Monte Carlo and analytical calculation of proton pencil beams for computerized treatment plan optimization

Proton pencil beams in water, in a format suitable for treatment planning algorithms and covering the radiotherapy energy range (50-250 MeV), have been calculated using a modified version of the Monte Carlo code PTRAN. A simple analytical model has also been developed for calculating proton broad-beam dose distributions which is in excellent agreement with the Monte Carlo calculations. Radial dose distributions are also calculated analytically and narrow proton pencil-beam dose distributions derived. The physical approximations in the Monte Carlo code and in the analytical model together with their limitations are discussed. Examples showing the use of the calculated set of proton pencil beams as input to an existing photon treatment planning algorithm based on biological optimization are given for fully 3D scanned proton pencil beams; these include intensity modulated beams with range shift and scanning in the transversal plane.     

Negative regulation of the anti-human immunodeficiency virus and chemotactic activity of human stromal cell-derived factor 1alpha by CD26/dipeptidyl peptidase IV

A method to characterize the energy distribution in the whole photon field is valuable when designing an accelerator for choosing target and flattening filter or scan pattern. Another field of application is beam characterization for treatment planning systems or other dosimetric purposes. This work is focused on the energy distribution in different 50 MV bremsstrahlung beams with different scanning of electrons on three different targets. Fluence differential in energy and angle at the exit of each target has been determined by Monte Carlo calculations for a narrow beam. Data for broad beams were obtained by convolution of the narrow beams with different scan patterns. Photon energy fluence differential in energy at SSD 100 were thus found to be rather different for the targets studied. The results are presented as mean energy profiles and narrow beam half-value layer (HVL) in water. Two different experimental setups were used to measure HVL at the central axis and at off-axis positions. The two methods gave results which differ by 5%-6% and the calculated data where within these experimental results. In conclusion, the presented method for characterization of the photon field energy distribution is well within the experimental results and can thus be used to improve accelerator design or dosimetric calculations, e.g., for treatment planning.     

Two replica blotting methods for fast immunological analysis of common proteins in two-dimensional electrophoresis

Knowledge of the photon spectrum of a radiotherapy beam is often needed for three-dimensional (3-D) dose calculations using Monte Carlo methods and/or algorithms employing energy deposition kernels. Direct measurement of the x-ray energy fluence spectrum is not feasible for the high-energy photon beams used clinically. In this paper, the spectrum is extracted from basic beam data that are readily obtained for a clinical beam. We describe the photon spectrum using just two parameters. One parameter, which determines the high-energy part of the spectrum, is obtained using the measured dose in the buildup region for a small field, where electron contamination of the beam can be neglected. The other parameter is extracted from the photon beam attenuation in water. The results compare favorably to spectra generated from Monte Carlo simulations.     

Monte Carlo study of fluence perturbation effects on cavity dose response in clinical proton beams

Current protocols for clinical proton beam dosimetry have not implemented any chamber-dependent correction factors for absorbed dose determination. The present work initiates a Monte Carlo study of these factors with emphasis on proton fluence perturbation effects and preliminary calculations of perturbation effects from secondary electrons. The proton Monte Carlo code PTRAN was modified to allow simulation of proton transport in non-homogeneous geometries of both unmodulated and modulated beams. The dose to water derived from the dose calculated in an air cavity agrees well with results from analytical calculations assuming a displacement of the point of measurement. For unmodulated beams small differences, limited to 0.8%, could be partially attributed to proton multiple scattering. Effects of replacing water around the cavity with wall material are explained by the introduction of a water-equivalent wall thickness. For modulated beams no significant perturbation effects arise. Secondary electron spectra are calculated analytically. Preliminary electron transport calculations with EGS4 show that wall perturbations of the order of 1% could result. Perturbation effects caused by the energy transport of secondary particles from inelastic nuclear interactions have not been studied here. Inclusion of inelastic nuclear energy transfers in the cavity dose, assuming total local absorption, indicate that separate scaling of this contribution with the ratio of total inelastic nuclear cross sections could be important.     

On compensator design for photon beam intensity-modulated conformal therapy

Recently the compensator has been shown to be an in expensive and reliable dose delivery device for photon beam intensity-modulated radiation therapy (IMRT). The goal of IMRT compensator design is to produce an optimized primary fluence profile at the patient's surface obtained from the optimization procedure. In this paper some of the problems associated with IMRT compensator design, specifically the beam perturbations caused by the compensator, are discussed. A simple formula is derived to calculate the optimal compensator thickness profile from an optimized primary fluence profile. The change of characteristics of a 6 MV beam caused by the introduction of cerrobend compensators in the beam is investigated using OMEGA Monte Carlo codes. It is found that the compensator significantly changes the energy spectrum and the mean energy of the primary photons at the patient's surface. However, beam hardening does not have as significant an effect on the percent depth dose as it does on the energy spectrum. We conclude that in most situations the beam hardening effect can be ignored during compensator design and dose calculation. The influence of the compensator on the contaminant electron buildup dose is found to be small and independent of the compensator thickness of interest. Therefore, it can be ignored in the compensator design and included as a correction into the final dose distribution. The scattered photons from the compensator are found to have no effect on the surface dose. These photons produce a uniform low fluence distribution at the patient's surface, which is independent of compensator shape. This is also true for very large fields and extremely asymmetric and nonuniform compensator thickness profiles. Compared to the primary photons, the scattered photons have much larger angular spread and similar energy spectrum at the patient's surface. These characteristics allow the compensator thickness profile and the dose distribution to be calculated from the optimized fluence profile of primary photons, without considering the scattered photons.     

The FE-lspd model for electron beam dosimetry

The FE-lspd model is a two-component electron beam model that distinguishes between electrons that can be described by small-angle transport theory and electrons that are too widely scattered for small-angle transport theory to be applicable. The two components are called the primary beam and the laterally scattered primary distribution (lspd). The primary beam component incorporates a simple version of the Fermi-Eyges model and dominates dose calculations at therapeutic depths. The lspd component corrects erros in the lateral spreading of the primary beam component, thereby improving the accuracy by which the FE-lspd model calculates dose distribution in blocked fields. Comparisons were made between dose profiles and central-axis depth dose distributions in small fields calculated by the FE-lspd, Fermi-Eyges and EGS4 Monte Carlo models for a 10 MeV beam in a homogeneous water phantom. The maximum difference between the dose calculated using the FE-lspd model and EGS4 Monte Carlo is about 6% at a field diameter of about 1 cm, and less than 2% for field sizes greater than 3 cm diameter. The maximum difference between the Fermi-Eyges and Monte Carlo calculations is about 18% at a field diameter of about 2.5 cm. A comparison was made with the central-axis depth dose distribution measured in water for a 3 cm diameter field in a 10 MeV clinical electron beam. The errors in the dose distribution were found to be less than 2% using the FE-lspd model but almost 18% using the Fermi-Eyges model. A comparison was also made with pencil beam profiles calculated using the second-order Fermi-Eyges transport model.     

Monte Carlo simulations of the differential beam hardening effect of a flattening filter on a therapeutic x-ray beam

A quantitative study of the differential beam hardening effect of the flattening filter on the 6-MV beam of Clinac 2100C has been conducted with Monte Carlo simulations using EGS4 code. The fluence-weighted photon energy of the unfiltered beam decreases from 1.35 MeV at central axis (CAX) to 1.22 MeV at an off-axis distance (OAD) of 20.0 cm. Compared to the unfiltered beam, the fluence-weighted photon energy of the filtered beam increases to 1.93 MeV at CAX and to 1.36 MeV at an OAD f 20.0 cm, respectively. The beam hardening effect was found to be 2.1 times higher at CAX than at an OAD of 20.0 cm. With the differential filtration of the flattening filter, the photon energy fluence reduced to 44% and 78% at CAX and an OAD of 20.0 cm respectively, resulting in the energy fluence of the filtered beam being flat from CAX to an OAD of 20.0 cm. The differential transmission ratios between the high energy and low energy photons decrease as the OAD increases. The percentage depth doses (PDDs) at field size of 10.0 cm x 10.0 cm for both the filtered and unfiltered 6-MV beams at CAX and at an OAD of 15.0 cm were calculated with a Monte Carlo technique based on the simulated spectra and fluence. The calculated PDDs were found to be consistent with the measured data for the filtered beam at CAX and an OAD of 15.0 cm. The beam quality (BQ) of the filtered beam at CAX is also higher than that of the same beam at an OAD of 15.0 cm. All the above results quantitatively demonstrate the differential beam hardening effects of a flattening filter on a therapeutic x-ray beam.     

A proton dose calculation algorithm for conformal therapy simulations based on Molière's theory of lateral deflections

An algorithm is developed for computing proton dose distributions in the therapeutic energy range (100-250 MeV). The goal is to provide accurate pencil beam dose distributions for two-dimensional or three-dimensional simulations of possible intensity-modulated proton therapy delivery schemes. The algorithm is based on Molière's theory of lateral deflections, which accurately describes the distribution of lateral deflections suffered by incident charged particles. The theory is applied to nonuniform targets through the usual pencil beam approximation which assumes that all protons from a given pencil beam pass through the same material at each depth. Fluence-to-dose conversion is made via Monte Carlo calculated broad-field central-axis depth-dose curves, which accounts for attenuation due to nuclear collisions and range straggling. Calculation speed is enhanced by using a best-fit Gaussian approximation of the radial distribution function at depth. Representative pencil beam and spread-out Bragg-peak computations are presented at 250 MeV and 160 MeV in water. Computed lateral full-widths-at-half-maximum's in water, at the Bragg peak, agree with the expected theoretical lateral values to within 1% at 160 MeV and to within 3% at 250 MeV. This algorithm differs from convolution methods in that the effect of the depth of any inhomogeneities in density or atomic composition are accounted for in a rigorous fashion. The algorithm differs from Fermi-Eyges based methods by accounting in a rigorous way for the effect of nonsmall-angle scattering and screening due to atomic electrons. The computational burden is only slightly greater than that expected using the less-rigorous Fermi-Eyges theory.     

Intensity modulation with electrons: calculations, measurements and clinical applications

Intensity modulation of electron beams is one step towards truly conformal therapy. This can be realized with the MM50 racetrack microtron that utilizes a scanning beam technique. By adjusting the scan pattern it is possible to obtain arbitrary fluence distributions. Since the monitor chambers in the treatment head are segmented in both x- and y-directions it is possible to verify the fluence distribution to the patient at any time during the treatment. Intensity modulated electron beams have been measured with film and a plane parallel chamber and compared with calculations. The calculations were based on a pencil beam method. An intensity distribution at the multileaf collimator (MLC) level was calculated by superposition of measured pencil beams over scan patterns. By convolving this distribution with a Gaussian pencil beam, which has propagated from the MLC to the isocentre, a fluence distribution at isocentre level was obtained. The agreement between calculations and measurements was within 2% in dose or 1 mm in distance in the penumbra zones. A standard set of intensity modulated electron beams has been developed. These beams have been implemented in a treatment planning system and are used for manual optimization. A clinical example (prostate) of such an application is presented and compared with a standard irradiation technique.     

Ex vivo light dosimetry and Monte Carlo simulations for endobronchial photodynamic therapy

The light distribution during photodynamic therapy of the bronchial tree has been estimated by measuring the fluence rate in ex vivo experiments on dissected pig bronchi. The trachea was illuminated (630 nm) with a cylindrical diffuser and the fluence rate was measured with a fibre optic isotropic probe. The experiment with the diffuser on the central axis was also simulated with Monte Carlo techniques using the optical properties that were determined with a double-integrating-sphere set-up. The results from ex vivo experiments and the Monte Carlo simulations were found to agree within the error of measurement (15%), indicating that the Monte Carlo technique can be used to estimate the light distribution for varying geometries and optical properties. The results showed that the light fluence rate in the mucosa of the tracheal tract may increase by a factor of six compared to the fluence rate in air (in the absence of tissue). This is due to the scattering properties of the tissue and the multiple reflections within the cavity. Further ex vivo experiments showed that the positioning of the diffuser is critical for the fluence rate in the lesion to be treated. When the position of the diffuser was changed from the central axis to near the lesion, the fluence rate in the mucosa increased significantly by several orders of magnitude as compared to the initial (central) illumination. The inter- and intraspecimen variations in this increase were large (+/- 35%) because of variations in optical and geometrical properties and light source positioning, respectively. These variations might cause under- or overdosage resulting in either insufficient tumour necrosis or excessive normal tissue damage.     

Measured molecular coherent scattering form factors of animal tissues, plastics and human breast tissue

Photon scattering angular distributions from various animal tissues were measured at two energies of a monochromatic synchrotron x-ray beam. Two plastics and human breast tissue were also measured. From these two measurements, the molecular coherent scattering form factor of each material was extracted. A new data analysis technique that uses Monte Carlo based corrections for air scattering, incoherent scattering and multiple scattering was used. The form factors of the 16 materials are presented in tabular form, suitable for use in computer calculations.     

Monte Carlo calculation of dose enhancement by neutron capture of 10B in fast neutron therapy

Since 1978 the Essen Medical Cyclotron Facility has been used for fast neutron therapy. The treatment of deep-seated tumours by d(14) + Be neutron beam therapy (mean energy = 5.8 MeV) is still limited because of the steep decrease in depth-dose distribution. The interactions of fast neutrons in tissue leads to a thermal neutron distribution. These partially thermalized neutrons can be used to produce neutron capture reactions with 10B. Thus incorporation of 10B in tumours treated with fast neutrons will increase the relative local tumour dose due to the reaction 10B (n, alpha) 7Li. The magnitude of dose enhancement by 10B depends on the distribution of the thermal neutron fluence, 10B concentration, field size of the neutron beam, beam energy and the specific phantom geometry. The slowing down of the fast neutrons, resulting in a thermal neutron distribution in a phantom, has been computed using a Monte Carlo model. This model, which includes a deep-seated tumour, was experimentally verified by measurements of the thermal neutron fluence rate in a phantom using neutron activation of gold foil. When non-boronated water phantoms were irradiated with a total dose of 1 Gy at a depth of 6 cm, the thermal fluencies at this depth were found to be 2 x 10(10) cm-2. The absorbed dose in a tumour with 100 ppm 10B, at the same depth, was enhanced by 15%.     

Numerical calculation of energy deposition by high-energy electron beams: III-B. Improvements to the 6D phase space evolution model

The phase space evolution model of Huizenga and Storchi, Morawska-Kaczyńska and Huizenga and Janssen et al has been modified to (i) allow application on currently available computer equipment with limited memory (128 Megabytes) and (ii) allow 3D dose calculations based on 3D computer tomographic patient data. This is a further development aimed at the use of the phase space evolution model in radiotherapy electrons beam treatment planning. The first modification regards the application of depth evolution of the phase space state combined with an alternative method to transport back-scattered electrons. This depth evolution method requires of the order of 15 times less computer memory than the energy evolution method. Results of previous and new electron transport methods are compared and show that the new electron transport method for back-scattered electrons hardly affects the accuracy of the calculated dose distributions. The second modification regards the simulation of electron transport through tissues with varying densities by applying distributed electron transport through similarly composed media with a limited number of fixed densities. Results of non-distributed and distributed electron transport are compared and show that the distributed electron transport method hardly affects the accuracy of the calculated dose distributions. It is also shown that the results of the new dose distribution calculations are still in good agreement with and require significantly less computation time than results obtained with the EGS4 Monte Carlo method.     

Intracellular protein transport to the thyrocyte plasma membrane: potential implications for thyroid physiology

Calculations of stopping power ratios, water to air, for the determination of absorbed dose to water in clinical proton beams using ionization chamber measurements have been undertaken using the Monte Carlo method. A computer code to simulate the transport of protons in water (PETRA) has been used to calculate sw.air-data under different degrees of complexity, ranging from values based on primary protons only to data including secondary electrons and high-energy secondary protons produced in nonelastic nuclear collisions. All numerical data are based on ICRU 49 proton stopping powers. Calculations using primary protons have been compared to the simple continuous slowing-down approximation (c.s.d.a.) analytical technique used in proton dosimetry protocols, not finding significant differences that justify elaborate Monte Carlo simulations except beyond the mean range of the protons (the far side of the Bragg peak). The influence of nuclear nonelastic processes, through the detailed generation and transport of secondary protons, on the calculated stopping-power ratios has been found to be negligible. The effect of alpha particles has also been analysed, finding differences smaller than 0.1% from the results excluding them. Discrepancies of up to 0.6% in the plateau region have been found, however, when the production and transport of secondary electrons are taken into account. The large influence of nonelastic nuclear interactions on proton depth-dose distributions shows that the removal of primary protons from the incident beam decreases the peak-to-plateau ratio by a large factor, up to 40% at 250 MeV. It is therefore emphasized that nonelastic nuclear reactions should be included in Monte Carlo simulations of proton beam depth-dose distributions.     

Correction factors for parallel-plate chambers used in plastic phantoms in electron dosimetry

In electron beam dosimetry using parallel-plate chambers solid phantoms are sometimes necessary. To obtain the dose to water from the ionization obtained in the solid phantom, fluence correction factors and perturbation factors have to be applied. In this study fluence factors in a perturbation free geometry have been determined experimentally for common phantom materials. Wall perturbation factors for simulated Attix, NACP, and Roos chambers have also been determined for the same materials. Comparative Monte Carlo calculations have been performed using the EGS4 Monte Carlo code. Comparison with data in newly published protocols such as IAEA and IPEMB shows an agreement with the results obtained in this paper to within 1%, demonstrating that the data published in these protocols may be used with reasonable accuracy if recommended phantoms are used. The results also show that if unsuitable phantom materials are used, the wall perturbation factors may differ for different chambers and for different phantom materials by more than 3% and perturbation factors have to be considered in order to obtain a high accuracy in the dose determination.     

Theoretical and experimental determination of phantom scatter factors for photon fields with different radial energy variation

The output factor used for monitor unit determination in radiotherapy can be divided into two factors: the head scatter factor and the phantom scatter factor. Theoretical and experimental phantom scatter factors have been compared for different beam qualities between 4 MV and 50 MV and field sizes from 5 cm x 5 cm to 30 cm x 30 cm. The theoretical data were obtained through a convolution method based on Monte Carlo calculated energy spectra and dose kernels. The calculations have been performed both for accelerators with a rather large energy variation within the field and for accelerators with a constant energy distribution in the field. Deviations between theoretical and experimental data were found to be less than 1%.     

Combined experimental and Monte Carlo verification of 137Cs brachytherapy plans for vaginal applicators

Dose rates in a phantom around a shielded and an unshielded vaginal applicator containing Selectron low-dose-rate 137Cs sources were determined by experiment and Monte Carlo simulation. Measurements were performed with thermoluminescent dosimeters in a white polystyrene phantom using an experimental protocol geared for precision. Calculations for the same set-up were done using a version of the EGS4 Monte Carlo code system modified for brachytherapy applications into which a new combinatorial geometry package developed by Bielajew was recently incorporated. Measured dose rates agree with Monte Carlo estimates to within 5% (1 SD) for the unshielded applicator, while highlighting some experimental uncertainties for the shielded applicator. Monte Carlo calculations were also done to determine a value for the effective transmission of the shield required for clinical treatment planning, and to estimate the dose rate in water at points in axial and sagittal planes transecting the shielded applicator. Comparison with dose rates generated by the planning system indicates that agreement is better than 5% (1 SD) at most positions. The precision thermoluminescent dosimetry protocol and modified Monte Carlo code are effective complementary tools for brachytherapy applicator dosimetry.     

Practical imaging in acute pancreatitis

This paper outlines the "voxel reconstruction" technique used to model the macroscopic human anatomy of the cranial, abdominal and cervical regions directly from CT scans. Tissue composition, density, and radiation transport characteristics were assigned to each individual volume element (voxel) automatically depending on its greyscale number and physical location. Both external beam and brachytherapy treatment techniques were simulated using the Monte Carlo radiation transport code MCNP (Monte Carlo N-Particle) version 3A. To obtain a high resolution dose calculation, yet not overly extend computational times, variable voxel sizes have been introduced. In regions of interest where high attention to anatomical detail and dose calculation was required, the voxel dimensions were reduced to a few millimetres. In less important regions that only influence the region of interest via scattered radiation, the voxel dimensions were increased to the scale of centimetres. With the use of relatively old (1991) supercomputing hardware, dose calculations were performed in under 10 hours to a standard deviation of 5% in each voxel with a resolution of a few millimetres--current hardware should substantially improve these figures. It is envisaged that with coupled photon/electron transport incorporated into MCNP version 4A and 4B, conventional photon and electron treatment planning will be undertaken using this technique, in addition to neutron and associated photon dosimetry presented here.     

Benchmarking the MCNP code for Monte Carlo modelling of an in vivo neutron activation analysis system

The Monte Carlo computer code MCNP (version 4A) has been used to develop a personal computer-based model of the Swansea in vivo neutron activation analysis (IVNAA) system. The model included specification of the neutron source (252Cf), collimators, reflectors and shielding. The MCNP model was 'benchmarked' against fast neutron and thermal neutron fluence data obtained experimentally from the IVNAA system. The Swansea system allows two irradiation geometries using 'short' and 'long' collimators, which provide alternative dose rates for IVNAA. The data presented here relate to the short collimator, although results of similar accuracy were obtained using the long collimator. The fast neutron fluence was measured in air at a series of depths inside the collimator. The measurements agreed with the MCNP simulation within the statistical uncertainty (5-10%) of the calculations. The thermal neutron fluence was measured and calculated inside the cuboidal water phantom. The depth of maximum thermal fluence was 3.2 cm (measured) and 3.0 cm (calculated). The width of the 50% thermal fluence level across the phantom at its mid-depth was found to be the same by both MCNP and experiment. This benchmarking exercise has given us a high degree of confidence in MCNP as a tool for the design of IVNAA systems.