Comparative analysis of auger electron emission libraries and Monte Carlo track structure codes for DNA-targeted auger electron therapy

Abstract

Background:

Over the past decade, theranostic radiopharmaceuticals have gained significant attention, driven by the clinical success of agents like [¹⁷⁷Lu]Lu-DOTATATE and [¹⁷⁷Lu]Lu-PSMA-617. This has spurred an interest in radionuclides that could produce an even more focal radiotoxicity. Radionuclides that decay by electron capture and /or internal conversion result in a cascade of low-energy Auger electrons that produce a dense cluster of ionizations local to the decay site. These radionuclides are especially potent when the decay occurs near or at the DNA. Among these, ¹²³I stands out for its clinical potential as a theranostic isotope.

Purpose:

This study aims to evaluate and compare two well-recognized data libraries to obtain the Auger electron energy spectra and three Monte Carlo (MC) track codes to analyze DNA-scale energy deposition from Auger electrons emitted by ¹²³I. By examining variability in simulation outputs, this study seeks to determine whether the data libraries yield different DNA double strand break (dsb) outcomes and to assess the sensitivity of the MC track codes.

Methods:

An in-house MC code was developed in MATLAB to obtain Auger electron energy spectra using the McGuire and Evaluated Atomic Data Library (EADL) datasets. A MC study using Geant4 utilized these spectra to analyze DNA dsb yields, applying a 17.5 eV threshold to define strand breaks. Subsequently, a sensitivity analysis compared energy deposition and dsb yields across MC track codes — Geant4, PHITS, and MCNP6.2 — assessing their effectiveness in modeling DNA damage from Auger emitters and bench-marking these findings against literature data using Moca7B.

Results:

The study found that the average dsb yields for the ¹²³I atom were similar using both McGuire and EADL libraries. Emission spectra indicated that while the McGuire library produced an average of 11.91 electrons per decay, the EADL library resulted in 13.96 electrons per decay. For different track codes, dsb yields were 0.91 for MCNP6.2, 0.60 for Geant4, and 0.43 for PHITS, whereas the dsb yield in the literature is 0.73. These discrepancies clearly emphasize the need for specific energy thresholds to align with the track code in use.

Conclusions:

The EADL library produces more electrons than McGuire, but this does not affect the amount of local DNA damage significantly, as most of the additional electrons fall below the 17.5 eV damage threshold. Both libraries yield similar DNA damage outcomes. In addition, our analysis highlights the need for specific energy thresholds in MC codes to ensure accurate DNA damage predictions in Auger electron studies.

1 |. INTRODUCTION

The last decade has played witness to a remarkable surge of interest in theranostic radiopharmaceuticals. Whereas the field is not new, this sudden growth spurt largely stems from the clinical successes and subsequent regulatory approvals of two theranostic agents bearing the β⁻-emitting radiometal lutetium-177 (t_1/2 = 6.8 d): [¹⁷⁷Lu]Lu-DOTATATE (i.e., LUTATHERA)¹ for the treatment of neuroendocrine cancers and [¹⁷⁷Lu]Lu-PSMA-617 (i.e., Pluvicto)² for the treatment of metastatic prostate cancer.

These successes have spurred interest in the pharmaceutical and academic communities in identifying radionuclides with more local radiotoxic effects, for example, radionuclides that emit high linear transfer (LET) α-particles. Along these lines, there has been a resurgence of enthusiasm in radionuclides that undergo Auger electron cascades caused by electron capture and/or internal conversion processes. Such radionuclides — including ⁶⁷Ga, ^99mTc, ¹¹¹In, ¹²³I and ²⁰¹Tl — can produce depositions of energy even more concentrated than those produced by α-emitting radioisotopes.

Electron capture and internal conversion processes create inner shell electron vacancies, most commonly within the K-shell. This vacancy can be filled via inner shell electron transitions, which result in the emission of a characteristic x-ray or (more commonly) an Auger electron as discovered by Lise Meitner and Pierre Auger in the early 20th century.^3,4 In the former process, the vacancy then moves up to a higher shell. In the latter, the energy gained from the vacancy-filling transition is transferred to another orbital electron, resulting in the ejection of that orbital electron and the formation of two vacancies. These new vacancies are progressively filled by additional transitions (governed by the inner shell transition probabilities of the individual atom) until all vacancies reach the outermost atomic shell. Depending upon the atomic number of the element and the electron capture/internal conversion yields, the number of electrons emitted per atomic disintegration can be extremely high: for example, an average of 21 for ¹²⁵I.⁵ The large number and the low energy of these electrons results in the super-position of several electron tracks, ultimately producing a dense cluster of ionizations resembling that produced by an α-particle but confined within a nanometer of the site of decay.

The radiotoxicity of these Auger electron-emitting radionuclides depends upon where they decay within a biological system. To wit, a radiopharmaceutical bearing an Auger electron-emitting radionuclide that decays outside of the cell has been shown to produce a radiotoxicity profile over a thousand-fold less than one that decays near the DNA, the principal target for the cytotoxic radiation. This striking relationship between the site of decay and the toxicity of Auger electrons has led to physicists attempting to understand the spatial dependence of the Auger electron energy deposition and why these radionuclides have the propensity to produce both low and high LET effects depending upon the location of the decay within the cell.⁶

For a detailed summary of Auger electron dosimetry and their predicted biological effects, the reader is referred to the paper by Humm & Charlton⁷ as well as the AAPM Nuclear Medicine task group report #6.⁸ Motivated by the results of this early radiobiological and microdosimetry work, a handful of pilot clinical trials were initiated in an attempt to probe the potential efficacy of Auger-electron therapy with radiopharmaceuticals—for example [¹²³I]-iododeoxyuridine—that are selectively incorporated into the DNA of proliferating cells.^9,10

A recent article by Kwon et al.¹¹ states, “Radiopharmaceutical therapy (RPT) is evolving as a promising strategy for treating cancer. As interest grows in short-range particles, like Auger electrons, understanding the dose-response relationship at the deoxyribonucleic acid (DNA) level has become essential.” In service of this goal, this manuscript is focused on comparing different data libraries used to generate Auger electron emission spectra as well as different Monte Carlo (MC) track structure codes used to simulate the local energy deposition within a geometrical model of DNA. MC track structure codes have been rigorously validated for high-energy electron, photon, and proton therapy beams. However, the energy of most Auger electrons falls between 10 to 10,000 eV, energies at which many codes typically discontinue tracking the electron trajectory and instead deposit the energy locally.¹² Therefore, it is important to evaluate different codes to establish a level of confidence in the nanodosimetry estimates for Auger electron-emitting radionuclides being made by groups around the world.

Several non-radiative and radiative data libraries and spectra have been studied over the years.^13–18 However, our research aims to understand whether differences between data libraries impact the energy deposition at the DNA scale. Given the sensitivity of DNA to Auger electron deposition at the nanoscale, even minor changes in electron emission or energy yield could lead to variations in the predicted number of DNA strand breaks, resulting in different simulation outcomes. In this study, non-radiative and radiative transitions were integrated into the stochastic MC code using transition probabilities provided by either the McGuire data library^19–23 or the Evaluated Atomic Data Library (EADL).²⁴

MC simulations have significantly advanced pharmaceutical design and clinical strategies for theranostic agents by enabling precise modeling of radiation transport, dose deposition, and biological effects.²⁵ In clinical applications, MC-based voxel-wise dosimetry enhances patient-specific treatment planning by improving dose accuracy from PET/SPECT imaging data while accounting for tumor heterogeneity.²⁶ These simulations also play a crucial role in refining imaging protocols for theranostics by modeling scatter and attenuation corrections in quantitative PET/SPECT imaging and optimizing contrast agent performance.²⁷ MC methods are a necessity when calculating the stochastics of energy deposition produced by Auger electron-emitting radionuclides.

While both ¹²⁵I and ¹²³I have been extensively studied concerning their Auger electron emissions, ¹²³I stands out as the most suitable radionuclide for clinical radio-theranostics because of its current widespread use for nuclear medicine and the alignment of its physical decay kinetics with the biokinetics of suitable targeting vectors. Therefore, the focus of this analysis is 123I. By analysing ¹²³I, this study aims to provide critical insights into the variability of the calculated energy deposition at the nanometer scale between the different MC track structure codes. Understanding how these codes perform when applied to ¹²³I is essential when comparing results between different groups that utilize different MC codes and when unifying the dosimetric estimates and reliability of predictions.

2 |. METHODS

2.1 |. Stochastic Auger electron spectra

A MC code in MATLAB 2022a was developed to simulate ¹²³I decay in the condensed phase, calculating the number and energy of emitted electrons per disintegration. The simulation followed a stochastic sequence of vacancy transitions and particle emissions in two stages: (i) electron capture and (ii) internal conversion.

Initial vacancies were assigned using probabilities from Humm,²⁸ incorporating electron capture and internal conversion probabilities. Given the multiple decay branches of 123I, the simulation applied a weighted random selection for the excited state of 123Te, which in 97% of cases is at 159 keV. The code then randomly selected the shell for electron capture, creating a vacancy. Non-radiative and radiative transitions were integrated using probabilities from the McGuire library^19–23 (non-radiative only) and the EADL.²⁴ Fluorescence yields were sourced from Charlton and Booz,⁵ assigning an 85.9% probability for radiative transitions and 14.1% for non-radiative ones when using the McGuire data library.

To determine the impact of data discrepancies on DNA damage, the simulation assigned random numbers to classify transitions as radiative or non-radiative. For radiative transitions, the subshell filling the vacancy was selected, and photon energy recorded. For non-radiative transitions, an electron was emitted, and its energy was computed. This iterative process continued until no further transitions occurred.²⁹

The internal conversion phase followed a similar approach: if a random number was ≤0.83, a gamma-ray was emitted; otherwise, an internal conversion event occurred, ejecting an electron. This cycle repeated until all transitions were completed. The simulation, repeated 10,000 times for statistical robustness, recorded the number and energy of emitted electrons and photons.

During the Auger process, an electron filling a lower-shell vacancy caused another electron to be ejected. Traditional models assume lower-shell vacancies fill first,²⁸ but alternative hypotheses suggest higher-shell vacancies may be prioritized, potentially increasing electron emission.^30–34 The impact of this ordering on DNA damage was assessed.

Finally, the obtained electron and photon spectra were used as inputs for MC track structure simulations. DNA strand break estimates from Geant4, MCNP6.2, PHITS, and literature results from Moca7B were compared.⁷

2.2 |. The DNA model

The DNA volume model used in this study was proposed by Humm & Charlton.^7,35 In this model, the DNA duplex is represented as a hollow cylinder divided into a central region with an internal diameter of 10Å and an external diameter of 22Å. Each sugar-phosphate moiety is represented by a semi-arc, and they are shifted along the DNA axis, rotating by 36 degrees per base pair. Figure 1 shows a section of one strand of the DNA model, illustrating the helical twist, with one full rotation occurring over 10 base pairs. In total, the DNA model comprises 59 base pairs. In this study, a sensitivity analysis was performed in which the variability of the energy deposition pattern in the DNA was determined by three different MC track codes compared to the initial literature data obtained with Moca7B.⁷ The source was set to the position of the iodine atom of incorporated iododeoxyuridine as assumed in the study by Humm and Charlton.⁷ Choosing the DNA cylinder axis as the z-axis, with the x-y plane lying perpendicular to the DNA axis, the coordinates of a decay event are (0.0, 1.5, 1.7) Å.

FIGURE 1.

Schematic representation of DNA structure modeled for simulating Auger electron interactions. The DNA is depicted as a cylindrical helix with 59 alternating base pairs illustrated in blue and orange. An ¹²³I Auger-emitting radionuclide source is positioned centrally within the DNA structure, initiating a single decay cascade that releases many individual electron tracks. These tracks, represented as black jagged lines extending from the decay site, illustrate the pathways of electrons as they deposit energy randomly (shown as red dots) along their trajectories. The zoomed inset illustrates the dimensions of the DNA at an atomic scale, showing a 10 Å inner helix diameter and 3.4 Å base pair spacing, with the angular offset of 36° between adjacent base pairs.

2.3 |. MC calculations

The structure codes were used to generate the tracks of each individual electron from the Auger spectrum produced by each decay, which was obtained from the stochastic cascade code as detailed in “Section 2.1 Stochastic Auger Electron Spectra.” A comprehensive sensitivity analysis of each MC track code is compared in this section. It should be highlighted that these comparisons were performed using the Auger spectrum obtained via the EADL data library allowing for a more accurate evaluation of each track code’s performance. Also, in these simulations, only direct damage to DNA were computed. Same coordinate of the incorporation site within the DNA model were employed for the track codes’ simulations, maintaining consistency across platforms with respect to the geometry (Figure 1). This approach ensured that all simulations were directly comparable, minimizing variability from spatial positioning and geometric representation.

Each electron was simulated based on its respective yield using different random seeds to ensure that every simulated electron had a distinct random direction. Each track code independently calculated the trajectories and interactions of the electrons within the DNA environment.³⁶ This allowed for a detailed analysis of how each simulation platform models the transport and energy deposition within the DNA volume. The energy deposition after one decay was computed by summing the energy depositions from the electrons emitted by each respective decay within the DNA cylinder. Since the DNA cylinder is divided into bases and strand regions with enumerated IDs used within each MC code, the pattern of energy deposition along each DNA strand was obtained, where each decay produced a unique pattern, which ultimately determined the extent of DNA damage.

Track structure codes model energy deposition in condensed matter through cross-sections for elastic scattering and inelastic interactions. At low projectile energies, these cross-sections depend on both the atomic composition and phase (gas, liquid, or solid) of the target. However, the scarcity of experimental data limits the validation of theoretical models describing molecular orbitals and electron interactions. As a result, most radiobiological modelling studies use liquid water as a surrogate for biological materials, including nuclear components like DNA.³⁷ Therefore, to simulate the biological environment, the DNA and surrounding environment were assumed to comprise of liquid water^38–40 but with geometric sub-compartments that exhibit an accurate correspondence to the DNA base regions and strands. In this way, the electron interactions are accurately spatially modeled, allowing for precise calculations of energy deposition within a geometric model of the DNA.

The MC software Geant4 version 11.2.0 was used to simulate electron transport and interactions within the DNA structure. The “G4EmDNAPhysics_option2” physics list was chosen to model these interactions, focusing specifically on direct damage with a default cut-off energy of 7.4 eV. While Geant4 offers other physics lists—such as “G4EmDNAPhysics_option4” and “G4EmDNAPhysics_option6”—that are also applicable to DNA damage studies, “option2” was selected as the most suitable and feasible option for this study.⁴¹

In MCNP6.2, the tally “*F8” was used because it reports energy deposits in eV, providing a detailed account of the distribution of energy deposition across DNA base pairs for each simulated electron. Additionally, MCNP6.2 includes an electron cross-section table that supports low-energy interactions down to a 12 eV cut-off,⁴² enabling accurate modeling of energy deposition at the DNA level. The default low-energy electron behavior in MCNP was modified using the “PHYS:E” card to enable single-event tracking, and the “CUT:E” card to prevent local energy deposition by electrons, as described in the MCNP low-energy photon/electron guide.⁴³

PHITS track code employed a combination of the Electron Gamma Shower (EGS5)⁴⁴ and the track-structure modes⁴⁵ for particle transport. A cut-off energy of 1.0 keV was used for electrons and photons in the EGS5 mode, while the track-structure mode was utilized below this cut-off down to a 0.01 eV.

2.4 |. Energy deposition in the DNA

In the literature, several methods exist to convert energy deposition into DNA damage.^38,46,47 In this study we applied the threshold method, as described by Charlton et al.,⁴⁶ where an threshold energy deposition of 17.5 eV within the geometric volume corresponding to a DNA strand to produce a DNA single strand break (ssb). This threshold energy was selected because it produced the best correlation between the energy deposited at each successive base location from the site of an ¹²⁵I decay and experimental data from Marin & Haseltine,⁴⁸ who measured the distance of DNA strand breaks from the site of the ¹²⁵I decay using an ¹²⁵I-labelled DNA plasmid. By adopting this consistent criterion, we enabled a direct comparison of simulation results and performed a sensitivity analysis across different MC track structure codes used for dosimetry calculations in Auger electron-emitting radionuclides. Comparing the MC simulation results with the experimental break length data allows for an assessment of the effectiveness and accuracy of the MC track codes in predicting radiation-induced DNA damage.

Another key sensitivity analysis focused on the comparison of double strand break (dsb) yields in the sugar-phosphate backbone volume. For Auger electron emitters, most energy deposition occurs within a few base pairs from the decay origin. A dsb is assumed to occur if ssbs happen on opposite strands that are no more than 10 base pairs apart. Additionally, the dsb yield includes complex strand breaks (csbs), where multiple strand breaks occur on opposite sides within 10 base pairs. Figure 2 illustrates examples of strand break types that might occur during the simulations. This analysis provides a comprehensive comparison of how different MC track codes simulate the formation of dsbs and csbs, allowing for a better understanding of the efficacy and accuracy of the MC track codes in modeling radiation-induced DNA damage, especially given the highly localized energy deposition characteristic of Auger emitters.

FIGURE 2.

Schematic of DNA damage classification. Damaged sugar phosphate volumes are represented in cyan. (a) Isolated sugar phosphate damage (ssb); (b) simple dsb with sugar phosphate damaged on opposite strands separated by less than 10 base pairs; (c) csb with multiple associated damaged backbones. CSB, complex strand breaks; DSB, double strand break; SSB, single strand break.

In the literature, for an applied threshold energy of 17.5 eV, the ¹²³I dsb yield was determined to be 0.73 dsb/decay when using the track code Moca7B as presented by Humm and Charlton.⁷ This finding includes an additional 0.21 dsb/decay contribution from the longer-range electrons produced during decay in a mammalian cell.^49,50 This comprehensive yield accounts for both the localized damage caused by Auger electrons and the more widespread damage resulting from longer-range electrons, providing a robust assessment of the total DNA damage induced by ¹²³I decay.

Experimental measurements of the dsb yield from ¹²³I-iododeoxyuridine in V79 cells obtained via neutral elution assays, reported 0.74 dsb/decay/cell.⁵¹ This result aligns remarkably well with the theoretical prediction from the Moca7B track structure. However, for different MC track codes, it is uncertain whether the same energy threshold will correlate with the same dsb yield, as variations in the sensitivity of different codes may result in differences in total energy deposition per decay and different energy deposition clustering patterns close to the site of the decay, resulting in different expected dsb yields. To further investigate this, the energy threshold for each track code required to produce a similar dsb yield of 0.73 dsb/decay was evaluated. The threshold energy was varied from 0.5 to 30 eV, and for each energy level, the corresponding dsb yield was calculated. This analysis will allow for comparisons between different track codes, enhancing our understanding of how energy deposition models differ across codes and ensuring a more reliable assessment of radiation-induced DNA damage across various simulations.

3 |. RESULTS

During the stochastic cascade process, the order in which vacancies are filled (i.e., whether lower or higher shells are prioritized) can influence the number of Auger electrons emitted and thus the extent of DNA damage. This occurs because if lower shells are filled first, some of the higher shells may be left without electrons toward the end of the cascade, rendering transitions in these shells forbidden and thereby reducing the total number of electrons emitted. In contrast, if higher shells are filled first, all potential electrons can be ejected, maximizing the number of electrons emitted. This effect is best illustrated in Figure 3, which compares the number of electrons emitted following electron capture using the EADL library. The left plot shows the frequency of electrons emitted when higher shells are prioritized, resulting in a smoother profile of electron emission. In contrast, the right plot—in which lower shells are filled first—shows a truncation in electron emission around 30 electrons.

FIGURE 3.

Spectra of the number of Auger electrons emitted by ¹²³I following electron capture only. The left plot represents decays where higher shell levels are prioritized for filling; the right plot shows decays where lower shells are filled first.

Despite the differences in the number of emitted electrons, this variation does not significantly impact the predicted DNA damage, as depicted in Figure 4. The minimal effect of these differences on overall DNA damage suggests that—in studies using ¹²³I atom—the variation in electron emission profiles has a negligible influence on the final damage outcome. Therefore, all results presented in this section are based on simulations in which the stochastic decay process prioritizes filling higher shell levels first.

FIGURE 4.

Double strand breaks per decay as a function of the energy threshold.

Table 1 presents the average decay spectra of a condensed phase ¹²³I atom including both electron capture and internal conversion, detailing the energy (in eV) as well as the corresponding radiative and non-radiative yields. These results are compared across data from the McGuire and EADL libraries and the values reported by Howell et al.¹⁴ The table highlights a good agreement between the stochastic Auger electron spectrum generated by the in-house code and the literature. This consistency between the data libraries and Howell et al.¹⁴ validates the reliability of the simulations for studying DNA strand breaks, ensuring accurate outcomes.

TABLE 1.

Average spectrum per decay for condensed ¹²³I.

	McGuire		EADL		Howell (1992)
Radiation	Energy (eV)	Yield	Energy (eV)	Yield	Energy (eV)	Yield
γ1	1.590E+05	8.20E-01	1.590E+05	8.20E-01	1.590E+05	8.39E-01
γ2	4.400E+05	2.90E-03	4.400E+05	2.90E-03	4.400E+05	3.90E-03
γ3	5.060E+05	2.40E-03	5.060E+05	2.10E-03	5.060E+05	2.80E-03
γ4	6.930E+05	1.45E-02	6.930E+05	1.39E-02	–	–
ce-K, γ1	1.272E+05	1.52E-01	1.272E+05	1.35E-01	1.270E+05	1.30E-01
ce-K, γ4	6.620E+05	7.00E-04	6.620E+05	1.00E-03	–	–
ce-L, γ1	1.541E+05	1.88E-02	1.541E+05	1.86E-02	1.540E+05	1.79E-02
ce-M, γ1	1.580E+05	2.90E-03	1.580E+05	4.20E-03	1.580E+05	5.30E-03
Kα1 × ray	2.746E+04	4.50E-01	2.746E+04	4.61E-01	2.750E+04	4.62E-01
Kα2 × ray	2.719E+04	2.47E-01	2.720E+04	2.46E-01	2.720E+04	2.37E-01
Kβ1 × ray	3.100E+04	7.88E-02	3.100E+04	8.19E-02	3.100E+04	8.13E-02
Kβ2 × ray	3.168E+04	2.59E-02	3.170E+04	2.76E-02	3.170E+04	2.37E-02
Kβ3 × ray	3.100E+04	3.95E-02	3.100E+04	4.35E-02	3.090E+04	4.45E-02
x-ray L	–	–	3.900E+03	7.75E-02	3.930E+03	7.90E-02
x-ray M	–	–	5.685E+02	3.40E-03	5.430E+02	2.30E-03
x-ray N	–	–	7.458E+01	3.00E-04	3.170E+04	1.30E-03
Auger—KLL	2.267E+04	9.73E-02	2.268E+04	8.24E-02	2.240E+04	8.38E-02
Auger—KLX	2.650E+04	3.79E-02	2.648E+04	3.71E-02	2.630E+04	3.84E-02
Auger—KXY	3.022E+04	3.20E-03	3.029E+04	3.70E-03	3.020E+04	3.50E-03
Auger—LLX	3.161E+02	1.66E-01	2.973E+02	1.45E-01	2.130E+02	1.56E-01
Auger—LMM	3.098E+03	7.89E-01	3.080E+03	7.19E-01	3.040E+03	7.51E-01
Auger—LMX	3.702E+03	2.53E-01	3.681E+03	2.01E-01	3.660E+03	2.02E-01
Auger—LXY	4.314E+03	1.89E-02	4.288E+03	1.40E-02	4.280E+03	1.30E-02
Auger—MMX	1.570E+02	9.25E-01	1.200E+02	8.69E-01	1.270E+02	8.69E-01
Auger—MXY	4.705E+02	2.05E+00	4.535E+02	1.94E+00	4.610E+02	1.97E+00
Auger—NNX	6.461E+01	2.13E+00	2.490E+01	2.46E+00	2.980E+01	2.10E+00
Auger—NXY	2.621E+01	5.24E+00	2.290E+01	7.30E+00	3.250E+01	6.54E+00

Abbreviation: EADL, Evaluated Atomic Data Library.

Figure 5 illustrates the ¹²³I electron energy spectra generated by the stochastic Auger spectrum code using the McGuire (left plot) and EADL (right plot) data libraries following electron capture and internal conversion. Both spectra demonstrate strong overall agreement with noticeable discrepancies occurring only at energies below 10 eV. This divergence is attributed to the fact that EADL data library indicates a higher yield of non-radiative transitions in the outer shells compared to the McGuire data library in the condensed phase approach.

FIGURE 5.

Spectra of the energy of Auger electrons emitted by ¹²³I. The left plot shows the energy spectrum obtained using the McGuire data library; the right plot displays the spectrum obtained from the EADL data library. EADL, Evaluated Atomic Data Library.

Figure 6 presents the abundance of electrons emitted from each shell, from both electron capture and internal conversion processes. The first heatmap (in orange) illustrates the abundance of electrons emitted when McGuire data library is used, while the second heatmap (in blue) shows the corresponding electronic emissions when the EADL data library is applied. The third heatmap represents the difference between the two electron kinetic energy spectra, highlighting the variations in electron emissions between the McGuire and EADL data sets. For atomic shells below the N-shell, there is strong agreement for both spectra, indicating that both libraries produce similar electron emission profiles for these atomic shells. However, the discrepancy in the outer shells—particularly the N₄-subshell and beyond—highlights that the EADL library indicates a higher rate of electron transitions for these atomic shells compared to the McGuire library. This difference results in the emission of a greater number of low-energy electrons. In addition, this higher yield of transitions slightly increases the total number of electrons emitted. However, these low-energy electrons are unlikely to contribute to DNA damage, as most of them do not even reach the DNA strands, and — for those that do — their energies fall below the critical 17.5 eV threshold required to cause strand breaks. This is further illustrated by simulations assessing DNA damage, in which both the McGuire and EADL libraries yielded a consistent dsb rate of approximately 0.60 per decay. Figure 7 shows the variation in dsbs per decay as the energy threshold is adjusted using Geant4. For energy thresholds below 17.5 eV, the McGuire library indicates a slightly higher dsb yield compared to the EADL library, but the results converge at the 17.5 eV threshold.

FIGURE 6.

Heatmaps showing electron emission abundance per subshell after 10,000 decay events for McGuire (orange) and EADL (blue) libraries, with a differential map highlighting variations. Both libraries show similar electron emissions for shells below the N-shell. However, the EADL library predicts a higher rate of outer-shell transitions, especially beyond the N4-subshell, leading to the increased emission of low-energy electrons. EADL, evaluated atomic data library.

FIGURE 7.

Double strand breaks per decay as a function of the energy threshold, assessed using Geant4 to evaluate DNA damage. Results are presented for both the McGuire and EADL data libraries. EADL, Evaluated Atomic Data Library.

Figure 8 presents the frequency distributions of the number of electrons emitted per decay after electron capture and internal conversion, with the left plot showing the results obtained from the McGuire library and the right plot those obtained with the EADL library. While the overall shapes of the distributions are similar, the average number of electrons emitted per decay differs slightly with the McGuire library yielding an average of 11.9 electrons, whereas the EADL library producing 13.9 electrons per decay. This discrepancy is due to the EADL library accounting for more electron transitions in the outer shells, leading to a higher total electron emitted. However, this increase did not significantly affect the predicted DNA strand break damage.

FIGURE 8.

Spectra of the number of Auger electrons emitted by ¹²³I following full decay, including contributions from electron capture and internal conversion. The left plot represents the spectrum generated using the McGuire data library; the right plot shows the spectrum obtained with the EADL data library. EADL, Evaluated Atomic Data Library.

Figure 9 illustrates the variation in dsbs per decay as a function of energy threshold for different track codes, using electron energies from the EADL library. If the critical energy threshold for a strand break of 17.5 eV⁴⁶ is selected then the dsb yields produced by the MCNP6.2, Geant4, and PHITS were 0.91, 0.60, and 0.43 per decay respectively. To match the experimental value of 0.74 dsbs per decay, the plot on the right highlights the corresponding energy thresholds of 22.6 eV for MCNP6.2, 14.0 eV for Geant4, and 11.05 eV for PHITS.

FIGURE 9.

Double strand breaks per decay as a function of the energy threshold, assessed using PHITS, Geant4, and MCNP6.2 to evaluate DNA damage. The plot on the left shows the dsb yields at a 17.5 eV energy threshold; the plot on the right illustrates the energy thresholds required to match the experimental dsb yield (0.74 dsb/decay/cell) for each track code. DSB, double strand break.

4 |. DISCUSSION

There is no significant difference in the overall shape of the electron number emission spectra between the McGuire and EADL data libraries, as expected from the transition probability data shown in Table 1. The main difference between the McGuire and EADL data library lies in the probabilities associated with outer shell transitions. The EADL library shows higher transition yields for these outer shells compared to the McGuire library most evident for the N-shell transitions. This discrepancy results in an average of 2 more electrons emitted on average per decay for ¹²³I when using the EADL data library. This difference translates in the electron kinetic energy spectra (Figure 3) to a higher frequency of electron energies below 10 eV. These additional low energy electrons were not found to impact the DNA strand break damage estimates because these energies fall below the energy threshold for strand break damage.

With condensed-phase approximations, the atom neutralizes the vacancies in the valence shell during Auger cascade processes in real-time. This approach prevents non-radiative transitions from becoming energetically forbidden, especially when vacancies occur in shells other than the K-shell. Consequently, non-radiative transitions are more likely to occur, leading the number of vacancies to double after each propagation step. This process results in an increased number of emitted electrons, with a preference for an odd number following electron capture process. In contrast, the Auger cascade that follows electron capture and internal conversion tends to favor an even number of emitted electrons. Given that only 17% of decays involve internal conversion, the majority (83%) of decays will thus show an odd number of emitted electrons. This observation supports the stepwise pattern that is seen in the frequency distribution of emitted electrons when using the EADL data library but not present when using outcomes from the McGuire library as illustrated in Figure 8.

There was no significant difference between the two libraries in terms of DNA strand break analysis. Simulations using the McGuire and EADL libraries produced similar dsb yields of 0.60, therefore the choice between the McGuire and EADL libraries has little impact on the final analysis of DNA damage, particularly when considering the limited potential of the low-energy electrons that make up much of the difference between the models to cause critical strand breaks. This finding implies that the DNA damage outcome results are likely to be consistent regardless of which data library is used for simulations of the deposition of Auger electron energy within DNA. Despite the consistency between both data libraries in terms of DNA damage, it is important to use the data library that best represents the atom being simulated. The EADL library is more up to date and therefore includes a higher number of shell transitions, resulting in a greater number of emitted electrons. These additional transitions also create a more realistic electron emission profile, making the EADL library more suitable for accurate and detailed simulations. Notably more pronounced discrepancies may exist for nuclides with different atomic numbers, electron capture, and/or internal conversion yields, potentially leading to different DNA damage outcomes.

To ensure the utmost reliability, the simulations using different track codes were conducted under identical conditions, accounting for the DNA geometry, material, source location, and the electron energies from the EADL library. Figure 7 illustrates the variation in dsb per decay as a function of assumed strand break energy threshold across the different track codes. At thresholds below approximately 10 eV, the dsb yield remains nearly identical across all codes. However, as the energy threshold for breaks increases, the extent of DNA damage begins to diverge between the track structure codes. Among the track structure codes evaluated, MCNP6.2 is the most sensitive, as it provides higher dsb yields for a given energy threshold; PHITS, in contrast, is the least sensitive, demonstrating lower dsb yields under the same conditions. This variation suggests that the 3 electron track structure codes result in different energy deposition clustering local to the decay site. As a consequence, different energy deposition thresholds are required to best replicate the same experimental dsb yields per decay values.

This observation is not surprising since the underlying physical models used in track-structure codes for electron elastic and inelastic cross-sections generally agree well with each other and with experimental data for electron energies above 10 keV. However, at lower energies, discrepancies between different cross-section datasets increase as energy decreases. Some studies indicate that cross-sections down to 100 eV have theoretical uncertainties of 5–10%, which are lower than the 20–40% uncertainties in the experimental data used for validation.^52,53 These uncertainties are comparable to those recommended by ICRU and NIST for electron-stopping powers in the 1–10 keV range. However, at even lower energies, uncertainties rise significantly, with reported inelastic cross-sections for electrons down to 10 eV varying by 20–100% or more.^37,53

To match the experimental value of 0.74 dsb per decay, the corresponding energy thresholds were 22.6, 13.85, and 11.05 eV for MCNP6.2, Geant4, and PHITS, respectively. Given the short range and low energy of Auger electrons, these results can also vary depending on the source location, DNA material, and DNA geometry.

MC track-structure codes such as Geant4-DNA contribute to the validation of radiobiological models by simulating direct and indirect DNA damage mechanisms, supporting the development of relative biological effectiveness (RBE) models for different radionuclides.⁵⁴ Furthermore, MC simulations can assist in the future design of clinical trials when considering the potential of Auger electron emitting radionuclides as theranostic agents.

5 |. CONCLUSION

Ultimately, we contend that our study reveals two important issues in the modeling of DNA damage by Auger electron-emitting radionuclides. First, the EADL library produces a greater number of emitted electrons than the McGuire library due to its higher transition rates in outer shells. However, this discrepancy has minimal impact on DNA damage outcomes since most additional electrons from the EADL library fall below the 17.5 eV threshold necessary for inducing DNA strand breaks. Thus, simulations using either library yield similar DNA damage results, even as the EADL’s more extensive transition data offers a marginally more realistic emission profile. Second, our analysis of MC track codes indicates the need for specific energy thresholds for each code to align with experimental values. This finding underscores the importance of carefully calibrating simulations to the sensitivity of each code, ensuring accurate predictions of DNA damage.

DATA AVAILABILITY STATEMENT

The presented data are summarized in this study. The complete datasets can be retrieved from the authors upon formal request from interested readers.