A simplified Monte Carlo algorithm considering large-angle scattering for fast and accurate calculation of proton dose.

PURPOSE: The purpose of this study is to improve dose calculation accuracy of the simplified Monte Carlo (SMC) algorithm in the low-dose region. Because conventional SMC algorithms calculate particle scattering in consideration of multiple Coulomb scattering (MCS) only, they approximate lateral dose profiles by a single Gaussian function. However, it is well known that the low-dose region spreads away from the beam axis, and it has been pointed out that modeling of the low-dose region is important to calculated dose accurately. METHODS: A SMC algorithm, which is named modified SMC and considers not only MCS but also large angle scattering resembling hadron elastic scattering, was developed. In the modified SMC algorithm, the particle fluence varies in the longitudinal direction because the large-angle scattering decreases residual range of particles in accordance with their scattering angle and tracking of the particles with large scattering angle is terminated at a short distance downstream from the scattering. Therefore, modified integrated depth dose (m-IDD) tables, which are converted from measured IDD in consideration of the fluence loss, are used to calculate dose. RESULTS: In the case of a 1-liter cubic target, the calculation accuracy was improved in comparison with that of a conventional algorithm, and the modified algorithm results agreed well with Geant4-based simulation results; namely, 98.8% of the points satisfied the 2% dose/2 mm distance-to-agreement (DTA) criterion. The calculation time of the modified SMC algorithm was 1972 s in the case of 4.4 × 108 particles and 16-threading operation of an Intel Xeon E5-2643 (3.3-GHz clock). CONCLUSIONS: An SMC algorithm that can reproduce a laterally widespread low-dose region was developed. According to the comparison with a Geant4-based simulation, it was concluded that the modified SMC algorithm is useful for calculating dose of proton radiotherapy.

A simulation study of MR-guided proton therapy system using iron-yoked superconducting open MRI: a conceptual study.

Radiotherapy platforms integrated with magnetic resonance imaging (MRI) have been significantly successful and widely used in X-ray therapy over the previous decade. MRI provides greater soft-tissue contrast than conventional X-ray techniques, which enables more precise radiotherapy with on-couch adaptive treatment planning and direct tracking of moving tumors. The integration of MRI into a proton beam irradiation system (PBS) is still in the research stage. However, this could be beneficial as proton therapy is more sensitive to anatomical changes and organ motion. In this simulation study, we considered the integration of PBS into the 0.3-T superconducting open MRI system. Our proposed design involves proton beams traversing a hole at the center of the iron yoke, which allows for a reduced fringe field in the irradiation nozzle while maintaining a large proton scan field of the current PBS. The shape of the bipolar MRI magnets was derived to achieve a large MRI field-of-view. To monitor the beam position and size accurately while maintaining a small beam size, the beam monitor installation was redesigned from the current system. The feasibility of this system was then demonstrated by the treatment plan quality, which showed that the magnetic field did not deteriorate the plan quality from that without the magnetic field for both a rectangular target and a prostate case. Although numerous challenges remain before the proposed simulation model can be implemented in a clinical setting, the presented conceptual design could assist in the initial design for the realization of the MR-guided proton therapy.

Technical note: Application of an optical hydrophone to ionoacoustic range detection in a tissue-mimicking agar phantom.

BACKGROUND: Ionoacoustics is a promising approach to reduce the range uncertainty in proton therapy. A miniature-sized optical hydrophone (OH) was used as a measuring device to detect weak ionoacoustic signals with a high signal-to-noise ratio in water. However, further development is necessary to prevent wave distortion because of nearby acoustic impedance discontinuities while detection is conducted on the patient's skin. PURPOSE: A prototype of the probe head attached to an OH was fabricated and the required dimensions were experimentally investigated using a 100-MeV proton beam from a fixed-field alternating gradient accelerator and k-Wave simulations. The beam range of the proton in a tissue-mimicking phantom was estimated by measuring γ-waves and spherical ionoacoustic waves with resonant frequency (SPIRE). METHODS: Four sizes of probe heads were fabricated from agar blocks for the OH. Using the prototype, the Î³-wave was detected at distal and lateral positions to the Bragg peak on the phantom surface for proton beams delivered at seven positions. For SPIRE, independent measurements were performed at distal on- and off-axis positions. The range positions were estimated by solving the linear equation using the sensitive matrix for the γ-wave and linear fitting of the correlation curve for SPIRE; they were compared with those measured using a film. RESULTS: The first peak of the γ-wave was undistorted with the 3 × 3 × 3-cm3 probe head used at the on-axis and 3-cm off-axis positions. The range positions estimated by the γ-wave agreed with the film-based range in the depth direction (the maximum deviation was 0.7 mm), although a 0.6-2.1 mm deviation was observed in the lateral direction. For SPIRE, the deviation was <1 mm for the two measurement positions. CONCLUSIONS: The attachment of a relatively small-sized probe head allowed the OH to measure the beam range on the phantom surface.

Ionoacoustic application of an optical hydrophone to detect proton beam range in water.

BACKGROUND: Proton range uncertainty has been the main factor limiting the ability of proton therapy to concentrate doses to tumors to their full potential. Ionoacoustic (IA) range verification is an approach to reducing this uncertainty by detecting thermoacoustic waves emitted from an irradiated volume immediately following a pulsed proton beam delivery; however, the signal weakness has been an obstacle to its clinical application. To increase the signal-to-noise ratio (SNR) with the conventional piezoelectric hydrophone (PH), the detector-sensitive volume needs to be large, but it could narrow the range of available beam angles and disturb real-time images obtained during beam delivery. PURPOSE: To prevent this issue, we investigated a millimeter-sized optical hydrophone (OH) that exploits the laser interferometric principle. For two types of IA waves [γ-wave emitted from the Bragg peak (BP) and a spherical IA wave with resonant frequency (SPIRE) emitted from the gold fiducial marker (GM)], comparisons were made with PH in terms of waveforms, SNR, range detection accuracy, and signal intensity robustness against the small detector misalignment, particularly for SPIRE. METHODS: A 100-MeV proton beam with a 27 ns pulse width and 4 mm beam size was produced using a fixed-field alternating gradient accelerator and was irradiated to the water phantom. The GM was set on the beam's central axis. Acrylic plates of various thicknesses, up to 12 mm, were set in front of the phantoms to shift the proton range. OH was set distal and lateral to the beam, and the range was estimated using the time-of-flight method for γ-wave and by comparing with the calibration data (SPIRE intensity versus the distance between the GM and BP) derived from an IA wave transport simulation for SPIRE. The BP dose per pulse was 0.5-0.6 Gy. To measure the variation in SPIRE amplitude against the hydrophone misalignment, the hydrophone was shifted by ± 2 mm at a maximum in lateral directions. RESULTS: Despite its small size, OH could detect γ-wave with a higher SNR than the conventional PH (diameter, 29 mm), and a single measurement was sufficient to detect the beam range with a submillimeter accuracy in water. In the SPIRE measurement, OH was far more robust against the detector misalignment than the focused PH (FPH) used in our previous study [5%/mm (OH) versus 80%/mm (FPH)], and the correlation between the measured SPIRE intensity and the distance between the GM and BP agreed well with the simulation results. However, the OH sensitivity was lower than the FPH sensitivity, and about 5.6-Gy dose was required to decrease the intensity variation among measurements to less than 10%. CONCLUSION: The miniature OH was found to detect weak IA signals produced by proton beams with a BP dose used in hypofractionated regimens. The OH sensitivity improvement at the MHz regime is worth exploring as the next step.

Biological effect of dose distortion by fiducial markers in spot-scanning proton therapy with a limited number of fields: a simulation study.

PURPOSE: In accurate proton spot-scanning therapy, continuous target tracking by fluoroscopic x ray during irradiation is beneficial not only for respiratory moving tumors of lung and liver but also for relatively stationary tumors of prostate. Implanted gold markers have been used with great effect for positioning the target volume by a fluoroscopy, especially for the cases of liver and prostate with the targets surrounded by water-equivalent tissues. However, recent studies have revealed that gold markers can cause a significant underdose in proton therapy. This paper focuses on prostate cancer and explores the possibility that multiple-field irradiation improves the underdose effect by markers on tumor-control probability (TCP). METHODS: A Monte Carlo simulation was performed to evaluate the dose distortion effect. A spherical gold marker was placed at several characteristic points in a water phantom. The markers were with two different diameters of 2 and 1.5 mm, both visible on fluoroscopy. Three beam arrangements of single-field uniform dose (SFUD) were examined: one lateral field, two opposite lateral fields, and three fields (two opposite lateral fields + anterior field). The relative biological effectiveness (RBE) was set to 1.1 and a dose of 74 Gy (RBE) was delivered to the target of a typical prostate size in 37 fractions. The ratios of TCP to that without the marker (TCP(r)) were compared with the parameters of the marker sizes, number of fields, and marker positions. To take into account the dependence of biological parameters in TCP model, α∕ß values of 1.5, 3, and 10 Gy (RBE) were considered. RESULTS: It was found that the marker of 1.5 mm diameter does not affect the TCPs with all α∕ß values when two or more fields are used. On the other hand, if the marker diameter is 2 mm, more than two irradiation fields are required to suppress the decrease in TCP from TCP(r) by less than 3%. This is especially true when multiple (two or three) markers are used for alignment of a patient. CONCLUSIONS: It is recommended that 1.5-mm markers be used to avoid the reduction of TCP as well as to spare the surrounding critical organs, as long as the markers are visible on x-ray fluoroscopy. When 2-mm markers are implanted, more than two fields should be used and the markers should not be placed close to the distal edge of any of the beams.

Technical Note: Range verification of pulsed proton beams from fixed-field alternating gradient accelerator by means of time-of-flight measurement of ionoacoustic waves.

PURPOSE: Ionoacoustics is one of the promising approaches to verify the beam range in proton therapy. However, the weakness of the wave signal remains a main hindrance to its application in clinics. Here we studied the potential use of a fixed-field alternating gradient accelerator (FFA), one of the accelerator candidates for future proton therapy. For such end, magnitude of the pressure wave and range accuracy achieved by the short-pulsed beam of FFA were assessed, using both simulation and experimental procedure. METHODS: A 100 MeV proton beam from the FFA was applied on a water phantom, through the acrylic wall. The beam range measured by the Bragg peak (BP)-ionization chamber (BPC) was 77.6 mm, while the maximum dose at BP was estimated to be 0.35 Gy/pulse. A hydrophone was placed 20 mm downstream of the BP, and signals were amplified and stored by a digital oscilloscope, averaged, and low-pass filtered. Time-of-flight (TOF) and two relative TOF values were analyzed in order to determine the beam range. Furthermore, an acoustic wave transport simulation was conducted to estimate the amplitude of the pressure waves. RESULTS: The range calculated when using two relative TOF was 78.16 ± 0.01 and 78.14 ± 0.01 mm, respectively, both values being coherent with the range measured by the BPC (the difference was 0.5-0.6 mm). In contrast, utilizing the direct TOF resulted in a range error of 1.8 mm. Fivefold and 50-fold averaging were required to suppress the range variation to below 1 mm for TOF and relative TOF measures, respectively. The simulation suggested the magnitude of pressure wave at the detector exceeded 7 Pascal. CONCLUSION: A submillimeter range accuracy was attained with a pulsed beam of about 21 ns from an FFA, at a clinical energy using relative TOF. To precisely quantify the range with a single TOF measurement, subsequent improvement in the measuring system is required.

On-line range verification for proton beam therapy using spherical ionoacoustic waves with resonant frequency.

In contrast to conventional X-ray therapy, proton beam therapy (PBT) can confine radiation doses to tumours because of the presence of the Bragg peak. However, the precision of the treatment is currently limited by the uncertainty in the beam range. Recently, a unique range verification methodology has been proposed based on simulation studies that exploit spherical ionoacoustic waves with resonant frequency (SPIREs). SPIREs are emitted from spherical gold markers in tumours initially introduced for accurate patient positioning when the proton beam is injected. These waves have a remarkable property: their amplitude is linearly correlated with the residual beam range at the marker position. Here, we present proof-of-principle experiments using short-pulsed proton beams at the clinical dose to demonstrate the feasibility of using SPIREs for beam-range verification with submillimetre accuracy. These results should substantially contribute to reducing the range uncertainty in future PBT applications.

Design of a ridge filter structure based on the analysis of dose distributions.

Dose distributions distorted by a periodic structure, such as a ridge filter, are analytically investigated. Based on the beam optics, the fluence distributions of scanned beams passing through the ridge filter are traced. It is shown that the periodic lateral dose distribution blurred by multiple Coulomb scattering can be expressed by a sum of cosine functions through Fourier transform. The result shows that the dose homogeneity decreases exponentially as the period of the structure becomes longer. This analysis is applied to the example case of a mini-ridge filter. The mini-ridge filter is designed to broaden sharp Bragg peaks for an energy-stacking irradiation method. The dose distributions depend on the period of the ridge filter structure and the angular straggling at the ridge filter position. Several cases are prepared where the period and angular straggling are supposed to be probable values. In these cases, the lateral distributions obtained by the analytical method are compared to Monte Carlo simulation results. Both distributions show good agreement with each other within 1%, which means that this analysis allows estimation of the dose distribution downstream of the ridge filter quantitatively. The appropriate period of grooves and scatterer width can be determined which ensures sufficient homogeneity.

Reduction of the number of stacking layers in proton uniform scanning.

Uniform scanning with a relatively large beam size can improve beam utilization efficiency more than conventional irradiation methods using scatterers and can achieve a large-field, long-range and large spread-out Bragg peak (SOBP). The SOBP is obtained by energy stacking in uniform scanning, but its disadvantage is that the number of stacking layers is large, especially in the low-energy region, because the Bragg peak of the pristine beam is very sharp. We applied a mini-ridge filter to broaden the pristine Bragg peak up to a stacked layer thickness of 1 or 2 cm in order to decrease the number of stacking layers. The number of stacking layers can be reduced to 20% or less than that in the case of pristine beam stacking. Although the distal falloff of the SOBP is deteriorated by applying the mini-ridge filter, we can improve the distal falloff to that of pristine beam stacking by introducing the distal filter to the irradiation of the most distal layer. Uniform scanning in combination with mini-ridge filter use can more than double the beam utilization efficiency over that of passive irradiation techniques.

A novel range-verification method using ionoacoustic wave generated from spherical gold markers for particle-beam therapy: a simulation study.

This study proposes a novel alternative range-verification method for proton beam with acoustic waves generated from spherical metal markers. When proton beam is incident on metal markers, most of the resulting pressure waves are confined in the markers because of the large difference in acoustic impedance between the metal and tissue. However, acoustic waves with frequency equal to marker's resonant frequency escape this confinement; the marker briefly acts as an acoustic transmitter. Herein, this phenomenon is exploited to measure the range of the proton beam. We test the proposed strategy in 3-D simulations, combining the dose calculations with modelling of acoustic-wave propagation. A spherical gold marker of 2.0 mm diameter was placed in water with a 60 MeV proton beam incident on it. We investigated the dependence of pressure waves on the width of beam pulse and marker position. At short beam pulse, specific high-frequency acoustic waves of 1.62 MHz originating from the marker were observed in wave simulations, whose amplitude correlated with the distance between the marker and Bragg peak. Results indicate that the Bragg peak position can be estimated by measuring the acoustic wave amplitudes from the marker, using a single detector properly designed for the resonance frequency.

Dual ring multilayer ionization chamber and theory-based correction technique for scanning proton therapy.

PURPOSE: To develop a multilayer ionization chamber (MLIC) and a correction technique that suppresses differences between the MLIC and water phantom measurements in order to achieve fast and accurate depth dose measurements in pencil beam scanning proton therapy. METHODS: The authors distinguish between a calibration procedure and an additional correction: 1-the calibration for variations in the air gap thickness and the electrometer gains is addressed without involving measurements in water; 2-the correction is addressed to suppress the difference between depth dose profiles in water and in the MLIC materials due to the nuclear interaction cross sections by a semiempirical model tuned by using measurements in water. In the correction technique, raw MLIC data are obtained for each energy layer and integrated after multiplying them by the correction factor because the correction factor depends on incident energy. The MLIC described here has been designed especially for pencil beam scanning proton therapy. This MLIC is called a dual ring multilayer ionization chamber (DRMLIC). The shape of the electrodes allows the DRMLIC to measure both the percentage depth dose (PDD) and integrated depth dose (IDD) because ionization electrons are collected from inner and outer air gaps independently. RESULTS: IDDs for which the beam energies were 71.6, 120.6, 159, 180.6, and 221.4 MeV were measured and compared with water phantom results. Furthermore, the measured PDDs along the central axis of the proton field with a nominal field size of 10 × 10 cm(2) were compared. The spread out Bragg peak was 20 cm for fields with a range of 30.6 and 3 cm for fields with a range of 6.9 cm. The IDDs measured with the DRMLIC using the correction technique were consistent with those that of the water phantom; except for the beam energy of 71.6 MeV, all of the points satisfied the 1% dose/1 mm distance to agreement criterion of the gamma index. The 71.6 MeV depth dose profile showed slight differences in the shallow region, but 94.5% of the points satisfied the 1%/1 mm criterion. The 90% ranges, defined at the 90% dose position in distal fall off, were in good agreement with those in the water phantom, and the range differences from the water phantom were less than ±0.3 mm. The PDDs measured with the DRMLIC were also consistent with those that of the water phantom; 97% of the points passed the 1%/1 mm criterion. CONCLUSIONS: It was demonstrated that the new correction technique suppresses the difference between the depth dose profiles obtained with the MLIC and those obtained from a water phantom, and a DRMLIC enabling fast measurements of both IDD and PDD was developed. The IDDs and PDDs measured with the DRMLIC and using the correction technique were in good agreement with those that of the water phantom, and it was concluded that the correction technique and DRMLIC are useful for depth dose profile measurements in pencil beam scanning proton therapy.

Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique.

PURPOSE: The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique. METHODS: The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations. RESULTS: The authors investigated the difference between double and triple Gaussian kernel models. The authors found that the difference between the two studied kernel models appeared at mid-depths and the accuracy of predicting the double Gaussian model deteriorated at the low-dose bump that appeared at mid-depths. When the authors employed the double Gaussian kernel model, the accuracy of calculations for the absolute dose at the center of the SOBP varied with irradiation conditions and the maximum difference was 3.4%. In contrast, the results obtained from calculations with the triple Gaussian kernel model indicated good agreement with the measurements within ±1.1%, regardless of the irradiation conditions. CONCLUSIONS: The difference between the results obtained with the two types of studied kernel models was distinct in the high energy region. The accuracy of calculations with the double Gaussian kernel model varied with the field size and SOBP width because the accuracy of prediction with the double Gaussian model was insufficient at the low-dose bump. The evaluation was only qualitative under limited volumetric irradiation conditions. Further accumulation of measured data would be needed to quantitatively comprehend what influence the double and triple Gaussian kernel models had on the accuracy of dose calculations.

Development and evaluation of a short-range applicator for treating superficial moving tumors with respiratory-gated spot-scanning proton therapy using real-time image guidance.

Treatment of superficial tumors that move with respiration (e.g. lung tumors) using spot-scanning proton therapy (SSPT) is a high-priority research area. The recently developed real-time image-gated proton beam therapy (RGPT) system has proven to be useful for treating moving tumors deep inside the liver. However, when treating superficial tumors, the proton's range is small and so is the sizes of range straggling, making the Bragg-peaks extremely sharp compared to those located in deep-seated tumors. The extreme sharpness of Bragg-peaks is not always beneficial because it necessitates a large number of energy layers to make a spread-out Bragg-peak, resulting in long treatment times, and is vulnerable to motion-induced dose deterioration. We have investigated a method to treat superficial moving tumors in the lung by the development of an applicator compatible with the RGPT system. A mini-ridge filter (MRF) was developed to broaden the pristine Bragg-peak and, accordingly, decrease the number of required energy layers to obtain homogeneous irradiation. The applicator position was designed so that the fiducial marker's trajectory can be monitored by fluoroscopy during proton beam-delivery. The treatment plans for three lung cancer patients were made using the applicator, and four-dimensional (4D) dose calculations for the RGPT were performed using patient respiratory motion data. The effect of the MRF on the dose distributions and treatment time was evaluated. With the MRF, the number of energy layers was decreased to less than half of that needed without it, whereas the target volume coverage values (D99%, D95%, D50%, D2%) changed by less than 1% of the prescribed dose. Almost no dose distortion was observed after the 4D dose calculation, whereas the treatment time decreased by 26%-37%. Therefore, we conclude that the developed applicator compatible with RGPT is useful to solve the issue in the treatment of superficial moving tumors with SSPT.

A patient-specific aperture system with an energy absorber for spot scanning proton beams: Verification for clinical application.

PURPOSE: In the authors' proton therapy system, the patient-specific aperture can be attached to the nozzle of spot scanning beams to shape an irradiation field and reduce lateral fall-off. The authors herein verified this system for clinical application. METHODS: The authors prepared four types of patient-specific aperture systems equipped with an energy absorber to irradiate shallow regions less than 4 g/cm(2). The aperture was made of 3-cm-thick brass and the maximum water equivalent penetration to be used with this system was estimated to be 15 g/cm(2). The authors measured in-air lateral profiles at the isocenter plane and integral depth doses with the energy absorber. All input data were obtained by the Monte Carlo calculation, and its parameters were tuned to reproduce measurements. The fluence of single spots in water was modeled as a triple Gaussian function and the dose distribution was calculated using a fluence dose model. The authors compared in-air and in-water lateral profiles and depth doses between calculations and measurements for various apertures of square, half, and U-shaped fields. The absolute doses and dose distributions with the aperture were then validated by patient-specific quality assurance. Measured data were obtained by various chambers and a 2D ion chamber detector array. RESULTS: The patient-specific aperture reduced the penumbra from 30% to 70%, for example, from 34.0 to 23.6 mm and 18.8 to 5.6 mm. The calculated field width for square-shaped apertures agreed with measurements within 1 mm. Regarding patient-specific aperture plans, calculated and measured doses agreed within -0.06% ± 0.63% (mean ± SD) and 97.1% points passed the 2%-dose/2 mm-distance criteria of the γ-index on average. CONCLUSIONS: The patient-specific aperture system improved dose distributions, particularly in shallow-region plans.