Creating a spread-out Bragg peak in proton beams

The model of Bortfeld and Schlegel (1996 Phys. Med. Biol. 41 1331-9) for determining the weights of proton beams required to create a spread-out Bragg peak (SOBP) gives a significantly tilted SOBP. However, by arbitrarily varying its parameter p, which relates the range of protons to their energy, we have been able to create satisfactory SOBPs. MCNPX Monte Carlo calculations have been carried out to determine p, demonstrating the success of this modification. Optimal values of p are tabulated for various combinations of maximum beam energy E(0) (50, 100, 150, 200 and 250 MeV) and SOBP width χ (15%, 20%, 25%, 30%, 35% and 40%), as well as for a correction factor needed to calculate the SOBP dose. An example shows the application of these results to analyzing the dose deposited by deuterons and alpha particles in broad proton beams.     

Optimization of current modulation function for proton spread-out Bragg peak fields

Proton treatments with spread-out Bragg peak (SOBP) fields often use a rotating modulation wheel of varying thickness to modulate the pristine Bragg peak in depth and intensity. The technique of modulating also the beam current independently over the wheel rotation provides an additional control over the intensities of the pulled-back Bragg peaks. As a result, a single wheel can be used over a large range of energies and SOBP parameters and field-specific wheels are no longer necessary. An essential task in commissioning a particular treatment depth is the determination of this current modulation function. We have developed a method for the optimization of the current modulation function. The basic idea is to treat the entire beam nozzle, housing the various beam scattering and modulating components, as a whole and to characterize its effect as a transformation from a modulating beam current to a depth-dose distribution. While this transformation is difficult to calculate theoretically due to the complex scattering paths in the nozzle and the phantom, it can, however, be determined by time-resolved dose measurements. Using this transformation, we can calculate SOBP depth-dose distributions for any current modulation function and optimize it by a simple numerical optimization. We have applied the new method to a number of proton beams with satisfactory results.     

The prediction of output factors for spread-out proton Bragg peak fields in clinical practice

The reliable prediction of output factors for spread-out proton Bragg peak (SOBP) fields in clinical practice remained unrealized due to a lack of a consistent theoretical framework and the great number of variables introduced by the mechanical devices necessary for the production of such fields. These limitations necessitated an almost exclusive reliance on manual calibration for individual fields and empirical, ad hoc, models. We recently reported on a theoretical framework for the prediction of output factors for such fields. In this work, we describe the implementation of this framework in our clinical practice. In our practice, we use a treatment delivery nozzle that uses a limited, and constant, set of mechanical devices to produce SOBP fields over the full extent of clinical penetration depths, or ranges, and modulation widths. This use of a limited set of mechanical devices allows us to unfold the physical effects that affect the output factor. We describe these effects and their incorporation into the theoretical framework. We describe the calibration and protocol for SOBP fields, the effects of apertures and range-compensators and the use of output factors in the treatment planning process.     

权重适配的布拉格峰展宽方法

目的:提供一种权重适配的布拉格峰展宽（SOBP）方法,得到平滑的展宽布拉格峰。 方法:通过重新拟合质子能量-射程的关系（盖格法则）,找出适配函数的函数形式,并对权重进行重新适配,通过求敏感参数k,得到平滑的SOBP,最后用蒙特卡洛程序FLUKA进行验证。 结果:SOBP的形状对参数k比参数P更加敏感,拟合得到4~32 cm的SOBP,中间平坦区偏差不超过±2%,并解决中间区坍塌的问题。 结论:蒙特卡洛模拟检验了权重适配的SOBP方法的有效性。     

Monitor unit calculations for range-modulated spread-out Bragg peak fields

We derive, from first principles, a model to predict the output factors for spread-out Bragg peak proton fields (SOBP). The model is based on the simple observation that the output factor is the ratio of SOBP plateau dose to the dose measured in the ionization reference chamber. The latter, in turn, equates to the entrance dose of the SOBP corrected for inverse square. We use a theoretical derivation of this ratio to establish the relationship between the output factor and the distal range and modulation width of the SOBP. In addition, the theoretical derivation reduces the dependence on the distal range and modulation width into a single factor r = (R - M)/M. We compare the theoretical derivation against measurements obtained at the Northeast Proton Therapy Facility for output factors for clinical fields. The agreement between measurements and prediction is 2.9%.     

Sensitivities in the production of spread-out Bragg peak dose distributions by passive scattering with beam current modulation

A spread-out Bragg peak (SOBP) is used in proton beam therapy to create a longitudinal conformality of the required dose to the target. In order to create this effect in a passive beam scattering system, a variety of components must operate in conjunction to produce the desired beam parameters. We will describe how the SOBP is generated and will explore the tolerances of the various components and their subsequent effect on the dose distribution. A specific aspect of this investigation includes a case study involving the use of a beam current modulated system. In such a system, the intensity of the beam current can be varied in synchronization with the revolution of the range-modulator wheel. As a result, the weights of the pulled-back Bragg peaks can be individually controlled to produce uniform dose plateaus for a large range of treatment depths using only a small number of modulator wheels.     

A method for achieving variable widths of the spread-out Bragg peak using a ridge filter

A method for designing a variable-SOBP (spread-out Bragg peak) ridge filter has been proposed. First, ridge filter parameters are determined by using a Monte Carlo calculation followed by a fast two-step iterative optimization. Then, tilting the ridge filter results in continuous variation of the SOBP width. Monte Carlo calculations show that depth dose uniformity changes from +/- 1.3% to +/- 1.6% for SOBP widths ranging from 10.3 cm to 14.5 cm. Advantages of the proposed tilting ridge filter include a capability of continuous SOBP variation and cost-effective installation for a given SOBP width range.     

An analytical solution to proton Bragg peak deflection in a magnetic field

The role of MR imaging for image-guided radiation therapy (IGRT) is becoming more and more important thanks to the excellent soft tissue contrast offered by MRI. Hybrid therapy devices with integrated MRI scanners are under active development for x-ray therapy. The combination of proton therapy with MRI imaging has only been investigated at the theoretical or conceptual level. Of concern is the deflection of the proton beam in the homogeneous magnetic field. A previous publication has come to the conclusion that the impact of a 0.5 T magnetic field on the dose distribution for proton therapy is very small and lateral deflections stay well below 2?mm. The purpose of this study is to provide new insights into the effects of magnetic fields on a proton beam coming to rest in a patient. We performed an analytical calculation of the lateral deflection of protons with initial energies between 50 MeV and 250 MeV, perpendicular to the beam direction and the magnetic field. We used a power-law range-energy relationship and the Lorentz force in both relativistic and non-relativistic conditions. Calculations were done for protons coming to rest in water or soft tissue, and generalized to other uniform and non-uniform media. Results were verified by comparisons with numerical calculations and Monte Carlo simulations. A key result of our calculations is that the maximum lateral deflection at the end of range is proportional to the third power of the initial energy. Accordingly, due to the strong dependence on the energy, even a relatively small magnetic field of 0.5 T will cause a deflection of the proton beam by 1?cm at the end of range of a 200 MeV beam. The maximum deflection at 200 MeV is more than 10?times larger than that of a 90 MeV beam. Relativistic corrections of the deflection are generally small but they can become non-negligible at higher energies around 200 MeV and above. Contrary to previous findings, the lateral deflection of a proton beam can be significant (1?cm and above) even in relatively small magnetic fields of 0.5 T. However, the curved path of a proton beam in a magnetic field is easily predictable and it should be possible to account for this in treatment planning.     

Improvement of spread-out Bragg peak flatness for a carbon-ion beam by the use of a ridge filter with a ripple filter

We have developed a novel design method of ridge filters for carbon-ion therapy using a broad-beam delivery system to improve the flatness of a biologically effective dose in the spread-out Bragg peak (SOBP). So far, the flatness of the SOBP is limited to about ±5% for carbon beams since the weight control of component Bragg curves composing the SOBP is difficult. This difficulty arises from using a large number of ridge-bar steps (e.g. about 100 for a SOBP width of 60 mm) required to form the SOBP for the pristine Bragg curve with an extremely sharp distal falloff. Instead of using a single ridge filter, we introduce a ripple filter to broaden the Bragg peak so that the number of ridge-bar steps can be reduced to about 30 for SOBP with of 60 mm for the ridge filter designed for the broadened Bragg peak. Thus we can manufacture the ridge filter more accurately and then attain a better flatness of the SOBP due to well-controlled weights of the component Bragg curves. We placed the ripple filter on the same frame of the ridge filter and arranged the direction of the ripple-filter-bar array perpendicular to that of the ridge-filter-bar array. We applied this method to a 290 MeV u(-1) carbon-ion beam in Heavy Ion Medical Accelerator in Chiba and verified the effectiveness by measurements.     

Monte Carlo simulation and analysis of proton energy-deposition patterns in the Bragg peak

The spatial pattern of energy depositions is crucial for understanding the mechanisms that modify the relative biological effectiveness of different radiation qualities. In this paper, we present data on energy-deposition properties of mono-energetic protons (1-20 MeV) and their secondary electrons in liquid water. Proton-impact ionization was described by means of the Hansen-Kocbach-Stolterfoht doubly differential cross section (DDCS), thus modelling both the initial energy and angle of the emitted electron. Excitation by proton impact was included to account for the contribution of this interaction channel to the electronic stopping power of the projectile. Proton transport was implemented assuming track-segment conditions, whereas electrons were followed down to 50 eV by the Monte Carlo code PENELOPE. Electron intra-track energy-deposition properties, such as slowing-down and energy-imparted spectra of electrons, were calculated. Furthermore, the use of DDCSs enabled the scoring of electron inter-track properties. We present novel results for 1, 5 and 20 MeV single-proton-track frequencies of distances between the nearest inter- (e(-)-e(-), e(-)-H+) and intra-track (e(-)-e(-), e(-)-H+, H+-H+) energy-deposition events. By setting a threshold energy of 17.5 eV, commonly employed as a surrogate to discriminate for elementary damage in the DNA, the variation in these frequencies was studied as well. The energy deposited directly by the proton represents a large amount of the total energy deposited along the track, but when an energy threshold is adopted the relative contribution of the secondary electrons becomes larger for increasing energy of the projectile. We found that the frequencies of closest energy-deposition events per nanometre decrease with proton energy, i.e. for lower proton energies a denser ionization occurs, following the trend of the characteristic LET curves. In conclusion, considering the energy depositions due to the delta electrons and at the core of the track, 1 MeV protons have an intrinsic capability of generating about five times more dual depositions within the characteristic 2 nm of the DNA-chain structure than 20 MeV protons.     

Bragg peak prediction from quantitative proton computed tomography using different path estimates

This paper characterizes the performance of the straight-line path (SLP) and cubic spline path (CSP) as path estimates used in reconstruction of proton computed tomography (pCT). The GEANT4 Monte Carlo simulation toolkit is employed to simulate the imaging phantom and proton projections. SLP, CSP and the most-probable path (MPP) are constructed based on the entrance and exit information of each proton. The physical deviations of SLP, CSP and MPP from the real path are calculated. Using a conditional proton path probability map, the relative probability of SLP, CSP and MPP are calculated and compared. The depth dose and Bragg peak are predicted on the pCT images reconstructed using SLP, CSP, and MPP and compared with the simulation result. The root-mean-square physical deviations and the cumulative distribution of the physical deviations show that the performance of CSP is comparable to MPP while SLP is slightly inferior. About 90% of the SLP pixels and 99% of the CSP pixels lie in the 99% relative probability envelope of the MPP. Even at an imaging dose of ～0.1 mGy the proton Bragg peak for a given incoming energy can be predicted on the pCT image reconstructed using SLP, CSP, or MPP with 1 mm accuracy. This study shows that SLP and CSP, like MPP, are adequate path estimates for pCT reconstruction, and therefore can be chosen as the path estimation method for pCT reconstruction, which can aid the treatment planning and range prediction of proton radiation therapy.     

A compact ridge filter for spread out Bragg peak production in pulsed proton clinical beams

A number of designs have been proposed for ridge filters and range modulators used in proton therapy to modify the beam in order to spread out the Bragg peak. Despite the variety of solutions, no simple design capable of providing large fields and easy variation of the spread out Bragg peak (SOBP) length in a pulsed beam has been developed. We propose a compact ridge filter that can be used in a proton beam of any time structure. It allows the production of depth dose distributions that meet the requirements of therapy dose fields.     

Leakage and scatter radiation from a double scattering based proton beamline

Proton beams offer several advantages over conventional radiation techniques for treating cancer and other diseases. These advantages might be negated if the leakage and scatter radiation from the beamline and patient are too large. Although the leakage and scatter radiation for the double scattering proton beamlines at the Loma Linda University Proton Treatment Facility were measured during the acceptance testing that occurred in the early 1990s, recent discussions in the radiotherapy community have prompted a reinvestigation of this contribution to the dose equivalent a patient receives. The dose and dose equivalent delivered to a large phantom patient outside a primary proton field were determined using five methods: simulations using Monte Carlo calculations, measurements with silver halide film, measurements with ionization chambers, measurements with rem meters, and measurements with CR-39 plastic nuclear track detectors. The Monte Carlo dose distribution was calculated in a coronal plane through the simulated patient that coincided with the central axis of the beam. Measurements with the ionization chambers, rem meters, and plastic nuclear track detectors were made at multiple locations within the same coronal plane. Measurements with the film were done in a plane perpendicular to the central axis of the beam and coincident with the surface of the phantom patient. In general, agreement between the five methods was good, but there were some differences. Measurements and simulations also tended to be in agreement with the original acceptance testing measurements and results from similar facilities published in the literature. Simulations illustrated that most of the neutrons entering the patient are produced in the final patient-specific aperture and precollimator just upstream of the aperture, not in the scattering system. These new results confirm that the dose equivalents received by patients outside the primary proton field from primary particles that leak through the nozzle are below the accepted standards for x-ray and electron beams. The total dose equivalent outside of the field is similar to that received by patients undergoing treatments with intensity modulated x-ray therapy. At the center of a patient for a whole course of treatment, the dose equivalent is comparable to that delivered by a single whole-body XCT scan.     

Degradation of the Bragg peak due to inhomogeneities

The rapid fall-off of dose at the end of range of heavy charged particle beams has the potential in therapeutic applications of sparing critical structures just distal to the target volume. Here we explored the effects of highly inhomogeneous regions on this desirable depth-dose characteristic. The proton depth-dose distribution behind a lucite-air interface parallel to the beam was bimodal, indicating the presence of two groups of protons with different residual ranges, creating a step-like depth-dose distribution at the end of range. The residual ranges became more spread out as the interface was angled at 3 degrees, and still more at 6 degrees, to the direction of the beam. A second experiment showed little significant effect on the distal depth-dose of protons having passed through a mosaic of teflon and lucite. Anatomic studies demonstrated significant effects of complex fine inhomogeneities on the end of range characteristics. Monoenergetic protons passing through the petrous ridges and mastoid air cells in the base of skull showed a dramatic degradation of the distal Bragg peak. In beams with spread out Bragg peaks passing through regions of the base of skull, the distal fall-off from 90 to 20% dose was increased from its nominal 6 to well over 32 mm. Heavy ions showed a corresponding degradation in their ends of range. In the worst case in the base of skull region, a monoenergetic neon beam showed a broadening of the full width at half maximum of the Bragg peak to over 15 mm (compared with 4 mm in a homogeneous unit density medium). A similar effect was found with carbon ions in the abdomen, where the full width at half maximum of the Bragg peak (nominally 5.5 mm) was found to be greater than 25 mm behind gas-soft-tissue interfaces. We address the implications of these data for dose computation with heavy charged particles.     

基于质子束激发热声信号的布拉格峰定位

目的:使用质子束激发热声信号对质子束的布拉格峰定位,分析其在质子治疗中应用的可行性。方法:通过Kwave工具包模拟质子束在水中的传播过程,使用放置的传感器接收质子束激发产生的γ波走时数据,再将走时数据进行反演得到布拉格峰位置的修正量,从而完成对布拉格峰定位。结果:在均匀介质中,当初始的布拉格峰位置在目标布拉格峰位置5 cm范围内,使用Kwave模拟得到的走时数据进行定位,无噪声的情况下,定位误差在1.3 mm以内,对其进行加噪处理后,定位误差仍在3 mm以内。使用波前扩展的线性走时插值射线追踪算法得到的走时数据进行反演,能完成零误差定位。结论:使用质子束激发热声信号,仅需要少量的传感器就能对质子束的布拉格峰进行实时定位,走时数据的准确性对定位算法有一定的影响。但是通过加噪实验发现,本算法具有较好的稳定性和收敛性。     

Density heterogeneities and the influence of multiple Coulomb and nuclear scatterings on the Bragg peak distal edge of proton therapy beams

Density heterogeneities in the path of proton beams are known to cause degradation of the Bragg peak and, thus, widening of its distal fall-off. Inadequate accounting for this effect may lead to unwanted dose delivered to normal tissue distal to the target volume. In low-density regions, such as the thorax, this may lead to large volumes of healthy tissue receiving unnecessary dose. Although it is known that multiple Coulomb scattering within the density heterogeneities is the main cause of Bragg peak degradation, no systematic attempt has been made to quantify the contribution of multiple Coulomb scattering and nuclear scattering. Through a systematic study using a 220 MeV proton beam, we show that nuclear scattering contributes to about 5% of the distal fall-off width and is only slightly dependent on heterogeneity complexity. Furthermore, we also show that the energy spectra of the proton fluence downstream of various heterogeneity volumes are well correlated with the Bragg peak distal fall-off widths. Based on this correlation, a novel method for predicting distal fall-offs is suggested. This method is tested for three clinical setups of a voxelized model of a human head based on computer tomography data. Results are within 3% of the distal fall-off values obtained using Monte Carlo simulations.     

Calibration of a proton beam energy monitor

Delivery of therapeutic proton beams requires an absolute energy accuracy of +/-0.64 to 0.27 MeV for patch fields and a relative energy accuracy of +/-0.10 to 0.25 MeV for tailoring the depth dose distribution using the energy stacking technique. Achromatic switchyard tunes, which lead to better stability of the beam incident onto the patient, unfortunately limit the ability of switchyard magnet tesla meters to verify the correct beam energy within the tolerances listed above. A new monitor to measure the proton energy before each pulse is transported through the switchyard has been installed into a proton synchrotron. The purpose of this monitor is to correct and/or inhibit beam delivery when the measured beam energy is outside of the tolerances for treatment. The monitor calculates the beam energy using data from two frequency and eight beam position monitors that measure the revolution frequency of the proton bunches and the effective offset of the orbit from the nominal radius of the synchrotron. The new energy monitor has been calibrated by measuring the range of the beam through water and comparing with published range-energy tables for various energies. A relationship between depth dose curves and range-energy tables was first determined using Monte Carlo simulations of particle transport and energy deposition. To reduce the uncertainties associated with typical scanning water phantoms, a new technique was devised in which the beam energy was scanned while fixed thickness water tanks were sandwiched between two fixed parallel plate ionization chambers. Using a multitude of tank sizes, several energies were tested to determine the nominal accelerator orbit radius. After calibration, the energy reported by the control system matched the energy derived by range measurements to better than 0.72 MeV for all nine energies tested between 40 and 255 MeV with an average difference of -0.33 MeV. A study of different combinations of revolution frequency and radial offsets to test the envelope of algorithm accuracy demonstrated a relative accuracy of +/-0.11 MeV for small energy changes between 126 and 250 MeV. These new measurements may serve as a data set for benchmarking range-energy relationships.     

Radiochromic film dosimetry of a low energy proton beam

In this work some dosimetric characteristics of MD-55-2 GafChromic films were studied in a low energy proton beam (21.5 MeV) directly in a water phantom. The nonlinearity of the optical density was quantified by a factor P(lin). A correction factor P(en), that accounts for optical density dependence on the energy, was empirically determined. The effects of detector thickness in depth dose measurements and of the film orientation with respect to beam direction were investigated. The results show that the MD-55-2 films provide dose measurements with the films positioned perpendicularly to the proton beam. A dosimetric formalizm is proposed to determine the dose to water at depth d, with films oriented perpendicularly to the beam axis. This formalism uses a calibration factor of the radiochromic film determined directly on the proton beam at a reference depth in water, and the P(lin) factor, that takes into account the nonlinearity of the calibration curve and the P(en) factor that, in turn takes into account the change of proton beam energy in water. The MD-55-2 films with their high spatial resolution and the quasiwater equivalent material are attractive, positioned perpendicularly along the beam axis, for the absolute dose determination of very small beam sizes and modulated proton beams.