Ridge Filter Research Articles

SU‐F‐T‐149: Development of the Monte Carlo Simulation Platform Using Geant4 for Designing Heavy Ion Therapy Beam Nozzle

Purpose:The significant issue of particle therapy such as proton and carbon ion was a accurate dose delivery from beam line to patient. For designing the complex delivery system, Monte Carlo simulation can be used for the simulation of various physical interaction in scatters and filters. In this report, we present the development of Monte Carlo simulation platform to help design the prototype of particle therapy nozzle and performed the Monte Carlo simulation using Geant4. Also we show the prototype design of particle therapy beam nozzle for Korea Heavy Ion Medical Accelerator (KHIMA) project in Korea Institute of Radiological and Medical Science(KIRAMS) at Republic of Korea.Methods:We developed a simulation platform for particle therapy beam nozzle using Geant4. In this platform, the prototype nozzle design of Scanning system for carbon was simply designed. For comparison with theoretic beam optics, the beam profile on lateral distribution at isocenter is compared with Mont Carlo simulation result. From the result of this analysis, we can expected the beam spot property of KHIMA system and implement the spot size optimization for our spot scanning system.Results:For characteristics study of scanning system, various combination of the spot size from accerlator with ridge filter and beam monitor was tested as simple design for KHIMA dose delivery system.Conclusion:In this report, we presented the part of simulation platform and the characteristics study. This study is now on‐going in order to develop the simulation platform including the beam nozzle and the dose verification tool with treatment planning system. This will be presented as soon as it is become available.

Detection of bubbles as concentric circular arrangements

A method for the detection of bubble-like transparent objects with multiple interfaces in a liquid is proposed. Depending on the lighting conditions, bubble appearance varies significantly, including contrast reversal and multiple inter-reflections. We formulate the bubble detection problem as the detection of Concentric Circular Arrangements (CCA). The CCAs are recovered in a hypothesize-optimize-verify framework. The hypothesis generation proceeds by sampling from the components of the non-maximum suppressed responses of oriented ridge filters followed by CCA parameter estimation. Parameter optimization is carried out by minimizing a novel cost-function by the simplex method. The proposed method for bubble detection showed good performance in an industrial application requiring estimation of gas volume in pulp suspension, achieving 1.5% mean absolute relative error.

Designing a range modulator wheel to spread-out the Bragg peak for a passive proton therapy facility

In proton beam therapy, a Spread-Out Bragg peak (SOBP) is used to establish a uniform dose distribution in the target volume. In order to create a SOBP, several Bragg peaks of different ranges, corresponding to different entrance energies, with certain intensities (weights) should be combined each other. In a passive beam scattering system, the beam is usually extracted from a cyclotron at a constant energy throughout a treatment. Therefore, a SOBP is produced by a range modulator wheel, which is basically a rotating wheel with steps of variable thicknesses, or by using the ridge filters. In this study, we used the Geant4 toolkit to simulate a typical passive scattering beam line. In particular, the CATANA transport beam line of INFN Laboratori Nazionali del Sud (LNS) in Catania has been reproduced in this work. Some initial properties of the entrance beam have been checked by benchmarking simulations with experimental data. A class dedicated to the simulation of the wheel modulators has been implemented. It has been designed in order to be easily modified for simulating any desired modulator wheel and, hence, any suitable beam modulation. By using some auxiliary range-shifters, a set of pristine Bragg peaks was obtained from the simulations. A mathematical algorithm was developed, using the simulated pristine dose profiles as its input, to calculate the weight of each pristine peak, reproduce the SOBP, and finally generate a flat dose distribution. Therefore, once the designed modulator has been realized, it has been tested at CATANA facility, comparing the experimental data with the simulation results.

Preliminary results, obtained by using a proton beam, for an active scanning system to installed on the KHIMA

The active scanning technique is a pencil beam delivery method in particle therapy. The active scanning beam delivery system consists of a beam scanner, beam monitor, energy modulator, and related programs, such as the irradiation control and planning programs. A proposed prototype active scanning system was designed and installed on MC-50 at the Korea Institute of Radiological and Medical Science (KIRAMS) with a 45-MeV proton beam. The laminated magnetic yoke of the scanning magnet supported fast ramping. The beam intensity and the beam profile monitors were designed for measuring the beam’s properties. Both the range shifter and the ridge filter modulate the incoming beam energy. The LabVIEW®-based beam-irradiation-control program operates the system in a sequential operation manner for use with the MC-50 cyclotron. In addition, an in-housecoded irradiation-planning program generates an optimal irradiation path. A scanning experiment was successfully completed to print the logo of the Korea Heavy Ion Medical Accelerator (KHIMA) on GaF film. Moreover, the beam’s position accuracy was measured as 0.62 mm in the x-direction and as 0.83 mm in the y-direction.

A comparison study of the ridge filter parameter by using FLUKA and GEANT4 simulation codes

We investigated the parameter optimization of the ridge filter’s thickness for carbon-ion therapy by using a Monte Carlo simulation. For this study, a ridge filter was designed for the spreadout Bragg peak (SOBP) by considering the relative biological effectiveness (RBE). The thickness, height, and width of the ridge filter were designed by using the FLUKA and the GEANT4 codes, and we analyzed and compared the results of the physical dose distributions for the FLUKA and the GEANT4 codes. The results showed that the minimum width of the groove for the ridge filter should be at least 0.5 cm for an appropriate biological dose. The SOBP sections were 8 cm, 9 cm, and 10 cm, respectively, when the heights were 3.5 cm, 4.0 cm, and 4.5 cm. The height of the ridge filter was designed to be associated with the SOBP width. Also, the results for the FLUKA and the GEANT4 codes showed that the average value of the difference was 3% and that the maximum error was 5%; however, the trends were similar. Therefore, the height and the width of the groove for the ridge filter are important parameters for deciding the length and the plateau of the SOBP.

The proton therapy nozzles at Samsung Medical Center: A Monte Carlo simulation study using TOPAS

To expedite the commissioning process of the proton therapy system at Samsung Medical Center (SMC), we have developed a Monte Carlo simulation model of the proton therapy nozzles using TOPAS. At SMC proton therapy center, we have two gantry rooms with different types of nozzles; a multi-purpose nozzle and a dedicated scanning nozzle. Each nozzle has been modeled in detail following the geometry information provided by the manufacturer, Sumitomo Heavy Industries, Ltd. For this purpose, novel features of TOPAS, such as the time feature or the ridge filter class, have been used. And the appropriate physics models for proton nozzle simulation were defined. Dosimetric properties, like percent depth dose curve, spread-out Bragg peak (SOBP), beam spot size, have been simulated and verified against measured beam data. Beyond the Monte Carlo nozzle modeling, we have developed an interface between TOPAS and the treatment planning system (TPS), RayStation. An exported RT plan data from the TPS has been interpreted by the interface and then translated into the TOPAS input text. The developed Monte Carlo nozzle model can be used to estimate non-beam performance of the nozzles such as the neutron background. Furthermore, the nozzle model can be used to study mechanical optimization in the design of the nozzle.

Designing a ridge filter based on a mouse foot skin reaction to spread out Bragg-peaks for carbon-ion radiotherapy

Background and purposeCarbon-ion radiotherapy uses spread-out Bragg peaks (SOBP) to produce uniform biological effects within a target volume. The relative biological effectiveness is determined by the in vitro cell kill after a single dose is employed to design the SOBP. A question remains as to whether biological effects for in vivo tissues after fractionated doses are also uniform within the SOBP. Material and methodsMouse foot skin was irradiated with fractionated doses of carbon ions at various linear energy transfer (LET) values. A new ridge filter was designed based on alpha and beta values for each LET to cause moderate skin reaction, and was studied concerning its uniformity. ResultsThe reciprocal total doses of intermediate-LET carbon ions and of reference gamma rays linearly increased with an increase of a dose per fraction in Fe-plots. As the single total dose of higher LET run off linearity, data obtained from 2 to 6 fractions were used to design a new ridge filter. The physical dose distribution of the new ridge filter was almost identical to, and indistinguishable from, the ridge filter designed based on the in vitro cell kill. ConclusionsThe LET dependence of alpha is a principle of the biological factor to be used for designing spread-out Bragg peaks of carbon-ion radiotherapy.

SU‐E‐T‐239: Monte Carlo Modelling of SMC Proton Nozzles Using TOPAS

Purpose:To expedite and cross‐check the commissioning of the proton therapy nozzles at Samsung Medical Center using TOPAS.Methods:We have two different types of nozzles at Samsung Medical Center (SMC), a multi‐purpose nozzle and a pencil beam scanning dedicated nozzle. Both nozzles have been modelled in Monte Carlo simulation by using TOPAS based on the vendor‐provided geometry. The multi‐purpose nozzle is mainly composed of wobbling magnets, scatterers, ridge filters and multi‐leaf collimators (MLC). Including patient specific apertures and compensators, all the parts of the nozzle have been implemented in TOPAS following the geometry information from the vendor. The dedicated scanning nozzle has a simpler structure than the multi‐purpose nozzle with a vacuum pipe at the down stream of the nozzle.A simple water tank volume has been implemented to measure the dosimetric characteristics of proton beams from the nozzles.Results:We have simulated the two proton beam nozzles at SMC. Two different ridge filters have been tested for the spread‐out Bragg peak (SOBP) generation of wobbling mode in the multi‐purpose nozzle. The spot sizes and lateral penumbra in two nozzles have been simulated and analyzed using a double Gaussian model. Using parallel geometry, both the depth dose curve and dose profile have been measured simultaneously.Conclusion:The proton therapy nozzles at SMC have been successfully modelled in Monte Carlo simulation using TOPAS. We will perform a validation with measured base data and then use the MC simulation to interpolate/extrapolate the measured data. We believe it will expedite the commissioning process of the proton therapy nozzles at SMC.

SU-E-T-594: Preliminary Active Scanning Results of KHIMA

Purpose: To verify the design criteria on heavy ion beam irradiation, developing a proto type active scanning system was purposed. The active scanning system consists of scanning magnet, power supplies, beam monitors, energy modulation system, and irradiation control system. Methods: Each components of the active scanning system was designed for carbon beam first. For the fast ramping a laminated yoke was purposed. To measure incoming dose and profile, a plate and strip type of ion chambers were designed. Also, ridge filter and range shifter was manufactured. And, the scanning system was modified to adopt 45 MeV of proton beam because of the absence of carbon ion beam in Korea. The system was installed in a beam line at MC-50, KIRAMS. Also, the irradiation control system and planning software was provided. Results: The scanning experiment was performed by drawing KHIMA logo on GaF film. The logo was scanned by 237 scanning points through time normalized intensity modulation. Also, a grid points scanning was performed to measure the scanning resolution and intensity resolution. Conclusion: A prototype active scanning system was successfully designed and manufactured. Also, an initial experiment to print out a drawing on GaF film through the scanning system was completed. More experiments would be required to specify the system performance.

WE-F-16A-02: Design, Fabrication, and Validation of a 3D-Printed Proton Filter for Range Spreading

Purpose: To design, fabricate and test a 3D-printed filter for proton range spreading in scanned proton beams. The narrow Bragg peak in lower-energy synchrotron-based scanned proton beams can result in longer treatment times for shallow targets due to energy switching time and plan quality degradation due to minimum monitor unit limitations. A filter with variable thicknesses patterned on the same scale as the beam's lateral spot size will widen the Bragg peak. Methods: The filter consists of pyramids dimensioned to have a Gaussian distribution in thickness. The pyramids are 2.5mm wide at the base, 0.6 mm wide at the peak, 5mm tall, and are repeated in a 2.5mm pseudo-hexagonal lattice. Monte Carlo simulations of the filter in a proton beam were run using TOPAS to assess the change in depth profiles and lateral beam profiles. The prototypes were constrained to a 2.5cm diameter disk to allow for micro-CT imaging of promising prototypes. Three different 3D printers were tested. Depth-doses with and without the prototype filter were then measured in a ~70MeV proton beam using a multilayer ion chamber. Results: The simulation results were consistent with design expectations. Prototypes printed on one printer were clearly unacceptable on visual inspection. Prototypes on a second printer looked acceptable, but the micro-CT image showed unacceptable voids within the pyramids. Prototypes from the third printer appeared acceptable visually and on micro-CT imaging. Depth dose scans using the prototype from the third printer were consistent with simulation results. Bragg peak width increased by about 3x. Conclusions: A prototype 3D printer pyramid filter for range spreading was successfully designed, fabricated and tested. The filter has greater design flexibility and lower prototyping and production costs compared to traditional ridge filters. Printer and material selection played a large role in the successful development of the filter.

Ridge filter design for a particle therapy line

The beam irradiation system for particle therapy can use a passive or an active beam irradiation method. In the case of an active beam irradiation, using a ridge filter would be appropriate to generate a spread-out Bragg peak (SOBP) through a large scanning area. For this study, a ridge filter was designed as an energy modulation device for a prototype active scanning system at MC-50 in Korea Institute of Radiological And Medical Science (KIRAMS). The ridge filter was designed to create a 10 mm of SOBP for a 45-MeV proton beam. To reduce the distal penumbra and the initial dose, [DM] determined the weighting factor for Bragg Peak by applying an in-house iteration code and the Minuit Fit package of Root. A single ridge bar shape and its corresponding thickness were obtained through 21 weighting factors. Also, a ridge filter was fabricated to cover a large scanning area (300 × 300 mm2) by Polymethyl Methacrylate (PMMA). The fabricated ridge filter was tested at the prototype active beamline of MC-50. The SOBP and the incident beam distribution were obtained by using HD-810 GaF chromatic film placed at a right triangle to the PMMA block. The depth dose profile for the SOBP can be obtained precisely by using the flat field correction and measuring the 2-dimensional distribution of the incoming beam. After the flat field correction is used, the experimental results show that the SOBP region matches with design requirement well, with 0.62% uniformity.

Updating of HIMAC beam delivery with broad beam method

Carbon ion radiotherapy at HIMAC started in 1994 using two horizontal and two vertical beam ports with broad beam method. The maximum beam energy extracted from accelerators was 400 MeV/n for the horizontal beam port, and 350 MeV/n for the vertical one. In recent years, the scope of diseases that can be treated by the carbon ion radiotherapy has widened and their tumor targets have varied in dimension and location. So, situations of shortage in the beam range in treatment planning have increased.In order to provide sufficient dose to the deeply seated target, we adopted higher energy beam, that is, 430 and 400 MeV/n for the horizontal port and the vertical port, respectively. For the introduction of the new energy beams, we carried out the following.(1) Adjustment of new parameter-sets of the accelerators for the high-energy beams.(2) Replacement of ridge filters with the redesigned ones for the high-energy beams.(3) Updating irradiation condition tables in the irradiation control system and registering new beam data in the treatment planning system, on the base of dose distribution measurements.As a result, the beam range for horizontal port and vertical port was extended ∼30 and 50 mm, respectively. This allows us to treat all patients without ingenuity of patient's posturing and beam weight for each direction.On the other hand, adding new operational energies leads to a decrease in whole throughput, because it takes time to switch among the beam energies. We have at the same time simplified the procedures for the dose calibration and beam adjustment in the switching of energy.The broad beam method has reached maturity as a standard irradiation method of carbon ion radiotherapy and has achieved superior clinical results. We will continue to make upgrades this system with maintenance of its performance and improve the usability of this systems.

Design of a ridge filter for spread-out Bragg-peak production in a pulsed 100-MeV proton beam

We designed a ridge-filter-type modulator suitable for 100-MeV pulsed proton beam modulation. It can be applied to a variety of experiments, such as in medical technology and space technology proton beam modulation from the surface to an 8-cm depth. We also designed a 2-cm spread-out Bragg peak for cancer research using a small experimental animal orthotopic tumor model. The minimum thickness of the range modulator is specified as 2 mm for the mechanical support, and the maximum thickness in the 8-cm and 2-cm SOBP are specified as 40 mm and 12 mm, respectively. The ridge interval and the drift distance are 8 mm and 30 cm, respectively. The design was carried out using the Stopping and Range of Ions in Matter and the Monte Carlo N-particle Extended codes. The results show that the two-dimensional dose distributions of the two range modulators are uniform.

Application of activity pencil beam algorithm using measured distribution data of positron emitter nuclei for therapeutic SOBP proton beam

Recently, much research on imaging the clinical proton-irradiated volume using positron emitter nuclei based on target nuclear fragment reaction has been carried out. The purpose of this study is to develop an activity pencil beam (APB) algorithm for a simulation system for proton-activated positron-emitting imaging in clinical proton therapy using spread-out Bragg peak (SOBP) beams. The target nuclei of activity distribution calculations are (12)C nuclei, (16)O nuclei, and (40)Ca nuclei, which are the main elements in a human body. Depth activity distributions with SOBP beam irradiations were obtained from the material information of ridge filter (RF) and depth activity distributions of compounds of the three target nuclei measured by BOLPs-RGp (beam ON-LINE PET system mounted on a rotating gantry port) with mono-energetic Bragg peak (MONO) beam irradiations. The calculated data of depth activity distributions with SOBP beam irradiations were sorted in terms of kind of nucleus, energy of proton beam, SOBP width, and thickness of fine degrader (FD), which were verified. The calculated depth activity distributions with SOBP beam irradiations were compared with the measured ones. APB kernels were made from the calculated depth activity distributions with SOBP beam irradiations to construct a simulation system using the APB algorithm for SOBP beams. The depth activity distributions were prepared using the material information of RF and the measured depth activity distributions with MONO beam irradiations for clinical therapy using SOBP beams. With the SOBP width widening, the distal fall-offs of depth activity distributions and the difference from the depth dose distributions were large. The shapes of the calculated depth activity distributions nearly agreed with those of the measured ones upon comparison between the two. The APB kernels of SOBP beams were prepared by making use of the data on depth activity distributions with SOBP beam irradiations that were made from the depth activity distributions with MONO beam irradiations and sorted in terms of energy, SOBP width, and thickness of FD. The data on APB kernels of SOBP beams were determined as installment data for the simulation system using the APB algorithm for SOBP beam irradiations. A method of obtaining the depth activity distributions and the APB algorithm for clinical use of SOBP beams have been developed. It is suggested that the simulation system for imaging the clinical irradiated volume with the APB algorithm can be used in clinical proton therapy using SOBP beams by preparing and investigating the data on APB kernels of SOBP beams.

Design of ridge filters for spread-out Bragg peaks with Monte Carlo simulation in carbon ion therapy

Spread-out Bragg peaks made by ridge filters or wheel range modulators are used in charged particle therapy with passive methods to achieve uniform biological responses in irradiated tumors. Following the biological responses needed to design the ridge filters, which were developed at the National Institute of Radiological Sciences in Japan, new ridge filters were designed using recent developments in heavy-ion reactions and dosimetry. The Monte Carlo code of Geant4 was used to calculate the qualities of carbon ion beams in a water phantom. The results obtained from the simulation were corrected so that they agreed with the measurements of depth dose distributions. The calculations of biological responses to fragments other than carbon ions were assumed to be for helium ions. The measured dose distributions with the designed ridge filters were compared to the calculated distributions. A beam modifying system using this adaptable method was successively applied to carbon ion therapy at Gunma University.

Influence of ridge filter material on the beam efficiency and secondary neutron production in a proton therapy system

In this work, the 3D proton dose profile is calculated in a homogenous water phantom using a Monte Carlo application developed with the Geant4 toolkit. The effect of the ridge filter material (for SOBP widths of 6, 9 and 12cm) on the homogeneity of the dose distribution, secondary neutron production and beam efficiency are investigated in a single ring wobbling irradiation system. The energy spectrum of secondary neutrons per primary proton at various locations around the phantom surface is calculated. The simulation revealed that most of the produced neutrons are released at slight angles which enable them to reach the patient and consequently to be hazardous. Also, the homogeneity of the dose distribution at the proximal edge of spread out Bragg peak (SOBP) field is deteriorated due to the scattering of protons in the ridge filter. It is found that for reducing the above mentioned destructive effects, usage of a PMMA ridge filter is better than Al one. For a similar value of 9cm water equivalent thickness, beam widening radius of Al at isocenter is twice of PMMA. Furthermore, for uniform irradiation of the target, the beam efficiency of the system for Al is less than of PMMA and also regarding to the secondary neutron production PMMA is a better choice.

SU-E-T-282: Preliminary Simulation Study for 3 Dimensional Dose Delivery in Carbon Beam Active Scanning System of KHIMA.

KHIMA (Korea Heavy Ion Medical Accelerator) project has a plan to develop and construct a research beam line for carbon beam active scanning system. The carbon beam line consists with scanning magnet, beam-monitoring system, energy modulation system. In this study, the significant components, scanning magnets and ridge filter, were designed for the carbon beam active scanning beam line. The designed scanning magnet and ridge filter were used for 3 dimensional active beam dose delivery simulation by Geant4 Monte Carlo code. The target volume of the active scanning was 10 × 10 × 5 cm2 on the water phantom with 400 MeV/u of carbon beam. The transvers plane on the target was scanned by 3mm of step size. And, the optimized weighting factors of transverse scanning were obtained by MINUIT fitting package of ROOT. An aluminum ridge filter was designed to generate 5 cm of physical SOBP through step shape, which was optimized through in-house iteration method and the MINUIT package.The simulation was performed with Geant4 through applying the transverse scanning with the obtained weighting factor and the designed ridge filter. The uniformity on the transverse plan will be expected below 4% when it considered scattered beam. Also, the uniformity for longitudinal plane will be expected lower then 5%. This preliminary computational study was shown a possibility of using ridge filter for acceptable 3 dimensional uniformity on active beam delivery system in carbon beam therapy line. The optimization process to reach an acceptable uniformity on clinical use should be followed. In addition, it would be used for the design of treatment planning system software for KIHMA project.

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.

SU‐GG‐T‐380: Treatment Time Reduction for Proton Modulated Scanning Beams Using a Ridge Filter

Purpose: Proton modulated beam scanning has the potential to significantly reduce dose to normal tissue, especially proximal to the target. However, the relatively long delivery time creates intrafractional motion uncertainty and limits the number of patients who could potentially benefit. To address this problem, a device that reduces the number of required energy layers by spreading the beam longitudinally has been designed. Materials and Methods: Using Geant4 code developed for scanning beam commissioning, a device was modeled within IBA's universal nozzle. Through Monte Carlo results, the shape, material, and location of the device were optimized for distal falloff preservation, dose uniformity, and minimized lateral spreading. Monte Carlo data was then used to commission a commercial treatment planning system. Results: The final design of the device resembled a bar ridge filter. The design is mostly air to preserve distal falloff. A low density plastic was selected for reduced neutron production and large‐angle scatter compared to higher Z materials. The ridge filter was positioned at 50 cm from the isocenter for clinical feasibility, although lateral penumbra decreases at closer distances. Commissioning the test system showed calculated dose delivered to a sphere (d=1.5cm) with the device remained within 3% when compared to an unobstructed beam while the number of energy layers decreased from 14 to 5. Because time switching between energy layers is a major contribution to the overall time, this reduction could approximately double treatment speed. Conclusion: Through Monte Carlo simulations, a device has been designed that significantly reduces the number of energy levels required for modulated beam scanning. The device could potentially increase treatment speed, which would decrease intrafractional motion margins and expand the number of patients being treated.

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.