Scattering Of Protons Research Articles

Parity Violation in Proton–Proton Scattering at High Energies

A new approach has been proposed to describe parity violation in the scattering of polarized protons by protons at high energies. It has been shown that the P-odd proton- proton scattering amplitude in the tree approximation is much smaller than the P-odd proton-neutron scattering amplitude. Radiative corrections caused by the charge-exchange strong interaction are mainly responsible for P-odd asymmetry in proton-proton scattering. It has been predicted that asymmetry in the inelastic scattering cross section is much smaller than asymmetry in the elastic scattering cross section.

A Beam-Angle-Selection Method to Improve Inter-Fraction Motion Robustness for Lung Tumor Irradiation With Passive Proton Scattering.

In terms of dose distribution, protons are more sensitive to range variations than photons due to their unique properties. The aim of this study was to develop a method to identify patient-specific robust proton beam angles for lung tumor irradiation by investigating the association between water equivalent thickness (WET) variation and inter-fraction motion-induced target dose degradation. Using 3-dimensional computed tomography (3D-CT) images, the impact of WET variations on the target dose coverage of a series of coplanar proton beams was evaluated for 4 patients with lung cancer. Using ray tracing, WET maps, or WET baseline, were estimated for the internal target volume (ITV) at every 5° gantry interval in the axial plane. After calculating the WET baseline, the planning CT was shifted 5 mm in each anterior-posterior (AP), superior-inferior (SI), and left-right (LR) direction, yielding a total of 6 shifted CTs, and differential WET maps between the planning CT and each shifted CT were calculated. Target dose differences were associated with the average WET change between the original planning CT and the shifted CTs for all 360° gantry rotation beams. Target and OAR dose metrics in the ΔWET-guided plans were compared with those of the clinical plans. The WET variation maps showed areas of both high and low WET variations, with overall similar patterns yet individual differences reflecting tumor position differences. For all 4 patients investigated in this study, the coplanar plans demonstrated a strong correlation between WET changes and ITV dose reductions. Target dose coverage was more stable with the ΔWET-guided plan while OAR doses were comparable to the clinical plan. The WET variation maps have been used in this pilot study to identify proton beam angles that are either sensitive or robust to WET changes in proton passive scattering. This work demonstrates the feasibility of using WET variation maps to assist the planner in inter-fraction motion-robust proton beam angle selection.

Large-amplitude quadrupole shape mixing probed by the $(p,p^\prime)$ reaction: A model analysis

Abstract To discuss a possible observation of large-amplitude nuclear shape mixing by nuclear reaction, we employ a simple collective model and evaluate the transition densities with which the differential cross sections are obtained through the microscopic coupled-channel calculation. Assuming the spherical-to-prolate shape transition, we focus on large-amplitude shape mixing associated with the softness of the collective potential in the $\beta$ direction. We introduce a simple model based on the five-dimensional quadrupole collective Hamiltonian, which simulates a chain of isotopes that exhibit spherical-to-prolate shape phase transition. Taking $^{154}$Sm as an example and controlling the model parameters, we study how the large-amplitude shape mixing affects the elastic and inelastic proton scatterings. The calculated results suggest that the inelastic cross section of the $2_2^+$ state shows us the important role of the quadrupole shape mixing.

ES16.01 Proton Therapy

Proton therapy is an attractive option for the treatment of lung cancer patients due to the physical properties of proton beams. Proton therapy allows a focused delivery of radiation at the Bragg peak, with very steep decline of the radiation dose beyond the target volume. These properties offer the possibility to 1) reduce toxicity by reducing the integral dose and the dose to adjacent normal tissues and 2) escalate the dose to the target in some patients. In this talk, I will summarise briefly the physics/radiobiology of protons and the need for adaptation. I will also discuss the rationale for the use of protons in patients with lung cancer, including reduction in integral dose, cardiac toxicity and reduction in haematological toxicity. The clinical trial evidence supporting the use of protons will be presented in early stage and locally advanced non-small cell lung cancer as well as in small-cell lung cancer. Finally I will discuss future research directions, including preclinical and drug-proton combination research, ongoing clinical trials, the model based-approach and the need for biomarkers. Liao Z, Lee JJ, Komaki R, eat l. Bayesian Adaptive Randomization Trial of Passive Scattering Proton Therapy and Intensity-Modulated Photon Radiotherapy for Locally Advanced Non-Small-Cell Lung Cancer. J Clin Oncol. 2018;36(18):1813-1822 Chang JY, Jabbour SK, De Ruysscher D, et al; International Particle Therapy Co-operative Group Thoracic Subcommittee.Consensus Statement on Proton Therapy in Early-Stage and Locally Advanced Non-Small Cell Lung Cancer. Int J Radiat Oncol Biol Phys. 2016;95(1):505-16. Vyfhuis MAL, Onyeuku N, Diwanji T, Mossahebi S, Amin NP, Badiyan SN, Mohindra P, Simone CB 2nd. Advances in proton therapy in lung cancer. Ther Adv Respir Dis. 2018 Jan-Dec;12:1753466618783878 C, Pawelke J, Seidlitz A, Peitzsch C, et al; “Radiobiology of Proton Therapy”: Results of an international expert workshop.Lühr A, von Neubeck Radiother Oncol. 2018; 128(1):56-67 Jin, J.Y., et al., Higher Radiation Dose to Immune System is Correlated With Poorer Survival in Patients With Stage III Non-small Cell Lung Cancer: A Secondary Study of a Phase 3 Cooperative Group Trial (NRG Oncology RTOG 0617). International Journal of Radiation Oncology Biology Physics, 2017. 99(2): p. S151-S152. Joseph, N., et al., Post-treatment lymphocytopaenia, integral body dose and overall survival in lung cancer patients treated with radical radiotherapy. Radiotherapy and Oncology, 2019. 135: p. 115-119. Durante, M., D.J. Brenner, and S.C. Formenti, Does Heavy Ion Therapy Work Through the Immune System? Int J Radiat Oncol Biol Phys, 2016. 96(5): p. 934-936. Lee, H.J., Jr., J. Zeng, and R. Rengan, Proton beam therapy and immunotherapy: an emerging partnership for immune activation in non-small cell lung cancer. Translational lung cancer research, 2018. 7(2): p. 180-188. Dess, R.T., et al., Cardiac Events After Radiation Therapy: Combined Analysis of Prospective Multicenter Trials for Locally Advanced Non-Small-Cell Lung Cancer. J Clin Oncol, 2017. 35(13): p. 1395-1402. McWilliam, A., et al., Radiation dose to heart base linked with poorer survival in lung cancer patients. Eur J Cancer, 2017. 85: p. 106-113. Schulz-Ertner, D. and H. Tsujii, Particle radiation therapy using proton and heavier ion beams. J Clin Oncol, 2007. 25(8): p. 953-64. Gameiro, S.R., et al., Tumor Cells Surviving Exposure to Proton or Photon Radiation Share a Common Immunogenic Modulation Signature, Rendering Them More Sensitive to T Cell-Mediated Killing. Int J Radiat Oncol Biol Phys, 2016. 95(1): p. 120-30.

Precision Measurement of the Proton Charge Radius in Electron Proton Scattering

This report presents a project of an experiment for precision studies of the elastic electron proton scattering in the low momentum transfer region. The project is based on an innovative experimental method which allows for detection of recoil protons in a hydrogen "active target". The goal of the experiment is to measure the $ep$ elastic scattering differential cross section in the $Q^2$ range from 0.001 GeV$^2$ to 0.04 GeV$^2$ with 0.1% relative and 0.2% absolute precision and to determine the proton charge radius with a sub-percent precision. The important advantages of the proposed experiment are low radiative corrections, inherent to the recoil proton method, and absolute measurements of the differential cross sections. The experiment will be performed in the 720 MeV electron beam of the Mainz electron accelerator MAMI. This accelerator can provide an electron beam with optimal for this experiment parameters. The Proposal was approved by the MAMI Program Advisory Committee, and a special Agreement aimed at realization of this experiment was signed between Petersburg Nuclear Physics Institute and Institute of Nuclear Physics of the Mainz University. Also, scientists from the following institutes will participate in this project: GSI Centre for Heavy Ion Research, Germany; Joint Institute for Nuclear Research, Russia; William and Mary College, USA; Mount Allison University, Canada; University of Regina, Canada; Saint Mary's University, Canada. The first measurements should be started in 2020.

Biological Effects of Spot Scanning and Passive Scattering Proton Beams at the Distal End of the Spread-Out Bragg Peak (SOBP) in Single Cells and Multicell Spheroids

Biological Effects of Spot Scanning and Passive Scattering Proton Beams at the Distal End of the Spread-Out Bragg Peak (SOBP) in Single Cells and Multicell Spheroids

Preliminary Report of Secondary Malignant Neoplasm Incidence in Pediatric Patients Receiving Proton versus Photon Craniospinal Irradiation for Medulloblastoma

Modeling studies have predicted fewer secondary malignant neoplasms (SMN) following treatment with proton beam therapy (PBT) compared to photon radiotherapy (XRT). However, there are concerns regarding secondary neutron production and possible associated excess SMN with passive scatter proton therapy (PSPT) compared to pencil beam proton therapy. We reviewed our multi-institutional experience treating pediatric medulloblastoma (MB) patients with craniospinal irradiation (CSI) using either XRT or PBT. We hypothesized that excess SMN would not be observed among patients treated with PBT. From 1996 to 2014, 166 patients with MB received CSI followed by tumor bed boost using either PSPT (n = 103) or XRT (n = 63). For the proton cohort, all patients received PSPT for the CSI portion and 93.9% received PSPT for the boost. For XRT patients, all received 3-D conformal RT CSI followed by an IMRT tumor bed boost. Median age was 8.0 years at time of radiotherapy (RT), (8.0 years PBT, 8.1 years XRT). A majority of patients were male (112/166, 67.5%) and a majority had standard-risk MB (102/166, 61.4%). Median follow-up was 78.5 months for the PBT cohort and 153.2 months for the XRT cohort (p < 0.001). The 5- and 10-year overall survival rates were 82.6% and 81.2% for standard-risk and 69.8% and 64.0% for high-risk patients, respectively. No OS difference was identified by RT modality (p=0.49). The 5- and 10-year actuarial SMN rate was 2.3% and 8.1% for the entire study population (N=166). By modality, 5- and 10-year SMN rates were 2.6% and 6.0% for PBT patients, and 0.0% and 8.0% for XRT patients (p=0.71). There was no difference in incidence of SMN according to age (p=0.99), gender (p=0.50) or CSI dose (p=0.61). There were a total of 8 SMN identified in total (4 in each cohort by RT modality), with a median time from RT completion to SMN diagnosis of 71.2 months (range: 5.8 - 145.6 months). Breaking down SMNs by histology, there were 3 sarcomas, 2 malignant gliomas, 1 papillary thyroid cancer, 1 parotid mucoepidermoid carcinoma, and 1 cerebellar malignant glioneuronal tumor. All 4 SMNs in the PBT cohort occurred either within the previously-irradiated target (n=2), or in the entrance dose region (n=2). For XRT patients, 3 SMN occurred in regions receiving exit dose while 1 was within the target. Our preliminary analysis demonstrates no difference in the rate of SMN between PBT-treated and XRT-treated patients up to 10 years following RT. Given the shorter follow-up time for PBT patients, longer-term follow-up remains necessary to understand differential SMN patterns across RT modalities better. It is notable that XRT-treated patients developed a higher rate of SMNs in regions of exit dose than in the target volume.

On the Double Spin Asymmetries in the Elastic Scattering of Electrons off Protons

Based on the obtained differential cross sections for the scattering of longitudinally polarized electrons, taking into account the polarization of the proton target or the longitudinal polarization of the recoil protons, the next single spin asymmetries are studied: breaking T-parity asymmetry in the spin of the target proton $${{A}^{{( \bot )}}}$$ , and the degree of longitudinal polarization of recoil protons $${{P}_{p}}$$ . Double spin asymmetries are also obtained and analyzed: asymmetry $${{A}_{{ep}}}$$ with respect to the correlation of the incident electron helicity and the spin of the target proton, and right-left asymmetry $${{D}_{p}}$$ of the degree of longitudinal polarization of the recoil proton. It is shown that these asymmetries make it possible to measure the ratios of the proton form factors $${{{{G}_{{Ep}}}} \mathord{\left/ {\vphantom {{{{G}_{{Ep}}}} {{{G}_{{Mp}}}}}} \right. \kern-0em} {{{G}_{{Mp}}}}}$$ and $${{{{G}_{{Mp}}}} \mathord{\left/ {\vphantom {{{{G}_{{Mp}}}} {{{G}_{{1p}}}}}} \right. \kern-0em} {{{G}_{{1p}}}}}$$ .

Spatial Dose Patterns Associated With Radiation Pneumonitis in a Randomized Trial Comparing Intensity-Modulated Photon Therapy With Passive Scattering Proton Therapy for Locally Advanced Non-Small Cell Lung Cancer

Radiation pneumonitis (RP) is commonly associated with thoracic radiation therapy, and its incidence is related to dose and volume of the normal lung in the path of radiation. Our aim was to investigate dose patterns associated with RP in patients enrolled in a randomized trial of intensity modulated radiation therapy (IMRT) versus passive scattering proton therapy (PSPT) for locally advanced non-small cell lung cancer. We analyzed 178 patients prospectively treated with PSPT or IMRT for non-small cell lung cancer to a prescribed dose of 66 or 74Gy in conventional daily fractionation with concurrent chemotherapy. Forty patients (22%) developed clinically symptomatic RP. Voxel-based analysis of local dose differences was done with a nonparametric permutation test accounting for multiple comparisons. From the obtained 3-dimensional significance maps, we derived clusters of voxels that exhibited dose differences between groups at a statistical significance level of 0.05. The voxel-based analysis highlighted that (1) significant dose differences between patients with and without RP were found in the lower part of the lungs and in the heart and (2) the anatomic regions significantly spared by PSPT and the clusters in which doses were significantly correlated with RP development were disjoint. The analyzed trial data provide an unprecedented opportunity to substantiate previous hypotheses regarding the role of the heart and the lower lungs in the development of RP. Knowledge of this relationship between RP and thoracic regional radiosensitivity should be considered in clinical practice and in the design of future trials.

Effects of Absorption in Small-angle Scattering of Polarized Protons

Effects of Absorption in Small-angle Scattering of Polarized Protons

A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes

A dispersive optical model analysis of the proton scattering by titanium element nucleus and its natural isotopes is applied to the construction of the complex single-particle mean field starting from Fermi energy value to the energy value 100MeV and for constant input values of the parameters of this mean field. This mean field is called (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations were compared with these resulting from global parameterization of the optical model potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section, polarization for selected energy showed the excellent agreement with available experimental data and with these resulted from global parameterization of the optical model potential.

Influence and Countermeasure of Respiratory Motion on Matchline Profile of Field Matching Technique in Passive Scattering Proton Therapy for Esophageal Cancer

This study aimed to evaluate the influence of change in respiratory motion on matchline (ML) and reduction of the effect by increasing ML levels of field matching technique in passive scattering proton therapy for esophageal cancer. To evaluate the influence of respiratory motion in terms of stability, we measured relative dose around ML using a respiratory motion phantom. The relative error was -0.5% when the respiratory motion phantom worked stable, whereas there was obvious change that the relative error was -25.5% when the difference of amplitude between upper field and lower field was one side 3 mm on each cranially and caudally direction. In clinical case of the seven esophageal cancer patients simulated by the treatment planning system, assuming the difference of amplitude was 3 mm, the relative error of maximum (minimum) dose in clinical target volume around ML against the original treatment plan were 5.8±1.2% (-6.0±2.7%), 3.3±0.9% (-3.8±1.0%), and 2.4±0.5% (2.6±0.8%) on average (±SD) when ML levels were 2, 4, and 6, respectively. Increasing ML levels can reduce the influence of respiratory motion.

Dirac phenomenological analyses for the proton scatterings from nickel isotopes

Relativistic Dirac coupled channel analyses are performed phenomenologically using an optical potential model for the intermediate energy proton inelastic scatterings from nickel isotopes, 58Ni and 60Ni. The first-order rotational collective model is used for the transition optical potentials to describe the low-lying excited collective states of the ground state rotational band. The complicated Dirac coupled channel equations are solved phenomenologically by varying the optical potential and the deformation parameters to reproduce the experimental data, using a computer program that uses a sequential iteration method. The channel-coupling effects of the multistep transition process for the excited states of the ground state rotational band are found to be strong and lead the calculation results to better agreement with the experimental data when the channel coupling between the excited states is added in the calculation. The Dirac equations are reduced to the second-order differential equations to obtain the Schrödinger equivalent effective central and spin–orbit optical potentials, and the obtained effective potentials are analyzed.

Long-Term Follow-up of Patients Treated at a Single Institution Using a Passively Scattered Proton Beam; Observations Around the Occurrence of Second Malignancies

To investigate the occurrence of second malignancies resulting from the secondary radiation from a passively scattered proton beam. A cohort of patients with long-term follow-up was defined. All were treated at the same institution with the same proton delivery system, consisting of a 200MeV fixed, horizontal, passively scattered beam combined with a robotic chair. This setup allows for stereotactic positioning and permits fractionated treatments. The majority of patients underwent cranial or intracranial stereotactic radiation therapy. Patients with previous photon therapy or a follow-up of 24months or less were excluded. For out-of-field secondary malignancies (SMs), the observed incidence in the study population was compared to the risk of developing a malignancy in the general population, taking patient sex into account. From September 1993 to May 2016, a total of 524 patients received proton beam therapy, and 322 patients could be evaluated for this study (164 female and 158 male). Age ranged from 2 to 85years, with a median of 40years. Follow-up ranged from 25 to 276months, with a median of 150months (12.5years). During the study observation period, 7 patients had out-of-field new malignant disease. Three female patients developed a malignancy, compared with an expected incidence of 4.09 (standardized incidence ratio, 0.73 [95% confidence interval, 0.24-2.27]); 4 male patients developed a malignancy, versus an expected incidence of 3.99 (standardized incidence ratio, 1.00 [95% confidence interval, 0.38-2.67]). New intracranial disease developed in 9 patients: 8 meningiomas and 1 carcinoma. For out-of-field SMs, no increased risk of developing a variety of malignancies was observed. For in-field SMs, only 1 malignant histology was noted 15years after the original proton therapy. No SM was observed in children and young adults.

Long Term Follow Up of Patients Treated at a Single Institution using a Passively Scattered Proton Beam; Observations Around the Occurrence of Second Malignancies

To report our observations around whether any patterns of secondary malignancies occurred in patients treated at a single institution, all with the same passively scattered proton beam delivery system. We examined case records from a single national particle therapy facility offering proton and neutron therapy over a 23 year period. Proton beam treatment at the institution started in October 1993 and uses a 200 MeV fixed horizontal beam line combined with a robotic chair. The vast majority of patients was treated for intracranial and cranial lesions and positioned using the stereophotogrammetric positioning system (SPG). Follow up was achieved by way of medical records, telephone calls to patients, and home visits by social workers or community nurses. All patients with 24 or fewer months of follow up were excluded, as well as patients who had previous photon therapy. Rates of observed malignancies in the patient population were compared with expected rates, which were obtained from the national cancer statistics. We analyzed the group as a whole, and also particular sub-populations, including children who were treated with the proton therapy. From October 1993 to May 2016 a total of 524 patients received proton beam therapy, with 322 patients evaluable (164 females & 158 males). Age ranged from 2 – 85 years, with a median of 40 years. Their follow up ranged from 25 to 276 months, with a median of 150 months (12.5 years). 9 patients developed new intracranial lesions consisting of 8 meningiomas and 1 carcinoma. Eight patients had new extracranial primary malignancies. No significant increased risk was observed in the patients who received proton therapy when compared with the expected risk in the general population. 37 pediatric patients (<20 years of age) were treated. No observed second malignancies were seen in this subgroup after a median follow-up of 15 years. No patient developed a second in field malignancy, and no apparent increased risk for a second out of field malignancy was observed. This is reassuring, especially in children and young adults. A solitary patient developed an intracranial carcinoma but this followed combined modality treatment with neutrons plus a proton boost. All other observed intracranial lesions were meningiomas. The findings of this study bode well for patients treated with pencil beam scanning systems, given the lower secondary neutron dose associated with that technique.

Patterns of Local-Regional Failure After Intensity Modulated Radiation Therapy or Passive Scattering Proton Therapy With Concurrent Chemotherapy for Non-Small Cell Lung Cancer

We compared differences in patterns of locoregional failure, and the influence of adaptive planning on those patterns, in patients who received passive scattering proton therapy (PSPT) versus intensity modulated photon therapy (IMRT) for non-small cell lung cancer. Treatment simulation computed tomography scans and dose distributions were registered with images depicting the recurrence. Local failure (LF) was defined as failure within the internal target volume (ITV); marginal failure (MF) as failure between the ITV and planning target volume (PTV) plus a 10-mm margin (PTV+10mm); and regional failure (RF) as outside the PTV+10mm. Weekly during-treatment 4-dimensional computed tomography simulation and verification plans were obtained for all patients. Adaptive plans were developed if the verification plan showed deviations in protocol-specified dose distribution, and failure locations were recorded for those patients as well. Of the 212 patients analyzed, most (152 [72%]) had no failure; of the 60 patients with failure, 27 (45%) had LF (within the ITV), 23 (38%) had MF (between the ITV and PTV+10mm), and 10 (17%) had RF (>10mm outside the PTV). MF rates were no different for IMRT patients (16 of 136 [12%]) or PSPT patients (7 of 76 [9%], log-rank P=.558). The only independent predictor of MF on Cox proportional hazards analysis was T3-4 status. Large tumors and use of PSPT independently predicted the need for adaptive planning. Although 5-year overall survival rates were poorer for patients with large tumors versus small tumors (P<.001), the rates were similar for patients with large tumors who received adaptive planning versus small tumors. No differences in LF, MF, or RF patterns were found for IMRT versus PSPT. Proton therapy more often required adaptive planning, and the techniques used for adaptive planning did not compromise tumor control. Response to chemoradiation by larger tumors predicted favorable survival.

Elastic and diffractive scatterings in the LHC era

We review the elastic and diffractive scatterings of protons (called also the “forward physics”) with emphasis on the LHC data, especially those deviating from the expectations based on extrapolations from earlier measurements at the ISR and Fermilab and thus triggering searches for new ideas, models and theories. We list these new data and provide a brief introduction of available theoretical approaches, mainly those based on analyticity, crossing symmetry and unitarity, particularly the Regge pole model realizing these concepts. Fits to the data are presented and tensions between theoretical predictions and the data that may indicate the way to further progress are in the focus of our paper.

Two-Photon Exchange Correction in Elastic Lepton–Proton Scattering

We present the dispersion relation approach based on unitarity and analyticity to evaluate the two-photon exchange contribution to elastic electron-proton scattering. The leading elastic and first inelastic $\pi N$ intermediate state contributions are accounted for in the region of small momentum transfer $Q^2 < 1~\mathrm{GeV}^2$ based on the available data input. The novel methods of analytical continuation allow us to exploit the MAMI form factor data and the MAID parameterization for the pion electroproduction amplitudes as input in the calculation. The results are compared to the recent CLAS, VEPP-3 and OLYMPUS data as well as to the full two-photon exchange correction in the near-forward approximation, which is based on the Christy and Bosted unpolarized structure functions fit. Additionally, predictions are given for a forthcoming muon-proton scattering experiment.

Considerations when treating lung cancer with passive scatter or active scanning proton therapy.

Lung cancer, due to its poor clinical outcomes and significant toxicity associated with standard photon-based radiation, is a disease site that has the potential to greatly benefit from accurate treatment with proton radiation therapy. The potential of proton therapy is the ability to increase the radiation dose to the tumor while simultaneously decreasing the radiation dose to surrounding healthy tissues. For lung cancer treatment, this could mean significant sparing of the uninvolved healthy lung, which is difficult to achieve with external photon beam therapy, or decreasing the heart dose. In treating lung cancer with proton therapy, some additional considerations need to be made compared to treating patients with external photon beam radiation therapy. These include accounting for the finite range of protons in the patient, understanding temporal effects, potential dose discrepancies and choosing an appropriate treatment planning system for the task. One final consideration is differences between the different available proton therapy delivery systems-passive scattered proton therapy (PSPT) and active scanning proton therapy.

A machine learning approach to the accurate prediction of monitor units for a compact proton machine.

Clinical treatment planning systems for proton therapy currently do not calculate monitor units (MUs) in passive scatter proton therapy due to the complexity of the beam delivery systems. Physical phantom measurements are commonly employed to determine the field-specific output factors (OFs) but are often subject to limited machine time, measurement uncertainties and intensive labor. In this study, a machine learning-based approach was developed to predict output (cGy/MU) and derive MUs, incorporating the dependencies on gantry angle and field size for a single-room proton therapy system. The goal of this study was to develop a secondary check tool for OF measurements and eventually eliminate patient-specific OF measurements. The OFs of 1754 fields previously measured in a water phantom with calibrated ionization chambers and electrometers for patient-specific fields with various range and modulation width combinations for 23 options were included in this study. The training data sets for machine learning models in three different methods (Random Forest, XGBoost and Cubist) included 1431 (~81%) OFs. Ten-fold cross-validation was used to prevent "overfitting" and to validate each model. The remaining 323 (~19%) OFs were used to test the trained models. The difference between the measured and predicted values from machine learning models was analyzed. Model prediction accuracy was also compared with that of the semi-empirical model developed by Kooy (Phys. Med. Biol. 50, 2005). Additionally, gantry angle dependence of OFs was measured for three groups of options categorized on the selection of the second scatters. Field size dependence of OFs was investigated for the measurements with and without patient-specific apertures. All three machine learning methods showed higher accuracy than the semi-empirical model which shows considerably large discrepancy of up to 7.7% for the treatment fields with full range and full modulation width. The Cubist-based solution outperformed all other models (P<0.001) with the mean absolute discrepancy of 0.62% and maximum discrepancy of 3.17% between the measured and predicted OFs. The OFs showed a small dependence on gantry angle for small and deep options while they were constant for large options. The OF decreased by 3%-4% as the field radius was reduced to 2.5cm. Machine learning methods can be used to predict OF for double-scatter proton machines with greater prediction accuracy than the most popular semi-empirical prediction model. By incorporating the gantry angle dependence and field size dependence, the machine learning-based methods can be used for a sanity check of OF measurements and bears the potential to eliminate the time-consuming patient-specific OF measurements.