponding to the last digit.

FIGURE 3.

Dosimetric comparison of Tr‐Au and Tr‐W. The left column shows depth doses, while the right column shows the comparison of fluence spectra. Rows (a), (b), and (c) compare PEN18 (KQP) with egs_brachy (KM), TOPAS_liv (2BN), and TOPAS_pen (KQP), respectively. Shaded areas represent the Type A uncertainties, k = 2.

FIGURE 4.

Dosimetric comparison between egs_brachy (KM) and PEN18 (KQP) simulating Rf‐W. a) and b) compare depth dose and fluence spectra, respectively. The transparent gray curves represent the differences between MC systems (shaded areas represent the Type A uncertainties, k = 2).

The depth doses calculated with egs_brachy and TOPAS_liv differ by ‐9% on average for the transmission mode (Tr‐Au and Tr‐W, see Figures 3) compared to PEN18. In contrast, TOPAS_pen’s agreement (see Figure 3) improves, reaching less than a 1% difference when the depth dose is compared for the same simplified models. The reflection mode (Rf‐W, see Figure 4) delivers lower differences for egs_brachy (‐2.7%). In the case of TOPAS_pen, its average difference is ‐3%, higher than the transmission mode.

3.3. Selection of the photoelectric library

Using different PEN18's photoelectric libraries (DHFS vs. MCDF) results in average differences of less than 1% in the depth dose and fluence spectra for all the eBT systems (simplified models). Similar results were obtained in the detailed model of the INTRABEAM system.

3.4. egs_kerma comparison

The simplified setup comparisons using the egs_kerma EGSnrc application are summarized in Table 4. egs_kerma using NRC + KM + EII‐penelope and NRC + KM + EII‐IK delivered ‐17% weighted average differences against PEN18 (KQP) when the bremsstrahlung component of the fluence spectra (excluding characteristic lines) was compared for the transmission mode (Tr‐Au, see Figure 5). Considering only the characteristic lines, egs_kerma using EII‐penelope performed akin to PEN18 and egs_brachy (lower than 3% difference). On the other hand, egs_kerma delivered higher disagreements with PEN18, averaging 28% differences, when EII‐IK is used.

TABLE 4.

Average differences between egs_kerma, using EII‐penelope and IK, relative to PEN18.

MC system	Quantity	Item	Tr−Au (%)
egs_kerma (KM + EII_pen)	Fluence spectrum	Full	−9.3 (2)
		Bremss.	−17.9 (2)
		Lines	3.0 (3)
	Depth dose	–	−11.1 (2)
egs_kerma (KM + EII_IK)	Fluence spectrum	Full	−1.0 (2)
		Bremss.	−16.6 (2)
		Lines	28.2 (2)
	Depth dose	–	−8.7 (2)

The fluence results are divided into the full spectrum (Full), the bremsstrahlung (Bremss), and characteristic lines (Lines) components. Type A uncertainty (k = 2) is in parentheses, corresponding to the last digit.

FIGURE 5.

Dosimetric comparison of Tr‐Au using egs_kerma. The left column shows depth doses, while the right column shows the comparison fluence spectra. Rows (a) and (b) compare PEN18 (KQP) with egs_kerma (KM) using EII‐penelope and EII‐IK, respectively.

The depth doses calculated with egs_kerma differ by −9% to −11% on average using EII‐penelopee EII‐IK (see Figure 5) compared to PEN18, whose differences presented the same pattern as egs_brachy, differing only in the surface in the case of egs_kerma using EII IK.

4. DISCUSSION

This work focuses on a purely MC comparison to highlight dosimetric differences arising from their different physics approaches when treating bremsstrahlung events. The agreement observed in this study differs significantly from that typically reported in photon‐only simulations. Such discrepancies may present challenges for researchers unfamiliar with x‐ray generation. These comparisons aim to provide foundational knowledge for understanding these variations, enabling future users to incorporate them into their analyses without unnecessary troubleshooting. Additionally, this work seeks to engage more researchers, both theoretical and experimental, in addressing and resolving these challenges. While the clinical relevance of our findings is an important consideration, its analysis would require a thorough and multifaceted evaluation that integrates the complex differences observed here (e.g., variations in beam flatness), which lie beyond the scope of this study. Instead, readers can find all the data necessary to perform relative, absolute, or normalized analyses in their clinical assessments in the Supplemental Material.

The spectral analysis requires the evaluation of its characteristic and bremsstrahlung components separately. The characteristic component contributes approximately 30%–40% of the total fluence at the phantom surface. Here, EGSnrc applications using EII‐penelope yield characteristic lines akin to PEN18, with less than a 3% difference on average (see Tables 3 and 4), except at energies near the 2‐keV M line, where PEN18 intensities are one order of magnitude higher. At this characteristic line, the PEN18 intensities coincide with the maximum of the bremsstrahlung component in the gold fluence spectrum (see Figures 3 and 5 presented here, and Figure S12 in Supplemental Material). This agreement is achieved because both MC systems use the same theory for the inner shell described by Bote and Salvat. ²² , ³⁸ In contrast, egs_kerma (EII‐IK) and TOPAS_liv show significant discrepancies with PEN18 for all lines, with 40% and 30% differences on average, respectively (see Figures 3 and 5). Although the agreement improves when comparing TOPAS_pen, PEN18 still delivers higher fluences by an average of 10% (Figure 3). This could be explained by the entirely different approximation taken by TOPAS and egs_kerma with EII‐IK to obtain its cross‐sections: Extracted directly from the EEDL in the case of TOPAS_liv or using a previous version of PENELOPE physics in the case of TOPAS_pen. The Geant4 physics manual warns that the cross‐section for inner‐shell ionization modeled in g4em‐penelope is “only roughly approximated.” ²⁰ , ³⁶ This limitation is also noted in the user manuals of previous PENELOPE versions, upon which this Geant4 physics list is based. For this reason, “In cases where inner‐shell ionization is directly observed (e.g., in the simulation of x‐ray emission by electron bombardment), a more accurate description of the process should be used.” ³⁶ Additionally, the EII‐IK model differs from the EII‐penelope because the former approach considers only the plane wave Born approximation (PWBA), which is reliable primarily at higher energies. ³⁸

Excluding the characteristic lines allows us to evaluate the spectrum's bremsstrahlung component. The average differences between the bremsstrahlung fluence spectra calculated by the EGSnrc applications (KM) and TOPAS_liv (2BN) compared to PEN18 (KQP) were between −10% and −18% for the transmission mode (see Tables 3 and 4 along with Figures 3 and 5). egs_brachy in reflection mode shows a better agreement, achieving a 4% difference. This data is consistent with Omar et al., who predicted a more intense beam in the transmission direction for KM and 2BN. ¹⁶ TOPAS_pen (KQP) is observed to have higher fluences at energies lower than 20 keV and matching PEN18 at increased energies. This trend is more noticeable in the reflection target mode (Rf‐W, see Figure S20 in Supplemental Material), where the weighted average difference is −12%.

Most of the depth‐dose differences show an initial trend in the first centimeters. As the egs_kerma comparisons show, these slopes are caused by the relatively high intensities in the characteristic lines (< 12 keV and 15 keV for W and Au, respectively) calculated by PEN18. In turn, those differences in intensity are primarily due to different EII approximations between the different MC systems. Figure 5 shows that the characteristic radiation gets rapidly attenuated, leading to the −9% to −10% difference observed at greater depths, where the bremsstrahlung angular distribution becomes increasingly important. TOPAS_liv and egs_kerma EII‐IK are clear examples whose disagreement went from 15% to −10% in the first centimeter (see Figures 3 and 5). Figure 3 also shows a gradient with depth between egs_brachy and PEN18 differences from +5% to −4% in half of a millimeter. This effect is caused by the characteristic line differences at ∼2 keV mentioned before. This could be explained by the different treatment that EGSnrc gives to the M lines compared to PEN18. The mean free path at 2 keV is ∼20 µm in water, meaning those photons are heavily attenuated in the flattening filter considered in the detailed case (see Figure 2). Consistent with comparisons of the bremsstrahlung component of spectra, the MC systems’ depth dose agreement is better in the reflection mode, which is also consistent with Omar et al. ¹⁶

It is worth mentioning that the observed dose discrepancies between codes cannot be solved by a scaling factor or normalizing to an arbitrary reference point. As mentioned above, the agreement between the MC systems improves in the reflection mode. This effect is produced because all bremsstrahlung angular distributions tested here converge at higher angles. ¹⁶ This behavior is markedly noted in the dose profile comparison shown in Figure 2, where egs_brachy delivers a higher intensity at the beam axis, matching PEN18's results near the beam edge. For this reason, PEN18 (KQP) calculates a more flattened beam compared to egs_brachy (KM) and TOPS_liv (2BN), which is the expected result of using different bremsstrahlung angular approximations. Comparing Figures 2 and 3 proves that simplified models are reasonable proxies for evaluating the overall dosimetric impact of the physics libraries in detailed geometries, provided that the reader considers the applicator filtering on the phantom surface. Previous comparisons have demonstrated good agreement between MC systems in pure photon simulations, where differences predominantly become statistical when using the same photoelectric library (as EGSnrc and PEN18 in this study). ¹⁵ As the impact of the photoelectric libraries is less than 1% in this work, the discrepancies are primarily produced at the target level, involving bremsstrahlung, EII, and atomic relaxation calculations.

More research is needed to assess the implications of these results in related calculations. For instance, the ratio between the absorbed dose to water and the dose in the detector cavity (crucial in dosimetry) is calculated mainly through MC methods, ⁷ , ⁶⁵ where the differences in the simulated spectra can modify the estimated detector response. Beam modeling in TPS is another example, affecting both MBDCA and TG‐43 formalism. If a TPS is built based on a specific MC system's result, its MBDCA will mirror the physics used in the simulations, complicating the benchmarking against other MC systems. Similarly, the data presented here could indicate disagreements in the TG‐43 anisotropy function, F(r, θ), around 0° (in TG‐43 reference frame).

5. CONCLUSION

The data show marked spectral and dosimetric differences between state‐of‐the‐art MC systems simulating eBT devices. Those differences are produced when bremsstrahlung (different approximations of angular emission), inner shell ionization (EII), and atomic relaxation processes are calculated within the target, with the transmission target mode being the most affected. Considering the spectral changes (phantom surface), the differences between bremsstrahlung angular emission reach a 15% average (considering only the fluence spectra's bremsstrahlung component), with PEN18 being consistently lower. Regarding the different EII approaches, their spectral differences reach an average of 22% (considering only the fluence spectra's characteristic component), this time PEN18 is presenting the higher output. All these disagreements generate an average difference of 10% in the depth dose using the transmission mode. More research is needed to evaluate the impact these disagreements have on related calculations (e.g., detector response or correction factors calculations, eBT TG‐43 parameters, among others) that require ratios at different depths or angles (or both) regarding the x‐ray source orientation.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

Supporting information

Supporting Information

Valdes‐Cortez C, Mansour I, Ayala Alvarez DS, et al. Dosimetric impact of physics libraries for electronic brachytherapy Monte Carlo studies. Med Phys. 2025;52:2520–2532. 10.1002/mp.17633