Experimental Validation of Proton Physics Models of Geant4 for Calculating Stopping Power Ratio

Abstract

In this work, we conducted experiments to validate the proton physics models of Geant4 (Version 10.6). The stopping power ratios (SPR) of 11 inserts, such as Acrylic, Delrin, High Density Polyethylene (HDPE), and Polytetrafluoroethylene (PTFE), et al., were measured using a superconducting synchrocyclotron that produces a scattering proton beam. The SPRs of the inserts were also calculated based on Geant4 simulation with six physics lists, i.e., QGSP_ FTFP_ BERT, QGSP_BIC_HP, QGSP_BIC, QGSP_FTFP_BERT, QSGP_BERT, and QBBC. The calculated SPRs were compared to the experimental SPRs, and relative percent error was used to quantify the accuracy of the simulated SPRs of inserts. The comparison showed that the five physics lists generally agree well with the experimental SPRs with a relative difference of less than 1%. The lowest overall percentage error was observed for QGSP_FTFP_BERT and the highest overall percentage error was observed for QGSP_BIC_HP. The 0.1 mm range cut value consistently led to higher percentage error for all physics lists except for QGSP_BIC_HP and QBBC. Based on the validation, we recommend QGSP_BERT_HP physics list for proton dose calculation.

1. Introduction

Proton beam therapy (PBT) has been growing as an important treatment modality for cancer patients due to its dosimetric advantage originating from the Bragg peak and the absence of exit dose beyond the particle range [1–3]. These dosimetric advantages are expected to reduce short-and long-term complications [4–9] while maintaining tumor control probability (TCP) for properly selected patients, especially pediatric patients. Precise estimation of proton range during treatment planning plays a critical key in unlocking proton radiotherapy’s full potential.

Monte Carlo (MC) simulation comprises a powerful tool for the calculation of accurate dose distribution in PBT by simulating the radiation transport in beam-shaping devices, monitoring systems, phantoms, and human tissues [10]. A variety of MC codes, such as MCNPX [11,12], FLUKA [13] and Geant4 [14] are considered gold standards for validating the dose calculation engine of treatment planning systems (TPS). In particular, Geant4 and its derivatives, such as TOPAS [15] and GATE [16], have gained popularity in hadron therapy applications [17–19], mainly due to their open-source and object-oriented nature that grant the end users easy access to the existing framework by instantiating useful class systems on which a unique and customized application framework is built. The accuracy of the physics model in Geant4 dominates the accuracy of dose calculation. Consequently, validating the physics models in Geant4 for proton therapy plays an important role in assuring the accuracy of dose calculation for proton therapy using Geant4.

In the setting of proton therapy, several studies compare predictions of the Geant4 physics models to experimental and simulated data. For instance, Lechner et al. validated Geant4 physics models for simulating carbon ion therapy against experimental data in the literature [10]. T. Aso et al. [20] compared simulated dose distributions for a proton delivery system using Geant4 and to the measured data. Peterson et al. [21] experimentally validated a Geant4-based Monte Carlo proton therapy nozzle model incorporating magnetically steered protons. Hall et al. [22] validated the nuclear models of Geant4 by comparing the simulated absolute dose distribution to an experiment of a 177 MeV proton pencil beam stopping in water. Testal et al. [23] experimentally validated the TOPAS/Geant4 Monte Carlo system for passive scattering proton therapy. Girrone et al. [24] did a comprehensive and rigorous validation of Geant4 electromagnetic and hadronic models pertinent to the simulation of the proton Bragg peak in water. Ivanchenko et al. validated the Geant4 simulation of proton interaction for space radiation effects [25]. Resch et al. evaluated the electromagnetic and nuclear scattering models in GATE/Geant4 for proton therapy [26]. Zarifi et al. validated GATE/Geant4 physics models for proton therapy by comparing the simulation results with NIST library data [27]. Toshito et al. validated Geant4 electromagnetic physics models for ion therapy applications [28].

However, most of these validation works are using water as the medium for measuring the stopping power profile so as to compare with the simulated profile. In clinical settings, a more relevant situation is with tissue heterogeneities and inhomogeneities [29]. Therefore, it is necessary to validate the physics model through different materials. The motivation of this work is to validate the Geant4 physics models for protons by comparing the experimentally obtained stopping power ratios (SPR) and the corresponding simulated stopping power ratios using Geant4.

2. Methods and Materials

2.1. Experiment

A total of 11 inserts composed of easy to acquire, or synthesize material in a laboratory were selected to span the range of stopping power ratios found in biological tissues. The customized tissue surrogates were divided into two categories: soft and bony tissue [30]. The bony materials included four liquid K₂HPO₄ solutions of varying density. The soft tissue materials consisted of water, three different alcohols (ethanol, propanol, and butanol) and four plastic materials (Acrylic, Delrin, HDPE, and PTFE). The composition, density, and classification of each insert are shown in Table 1. The four plastic inserts were cylindrical in shape with 5 cm diameter and 10 cm length.

Table 1:

A summary of the properties of the inserts used in the experiments.

Category	Material	Composition	Density
Soft	Ethanol	C2H5OH	0.788 g/mL
	n-Propanol	C3H7OH	0.803 g/mL
	n-Butanol	C4H9OH	0.807 g/mL
	Acrylic	(C5O2H8)n	1.186 g/cm3
	Delrin	(CH2O)n	1.429 g/cm3
	HDPE	(C2H4)n	0.930 g/cm3
	PTFE	(C2F4)n	2.178 g/cm3
Bony	KP-1	K2HPO4	1.085 g/mL
	KP-2	K2HPO4	1.189 g/mL
	KP-3	K2HPO4	1.273 g/mL
	KP-4	K2HPO4	1.336 g/mL

The SPRs of all the inserts were measured directly in a MEVION S 250 passive scattering proton therapy facility with a superconducting synchrocyclotron producing a 250 MeV proton beam. The proton beam was collimated to 0.25 cm² by brass apertures with a circular shaped aperture. The solid inserts or the liquid solutions contained in a PVC container were placed in between the brass apertures and a water tank with 10×10 cm² cross sectional area outfitted with a moving ionization chamber. The proton beam passed through each insert individually, and an IBA PPC05 parallel plane ionization chamber was used to measure the central-axis relative dose distribution by scanning along the beam central axis to locate the Bragg peak. The step size of ionization chamber was 1 mm along the beam path and the dwell time at each measuring point was 8 seconds. The measurement setup is shown in Figure 1.

Figure 1:

The setup for measuring proton stopping power range. The insert is placed between the brass blockers and the water tank.

The stopping power ratio of each liquid insert (LI) relative to water determined by

$$SP{R}_{LI}=\frac{R_{air}-R_{insert}}{R_{air}-R_{water}},$$ (1)

where $R_{air}$ is the location of the Bragg peak (proton range) for protons going through the empty PVC container, $R_{insert}$ is the proton range through the insert, and $R_{water}$ is the range through a water-filled PVC container. The stopping power ratio of the solid insert (SI) relative to water was determined by

$$SP{R}_{SI}=\frac{R_{air}-R_{insert}}{L},$$ (2)

where L is the length of the insert, which was measured on the day of conducting the experiment.

To determine the impact of the fitting model in the uncertainty of the estimated range, each sample’s measured depth-ionization curve was normalized and fitted to three functions: a five-term Gaussian, a seven-term sine series, and a six-term Fourier series. Next, the depth of maximum relative ionization of each fitting model was used to estimate the range of each parameterization. Finally, the residual range was determined to be half of the maximum variation among the ranges estimated from the three different parametrization curves. The estimated ranges were then used along with Eqs. (1) and (2) to calculate SPR for each analyzed material. We also calculated the width of pristine distal 80% dose point and 20% dose point of the Bragg peak curve, and the width of pristine proximal 95% dose point and distal 90% dose point of the Bragg peak curve.

2.2. Geant4 Simulation

The water tank was modeled as a cubic water phantom with dimensions of 50×50×50 cm³. The inserts were modeled accurately in shape and dimension according to the experimental inserts. The source of protons was modeled as a circular plane source with a diameter of 2 mm. The energy of the protons was modeled as a Gaussian distribution with a standard deviation of 1 MeV and a mean 200 MeV. The source was located at 1 cm from one end of the insert with the beam entering the insert perpendicularly from one end of the insert.

In this work, six reference lists in Geant4 (Version 10.6) [14] were used, i.e., QBBC [31], QGSP_BIC [31,32], QGSP_BIC_HP [31,32], QGSP_BERT [31,33], QSGP_FTFP_BERT [31,33,34], and QGSP_BERT_HP [31,33]. QGSP stands for Quark Gluon string with Precompound model, FTFP stands for Fritiof model, BERT stands for Bertini intranuclear cascade model, BIC stands for Binary cascade model, HP stands for high precision neutron model, and QBBC uses both Bertini cascade model and Binary cascade model.

The QGSP_BIC is recommended for medical applications and ion beam therapy [17,27]. The QBBC is recommended for medical and space physics simulations [35,36]. QBBC includes combinations of BIC, BIC-Ion, BERT, CHIPS, QGSP and FTFP models and it has higher precision [36]. The QGSP_BERT is the former GEANT4 default physics model [35,37]. The QGSP_BERT_HP is identical to QGSP_BERT except that it simulates neutrons of 20 MeV and lower with high precision neutron models. The QSGP_BERT_HP was recommended for simulating proton therapy in a few studies [38–40].

The ionization potential of water was set to 78 eV which is the default value for Geant4 (version 10.6). Two range cut values were used in the simulation, i.e., 0.1 mm and 0.01 mm. The simulation history for each insert was set to 10 million which leads to about 1% uncertainty within the simulated Bragg curves. The energy deposited along the beam direction was recorded every other 1 mm to obtain the depth dose curves. The simulated SPRs were calculated in the same way for the experimental inserts.

2.3. Uncertainty analysis

The Type A (random) and Type B (systematic) uncertainty contributions for each simulated SPR was then identified and added in quadrature to assess the total uncertainty in estimated SPR per the basic principles of uncertainty analysis [41,42]. The uncertainty analysis in this study was based on the methodology we followed in our previous publication to quantify the uncertainty of experimental stopping power ratio measurements. As per our previous studies, the major contributors to the total uncertainty of the simulated SPR values came from curve fit error (errors in using a curve-fit model to estimate depth of maximum relative ionization) and statistical noise (errors due to noise fluctuations in scored depth-ionization curves) [43]. A brief description of each uncertainty component and their evaluation in our total SPR uncertainty calculations can be found in Appendix A.

Once each individual uncertainty contribution is identified and quantified, the total uncertainty in simulated SPR values can be calculated as follows:

$${\sigma }_{SPR,tot}=\sqrt{\sum _i^N{\left(\frac{\partial SPR(\alpha )}{\partial {\alpha }_i}\right)}^2{\sigma }_{{\alpha }_i}^2},$$ (3)

where ${\sigma }_{SPR,tot}$ is the total SPR uncertainty, ${\alpha }_i$ and ${\sigma }_{{\alpha }_i}^2$ represent the i-th input and it is corresponding to k=1 uncertainty, and $\left(\frac{\partial SPR(\alpha )}{\partial {\alpha }_i}\right)$ correspond to the sensitivity of SPR with respect to input ${\alpha }_i$. The input ${\alpha }_i$ that were considered in this study were curve fit error and simulation statistical noise. The final relative uncertainty in percent was then determined as $\frac{{\sigma }_{{\alpha }_i}}{{\alpha }_i}\cdot 100\%$

The relative percent error between simulated and measured SPR values can be calculated as

$$e_x=\left(\frac{SP{R}_{simulated}-SP{R}_{measured}}{SP{R}_{measured}}\right)\times 100\%$$ (4)

where $e_x$ is the relative percent error of the x sample, $SP{R}_{simulated}$ is the SPR values estimated through Geant4 and $SP{R}_{measured}$ is the SPR values determined directly from proton machine measurements.

3. Results and Discussion

The experimental depth dose curves of Acrylic, Delrin, HDPE, and PTFE are shown in Figure 2. The measuring range was set to a reasonable length to reduce the beam time while including the Bragg peak. Due to the relatively lower ionizations towards to proximal surface, the dose curve shows more fluctuations in the proximal region compared to the Bragg peak region. A similar pattern could be observed in the distal region of the depth dose curve. The fluctuations could be reduced by prolonging the dwelling time at each measurement point. The experimental SPRs for these four inserts are shown in Table 2 and Table 3 for the two range cut values of 0.01 mm and 0.1 mm, respectively. After applying curve fitting for the measured depth dose curve, the fluctuation can be reduced to marginal impact on the accuracy of determining the position of the Bragg peak.

Figure 2:

Experimental depth dose curve of air, PTFE, Delrin, Acrylic, and HDPE inserts

Table 2:

Absolute SPR values with percentage uncertainty in parenthesis calculated for different Geant4 simulations defined by six different physics lists with range cut value as 0.01 mm.

Insert	Exp. Values	Geant4 physics lists results
		QGSP_FTFP_BERT	QGSP_BIC_HP	QGSP_BIC	QGSP_BERT_HP	QGSP_BERT	QBBC
K2HPO4_1	1.070	1.065 (0.129%)	1.064 (0.135%)	1.065 (0.131%)	1.064 (0.121%)	1.064 (0.122%)	1.064 (0.123%)
K2HPO4_2	1.148	1.145 (0.123%)	1.145 (0.12%)	1.145 (0.125%)	1.145 (0.12%)	1.144 (0.123%)	1.145 (0.122%)
K2HPO4_3	1.205	1.211 (0.113%)	1.210 (0.112%)	1.211 (0.116%)	1.210 (0.11%)	1.210 (0.113%)	1.210 (0.11%)
K2HPO4_4	1.251	1.253 (0.114%)	1.253 (0.111%)	1.253 (0.113%)	1.253 (0.109%)	1.253 (0.111%)	1.254 (0.108%)
Ethanol	0.824	0.824 (0.171%)	0.825 (0.172%)	0.825 (0.169%)	0.824 (0.168%)	0.824 (0.169%)	0.824 (0.171%)
Propanol	0.842	0.843 (0.165%)	0.844 (0.168%)	0.843 (0.17%)	0.843 (0.166%)	0.842 (0.166%)	0.843 (0.16%)
Butanol	0.849	0.858 (0.162%)	0.859 (0.162%)	0.858 (0.162%)	0.858 (0.163%)	0.858 (0.166%)	0.858 (0.162%)
Acrylic	1.158	1.170 (0.098%)	1.169 (0.106%)	1.170 (0.098%)	1.170 (0.098%)	1.170 (0.1%)	1.170 (0.1%)
HDPE	0.992	0.992 (0.144%)	0.992 (0.146%)	0.992 (0.171%)	0.992 (0.14%)	0.992 (0.138%)	0.992 (0.14%)
Delrin	1.370	1.382 (0.104%)	1.382 (0.104%)	1.382 (0.101%)	1.382 (0.098%)	1.382 (0.098%)	1.382 (0.102%)
PTFE	1.805	1.814 (0.079%)	1.814 (0.078%)	1.814 (0.08%)	1.814 (0.077%)	1.814 (0.077%)	1.814 (0.078%)

Table 3:

Absolute SPR values with percentage uncertainty in parenthesis calculated for different Geant4 simulations defined by six different physics lists with range cut value as 0.1 mm.

Insert	Exp. Values	Geant4 physics lists results
		QGSP_FTFP_BERT	QGSP_BIC_HP	QGSP_BIC	QGSP_BERT_HP	QGSP_BERT	QBBC
K2HPO4_1	1.07	1.065 (0.123%)	1.065 (0.111%)	1.064 (0.129%)	1.064 (0.118%)	1.064 (0.124%)	1.064 (0.123%)
K2HPO4_2	1.148	1.145 (0.122%)	1.144 (0.122%)	1.145 (0.118%)	1.145 (0.116%)	1.144 (0.119%)	1.145 (0.121%)
K2HPO4_3	1.205	1.210 (0.111%)	1.210 (0.115%)	1.211 (0.115%)	1.211 (0.111%)	1.210 (0.112%)	1.211 (0.115%)
K2HPO4_4	1.251	1.253 (0.111%)	1.252 (0.11%)	1.254 (0.111%)	1.253 (0.109%)	1.253 (0.109%)	1.253 (0.108%)
Ethanol	0.824	0.824 (0.171%)	0.825 (0.173%)	0.824 (0.172%)	0.824 (0.164%)	0.824 (0.17%)	0.824 (0.171%)
Propanol	0.842	0.843 (0.165%)	0.844 (0.165%)	0.843 (0.163%)	0.843 (0.16%)	0.843 (0.167%)	0.843 (0.167%)
Butanol	0.849	0.858 (0.164%)	0.859 (0.164%)	0.858 (0.166%)	0.858 (0.159%)	0.858 (0.162%)	0.858 (0.163%)
Acrylic	1.158	1.171 (0.114%)	1.169 (0.099%)	1.170 (0.094%)	1.170 (0.097%)	1.170 (0.096%)	1.170 (0.097%)
HDPE	0.992	0.992 (0.141%)	0.992 (0.14%)	0.992 (0.139%)	0.992 (0.134%)	0.992 (0.14%)	0.992 (0.143%)
Delrin	1.37	1.382 (0.102%)	1.382 (0.101%)	1.382 (0.098%)	1.382 (0.096%)	1.382 (0.101%)	1.382 (0.233%)
PTFE	1.805	1.814 (0.078%)	1.814 (0.078%)	1.814 (0.077%)	1.814 (0.074%)	1.814 (0.078%)	1.814 (0.079%)

The experimental depth dose curves for KP-1, KP-2, KP-3, KP-4, butanol, propanol, and ethanol inserts are shown in Figure 3. The experimental SPRs for these inserts are shown in Table 2 and Table 3 for the two range cut values respectively. Similarly, due to relatively lower ionizations, the dose in the proximal and distal region of depth dose curve tends to have some fluctuations. But the fluctuation posed limited influence on calculating the SPR after curve fitting.

Figure 3:

Experimental depth dose curve of air, water, KP-1, KP-2, KP-3, KP-4, Butanol, Propanol, and Ethanol inserts.

The simulated depth dose curves for all the inserts are shown in Figure 4. The simulation generates smooth depth dose curves for all the inserts. The simulated SPRs are shown in Table 2 and Table 3 for range cut values of 0.01 mm and 0.1 mm, respectively. Total relative SPR uncertainty of all the inserts using the five physics lists are shown in Table 2 and Table 3 for range cut values respectively.

Figure 4:

Simulated normalized depth dose curves for all the experimental inserts. The physics model used for this simulation was QGSP_BERT_HP, and the range cut value is 0.01 mm.

Table 2 and Table 3 show the SPR values calculated from the normalized depth dose curves simulated for eleven inserts for each of the six studied physics lists. Experimental benchmark values are provided as a reference.

By comparing the simulated SPRs and the reference SPRs, we know that the simulated SPRs from the six physics lists generally agree well with the experimental SPRs. For all the inserts, the simulated SPR has difference less than 1%.

By comparing the simulated SPRs and the reference SPRs, we know that the simulated SPRs from the six physics lists generally agree well with the experimental SPRs. For all the inserts, the simulated SPR has difference less than 1%.

Table 4 shows the average of the total relative SPR uncertainties for different physics lists and range cut values. For range cut value, 0.01 mm, QGSP_BIC has the maximum average of the total relative SPR uncertainties for all the inserts. For range cut value, 0.1 mm, QBBC has the maximum average of the total relative SPR uncertainties for all the inserts.

Table 4:

Average relative uncertainty of SPR values simulated with different physics lists and range cut values, calculated by averaging the total relative uncertainty for all eleven samples.

Average Relative Uncertainty of Stopping Power Ratio Values (%)
Range cut value	QGSP_FTFP_BERT	QGSP_BIC_HP	QGSP_BIC	QGSP_BERT_HP	QGSP_BERT	QBBC
0.01 mm	0.127	0.129	0.131	0.125	0.126	0.125
0.1 mm	0.127	0.125	0.126	0.122	0.125	0.138

Table 5 and Table 6 show the percent error for different Geant4 physics lists for the two different range cut values respectively. Table 7 shows the average percent error for physics lists and range cut values. The lowest overall percentage error was observed for QGSP_FTFP_BERT and the highest overall percentage error was observed for QGSP_BIC_HP. The 0.1 mm range cut values consistently led to higher percentage error for all physics lists except for QGSP_BIC_HP and QBBC.

Table 5:

Percent error for different physics lists with range cut value as 0.01 mm.

Insert	Geant4 physics lists results
	QGSP_FTFP_BERT	QGSP_BIC_HP	QGSP_BIC	QGSP_BERT_HP	QGSP_BERT	QBBC
K2HPO4_1	0.467	0.561	0.467	0.561	0.561	0.561
K2HPO4_2	0.261	0.261	0.261	0.261	0.348	0.261
K2HPO4_3	0.498	0.415	0.498	0.415	0.415	0.415
K2HPO4_4	0.160	0.160	0.160	0.160	0.160	0.240
Ethanol	0.000	0.121	0.121	0.000	0.000	0.000
Propanol	0.119	0.238	0.119	0.119	0.000	0.119
Butanol	1.060	1.178	1.060	1.060	1.060	1.060
Acrylic	1.036	0.950	1.036	1.036	1.036	1.036
HDPE	0.000	0.000	0.000	0.000	0.000	0.000
Delrin	0.876	0.876	0.876	0.876	0.876	0.876
PTFE	0.499	0.499	0.499	0.499	0.499	0.499

Table 6:

Percent error for different physics lists with range cut value as 0.1 mm.

Insert	Geant4 physics lists results
	QGSP_FTFP_BERT	QGSP_BIC_HP	QGSP_BIC	QGSP_BERT_HP	QGSP_BERT	QBBC
K2HPO4_1	0.467	0.467	0.561	0.561	0.561	0.561
K2HPO4_2	0.261	0.348	0.261	0.261	0.348	0.261
K2HPO4_3	0.415	0.415	0.498	0.498	0.415	0.498
K2HPO4_4	0.160	0.080	0.240	0.160	0.160	0.160
Ethanol	0.000	0.121	0.000	0.000	0.000	0.000
Propanol	0.119	0.238	0.119	0.119	0.119	0.119
Butanol	1.060	1.178	1.060	1.060	1.060	1.060
Acrylic	1.123	0.950	1.036	1.036	1.036	1.036
HDPE	0.000	0.000	0.000	0.000	0.000	0.000
Delrin	0.876	0.876	0.876	0.876	0.876	0.876
PTFE	0.499	0.499	0.499	0.499	0.499	0.499

Table 7:

Average percent error of each library for different dose sampling.

Average Stopping Power Ratio Percent Error (%)
Range cut value	QGSP_FTFP_BERT	QGSP_BIC_HP	QGSP_BIC	QGSP_BERT_HP	QGSP_BERT	QBBC
0.01 mm	0.452	0.478	0.463	0.453	0.450	0.461
0.1 mm	0.453	0.470	0.468	0.461	0.461	0.461

For the same physics list, using different range cut value may lead to different simulated SPR. The reason for this is that the simulation noise (fluctuation) is different for different range cut values. We calculated the simulation noise, and the noise was quantified by calculating the RMS error between original depth dose measurements and a box-cart filter smoothed-out version of the original depth dose curve. Table 8 and Table 9 show the percent noise in each of the simulated depth dose for different physics lists and range cut values. Table 10 provides the average percent noise for different physics lists and range cut values. As expected, higher noise was observed in the depth dose measurements performed with coarser range cut values (0.1 mm).

Table 8.

Percent noise of normalized depth dose curve for different Geant4 physics lists with range cut values as 0.01 mm.

Insert	Geant4 physics lists results
	QGSP_FTFP_BERT	QGSP_BIC_HP	QGSP_BIC	QGSP_BERT_HP	QGSP_BERT	QBBC
K2HPO4_1	0.36	0.34	0.35	0.34	0.37	0.41
K2HPO4_2	0.31	0.29	0.32	0.31	0.31	0.30
K2HPO4_3	0.29	0.27	0.30	0.29	0.28	0.29
K2HPO4_4	0.28	0.28	0.30	0.27	0.28	0.27
Ethanol	0.42	0.55	0.42	0.41	0.42	0.42
Propanol	0.41	0.47	0.43	0.42	0.40	0.39
Butanol	0.40	0.39	0.41	0.41	0.41	0.41
Acrylic	0.26	0.26	0.23	0.23	0.22	0.24
HDPE	0.34	0.35	0.37	0.33	0.33	0.37
Delrin	0.26	0.25	0.25	0.23	0.24	0.26
PTFE	0.19	0.19	0.18	0.19	0.18	0.19

Table 9.

Percent noise of normalized depth dose curve for different Geant4 physics lists with range cut values as 0.1 mm.

Insert	Geant4 physics lists results
	QGSP_FTFP_BERT	QGSP_BIC_HP	QGSP_BIC	QGSP_BERT_HP	QGSP_BERT	QBBC
K2HPO4_1	0.38	0.51	0.43	0.46	0.42	0.36
K2HPO4_2	0.36	0.31	0.30	0.36	0.37	0.32
K2HPO4_3	0.33	0.30	0.30	0.33	0.33	0.31
K2HPO4_4	0.32	0.28	0.29	0.33	0.35	0.34
Ethanol	0.47	0.44	0.52	0.52	0.51	0.49
Propanol	0.50	0.45	0.50	0.51	0.47	0.44
Butanol	0.44	0.44	0.43	0.49	0.48	0.42
Acrylic	0.39	0.25	0.42	0.25	0.39	0.42
HDPE	0.36	0.34	0.41	0.43	0.43	0.37
Delrin	0.31	0.25	0.30	0.29	0.29	0.27
PTFE	0.22	0.20	0.22	0.22	0.23	0.22

Table 10.

Average percent noise in simulated depth dose curve measurements for different Geant4 physics lists and range cut values.

Average Percent Noise of Simulated Depth Dose Measurements (%)
Range cut value	QGSP_FTFP_BERT	QGSP_BIC_HP	QGSP_BIC	QGSP_BERT_HP	QGSP_BERT	QBBC
0.01 mm	0.32	0.33	0.32	0.31	0.31	0.32
0.1 mm	0.37	0.34	0.38	0.38	0.39	0.36

The difference of the pristine 90% dose point between the measured Bragg peak curve and the simulated Bragg peak curves for all the inserts with different physics lists are shown in Table B1 and Table B4 for two range cut values respectively in the appendix B. The difference between the width (distal 80% - distal 20%) of measured Bragg peak curve and the simulated Bragg peak curves for six different physics lists are shown in Table B2 and Table B5 for two range cut values respectively. The difference between the width (pristine 95% - distal 90%) of measured Bragg peak curve and the simulated Bragg peak curves for six different physics lists are shown in Table A3 and Table 6 for two range cut values respectively. The difference among the six physics lists is reasonably small, which means the shape of the simulated Bragg peak curve by these different physics lists is almost same.

4. Conclusion

In this study, we validate the Geant4 physics lists for calculating the SPRs for 11 types of materials. By comparing the experimental SPRs and simulated SPRs of inserts, we find that QGSP_FTFP_BERT physics list performs best for estimating the SPR of a material. This validation study indicates that Geant4 (Version 10.6) is suitable for calculating the SPRs of different types of material and is a suitable tool for proton dose calculation. Hence, the QGSP_FTFP_BERT physics list option should favorably be considered for proton dose calculation with a range cut value 0.01 mm.

Appendix

Appendix A

The following table provides a description of the Type A uncertainty components of the scored SPR values, and the method used to evaluate them in Equation 4.

Type	Uncertainty Source $\left({\alpha }_i\right)$ and Symbol	Source of assumed value	Evaluation of $\text{k}=1{\sigma }_{{\alpha }_i}$	Evaluation of $\left(\frac{\partial SPR}{\partial {\alpha }_i}\right)$
A	Curve Fit Error	The depth of maximum relative ionization of each sample is assumed to be uniformly distributed between the minimum and maximum ranges predicted by the three different curve-fit models. Therefore, the assumed value is the average of the maximum and minimum proton beam ranges estimated using 3 different curve fit methods.	Following the uniform distribution assumption, ${\sigma }_{{\alpha }_i}$ will then be the standard deviation of the uniform distribution characterized by the maximum and minimum estimated ranges from the three different curve fit models. $\left[{\text{R}}_{\min },{\text{R}}_{\max }\right]$	Analytical derivatives of Eq. (1) for ${\alpha }_i$ and ${\sigma }_{{\alpha }_i}$ for each substance considered in each Geant4 physics list simulation.
A	Detector Noise	Derived from dose fluctuations in simulations.	${\sigma }_{noise}$ = root mean square differences between boxcar-filtered and original depth-ionization curves.	Add 1% and 3% Gaussian noise to boxcar-filtered depth ionization curves. Repeat curve fitting to get SPR. Then evaluate $\frac{SPR(3\%noise)-SPR(1\%noise)}{(3\%-1\%)}$

Appendix B

Table B1:

The difference between the pristine distal 90% dose point of measured Bragg peak curve and the simulated Bragg peak curves for six different physics lists with range cut value as 0.1 mm.

Insert	pristine distal 90% dose point difference
	$\left|Z_{meas}-Z_{ZQGS\text{\_}FTFP\text{\_}BERT}\right|$	$\left|Z_{meas}-Z_{ZQGS\text{\_}BIC\text{\_}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BIC}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BER{T}_{-}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BERT}\right|$	$\left|Z_{meas}-Z_{QBBC}\right|$
K2HPO4_1	−0.74	−0.761	−0.735	−0.735	−0.738	−0.74
K2HPO4_2	−11.314	−11.333	−11.315	−11.312	−11.309	−11.312
K2HPO4_3	−19.44	−19.454	−19.439	−19.441	−19.437	−19.439
K2HPO4_4	−36.738	−36.748	−36.739	−36.737	−36.74	−36.74
Ethanol	−57.374	−57.405	−57.375	−57.377	−57.376	−57.374
Propanol	−62.369	−62.397	−62.361	−62.366	−62.368	−62.367
Butanol	−54.05	−54.081	−54.054	−54.053	−54.055	−54.055
Acrylic	−131.393	−131.412	−131.388	−131.39	−131.389	−131.391
HDPE	−146.571	−146.593	−146.57	−146.569	−146.57	−146.571
Delrin	−112.676	−112.701	−112.677	−112.677	−112.68	−112.677
PTFE	−73.163	−73.186	−73.16	−73.162	−73.163	−73.159

Table B2:

The difference between the width (distal 80% - distal 20%) of measured Bragg peak curve and the simulated Bragg peak curves for six different physics lists with range cut value as 0.1 mm.

Insert	distal 80% and distal 20% dose points difference
	$\left|Z_{meas}-Z_{ZQGS\text{\_}FTFP\text{\_}BERT}\right|$	$\left|Z_{meas}-Z_{ZQGS\text{\_}BIC\text{\_}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BIC}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BER{T}_{-}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BERT}\right|$	$\left|Z_{meas}-Z_{QBBC}\right|$
K2HPO4_1	−7.609	−7.616	−7.602	−7.602	−7.607	−7.606
K2HPO4_2	−7.432	−7.432	−7.431	−7.43	−7.43	−7.432
K2HPO4_3	−7.117	−7.115	−7.115	−7.116	−7.114	−7.118
K2HPO4_4	−6.948	−6.947	−6.949	−6.948	−6.949	−6.95
Ethanol	−7.089	−7.091	−7.088	−7.09	−7.088	−7.089
Propanol	−7.041	−7.043	−7.037	−7.04	−7.039	−7.041
Butanol	−7.26	−7.262	−7.261	−7.26	−7.261	−7.262
Acrylic	−7.044	−7.043	−7.036	−7.04	−7.038	−7.04
HDPE	−6.999	−6.999	−6.999	−6.999	−6.999	−6.999
Delrin	−6.795	−6.802	−6.797	−6.797	−6.795	−6.798
PTFE	−7.223	−7.225	−7.221	−7.221	−7.222	−7.221

Table B3:

The difference between the width (pristine 95% - distal 90%) of measured Bragg peak curve and the simulated Bragg peak curves for six different physics lists with range cut value as 0.1 mm.

Insert	Pristine 95% and distal 90% dose points difference
	$\left|Z_{meas}-Z_{ZQGS\text{\_}FTFP\text{\_}BERT}\right|$	$\left|Z_{meas}-Z_{ZQGS\text{\_}BIC\text{\_}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BIC}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BER{T}_{-}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BERT}\right|$	$\left|Z_{meas}-Z_{QBBC}\right|$
K2HPO4_1	−5.483	−5.485	−5.487	−5.485	−5.485	−5.489
K2HPO4_2	−5.915	−5.921	−5.921	−5.92	−5.909	−5.915
K2HPO4_3	−5.788	−5.79	−5.792	−5.794	−5.78	−5.786
K2HPO4_4	−5.247	−5.237	−5.25	−5.243	−5.251	−5.253
Ethanol	−5.326	−5.336	−5.336	−5.339	−5.338	−5.335
Propanol	−5.576	−5.57	−5.557	−5.577	−5.579	−5.572
Butanol	−5.958	−5.965	−5.973	−5.973	−5.979	−5.978
Acrylic	−5.89	−5.897	−5.876	−5.881	−5.878	−5.885
HDPE	−5.998	−5.996	−6	−5.996	−5.997	−5.998
Delrin	−6.043	−6.052	−6.048	−6.046	−6.055	−6.048
PTFE	−6.139	−6.142	−6.136	−6.144	−6.138	−6.133

Table B4:

The difference between the pristine distal 90% dose point of measured Bragg peak curve and the simulated Bragg peak curves for six different physics lists with range cut value as 0.01 mm.

Insert	pristine distal 90% dose point difference
	$\left|Z_{meas}-Z_{ZQGS\text{\_}FTFP\text{\_}BERT}\right|$	$\left|Z_{meas}-Z_{ZQGS\text{\_}BIC\text{\_}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BIC}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BER{T}_{-}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BERT}\right|$	$\left|Z_{meas}-Z_{QBBC}\right|$
K2HPO4_1	−0.758	−0.771	−0.753	−0.756	−0.753	−0.752
K2HPO4_2	−11.325	−11.346	−11.324	−11.328	−11.328	−11.325
K2HPO4_3	−19.451	−19.466	−19.451	−19.452	−19.453	−19.451
K2HPO4_4	−36.755	−36.765	−36.751	−36.754	−36.759	−36.754
Ethanol	−57.39	−57.414	−57.389	−57.389	−57.392	−57.392
Propanol	−62.381	−62.408	−62.379	−62.381	−62.377	−62.377
Butanol	−54.07	−54.094	−54.067	−54.067	−54.066	−54.064
Acrylic	−131.408	−131.419	−131.405	−131.407	−131.407	−131.407
HDPE	−146.583	−146.604	−146.583	−146.587	−146.585	−146.583
Delrin	−112.697	−112.712	−112.694	−112.692	−112.694	−112.694
PTFE	−73.177	−73.201	−73.179	−73.18	−73.184	−73.179

Table B5:

The difference between the width (distal 80% - distal 20%) of measured Bragg peak curve and the simulated Bragg peak curves for six different physics lists with range cut value as 0.1 mm.

Insert	distal 80% and distal 20% dose points difference
	$\left|Z_{meas}-Z_{ZQGS\text{\_}FTFP\text{\_}BERT}\right|$	$\left|Z_{meas}-Z_{ZQGS\text{\_}BIC\text{\_}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BIC}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BER{T}_{-}HP}\right|$	$\left|Z_{meas}-Z_{ZQG{S}_{-}BERT}\right|$	$\left|Z_{meas}-Z_{QBBC}\right|$
K2HPO4_1	−7.609	−7.606	−7.605	−7.606	−7.607	−7.606
K2HPO4_2	−7.43	−7.435	−7.428	−7.43	−7.43	−7.429
K2HPO4_3	−7.115	−7.117	−7.114	−7.113	−7.113	−7.115
K2HPO4_4	−6.949	−6.951	−6.948	−6.949	−6.951	−6.95
Ethanol	−7.09	−7.092	−7.089	−7.089	−7.089	−7.088
Propanol	−7.04	−7.044	−7.041	−7.042	−7.038	−7.037
Butanol	−7.263	−7.265	−7.26	−7.26	−7.257	−7.258
Acrylic	−7.039	−7.042	−7.039	−7.04	−7.04	−7.041
HDPE	−6.998	−6.999	−6.997	−7.001	−6.998	−6.996
Delrin	−6.8	−6.8	−6.8	−6.795	−6.796	−6.798
PTFE	−7.223	−7.224	−7.221	−7.223	−7.226	−7.222

Table B6:

The difference between the width (pristine 95% - distal 90%) of measured Bragg peak curve and the simulated Bragg peak curves for six different physics lists with range cut value as 0.1 mm.

Insert	Pristine 95% and distal 90% dose points difference
	$\left|Z_{mes}-Z_{ZQGS\text{\_}FTFP\text{\_}BERT}\right|$	$\left|Z_{mes}-Z_{ZQGS\text{\_}BIC\text{\_}HP}\right|$	$\left|Z_{mes}-Z_{ZQG{S}_{-}BIC}\right|$	$\left|Z_{mes}-Z_{ZQG{S}_{-}BER{T}_{-}HP}\right|$	$\left|Z_{mes}-Z_{ZQG{S}_{-}BERT}\right|$	$\left|Z_{mes}-Z_{QBBC}\right|$
K2HPO4_1	−5.494	−5.489	−5.486	−5.49	−5.48	−5.485
K2HPO4_2	−5.907	−5.912	−5.906	−5.912	−5.919	−5.912
K2HPO4_3	−5.774	−5.777	−5.785	−5.786	−5.789	−5.785
K2HPO4_4	−5.252	−5.244	−5.245	−5.249	−5.255	−5.246
Ethanol	−5.335	−5.327	−5.331	−5.329	−5.338	−5.334
Propanol	−5.566	−5.575	−5.567	−5.565	−5.563	−5.557
Butanol	−5.969	−5.964	−5.968	−5.966	−5.962	−5.96
Acrylic	−5.883	−5.879	−5.878	−5.886	−5.881	−5.888
HDPE	−5.99	−5.993	−5.993	−6.001	−5.995	−5.995
Delrin	−6.055	−6.051	−6.047	−6.048	−6.049	−6.046
PTFE	−6.138	−6.15	−6.148	−6.147	−6.15	−6.146