Feasibility of using megavoltage computed tomography to reduce proton range uncertainty: A simulation study

Abstract Purpose To demonstrate that variation in chemical composition has a negligible effect on the mapping curve from relative electron density (RED) to proton stopping power ratio (SPR), and to establish the theoretical framework of using Megavoltage (MV) computed tomography (CT), instead of kilovoltage (kV) dual energy CT, to accurately estimate proton SPR. Methods A simulation study was performed to evaluate the effect of chemical composition variation on kVCT number and proton SPR. The simulation study involved both reference and simulated human tissues. The reference human tissues, together with their physical densities and chemical compositions, came from the ICRP publication 23. The simulated human tissues were created from the reference human tissues assuming that elemental percentage weight followed a Gaussian distribution. For all tissues, kVCT number and proton SPR were obtained through (a) theoretical calculation from tissue’s physical density and chemical composition which served as the ground truth, and (b) estimation from RED using the calibration curves established from the stoichiometric method. Deviations of the estimated values from the calculated values were quantified as errors in using RED to estimate kVCT number and proton SPR. Results Given a chemical composition variation of 5% (1σ) of the nominal percentage weights, the total estimation error of using RED to estimate kVCT number was 0.34%, 0.62%, and 0.77% and the total estimation error of using RED to estimate proton SPR was 0.30%, 0.22%, and 0.16% for fat tissues, non‐fat soft tissues and bone tissues, respectively. Conclusion Chemical composition had a negligible effect on the method of using RED to determine proton SPR. RED itself is sufficient to accurately determine proton SPR. MVCT number maintains a superb linear relationship with RED because it is highly dominated by Compton scattering. Therefore, MVCT has great potential in reducing the proton range uncertainty.


| INTRODUCTION
Proton therapy 1,2 utilizes high-energy proton beams to deposit therapeutic level radiation dose to the tumor through direct ionization and excitation. An attractive feature of proton interaction with matter is that proton has a finite penetration depth that can be controlled through proton energy. Thus, proton therapy can completely eliminate dose deposition beyond the distal edge of the tumor (i.e., no exit dose) and achieve better dose sparing for surrounding organs-at-risk (OARs). [3][4][5] The benefit of proton therapy, however, is partially offset by uncertainties in proton range estimation. 6,7 Although proton range may be affected by various factors such as setup and motion uncertainties, in a rigorous definition, adopted for the purpose of this work, the proton range uncertainty refers to as the uncertainty associated with the computed tomography (CT) number (in Hounsfield unit or HU) to proton stopping power ratio (SPR) calibration curve. The proton range uncertainty comes from the degeneracy effect. Materials with different chemical compositions may have the same CT number but different proton SPRs. In clinical treatment planning systems, proton SPR is determined solely from CT number using a CT number to proton SPR calibration curve. It does not require information regarding tissue chemical composition. Since the calibration curve maps one CT number to one proton SPR, it cannot handle the degeneracy effect caused by unknown chemical compositions of individual patients, resulting in the proton range uncertainty. Clinically, either an extra margin of~3.5% of the water equivalent depth 8,9 is added to compensate the proton range uncertainty, or a similar level of the range uncertainty is included in robustness analysis. 10,11 In the current practice, the stoichiometric method 12,13 is often used to establish the CT number to proton SPR calibration curve. It uses calculated CT numbers and proton SPRs from reference human tissues, instead of measured CT numbers and proton SPRs from tissue equivalent substitutes, to minimize the bias caused by chemical composition difference between human tissues and tissue equivalent substitutes. The stoichiometric method, however, cannot address the proton range uncertainty caused by unknown tissue chemical composition of individual patients and uncertainties in mean excitation energy of water and human tissues.
To reduce proton range uncertainty, calibration methods based on dual energy CT (DECT) have been investigated. [14][15][16] The most recent technical advances can be found in a review paper by Wohlfahrt et al. 17 Dual energy CT can provide more information regarding tissue chemical composition, for example, effective atomic number (Z eff ), and relative electron density (RED). In a theoretical investigation, Yang et al. 14 proposed a method to derive proton SPR using Z eff and RED obtained from DECT. They reported that, without image noise, kilovoltage (kV) DECT could achieve a root-meansquare (RMS) error of 0.26% for SPR estimation. 14  They demonstrated in their simulation study that the JSIR-BVM method was less sensitive to image noise. The RMS error in SPR estimation only increased from 0.2% under the idealized situation to 0.3% with image noise. The JSIR-BVM method, however, is highly empirical and has many assumptions (e.g., selection of basis materials). Its implementation in clinical practices still requires lots of developmental efforts.
The purpose of this work was to demonstrate that the proton range uncertainty caused by unknown chemical composition of individual patients was primarily due to our inability to accurately determine kVCT number, rather than proton SPR. In a simulation study, we investigated the relationship between RED and kVCT number, as well as between RED and proton SPR, under various tissue chemical compositions. It was found out that using RED to determine proton SPR was insensitive to chemical composition variation and therefore can be used to accurately determine proton SPR. Accurate RED information can be obtained using fan-beam or multi-slice MVCT.
Compared to kVCT, MVCT is highly dominated by Compton scattering. The photoelectric interaction in MVCT is further reduced to a negligible level, resulting in a strict linear relationship between MVCT number and RED. Based on our investigation, MVCT has great potential in reducing the proton range uncertainty. which is simply CT number plus 1000) and proton SPR according to tissue RED and chemical composition information are listed below.

2.A | Stoichiometric method
In Eq. (1), Here, N g and N i g are the total number of electrons per unit mass and the number of electron per unit mass contributed by the i th element, respectively. Given Z i , A i , and ω i are the atomic number, atomic weight and weight proportion for the i th element and N A is the Avogadro's number, then The

2.C | Reference and simulated human tissues
The reference human tissues used in this study were from the ICRP publication 23. 18 Physical densities and chemical compositions of the reference human tissues were listed in Table 1. Two tissues, cell nucleus and breast, were excluded from the study. Cell nucleus was excluded because it never exists by itself in human body. Breast was excluded because the reported chemical composition was for the entire breast which was a mixture of fat and glandular tissues. However, on CT images at the voxel level, fat and glandular tissues are clearly separated. Voxels in breast belong to either fat or glandular tissues except for a few voxels near the tissue boundary (i.e., the partial volume effect). Based on similarity in chemical composition, tissues were grouped into fat tissues, non-fat soft tissues and bone tissues, as shown in Table 1.
The simulated human tissues were generated from the reference human tissues. Assuming that human tissue elemental percentage weights follow the Gaussian distribution, the simulated human tissues were created by sampling the Gaussian distribution based on the mean (µ) and standard deviation (σ) of the percentage weight for each element. From each reference human tissue, 100 simulated human tissues were generated. In the process of generating the simulated human tissues, we used the elemental percentage weights of the reference human tissue as the mean and 5% of the elemental percentage weights of the reference human tissue as the standard deviation.
Creation of the simulated human tissues was performed using the MATLAB software (Version R2018a, The MathWorks, Inc., Natick, MA, USA). It involved multiple steps. First, a reference tissue was selected. Second, 100 random samples were generated for each element based on the element's mean percentage weight and standard deviation. Third, in a sequential order, 100 samples from all elements were put together to form 100 combinations of the chemical composition. Fourth, for each combination, the sum of percentage weights from all elements was normalized to 100% to mimic realistic scenarios. At this point, 100 simulated human tissues were created from that specific reference human tissue. Fifth, we repeated step 1-4 for all reference human tissues. In total, 3200 simulated human tissues were created from 32 reference human tissues.

2.D | Quantification of uncertainties
For all reference and simulated human tissues, kVCT number and proton SPR were calculated using two methods. The first method used Eqs. (1) and (2) to calculate kVCT number and proton SPR HU ET AL.  was developed to obtain phase-space files behind the phantom, for an infinitively small photon beamlet 19,20 at 60 keV or 0.8 MeV. For each run, the phantom was filled with a single type of material, either water or one of the 32 reference human tissues as defined in Table 1.
The physics model used in the Monte Carlo simulation was the builtin "QGSP_BIC_EMY" model. 12 million photon particles were used in the simulation. The phase-space files contained particle information such as particle type, position, momentum and energy, that went through a plane perpendicular to the beamlet at 1 meter downstream from the phantom. The number of un-scattered photons, which went through the phantom without any interaction with the phantom material, were obtained from the phase-space file. The ratio of the un-scattered photons over the incident photons was used to calculate the photon attenuation coefficient. The scaled CT numbers (CT number plus 1000) for both kV and MV beams were calculated from the attenuation coefficients using Eq. (5). For comparison, the scaled kV and MV CT numbers were plotted against RED in the same figure.
HU scale ¼ 1000 þ 1000 Â μ À μ water ð Þ =μ water (5)    systematic uncertainty in kVCT HU scale is much higher than that in proton SPR among all tissue categories. The statistical uncertainty in kVCT HU scale , however, is low for fat and non-fat soft tissues but high for bone tissues, compared to that in proton SPR. It is consistent with assumption that the kVCT HU scale is more sensitive to high Z elements (e.g., Ca) which have a higher proportion in bone tissues.

| RESULTS
Combining the systematic and statistical uncertainties, the total uncertainty among all tissue categories is 0.65% for kVCT HU scale and 0.21% for proton SPR.

| DISCUSSION
In this work, we demonstrated that when kVCT was used to estimate proton SPR, the primary source of range uncertainty came from the inability to accurately determine kVCT number, rather than proton SPR. In fact, proton SPR was quite insensitive to chemical composition variation. Based on our investigation, using RED to determine SPR could achieve a systematic uncertainty of 0.11% among all reference human tissues. As a comparison, the systematic uncertainty of using kVCT to determine proton SPR was 0.89%. 14 Using kV DECT to determine proton SPR could potentially reduce the proton range uncertainty. 17 Under the ideal (or noiseless) condition, the reported systematic uncertainty of using kV DECT to determine proton SPR was 0.26% in Yang et al's study 14 and 0.16% in Zhang et al's study. 16 For the statistical uncertainty, our study showed that using RED to determine proton SPR could achieve a statistical uncertainty of 0.18% among all simulated human tissues, which was lower than the reported statistical uncertainty that can be achieved by kVCT (0.18%, 1.2%, and 1.6% for lung, soft, and bone tissues, respectively). 9 In the process of obtaining the statistical uncertainty, 5% of ele-  T A B L E 2 Systematic, statistical, and total uncertainties, as well as maximum absolute percentage deviation, in kVCT HU scale and proton SPR estimation using the calibration curve method. Although the superb linear relationship was demonstrated qualitatively in previous work between RED and proton SPR, 22 as well as between MVCT number and proton SPR, 23 none of these studies provided quantitative results regarding the uncertainty of using RED or MVCT number to predict proton SPR, especially under the condition of chemical composition variation. In this work, we quantified the systematic, statistical and total uncertainties of using RED to predict kVCT number and proton SPR. The results clearly demonstrated that most uncertainties were due to our inability to accurately determine kVCT number, rather than proton SPR (0.65% vs 0.21% for the total uncertainty). If we use MVCT, instead of kVCT, to predict proton SPR, we can reduce the sensitivity of the calibration curve to chemical composition variation and improve the accuracy of proton range estimation. Although DECT does not require image registration, patient position may still vary between simulation and treatment, causing deviation in planned and delivered doses. MVCT does require image registration, but it is reasonable to assume its position is closer to the treatment position and therefore may help minimize deviation between planned and delivered doses. In both cases, this can be sufficiently covered by the setup margin. Using MVCT to determine proton SPR has some additional advantages compared to kVCT. First, it eliminates additional image processing that is required to obtain physical quantities from DECT images. Thus, it is more robust to image noise.

Systematic
Second, MVCT is less sensitive to the beam hardening effect due to its higher penetration power. Third, it has significantly less imaging artifacts from metal implants.
The main purpose of the manuscript was to demonstrate the potential of MVCT in reducing the proton range uncertainty. Other promising methods to reduce the proton range uncertainty include DECT and proton CT. In fact, DECT and proton CT have been investigated extensively, but MVCT, as an alternative method, has not received enough investigation. There are many challenges, for example, image acquisition time, imaging dose, etc., that need to be sufficiently addressed before MVCT can be evaluated for clinical use and compared with other promising methods like DECT and proton CT.
We hope that by demonstrating the potential of MVCT, we can stimulate more interests in the development of fan-beam MVCT as it may provide a practical solution to reduce the proton range uncertainty in future.

| CONCLUSION
We demonstrated that chemical composition variation had a negligible effect on the method of using RED to determine proton SPR.
Therefore, RED itself may be sufficient to accurately determine proton SPR. MVCT number maintains a superb linear relationship with RED because it is highly dominated by Compton scattering. Thus, MVCT has great potential in reducing the proton range uncertainty.

ACKNOWLEDG MENTS
This work was supported in part by the "Matteson Funds to Support Proton Clinical Research".

AUTHOR CONTRIBUTION STATEMENT
YH, XD, JS, MB, WL, YK, SL, and LY contributed to the study design, interpretation of results, and preparation of the manuscript. YH and XD contributed to the writing of simulation codes and data analysis.

CONFLI CT OF INTEREST
There is no conflict of interest.