Microdosimetric measurements of a clinical proton beam with micrometersized solid-state detector

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1 Microdosimetric measurements of a clinical proton beam with micrometersized solid-state detector Sarah E. Anderson a) and Keith M. Furutani Department of Radiation Oncology, Mayo Clinic, Rochester, MN 55902, USA Linh T. Tran, Lachlan Chartier, Marco Petasecca, and Michael Lerch Centre for Medical Radiation Physics, University of Wollongong, Wollongong, NSW 2522, Australia Dale A. Prokopovich and Mark Reinhard Institute of Materials Engineering, Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW 2234, Australia Vladimir L. Perevertaylo SPA-BIT, Kiev 02232, Ukraine Anatoly B. Rosenfeld Centre for Medical Radiation Physics, University of Wollongong, Wollongong, NSW 2522, Australia Michael G. Herman and Chris Beltran Department of Radiation Oncology, Mayo Clinic, Rochester, MN 55902, USA (Received 30 March 2017; revised 9 August 2017; accepted for publication 18 August 2017; published 13 October 2017) Purpose: Microdosimetry is a vital tool for assessing the microscopic patterns of energy deposition by radiation, which ultimately govern biological effect. Solid-state, silicon-on-insulator microdosimeters offer an approach for making microdosimetric measurements with high spatial resolution (on the order of tens of micrometers). These high-resolution, solid-state microdosimeters may therefore play a useful role in characterizing proton radiotherapy fields, particularly for making highly resolved measurements within the Bragg peak region. In this work, we obtain microdosimetric measurements with a solid-state microdosimeter (MicroPlus probe) in a clinical, spot-scanning proton beam of small spot size. Methods: The MicroPlus probe had a 3D single sensitive volume on top of silicon oxide. The sensitive volume had an active cross-sectional area of 250 lm 9 10 lm and thickness of 10 lm. The proton facility was a synchrotron-based, spot-scanning system with small spot size (r 2 mm). We performed measurements with the clinical beam current (1 na) and had no detected pulse pile-up. Measurements were made in a water-equivalent phantom in water-equivalent depth (WED) increments of 0.25 mm or 1.0 mm along pristine Bragg peaks of energies 71.3 MeV and MeV, respectively. For each depth, we measured lineal energy distributions and then calculated the dose-weighted mean lineal energy, y D. The measurements were repeated for two field sizes: 4 9 4cm 2 and cm 2. Results: For both 71.3 MeV and MeV and for both field sizes, y D increased with depth toward the distal edge of the Bragg peak, a result consistent with Monte Carlo calculations and measurements performed elsewhere. For the 71.3 MeV, 4 9 4cm 2 beam (range at 80% distal falloff, R 80 = 3.99 cm), we measured y D ¼ 1:96 0:08 kev/lm at WED = 2 cm, and y D ¼ 10:6 0:32 kev/lm at WED = 3.95 cm. For the 71.3 MeV, cm 2 beam, we measured y D ¼ 2:46 0:12 kev/lm at WED = 2.6 cm, and y D ¼ 11:0 0:24 kev/lm at WED = 3 cm. For the MeV, 4 9 4cm 2 beam (R 80 = 17.7 cm), y D ¼ 2:24 0:15 kev/lm at WED = 5 cm, and y D ¼ 8:99 0:71 kev/lm at WED = 17.6 cm. For the MeV, cm 2 beam, y D ¼ 2:56 0:10 kev/lm atwed= 5 cm, and y D ¼ 9:24 0:73 kev/lm at WED = 17.6 cm. Conclusions: We performed microdosimetric measurements with a novel solid-state, silicon-oninsulator microdosimeter in a clinical spot-scanning proton beam of small spot size and unmodified beam current. For all of the proton field sizes and energies considered, the measurements of y D were in agreement with expected trends. Furthermore, we obtained measurements with a spatial resolution of 10 lm in the beam direction. This spatial resolution greatly exceeded that possible with a conventional gaseous tissue-equivalent proportional counter and allowed us to perform a high-resolution investigation within the Bragg peak region. The MicroPlus probe is therefore suitable for applications in proton radiotherapy American Association of Physicists in Medicine [ /mp.12583] Key words: LET, microdosimetry, proton trapy 6029 Med. Phys. 44 (11), November /2017/44(11)/6029/ American Association of Physicists in Medicine 6029

2 6030 Anderson et al.: Solid-state microdosimetry of a proton beam INTRODUCTION The biological effects of radiation on cells depend on microscopic patterns of energy deposition within the cells. An understanding of the relationship between energy deposition and biological effect is important in the field of radiotherapy, where it is desired to deliver a lethal dose to tumor while sparing normal tissue. The field of microdosimetry offers methods for measuring energy deposition patterns in volumes that mimic cell sizes, allowing correlation of the deposition pattern with biological effects. The traditional method for measuring microdosimetric quantities uses a gaseous tissueequivalent proportional counter (TEPC). 1 4 Limitations of the TEPC approach to microdosimetry, however, include the high voltage and gas system needed for operation of the device as well as its low spatial resolution. In contrast, solidstate microdosimeters have recently been developed at the Centre for Medical Radiation Physics (CMRP), Australia, that offer advantages over TEPCs in microdosimetric measurements. 5,6 These solid-state microdosimeters consist of silicon sensitive volumes with dimensions on the order of 10 lm and require no high voltage or gas system for operation. With micron-sized spatial resolution, these solid-state microdosimeters are suitable for making highly resolved microdosimetric measurements within radiation fields used for radiotherapy. Microdosimetric detectors measure the quantity lineal energy. Lineal energy is a stochastic quantity defined as y ¼ e=l, where ɛ is the energy deposited in a microscopic (size scale of a cell) site by a single event (particle track), and l is the mean chord length of the site. For microdosimetric detectors, the site of interest is the sensitive volume of the detector. By measuring the lineal energy spectrum for a large number of events, one obtains a probability distribution of lineal energy. The probability distribution can then be used to calculate the average value of dose-weighted mean lineal energy, 7 y D. This quantity is analogous, while not always equal, to the macroscopic quantity dose-weighted linear energy transfer, 8 LET d. The quantities LET and y D are generally expected to exhibit similar trends. However, y D is tied to a biologically relevant (cell or cell nucleus) size scale and is potentially a better predictor of the radiobiological effect of radiation. For clinical proton beams, the y D values are known to increase towards the distal end of the beam range; this variation in y D has implications for biological effects in patients undergoing proton beam therapy. 9 y D is therefore a relevant and vital quantity to characterize. A high-resolution, solidstate microdosimer could thus be valuable in investigating variations in y D in proton radiotherapy fields. In this paper, we examine a solid-state microdosimeter developed and fabricated at CMRP, named the MicroPlus probe, in a clinical proton beam. The proton beam is a spotscanning beam operated with small (r 2 mm) spot size and at the clinical beam current. To the best of our knowledge, this work provides the first demonstration of this device in such a proton beam. Using the MicroPlus probe, we perform measurements of lineal energy distributions and associated y D as a function of water-equivalent depth for several single-energy fields. Depth increments for the measurements are between 0.25 and 1.0 mm, thus allowing measurements in the distal Bragg peak with high spatial resolution. We investigate the dependence of the MicroPlus probe response on field size and beam energy. 2. MATERIALS AND METHODS 2.A. MicroPlus probe detector and pulse-processing electronics The MicroPlus probe detector was developed at CMRP at the University of Wollongong, Australia. 6 It contains several microdosimeter detectors with different-sized sensitive volumes (SVs) that can be selected independently. The MicroPlus probe is fabricated using silicon-on-insulator wafers with 10 lm thick silicon active volume. Each microdosimeter detector is fabricated using 3D-mesa technology and has a silicon substrate of area 0.6 mm mm with a single, silicon 3D SV of rectangular-parallel piped shape on top of silicon oxide. The p+ and n+ regions of the single 3D SV are electrically connected to contact pads using 1 lm thick Al connectors placed on top of a passive silicon bridge. Further details about CMRP bridge microdosimeter technology with an array of 3D SVs can be found in Ref. [12]. The cross-sectional areas of the independently selectable single SVs in the MicroPlus probe have a width 10 lm and lengths that range lm. The SVs, fabricated on the same wafer, are diced and wire bonded to a DIL 20 chip package; this is shown in Fig. 1(a). In Fig. 1(b), we show the MicroPlus probe within a waterproof PMMA sheath. The microdosimeter detector, with the 3D SVs, is located at the tip of the probe. The desired SV can be selected via jumpers located on the probe. The SV selected for use in this work has an active cross-sectional area of 250 lm 9 10 lm. It is operated with a bias voltage of +3 V. As protons pass through the SV in the MicroPlus probe, energy is deposited by the protons, and this results in electron-hole pairs that are subsequently collected by electrodes. The height of the output pulse is proportional to the energy deposited by the protons in the SV. The output pulse from the SV is processed by low noise front-end electronics on Micro- Plus probe [Fig. 1(b)], followed by a pulse-shaping amplifier and a multi-channel analyzer (MCA). The MCA measures the pulse heights, bins them into channels, and provides a histogram of pulse heights. In this work, the MCA settings were such that 4096 channels spanned a 0 1 V range. A lower level discriminator voltage threshold was set (at channel 100) to eliminate lowenergy background noise. To eliminate stray RF interference in the detector, the probe was placed in a waterproof PMMA sheath wrapped in Al foil tape to act as a Faraday cage. A small opening in the Al foil over the sensitive region of the detector allowed the protons to pass through unaffected for detection. Calibration of MCA channel number to energy was performed using a calibrated pulse generator. The pulse

3 6031 Anderson et al.: Solid-state microdosimetry of a proton beam 6031 FIG. 1. (a) Close-up view of sensitive volumes, which vary in cross-sectional area and are independently selectable, in the MicroPlus microdosimeter. (b) MicroPlus probe in PMMA sheath, with active area from (a) indicated by black lines. (c) Experimental setup for microdosimetric measurements in a clinical spotscanning proton beam. [Color figure can be viewed at wileyonlinelibrary.com] generator was calibrated to a 300 lm thick planar, silicon, fully depleted PIN diode in response to MeV alpha particles from an Am-241 source.12 This calibration approach was facilitated by the linear response of the MicroPlus probe. The linearity of the response of the device was verified using different types of ions, including protons and He ions.11 In these tests, charge collection was studied using microbeams of 2 MeV protons (LET in Si of approximately kev/ and 5.5 MeV He2+ ions (LET in Si of approximately kev/. The peak of the deposited energy distribution in the 10 lm thick detector was 245 kev and 1400 kev for the 2 MeV protons and 5.5 MeV He2+ ions, respectively. These values were close to the expected energy deposition of 270 kev and 1480 kev for 2 MeV protons and 5.5 MeV He2+ in a 10 lm active silicon layer, as calculated by a Geant4 simulation toolkit. Thus, the MicroPlus probe exhibited a linear response over a wide range of LET values. In addition to Am-241, the calibration was verified using two distinct photopeaks (at 22 and 27 kev) of an I-125 gamma source. Since the expected energy deposited in the detector for I-125 corresponded to the LET of protons in the entrance region of the Bragg peak, this allowed for accurate measurements of the plateau region of the Bragg peak. The range of yd that could be measured with the MicroPlus probe in this work was kev/lm. However, it should be noted that if the MCA was changed to a larger range setting, then the range of lineal energy that could be measured would be extended. In other work with the MicroPlus probe performed at heavy ion facilities, the device measured the distal edge of the carbon ion Bragg peak,12 where LET can be as high as 1000 kev/lm. The dose delivered to the detector in this work ranged from 1.5 Gy at the entrance to 6 Gy at the Bragg peak. To examine the radiation hardness of the device, a separate experiment was performed in which leakage current was monitored during irradiation and alpha spectroscopy was taken after the irradiation. No significant change in terms of the charge collection was observed for this device after applying proton doses in the range of those used for this experiment. 2.B. Proton facility and experimental setup The measurements were performed in patient treatment rooms at the proton beam facility at Mayo Clinic, Rochester, MN. The Mayo proton facility is a synchrotron-based, pencil beam scanning system with small spot size (r 2 mm). The microdosimetric measurements were taken with the synchrotron operating at the clinical current of 1 na. The experimental setup for microdosimetry is depicted in Fig. 1 (c). The MicroPlus probe was placed in a water-equivalent (PMMA) phantom at a distance of 60 cm from the end of the gantry nozzle. The nozzle of the proton gantry pointed vertically downward, and the proton beam was incident perpendicular to the plane of the detector. The proton fields had energies of 71.3 MeV or MeV and had field sizes of cm2 or cm2. The proton spot spacing within each field was 3 mm. Data as a function of depth along pristine Bragg peaks were obtained by varying the water-equivalent thickness of PMMA sheets placed over the detector. Water-equivalent depth (WED) increments were 0.25 mm in the Bragg peak region for the 71.3 MeV measurements and 1 mm for MeV. The step sizes were achieved through combinations of PMMA sheets with thicknesses 1, 1.5, 1.75, 2, 5, 10, 20, and 50 mm. Range shifters placed in the nozzle of the gantry ensured that there was no pulse pile-up in the MicroPlus probe. Pulse pile-up would occur within the MicroPlus probe if multiple

4 6032 Anderson et al.: Solid-state microdosimetry of a proton beam 6032 events arrived within a time interval that was smaller than the time-resolution of the device. The height of the resultant output pulse would, in this case, be artificially high. For our spot-scanning proton facility, the addition of the range shifters effectively increased the spot size at the detector, which thereby decreased the instantaneous particle fluence rate. Decreasing the instantaneous particle rate ensured that there were no particles overlapping in time within the SV of the detector, which would result in an artificially large measurement of lineal energy. We used a 2.5 cm range shifter for the 71.3 MeV beam and a 4.5 cm range shifter for the MeV beam. The range shifters are also used in some clinical treatments. To verify that there was no detector pile-up under these conditions, we made measurements with the MicroPlus probe as a function of distance from the nozzle. As distance from the nozzle increased, the spot size also increased; this, in turn, decreased the particle rate. If there were pile-up in the detector, we would expect that the measured values of y D would decrease with distance from the nozzle, since there would be fewer particles overlapping in time. We took measurements of y D at several distances ranging from 60 cm to 2 m from the source. The particle rate over this range decreased by a factor of 10. Throughout this range, the variation in measurements of y D was minimal. We thus concluded that there was no pile-up. Therefore, we will only report data in this work for the nominal distance. Due to the absence of pile-up and the linearity of the MicroPlus probe, correction to our measurement results for pile-up or recombination effects was not necessary. 2.C. Data analysis The calibrated output of the MCA yields a plot of number of events on the y-axis versus energy deposited on the x-axis. For each measurement, this graph thus displays the spectrum of events. To determine microdosimetric quantities from this output, we first convert the x-axis to lineal energy. As mentioned, lineal energy is defined as y ¼ e=l, where ɛ is the energy deposited in the SV of the detector and l is the mean chord length of the volume. For the MicroPlus probe, we assume that all protons have straight trajectories passing perpendicularly through the SV, and the mean path length is thus 10 lm in silicon. However, since we are ultimately interested in quantities relevant to human tissue, we use the mean path length in tissue. The corresponding tissueequivalent mean path length was determined by Monte Carlotobe 13, lm. In the simulation, energy deposition was calculated in the silicon SV exposed to a 150 MeV proton beam radiation field along the Bragg peak. The energy deposition distribution was then calculated again in the same radiation field with tissue-equivalent material filling the SV. The size of the tissue-equivalent volume was varied to obtain the same energy deposition spectrum as the one obtained in silicon SV, and a silicon-tissue scaling factor was obtained. A detailed description of this method can be found in Ref. [14]. By dividing energy on the x-axis of the MCA output by the tissue-equivalent mean chord length, we obtain lineal energy on the x-axis. Normalizing the area under the curve gives a probability distribution of lineal energy, fðþvs. y y. The probability distribution can then be used to calculate the microdosimetric quantities of frequency-weighted mean lineal energy, y F ¼ R 1 0 yfðþdy, y and dose-weighted mean R lineal energy, 1,7 y D ¼ y 1 1 F 0 y 2 fðþdy. y Note that y D ¼ \y2 [ \y[ is a measure of the second moment of the deposited energy spectrum over the first moment 15 and that the second moment is directly related to the relative variance: r 2 y \y[ ¼ \y2 [ 2 \y[ 1: 2 In this work, we determined y D from the measured microdosimetric spectra as a function of depth. For display of the microdosimetric distribution, we plotted the microdosimetric spectra using the standard representation of ydðþvs. y logðþ, y where the dose-weighted probability distribution is dðyþ ¼ yf ðyþ=y F : 2.D. Calculation of dose-weighted linear energy transfer and depth dose For comparison with our measured y D, we calculated values of LET d as a function of depth in the same proton fields used for measurements. While quantities of y D and LET d are analogous, they are not equal, and the comparison is thus not exact. However, as is established practice elsewhere, 3,8 LET d and y D can be used as surrogates for one another. We therefore used LET d, calculated via Monte Carlo simulation, as a surrogate for studying expected trends of y D.Wediscuss the relationship between y D and LET d in the Discussion section below. In addition to LET d, we calculated depth dose curves via Monte Carlo simulation for each proton field to display with the measured data, to give an indication of the Bragg peak location. The physical dose deposition and LET d were simulated using an in-house code (Ref. [16]). The simulation was done with 1 mm 3 voxels, 100 million protons per field, and with the same setup that was used experimentally. A comparison of LET d as calculated by the in-house system and Geant4 has been previously published (Ref. [17]). 3. RESULTS 3.A. Results for the 71.3 MeV proton beam Experimental results for the 71.3 MeV proton beam are displayed in Fig. 2 and Table I for field sizes of 4 9 4cm 2 and cm 2. In Figs. 2(a) and 2(b), we graph the measured y D (diamonds) as a function of depth for field sizes of 4 9 4cm 2 and cm 2, respectively. For comparison, we show the calculated values of LET d (solid lines). We include the calculated depth dose curves (dotted lines) for reference; the range of this beam at 80% distal falloff, R 80,is 3.99 cm.

5 6033 Anderson et al.: Solid-state microdosimetry of a proton beam 6033 FIG. 2. Results for a 71.3 MeV proton beam with field sizes of 4 9 4cm 2 (a), (c) and cm 2 (b), (d). (a), (b): Measured values of dose-weighted lineal energy (diamonds), calculated values of LET d (solid lines), and calculated depth dose (dotted lines). Horizontal bars represent positional uncertainties in depth; vertical bars, statistical (1r) and y D -calculation uncertainties. (c), (d): Microdosimetric spectra at selected depths for measurements shown on top. [Color figure can be viewed at wileyonlinelibrary.com] For both field sizes in Figs. 2(a) and 2(b), we observe that the values of y D increase rapidly towards the distal edge of the Bragg peak. The y D values in the entrance region in both TABLE I. Measurement results for y D with associated statistical and y D -calculation uncertainties as a function of depth for the 71.3 MeV proton beam. Calculated LET d is shown for comparison. Depth (cm) LET d 4 9 4cm cm 2 y D Stat. Calc. LET d y D Stat. Calc cases are 2 kev/lm and increase to 12 kev/lm at4cm depth. Furthermore, we observe that the y D values in both cases are generally in agreement with the trends observed for calculated LET d. For the cm 2 field size in Fig. 2(b), we observe a bump in the y D values at 3 cm depth that is not seen for the 4 9 4cm 2 field size. The results for y D are presented numerically in Table I. Horizontal and vertical bars are present for each point in Fig. 2, although not all are large enough to be discernable. Numerical values for the uncertainties are listed in Table I. Vertical bars represent statistical and calculation uncertainties added in quadrature. The statistical uncertainties are a standard deviation of measurements. For the 4 9 4cm 2 field,weperformedbetween2and4measurements at each depth. For the cm 2 field, only one measurement was possible for most of the data points, due to time constraints with running a large field. Depths with multiple measurements have statistical uncertainties indicated in Table I. They D -calculation uncertainties are determined by propagation following the uncertainty in the number of counts. Horizontal uncertainties results from positional uncertainty in depth, due to variations in beam energy. The positional uncertainty was 0.1 mm for all cases. In Figs. 2(c) and 2(d), we show microdosimetric spectra for selected depths that correspond to measurements in (a) and (b), respectively. For both field sizes, we observe that the microdosimetric spectra generally shift to larger values of y as depth increases. For the cm 2 field size, we observe a high-y shoulder in the spectrum (y values 4 11 kev/ for depths near 3 cm, which gives the bump in y D at 3 cm depth.

6 6034 Anderson et al.: Solid-state microdosimetry of a proton beam B. Results for the MeV proton beam Experimental results for the MeV proton beam are displayed Fig. 3 and Table II for field sizes of 4 9 4cm 2 and cm 2. In Figs. 3(a) and 3(b), we present the measured values of y D (diamonds) as a function of depth for field sizes of 4 9 4cm 2 and cm 2, respectively. For comparison, we again show calculated values of LET d (solid lines) and depth dose (dotted lines; for this beam, R 80 = 17.4 cm). For both field sizes, we observe that the values of y D increase rapidly towards the distal edge of the Bragg peak. The y D values increase from 2.2 kev/lm in the entrance region to 9 kev/lm at 17.5 cm depth. Horizontal and vertical bars are again present for every point and represent positional uncertainties (horizontal) and statistical and y D -calculation uncertainties (vertical). The uncertainties here are calculated as in Fig. 2. The results for y D are presented numerically in Table II along with the associated statistical and calculation uncertainties. In Figs. 3(c) and 3(d), we plot microdosimetric spectra for selected depths that correspond to measurements on top. For both field sizes, the microdosimetric spectra again shift to larger values of y as depth increases. 4. DISCUSSION The microdosimetric spectra and y D values measured with the MicroPlus probe are in agreement with expected trends for both energies and field sizes. For all cases considered, the measured microdosimetric spectra shift to higher values of lineal energy with increasing depth. The shift of the spectra to higher lineal energies is expected towards the end of the proton range, where the protons deposit more energy in the TABLE II. Measurement results for y D with associated statistical and calculation uncertainties as a function of depth for the MeV proton beam. Calculated LET d is shown for comparison. Depth (cm) LET d 4 9 4cm cm 2 y D Stat. Calc. LET d y D Stat. Calc SV. It is also consistent with microdosimetric spectral trends observed for TEPCs in clinical proton beams. 3,18 21 Similarly, the behavior of measured y D values is in close agreement with trends expected from the calculated LET d. The y D and LET d values for all cases exhibit a sharp increase at depths FIG. 3. Results for a MeV proton beam with field sizes of 4 9 4cm 2 (a), (c) and cm 2 (b), (d). (a), (b): Measured values of dose-weighted lineal energy (diamonds), calculated values of LET d (solid lines), and calculated depth dose (dotted lines). Horizontal bars represent positional uncertainties in depth; vertical bars, statistical (1r) and y D -calculation uncertainties. (c), (d): Microdosimetric spectra at selected depths for measurements shown on top. [Color figure can be viewed at wileyonlinelibrary.com]

7 6035 Anderson et al.: Solid-state microdosimetry of a proton beam 6035 corresponding to the distal edge of the Bragg peak. Differences between y D and LET d values, for example, in the entrance region of the MeV proton beam, can be understood by considering the fundamental differences between those quantities, which will be discussed below. Towards the distal edge of the Bragg peak in our results for the 71.3 MeV and MeV fields, the values of y D appear to approach a limit, while the values of LET d appear to continue increasing dramatically. This trend is expected. The experimentally measured values of y D have a cutoff on the distal edge, since a certain amount of energy must be deposited in the detector to be measureable above noise. In contrast, the calculated values of LET d do not have a similar constraint. The calculated values can continue to increase dramatically with LET although the dose associated with those particles is essentially zero. Analyzing our results as a function of field size, we observe that the y D values at a given depth are larger for the cm 2 fields than for the 4 9 4cm 2 fields. For the 71.3 MeV beam, the y D values are on average 12% larger for the cm 2 field. For the MeV beam, the y D values are on average 9% larger. This trend may be due to a larger number of oblique proton tracks though the SV for the larger field size. Such oblique tracks are not taken into account in the calculation of mean chord length for this case of a directed proton beam, 14 and hence, the calculated y D would be larger in the presence of oblique tracks. Also, for the 71.3 MeV beam with field size of cm 2, we see a bump in y D values at 3 cm depth that is not observed for the 4 9 4cm 2 field, nor for either of the MeV fields. The higher y D value at 3 cm depth is corroborated by the high-y shoulder in the lineal energy spectrum in Fig. 2(d). The underlying reason for these trends with field size warrants further investigation, but the measurement results have been repeatedly verified. Fundamentally, LET is a calculated quantity that describes energy lost by a particle within a given volume, and y is a measureable quantity that describes the energy imparted in the sensitive volume. The relationship between the two depends on how d-rays are included in the volume of interest. 22,23 For example, in cases where the range of the d-rays is less than or equal to the voxel size for y, LET and y have very similar values. Towards the distal part of the MeV Bragg peak, the range of the d-rays is similar to the voxel size for y; we observe that the values of LET d and are in close agreement. In the entrance region of the MeV beam, the range of the d-rays exceeds the voxel size, and we observe greater differences between the two quantities. Furthermore, since the relationship between LET d and y D depends on the range of d-rays with respect to the volume of interest, these two quantities depend on the size of the volume under consideration. LET d is typically calculated in voxel sizes of 1 mm, while y D is typically determined in volumes of 1 lm. This discrepancy in voxel size can also result in differences between the two quantities. The fact that the quantities of LET d and y D depend on the size of the volume under consideration has been well established. Lindborg et al. reported that, for proton beams of energy MeV, calculated y D values decreased as the voxel size increased from a few nm to a few lm. Furthermore, they found that the values of y D approached the unrestricted LET values for voxel sizes on the order of lm s. 23 Cortes-Giraldo and Carabe performed Monte Carlo calculations of LET d in 160 MeV proton beams and found that the calculated values of LET d in the plateau region increased as the voxel size decreased from 2 mm to 0.2 mm (by an amount dependent on the calculation method of LET d ). 24 Our results in the entrance region of the MeV beam are consistent with this published literature. Our values of y D in this region, measured in a volume of size 20 lm, are larger than the LET d values, which were calculated with a voxel size of 2 mm. If the voxel sizes were to approach each other, we would expect the values of LET d to increase, the y D values to decrease, and the quantities to thus also approach one another. Liamsuwan et al. similarly found in Monte Carlo calculations of a 160 MeV proton beam that the calculated values of y D for targets of sizes 10 nm and 100 nm were larger than the LET d values. The y D values for the 100 nm target were closer to the LET d values (approximately four times larger in the entrance region) than the smaller target size (approximately 10 times larger). 25 Quantitatively, the relationship between y D and LET d has been derived and discussed in detail by Kellerer. 15 For a spherical volume, he derives the relationship, y D ¼ 9 8 LET d þ 3d 2 2d. Here, the quantity d 2 is the weighted average of the energy imparted per collision of the traversing charged particle, and d is the diameter of the volume. For a planar volume, such as the MicroPlus probe, the relationship becomes y D ¼ LET d þ d 2 l, where l is the mean chord length of the volume. When the range of the d-rays is comparable to the size of the volume of interest, the effect of the d-rays (d 2 ) disappears, and y D and LET d are comparable in value. Comparing LET d and y D, the quantity that is more appropriate for describing clinical proton beams depends on the situation under consideration. LET and y describe energy lost and energy imparted, respectively. LET is widely used for quantifying the quality of the proton beam. It is a mean quantity; however, for biological effects at the microscopic l, stochastic quantities such as y become important. The value of y D is tied to a size scale of biological regions of interest and may be a better predictor of biological effect. In contrast to LET, y is a measureable quantity. Additionally, in some cases, the microdosimetric spectrum, and not y D, may be the most appropriate quantifier. For further discussion, see Ref. [22]. Measurements of y D of clinical proton beams that are found in the literature are usually measured with gaseous TEPCs, which serve as the gold standard in microdosimetric measurements. TEPCs typically have spherical volumes of 1 cm diameter and contain a low-density gas that simulates volumes with diameters on the order of 1 lm. Due to their centimeter-scale size, TEPC measurements in clinical proton beams are limited in spatial resolution in comparison to pristine Bragg peak widths (1 5 mm). The body of literature presenting high-resolution measurements within the Bragg peak is therefore also limited. Kliauga et al. measured y D in

8 6036 Anderson et al.: Solid-state microdosimetry of a proton beam MeV SOBPs and pristine peaks with a TEPC of 0.64 cm diameter simulating a 1 lm site. The measured values of y D increased from 4.5 kev/lm in the plateau region to 8.49 kev/lm at the pristine peak. 4 Kase et al. employed a TEPC with 12.7 mm diameter simulating a volume of 1 lm diameter to measure a 155 MeV pristine peak. The measured values of y D increased from 3.5 kev/lm in the entrance region to 11 kev/lm at the peak. 18 Cosgrove et al. used a planar TEPC of 3 cm thickness to measure y D in a 62 MeV proton beam and found y D to increase from 2.33 kev/lm in the plateau region to kev/lm at the peak. 20 Coutrakon et al. used a 0.5 cm diameter TEPC simulating a site of 1 lm diameter to measure SOBPs of energies ranging MeV. For 155 MeV the measured values of y D increased from kev/lm in the entrance region to kev/lm in the center of the SOBP. Notably, the authors pointed out the need for measurements with finer resolution within the distal edge of the Bragg peak. 3 Borak et al. performed measurements of proton beams of pristine energies using a TEPC of 1 mm diameter simulating a volume of 3 lm. The measured y D values increased from 1.39 kev/lm for172mevto 2.59 kev/lm for 47 MeV. 26 Due to the spatial limitations of the conventional TEPC, mini-tepcs have been developed. Rollet et al. used a cylindrical mini-tepc of 1 mm dimensions to simulate a volume of 1 lm diameter. Measurements within a 62 MeV proton beam demonstrated y D to increase from 10 kev/lm within the SOBP to 22 kev/lm at the 50% distal fall-off. 19 As for Monte Carlo calculations of y D in clinical proton beams, Liamsuwan et al. calculated y D values in a pristine 160 MeV beam for cylindrical sites of varying sizes. For a site diameter of 100 nm, the y D values increased from 6.7 kev/lm in the plateau region to 9.7 kev/lm near the Bragg peak. 25 Since the measurements of y D found in the literature differ from our experimental conditions in terms of SV size and spatial resolution, there is not an exact one-toone correlation with which we can compare our results. Even so, our values are within the reported range. The limited spatial resolution of the TEPC in comparison to narrow Bragg peaks, and the corresponding limited body of high-resolution measurements within the Bragg peak found in the literature, illustrates why the MicroPlus probe offers a valuable approach for microdosimetric measurements in clinical proton beams. In addition to solid-state microdosimeters and tissue equivalent proportional counters, there are other detectors that have been used to perform measurements of LET, such as OSLDs 27 and Fluorescent Nuclear Track detectors, 28 for example. These detectors have an LET-dependent response that can be calibrated to a known LET and then employed for LET measurements. These detectors do not, however, perform fundamental measurements of lineal energy, as with solid-state microdosimeters or tissue equivalent proportional counters. The MicroPlus probe microdosimeter provided microdosimetric measurements of clinical proton beams of different energies and field sizes with results being in agreement with expected trends. Notably, these measurements were performed with high spatial resolution within narrow Bragg peaks. The MicroPlus probe had a spatial resolution of 10 lm in the beam direction, and we performed measurements with step sizes ranging mm in the region of the Bragg peaks. We have therefore been able to obtain microdosimetric measurements of a region that has previously been difficult to measure because of the stringent requirements on spatial resolution. The Bragg peak is a critical region to characterize because of implications for biological effects. Since the detector is on the size scale of relevant biological targets, the MicroPlus probe can be used for correlation with cell or animal studies. 5. CONCLUSION We presented lineal energy distributions and corresponding microdosimetric quantities measured with a solid-state MicroPlus probe microdosimeter in a clinical, spot-scanning proton beam. We investigated the MicroPlus probe response as a function of depth along pristine Bragg peaks for varying field sizes and beam energies. The results were in agreement with expectation, showing a sharp increase in y D at the distal edge of the Bragg peak, and were consistent with calculated LET d. The MicroPlus probe, with sensitive volume dimensions of 10 lm in the beam direction, therefore, allowed high-spatial resolution measurements of y D at the distal edge of the Bragg peak. 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