Ion track reconstruction in 3D using alumina-based fluorescent nuclear track detectors
Martin Niklas, James A. Bartz, Mark S. Akselrod, Amir Abollahi, Oliver Jäkel, Steffen Greilich
aa r X i v : . [ phy s i c s . m e d - ph ] J un Ion track reconstruction in 3D using alumina-basedfluorescent nuclear track detectors
M Niklas , , J A Bartz , , M S Akselrod , A Abollahi , − , OJ¨akel , , , and S Greilich , German Cancer Research Center (DKFZ), Division of Medical Physics in RadiationOncology, INF 280, 69120 Heidelberg, Germany, German Cancer Consortium(DKTK), National Center for Radiation Research in Oncology, Heidelberg Institute ofRadiation Oncology, INF450/400, Heidelberg Germany, Oklahoma State University,Physics Department, Stillwater, OK 74078-3072, USA, Landauer Inc., StillwaterCrystal Growth Division, 723 1/2 Eastgate, Stillwater, OK 74074, USA, Molecular& Translational Radiation Oncology, Heidelberg Ion-Beam Therapy Center (HIT),University of Heidelberg Medical School and National Center for Tumor Diseases(NCT), German Cancer Research Center (DKFZ), 69120 Heidelberg, Germany, Department of Radiation Oncology and Radiation Therapy, University HospitalHeidelberg, INF 400, 69120 Heideberg, Germany, Heidelberg Ion-Beam TherapyCenter (HIT), Im Neuenheimer Feld 450, 69120 Heidelberg, Germany, Center ofCancer Systems Biology, Nasa Specialized Center Of Research (NSCOR), St.Elizabeth’s Medical Center, Tufts University School of Medicine, Boston, MA, USAE-mail: [email protected]
Abstract.
Fluorescent nuclear track detectors (FNTDs) based on Al O :C,Mg single crystalcombined with confocal microscopy provide 3D information on ion tracks with aresolution only limited by light diffraction. FNTDs are also ideal substrates tobe coated with cells to engineer cell-fluorescent ion track hybrid detectors. Thisradiobiological tool enables a novel platform linking cell responses to physical dosedeposition on a sub-cellular level in proton and heavy ion therapies. To achieve spatialcorrelation between single ion hits in the cell coating and its biological response the iontraversals have to be reconstructed in 3D using the depth information gained by theFNTD read-out. FNTDs were coated with a confluent human lung adenocarcinomaepithelial cell layer. Carbon ion irradiation of the hybrid detector was performedperpendicular and angular to the detector surface. In-situ imaging of the fluorescentlylabeled cell layer and the FNTD was performed in a sequential read-out. Makinguse of the trajectory information provided by the FNTD the accuracy of 3D trackreconstruction of single particles traversing the hybrid detector was studied. Theaccuracy is strongly influenced by the irradiation angle and therefore by complexity ofthe FNTD signal. Perpendicular irradiation results in highest accuracy with error ofsmaller than 0.10 ◦ . The ability of FNTD technology to provide accurate 3D ion trackreconstruction makes it a powerful tool for radiobiological investigations in clinicalion beams, either being used as a substrate to be coated with living tissue or beingimplanted in vivo. on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors PACS numbers: 61.80.Jh, 87.53.Bn, 87.53.Jw, 87.64.mk, 87.64.kv, 87.85.-d, 87.90.+y
Keywords : FNTD, particle irradiation, track reconstruction, ion radiotherapy,radiobiology on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors
1. Introduction Al O :C,Mg based fluorescent nuclear track detectors (FNTDs) [Akselrod and Sykora 2011]are ideal candidates for engineering cell-fluorescent ion track hybrid detectors[Niklas et al et al et al et al et al et al et al et al et al O :C,Mg - and their corresponding centers belonging to a single ion trackwere precisely located in the acquired FNTD image stack (a sequence of optical slicesin z). Linear regression analysis was then applied to fit the ion track. Each track wasextrapolated above the detector surface into a cell layer grown on top of the FNTD.Due to a refractive index mismatch in the optical path of the imaging of the hybrid de-tector correction of spherical aberrations [Hell et al
2. Materials and methods O :C,Mg based FNTD FNTDs are made of alumina single crystals ( α -Al O ) doped with magnesium andcarbon ions and exhibit high concentrations of F (2Mg) aggregate defects (excitation at435 nm and emission of fluorescence at 515 nm) [Akselrod and Sykora 2011]. F (2Mg)undergo radiochromic transformation. The resulting stable, transformed color centers,F +2 (2Mg), absorb light in the band centered at 620 nm, prompting fast 750 nm on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors et al et al > µ m[Akselrod and Sykora 2011]. The current limit of maximum countable track fluenceis in the range of 0 . · cm − [Osinga et al C, 90 MeV u − ). FNTDs have one 4mm by 8 mm surface polished to optical quality for read-out. The optical c -axis of thecrystal is aligned parallel to the longer side of the detector (figure 2a). The polished surface of sterilized FNTDs were coated with a confluent humanlung adenocarcinoma epithelial (A549) cell layer with the protocol described in[Niklas et al − , culture medium: Dulbecco’smodified Eagle medium, Biochrom AG, Cat. No. FG 0415). A549 cells wereobtained from Deutsche Sammlung von Mikroorganismen und Zellkulturen (DSMZ,Braunschweig, Germany). 15 minutes after the irradiation the cells remaining on theFNTD crystal were fixed with 4% paraformaldehyde (PFA) in phosphate buffered saline(PBS) for 10 min at room temperature. Cell nuclei were stained with HOECHST 33342fluorescent dye (Molecular Probes R (cid:13) , Cat. No. H1399, final concentration: 2 µ g ml − )as described in [Niklas et al θ (angle between the direction ofpropagation of the ions ~s and the k -axis of Al O :C,Mg) of 0 ◦ ± ◦ and 60 ◦ ± ◦ (figure2a). The azimuth angle φ (angle between the optical c-axis and ~e x,y , the projection of theion beam onto the exposed FNTD surface) only played a minor role for the setup. Forperpendicular irradiation ( θ = 0 ◦ ) the ion beam fluence was adjusted to 1 . · cm − .For angular irradiation ( θ = 60 ◦ ) the fluence at the FNTD surface corresponded to1 . · cm − . In both cases, a 12 x 12 cm field was irradiated homogeneously usingraster scanning with a pencil beam of 10.1 mm in diameter (full width at half maximum)and a distance of 2 mm between two raster spots. Approximately 60,000 particles weredelivered in each spot. The Bragg peak was broadened in depth by using a 3 mm Ripplefilter. The cell-coated FNTDs, mounted with agarose in a 24 multiwell plate filled withculture medium [Niklas et al − , corresponding equivalent range in water r H O = 13.70 cm). For the irradiation under θ = 0 ◦ ( θ = 60 ◦ ) 11.70 cm (11.05 cm) ofPMMA absorber with a corresponding r H O = 13.63 cm (r H O = 12.87 cm) was placed infront of the multiwell plate. For angular irradiation at θ = 60 ◦ the multiwell plate wasplaced at an angle of γ = 30 ◦ ± ◦ ( γ = 90 ◦ − θ , defined for practical purpose) towards theincident ion beam. The different PMMA thicknesses result from the different thicknesses on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors θ = 0 ◦ : r H O = 1.2 mm, θ = 60 ◦ :r H O = 2.5 mm). The air gap between the culture well and the PMMA was not consideredin the total r H O . The amount of material in the beam from vacuum exit window toisocenter corresponds to a r H O of 2.89 mm. For the sequential read-out of the cell-coated FNTD we used the Zeiss LSM710 ConfoCor 3 confocal microscopy equipped with a z-piezo stage, 63x/1.45numerical aperture (NA) Oil DIC M27 objective, photomultiplier tubes (PMT) andavalanche photo diodes (APDs). We used the protocols as previously describedin [Greilich et al et al τ was set to4.97 µ s (2.80 µ s) and the line-scanning repetition R was limited to 4 (4). For the celllayer acquisition (HOECHST 33342) we used a 405 nm diode laser line (30 mW, 4%transmission) with τ = 2.80 µ s and R = 4. The microscope detector pinhole aperturewas set to 1 Airy disk unit (AU). For angular (perpendicular) irradiated FNTDs asingle imaging field comprised 1300 x 1300 pixel (1152 x 1152 pixel) with a pixelsize of 0.104 x 0.104 µ m (0.117 x 0.117 µ m ). The acquired image stacks of theangular irradiated FNTDs covered an axial range of approximately 90 µ m (measuredfrom the detector surface). Concerning the perpendicular irradiated FNTD the imagestacks covered an axial range of approximately 120 µ m. In both cases the z-interval d ∆ z between two consecutive image planes was adjusted to 3 µ m. For imaging, thecell-coated FNTD was placed in uncoated glass bottom culture dish (MatTek Corp.,Part No. P35G-1.5-20C) with the cell-layer facing the glass bottom. The culturedish was filled with PBS. Anisotropic fluorescence properties of Al2O3:C,Mg crystals[Sanyal and Akselrod 2005, Greilich et al TM
518 F(n= 1.51 for λ = 643.8 nm at 23 ◦ C) was used as an immersion medium. The imagesacquired were stored with a bit depth of 16-bit in the LSM format.The position of the polished FNTD surface was identified by using the HOECHST33342 fluorescent signal from the nuclear staining. It disappears at the transition intothe FNTD crystal. In addition, excitation by 405 nm causes a photoionization of thepristine F (2Mg) aggregate defects located in close vicinity to the detector surfacehence increasing the background in the HOECHST 33342 channel.
For image segmentation the acquired 16-bit integer FNTD images were converted intofloating point data (with pixel values in the interval [0; 1]). A window limited to 30x 30 pixels for perpendicular and 120 x 30 pixels for angular irradiation was used todefine regions of interest (ROIs) within a plane of the FNTD image stack. Each ROIcontained a single track spot. Thresholding in the ROIs was applied to identify all track on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors iw centroid ):all pixels within the ROI with values greater than a manually defined globalthreshold of 0.4 were considered for the calculation of the intensity-weightedcentroid.(B) Detection of intensity-weighted centroids applying a dynamic threshold ( rel thres ):the threshold was set to 2 / abs max ):the pixel with the maximum value within the ROI was considered as the track spotcenter.No background correction of the FNTD raw images was applied. For reconstruction of the ion trajectory in 3D we assumed the ion to follow a straight line.A line was expected as due to the high energies of the ions, multi-coulomb scatteringof the projectile in the crystal lattice is very small. Due to statistical variation inenergy deposition and inhomogenities of the color-center density, only uncertaintiesin the horizontal coordinates (x,y) of the ion track centers were taken into account.Uncertainty in z by the high-precision z-piezo stage (in the nm range) were neglected.The fitting procedure was split up into two separate linear regression analysis (LRA,using least-square estimation [Montgomery et al x ( z ) = a x + b x · z (1) y ( z ) = a y + b y · z (2)The flight direction of the incident ions was parameterized by θ and φ . θ (figure 2a)was calculated by θ = 90 ◦ − γ, (3) γ = arctan[(tan − α + tan − β ) − . ] (4)with tan α = b x and tan β = b y . φ was calculated by φ = arctan[tan( α ) / tan( β )] . (5) on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors µ m partly startingat different depths in the FNTD. This is the range allowing to track a traversing ionwithin a single imaging field (135x135 µ m ) under angular irradiation (for greater rangesthe imaging field has to be moved, i.e. tile scans have to be performed).The ion trajectories obtained by fitting were extrapolated into the A549 cell-layer of 10 µm thickness (nominal thickness without correction for distortion, see section Correctionfor axial geometrical distortion , below) grown on top of the FNTD. The 95% predictionintervals PI x , y on future observation ( x , y ) with PI x , y = [ x − a x − b x · z , y − a y − b y · z ]were calculated by P I x = s · t n − , . · s n + 1ˆ s ( z − ¯ z ) (6) s = s P ni =1 ( a x + b x · z i − x i ) n − s = n X i =1 ( z i − ¯ z ) (8)¯ z = 1 n · n X i =1 z i (9)and analog for P I y using y i , a y and b y in (7). Parameter n is the number of trackspot centers (with coordinates x i , y i , z i ) considered for the fit, and t n − , . is the 97.5%quantile of the t-distribution with n − µ m below the FNTD crystal surface.Accuracy of ion track reconstruction in 3D was expressed by ∆ θ , ∆ φ (95% confidenceintervals gained by the LRA) and PI x , y . To study the impact of the parameter n onaccuracy we varied the distance in z between two consecutive track spots ∆ z (nominaldistance without correction for distortion, see section Correction for axial geometricaldistortion , below). We further compared three different approaches for the identificationof the track spot center coordinates ( iw centroid, rel thres, abs max , see section
Detectionof the center of a track spot , above):(i) ∆z= 3 µ m, n= 21 track spots(ii) ∆z= 6 µ m, n= 11 track spots(iii) ∆z= 15 µ m, n= 5 track spotsWe analysed 20 tracks each for angular and perpendicular irradiated FNTDs. Correction for axial geometrical distortion
In the optical path of the confocal imaging a mismatch in index of refraction occursat the interface between the immersion oil and cell layer and at the interface betweencell layer and FNTD. The refractive index of the glass bottom dish and the immersionoil was assumed to equal. The mismatch causes axial distortion of the nominal focalposition (position in z without spherical aberration) from the actual one (presence ofspherical aberrations) [Jacobsen and Hell 1995, Van Elburg et al on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors oil = 1 . > n cell = 1 .
47 [Hell et al et al z in the cell layer was determined by: ASF = c ∆ n/n oil + c arctan( c ∆ n/n oil ) (10)with c = 1 . c = 0 . c = 100 and ∆ n = ( n cell − n oil ). To account forthe positive mismatch at the cell layer-FNTD boundary (n Al O :C , Mg = 1 . > n cell )we used the paraxial approximation ASF = n Al O : C,Mg /n cell . We used the thisapproximation as n Al O : C,Mg exceeds the range of mismatch being considered for theimproved linear correction method [Van Elburg et al et al z act (origin is at the bottom of the culture dish) was thencalculated by z act ( z ) = ASF · z + ASF · z (11)with z being the nominal thickness of the cell layer (distance between the dish bottomand the detector surface) and z being the nominal position in the FNTD (measuredfrom the detector surface). The aqueous medium between dish bottom and cells wasneglected in the correction for axial distortion.Uncertainties in the position of the surface ∆ s translate into an error ˆ x of the locationof the track in the horizontal: z act ( z, ∆ s ) = z act ( z ) ± ( ASF − ASF )∆ s (12)ˆ x = ( ASF − ASF )∆ s/ tan(90 ◦ − θ ) (13)starting from z act ( z ) = ASF ( s − o ) + ASF h (ˆ n − d ∆ z − ( s − o ) i (14)and defining z := (ˆ n − z as a function of the actual plane number ˆ n of the acquiredimage stack and the interval between two consecutive image planes d ∆ z . o and o arethe respective positions of the first image plane of the cell and FNTD image stack.
3. Results
In figure 3 track spots - the ion’s footprint left in the Al O :C,Mg crystal - resulting fromirradiation perpendicular ( θ = 0 ◦ ) and angular ( θ = 60 ◦ ) towards the FNTD surface areshown. Under perpendicular irradiation the track spots have an almost radial symmetricintensity profile with a steep intensity gradient in the track core (halo around the trackspot center) and branching trajectories from secondary electrons of higher energy. Theirlocal intensity maxima are due to the track ends.Under angular irradiation the track spots are deformed into ellipsoidal objects extendedalong beam direction (x) with tattered edges and with branching secondary electron on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors µ m - comparedto the diameter of 0.9 µ m of a symmetrical track spot.The inserts in figure 3a,b show the examples of the track spot centers for all threeidentification approaches ( iw centroid, rel thres, abs max, see section Fitting andextrapolation procedure , above). Under perpendicular and angular irradiations thepositions of the intensity-weighted track spot centers detected by applying a globalthreshold and dynamic thresholding are nearly identical. Larger deviations from thesepositions occur for identifying the absolute intensity maximum. The spatial mismatchis much more pronounced under angular than under perpendicular irradiation.
For all LRA (angular and perpendicular irradiation) the residual plots generallydisplayed a normal distribution (not shown). Figure 4 presents the mean absoluteresiduals (in an initial step the absolute residuals corresponding to a single fit wereaveraged) including the standard error of the mean (SEM).In the case of angular irradiation the residuals in x (perpendicular to beam direction) andin y (along beam direction) resulting from identification approach A and B ( iw centroid,rel thres ) fluctuate around 0.10 µ m and 0.58 µ m respectively for all ∆ z (figure 4a). Theresiduals concerning identification of the absolute maximum ( abs max , approach C) arelarger (x: ≈ . µ m, y: ≈ µ m). SEMs in x ( ≤ . µ m) and y ( ≈ µ m)approximately equal for all ∆ z and all identification approaches; the largest values areobtained for approach C.For perpendicular irradiation the residuals in x and in y, resulting from identificationapproach A and B (∆ z = 3 and 6 µ m) fluctuate between 0.03 µ m and 0.04 µ m anddecrease for ∆ z = 15 µ m (figure 4b). Concerning identification approach C the residualsin x and in y lie between 0.04 µ m and 0.05 µ m. All SEMs are smaller than 0.01 µ m. For angular irradiation the mean values θ = 59 . ◦ and φ = 84 . ◦ defining the directionof the traversing ions differ of maximum 0.07 ◦ and 0.01 ◦ respectively for all LRA (table1). The error ∆ θ , figure 5a, is smallest (0.89 ◦ ) for approach A at ∆ z = 3 µ m and isincreasing to 3.45 ◦ for approach C at ∆ z = 15 µ m. Except for ∆ z = 15 µ m, ∆ φ issmaller than 0.2 ◦ for all LRA (figure 5b). Concerning the mean PIs (figure 6a,b andtable 1) in the cell-layer of 10 µ m thickness on top of the FNTD the values in x aresmaller than 0.4 µ m (∆ z < µ m, for all identification approaches) and are increasingto 0.77 µ m for approach C at ∆ z = 15 µ m. PI y is has its lowest value (1.72 µ m) forapproach A at ∆ z = 3 µ m and is increasing to 4.58 µ m for approach C at ∆ z = 15 µ m.Concerning perpendicular irradiation, θ ≈ . ◦ differs less than 0.02 ◦ for all LRA (table on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors φ lies between 45 ◦ and 46 ◦ . For ∆ z < µ m and all identificationapproaches ∆ θ is smaller than 0.15 ◦ and is increasing to 0.26 ◦ for ∆ z = 15 µ m (approachC, figure 5c). ∆ φ covers a broad range - between 1.53 ◦ and 4.77 ◦ (figure 5d). The meanPIs in x and in y are generally much smaller than 0.3 µ m (figure 6c,d and table 2).Both, the distributions of ∆ θ and ∆ φ (perpendicular and angular irradiation) indicatedby their standard deviation (s.d.) and mean values show a steep rise between ∆ z = 6 µ m and ∆ z = 15 µ m. This is independent of the identification approach used (figure5). The effect is especially pronounced under angular irradiation. The mean PIs behavesimilarly (figure 6).
4. Discussion
Accuracy of ion track reconstruction in 3D using the FNTD depth information is stronglyinfluenced by the irradiation angle θ and therefore by complexity of the intensity profileof a track spot as well as by the approach for identification of its center. The size and shape of a track spot depends on the energy of the incident ions[Akselrod and Sykora 2011, Niklas et al θ governing the geometrical crosssection of the traversing particles with the detector material. High-energy carbon ionirradiation produces a high density of secondary electrons of low energies responsiblefor the generally symmetrical as well as ellipsoidal intensity profile of the track spots(figure 3). The sprouting electron trajectories with a broad angular distribution arecaused by δ electrons having enough energy to leave the track-core. These trajectories,although less probable, and their random formation (due to frequent scattering of the δ electrons) distort the original symmetrical intensity profile.The track spots under angular irradiation seem to comprise more sprouting electrontrajectories than the symmetrical track spots. Due to a greater geometrical crosssection the probability of producing fast δ electrons increases including the formationof tattered track spot edges. In addition, electron trajectories of neighboring iontraversals from above or below crossing as well as being scattered in the image plane arebeing detected. On the contrary, under perpendicular irradiation mainly the electrontrajectories perpendicular to the flight direction of the incident ion are visible.The track spot is masked by the point spread function (PSF) of the imaging system(figure 3) [Niklas et al O :C,Mg interface causing spherical aberrations[Carlsson 1991, Hell et al et al on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors The thresholds based methods A and B ( iw centroid, rel thres ) using a value of 0.4for identifying intensity-weighted centroids and 2/3 of the maximum pixel value withinan ROI (dynamic thresholding) showed best suitability for carbon ion irradiation andminimize the probability to detect δ electron structures (including their Bragg-peaks)as well as the tattered track spot edges. As the gradient of the intensity profile isrelatively steep, 2/3 of the maximum is not too high running the risk of approachingthe global maximum which is likely not to coincide with the center of the track spotcore. Statistical fluctuation of energy deposition and local fluctuation of the color centerdensity could be the main reason for this mismatch. Weighting by intensity seems toapproach the actual track core best. This coincides well with smaller residuals (figure 4)and hence more accurate track reconstruction (figures 5 and 6) than the detection of theabsolute intensity maximum ( abs max , method C). In addition, dynamic thresholdinghas the advantage of responding to different intensity profiles (variation in the maximumintensity [Niklas et al et al et al Complexity of the track spot geometry and hence the irradiation angle θ have a majorimpact on accuracy expressed by ∆ θ , ∆ φ and PI. The radial symmetrical intensity profile( θ = 0 ◦ ) is reflected in nearly identical residuals in x and in y (figure 4b) for all LRA.On the contrary the elongation (along beam direction) and much higher complexity ofthe track spots under angular irradiation ( θ = 60 ◦ ) causes much greater discrepancybetween the residuals in x and in y - by a factor of approximately six - irrespective ofthe identification approach of the track spot center (figure 4a). This is directly reflectedin the increased error ∆ θ by a factor of approximately ten (comparing θ = 60 ◦ and θ = 0 ◦ , figure 5a,c). This is also reflected in much greater PIs (figure 6), especially forPI y under angular irradiation being more than ten times larger than the symmetricalPIs under perpendicular irradiation.The surprisingly great values of ∆ φ under perpendicular irradiation (figure 5d) arisefrom the narrow distribution of the projections of the track spots onto the yz plane.Small fluctuations have a great impact leading to large variations in the coefficientinterval of b y in the LRA (equation 2). To gain more reliable values and to decrease ∆ φ on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors ◦ we increased the number of track spots by extending the total range in z forthe LRA for perpendicular irradiation to 114 µ m with ∆z= 3 µ m (table 3).To principally minimize the PIs and irrespective of the irradiation angle it is favorable tostart the FNTD read-out near the detector surface. This assures a minimal extrapolationinterval into the cell layer. This also reduces the PIs as the interval between the meanz-coordinate of identified track spots and z-coordinate of extrapolation gets minimized(equation 6).The strong decrease in accuracy (and larger s.d.) for ∆ z = 15 µ m, all identificationapproaches (figure 5, 6), could arise from the insufficient averaging and the statisticalnature of energy deposition. Under perpendicular irradiation a reasonable trade-offbetween fast detector read-out and high accuracy is yet possible by increasing ∆z to15 µ m (figure 5c). ∆ θ increases but is still less than 0.3 ◦ . ∆ φ has little significance.The PIs are however increasing as they depend on the inverse number of track spotsconsidered for the LRA. The surprising decrease of the residuals (∆ z = 15 µ m, all threeidentification approaches, figure 4b) has no impact on the increase of ∆ θ , ∆ φ and PIs. The distortion induced by refractive index mismatch only affects the axial position ofthe focal point and hence θ - the trajectory of the particles. Introducing non-linear cor-rection [Van Elburg et al et al et al O :C,Mg boundary has to be considered for axial correction. To further reducespherical aberrations, perpendicular irradiation should be employed in particular forlive cell imaging. Despite the presence of the refractive index mismatch at the cell-Al O :C,Mg boundary the nominal can be approximated with the actual focal position.Concerning uncertainty in the position of the FNTD surface ∆ s , the error term( ASF − ASF )∆ s in (12), which affects the actual focal position z act is independent of z and does not influence the LRA and thus trajectory of the incident ions (parameterizedby θ and φ ). The resulting error ˆ x (13) of the position of the ion track in the horizontaldirection is governed by θ and the product ( ASF − ASF )∆ s . ∆ s = 1 µm at θ = 60 ◦ yields ˆ x = 0 . µm . For shallow irradiation angles, i.e. θ < ◦ , ˆ x decreases steeply aslong as ( ASF − ASF ) <
1. ˆ x becomes yet more relevant if the ion traversal in theintracellular space has to be localized. on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors
5. Conclusions
It is possible to perform accurate ion track reconstruction in 3D and extrapolate an ion’strajectory into a cell layer covering the FNTD by using depth information provided bydetector read-out. The accuracy of the track reconstruction procedure strongly dependson the irradiation angle θ and by the approach used to identify individual track spotcenters. The use of intensity-weighted centroids and dynamic thresholding yield thehighest accuracy. Steep irradiation angles distort the otherwise symmetrical track spots,resulting in reduced accuracy of centroid prediction. To achieve the desired accuracyin determining the angle θ with an error smaller than 1 ◦ under angular irradiation at θ = 60 ◦ the intensity-weighted centroid detection and a 21 image stack separated by d ∆ z = 3 µ m was found as the best set of image acquisition and processing parameters.Increasing d ∆ z to 6 µ m (i.e. half the number of track spots) deteriorates the accuracy,i.e. ∆ θ and PI, roughly by 30% and 20% respectively. Concerning angles of irradiationwith θ close to 0 ◦ and using the same fit parameters, ∆ θ decreases by a factor of at least10 with nearly symmetrical lateral error distribution.The required increase in accuracy of track reconstruction also increases the total read-out time of the detector. To further improve accuracy if necessary one could extend thetotal axial range of the image stack, to increase the number of images and decrease theimage depth increment between two consecutive image planes ( d ∆ z ). This, however, ismore time consuming. Naturally the total microscope time is directly affected by theacquisition time of a single image plane (mainly governed by laser power p , dwell time τ ,number of rescans R and total number of spots per imaging field [Greilich et al et al Author’s contributions
MN performed experiments, analyzed data and wrote the manuscript. JB participated inthe axial geometrical correction. MA developed the crystal (FNTD) material and FNTDimaging technique. MN, AA, OJ and SG designed experiments and interpreted the data.All authors edited the paper. All authors read and approved the final manuscript.
Acknowledgements
We are grateful to S. Brons for generously providing support and technical irradiationassistance at the Ion Beam Therapy Center of Heidelberg University Hospital. Weshould also like to thank F. Bestvater and M. Brom of the DKFZ’s light microscopy core on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors
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Microsc. Res. Tech. J. Microsc. on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors Figure 1.
Spatial correlation between single carbon ion traversal and cell damage[Niklas et al γ -H2AX,immunofluorescent staining, green spots). Cell nuclei are labeled in blue (HOECHST33342 staining). Scale bar, 5 µ m. yxz kc θ = (k, s) ϕ = (c, e x,y ) e x , y ϕ θ γ xz yz αβ a b z γ = 90°- θ s y x s = (0,0,1)e x,y = (1,1,0) Beam exitIon beam
Figure 2.
Irradiation setup and particle track reconstruction. (a) The ions aretraversing the detector under the angle θ - the angle between direction of propagation ofthe ions ~s and k-axis of the FNTD (of dimension 4x8x0.5 µm ). ~k, ~c, ~e x,y and all anglesrefer to the coordinate system of the FNTD. ~s refers to the beam coordinate system.The cell-coating is indicated by the gray layer. (b) Splitting of fitting procedure intotwo separate linear regression analysis for the x- and y-coordinate of the track spotcenters. on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors a b y xy x sec e- Figure 3.
Intensity profile of FNTD read-out signal after (a) perpendicular ( θ = 0 ◦ )and (b) angular irradiation ( θ = 60 ◦ ). The track core (masked by the point spreadfunction of the imaging system [Niklas et al µ m and (b) 1 µ m. a b iw centroid (A)rel thres (B)abs max (C) Res x Res y Figure 4.
Mean absolute residuals in x (circles) and y (solids) resulting from differentfitting procedures. The distance ∆ z between two consecutive track spots was variedand different approaches to detect the track spot centers were used (red: intensity-weighted centroid, green: dynamic thresholding, blue: absolute maximum). Theerror bars are the standard errors of the mean. (a) angular irradiation, θ = 60 ◦ (b) perpendicular irradiation, θ = 0 ◦ . on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors iw centroid (A)rel thres (B)abs max (C) ab cd Figure 5.
Errors ∆ θ and ∆ φ of the different fitting procedures (red: intensity-weighted centroid, green: dynamic thresholding, blue: absolute maximum). ∆ z isthe distance in z between two track spots. (a)-(b) angular irradiation, θ = 60 ◦ , (c)-(d)perpendicular irradiation, θ = 0 ◦ . The error bars are the standard deviations. Table 1.
Angular irradiation, θ = 60 ◦ . Accuracy of ion track reconstruction usingdifferent fitting procedures. ∆ z : distance in z between two track spots. The errors arethe s.d. Total range in z: 60 µ m. θ [ ◦ ] ∆ θ [ ◦ ] φ [ ◦ ] ∆ φ [ ◦ ] PI x [ µ m] PI y [ µ m] n = 21 track spots, ∆ z = 3 µm iw centroid (A) 58 .
97 0 . ± .
22 84 .
69 0 . ± .
06 0 . ± .
12 1 . ± . .
98 0 . ± .
19 84 .
69 0 . ± .
06 0 . ± .
10 1 . ± . .
98 1 . ± .
23 84 .
69 0 . ± .
06 0 . ± .
11 2 . ± . n = 11 track spots, ∆ z = 6 µm iw centroid (A) 59 .
00 1 . ± .
34 84 .
68 0 . ± .
09 0 . ± .
17 2 . ± . .
01 1 . ± .
33 84 .
68 0 . ± .
09 0 . ± .
13 2 . ± . .
03 1 . ± .
37 84 .
68 0 . ± .
11 0 . ± .
17 2 . ± . n = 5 track spots, ∆ z = 15 µm iw centroid (A) 59 .
08 2 . ± .
03 84 .
67 0 . ± .
23 0 . ± .
45 3 . ± . .
09 2 . ± .
08 84 .
68 0 . ± .
24 0 . ± .
33 3 . ± . .
09 3 . ± .
21 84 .
68 0 . ± .
29 0 . ± .
47 4 . ± . on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors iw centroid (A)rel thres (B)abs max (C) ab cd Figure 6.
Mean prediction intervals (PI) for x and y resulting from the extrapolationof the particle track into a cell layer of 10 µ m thickness for different fitting procedures(red: intensity-weighted centroid, green: dynamic thresholding, blue: absolutemaximum). ∆ z is the distance in z between two track spots. (a)-(b) angularirradiation, θ = 60 ◦ , (c)-(d) perpendicular irradiation, θ = 0 ◦ . The error bars arethe standard deviations. Table 2.
Perpendicular irradiation, θ = 0 ◦ . Accuracy of ion track reconstructionusing different fitting procedures. ∆ z : distance in z between two track spots. Theerrors are the s.d. Total range in z: 60 µ m. θ [ ◦ ] ∆ θ [ ◦ ] φ [ ◦ ] ∆ φ [ ◦ ] PI x [ µ m] PI y [ µ m] n = 21 track spots, ∆ z = 3 µm iw centroid (A) 1 .
20 0 . ± .
01 45 .
16 1 . ± .
04 0 . ± .
02 0 . ± . .
21 0 . ± .
01 44 .
99 1 . ± .
87 0 . ± .
02 0 . ± . .
22 0 . ± .
01 45 .
30 2 . ± .
42 0 . ± .
02 0 . ± . n = 11 track spots, ∆ z = 6 µm iw centroid (A) 1 .
21 0 . ± .
02 44 .
95 3 . ± .
78 0 . ± .
04 0 . ± . .
22 0 . ± .
02 44 .
92 2 . ± .
47 0 . ± .
03 0 . ± . .
24 0 . ± .
03 45 .
94 2 . ± .
86 0 . ± .
04 0 . ± . n = 5 track spots, ∆ z = 15 µm iw centroid (A) 1 .
21 0 . ± .
05 45 .
21 4 . ± .
36 0 . ± .
08 0 . ± . .
22 0 . ± .
05 45 .
39 4 . ± .
71 0 . ± .
07 0 . ± . .
24 0 . ± .
08 45 .
70 4 . ± .
45 0 . ± .
12 0 . ± . on track reconstruction in 3D using alumina-based fluorescent nuclear track detectors Table 3.
Perpendicular irradiation, θ = 0 ◦ . Accuracy of ion track reconstructionusing different fitting procedures. ∆ z : distance in z between two track spots. Theerrors are the s.d. Total range in z: 114 µ m. θ [ ◦ ] ∆ θ [ ◦ ] φ [ ◦ ] ∆ φ [ ◦ ] PI x [ µ m] PI y [ µ m] n = 39 track spots, ∆ z = 3 µm iw centroid (A) 1 .
17 0 . ± .
005 45 .
63 0 . ± .
45 0 . ± .
02 0 . ± . .
17 0 . ± .
005 45 .
53 0 . ± .
42 0 . ± .
02 0 . ± . .
18 0 . ± .
005 45 .
53 0 . ± .
61 0 . ± .
02 0 . ± ..