Monoenergetic Pencil Beams Research Articles

Improvement of the penumbra for small radiosurgical fields using flattening filter free low megavoltage beams

BackgroundIn stereotactic radiosurgery, sharp beam edges have clear advantages to spare normal tissues. In general, the dose gradient is a limiting factor in minimizing dose to nearby critical structures for clinical cases. Therefore the penumbral width should be diminished. MethodsA Varian Clinac 2100 linear accelerator equipped with in-house designed radiosurgical collimator was modeled using the EGSnrc/BEAMnrc Monte Carlo code and compared with the measurements. The 0.015 cm3 PinPoint chamber was used to measure the 6 MV photon beam characteristics and to validate Monte Carlo calculations. Additional to the standard (STD) linac, a flattening filter free (FFF) linac was simulated. Percent depth doses, beam profiles and output factors were calculated for small field sizes with diameter of 5, 10, 20 and 30mm with DOSXYZnrc. The mean energy and photon fluence at the water surface were calculated with BEAMDP for both FFF linac and STD linacs. ResultsThe penumbra width (80%-20%) was decreased by 0.5, 0.3, 0.2 and 0.2mm for field sizes of 5, 10, 20 and 30mm respectively when removing the FF. The fluence of photons at the surface increased up to 3.6 times and the mean energy decreased by a factor of 0.69 when removing the FF. The penumbra width (80%-20%) decreased by 17% when a 2 MeV monoenergetic electron pencil beam incident on the target is used instead of 6.2 MeV. ConclusionsIt was found that the penumbra of small field sizes is decreased by removing the FF. Likewise using low megavoltage photons reduced the beam penumbra maintaining adequate penetration and skin sparing.

Macro Monte Carlo for dose calculation of proton beams

Although the Monte Carlo (MC) method allows accurate dose calculation for proton radiotherapy, its usage is limited due to long computing time. In order to gain efficiency, a new macro MC (MMC) technique for proton dose calculations has been developed. The basic principle of the MMC transport is a local to global MC approach. The local simulations using GEANT4 consist of mono-energetic proton pencil beams impinging perpendicularly on slabs of different thicknesses and different materials (water, air, lung, adipose, muscle, spongiosa, cortical bone). During the local simulation multiple scattering, ionization as well as elastic and inelastic interactions have been taken into account and the physical characteristics such as lateral displacement, direction distributions and energy loss have been scored for primary and secondary particles. The scored data from appropriate slabs is then used for the stepwise transport of the protons in the MMC simulation while calculating the energy loss along the path between entrance and exit position. Additionally, based on local simulations the radiation transport of neutrons and the generated ions are included into the MMC simulations for the dose calculations. In order to validate the MMC transport, calculated dose distributions using the MMC transport and GEANT4 have been compared for different mono-energetic proton pencil beams impinging on different phantoms including homogeneous and inhomogeneous situations as well as on a patient CT scan. The agreement of calculated integral depth dose curves is better than 1% or 1 mm for all pencil beams and phantoms considered. For the dose profiles the agreement is within 1% or 1 mm in all phantoms for all energies and depths. The comparison of the dose distribution calculated using either GEANT4 or MMC in the patient also shows an agreement of within 1% or 1 mm. The efficiency of MMC is up to 200 times higher than for GEANT4. The very good level of agreement in the dose comparisons demonstrate that the newly developed MMC transport results in very accurate and efficient dose calculations for proton beams.

Synchrotron-based coherent scatter x-ray projection imaging using an array of monoenergetic pencil beams

Traditional projection x-ray imaging utilizes only the information from the primary photons. Low-angle coherent scatter images can be acquired simultaneous to the primary images and provide additional information. In medical applications scatter imaging can improve x-ray contrast or reduce dose using information that is currently discarded in radiological images to augment the transmitted radiation information. Other applications include non-destructive testing and security. A system at the Canadian Light Source synchrotron was configured which utilizes multiple pencil beams (up to five) to create both primary and coherent scatter projection images, simultaneously. The sample was scanned through the beams using an automated step-and-shoot setup. Pixels were acquired in a hexagonal lattice to maximize packing efficiency. The typical pitch was between 1.0 and 1.6 mm. A Maximum Likelihood-Expectation Maximization-based iterative method was used to disentangle the overlapping information from the flat panel digital x-ray detector. The pixel value of the coherent scatter image was generated by integrating the radial profile (scatter intensity versus scattering angle) over an angular range. Different angular ranges maximize the contrast between different materials of interest. A five-beam primary and scatter image set (which had a pixel beam time of 990 ms and total scan time of 56 min) of a porcine phantom is included. For comparison a single-beam coherent scatter image of the same phantom is included. The muscle-fat contrast was 0.10 ± 0.01 and 1.16 ± 0.03 for the five-beam primary and scatter images, respectively. The air kerma was measured free in air using aluminum oxide optically stimulated luminescent dosimeters. The total area-averaged air kerma for the scan was measured to be 7.2 ± 0.4 cGy although due to difficulties in small-beam dosimetry this number could be inaccurate.

Design optimization of a 2D prompt-gamma measurement system for proton dose verification

To verify in-vivo proton dose distribution, a 2-dimensional (2D) prompt-gamma measurement system, comprised of a multi-hole collimation system, a 2D array of CsI(Tl) scintillators, and a position-sensitive photomultiplier tube (PS-PMT), is under development. In the present study, to determine the optimal dimension of the measurement system, we employed a series of Monte Carlo simulations with the MCNPX code. To effectively measure the high-energy prompt gammas while minimizing background gammas, we determined the collimator hole size, collimator thickness, and scintillator length to be 0.4 × 0.4 cm2, 15 cm, and 5 cm, respectively. Thereafter, the performance of the optimized measurement system was estimated for monoenergetic proton pencil beams. The peak locations of the prompt-gamma distributions for 80- and 150-MeV proton beams were clearly distinguished, and the correlation between the beam range and the peak location was confirmed by using the measurement system. For a 200-MeV proton beam, however, the peak location could not be determined due to the dominance of background gammas and the lateral dispersion of the proton beam at the end of the beam range. Based on these simulation results, a prototype 2D prompt-gamma measurement system currently is under construction and, upon completion, will be tested with therapeutic proton beams.

MO-F-BRB-02: Macro Monte Carlo for Proton Dose Calculation in Different Materials.

Although the Monte Carlo (MC) method allows accurate dose calculation its usage is limited due to long computing time. In order to gain efficiency, a new macro MC (MMC) technique for proton dose calculations in homogeneous materials has been developed. The macro MC is based on a local to global MC approach. The local simulations using Geant4 consist of mono-energetic proton pencil beams (10 to 250 MeV) impinging perpendicularly on slabs of different thicknesses (1-10 mm) and different materials (water, lung, muscle, adipose, bone). During the local simulation multiple scattering, ionization, elastic and inelastic interactions have been taken into account and the physical characteristics such as lateral displacement and energy loss have been scored for primary and secondary particles. The scored data from appropriate slabs is then used for the stepwise transport of the protons in the MMC simulation while calculating the energy loss along the path between entrance and exit position. Additionally, ions and neutrons are taken into account for the dose calculation. In order to validate the MMC, calculated dose distributions using the MMC transport and Geant4 have been compared for different mono-energetic proton pencil beams impinging on phantoms with different homogeneous materials. The agreement of calculated integral depth dose curves is better than 1% or 1 mm for all pencil beams and materials considered. For the dose profiles the agreement is within 1% or 1 mm for all energies, depths and materials. The efficiency of MMC is about 200 times higher than for Geant4. The dose comparisons demonstrate that the new MMC results in very accurate and efficient dose calculations for proton beams in homogeneous materials. In future, the MMC method will be extended to inhomogeneous situations in order to allow patient dose calculations for proton beams. This work was supported by Varian Medical Systems.

Gamma electron vertex imaging and application to beam range verification in proton therapy

This paper describes a new gamma-ray imaging method, "gamma electron vertex imaging (GEVI)," which can be used for precise beam range verification in proton therapy. In GEVI imaging, the high-energy gammas from a source or nuclear interactions are first converted, by Compton scattering, to electrons, which subsequently are traced by hodoscopes to determine the location of the gamma source or the vertices of the nuclear interactions. The performance of GEVI imaging for use in-beam range verification was evaluated by Monte Carlo simulations employing geant4 equipped with the QGSP_BIC_HP physics package. Our simulation results show that GEVI imaging can determine the proton beam range very accurately, within 2-3 mm of error, even without any sophisticated analysis. The results were obtained under simplified conditions of monoenergetic pencil beams stopped in a homogeneous phantom and on the basis of the obtained results it is expected to achieve submillimeter accuracy in proton beam range measurement. If future experimental work confirms the simulated results presented in this paper, the use of GEVI imaging is expected to have a great potential in increasing the accuracy of proton beam range verification in a patient, resulting in significant improvement of treatment effectiveness by enabling tight conformation of radiation dose to the tumor volume and patient safety.

Effects of physics change in Monte Carlo code on electron pencil beam dose distributions

Pencil beam algorithms used in computerized electron beam dose planning are usually described using the small angle multiple scattering theory. Alternatively, the pencil beams can be generated by Monte Carlo simulation of electron transport. In a previous work, the 4th version of the Electron Gamma Shower (EGS) Monte Carlo code was used to obtain dose distributions from monoenergetic electron pencil beam, with incident energy between 1 MeV and 50 MeV, interacting at the surface of a large cylindrical homogeneous water phantom. In 2000, a new version of this Monte Carlo code has been made available by the National Research Council of Canada (NRC), which includes various improvements in its electron-transport algorithms. In the present work, we were interested to see if the new physics in this version produces pencil beam dose distributions very different from those calculated with oldest one. The purpose of this study is to quantify as well as to understand these differences. We have compared a series of pencil beam dose distributions scored in cylindrical geometry, for electron energies between 1 MeV and 50 MeV calculated with two versions of the Electron Gamma Shower Monte Carlo Code. Data calculated and compared include isodose distributions, radial dose distributions and fractions of energy deposition. Our results for radial dose distributions show agreement within 10% between doses calculated by the two codes for voxels closer to the pencil beam central axis, while the differences are up to 30% for longer distances. For fractions of energy deposition, the results of the EGS4 are in good agreement (within 2%) with those calculated by EGSnrc at shallow depths for all energies, whereas a slightly worse agreement (15%) is observed at deeper distances. These differences may be mainly attributed to the different multiple scattering for electron transport adopted in these two codes and the inclusion of spin effect, which produces an increase of the effective range of electrons.

SU‐E‐T‐700: PMMC ‐ a High‐Performance Monte Carlo Code for Proton Beam Dose Calculation

Purpose: The proton macro Monte Carlo (PMMC) method uses a fast macro Monte Carlo radiation transport algorithm for high‐energy proton transport through an absorbing medium. Methods: PMMC uses results derived from traditional Monte Carlo simulations of proton transport through macroscopic cylinders of varying length, radii and material composition. These traditional Monte Carlo simulations are done for many incident proton energies and the results are used to transport protons through an absorber geometry in a step‐by‐step manner. The absorber geometry consists of a three‐dimensional (3D) density matrix that can represent objects like a water phantom or computed tomography data. The source is specified by the user in terms of gantry angle and beam characteristics like position, energy and size. During proton transport, energy lost by the protons during each step is scored in a 3D dose grid. The creation of secondary neutrons is tracked as well to allow for estimation of the neutron dose. Results: The algorithm, which was written in C++, is currently capable of simulating 1 million protons per minute. The accuracy of the PMMC simulations was assessed by comparing the results to simulations done with the same source parameters in MCNPX. The simulations consisted of monoenergetic pencil beams and Gaussian‐shaped beams directed onto a water phantom. In general, PMMC and MCNPX are in good agreement in the high‐energy proton region before the Bragg peak, differing by less than 3%. PMMC performs worse at the depth of maximum dose, differing by as much as 10%. Conclusions: Forthcoming modifications to PMMC will address the discrepancies in the Bragg peak region and further modifications are underway to allow PMMC to be used with absorbers that are heterogeneous in density and material composition.

Comparison of GATE/GEANT4 with EGSnrc and MCNP for electron dose calculations at energies between 15 keV and 20 MeV

The GATE Monte Carlo simulation platform based on the GEANT4 toolkit has come into widespread use for simulating positron emission tomography (PET) and single photon emission computed tomography (SPECT) imaging devices. Here, we explore its use for calculating electron dose distributions in water. Mono-energetic electron dose point kernels and pencil beam kernels in water are calculated for different energies between 15 keV and 20 MeV by means of GATE 6.0, which makes use of the GEANT4 version 9.2 Standard Electromagnetic Physics Package. The results are compared to the well-validated codes EGSnrc and MCNP4C. It is shown that recent improvements made to the GEANT4/GATE software result in significantly better agreement with the other codes. We furthermore illustrate several issues of general interest to GATE and GEANT4 users who wish to perform accurate simulations involving electrons. Provided that the electron step size is sufficiently restricted, GATE 6.0 and EGSnrc dose point kernels are shown to agree to within less than 3% of the maximum dose between 50 keV and 4 MeV, while pencil beam kernels are found to agree to within less than 4% of the maximum dose between 15 keV and 20 MeV.

A Monte Carlo Comparison of Three Different Media for Contrast Enhanced Radiotherapy of the Prostate

Contrast-enhanced radiotherapy makes use of a kilovoltage X-ray beam, either from a diagnostic X-ray tube or modified megavoltage linear accelerator, in conjunction with a high-Z contrast medium deposited into the target volume to enhance the absorption of radiation. In this work, using the Monte Carlo code PENELOPE and the voxelized Zubal phantom to model a prostate radiotherapy treatment, a comparison between the physical absorbed dose distributions rendered by three different enhancing agents namely bismuth, gadolinium, and iodine is performed. It is assumed that there exists a concentration of 10 mg of enhancing agent per 1 g of tissue in the target volume while in the background a concentration of 1.5 mg per 1 g of tissue is present. The X-ray beam energy spectrum was obtained by means of Monte Carlo simulation of a tungsten target upon which a 220 keV mono-energetic electron pencil beam is made to impinge, and the resultant photon beam is heavily filtrated by 0.2 cm of copper. The treatment delivery is simulated as a 3608 arc collimated to conform to the target from every direction. Cumulative dose-volume histograms and isodose curves are presented for the target as well as five organs-at-risk, namely rectal wall, bladder, femoral heads, skin, and bone marrow. It is shown that under these conditions clinically acceptable treatment plans are obtained for all three contrast agents. A 72 Gy dose to 100% of the target volume results in maximum absorbed doses to the above mentioned organs-at-risk of 65, 56, 44, 32 and 65 Gy respectively when bismuth is used as the contrast agent, but the results obtained with gadolinium follow closely.

Maximum proton kinetic energy and patient‐generated neutron fluence considerations in proton beam arc delivery radiation therapy

Several compact proton accelerator systems for use in proton therapy have recently been proposed. Of paramount importance to the development of such an accelerator system is the maximum kinetic energy of protons, immediately prior to entry into the patient, that must be reached by the treatment system. The commonly used value for the maximum kinetic energy required for a medical proton accelerator is 250 MeV, but it has not been demonstrated that this energy is indeed necessary to treat all or most patients eligible for proton therapy. This article quantifies the maximum kinetic energy of protons, immediately prior to entry into the patient, necessary to treat a given percentage of patients with rotational proton therapy, and examines the impact of this energy threshold on the cost and feasibility of a compact, gantry-mounted proton accelerator treatment system. One hundred randomized treatment plans from patients treated with IMRT were analyzed. The maximum radiological pathlength from the surface of the patient to the distal edge of the treatment volume was obtained for 180 degrees continuous arc proton therapy and for 180 degrees split arc proton therapy (two 90 degrees arcs) using CT# profiles from the Pinnacle (Philips Medical Systems, Madison, WI) treatment planning system. In each case, the maximum kinetic energy of protons, immediately prior to entry into the patient, that would be necessary to treat the patient was calculated using proton range tables for various media. In addition, Monte Carlo simulations were performed to quantify neutron production in a water phantom representing a patient as a function of the maximum proton kinetic energy achievable by a proton treatment system. Protons with a kinetic energy of 240 MeV, immediately prior to entry into the patient, were needed to treat 100% of patients in this study. However, it was shown that 90% of patients could be treated at 198 MeV, and 95% of patients could be treated at 207 MeV. Decreasing the proton kinetic energy from 250 to 200 MeV decreases the total neutron energy fluence produced by stopping a monoenergetic pencil beam in a water phantom by a factor of 2.3. It is possible to significantly lower the requirements on the maximum kinetic energy of a compact proton accelerator if the ability to treat a small percentage of patients with rotational therapy is sacrificed. This decrease in maximum kinetic energy, along with the corresponding decrease in neutron production, could lower the cost and ease the engineering constraints on a compact proton accelerator treatment facility.

Effects of energy spectrum on dose distribution calculations for high energy electron beams

In an early work we have demonstrated the possibility of using Monte Carlo generated pencil beams for 3D electron beam dose calculations. However, in this model the electron beam was considered as monoenergetic and the effects of the energy spectrum were taken into account by correction factors, derived from measuring central-axis depth dose curves. In the present model, the electron beam is considered as polyenergetic and the pencil beam distribution of a clinical electron beam, of a given nominal energy, is represented as a linear combination of Monte Carlo monoenergetic pencil beams. The coefficients of the linear combination describe the energy spectrum of the clinical electron beam, and are chosen to provide the best-fit between the calculated and measured central axis depth dose, in water. The energy spectrum is determined by the constrained least square method. The angular distribution of the clinical electron beam is determined by in-air penumbra measurements. The predictions of this algorithm agree very well with the measurements in the region near the surface, and the discrepancies between the measured and calculated dose distributions, behind 3D heterogeneities, are reduced to less than 10%. We have demonstrated a new algorithm for 3D electron beam dose calculations, which takes into account the energy spectra. Results indicate that the use of this algorithm leads to a better modeling of dose distributions downstream, from complex heterogeneities.

SU-FF-T-331: Optimization of the Beam Width in a Universal Proton Therapy Nozzle

Introduction: In Intensity Modulated Proton Therapy (IMPT), the position and quantity of the dose deposited by monoenergetic pencil beams are simultaneously controlled. We are developing the ability to treat patients with IMPT and double scattering in a single nozzle mounted on a gantry, which is called a universal proton therapy nozzle. The beam width in IMPT, which is useful in achieving dose conformality, is dependent upon the materials in the nozzle. Optimization of these materials is necessary to allow both IMPT and scattering techniques. Methods: A GEANT Monte Carlo simulation was used to determine the pencil beam width obtainable for different materials in the beam path. Consideration was given to beam instrumentation, vacuum windows, the distribution of air, vacuum or helium in the nozzle, and the beam optics. The results of these simulations were compared to calculations based on the multiple-scattering theory of Moliere. Results: The advantages and disadvantages of various configurations will be discussed together with estimates of the beam width. Furthermore, some of these estimates were compared with measurements made with some of the components in the universal nozzle. Monte Carlo simulations should provide a good prediction of the expected beam width, however, the initial beam conditions are a little harder to establish in order to get full agreement. Conclusions: The optimum beam width in IMPT should, on the one hand be as small as possible to reduce the dose delivered to healthy tissue, or on the other hand be large enough to allow a practical beam delivery capability and time frame while maintaining high standards of patient safety. Modifications designed to improve the beam width must also have acceptable impact on double-scattering treatments [See abstract 7586]. A system that obtains a reasonable optimization of both solutions has been developed.

SU-FF-T-137: Design of a Vacuum Chamber for a Universal Proton Therapy Nozzle

Introduction: In Intensity Modulated Proton Therapy (IMPT), the position and quantity of the dose deposited by monoenergetic pencil beams are simultaneously controlled, which can offer a more tumor‐conformal dose compared to IMRT and 3D conformal proton therapies. We are developing the ability to treat patients with IMPT and double scattering in a single nozzle mounted on a gantry, which is called a universal proton therapy nozzle. A vacuum chamber is one useful method to reduce the beam width in IMPT, however, interactions of the protons with the chamber walls could reduce the energy of the protons and change the lateral profile of the beam in double scattering. Methods: A GEANT Monte Carlo simulation was used to compare large‐diameter double‐scattering fields. Simulated depth‐dose distributions and profiles of the dose deposited in the lateral directions in a water phantom were produced to compare configurations with the vacuum chamber to one without a vacuum chamber. Regions of the vacuum chamber that affected the properties of the beam were identified and optimized. Experimental data were obtained using a proton beam with a prototype vacuum chamber installed in the nozzle. Results: Without special care, a vacuum chamber designed only to fit the geometry constraints limited the lateral beam profile and adversely affected the longitudinal dose distribution. A properly designed fiberglass‐walled vacuum chamber can be constructed that will have negligible impact on the longitudinal dose distribution in double scattering. The flatness of the dose deposited in the lateral direction will be reduced slightly in the direction of the axis of rotation of the gantry. Conclusions: It is possible to design an optimized fiberglass‐walled vacuum chamber that will be suitable for installation in a universal nozzle. Ongoing studies include simulating a helium‐filled chamber as an alternative to a vacuum chamber.

Investigating the effect of K-characteristic radiation on the performance of nuclear medicine scintillators by Monte Carlo methods

The aim of this study was to evaluate the effect of K-characteristic radiation on the performance of scintillator crystals incorporated in nuclear medicine detectors (LSO, BGO, GSO). K-characteristic radiation is produced within materials of at least one high atomic number element (e.g. Lu, Gd, Bi). This radiation may either be reabsorbed or it may escape the scintillator. In both cases the light emission efficiency of the scintillator may be affected resulting in either spatial or energy resolution degradation. A computational program, based on Monte Carlo methods, was developed in order to simulate the transport of K-characteristic radiation within the most commonly used scintillator materials. Crystal thickness was allowed to vary from 0.5 up to 15 mm. A monoenergetic pencil beam, with energy varying from 0.60 to 0.511 MeV was considered to fall on the center of the crystal surface. The dominant γ-ray interactions (elastic and inelastic scattering and photoelectric absorption) were taken into account in the simulation. Results showed that, depending on crystal thickness, incident photon energy and scintillator's intrinsic properties (L or K-fluorescence yield, effective atomic number and density), the scintillator's emission efficiency may be significantly reduced and affect spatial or energy resolution.

A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation

We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near monoenergetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the orientation of the beam with respect to the dose grid was also investigated. The maximum acceptable dose grid size depends on the gradient of dose profile and in turn the range of proton beam. In the case that only the phantom scattering was considered and that the beam was aligned with the dose grid, grid sizes from 0.4 to 6.8 mm were required for proton beams with ranges from 2 to 30 cm for 2% error limit at the Bragg peak point. A near linear relation between the maximum acceptable grid size and beam range was observed. For this analysis model, the resolution requirement was not significantly related to the orientation of the beam with respect to the grid.

SU-FF-T-280: Verification of Monte Carlo Simulations of Proton Dose Distributions in Biological Media

Purpose: Aim of this work is to suggest a method for verifying the ability of Monte Carlo codes at simulating proton transport through biological tissues defined by CT Hounsfield units. Method and Materials: The method is based on the assumption that the main physical processes leading to protonenergy deposition are Coulomb interactions. It consists first in simulating the two‐ or three‐dimensional dose distributions from a monoenergetic proton pencil beam impinging in various homogeneous phantoms filled with water and with biological tissue. The indicators for the Coulomb interactions are extracted from the dose distributions: these are the protonstopping powers relative to water and the lateral scaling factors, which characterize respectively the longitudinal loss of energy and the scattering properties in the material traversed. Third, these values extracted from the Monte Carlo simulations are compared to the expected analytical values of the stopping powers and of the lateral scaling factors for various protonenergies in water and in several biological materials. Results: This method was applied to two versions of the Monte Carlo code GEANT4. Results show that while the values for the stopping powers extracted from the simulations are in good agreement with the analytical or tabulated values, non negligible discrepancies in the simulation of proton scattering exist between the former version of GEANT4 and the analytical predictions: in the former version about 16.0% deviations were found in the simulation of the proton beam broadening in water and in material. The best agreement with the analytical values for the Coulomb indicators (less than 3.0%) was provided by the current latest version GEANT4.7.0 Conclusion: The evaluation of GEANT4 using this validation method for Coulomb interactions shows that GEANT4 can be used as a benchmarking tool for proton dose calculations on CT data. Conflict of Interest: Research supported by Siemens OCS.

The energy-dependent electron loss model for pencil beam dosekernels

The `monoenergetic' electron loss model was derived in a previous work toaccount for pathlength straggling in the Fermi-Eyges pencil beam problem.In this paper, we extend this model to account for energy-loss stragglingand secondary knock-on electron transport in order to adequately predict adepth dose curve. To model energy-loss straggling, we use a weightedsuperposition of a discrete number of monoenergetic pencil beams withdifferent initial energies where electrons travel along the depth-energycharacteristics in the continuous slowing down approximation (CSDA). Theenergy straggling spectrum at depth determines the weighting assigned toeach monoenergetic pencil beam. Supplemented by a simple transport modelfor the secondary knock-on electrons, the `energy-dependent' electron lossmodel predicts both lateral and depth dose distributions from the electronpencil beams in good agreement with Monte Carlo calculations andmeasurements. The calculation of dose distribution from a pencil beam takes0.2 s on a Pentium III 500 MHz computer. Being computationally fast, the`energy-dependent' electron loss model can be used for the calculation of3D energy deposition kernels in dose optimization schemes without usingprecalculated or measured data.

The transport theory of beams

In this paper we review analytic solution methods for the problem of a monoenergetic pencil beam of radiation impinging perpendicularly upon a thin source-free slab, infinite in the transverse directions. If the scattering is highly peaked in the forward direction, and if the slab is sufficiently thin, this beam will remain nearly collimated as it passes through the slab. Making the continuous slowing down and straightahead approximations, the energy variable can be analytically eliminated from the problem. If a simplified Fokker-Planck approximation in angle is introduced into the resulting monoenergetic transport equation, a very simple analytic solution is possible. This result for the scalar flux is known as the Fermi-Eyges solution, and is Gaussian in radius. For scattering phase functions which do not admit a Fokker-Planck representation in angle, a very recent formalism is discussed for addressing this monoenergetic problem. A classic example is the widely used Henyey-Greenstein scattering phase function, and in this case an analytic solution, algebraic in radius, is obtained for the scalar flux. For screened Rutherford scattering, this formalism leads to a quadrature result for the scalar flux. An asymptotic numerical evaluation of this result shows good agreement with benchmark Monte Carlo calculations.

Secondary electron fluence perturbation by high- Z interfaces in clinical proton beams: a Monte Carlo study

Fluence perturbation of secondary electrons from clinical proton beams (50-250 MeV) by thin high- Z planar interfaces was studied with Monte Carlo simulations. Starting from monoenergetic proton pencil beams, proton depth doses and proton fluence spectra were calculated, both in homogeneous water and near thin high- Z interfaces by using the proton transport Monte Carlo code PTRAN. This code was modified extensively to enable modelling of proton transport in non-homogeneous geometries. From the proton fluence spectra in water and in the interface materials, electron generation spectra were calculated analytically and were then used as input for an electron transport calculation with the Monte Carlo code EGS4/PRESTAII to obtain electron doses and electron fluence spectra. The interface materials used in the study were graphite, Al, Ti, Cu, Sn and Au. We found significant electron fluence perturbations on both sides of the planar interfaces, resulting in an electron dose increase upstream and a decrease downstream from the interfaces, with the magnitude of the effect depending strongly on the atomic number of the interface. For the most extreme case studied, 250 MeV protons and a gold interface, we obtained an electron dose increase of 41% upstream of the interface and a decrease of 15% downstream with both perturbations having a spatial extent of about 700 m. The total dose perturbation due to this effect amounts to a 5% increase upstream and a 2% decrease downstream. A detailed analysis of dose and fluence perturbation is presented for a wide range of materials and proton energies.