TY - JOUR
AB - Abstract The measurement of single-track intensity in fluorescence nuclear track detectors can yield relative linear energy transfer (LET)-spectra with small line-width. The absolute determination of LET is, however, currently hampered by the inter-detector variability of crystal coloration and hence detector sensitivity. We therefore investigated the LET response of three additional quantities (average width and the variation of intensity and width along single tracks) using detectors irradiated with mono-energetic ion beams with LETs from 1.5 to 150 keV/μm in alumina. All quantities showed in fact smaller inter-detector variability, but at the same time larger line-width and limited dynamic range as the average intensity along a track. The additional quantities might therefore serve as a helpful complement, but not as a replacement for the current approach. INTRODUCTION Beams of protons and heavier, mostly carbon ions are increasingly used for therapy of malignant tumors(1). Besides absorbed dose, the ionization density of these particles determines their effect on tissue. This ionization density is usually characterized by the energy loss dE per unit path length dz, i.e. the electronic stopping power or—equivalent in this context—the unrestricted linear energy transfer (LET) L=dE/dz(2). L depends both on the kinetic energy T and the charge Z of a particle. Due to slowing-down, energy straggling and inelastic nuclear scattering of the primary ions, a complex particle- and energy-, and consequently LET-spectrum ΦL=dΦ(L)/dL inevitably emerges when the beam traverses material or tissue. Fluorescence nuclear track detectors (FNTDs) together with confocal laser scanning microscopy allow characterizing the fluence ΦL with respect to the particles’ LET(3, 4) similar to track-etch plastic detectors (PNTDs)(5). In addition, FNTDs are sensitive to low-LET particles down to LAl2O3≈0.2keV/μm(6) and hence a significant part of ΦL in proton and ion beam therapy not recorded by common PNTDs. While the fluence is determined via the particle area-density or equivalent measures, the LET can be estimated by the average fluorescence intensity of ‘trackspots’, i.e. the ion’s footprints in one or multiple images, along a track(8, 7). However, current alumina-based detectors are subject to considerable fluctuation in coloration (color center concentration) between individual detectors(9) which directly influences LET estimation. In this study, we therefore investigated additional LET-dependent quantities that can be derived from ion-track analysis in FNTDs with a dedicated focus on their inter-detector variability. MATERIALS AND METHODS Detectors Aluminum-oxide single crystals doped with carbon and magnesium (Al2O3:C,Mg) exhibit a high concentration of complex F22+ (2 Mg) color centers that undergo radiochromatic transformation into F2+ (2 Mg) centers when exposed to ionizing radiation. The number of centers transformed depends on the local energy deposition and the centers available. The F2+ (2 Mg) centers show high quantum-yield intra-center fluorescence at 750 nm when excited around 620 nm with a short life-time of 75 ± 5 ns. This allows for the use of confocal laser scanning microscopy to assess 3D energy deposition patterns with μm-resolution and reconstruction of single ion tracks and their energy loss(3, 4). All detectors used in this study were produced by the Crystal Growth Division of Landauer Inc. (Stillwater, OK, USA), cut along the optical C-axis into small rectangular plates (4.0 × 8.0 × 0.5 mm3) and polished on one of their large sides to optical quality. Irradiation and read-out The same set of 66 detectors as used in(4) was investigated. In brief, the detectors had been irradiated with mono-energetic beams of four different ion types (protons, helium, carbon, oxygen) at 22 LET-levels ranging from ~1.5 to 150 keV/μm in alumina at the Heidelberg Ion Beam Therapy Center (HIT). In contrast to the previous study, the detectors were read-out using a Landauer FXR700RG reader—a research version of the commercial system(10) with 2D scanning and allowing for high sample throughput. Per sample, 2 × 2 frames (image stacks) of 100 × 100 μm2 (504 × 504 pixel) were acquired with 21 slices in depth (0–100 μm in 5 m steps). The first slice was discarded routinely prior to analysis due to image artifacts at the detector surface. Image processing and data analysis A histogram-based routine from the Mosaic ToolSuite for ImageJ(11) was used for background subtraction, and a refined version of the Mosaic feature point extraction algorithm(12, 13) subsequently employed to identify ion tracks. In total, more than 1 000 000 trackspots corresponding to 50 000 tracks were analyzed. For each trackspot, the fluorescence intensity η of the trackspots was evaluated as the maximum Iˆ of pixel intensities I(x,y) within a six pixel radius, using local coordinates x and y with respect to the trackspot center as found by the track identification tool. In addition, the width w was quantified as the average of the second intensity-weighted central moments in x and y, i.e. w=1/2⋅[m02+m20]. The latter are defined as mpq=∑x∑y(x−M10M00)⋅(y−M01M00)⋅I(x,y) with Mpq=∑x∑yxp⋅yq⋅I(x,y).This procedure proved to yield more robust results than fitting a Gaussian model function. Corrections for sensitivity-fluctuation across the detector area, spherical aberration, field-of-view non-uniformity and angular dependence of the fluorescence intensity were applied as described in(14). Four quantities were then derived for each track with i=1,⋯,N trackspots:(4) 1. The average fluorescence intensity along a track: η¯=1/N∑iηi (1) 2. The variation of fluorescence intensity along a track, expressed as coefficient of variation (CV), i.e. the standard deviation over the average (cf.(4)): σˆη=1/N∑i(ηi−η¯)2/η¯ (2) 3. The average width w¯, analogously to Equation (1). 4. The variation in width σˆw, analogously to Equation (2). Due to their definition, quantities in 2–4 are expected to be less dependent on crystal coloration. For each of the above quantities, the response with respect to LET was evaluated. To this end, each quantity η¯, σˆη, w¯ and σˆw was averaged across the ~100–200 tracks per frame, four frames per sample, and three samples per LET level. In addition, the line-width λl for each quantity was evaluated as the relative standard deviation of single-track values within frames averaged within an LET level l, as well as the inter-detector variation σˆD,l as the relative standard deviation of the average across samples within one LET level. σˆD,l was not corrected for the influence of intra-detector and intra-image variation (i.e. between frames and between tracks within a frame). Intra-detector variation proved to be small compared to σˆD,l (~4% in the case of η¯(4)) and is further minimized by the above mentioned sensitivity-fluctuation correction. The impact of the uncertainty from intra-image variation on σˆD,l was assumed to be small due to the large number of tracks per frame. RESULTS AND DISCUSSION Figure 1 shows the LET response of the four track-quantities investigated. Each quantity, not only the average fluorescence intensity, exhibits a clear dependence on LET while no obvious influence of particle type was found. Figure 1. View largeDownload slide LET response of the four quantities describing average intensity and width and their respective relative variation along recorded ion tracks. While the black error-bars indicate the respective line-widths λl, the color error-bars refer to the inter-detector variability σˆD,l. In addition, analytical response functions with their best-fit parameters are given. A non-linear least-squares approach was used with the inverse squares of the standard errors ul as weights. ul is determined by both σˆD,l and λl and the corresponding number of detectors, frames and tracks. Figure 1. View largeDownload slide LET response of the four quantities describing average intensity and width and their respective relative variation along recorded ion tracks. While the black error-bars indicate the respective line-widths λl, the color error-bars refer to the inter-detector variability σˆD,l. In addition, analytical response functions with their best-fit parameters are given. A non-linear least-squares approach was used with the inverse squares of the standard errors ul as weights. ul is determined by both σˆD,l and λl and the corresponding number of detectors, frames and tracks. However, the magnitude of response is very different for the quantities investigated as expressed by the dynamic range d in Table 1. While the average intensity changes by more than a factor of 10 for an LET change of ~100, the other quantities are less sensitive, with the width only changing by 14%. It is understandable that the latter only shows a minute effect since the point-spread function of the microscope largely masks changes in the actual, smaller fluorescence pattern of the ion(15). The effect can be seen here due to the large number of tracks studied. Table 1. Characteristics of LET-dependent track-quantities. The principle accuracy of the system to measure the respective quantity as described by the line-width λ was separated from the inter-detector variability σˆD assessing the effect of coloration fluctuation. The dynamic range d—defined as the relative difference between the maximum and minimum value found for the LET range investigated and hence positive if values increase with LET and vice versa—describes the magnitude of response. For successful separation of ions with different LET, d should be considerably larger than λ and σˆD. Quantity Line-widtha,b λ/% Inter-detector variabilitya σˆD/% Dynamic range d/% Average intensity η¯ 5.2 [6.5; 3.8] 19.7 +170 Variation of intensity ση 24 [30; 20] 4.14 −87 Average width w¯ 3.3 [7.5; 2.0] 0.76 +12 Variation of width σw 32 [44; 25] 9.56 −150 Quantity Line-widtha,b λ/% Inter-detector variabilitya σˆD/% Dynamic range d/% Average intensity η¯ 5.2 [6.5; 3.8] 19.7 +170 Variation of intensity ση 24 [30; 20] 4.14 −87 Average width w¯ 3.3 [7.5; 2.0] 0.76 +12 Variation of width σw 32 [44; 25] 9.56 −150 aAverage value for all LETs, i.e. λ=<λ>l and σˆD=<σˆD,l>l, bValues for low and high-LET limits given in brackets. Table 1. Characteristics of LET-dependent track-quantities. The principle accuracy of the system to measure the respective quantity as described by the line-width λ was separated from the inter-detector variability σˆD assessing the effect of coloration fluctuation. The dynamic range d—defined as the relative difference between the maximum and minimum value found for the LET range investigated and hence positive if values increase with LET and vice versa—describes the magnitude of response. For successful separation of ions with different LET, d should be considerably larger than λ and σˆD. Quantity Line-widtha,b λ/% Inter-detector variabilitya σˆD/% Dynamic range d/% Average intensity η¯ 5.2 [6.5; 3.8] 19.7 +170 Variation of intensity ση 24 [30; 20] 4.14 −87 Average width w¯ 3.3 [7.5; 2.0] 0.76 +12 Variation of width σw 32 [44; 25] 9.56 −150 Quantity Line-widtha,b λ/% Inter-detector variabilitya σˆD/% Dynamic range d/% Average intensity η¯ 5.2 [6.5; 3.8] 19.7 +170 Variation of intensity ση 24 [30; 20] 4.14 −87 Average width w¯ 3.3 [7.5; 2.0] 0.76 +12 Variation of width σw 32 [44; 25] 9.56 −150 aAverage value for all LETs, i.e. λ=<λ>l and σˆD=<σˆD,l>l, bValues for low and high-LET limits given in brackets. Both the variation of intensity and of width show a higher dynamic range than the average width w¯, but the response flattens out for LET-levels above 20 keV/μm. At low-LET, both values are determined by the stochastic nature of energy deposition in thin layers (some μm in this case) whose relative variation decreases with LET(16). In the high-LET limit this effect is masked by the small-scale media-noise in the FNTDs for which similar values (~7%) have been reported(17). The stochastic energy loss also affects the relative line-width found for intensity λl(η¯) (Table 1) but to a smaller extend due to averaging along a track. To some extend, λl(η¯) could be further minimized using more image slices in depth. For high-LET, it approaches the values reported in(14). σˆη and σˆw were found not to be correlated (data not shown), which retrospectively also supports to use the maximum intensity Iˆ rather than the sum I˜=∑x∑yI(x,y) for determination of η. The latter shows an inferior line-width as the additional variation in w is included. Linewidths for the average quantities η¯ and w¯ are considerably smaller than for the straggling quantities σˆη and σˆw. This reflects the fact that the estimation of a variance is inherently less accurate for the same number of observations. The inter-detector variability σˆD,l was, in contrast to λl, not significantly dependent on LET. For the intensity, a value of ~20% was found in accordance with(4) but larger than for FNTD batches in other studies(18). In either case, the inter-detector variability translates—due to the exponential dependence of LET on η¯—into a large uncertainty (up to 50%), which deteriorates any attempt to determine accurate absolute LET using FNTDs without additional corrections. For all other quantities, the inter-detector variability σˆD was smaller—as expected—but only for σˆD,w¯ a considerable reduction is seen. In contrast to the average intensity, the line-widths in all three cases are larger than the inter-detector variability (see error-bars in Figure 1). It seems obvious that the large line-widths in case of σˆη and σˆw influences their apparent inter-detector variability and the approximation used in case of η¯ does not hold here. The small deviation from the model function (residuals) seen in the respective panels in Figure 1 for the model functions supports the assumption that the actual inter-detector variability is smaller. CONCLUSION The analysis of single ion tracks in FNTDs yields additional, LET-dependent quantities that might complement the average fluorescence intensity commonly used for LET estimation in ion beams. Due to their nature, these quantities show smaller dependency on coloration but were found to exhibit a number of inferior other properties, namely larger line-width and smaller dynamic range over the entire or parts of the LET range studied. 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TI - Evaluation of Additional Track Parameters from Fluorescent Nuclear Track Detectors to Determine the LET of Individual Ions
JF - Radiation Protection Dosimetry
DO - 10.1093/rpd/ncx228
DA - 2018-08-01
UR - https://www.deepdyve.com/lp/oxford-university-press/evaluation-of-additional-track-parameters-from-fluorescent-nuclear-HIqt2ItO2T
SP - 206
EP - 209
VL - 180
IS - 1
DP - DeepDyve
ER -