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.     

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.     

Monte Carlo simulation of a miniature, radiosurgery x-ray tube using the ITS 3.0 coupled electron-photon transport code

A miniature, interstitial x-ray generator has recently been developed and is currently undergoing clinical trials for the treatment of brain tumors. The maximum photon energy from this x-ray tube is 50 keV, although most of the initial testing has been carried out at 40 keV. Dose rates of up to 2 Gy/min in a water phantom at a distance of 10 mm from the tube tip are produced. In this paper we describe the modeling and simulation of x-ray production from this device using the ITS 3.0 Monte Carlo code. Verification of the simulation of x-ray production in the device was carried out by comparing predictions of spatial photon distribution, energy spectrum, and dose versus depth in water with experimentally obtained measurements. Agreement between the simulated results and experimental measurements was fairly good when comparing the angular distribution of photons emitted from the x-ray tube and very good when comparing dose rate versus depth in a water phantom. Discrepancies observed when comparing the calculated and measured estimates of characteristic line radiation were reduced by incorporation of a modification to the ITS code. Possible causes of the remaining discrepancy in bremsstrahlung intensity are discussed.     

Limiting values of backscatter factors for low-energy x-ray beams

Models for the calculation of upper and lower limiting values to the backscatter factor (BSF) are presented. The upper limit is obtained from Monte Carlo simulations of infinite parallel beams incident on semi-infinite phantoms with the dose contributions from all orders of photon scatter considered. The lower limits are calculated using an analytical photon transport model which considers only the primary dose and the scatter dose from photons that have undergone single scattering interactions in the phantom. The limiting values can be used to evaluate measured and modelled BSF values for x-ray beams with photons of < or = 150 keV. A parametrization of the limiting values in terms of photon energy and irradiation field size is presented so that results determined for monoenergetic beams can be extended to polyenergetic spectra. The utility of the limits is illustrated by comparisons made with BSFs from the literature.     

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.     

Study of dosimetry consistency for kilovoltage x-ray beams

In this paper, the consistency of kilovoltage (tube potentials between 40 and 300 kV) x-ray beam dosimetry using the "in-air" method and the in-phantom measurement has been studied. The procedures for the measurement of the central-axis depth-dose curve, which serve as a link between the dose at the reference depth to the dose elsewhere in a phantom, were examined. The uncertainties on the measured dose distributions were analyzed with the emphasis on the surface dose measurement. The Monte Carlo method was used to calculate the perturbation correction factors for a photon diode and a NACP plane-parallel ionization chamber at different depths in a water phantom irradiated by 100-300 kV (2.43 mm Al-3.67 mm Cu half-value layer) x-ray beams. The depth-dose curves measured with these two detectors, after correcting for the perturbation effect (up to 15% corrections), agreed with each other to within 1.5%. Comparisons of the doses at the phantom surface and at 2 cm depth in water for photon beams of 100-300 kV tube potential obtained using the "backscatter" method and those using the "in-phantom" measurement have shown that the "in-air" method can be equally applied to this energy range if the depth-dose curve can be measured accurately. To this end, measured depth ionization curves require depth-dependent correction factors.     

Monte Carlo dosimetry study of a 6 MV stereotactic radiosurgery unit

Small-field and stereotactic radiosurgery (SRS) dosimetry with radiation detectors, used for clinical practice, have often been questioned due to the lack of lateral electron equilibrium and uncertainty in beam energy. A dosimetry study was performed for a dedicated 6 MV SRS unit, capable of generating circular radiation fields with diameters of 1.25-5 cm at isocentre using the BEAM/EGS4 Monte Carlo code. With this code the accelerator was modelled for radiation fields with a diameter as small as 0.5 cm. The radiation fields and dosimetric characteristics (photon spectra, depth doses, lateral dose profiles and cone factors) in a water phantom were evaluated. The cone factor (St) for a specific cone c at depth d is defined as St(d, c) = D(d, c)/D(d, c(ref)), where c(ref) is the reference cone. To verify the Monte Carlo calculations, measurements were performed with detectors commonly used in SRS such as small-volume ion chambers, a diamond detector, TLDs and films. Results show that beam energies vary with cone diameter. For a 6 MV beam, the mean energies in water at the point of maximum dose for a 0.5 cm cone and a 5 cm cone are 2.05 MeV and 1.65 MeV respectively. The values of St obtained by the simulations are in good agreement with the results of the measurements for most detectors. When the lateral resolution of the detectors is taken into account, the results agree within a few per cent for most fields and detectors. The calculations showed a variation of St with depth in the water. Based on calculated electron spectra in water, the validity of the assumption that measured dose ratios are equal to measured detector readings was verified.     

Conversion of ionization measurements to radiation absorbed dose in non-water density material

The radiation absorbed dose to non-water equivalent materials of interest in radiotherapy is the dose to lung and the dose to bone. The measurement and calculation of dose to the lung has been of great interest and much effort has gone into the development of accurate lung dose calculation methods. The radiation absorbed dose to the bone is usually not calculated and most absorbed dose calculations have been done without correcting for the presence of bone. For the lower megavoltage photon beams this may be appropriate, however, as the energy of the photon beam increases, the region of electronic disequilibrium becomes larger and pair production which depends on the atomic number of the material becomes significant. Therefore the bone will produce greater perturbations of the dose distribution. The dose to lung-equivalent material is uniquely obtained from ionization measurements. However, in bone-equivalent materials two different calculations of absorbed dose are possible: the absorbed dose to soft tissue plastic (polystyrene) within bone-equivalent material and the dose to the bone-equivalent material itself. Both can be calculated from ionization measurements in phantoms. These two calculations result in significantly different doses in a heterogeneous phantom composed of polystyrene and aluminium (a bone substitute). The dose to a thin slab of polystyrene in aluminium is much higher than the dose to the aluminium itself at the same depth in the aluminium. Monte Carlo calculations confirm that the calculation of dose to polystyrene in aluminium can be accurately carried out using existing dosimetry protocols. However, the conversion of ionization measurements to absorbed dose to high atomic number materials cannot be accurately carried out with existing protocols and appropriate conversion factors need to be determined.     

Calculation of effective doses for broad parallel photon beams

Values of effective dose (E) were calculated for the entire range of incident directions of broad parallel photon beams for selected photon energies using the Monte Carlo N-Particle (MCNP) transport code with a hermaphroditic phantom. The calculated results are presented in terms of conversion coefficients transforming air kerma to effective dose. This study also compared the numerical values of E and H(E) over the entire range of incident beam directions. E was always less than H(E) considering all beam directions and photon energies, but the differences were not significant except when a photon beam approaches some specific directions (overhead and underfoot). This result suggests that the current H(E) values can be directly interpreted as E or, at least, as a conservative value of E without knowing the details of irradiation geometries. Finally, based on the distributions of H(E) and E over the beam directions, this study proposes ideal angular response factors for personal dosimeters that can be used to improve the angular response properties of personal dosimeters for off-normal incident photons.     

In-water calibration of PDR 192Ir brachytherapy sources with an NE2571 ionization chamber

An ionometric calibration procedure for 192Ir PDR brachytherapy sources in terms of dose rate to water is presented. The calibration of the source is performed directly in a water phantom at short distances (1.0, 2.5 and 5.0 cm) using an NE2571 Farmer type ion chamber. To convert the measured air-kerma rate in water to dose rate to water a conversion factor (CF) was calculated by adapting the medium-energy x-ray dosimetry protocol for a point source geometry (diverging beam). The obtained CF was verified using two different methods. Firstly, the CF was calculated by Monte Carlo simulations, where the source-ionization chamber geometry was modelled accurately. In a second method, a combination of Monte Carlo simulations and measurements of the air-kerma rate in water (at 1.0, 2.5 and 5.0 cm distance) and in air (1 m distance) was used to determine the CF. The obtained CFs were also compared with conversion factors calculated with the adapted dosimetry protocol for high-energy photons introduced by T?lli. All calculations were done for a Gammamed PDR 192Ir source-NE2571 chamber geometry. The conversion factors obtained with the four different methods agree to within 1% at the three distances of interest. We obtained the following values (medium-energy x-ray protocol): CF(1 cm) = 1.458; CF(2.5 cm) = 1.162; CF(5.0 cm) = 1.112 (1 sigma = 0.7% for the three distances of interest). The obtained results were checked with TLD measurements. The values of the specific dose rate constant and the radial dose function calculated in this work are in accordance with the literature data.     

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.     

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.     

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.     

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.     

Accounting for the variation in collision kerma-to-terma ratio in polyenergetic photon beam convolution

In photon beam convolution, the distribution of energy deposition about a primary photon interaction site due to charged particles set in motion at that site is represented by the primary kernel. Energy deposited due to scattered photons, bremsstrahlung, and annihilation photons is represented by the scatter kernel. As the energy deposited in each kernel voxel is normalized to the energy imparted at the interaction site, it is known as a fractional energy distribution. In terma-based convolution, where kernels are normalized to total energy imparted at the interaction site and are convolved with the terma in the dose calculation process, the sum of fractional energies contained in the primary kernel is equal to the ratio of collision kerma (Kc) to terma (T) corresponding to the energy spectrum used to generate the kernel. Since the ratio of collision kerma to terma increases with depth as the beam hardens, the integral fractional energy in a primary kernel formed for the spectrum at the surface is less than the ratio Kc/T at depth. This causes primary dose to be increasingly underestimated with depth and scatter dose to be increasingly overestimated. Single polyenergetic convolution (using polyenergetic primary and scatter kernels formed using a polyenergetic primary photon spectrum) is thus not as rigorous as if a separate convolution is performed for each energy component. The ratio of true primary dose to single polyenergetic primary dose increases almost linearly with depth and is almost equal to the Kc/T ratio. Primary and scatter dose are calculated correctly if a single polyenergetic convolution is performed in terms of Kc (for primary) and T-Kc (for scatter), where the kernels are weighted sums of monoenergetic kernels normalized to Kc and T-Kc. With this method, it is ensured that total primary energy deposited due to primary photon interactions in a unit mass at a point is equal to Kc at that point.     

Personal dose equivalent for photons and its variation with dosimeter position

This work presents conversion coefficients per air kerma free-in-air for the personal dose equivalent, Hp(10), calculated according to its definition by the International Commission on Radiation Units and Measurements as a quantity in the human body. The values were calculated using Monte Carlo methods for various dosimeter positions in the trunk of a voxel model of an adult male, and they are given for various directions of incidence of broad parallel photon beams with energies between 10 keV and 10 MeV. It is shown that the numerical values of the personal dose equivalent depend on the exact position of the dosimeter, with maximum differences between 12% and 80%, depending on the beam geometry. It is further shown that the recommended calibration quantity Hp slab(10), which has been used in ICRP Publication 74 and ICRU Report 57 in the absence of data in the human body to approximate personal dose equivalent, does represent the latter quantity in a sensible way for some, but not all, beam geometries. Comparison of the values for the personal dose equivalent of this work with effective dose revealed that Hp(10) is a conservative estimate or close approximation of E for most irradiation geometries and photon energies.     

A dual source photon beam model used in convolution/superposition dose calculations for clinical megavoltage x-ray beams

A realistic photon beam model based on Monte Carlo simulation of clinical linear accelerators was implemented in a convolution/superposition dose calculation algorithm. A primary and an extra-focal sources were used in this beam model to represent the direct photons from the target and the scattered photons from other head structures, respectively. The effect of the finite size of the extra-focal source was modeled by a convolution of the source fluence distribution with the collimator aperture function. Relative photon output in air (Sc) and in phantom (Scp) were computed using the convolution method with this new photon beam model. Our results showed that in a 10 MV photon beam, the Sc, Sp (phantom scatter factor), and Scp factors increased by 11%, 10%, and 22%, respectively, as the field size changed from 3 x 3 cm2 to 40 x 40 cm2. The variation of the Sc factor was contributed mostly by an increase of the extra-focal radiation with field size. The radiation backscattered into the monitor chamber inside the accelerator head affected the Sc by about 2% in the same field range. The output factors in elongated fields, asymmetric fields, and blocked fields were also investigated in this study. Our results showed that if the effect of the backscattered radiation was taken into account, output factors in these treatment fields can be predicted accurately by our convolution algorithm using the dual source photon beam model.     

Calculating dose and output factors for wedged photon radiotherapy fields using a convolution/superposition method

To account for clinical divergent and polychromatic photon beams, we have developed kernel tilting and kernel hardening correction methods for convolution dose calculation algorithms. The new correction methods were validated by Monte Carlo simulation. The accuracy and computation time of the our kernel tilting and kernel hardening correction methods were also compared to the existing approaches including terma divergence correction, dose divergence correction methods, and the effective mean kernel method with no kernel hardening correction. Treatment fields of 10 x 10-40 x 40 cm2 (field size at source to axis distance (SAD)) with source to source distances (SSDs) of 60, 80, and 100 cm, and photon energies of 6, 10, and 18 MV have been studied. Our results showed that based on the relative dose errors at a depth of 15 cm along the central axis, the terma divergence correction may be used for fields smaller than 10 x 10 cm2 with a SSD larger than 80 cm; the dose divergence correction with an additional kernel hardening correction can reduce dose error and may be more applicable than the terma divergence correction. For both these methods, the dose error increased linearly with the depth in the phantom; the 90% isodose lines at the depth of 15 cm were shifted by about 2%-5% of the field width due to significant underestimation of the penumbra dose. The kernel hardening effect was less prominent than the kernel tilting effect for clinical photon beams. The dose error by using nonhardening corrected kernel is less than 2.0% at a depth of 15 cm along the central axis, yet it increased with a smaller field size and lower photon energy. The kernel hardening correction could be more important to compute dose in the fields with beam modifiers such as wedges when beam hardening is more significant. The kernel tilting correction and kernel hardening correction increased computation time by about 3 times, and 0.5-1 times, respectively. This can be justified by more accurate dose calculations for the majority of clinical treatments.     

A comparative study of dosimetric properties of Plastic Water and Solid Water in brachytherapy applications

In this study the dosimetric properties of Plastic Water and Solid Water phantom materials are evaluated using Monte Carlo photon transport simulations. In particular, their water-equivalence with respect to absorption and attenuation of photons in the brachytherapy energy range are examined. For the given chemical compositions of the materials, the linear attenuation coefficients were calculated for photons of 1 keV-2 MeV. Moreover, absorbed doses to water in each phantom material were calculated at distances of 0.5-12.0 cm from point sources of 20 keV to 60Co gamma rays. These results show that at low photon energies (below 100 keV), there are substantial differences (up to a factor of 5) between the absorbed dose in Plastic Water and that in liquid water. The differences decrease as photon energy increases, and they become insignificant at 60Co gamma rays, as claimed by the manufacturer. In contrast, calculations show that the difference in absorbed dose in Solid Water from that in liquid water, over the entire range of photon energies employed in this study, is less than 25%. The results of this study demonstrate the necessity of careful dosimetric evaluation of a new phantom material, before its clinical application, particularly in energy ranges outside those referred to by the manufacturer.