Erratum: The impact of sensitive volume thickness for silicon on insulator microdosimeters in hadron therapy (Phys. Med. Biol. (2020) 65 (035004) DOI: 10.1088/1361-6560/ab623f)
Physics in Medicine and Biology
The original published paper titled ‘The impact of sensitive volume (SV) thickness for silicon on insulator microdosimeters in hadron therapy’ (Bolst et al 2020), showed the effect which the SV size had on microdosimetric values by means of Monte Carlo simulations. Wehave since discovered that the electron production used in these simulation were 250 keV instead of the stated value of 250 eV in the publication. The electron production is the minimum kinetic energy that a secondary electron must have in order to be produced in the simulation, such as via ionisation. If an ionisation interaction were to occur in the simulation where the secondary electron would have a kinetic energy below the production threshold, then the electron would not be produced/tracked in the simulation. Instead, the electrons kinetic energy that it would have had, is deposited at the point where it would have been generated, instead of transporting the electron in the simulation and depositing energy at multiple positions. The main consequence of the simulation having a higher production value is when a charged particle traverses a detectors SV or its surrounding material. Many of the delta electrons which would have been produced with a kinetic energy of less than 250 keV in the SV would not have deposited all their energy in the volume, instead only a fraction of their energy. This results in the lineal energy values calculated being derived from an energy deposition which is shifted towards the energy lost value (linear energy transfer (LET)). The higher production threshold effects thinner SVs the most, since a thicker volume will have the same amount of energy being artificially deposited, causing smaller SVs to have higher values of lineal energy. In addition to thinner SVs being more strongly effected, lower LET beams (protons in this context) will be more effected due to having an LET much more closer to electrons compared to higher LET beams such as carbon ions. Wesincerely apologise for this error and any confusion that the original results may have caused with the production threshold of 250 keV instead of the stated value of 250 eV. The simulations have consequently been re-run with the more appropriate production threshold of 250 eV, with the updated results/figures provided. For the benefit of the reader, an explanation is provided for each updated figure, describing the reason for the distributions values changing from the original. Despite the updated results shifting from their original values, the general conclusion of the original paper does not change. This being that microdosimetric quantities measured with different sized SVs can greatly vary due to the effects of straggling and the track density (electron production) of the beam and care should be taken when comparing two measurements against one another. However, the specific values have shifted from their original as a result of the updated electron production threshold. Figure 3—shows the lineal energy distributions for H, He andCbeams at depths of 10 and 140mmin water for different thicknesses of SVs. The updated results change fairly subtly from the original, since the spectra mostly shows the primary beams peak, the peak itself will not be strongly changed from the energy lost versus the energy it deposits in the energy range. However, due to extra electrons being produced you can see an increase in the far left of the spectra, where delta electrons enter the SV and deposit energy. Figure 4—plots the width and position of the primary beams peak for the different thicknesses of SVs. These results again remain largely unchanged since the primary beam will deposit a significant portion of the energy in the SV compared to its delta electrons it produces in the SV.that the position of the peaks of the original spectrawere lower than those in figure 3, thiswas due to the silicon to tissue conversion factor being applied twice instead of oncewhen plotting the log binned data, shifting the spectra to lower lineal energies. Figure 6—shows the mean lineal energy, yF, at different depths in water for different thicknesses of SVs/ detectors. The overall trends and cause of the results do not vary significantly, however the lower LET beams (proton and helium) now show a larger dependency on the SV thickness. This is due to so few electrons being produced originally for these beams, making yF being close to LET, especially for protons. Like previous results, the larger SVs have larger values of yF, due to the range of electrons being relatively small, causing the LET of electrons to increase within the SV. As a comparison, a 10, 30 and 125 keV electron will have ranges of~1, 10 and 100 µmin silicon, respectively, with the LET being~4, 2 and 1 keV µm-1. Figure 7—shows the dose mean lineal energy, yD, at different depths in water for different thicknesses of SVs. The updated yD results show noticeable differences with the original, with the original showing higher values with thinner SVs due to electrons below 250 keV, which would have been created in the SV, depositing all their energy in the SV regardless of the thickness, causing thinner volumes to have higher maximum lineal energy values. Since yD is the second moment of the lineal energy distribution divided by yF, it means that the higher lineal energy events contribution will be amplified. Figure 8—compares the yD values of 1 µmthick SVs in proton beams, calculated using different maximum lineal energy values for the spectra. As mentioned above for figure 7, yD will amplify the contribution of higher lineal energy events, which will be artificially higher with a higher electron production threshold. With the updated results lower production threshold, the extent of the higher lineal energy events are reduced, minimising the impact of calculating yD with higher maximum lineal energies. Figure 9—compares the RBE values estimated using theMKmodel. The updated RBE trends are similar to the updated yD, however RBE reduces the fluctuations caused by high lineal energy events, resulting in clearer trends. As with the original yD results, the original RBE results showed a simple trend of the smaller SVs having larger values, for the case of protons this trend still exists for the updated results but for the reasons mentioned for yD, the extent of this is diminished. For the carbon ion beam results however, the updated results show the smaller SVs having smaller values. The reason for these opposite trends of the proton and carbon beams is due to the different densities of delta electrons, with carbon having a much higher number of electrons produced. Lower electron density means higher energy deposition straggling (wider distributions), which when weighting events by lineal energy (yD and RBE) causes the wider distributions to have higher values. Additionally, as mentioned for yF, with the relatively short range of electrons, their LET can increase significantly the further they travel in the SV. The updated helium beam results are a mix between the proton and carbon results, resulting in it being the least sensitive to thickness out of these configurations. Figure 10—shows the yF, yD and RBE values of various different sized volumes for proton beams but considers hits in the detector in terms of if the particle track is a (1) electron or (2) a primary ion track, entering the SV.
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