calibration and geant4 simulations of the phase ii...

FERMILAB-TM-2617-AD-CD-E

Calibration and GEANT4 simulations of the Phase II

Proton Compute Tomography (pCT) Range Stack

Detector

December 29, 2015

S. A. Uzunyan, G. Blazey, S. Boi, G. Coutrakon,A. Dyshkant, K. Francis, D. Hedin, E. Johnson, J. Kalnins, V. Zutshi,

Department of Physics, Northern Illinois University, DeKalb, IL 60115, USA;R. Ford, J .E. Rauch, P. Rubinov, G. Sellberg , P. Wilson,

Fermi National Accelerator Laboratory, Batavia, IL 60510, USA;M. Naimuddin, Delhi University, 110007, India

1 Introduction

Northern Illinois University in collaboration with Fermi National Accelerator Laboratory(FNAL) and Delhi University has been designing and building a proton CT scanner [1]for applications in proton treatment planning. In proton therapy, the current treatmentplanning systems are based on X-ray CT images that have intrinsic limitations in terms ofdose accuracy to tumor volumes and nearby critical structures. Proton CT aims to overcomethese limitations by determining more accurate relative proton stopping powers directly as aresult of imaging with protons. Fig. 1 shows a schematic proton CT scanner, which consists ofeight planes of tracking detectors with two X and two Y coordinate measurements both beforeand after the patient. In addition, a calorimeter consisting of a stack of thin scintillator tiles,arranged in twelve eight-tile frames, is used to determine the water equivalent path length(WEPL) of each track through the patient. The X-Y coordinates and WEPL are requiredinput for image reconstruction software to find the relative (proton) stopping powers (RSP)value of each voxel in the patient and generate a corresponding 3D image. In this note wedescribe tests conducted in 2015 at the proton beam at the Central DuPage Hospital inWarrenville, IL, focusing on the range stack calibration procedure and comparisons with theGEANT 4 range stack simulation.

2 The GEANT 4 model

To verify measurements obtained by the scanner at the CDH proton beam the scannerresponse was simulated using a detailed model based on the GEANT-4 software. Fig. 2

1

Operated by Fermi Research Alliance, LLC under Contract No. De-AC02-07CH11359 with the United States Department of Energy

Figure 1: Four (X,Y) stations measure the proton trajectory before and after the patient.A stack of 3.2 mm thick scintillator tiles measures the residual energy or range after thepatient.

shows a spherical water phantom between the tracker planes of the scanner model. Thesimulated responses of the range stack and tracker stations were analyzed with the samesoftware as for the data.

Figure 2: The GEANT4 visualization of the scanner model used in the simulations.

3 The CDH test beam

Figure 3 shows the NIU scanner mounted on a cart in a treatment room at Central DuPageHospital. The proton beam enters the upstream tracker planes from the right followed bythe downstream tracker planes and finally the range stack. In this note the range stack tilesare labeled from zero (the tile closest to the tracker) to 95. Data were obtained using proton

2

beams of energy in range from 103-225 MeV, equivalent to 8-32 cm proton stopping rangein water.

Figure 3: Fully assembled proton CT scanner at CDH Proton center. From right to left,beam enters the upstream tracker planes followed by the downstream tracker planes andfinally the range stack. The gap in the middle is the position of the rotation stage for thehead phantom in the horizontal plane.

3.1 Data acquisition (DAQ) system and event selection

The DAQ system of the scanner is described in [2]. The range stack data are collectedby twelve front-end boards. Each board provides the readout of one eight-tile range stackframe in form of time-stamped records of signal amplitudes in all tiles of the frame. We formthe proton candidate event by combining records with close time-stamps. We remove eventscandidates with duplicated frames (overlapped tracks). We then found the frame with aBragg peak, or stopping frame, and check that all frames before the stopping frame are alsopresent in the event.

3.2 Units of measurement

The CDH accelerator control system is tuned to operate with proton beams with energiesexpressed in units of the proton stopping range in water in cm, Rw(cm). One can also expressthe proton stopping range Rw, and thus the beam energy Ebeam, in density-independent unitsof g/cm2 :

Ebeam(g/cm2) ≡ Rw(g/cm2) = Rw(cm) × ρw(g/cm3) (1)

To obtain the energy Ebeam in MeV we use proton energy-range tables (a.k.a. Janni’stables) [4]. A fit of the stopping range Rw(g/cm2) as a function of E(MeV ) is shown inFig. 4(a). We use

Rw(g/cm2) = 0.0022 × E(1.77)MeV (2)

to convert beam energies between MeV and g/cm2 units.We calculate the proton stopping range in the range stack Rrs(g/cm2) using the measured

proton stopping position as described in Section 5. We compare the Rrs(g/cm2) with the

3

range calculated from the total energy measured by the range stack using the energy-rangedependence in polystyrene shown in Fig. 4(b).

Proton energy, MeV10 210

Ran

ge, 0

.1*(

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900 / ndf 2χ 201.4 / 42

p0 0.0001327± 0.02153

p1 0.001395± -1.773

/ ndf 2χ 201.4 / 42

p0 0.0001327± 0.02153

p1 0.001395± -1.773

Proton Range vs Energy in water


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p0 0.0001796± 0.02064

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/ ndf 2χ 102.3 / 42

p0 0.0001796± 0.02064

p1 0.001989± -1.78

Proton Range vs Energy in polystyrene

(a) (b)

Figure 4: a) The proton stopping range in water Rw(g/cm2) (black dots) versus proton energy

E(MeV ), as measured in [4]. The fit Rw(g/cm2) = 0.0022×E(1.77)MeV conversion function (the

red line) is used to find beam energies in MeV that correspond to nominal CDH energies incm. b) The proton stopping range in polystyrene Rpoly(g/cm2) (black dots) versus protonenergy E(MeV ).

4 Stack calibration procedure

Energy deposition in each range stack scintillator tile is measured by two SiPMs connectedto the tile’s single wavelength shifting (WLS) fiber. After passage of a proton, for each of thetwo SiPMs the maximum digitized signal, Amax

SiPM , is collected by the DAQ system. Thus themeasured energy deposition in each range stack tile, AADC

tile , is obtained as a sum of AmaxSiPM

signals from SiPMs connected to this tile. This measurement varies from tile to tile evenfor protons of similar energy due to differences in the SiPM’s properties and the settings ofcorresponding readout channels. The following four step procedure is applied to calibratethe range stack detector.

1) We measure pedestal amplitudes ApdSiPM1tn , ApdSiPM2

tn and amplitudes A1peSiPM1tn ,

A1peSiPM2tn of the first photo-electron (PE) peak for all range stack tiles, tn, by collecting

events with no beam. Fig. 5(a) and Fig. 5(b) show these distributions for SiPM1 and SiPM2of Tile0. The combined SiPM1+SiPM2 no-beam signal in Tile0 is shown in Fig. 5(c).Figure 6 shows calibration signals for all 16 SiPMs of the first range stack frame. From thesedata the ADC to PE conversion coefficients for each SiPM are calculated as

KpeSiPMtn = A1peSiPM

tn − ApdSiPMtn

Ratios of PE conversion coefficients KpeSiPM0tn /KpeSiPM0

t0 of the first and second SiPM ineach tile to the conversion coefficient in the first SiPM in Tile0 are shown in Fig. 7(a) andFig. 7(b). Most sensors have a response within 10% of one another.

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<Pedestal> = 102.84 ADC

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PE/ADC = 18.0055

BID= 30, Tile = 0:: Channels (0,16)

(a) (b) (c)

Figure 5: Measured Tile0 signal amplitudes : a) pedestal and the first photo-electron (PE)peak in the SiPM1 of Tile 0 in events with no beam. b) pedestal and the first photo-electron(PE) peak in the SiPM2 of Tile 0 in events with no beam. c) SiPM1+SiPM2 combined.

2) The proton energy deposition in each tile Epetn in PE units is obtained via

Epetn = (AsSiPM1

tn − ApdSiPM1tn )/KpeSiPM1

tn + (AsSiPM2tn − ApdSiPM2

tn )/KpeSiPM2tn .

Fig. 8(a) and Fig. 8(b) show the PE signals of SiPM1 and SiPM2 in Tile0, Fig. 8(c) showsthe combined SiPM1+SiPM2 signal, Ape

t0 , in Tile0.

3) We measure signals EclbExptn of all range stack tiles in the region far away from the Bragg

peak. We conducted two calibration runs at an energy of 32 cm (225 MeV). For the secondrun, the assembled scanner was turned 180 degrees to expose the back tiles to the beam first.The “front” run is used to calibrate the first front 48 tiles of the stack, while the “back” runis used to calibrate the 48 back tiles. We assume that the “true” EclbTrue

tn amplitudes of thetile signals follow energy profiles calculated from proton energy-range tables for polystyrene(the material used for the range stack tiles).

Figure 9(a) shows the tabulated proton dE/dx dependence. Fig. 9(b) and Fig. 9(c) showenergy profiles calculated for protons entering the range stack with energies of 30.6 cm inthe “front” run and 31.4 cm in the “back” run (corrections to the nominal CDH acceleratorenergy were applied to account for material in the tracker which is only present in the “front”run configuration and material in the CDH beam transport line, as discussed in Section 5.3).All “true” EclbTrue

tn , tn = 0, 95 amplitudes are normalized to the signal EclbExpt0 of the Tile0

in the “front” run. That is, we take the observed energy in Tile0 as to be correct.The comparison of signals observed in Tile0 in runs of different energies and expected

signals obtained by integration of the tabulated proton dE/dx dependence are shown inFig. 10. The expected signals are normalized to the mean Tile0 data signal in the 32 cmrun. The measured and calculated amplitudes are in good agreement, however the datasignals are about 5% higher at low proton energies.

4) We extract normalization coefficients Kclbtn ≡ EclbTrue

tn

EclbExptn

and use them in all data runs to

correct the observed signals in the range stack tiles. Figures 11(a) and (b) show the correctedenergy deposition profiles (the mean number of photoelectrons from about 10000 protons pertile as function of tile number) for 200 MeV protons. Corrected energy profiles for differentbeam energies are shown in Fig. 12 through Fig. 14. Slight variations are attributed to

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Figure 6: No beam signals used for PE calibration for the first eight tiles of the range stack.

6

Tile number

0 10 20 30 40 50 60 70 80 90

PE

(tN

)/P

E(t

0)

0

0.2

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0)

0

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0.4

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0.8

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1.6

1.8

2

(a) (b) hfill

Figure 7: a) The ratio of PE conversion coefficients KpeSiPM0tn/KpeSiPM0t0 for the firstSiPMs. b) The ratio of PE conversion coefficients KpeSiPM1tn/KpeSiPM0t0 for the secondSiPMs.

statistical effects.

5 Range and energy measurements

The NIU image reconstruction software uses the WEPL of a scanned object, weplobj. Foreach proton the weplobj can be obtained from WEPL of the range stack, weplrs,

weplobj = Ebeam(cm) − weplrs,To find weplrs one need calibrate the total energy Ers or the stopping range Rrs measured bythe range stack detector using a set of phantoms with known WEPL [3]. Here we comparethe accuracy of Rrs and Ers to choose what measurement is preferrable for the WEPLcalibration.

To find the total energy Ers deposited in the range stack we first search for the framewith a stopping tile (the “stopping” frame), then sum signals (in PE units) from all tilesand all frames including the stopping frame. Only events with no missing frames before thestopping frame were selected. Figure 15(a) shows the total Ers in PE measured in a runwith Ebeam = 26 cm.

To find Rrs we use the Z-position of the tile with the maximum signal (the “stopping”tile, labeled as ntstop). We calculate Rrs as

Rrs = (ntstop + 1) × (tileW × tileD + alW × alD + mlrW × mlrD)+

nframe × (alW × alD + mlrW × mlrD), ntstop = [0, 95]; nframe = [0, 11]

where (tileW, alW,mlrW ) = (3.2, 0.00022, 0.00625) mm are the widths of scintillator andwrapper (aluminized mylar) layers, and (tileD, alD, mlrD) = (1.011, 2.700, 1.397) g/cm3 arethe densities of these materials. The second term accounts for the extra layer of the wrapperin the end of each range stack frame.

Note, the stopping ranges in polysterene and mylar expressed in g/cm2 are approximatelyequal to the proton stopping range in water Rw:

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Constant 38.4± 5955 Mean 0.03± 11.46 Sigma 0.051± 4.237

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/ ndf 2χ 46.44 / 7

Constant 38.4± 5955 Mean 0.03± 11.46 Sigma 0.051± 4.237

BID= 30, Tile = 0:: Channels (0,16)

(a) (b) (c)

Figure 8: Measured signal amplitudes (PE units) in Tile0 at a beam energy of 26 cm (200MeV) after subtracting pedestals : a) in SiPM1; b) in SiPM2; c) sum of SiPM1 and SiPM2.The means of Gaussian fits of combined signals away from the Bragg peak at a beam energyof 32 cm (225 MeV) were used to extract the normalization coefficients for the range stacktiles.

Rw(cm) =

∫ Rm

0

RSPmdL (3)

where RSPm is the proton stopping power of the medium relative to water and L is thephysical proton path length along the calorimeter and Rm is the physical depth at whichthe proton stops in the range stack. Then, neglecting small variations ( < 0.5%) in meanionization potential between water, polystyrene and mylar, as used in the Bethe Blochequation, the water equivalent range of the proton becomes

Rw(cm) '∫ Rm

0

ρm/ρwdL, and, forρw = 1.0 g/cm3, Rw(g/cm2) '∫ Rm

0

ρmdL

Thus we expect Rrs to have linear dependency on the beam energy, Ebeam, expressed in cm.Figure 16 shows Rrs in a run with Ebeam = 26 cm.

We also can find the Rrs from the total energy Ers using Janni’s range-energy tables Thismethod requires expression of Ers in MeV, and we use the conversion coefficient calculatedas the ratio of the mean amplitude of the data signal (in number of photoelectrons) to themean amplitude of the estimated MC signal (in MeV) in Tile0, in 26 cm runs. Figure 15(b)shows the proton stopping range in the range stack Rconv

rs (g/cm2) calculated from Ers via

the Rconvrs = 0.0021 × E

(1.78)rs conversion function obtained from Janni’s tables. Finally, we

can find weplrs directly, from the WEPL of a scanned object calculated from Ers using theBethe-Bloch equation. Howewer, this will also require calibration, as the measured Ers onlyincludes the visible part of deposited energy. Figure 15(c) shows the WEPL of the rangestack weplcalc

rs (cm) calculated from Ers via

weplcalcrs = Ebeam(cm) −

∫ Ers

Ebeam

1

S(Ep)dE (4)

where S(Ep) = −dE/dx is a water stopping power for proton with energy Ep.

8


dE/d

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eV/(

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/ ndf 2χ 7.908 / 36

p0 1.506± 0.9988

p1 0.2319± 0.02188

p2 6.061± -311.2

p3 0.0169± -0.8435

/ ndf 2χ 7.908 / 36

p0 1.506± 0.9988

p1 0.2319± 0.02188

p2 6.061± -311.2

p3 0.0169± -0.8435

Proton Energy loss in polystyrene

Tile number0 20 40 60 80 100

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140Corrected CDH energy: 30.616 cmDeposited energy: 219.268 MeVDeposited energy: 1771.89 PE

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140Corrected CDH energy: 31.441 cmDeposited energy: 221.587 MeVDeposited energy: 1790.63 PE

(a) (b) (c)

Figure 9: a) The proton dE/dX dependency in polystyrene as tabulated in Janni’s protonenergy-range tables. b) The “true” front run signal profile used for calibration of tiles (0-47)of the range stack. c) The “true” back run signal profile used for calibration of tiles (48-95)of the range stack.

We fit peaks of the Rrs and Ers distributions with a Gaussian and use the mean and σparameters of the fits to study the linearity (Rrs and Ers as functions of the beam energy)and resolution (σ(Ers)/Ers and σ(Rrs)/Rrs as functions of Ers and Rrs) of the range stackdetector. The linearity and resolution plots for the proton stopping position Rrs are shownin Fig. 17 and the linearity and resolution plots for the energy measurement are shown inFig. 18. The good linearity with a non zero intercept of the Rrs shows there is material infront of the range stack at all energies. The energy measurement has lower accuracy (energyresolution ranges from 5.5% to 3.5% , compared to 2.2-1.2% for Rrs) and also shows anunexpected suppression at beam energies of 27 cm and 28 cm. Additionally, Figures 15(a)and (b) show that if we try to extract the stopping range or WEPL in the range stack fromthe direct energy measurement, the Rconv

rs and distributions with σ(Rconvrs ) = 11.7 mm and

σ(weplcalcrs ) = 11.8 mm are significantly wider than Rrs distribution with σ(Rrs) = 3.3 mm.

Thus, the direct Rrs measurement is preferred for the WEPL calibration.

5.1 Comparison with GEANT 4 simulations

A GEANT 4 simulation of the pCT detector was used to obtain the energy deposition Eg4tn

in the range stack tiles for different beam energies. We converted the range Rp to energy Ep

using the inverse of the Janni fit:Ep = (Rp/0.0022)(1/1.77).

To compare energy profiles and total energy deposition in the range stack, the G4 signals inthe tiles were expressed in the number of photoelectrons by normalizing to the data signalin Tile0 in the 26 cm beam run.

5.2 Smearing of simulated tile signals

To account for photo-statistics and SiPM readout, smearing of the G4 signals in each tilewas done as:

Sg4tn = G(< Sped

tn >) + P (Eg4tn )− < Sped

tn > ,where < Sped

tn > is a mean sum of SiPM pedestals in tile n from calibration runs, Eg4tn is the

9

Proton Energy, 0.1*(g/cm2)0 50 100 150 200 250 300 350

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nal a

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itude

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ile0,

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elec

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s

10

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18

20

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24

/ ndf 2χ 0.1631 / 11p0 0.3634± 22.5 p1 0.003388± -0.06578 p2 7.531e-06± 9.186e-05

/ ndf 2χ 0.1631 / 11p0 0.3634± 22.5 p1 0.003388± -0.06578 p2 7.531e-06± 9.186e-05

Data

Janni’s tables

Figure 10: Measured signal amplitudes (blue crosses) and expected amplitudes calculatedfrom Janni’s tables (red line) in Tile0 of the range stack for different proton energies. Theexpected signals normalized to the mean (over 10000 protons) Tile0 data signal in the 32 cmrun.

energy deposition in tile n obtained from GEANT, and G(Spedtn ) and P (Eg4

tn ) are the sum ofSiPM pedestals smearing using Gaussian and Eg4

tn smeared using Poisson distribution. Theeffect of smearing is shown in Fig. 19, where the left plot shows the total energy depositionin the range stack at a beam energy of 26 cm (or 200 MeV) in data; the center histogramshows the unsmeared simulated signal, and the right histogram shows the smeared signal.Comparison of data and simulated signals from 200 MeV protons in Tile0 and in Tile74 (thestopping tiles with the maximal signal for this energy) are shown in Fig. 20.

5.3 Beam energy correction and smearing for the MC simulations

The total stopping range of all material along the proton path, Rtotal, before the protonstopping position is equal to the nominal beam energy of the accelerator in g/cm2, Rtotal ≡Ebeam

total . In our test beam configuration, the total stopping range can be expressed as:

Rtotal = Rrs + Rbeamline + Rtracker + sft const,

where Rrs, Rbeamline, Rtracker are the proton ranges in the range stack, any material in theaccelerator beam line, and the tracker, respectively.

The sft const is the systematic shift of the range measurement due to initial and arbi-trary origin of the range calculation. We extract the stopping range using the position ofthe tile with the maximum signal and the total width of scintillator and wrapping layersincluding this stopping tile. The definition of stopping position is arbitrary and for con-sistency estimated with the MC. We estimate the sft const using simulations of the rangestack response in configuration with no tracker. In the GEANT model we do not have anyother material before the range stack, and the sft const can be obtained from the fit of theproton stopping positions at different beam energies, as shown in Fig. 21(a). Evaluationof the fit function at zero beam energy results in sft const=0.7 ± 0.4 mm in water (the−p0 parameter of the fit). From the fit of the measured proton stopping position Rrs in

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<A-max>, PE counts


(a) (b)

Figure 11: The mean number of photoelectrons in the range stack tiles as a function of tilenumber produced by protons with energy 26 cm (200 MeV) (a) raw; (b) calibrated. Theerrors bars reperesent ±1 sigmas of Gaussian fits about the average, for an example seeFig. 8(c) .

Fig. 17(a) the Rbeamline +Rtracker +sft const is equal to 14.3±0.4 mm. This means that theproton energy at the range stack entry point, Epentry, is lower than the nominal acceleratorbeam energy by 13.6 ± 0.5 mm (after subtracting the 0.7 mm sft const parameter) for alltest runs. To accurately compare the energy and range measurement with simulations, theEpentry should be the same in data and in MC. Figure 21(b) shows the simulated protonstopping positiom Rrs in a configuration with the tracker, and here the Rtracker + sft constis equal to 7.9 ± 0.5 mm (again 0.7 mm is subtracted from the −p0 parameter of the fit).Thus for simulations we subtract the difference of 5.7 mm (between the 13.6 mm observedin data and the 7.9 mm observed in MC) from all nominal beam energy points in GEANTruns to compensate. The corrected results are shown in Fig. 21(c) and now the Epentry inGEANT runs is equal to the Epentry in data runs.

Simulations also predict that this method of upstream material width estimation fromthe range stack measurements works with an accuracy of about 0.5 mm in a configurationwith a variable width of a rectangular water phantom installed before the range stack. Forthe water phantom width of 2 mm, 5 mm, 10 mm, and 15 mm the simulated measurementsare 2.1 mm, 5.4 mm, 10.3 mm and 14.3 mm, respectively.

Additionally we smear Epentry in GEANT in a range between 0.05% at 100 MeV to 0.02%at 200 MeV to account for the CDH beam energy spread.

5.4 Comparison of proton stopping position measurements

The linearity and resolution plots for the proton stopping position Rrs are shown in Fig. 22.Fits correspond to the simulated results. We observe excellent agreement both in linearityand resolution. We used the detector model in which the density of the scintillator tilesis decreased by 1% compare to the nominal value of 1.025 ± 0.010 g/cm3, which providesthe best agreement between measured and simulated proton stopping positions for differentbeam energies, as shown in Figure 23.

11

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n si

gnal

am

plitu

de, P

E c

ount

s

0

20

40

60

80

100

120

<A-max>, PE counts


Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n si

gnal

am

plitu

de, P

E c

ount

s

0

20

40

60

80

100

120

<A-max>, PE counts

Energy deposition in tilesRun: run_Feb28_024905_bmr31_r32_stackBack_cdh_pctmonTree

(a) (b)

Figure 12: The mean number of photoelectrons in the range stack tiles as a function of tilenumber produced by protons with energy (a) 32 cm (225 MeV), “front” run ; (b) 32 cm (225MeV), “back” run, no tracker. The errors bars reperesent ±1 sigmas of Gaussian fits aboutthe average.

5.5 Comparison of energy measurements

The linearity and resolution plots for the energy measurements Ers =∑

Etn in the rangestack are shown in Fig. 24. Fits correspond to the simulated results. The instrumentaldepression in the data linearity plot at beam energies of 27 cm and 28 cm is not presentin simulations. The MC model response shows good linearity. The resolution is between4% and 2% that is higher than observed in data (between 5% and 3%). A comparisonof measured (blue crosses) and simulated (black square) energy measurements in Tile0 fordifferent proton energies is shown in Fig. 25.

The normalized simulated energy amplitude profiles in the range stack in Fig. 27 (redhistograms) show fair agreement with the calibrated data (black dots) but diverge in ampli-tude at low proton energies (consistent with Fig. 25). The divergence could be due to higherevent rates in high proton energy runs, shown in Fig. 26.

6 Stopping range measurements in presence of a phan-

tom

Figure 28(a) and Fig. 28(b), respectively, show the distribution of proton stopping range inthe range stack and the simulated (X,Y ) distribution of protons at the first tracker stationof the GEANT 4 detector model obtained in the presence of a spherical (D = 14 cm)water phantom. The first peak in the stopping range distribution corresponds to protonsgoing through the center of the phantom, while the second peak corresponds to the stoppingrange of protons that missed the phantom. Different colors for the reconstructed trackscorrespond to the simulated proton stopping ranges. Figures 29(a) and (b) show similarplots for the head phantom obtained using 50K reconstructed protons of energy 200 MeVat CDH. Contours corresponding to the different material width are clearly visible. Themissing bands correspond to missing tracking channels.

12

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n si

gnal

am

plitu

de, P

E c

ount

s

0

20

40

60

80

100

120

<A-max>, PE counts


Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n si

gnal

am

plitu

de, P

E c

ount

s

0

20

40

60

80

100

120

<A-max>, PE counts

Energy deposition in tilesRun: run_Feb28_024340_bmr30_r26_stackBack_cdh_pctmonTree

(a) (b)

Figure 13: The mean number of photoelectrons in the range stack tiles as a function of tilenumber produced by protons with energy (a) 26 cm (200 MeV, “front run” ) ; (b) 26 cm (200MeV, “back run” ), no tracker. The errors bars reperesent ±1 sigmas of Gaussian fits aboutthe average. The three tile difference in the stopping position (ntstop = 74 in the front run,while ntstop=77 in the back run run without the tracker) agrees with the tracker stoppingpower, 3.2 × 1.01 × 3 = 0.97 cm.

7 Summary

The stopping position measurements have better linearity and accuracy (2.2-1.2%) than theenergy measurements (5.5% to 3.5%), confirmed by simulations, and thus are expected toprovide more accurate WEPL calibration for the image reconstruction. The behavior of rangestack detector is well modelled by GEANT, with a few dicrepancies in energy deposition atlow energy and energy resolution.

References

[1] G. Coutrakon et al., Proceedings AccApp 2013, Bruges, Belgium.

[2] S. Uzunyan et al., Proceedings of the New Trends in High-Energy Physics, p. 152-157,Alushta, Crimea, Ukraine, Sep. 2013, ISBN 978-966-02-7015-2.

[3] R. F. Hurleyet al., “Water-equivalent path lengh claibration of a prototype proton CTscaner”, Med. Phys. 39(5), May 2012.

[4] J. F. Janni, ”Proton Range-Energy Tables, 1 keV-10 GeV, Energy Loss, Range, PathLength, Time-of-Flight, Straggling, Multiple Scattering, and Nuclear Interaction Prob-ability. Part I. For 63 Compounds”, Atomic Data and Nuclear Data Tables, 27, 147,(1982).

13

Tile number

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n si

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de, P

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20

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80

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<A-max>, PE counts


Tile number

0 10 20 30 40 50 60 70 80 90

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n si

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de, P

E c

ount

s

0

20

40

60

80

100

120

<A-max>, PE counts


Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n si

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am

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de, P

E c

ount

s

0

20

40

60

80

100

120

<A-max>, PE counts


(a) (b) (c)

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n si

gnal

am

plitu

de, P

E c

ount

s

0

20

40

60

80

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<A-max>, PE counts


Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n si

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de, P

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ount

s

0

20

40

60

80

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120

<A-max>, PE counts


Tile number

0 10 20 30 40 50 60 70 80 90M

ean

sign

al a

mpl

itude

, PE

cou

nts

0

20

40

60

80

100

120

<A-max>, PE counts


(d) (e) (f)

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n si

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de, P

E c

ount

s

0

20

40

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Tile number

0 10 20 30 40 50 60 70 80 90

Mea

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20

40

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Tile number

0 10 20 30 40 50 60 70 80 90

Mea

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de, P

E c

ount

s

0

20

40

60

80

100

120

<A-max>, PE counts


(g) (h) (i)

Figure 14: The mean number of photoelectrons in the range stack tiles as a function of tilenumber produced by protons with energy (a) 8 cm (103 MeV); (b) 12 cm (117 MeV); (c)16 cm (129 MeV); (d) 18 cm (162 MeV) ; (e) 20 cm (172 MeV); (f) 24 cm (191 MeV); (g)25 cm (196 MeV) ; (h) 27 cm (204 MeV); (i) 31 cm (221 MeV).

14

/ ndf 2χ 9.404 / 10

Constant 20.4± 2112

Mean 0.5± 1468 Sigma 0.6± 46.8

Proton energy deposition, PE1.3 1.4 1.5 1.6 1.7 1.8 1.9

310×

Eve

nts/

bin

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

310× / ndf 2χ 9.404 / 10


Mean 0.5± 1468 Sigma 0.6± 46.8

Beam range =r26cm

Stopping range in the range stack (via Janni’s tables), 0.1*g/cm2160 180 200 220 240 260 280 300 320 340

Eve

nts/

bin

0

0.5

1

1.5

2

2.5

3

310× hrange_wtr_conv_r26cm


/ ndf 2χ 718.9 / 30Constant 24.1± 2840 Mean 0.1± 188.7 Sigma 0.07± 11.67

Proton WEPL in the range stack (via Bethe-Bloch), mm160 180 200 220 240 260 280 300 320 340

Eve

nts/

bin

0

0.5

1

1.5

2

2.5

3

310× hrange_wtr_calc_r26cm


/ ndf 2χ 720.5 / 24Constant 24.0± 2818 Mean 0.1± 186.7 Sigma 0.07± 11.81

(a) (b) (c)

Figure 15: (a) the total energy, Ers, in PE measured with the range stack detector in aEbeam = 26 cm run; (b) the proton stopping range in the range stack Rconv

rs (g/cm2) obtained

from Ers via Rconvrs = 0.0022×E

(1.77)rs ; (c) the proton WEPL in the range stack weplcalc

rs , mmcalculated from Ers via energy loss equation.

Stopping position in the range stack (measured), 0.1*g/cm2160 180 200 220 240 260 280 300 320 340

Eve

nts/

bin

0

2

4

6

8

10

310× hrange_wtr_r26cmEntries 27803

Mean 243.2

RMS 5.112

/ ndf 2χ 462.5 / 9

Constant 7.716e+01± 1.037e+04

Mean 0.0± 243.6

Sigma 0.015± 3.383

Signal maximum is in tile 74

Beam range =r26cm

Figure 16: The measured proton stopping range, Rrs, in the range stack, Ebeam = 26 cmrun.

15

Beam energy, 0.1*g/cm20 50 100 150 200 250 300 350

Pro

ton

stop

ping

pos

ition

, 0.1

*g/c

m2

0

50

100

150

200

250

300

/ ndf 2χ 10.5 / 13

p0 0.3956± -14.25

p1 0.001863± 0.9913

/ ndf 2χ 10.5 / 13

p0 0.3956± -14.25

p1 0.001863± 0.9913

/ ndf 2χ 10.5 / 13

p0 0.3956± -14.25

p1 0.001863± 0.9913

Stopping position, 0.1*g/cm20 50 100 150 200 250 300 350

(Pst

op)/

Pst

op, %

σ

0

0.5

1

1.5

2

2.5

3 / ndf 2χ 7369 / 11

p0 0.01851± 2.887

p1 0.0001965± -0.01124

p2 4.866e-07± 1.772e-05

/ ndf 2χ 7369 / 11

p0 0.01851± 2.887

p1 0.0001965± -0.01124

p2 4.866e-07± 1.772e-05

Proton stopping position resolution

(a) (b)

Figure 17: (a) The linearity of the directly measured proton stopping position measurementRrs ; (b) the Rrs resolution. The linearity fit allows an estimate of the width of the extramaterial in front of the range stack (≈14.0 mm).

Beam energy, MeV0 50 100 150 200 250 300 350

Pro

ton

ener

gy d

epos

ition

, PE

0

200

400

600

800

1000

1200

1400

1600

1800

2000

PE linearity

Proton energy deposition, PE0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

310×

(E)/

E, %

σ

0

1

2

3

4

5

6

7

PE resolution

(a) (b)

Figure 18: (a) the linearity of the energy measurement Ers; (b) the Ers resolution.

16

/ ndf 2χ 9.404 / 10


Mean 0.5± 1468 Sigma 0.6± 46.8


310×

Eve

nts/

bin

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

310× / ndf 2χ 9.404 / 10


Mean 0.5± 1468 Sigma 0.6± 46.8

Beam range =r26cm

/ ndf 2χ 29.06 / 1


Mean 0.1± 1454

Sigma 0.071± 6.688


310×E

vent

s/bi

n

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5310× / ndf 2χ 29.06 / 1


Mean 0.1± 1454

Sigma 0.071± 6.688

/ ndf 2χ 7.593 / 5

Constant 15.3± 740.4

Mean 1.0± 1451 Sigma 1.90± 38.67


310×

Eve

nts/

bin

0

100

200

300

400

500

600

700

800 / ndf 2χ 7.593 / 5

Constant 15.3± 740.4

Mean 1.0± 1451 Sigma 1.90± 38.67

(a) (b) (c)

Figure 19: (a) the total energy deposition in the range stack at beam energy of 26 cm(200 MeV ) in data; (b) the unsmeared total energy deposition in the range stack at beamenergy of 26 cm (200 MeV) in GEANT; (c) the smeared range stack energy measurement atbeam energy of 26 cm (200 MeV) in GEANT.

h2fitBSpe_mc_bid30_tile0

Entries 7741

Mean 12.13

RMS 3.782

number of PE0 20 40 60 80 100

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24 h2fitBSpe_mc_bid30_tile0

Entries 7741

Mean 12.13

RMS 3.782

h2fitBSpe_data_bid30_tile0

Entries 27803

Mean 12.4

RMS 4.434

MC:: BID= 30, Tile = 0:: Channels (0,16)


Entries 7642

Mean 48.62

RMS 25.16

number of PE0 20 40 60 80 100

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14


Entries 7642

Mean 48.62

RMS 25.16

h2fitBSpe_data_bid61_tile2

Entries 27803

Mean 49.79

RMS 25.24

MC:: BID= 61, Tile = 2:: Channels (2,18)

(a) (b)

Figure 20: Comparison of data (blue histograms) and simulated signals (red histograms)from 200 MeV protons in (a) Tile0 and (b) Tile74 (the stopping tile, maximal signal).

17

Beam energy, 0.1*g/cm20 50 100 150 200 250 300 350

Pro

ton

stop

ping

pos

ition

(M

C),

0.1

*g/c

m2

0

50

100

150

200

250

300

/ ndf 2χ 19.49 / 12

p0 0.4105± -0.6793

p1 0.002021± 0.9935

/ ndf 2χ 19.49 / 12

p0 0.4105± -0.6793

p1 0.002021± 0.9935

/ ndf 2χ 19.49 / 12

p0 0.4105± -0.6793

p1 0.002021± 0.9935

Width of extra material MC (0.1*g/cm2) = 0.67928

Beam energy, 0.1*g/cm20 50 100 150 200 250 300 350

Pro

ton

stop

ping

pos

ition

(M

C),

0.1

*g/c

m2

0

50

100

150

200

250

300

/ ndf 2χ 18.84 / 13

p0 0.3967± -8.605

p1 0.001871± 0.993

/ ndf 2χ 18.84 / 13

p0 0.3967± -8.605

p1 0.001871± 0.993

/ ndf 2χ 18.84 / 13

p0 0.3967± -8.605

p1 0.001871± 0.993


Beam energy, 0.1*g/cm20 50 100 150 200 250 300 350

Pro

ton

stop

ping

pos

ition

(M

C),

0.1

*g/c

m2

0

50

100

150

200

250

300

/ ndf 2χ 27.61 / 13

p0 0.3969± -14.43

p1 0.001871± 0.9943

/ ndf 2χ 27.61 / 13

p0 0.3969± -14.43

p1 0.001871± 0.9943

/ ndf 2χ 27.61 / 13

p0 0.3969± -14.43

p1 0.001871± 0.9943


(a) (b) (c)

Figure 21: (a) the linearity of the proton stopping position measurement Rrs obtained withGEANT using the nominal CDH beam energy points in a configuration with no trackerbefore the range stack; (b) the Rrs linearity for nominal CDH beam energy points includingthe tracker; (c) the Rrs linearity after correcting beam energies by adding “extra material”observed in data (5.7 mm).

Beam energy, 0.1*g/cm20 50 100 150 200 250 300 350

Pro

ton

stop

ping

pos

ition

, 0.1

*g/c

m2

0

50

100

150

200

250

300

/ ndf 2χ 27.61 / 13

p0 0.3969± -14.43

p1 0.001871± 0.9943

/ ndf 2χ 27.61 / 13

p0 0.3969± -14.43

p1 0.001871± 0.9943

/ ndf 2χ 27.61 / 13

p0 0.3969± -14.43

p1 0.001871± 0.9943

Stopping position, 0.1*g/cm20 50 100 150 200 250 300 350

(Pst

op)/

Pst

op, %

σ

0

0.5

1

1.5

2

2.5

3 / ndf 2χ 1375 / 12

p0 0.02589± 2.945

p1 0.0002809± -0.01186

p2 7.112e-07± 2.04e-05

/ ndf 2χ 1375 / 12

p0 0.02589± 2.945

p1 0.0002809± -0.01186

p2 7.112e-07± 2.04e-05

/ ndf 2χ 1375 / 12

p0 0.02589± 2.945

p1 0.0002809± -0.01186

p2 7.112e-07± 2.04e-05

Proton stopping position resolution

(a) (b)

Figure 22: Comparison of (a) the linearity and (b) resolution of the proton stopping positionmeasurement Rrs in data and GEANT. Fits correspond to simulated results (black squares).Data shown as “blue crosses“.

18

Beam energy, 0.1*g/cm20 50 100 150 200 250 300 350

Ran

ge d

iffer

ence

(MC

-DA

TA),

0.1

*g/c

m2

-5

-4

-3

-2

-1

0

1

2

3

4

5

Beam energy, 0.1*g/cm20 50 100 150 200 250 300 350

Ran

ge d

iffer

ence

(MC

-DA

TA),

0.1

*g/c

m2

-5

-4

-3

-2

-1

0

1

2

3

4

5

Beam energy, 0.1*g/cm20 50 100 150 200 250 300 350

Ran

ge d

iffer

ence

(MC

-DA

TA),

0.1

*g/c

m2

-5

-4

-3

-2

-1

0

1

2

3

4

5Rdiff/AbsRdiff/SigmaRdiff2 -2.52/2.56/1.03

(a) (b) (c)

Figure 23: The difference between measured and simulated proton stopping positions for aGEANT models with (a) nominal scintillator density of 1.025 ± 0.010 g/cm3; (b) nominaldensity decreased by 1% (used in this Note); (c) nominal density decreased by 2%.

Beam energy, MeV0 50 100 150 200 250 300 350

Pro

ton

ener

gy d

epos

ition

, PE

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2310×

/ ndf 2χ 3.823 / 13

p0 5.4± -244.7

p1 0.03158± 8.495

/ ndf 2χ 3.823 / 13

p0 5.4± -244.7

p1 0.03158± 8.495

PE linearity

Proton energy deposition, PE400 600 800 1000 1200 1400 1600 1800 2000

(E)/

E, %

σ

0

1

2

3

4

5

6

7 / ndf 2χ 11.4 / 12

p0 0.3765± 5.694

p1 0.0006752± -0.003038

p2 2.854e-07± 6.334e-07

/ ndf 2χ 11.4 / 12

p0 0.3765± 5.694

p1 0.0006752± -0.003038

p2 2.854e-07± 6.334e-07

/ ndf 2χ 11.4 / 12

p0 0.3765± 5.694

p1 0.0006752± -0.003038

p2 2.854e-07± 6.334e-07

PE resolution

(a) (b)

Figure 24: Comparison of (a) the linearity and (b) resolution of the energy measurements inthe range stack in data and GEANT. Fits correspond to simulated results (black squares).Data shown as “blue crosses“.

19

Proton Energy, mm0 50 100 150 200 250 300 350

Mea

n si

gnal

am

plitu

de in

Tile

0, P

E c

ount

s

10

12

14

16

18

20

22

24

Figure 25: Comparison of the measured (blue crosses) and simulated (black square) signalamplitudes in Tile0 for different proton energies.

Proton energy, 0.1*g/cm20 50 100 150 200 250 300 350

Eve

nt r

ate,

MH

z

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 26: Event rate as function of beam energy.

20

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n en

ergy

dep

ositi

on, P

E

0

10

20

30

40

50

60

70

80

Beam range =8cm

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n en

ergy

dep

ositi

on, P

E

0

10

20

30

40

50

60

70

80

Beam range =12cm

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n en

ergy

dep

ositi

on, P

E

0

10

20

30

40

50

60

70

80

Beam range =16cm

(a) (b) (c)

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n en

ergy

dep

ositi

on, P

E

0

10

20

30

40

50

60

70

80

Beam range =18cm

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n en

ergy

dep

ositi

on, P

E

0

10

20

30

40

50

60

70

80

Beam range =20cm

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n en

ergy

dep

ositi

on, P

E

0

10

20

30

40

50

60

70

80

Beam range =24cm

(d) (e) (f)

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n en

ergy

dep

ositi

on, P

E

0

10

20

30

40

50

60

70

80

Beam range =26cm

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n en

ergy

dep

ositi

on, P

E

0

10

20

30

40

50

60

70

80

Beam range =28cm

Tile number

0 10 20 30 40 50 60 70 80 90

Mea

n en

ergy

dep

ositi

on, P

E

0

10

20

30

40

50

60

70

80

Beam range =31cm

(g) (h) (i)

Figure 27: Comparison of the measured (black dots) and expected (red histograms) signalprofiles in the range stack from protons of incident energy of (a) 8 cm (103 MeV); (b) 12 cm(117 MeV); (c) 16 cm (129 MeV); (d) 18 cm (162 MeV); (e) 20 cm (172 MeV); (f) 24 cm(191 MeV); (g) 26 cm (200 MeV); (h) 28 cm (208 MeV); (i) 31 cm (221 MeV).

21

h1wREntries 261253Mean 170.2RMS 59.1

Proton stopping position, 0.1*g/cm2

0 50 100 150 200 250 300 350

Eve

nts

/bin

0

5

10

15

20

25

310× h1wREntries 261253Mean 170.2RMS 59.1


0

50

100

150

200

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Stopping Range (profile) via UTP1Stopping Range (profile) via UTP1

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Figure 28: Water phantom (diameter of 14 cm) exposed to 300K protons of energy 200 MeVin GEANT simulations (a) the stopping range distribution (b) the stopping range profile asfunction of incident proton position at the first tracker station.


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310× h1wREntries 48675Mean 145.8RMS 73.11


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Figure 29: Head phantom exposed to 50K protons of energy 200 MeV at CDH (a) thestopping range distribution (b) the stopping range profile as a function of incident protonposition at the first tracker station.

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calibration and geant4 simulations of the phase ii...

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