A novel hybrid microdosimeter for radiation field characterization based on TEPC detector and LGADs tracker: a feasibility study
M. Missiaggia, E. Pierobon, M. Castelluzzo, A. Perinelli, F. Cordoni, M. Centis Vignali, G. Borghi, V. E. Bellinzona, E. Scifoni, F. Tommasino, V. Monaco, L. Ricci, \\M. Boscardin, C. La Tessa
AA novel hybrid microdosimeter for radiation field characterizationbased on TEPC detector and LGADs tracker: a feasibility study
M. Missiaggia , , , E. Pierobon , M. Castelluzzo , A. Perinelli ,F. Cordoni , , M. Centis Vignali , G. Borghi , , V. E. Bellinzona , ,E. Scifoni , F. Tommasino , , V. Monaco , L. Ricci , ,M. Boscardin , , C. La Tessa , Abstract
In microdosimetry, lineal energies y are calculated from energy depositions (cid:15) inside the micro-dosimeter divided by the mean chord length , whose value is based on geometrical assumptions onboth the detector and the radiation field. This work presents an innovative two-stages hybrid de-tector (HDM: hybrid detector for microdosimetry) composed by a Tissue Equivalent ProportionalCounter (TEPC) and a silicon tracker made of 4 Low Gain Avalanche Diode (LGAD). This designprovides a direct measurement of energy deposition in tissue as well as particles tracking with asubmillimeter spatial resolution. The data collected by the detector allow to obtain the real tracklength traversed by each particle in the TEPC and thus estimates microdosimetry spectra withoutthe mean chord length approximation. Using Geant4 toolkit, we investigated HDM performancesin terms of detection and tracking efficiencies when placed in water and exposed to protons andcarbon ions in the therapeutic energy range. The results indicate that the mean chord lengthapproximation underestimate particles with short track, which often are characterized by a highenergy deposition and thus can be biologically relevant. Tracking efficiency depends on the LGADconfigurations: 34 strips sensors have a higher detection efficiency but lower spatial resolution than71 strips sensors. Further studies will be performed both with Geant4 and experimentally to opti-mize the detector design on the bases of the radiation field of interest.The main purpose of HDM is to improve the assessment of the radiation biological effectivenessvia microdosimetric measurements, exploiting a new definition of the lineal energy ( y T ), defined asthe energy deposition (cid:15) inside the microdosimeter divided by the real track length of the particle. Microdosimetry was developed to study the effect of radiation on cells. At a scale comparable tothe structures of interest, the energy deposition is affected by stochastic fluctuations and cannot beaccurately described with macroscopic mean values, such as the dose or the LET [Andreo et al., 2017].Measuring the energy loss in a microscopic volume called for the development of new detectiontechniques. Currently, there are two types of microdosimeters: tissue equivalent proportional counters(TEPCs) and semiconductor-based detectors. The latter category includes silicon detectors based ondifferent technologies (telescope detectors, silicon on insulator (SOI) detectors, arrays of cylindricalp-n junctions with internal amplification [Agosteo and Pola, 2011]) and diamond microdosimeterswhich are under study for their radiation hardness and tissue equivalence [Davis et al., 2019].The TEPC was invented by Harald H. Rossi and co-workers, who were the first to explore thefield of experimental microdosimetry [Rossi and Rosenzweig, 1955], and is considered the referencemicrodosimeter [Lindborg and Waker, 2017]. The TEPC detection system is based on the fact thatthe detection gas parameters (e.g. composition and density) are adjusted to match the stopping powerof the desired tissue equivalent volume. Department of Physics, University of Trento, Trento, ITALY TIFPA, INFN, Trento, ITALY FBK, Trento, ITALY Department of Physics, University of Torino, Torino, ITALY Department of Computer Science, University of Verona, Verona, ITALY a r X i v : . [ phy s i c s . i n s - d e t ] J u l he basic microdosimetric quantity provided by all detectors is the energy (cid:15) imparted to the matterin the volume of interest, from which the lineal energy y , defined as the ratio between (cid:15) and the meanchord length ¯ l [Zaider et al., 1996], is calculated. The yf ( y ) and yd ( y ) spectra are the standardmicrodosimetric distributions, where f ( y ) is the frequency distribution of y and d ( y ) is equal to yf ( y ),hence representing the dose distribution.A limitation shared by all microdosimeters is that while (cid:15) is directly measured, the value of ¯ l hasto be theoretically estimated as the mean path travelled by a particle inside the detector, and thusit depends on the detector geometry. In addition, ¯ l values calculated for standard geometries can beused only if the microdosimeter is exposed to a homogeneous and isotropic field (also called uniformisotropic randomness) [Kellerer et al., 1985] and a different ¯ l value will be obtained under differentirradiation conditions, i.e. for other types of randomness. Few theoretical studies focussed on findinga formula of the mean path length for both uniform [Cruz et al., 2001] and non uniform [Santa Cruzet al., 2001] radiation fields. So far, only the calculation for a uniform isotropic randomness could besuccessfully applied to experimental methodologies. Estimating the path length l is a critical param-eter in microdosimetry that will influence the accuracy of the radiation field quality characterization[Abolfath et al., 2020]. In fact, for a given energy (cid:15) deposited in the detector, the resulting y valuecan assume a wide range of values depending on the l . For example, if (cid:15) =10 keV in a 2 µ m diametersphere made of tissue, y can varies from 5 keV/ µ m to 1000 keV/ µ m just considering l values rangingfrom the sphere diameter to 0.01 µ m.For this reason, since the quantity y is traditionally intended as the (cid:15) over the mean chord lengthvalue ¯ l , we introduce a new quantity y T , defined as (cid:15) divided by the particle real track length l .In this work, we present a novel two-stage hybrid microdosimeter (HDM: hybrid detector formicrodosimetry) designed to measure the y T . This detector have been specifically intended for particletherapy application, where a knowledge of the y T yields a more direct link to the biological damage.Together with providing a direct measurement of the track length l , this design also improve the spatialresolution of existing TEPCs. HDM is composed of a spherical TEPC followed by four layers of LowGain Avalanche Detectors (LGADs) [Pellegrini et al., 2014]. LGAD is a recent technology in siliconsystems featuring detection of particles in a wide energy range with improved accuracy for timingand tracking measurements [Pellegrini et al., 2014]. The LGAD application in particle therapy hasbeen also recently investigated [Vignati et al., 2017]. In the proposed setup, the TEPC will providethe energy deposition (cid:15) directly in a tissue-equivalent medium while the LGADs will offer informationabout particle spatial distribution with a precision of about 200 or 300 µ m, depending on the chosenconfiguration.Details of the detector components, geometrical configurations as well as read-out solutions areillustrated here. Using GEANT4 toolkit, we investigated HDM performances when exposed to protonsand carbon ions in the therapeutic energy range. The influence on all microdosimetric quantities whenthe real l is used instead of the mean track length approximation is discussed. Detection efficiencyand tracking precision are also reported. A detailed description of the proposed hybrid detector is given here. The components as wellas the whole setup, including the read-out electronics, are presented. Additionally, the geometry ofall Monte Carlo simulations performed to study the HDM performances when exposed to a mixedradiation beam is illustrated. As TEPC efficiency studies can be found in literature, we focused onthe tracking efficiency of the proposed setup, being the novel aspect to the existing microdosimeter.
TEPC
Tissue equivalent proportional counters have two main advantages compared to other microdosime-ters: i) the sensitive volume is confined in a macroscopic region of a well defined size and ii) the energydeposition is directly measured in tissue and thus does not require a conversion. Furthermore, thegas-based detection offers a large dynamic range of energy depositions down to 0.1 keV/ µ m. The2ain disadvantages are: i) large physical size (above 0.5 mm), which limits the spatial resolution andii) wall effects. The latter stems from the interaction of the incoming radiation with the gas containerand leads to the production of secondary particles, which can deposit additional energy in the de-tector. This effect does not occur in a homogeneous medium and causes an overestimate of energydeposition [Farahmand, 2004].The TEPC included in the detector design is the commercial model type LET-1/2 from FarWest Technology, Inc. The detector sensitive volume is a sphere made of A-150 tissue-equivalentplastic and filled with a pure propane gas whose pressure is adjusted to reach a density of 1.08 10 − g/cm [Chiriotti et al., 2015]. Under these conditions, the detector simulates a tissue-equivalent sphereof 2 µ m diameter. For this TEPC, the mean chord length is 2/3 · LGAD
LGAD is a recent technology in silicon detection system. It was first fabricated at CNM-IMB [CNM-IMB, ] clean room facilities by diffusing a p-type layer just below the n+ electrode [Pellegrini et al.,2014]. From then it has been used for particle timing and tracking and, more recently, its applicationin radiotherapy has been explored [Vignati et al., 2017]. LGADs, using n-in-p silicon diodes, differfrom standard Avalanche Photodiodes (APDs) due to their low and controlled internal multiplicationmechanism for detecting charged particles. This technique allows also to produce thinner sensors withthe same output signal of standard thick substrates.The main features of the LGADs used for the HDM prototype can be found in [Sola et al., 2019].In particular, the active region is 50 µ m thick while the substrate is 300 µ m and can be thinned downto 100 µ m postproduction.An additional LGAD production for HDM is under development at FBK and will include sensorswith alternative geometries and active layer doping in order to obtain different spatial resolutions andgains. A main constrain on the detector geometry is that the total active area has to be less than ∼ to achieve the maximum capacitance required by the read-out chip. Furthermore, the deadarea between two strips must be 66 µ m wide independently of the strip width. Thus, narrower stripsresult into a higher spatial resolution but also a decreased detection efficiency due to a larger deadarea and a resulting lower fill factor. In addition, to cover the same area more strips are needed, whichtranslates into a larger number of channels to be read-out.To find the optimal detector geometry for our application, we simulated three configurations: i) 34strips, each 294 µ m wide and 12.5 mm high (sensor height 13.8 mm and width 13.4 mm); ii) 71 strips,each 114 µ m wide and 12.5 mm high (sensor width 14 mm and height 13.8 mm) and iii) 288 strips,each 114 µ m wide and 50.22 mm high (sensor height 51.52 mm and width 51.84 mm). An image ofthe design project of this configuration of the complete sensor is given in Fig. 1 (left panel). Whilethe first two configurations are now being produced, configuration (iii) is not currently feasible andwas tested to investigate the tracking efficiency for a larger detector with the same spatial resolutionof the 71 strips detector (ii). The LGAD position with respect to the TEPC determine the detector performances and theoptimal configuration depends on the goal of the specific measurement. In this paper, we investigatedthe configuration with the TEPC upstream of the 4 LGAD layers. This setup has been chosen becausewe wanted to characterize the radiation field with standard microdosimetric measurements, withoutpossible artifacts due to the LGADs in front. The distances between the detectors can be found inFig.1 (right panel). In particular, the first LGAD have been placed as close as possible to the TEPCto minimize lateral scattering and energy loss of particles exiting the microdosimeter.
Read-out system
LGAD sensors are read out through the ABACUS chip [Mazza et al., 2019] designed and producedat the University and INFN of Turin (Italy). Each chip reads 24 channels. By default, the outputdriver provides data via a Current Mode Logic (CML) differential stage, which, for HDM purposesand practical reasons, is converted into a Low-Voltage Differential Signaling (LVDS) logic.3fter the conversion, the read-out signals are fed to a board hosting an FPGA and an ARM pro-cessor running Linux. A suitable FPGA program identifies events according to the time of occurrencewith a 1 µ s resolution, along with the channel number corresponding to the detector strip hit by aparticle. The data are then saved in the on-board RAM memory. The board processor allows toprogram the FPGA and to read out the data out of the RAM. The board can be remotely accessedvia Ethernet, and data transferred as simple text files. To investigate the detector performances, we run Monte Carlo calculations using Geant4 toolkit [Agostinelliet al., 2003]. As the HDM design is optimized for applications in particle therapy, we focused thestudy on the response to protons and carbon ions at therapeutic energies. Several physics lists areavailable in Geant4 for different energy ranges. For electromagnetic interactions, the high accuracy list
G4EmLivermorePhysics based on Livermore physics model has been used while hadronic interactionswere managed by
QGSP BIC . All calculations were run to acquired a minimum of 10 events on theTEPC, which is considered an adequate statistics for experimental measurements [Missiaggia et al.,2020].In addition, since microdosimetry deals with patterns of single energy deposition in tissue at themicrometer scale, we computed the energy deposition (cid:15) of a particle traversing the TEPC as the sumof the energy deposited by the primary event and all the related secondary particles that entered thedetector.The simulation geometry consisted of a water phantom with PMMA walls (1.74 cm water equivalentthickness) where the hybrid system was placed. To reproduce a realistic setup, HDM was containedin an additional air box 2.8 × × ∼
160 mm). The beam spots were circular with a 3 cm radius to ensure thatthe detectors were fully immersed in a homogeneous and isotropic radiation field. The detector boxwas placed at 10.74 cm in water along the beam direction. This depth represented a good compromiseto assess HDM performances in a relatively mixed field in terms of particle species and energies, butupstream of the Bragg peak, where most particles have a low energy and thus might stop inside theTEPC.
Tracking algorithm
To measure a particle track, the LGADs were positioned to have the strips in different directions,two horizontals (x plane) and two verticals (y plane). By coupling two sensors with different orienta-tions, a spatial position for a particle can be measured. Thus, two pairs of sensors are the minimumrequirement for reconstructing a particle track. To reproduce a realistic experimental scenario, inthe simulation we scored only the position of the strip hit by the particle. Then, we used a linealinterpolation to reconstruct the particle path inside the TEPC, from which we could estimate the realtrack length.
Tracking efficiency
Using Geant4 simulations, we studied the HDM tracking efficiency. As a first step, we focused onidentifying the lost events and divided them into three categories:1. particles that reach all the detectors, but traverse an inter-strip dead zone in at least one of theLGADs;2. particles that range out before reaching the fourth LGAD;3. particles that undergo lateral scattering and are deflected outside the solid angle covered by alldetectors. 4ategory 1 is related to the probability to hit a dead region and thus depends on the LGADgeometry. Assuming a uniform radiation field, the probability to reach an active strip is given by A act /A tot , where A act is the total area covered by active strips and A tot the total area of the sensor,including both active strips and dead inter-strips. As the probabilities of hitting the active regionof two sensors are independent, the overall probability of the joint event is the product of the singleprobabilities. To test the validity of these assumptions, in the simulation we also scored the particlestraversing the inter-strip regions.For category 2, we investigated the minimum detectable kinetic energy for each ion type, i.e. theminimum energy that a particle must have to pass through all detectors. The values for all particlespecies of interest have been estimated with LISE++ toolkit version 10.0.6a [Tarasov and Bazin,2008]. These kinetic energy cutoffs depends only electromagnetic interactions in the detector layersand do not take into account additional losses due to multiple Coulomb scattering (MCS). To estimatea realistic kinetic energy detection threshold, we performed simulations of HDM exposed to a givenparticle species and decreases the initial energy until we found the minimum value required to traverseall detectors. We then repeated the test for the ion types of most interest.The percentage of particles deflected outside the solid angle covered by all detectors (category 3)dependent on the LGADs size. To assess this value and its dependence on the LAGDs geometry, weperformed simulations for every configuration described in 2.1.For the events seen by the TEPC and by an active zone of each of the 4 silicon layers (i.e. thetrackable particles), we investigated the tracking accuracy using the algorithm described in 2.4. Fromthe simulations, we could extract the real particle track and compare it to that reconstructed withthe tracking algorithm, estimating a mean discrepancy between the predicted and actual values. Thetests were repeated for all LGADs configurations taken into consideration. The composition of the radiation field entering the TEPC was investigated at a depth of 10.74 cmin beam. The results include kinetic energy spectra of all particle species, track length distributionsand microdosimetric spectra yd ( y ) obtained with both the real track length and the mean chordlength. The results are shown in Figs. 3 and 4 for protons and carbon ions, respectively. In detail:panels A and B illustrate the kinetic energy distributions of all particles entering the TEPC, with andwithout the contribution from the primary ions (in both cases the energy distributions of the singlecomponents are normalized to one); the track distributions of all the particles are plotted in panels C ,with the mean chord length of 8.47 mm marked with a dashed red line; panels D contain a comparisonbetween the microdosimetric spectra calculated with the mean chord length approximation ( yd ( y )) orthe real track length ( y T d ( y T )). Furthermore, the mean values and standard deviations of the tracklength distributions are also reported in Table 1 for both ions of interest.Secondaries produced by protons, are mostly low-energy (below 10 MeV) and the distributiondoes not have a peak. For carbon ions, the energy of all fragments species peaks around 170 MeV/u,which is the residual primary beam energy (3, panel A ). Protons can only generate fragments fromthe target nuclei, and thus their energy will be relatively low [Tommasino and Durante, 2015]. Carbonions, instead, can produce both projectile and target fragments, whose kinetic energies have a muchwider range, peaking at the same value as the primary ions [Mohamad et al., 2018, Tommasino et al.,2015].The track length distributions of both protons and carbon ions are very broad and do not presenta peak. Furthermore, the mean track length calculated for both protons and carbon ions is higherthan the mean chord length, indicating that the latter does not provide an accurate description ofthe system. The limitation of the mean chord length approximation can be further investigatedby comparing the standard microdosimetric yd ( y ) spectra with those obtained with the real tracklength ( y T d ( y T )). The latter distributions show a non negligible contribution in the high y T region.Those contributions are due to events that deposit energy along a small chord length and they areunderestimated in the yd ( y ) spectra where the mean chord length value is used. These events have avery high y T and thus are extremely relevant for radiobiological effects.5 articles tracked by HDM We investigated HDM tracking efficiency as well as the characteristics of the tracked events. Tab.2 illustrates for carbon ions and protons the percentage of particles tracked by HDM, their mean tracklength values, their standard deviations and the average discrepancy between the reconstructed andthe real track length. The latter values are reported for the three sensor geometries (34, 71 and 288strips) described in 2.1.The results show that, as expected, the 71 strips configuration collects the least amount of eventsbecause of the reduced fill factor. Increasing the sensor dimension while keeping the same fill fac-tor increases the number of collected events (288 strips configuration). The mean track length andstandard deviation obtained with the tracking algorithm are in good agreement with the real valuesobtained directly from the simulation. This is confirmed also by the small values of the mean absoluteerror, defined as the average absolute value of the difference between the real track length and thereconstructed one.The accuracy of the reconstructed tracks in the three sensor configurations (34, 71 and 288 strips)was further studied in Figs. 5 and 7 for protons and carbon ions, respectively. We compared the tracklength distribution obtained directly from Geant4 with that reconstructed with the algorithm. Thedata are presented as density color plots in panels
A, C and E ; the green dotted line marks a perfectprediction of the algorithm, the red and blue colors represent regions of high and low events density,respectively. The distributions have a cone-like shape, implying a better accuracy of the reconstructedtracks of large lengths. This result is further supported by the presence of high density regions aroundthe green line in the large track lengths zones.To further assess the accuracy of the tracking algorithm, in panels B, D and F we comparedthe track distributions of all particles traversing the TEPC with those detected by HDM and eitherobtained directly from the simulation or estimated with the tracking algorithm. Independently of theprimary ion type, the 34 and 71 strips configurations systematically underestimate the distributionsfor small tracks. On the contrary, the 288 strips configurations provide a more accurate estimation ofthe whole track distributions, especially for protons.The track distributions obtained with the three configurations were used to calculate microdosi-metric yd ( y ) and y T d ( y T ) spectra for all particles tracked by HDM. The results are shown in Figs.6 and 8 for protons and carbon ions respectively. Results show that the yd ( y ) spectra differ fromthe y T d ( y T ) ones, with a peak value shifted to the right in all cases. On the contrary, the y T d ( y T )distributions obtained with the real track length and with the reconstructed track length are similarmostly in the bell shape regions. It can be nonetheless seen that they differ in the tails due to thehigher discrepancy between the real track length and the reconstructed ones for small track lengths.The accuracy between the two increases from the first sensor configuration (panels A ) to the last one(panels C ) under both radiation fields. Particles lost by HDM
As discussed in Section 2.4, we can group lost particles into three categories: i) particles with akinetic energy under the minimum required to traverse all the detectors, ii) particles lost due to MCSand iii) particles that reach all detectors, but cross an inter-strip in at least one LGAD.The minimum kinetic energies necessary to pass all detectors have been studied and are reportedin Tab. 3 for all particles of interest. The values calculated with LISE++ are indicated for allparticles while those obtained with Geant4 only for selected ions representative of the radiation field.The results obtained with the two methodologies agree very well for protons but have a a higherdiscrepancy for carbon ions.Using Geant4 outputs, we characterized the particles lost in terms of kinetic energy when enteringthe TEPC and track length traversed inside the detector. The results are reported in Figs. 9 and 10for protons and carbon ions, respectively. In panels A and B the kinetic energies of all particle typesare plotted with and without the contribution from the primaries, respectively. Independently of thefragment type, the energy spectra have the same shape of those reported in Figs.3 and 4, where allevents are considered. These result indicate that the probability for a particle to be lost is independentof the charge and energy (foe energies above the minimum threshold reported in Tab. 3). Panels C D , the microdosimetric yd ( y ) and y T d ( y T ) spectra of particles that are not tracked by HDM are shown. Similarly to whathappens in panels D of Figs. 3 and 4 where all the particles were taken into account, the peak ofthe y T d ( y T ) distributions are shifted to the left for both protons and carbon ions radiation fields.Further, the high y regions are significantly lower than the high y T regions; again, this is due to theoverestimation of the real track lengths performed using the mean chord length value.Finally, the particles that reach at least one of the inter-strip passive regions with respect to thetotal number of events reaching the detectors (i.e. traversing either an active strip or an inter-stripregion) have been estimated to be 63% for the 34 strips configuration and 81.5% for the 71 stripsconfiguration. Increasing the number of strips in each sensor results in a substantial increase of thedetection efficiency. A innovative design for a hybrid microdosimeter (HDM: hybrid detector for microdosimetry) ispresented in this paper. HDM is a two-stage detector composed by a TEPC and four layers ofLGAD sensors. The combination of two different types of sensors (gas- and silicon-based) results insuperior features and detection performances not offered by any existing microdosimeter. In fact, theTEPC gives a direct measurement of energy deposition in tissue while the LGADs provides particletracking. The latter information has two main advantages: it improves the TEPC spatial resolution tosubmillimetric precision and offer the real track length traverse by each particle in the TEPC. Thus,the microdosimetry spectra obtained from HDM are calculated using real track lengths instead of themean chord approximation.To assess the detector capability, we performed Monte Carlo simulations using Geant4 toolkit.As the primary application of HDM is particle therapy, we investigated its performances exposed toprotons and carbon ions at a certain water depth.The limitations of the mean chord length for our geometry are evident by looking at the track lengthdistributions of all particles traversing the TEPC (Figs. 3,4 and Tab. 1). This approximation is basedon the specific assumption that the TEPC is exposed to a uniform isotropic radiation field. In thecases considered here, although the beam generates such type of randomness, the water surroundingthe TEPC causes the isotropy assumption to drop, with a direct consequence on the resulting meantrack length. To further validate this, simulations without the water phantom has been performedand a mean track length value of 8.56 has been obtained for protons and 8.45 for carbon ions, bothin accordance to the nominal mean chord length value.However, even if a mean value of chord length based on more appropriate kind of randomness isused, the data reveal that a mean value is non representative of the whole track length distribution,since the standard deviations are rather large. This behavior is noticeable by the broadness of thetrack distributions in panels C of the Figs. 3 and 4.Discrepancies between the mean chord and the real track length translate into difference betweenthe standard yd ( y ) and the alternative y T d ( y T ) microdosimetry spectra (Figs. 3,4), the more evidentbeing in the high y T regions. The majority of particles populating these areas have a track lengthsubstantially smaller than the mean chord, and thus their actual lineal energy is is systematicallyunderestimated if using the mean chord approximation.The detector efficiency is defined by the number of particles that traverse the LGADs active regions,i.e. those that are tracked. This number depends on the LAGD configuration, i.e. the number ofdetection strips contained in a sensor. As the dead interstrip area is the same independently of theconfiguration, for a given total area of the sensor, by lowering the number of strips the detectionefficiency increases. However, a larger number of strips results in a superior spatial resolution. Tooptimize the detector design for our application, we investigated HDM performances using threedifferent LGAD configurations: 34, 71 and 288 strips per sensor.Detection and tracking efficiencies were assessed by studying the composition of the radiation field7etected by HDM versus the radiation field incoming on the TEPC. We identified three categoriesof events: i) particles detected by the entire system (i.e tracked events); ii) particles lost (i.e. onlytraversing the active volume of some detectors); iii) particles non-trackable (i.e. those with not enoughenergy to reach the fourth LGAD).For each category, we studied the kinetic energy spectra, track length distribution, real track versustrack reconstructed with the tracking algorithm and microdosimetric spectra.Independently of the primary ion and LGAD configuration, the mean track length of the trackedevents is always higher that the value of all incoming particles. Events traversing the TEPC with asmall track have a higher probability to miss the LGAD detectors. In fact, LGADs with 34 and 71 stripsconfigurations have a total height and width comparable to the TEPC diameter, so if a particle reachesthe TEPC with a given angle with respect to the primary beam direction, it is probable that its pathwill not cross all the LGADs. This hypothesis is confirmed by the fact that the 288 strips configurationcollects a significantly higher portion of small-track particles (Figs. 5 and 7 ). Furthermore, for thisconfiguration the mean track length of the tracked events is closer to the value of all particles (seeTab. 2). The mean tracks obtained when HDM is exposed to protons and carbon ions are similar forthe 34 and 71 strips configurations. For the 288 strips configuration, HDM provides a more accuratetrack distribution for protons than for carbon ions. In fact, secondary fragments produced by protonsreach, on average, smaller scattering angles compared to those generated by carbon ions [Rovitusoand La Tessa, 2017].However, those are the chords that suffer most from a high error on the tracking, as panels A,C,E of Figs 5 and 7 show for all the configurations. Furthermore, panels A , D and G , besides confirmingthe above mentioned fact that the bigger sensor takes better into account lower track lengths, theydemonstrate also that the spatial resolution of the sensors, namely the widths of their strips, has aclear effect on the homogeneity of the track distribution. In fact, it can be noticed that the lower thespatial resolution is, the more the reconstructed tracks will have some preferential track lengths.Finally, a comparison between panels F of Fig.5 and 7 reaffirms that for protons the
288 strips configuration is able to collect a track distribution which is very similar to the real one, while forcarbon ions the distribution is still slightly underestimated at short tracks.Differences in the track length distributions for the LGAD configurations translate into differentmicrodosimetric y T d ( y T ) spectra (Figs. 6 and 8). A bigger sensor, like the 288 strips configuration,is able to collect more events with smaller TEPC tracks, which are the main contributors of the high y T region.The characterization of lost events indicates that the majority is caused to the LGADs fill-factor(interstrip regions). Thus, this issue can be resolved by increasing the measurement time to collectenough statistics.For events that suffer MCS in the detectors, if the deviation angle is large enough they will belost. In fact, even trying to enlarge LGADs or place them at a given angle with respect to the beamdirection, the reconstructed track would be affected by errors too large to make the data of any value.The probability of loosing a particle because of MCS strongly depends on the HDM position in theradiation field. Depths in the Bragg peak regions as well as distal positions represent the worst casesbecause of the low kinetic energy of the particles populating these regions.Finally, particles that do not have enough kinetic energy to reach all detectors are also a limit ofHDM detection efficiency. Nonetheless, this issue can be partly solved by exploring the possibility ofproducing LGADs with thinner active layers or decreasing the substrate width. For instance, reducingthe total LGAD thickness down to 100 µ m is considered achievable in the near future. The design of a new hybrid detector for microdosimetry (HDM: hybrid detector for microdosimetry)is presented in this work. HDM is composed by a TEPC followed by four LGADs, and provides energydeposition in tissue as well as tracking of single particles with a submillimeter spatial precision. HDMunique feature is that it can provide the real track length that a particle travel inside the TEPC, fromwhich the microdosimetric spectra can be calculated without using the mean chord approximation.To investigate the detector efficiency, we performed Monte Carlo simulations with Geant4 toolkit and8xposed HDM to both protons and carbon ions at therapeutic energies.Results show evidence on both the feasibility of the proposed hybrid system and on the advancesthat this detector will contribute to in particle therapy. The possibility of exploiting a tracker insteadof geometrical assumptions are of great help in several situations, especially in a mixed and nonisotropic radiation field. In addition, a precise a priori knowledge of the beam characteristics is notalways easy to achieve.The LGAD technology chosen for this scope is constantly evolving and improving. The possibilityof using more advanced versions of LGADs will be considered in future, for example to drasticallyincrease the fill factor by reducing the interstrip layers, while keeping the same spatial resolution.Moreover, as the spatial resolution can be improved by using narrower strips, we will test theseconfigurations, which can also increase the tracking efficiency. Additionally, the advantage of beingable to select the gain of LGADs according to specific experimental needs is of great help in view ofa wide-ranging use of HDM in different irradiation scenarios.Further, additional efforts will be put on studying more advanced tracking algorithms to bettertake into account significant deviations from a linear track, with specific reference to scattering events.Finally, to improve the field characterization, we will explore the possibility to use the LGADs foracquiring information on the particle charge.
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financialrelationships that could be construed as a potential conflict of interest.
Acknowledgments
This work was supported by the Italian National Institute for Nuclear Physics (INFN) CSN5 CallNEPTUNE. The authors thank Valeria Conte for the many precious suggestions and useful discussionsthat helped improve the quality of this work.
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Microdosimetry and itsApplications . Springer. 10 on Mean tracklength [mm] Standarddeviation [mm]Carbon
Proton
Ion Configuration Trackedparticles [%] Mean track lengthof trackedparticles [mm] Standarddeviation [mm] Mean absolutetrackingerror [mm]Real Reconstructed Real ReconstructedCarbon
34 strips
71 strips
288 strips
Proton
34 strips
71 strips
288 strips
Table 2: Percentage of particles tracked by HDM, including their mean track length, standard devi-ations and the absolute values of the mean tracking error of the algorithm with respect to the actualvalue. The results are reported for both protons and carbon ions and for three LGAD configurations(34, 71 and 288 strips).
Figure captions
Proton[MeV/A] Deuterium[MeV/A] Tritium[MeV/A] Helium-3[MeV/A] Helium-4[MeV/A] Lithium-7[MeV/A] Beryllium-9[MeV/A] Boron-11[MeV/A] Carbon-12[MeV/A]
LISE++ 17 11 8 20 17 20 24 28 34GEANT4 17 12 9 - 17 - - - 37
Table 3: Minimum kinetic energies for several isotope types necessary to traverse all the detectors.The values have been calculated with LISE++ toolkit and, for the most representative of the radiationfield, also with Geant4. 11igure 1: Panel (A) : design of one LGAD sensor with 34 active strips. Panel (B) : Scheme of the HDMsetup, showing the TEPC followed by four LGAD layers. Distances between detectors are reported inmillimeters.Figure 2: 3D scheme of the geometry used for all Geant4 simulations. Both the TEPC and thefour 24-strips LGADs are contained in PMMA box filled with air. The box is placed inside a waterphantom, whose walls are made of PMMA. A broader view is show in panel (A) ), while a zoom onHDM is illustrated in panel (B) . 12 rotons
A BC D
Figure 3: Characterization of the radiation field generated by 150 MeV protons after traversing 10.74cm of water and seen by the TEPC. Panels A and B : kinetic energy spectra of the most abundantcomponents of the radiation field including and excluding the primary ions. Panel C : track lengthdistribution of all the particles detected by the TEPC. The mean chord length at 8.47 mm is markedwith a red dotted line. Panel D : microdosimetric yd(y) spectra obtained with the mean chord lengthapproximation (red line) and microdosimetric y T d ( y T ) spectra obtained using the real chord lengthvalues (blue line) . 13 arbon ions A BC D
Figure 4: Characterization of the radiation field generated by 290 MeV/u carbon ions after traversing10.74 cm of water and seen by the TEPC. Panels A and B : kinetic energy spectra of the most abundantcomponents of the radiation field including and excluding the primary ions. Panel C : track lengthdistribution of all the particles detected by the TEPC. The mean chord length at 8.47 mm is markedwith a red dotted line. Panel D : microdosimetric yd(y) spectra obtained with the mean chord lengthapproximation (red line) and microdosimetric y T d ( y T ) spectra obtained using the real chord lengthvalues (blue line). 14 rotons A B
C D
E F
Figure 5: HDM performances when exposed to 150 MeV protons at 10.74 cm depth in water. Theresults are shown for 34, 71 and 288 strips LGAD configurations. Panels
A, C, E shows 2D colorplots of track length obtained with HDM versus real track length calculated directly with Geant4.The green dashed line at 45 degrees indicates the perfect agreement between the two datasets. Thecolors represent regions with a high (red) or low (blue) density of events. Panels
B, D, F illustratethe comparison between the track length distributions of particles tracked by HDM considering thereal track lengths calculated with Geant4 (blue line) or that reconstructed with the tracking algorithm(green line). The distributions of the real track lengths obtained directly from the simulation is alsoshown (red line). 15 rotons A B C Figure 6: Microdosimetric spectra of all particles tracked by HDM when irradiated with 150 MeVprotons at a depth or 10.74 cm in water. The distributions include the standard yd ( y ) spectracalculated with the mean chord length (red line) and the y T d ( y T ) spectra obtained either with thereal track length (green line) or with the value estimated with the tracking algorithm (blue line). Thedistributions are shown for LGAD configurations with 34 (panel A ), 71 (panel B ) and 288 (panel C )strips.. 16 arbon ions A B
C D
E F
Figure 7: HDM performances when exposed to 290 MeV/u carbon ions at 10.74 cm depth in water.The results are shown for 34, 71 and 288 strips LGAD configurations. Panels
A, C, E shows 2D colorplots of track length obtained with HDM versus real track length calculated directly with Geant4.The green dashed line at 45 degrees indicates the perfect agreement between the two datasets. Thecolors represent regions with a high (red) or low (blue) density of events. Panels
B, D, F illustratethe comparison between the track length distributions of particles tracked by HDM considering thereal track lengths calculated with Geant4 (blue line) or that reconstructed with the tracking algorithm(green line). The distributions of the real track lengths obtained directly from the simulation is alsoshown (red line). 17 arbon ions A B C Figure 8: Microdosimetric spectra of all particles tracked by HDM when irradiated with 290 MeV/ucarbon ions at a depth or 10.74 cm in water. The distributions include the standard yd ( y ) spectracalculated with the mean chord length (red line) and the y T d ( y T ) spectra obtained either with thereal track length (green line) or with the value estimated with the tracking algorithm (blue line). Thedistributions are shown for LGAD configurations with 34 (panel A ), 71 (panel B ) and 288 (panel C )strips. 18 rotons A BC D
Figure 9: Characterization of the particles lost by HDM when irradiated with 150 MeV protons at adepth or 10.74 cm in water. Panels A and B : kinetic energy spectra of the most abundant componentsof the radiation field including and excluding the primary ions. Panel C : track length distribution ofall the particles detected by the TEPC. The mean chord length at 8.47 mm is marked with a red dottedline. Panel D : microdosimetric yd(y) spectra obtained with the mean chord length approximation (redline) and microdosimetric y T d ( y T ) spectra obtained using the real chord length values (blue line).19 arbon ions A BC D