Radiological properties of normoxic polymer gel dosimeters

The radiological properties of the normoxic polymer gel dosimeters MAGIC, MAGAS, and MAGAT [methacrylic and ascorbic acid in gelatin initiated by copper; methacrylic acid gelatine gel with ascorbic acid; and methacrylic acid gelatine and tetrakis (hydroxymethyl) phosphonium chloride, respectively] have been investigated. The radiological water equivalence was determined by comparing the polymer gel macroscopic photon and electron interaction cross sections over the energy range from 10 keV to 20 MeV and by Monte Carlo modeling of depth doses. Normoxic polymer gel dosimeters have a high gelatine and monomer concentration and therefore mass density (kg m(-3)) up to 3.8% higher than water. This results in differences between the cross-section ratios of the normoxic polymer gels and water of up to 3% for the attenuation, energy absorption, and collision stopping power coefficient ratios through the Compton dominant energy range. The mass cross-section ratios were within 2% of water except for the mass attenuation and energy absorption coefficients ratios, which showed differences with water of up to 6% for energies less than 100 keV. Monte Carlo modeling was undertaken for the polymer gel dosimeters to model the electron and photon transport resulting from a 6 MV photon beam. The absolute percentage differences between gel and water were within 1% and the relative percentage differences were within 3.5%. The results show that the MAGAT gel formulation is the most radiological water equivalent of the normoxic polymer gel dosimeters investigated due to its lower mass density measurement compared with MAGAS and MAGIC gels.     

On two-parameter models of photon cross sections: application to dual-energy CT imaging

The goal of this study is to evaluate the theoretically achievable accuracy in estimating photon cross sections at low energies (20-1000 keV) from idealized dual-energy x-ray computed tomography (CT) images. Cross-section estimation from dual-energy measurements requires a model that can accurately represent photon cross sections of any biological material as a function of energy by specifying only two characteristic parameters of the underlying material, e.g., effective atomic number and density. This paper evaluates the accuracy of two commonly used two-parameter cross-section models for postprocessing idealized measurements derived from dual-energy CT images. The parametric fit model (PFM) accounts for electron-binding effects and photoelectric absorption by power functions in atomic number and energy and scattering by the Klein-Nishina cross section. The basis-vector model (BVM) assumes that attenuation coefficients of any biological substance can be approximated by a linear combination of mass attenuation coefficients of two dissimilar basis substances. Both PFM and BVM were fit to a modern cross-section library for a range of elements and mixtures representative of naturally occurring biological materials (Z = 2-20). The PFM model, in conjunction with the effective atomic number approximation, yields estimated the total linear cross-section estimates with mean absolute and maximum error ranges of 0.6%-2.2% and 1%-6%, respectively. The corresponding error ranges for BVM estimates were 0.02%-0.15% and 0.1%-0.5%. However, for photoelectric absorption frequency, the PFM absolute mean and maximum errors were 10.8%-22.4% and 29%-50%, compared with corresponding BVM errors of 0.4%-11.3% and 0.5%-17.0%, respectively. Both models were found to exhibit similar sensitivities to image-intensity measurement uncertainties. Of the two models, BVM is the most promising approach for realizing dual-energy CT cross-section measurement.     

A parameterization scheme for the x-ray linear attenuation coefficient and energy absorption coefficient

A novel parameterization of x-ray interaction cross-sections is developed, and employed to describe the x-ray linear attenuation coefficient and mass energy absorption coefficient for both elements and mixtures. The new parameterization scheme addresses the Z-dependence of elemental cross-sections (per electron) using a simple function of atomic number, Z. This obviates the need for a complicated mathematical formalism. Energy dependent coefficients describe the Z-direction curvature of the cross-sections. The composition dependent quantities are the electron density and statistical moments describing the elemental distribution. We show that it is possible to describe elemental cross-sections for the entire periodic table and at energies above the K-edge (from 6 keV to 125 MeV), with an accuracy of better than 2% using a parameterization containing not more than five coefficients. For the biologically important elements 1 < or = Z < or = 20, and the energy range 30-150 keV, the parameterization utilizes four coefficients. At higher energies, the parameterization uses fewer coefficients with only two coefficients needed at megavoltage energies.     

Studies on effective atomic number, electron density and kerma for some fatty acids and carbohydrates

The effective atomic number, Z(eff), the effective electron density, N(el), and kerma have been calculated for some fatty acids and carbohydrates for photon interaction in the extended energy range from 1 keV to 100 GeV using an accurate database of photon-interaction cross sections and the WinXCom program. The significant variation of Z(eff) and N(el) is due to the variations in the dominance of different interaction processes in different energy regions. The maximum values of Z(eff) and N(el) are found in the low-energy range, where photoelectric absorption is the main interaction process. The minimum values of Z(eff) and N(el) are found at intermediate energies, typically 0.05 MeV < E < 5 MeV, where Compton scattering is dominant. In this case, Z(eff) is equal to the mean atomic number of the bio-molecule. Wherever possible, the calculations are compared with experimental results. A comparison is also made with the single values of the Z(eff) and N(el) provided by the program XMuDat. It is also observed that carbohydrates have a larger kerma than fatty acids in the low-energy region, where photoelectric absorption dominates. In contrast, fatty acids have a larger kerma than carbohydrates in the MeV range, where Compton scattering is the main interaction process.     

A dosimetric evaluation of water equivalent phantoms for kilovoltage x-ray beams

Solid phantoms are widely used in radiation therapy for both relative and reference dosimetry. Two water equivalent phantoms, RMI-457 Solid Water and Plastic Water, were evaluated for use in kilovoltage x-ray dosimetry in the energy range from 75 to 300 kVp. Relative and reference dosimetry measurements were performed in the solid phantoms and compared with water. The results indicate that RMI-457 Solid Water could be used for output factor determination for all energies tested and the measurement of percentage depth doses for the 300 kVp x-ray beam, with data agreeing to within 1%, compared to the same measurements in water. For the same criteria, Plastic Water could only be used for output factor determination of the 300 kVp x-ray beam. The superior agreement of the calculated mass-energy absorption coefficients for Solid Water and water, as compared to Plastic Water and water was consistent with the experimental results. Reference dosimetry is not recommended with the solid phantoms for the energies studied due to the lack of published correction factors. It is recommended that any solid phantom be tested by comparison with water in the same manner before being used for the dosimetry of kilovoltage x-ray beams.     

Brachytherapy dosimetry of 125I and 103Pd sources using an updated cross section library for the MCNP Monte Carlo transport code

Permanent implantation of low energy (20-40 keV) photon emitting radioactive seeds to treat prostate cancer is an important treatment option for patients. In order to produce accurate implant brachytherapy treatment plans, the dosimetry of a single source must be well characterized. Monte Carlo based transport calculations can be used for source characterization, but must have up to date cross section libraries to produce accurate dosimetry results. This work benchmarks the MCNP code and its photon cross section library for low energy photon brachytherapy applications. In particular, we calculate the emitted photon spectrum, air kerma, depth dose in water, and radial dose function for both 125I and 103Pd based seeds and compare to other published results. Our results show that MCNP's cross section library differs from recent data primarily in the photoelectric cross section for low energies and low atomic number materials. In water, differences as large as 10% in the photoelectric cross section and 6% in the total cross section occur at 125I and 103Pd photon energies. This leads to differences in the dose rate constant of 3% and 5%, and differences as large as 18% and 20% in the radial dose function for the 125I and 103Pd based seeds, respectively. Using a partially updated photon library, calculations of the dose rate constant and radial dose function agree with other published results. Further, the use of the updated photon library allows us to verify air kerma and depth dose in water calculations performed using MCNP's perturbation feature to simulate updated cross sections. We conclude that in order to most effectively use MCNP for low energy photon brachytherapy applications, we must update its cross section library. Following this update, the MCNP code system will be a very effective tool for low energy photon brachytherapy dosimetry applications.     

Experimental verification of beam quality in high-contrast imaging with orthogonal bremsstrahlung photon beams

Since taken with megavoltage, forward-directed bremsstrahlung beams, the image quality of current portal images is inferior to that of diagnostic quality images produced by kilovoltage beams. In this paper, the beam quality of orthogonal bremsstrahlung beams defined as the 90 degrees component of the bremsstrahlung distribution produced from megavoltage electron pencil beams striking various targets is presented, and the suitability of their use for improved radiotherapy imaging is evaluated. A 10 MeV electron beam emerging through the research port of a Varian Clinac-18 linac was made to strike targets of carbon, aluminum, and copper. PDD and attenuation measurements of both the forward and orthogonal beams were carried out, and the results were also used to estimate the effective and mean energy of the beams. The mean energy of a spectrum produced by a carbon target dropped by 83% from 1296 keV in the forward direction to 217 keV in the orthogonal direction, while for an aluminum target it dropped by 77% to 412 keV, and for a copper target by 65% to 793 keV. An in-depth Monte Carlo study of photon yield and electron contamination was also performed. Photon yield and effective energy are lower for orthogonal beams than for forward beams, and the differences are more pronounced for targets of lower atomic number. Using their relatively low effective energy, orthogonal bremsstrahlung beams produced by megavoltage electrons striking low atomic number targets yield images with a higher contrast in comparison with forward bremsstrahlung beams.     

Polymer gel water equivalence and relative energy response with emphasis on low photon energy dosimetry in brachytherapy

The water equivalence and stable relative energy response of polymer gel dosimeters are usually taken for granted in the relatively high x-ray energy range of external beam radiotherapy based on qualitative indices such as mass and electron density and effective atomic number. However, these favourable dosimetric characteristics are questionable in the energy range of interest to brachytherapy especially in the case of lower energy photon sources such as 103Pd and 125I that are currently utilized. In this work, six representative polymer gel formulations as well as the most commonly used experimental set-up of a LiF TLD detector-solid water phantom are discussed on the basis of mass attenuation and energy absorption coefficients calculated in the energy range of 10 keV-10 MeV with regard to their water equivalence as a phantom and detector material. The discussion is also supported by Monte Carlo simulation results. It is found that water equivalence of polymer gel dosimeters is sustained for photon energies down to about 60 keV and no corrections are needed for polymer gel dosimetry of 169Yb or 192Ir sources. For 125I and 103Pd sources, however, a correction that is source-distance dependent is required. Appropriate Monte Carlo results show that at the dosimetric reference distance of 1 cm from a source, these corrections are of the order of 3% for 125I and 2% for 103Pd. These have to be compared with corresponding corrections of up to 35% for 125I and 103Pd and up to 15% even for the 169Yb energies for the experimental set-up of the LiF TLD detector-solid water phantom.     

A new approach to film dosimetry for high-energy photon beams using organic plastic scintillators

This study is concerned with dose measurement of photon beams, both dynamic and static, by using x-ray film. As discussed in our last study (Burch et al 1997, Yeo et al 1997), x-ray film, as an integrating dosimeter, can be an ideal candidate if the over-response problem to low-energy photons (energies below 400 keV) is solved. In summary, the problem of the over-response can be explained as follows. Because the mass energy absorption coefficient of x-ray film increases as photon energy decreases, softening of the photon spectra with depth in a phantom makes the extent of film over-response a function of phantom depth (Burch et al 1997, Yeo et al 1997). Film dosimetry is based upon (a) calibration of the film response (i.e. optical density) at some specific depth in a phantom and (b) conversion of the film density which can cover whole depths in a phantom to dose by using the calibration curve. In megavoltage dosimetry, this normally causes over-response in doses at depths greater than the calibration depth.     

Comparative study of a low-Z cone-beam computed tomography system

Computed tomography images have been acquired using an experimental (low atomic number (Z) insert) megavoltage cone-beam imaging system. These images have been compared with standard megavoltage and kilovoltage imaging systems. The experimental system requires a simple modification to the 4 MeV electron beam from an Elekta Precise linac. Low-energy photons are produced in the standard medium-Z electron window and a low-Z carbon electron absorber located after the window. The carbon electron absorber produces photons as well as ensuring that all remaining electrons from the source are removed. A detector sensitive to diagnostic x-ray energies is also employed. Quantitative assessment of cone-beam computed tomography (CBCT) contrast shows that the low-Z imaging system is an order of magnitude or more superior to a standard 6 MV imaging system. CBCT data with the same contrast-to-noise ratio as a kilovoltage imaging system (0.15 cGy) can be obtained in doses of 11 and 244 cGy for the experimental and standard 6 MV systems, respectively. Whilst these doses are high for everyday imaging, qualitative images indicate that kilovoltage like images suitable for patient positioning can be acquired in radiation doses of 1-8 cGy with the experimental low-Z system.     

Choice of material for HVL measurements in megavoltage x-ray beams

The relative sensitivity of the half-value layer (HVL) method as a quality index for megavoltage x-ray beams is examined by theoretical calculation and experimental measurements for 4-, 6-, 10-, and 25-MV x-ray beams. It is shown that lower atomic number materials are more sensitive to beam quality changes than higher atomic number materials, and that aluminum is a reasonable choice of material for HVL measurements in megavoltage x-ray beams. Further, it was found that the HVL in aluminum or polystyrene is a more sensitive index of spectral quality than the ionization ratio method, recommended by recent dosimetry protocols.     

Measurement of energy dependence for XRCT radiochromic film

Gafchromic XRCT, radiochromic film is assessed over a broad energy range, from kilovoltage to megavoltage x rays for variations in reflected optical density to dose response. A large energy dependence was found with reflected optical density output for the same delivered dose varying from 7.8 +/- 0.35 at 25.5 keV (50 kVp) peaking at 12.1 +/- 0.5 at 54 keV (125 kVp) to 0.975 +/- 0.03 at 2300 keV (10 MV) when normalized to 1 at 1400 keV (6 MV) energy. The response is constant (within 3%) in the 36-69 keV equivalent photon energy range, which corresponds to x-ray tube generating potentials of approximately 100-150 kVp. This matches well with beam qualities for diagnostic computed topography applications.     

Dose response of BaFBrl: Eu2+ storage phosphor plates exposed to megavoltage photon beams

The BaFBrI:Eu2+ storage phosphor plate (SPP) is a reusable radiation image detector, widely used in diagnostic computed radiography, x-ray crystallography and radioactive tracer studies. When exposed to ionizing radiation, the SPP stores a latent image until it is scanned with a red reading laser which causes blue photostimulated luminescent (PSL) photons to be emitted. The mechanism of formation of the latent image is still poorly understood, especially for megavoltage photon beams. In order to gain insight into this mechanism and aid applications to high-energy beam dosimetry, the authors have directly determined the SPP generation efficiency, W, the energy required to produce one quantum of emitted PSL when it is irradiated by 60Co and 6 MV photon beams. This was done in four steps: 1. The SPP, in a water-equivalent plastic (WEP) phantom, was exposed to a 60Co or 6 MV beam, which had been calibrated to give a known absorbed dose to water in a water phantom at the position of the sensitive layer of the SPP. 2. Monte Carlo simulations were used to calculate the ratio of the dose to the sensitive layer in the WEP phantom to the dose to water at the same position in a water phantom. 3. A bleaching experiment was used to determine the number of photons emitted by a plate given a known dose. 4. The generation efficiency was calculated from the number of photons and the dose. This method is much more direct than previous calculations for kilovoltage x-ray beams based on quantum noise analysis. W was found, within experimental uncertainty, to be 190 eV for 60Co and 160 eV for 6 MV, independent of dose. The values for kilovoltage x-ray beams determined previously agree, within their large uncertainty, with these values for megavoltage beams.     

Effective atomic numbers for low-energy total photon interactions in human tissues

A new method is introduced in which the total photon interaction cross sections per electron of human tissues are used to define effective atomic numbers for blood, bone, brain, fat, heart, kidney, liver, lung, muscle, ovary, pancreas, spleen, and water. These effective atomic numbers are equal within 4% from 10 to 200 keV in each soft tissue, whereas for bones of different chemical compositions the variation ranges from 2.86% to 5.03%. This effective atomic number definition is less energy dependent than a previous definition based on the total photon interaction cross section per atom averaged over all elements in the tissue, from which the computed effective atomic numbers varied by as much as 50% (in bone) as a function of photon energy over the energy range from 10 to 200 keV.     

Derivation of linear attenuation coefficients from CT numbers for low-energy photons.

One can estimate photon attenuation properties from the CT number. In a standard method one assumes that the linear attenuation coefficient is proportional to electron density and ignores its nonlinear dependence on atomic number. When the photon energy is lower than about 50 keV, such as for brachytherapy applications, however, photoelectric absorption and Rayleigh scattering become important. Hence the atomic number must be explicitly considered in estimating the linear attenuation coefficient. In this study we propose a method to more accurately estimate the linear attenuation coefficient of low-energy photons from CT numbers. We formulate an equation that relates the CT number to the electron density and the effective atomic number. We use a CT calibration phantom to determine unknown coefficients in the equation. The equation with a given CT number is then solved for the effective atomic number, which in turn is used to calculate the linear attenuation coefficient for low-energy photons. We use the CT phantom to test the new method. The method significantly improves the standard method in estimating the attenuation coefficient at low photon energies (20 keV < or = E < or = 40 keV) for materials with high atomic numbers.     

Signal and noise transfer properties of photoelectric interactions in diagnostic x-ray imaging detectors

Image quality in diagnostic x-ray imaging is ultimately limited by the statistical properties governing how, and where, x-ray energy is deposited in a detector. This in turn depends on the physics of the underlying x-ray interactions. In the diagnostic energy range (10-100 keV), most of the energy deposited in a detector is through photoelectric interactions. We present a theoretical model of the photoelectric effect that specifically addresses the statistical nature of energy absorption by photoelectrons, K and L characteristic x rays, and Auger electrons. A cascaded-systems approach is used that employs a complex structure of parallel cascades to describe signal and noise transfer through the photoelectric effect in terms of the modulation transfer function, Wiener noise power spectrum, and detective quantum efficiency (DQE). The model was evaluated by comparing results with Monte Carlo calculations for x-ray converters based on amorphous selenium (a-Se) and lead (Pb), representing both low and high-Z materials. When electron transport considerations can be neglected, excellent agreement (within 3%) is obtained for each metric over the entire diagnostic energy range in both a-Se and Pb detectors up to 30 cycles/mm, the highest frequency tested. The cascaded model overstates the DQE when the electron range cannot be ignored. This occurs at approximately two cycles/mm in a-Se at an incident photon energy of 80 keV, whereas in Pb, excellent agreement is obtained for the DQE over the entire diagnostic energy range. However, within the context of mammography (20 keV) and micro-computed tomography (40 keV), the effects of electron transport on the DQE are negligible compared to fluorescence reabsorption, which can lead to decreases of up to 30% and 20% in a-Se and Pb, respectively, at 20 keV; and 10% and 5%, respectively, at 40 keV. It is shown that when Swank noise is identified in a Fourier model, the Swank factor must be frequency dependent. This factor decreases quickly with frequency, and in the case of a-Se and Pb, decreases by up to a factor of 3 at five cycles/mm immediately above the K edge. The frequency-dependent Swank factor is also equivalent to what we call the "photoelectric DQE," which describes signal and noise transfer through photoelectric interactions.     

Kilovision: thermal modeling of a kilovoltage x-ray source integrated into a medical linear accelerator

The thermal and thermo-mechanical (fatigue) properties of a stationary-anode kilovoltage x-ray source that can be integrated into the head of a medical linear accelerator have been modeled. A finite element program has been used to model two new target designs. The first design makes minor modifications to the existing target assembly of a Varian medical linear accelerator, while the second design adds an additional cooling tube, changes the target angle, and uses a tungsten-rhenium alloy rather than tungsten as the kilovoltage target material. The thermal calculations have been used to generate cyclic stress/strain values from which estimates of fatigue in the target designs have been made. Both kilovoltage and megavoltage operation have been studied. Analysis of the megavoltage operation shows that there are only small differences in the thermal and fatigue characteristics after the target assembly is modified to include a kilovoltage target. Thus, megavoltage operation should not be compromised. The first kilovoltage target design can handle a 900 W heat load (e.g., 120 kVp, 7.5 mA, 2 x 2 mm2 source size); the heat load being limited by the temperature at the surface of the cooling tubes and mechanical fatigue at the surface of the target. The second design can handle a 1250 W heat load (e.g., 120 kVp, approximately 10.4 mA, 2 x 2 mm2 source size). Our calculations show that installation of a kilovoltage x-ray target is practical from thermal and thermo-mechanical perspectives.     

Clinical implementation of AAPM TG61 protocol for kilovoltage x-ray beam dosimetry

Historically, there have been a variety of dosimetry protocols used for kilovoltage x-ray therapy beams with a set of conversion factors and correction factors taken from different references. Corresponding to the continued installation and use of kilovoltage machines, the American Association of Physicists in Medicine (AAPM) presented a unified protocol developed by Task Group 61 (TG61). TG61 determines the absorbed dose to water with an ionization chamber calibrated in air in terms of air kerma (Nk). TG61 presents both an in-air method and an in-phantom method. In this work we only examine the TG61 in-air method. Our traditional dosimetry procedure, which is based upon NCRP Report 69 and on material found in standard medical physics texts, has been compared to the TG61. A variety of kilovoltage beam energies were examined with a set of various field sizes and source to surface distances. TG61 published updated data for the mass absorption coefficient ratios, backscatter factors, and the average energy per ion pair factor. The following conclusions have been reached: (1) Our traditional procedures and the TG61 protocol for in-air measurements are equivalent. (2) The conversion and correction factors used in TG61 are different by up to 4.5% compared to the old factors that we have used. (3) The application of the TG61 factors can result in up to 5% differences in the determination of the absorbed dose.     

Does kV-MV dual-energy computed tomography have an advantage in determining proton stopping power ratios in patients?

Conventional kilovoltage (kV) x-ray-based dual-energy CT (DECT) imaging using two different x-ray energy spectra is sensitive to image noise and beam hardening effects. The purpose of this study was to evaluate the theoretical advantage of the DECT method for determining proton stopping power ratios (SPRs) using a combination of kV and megavoltage (MV) x-ray energies. We investigated three representative x-ray energy pairs: 100 and 140 kVp comprised the kV-kV pair, 100 kVp and 1 MV comprised the kV-MV pair, and two 1 MV x-ray beams-one with and one without external filtration-comprised the MV-MV pair. The SPRs of 34 human tissues were determined using the DECT method with these three x-ray energy pairs. Small perturbations were introduced into the CT numbers and x-ray spectra used for the DECT calculation to simulate the effects of random noise and beam hardening. An error propagation analysis was performed on the DECT calculation algorithm to investigate the propagation of CT number uncertainty to final SPR estimation and to suggest the best x-ray energy combination. We found that the DECT method using each of the three beam pairs achieved similar accuracy in determining the SPRs of human tissues in ideal conditions. However, when CT number uncertainties and artifacts such as imaging noise and beam hardening effects were considered, the kV-MV DECT improved the accuracy of SPR estimation substantially over the kV-kV or MV-MV DECT methods. Furthermore, our error propagation analysis showed that the combination of 100 kVp and 1 MV beams was close to the optimal selection when using the DECT method to determine SPRs. Overall, the kV-MV combination makes the DECT method more robust in resolving the effective atomic numbers for biological tissues than the traditional kV-kV DECT method.     

Quantitative measurement of small-angle gamma ray scattering from water, nylon, and Lucite

The small-angle (2 degrees-10 degrees) total-differential-scattering cross sections of water, methyl methacrylate, and nylon 6 have been measured at a photon energy of 59.54 keV. An annular target geometry has been used with an acceptance of +/- 0.5 degrees and an experimental uncertainty of approximately 4% achieved. The experimental methods and data corrections necessary to obtain this accuracy are discussed in detail. The results demonstrate clearly the contribution of intermolecular effects to the scattering process and allow critical comparison with calculations using molecular form factors for water obtained from interpolated x-ray diffractometer data; agreement is obtained within the experimental uncertainties. They also support earlier Monte Carlo predictions of scattering in water at angles of the order of 2 degrees which are in disagreement with certain published experimental data.