X-Ray Spectra from Accelerators in the range 2 to 6 MeV

Determination of the photon spectrum of a therapeutic linear accelerator near the maze entrance: Comparison of Monte Carlo modeling and measurements using scintillation detectors corrected for pulse pile-up

PURPOSE

The determination of x-ray spectra near the maze entrance of linear accelerator (LINAC) rooms is challenging due to the pulsed nature of the LINAC source. Mathematical methods to account for pulse pile-up have been examined. These methods utilize the highly periodic pulsing structure of the LINAC, differing from the effects of high-intensity radioactive sources.

METHODS

Sodium iodide (NaI) and plastic scintillation detectors were used to determine the energy spectra at different points near the maze entrance of a medical LINAC. Monte Carlo calculations of the energy distribution of scattered photons were used to simulate the energy spectrum at the maze entrance. The proposed algorithm uses the Monte Carlo code, FLUKA, to calculate a response function for both detectors. To determine the effects of the pile-up in the spectra, the Poisson distribution was used, employing the average number of photons per pulse (μ) interacting with the detector. The quantity, μ, was obtained from the ratio of the number of events detected to the number of pulses delivered. The energy spectra at various distances from the maze entrance were measured using NaI and plastic scintillation detectors. From these measurements, the values of µ were calculated, and the pile-up probability was determined. The FLUKA Monte Carlo code was used to calculate the spectrum at the maze entrance and the response matrices of the NaI and plastic scintillation detectors. The algorithm based on the Poisson distribution was applied to calculate the spectrum.

RESULTS

The agreement between the calculated and measured spectra was within the first standard deviation of the variance expected in µ. This agreement confirms that photons at the maze entrance have energies between 30 and 240 keV for a maze with three turns, with an average energy of around 85 keV. After pile-up correction, the range of the pulse height distribution with the plastic scintillation detector, which has a low atomic number, was decreased (0 to 140 keV). In contrast, the range of the pulse height distribution with the NaI scintillation detector was closer to the photon spectrum (0 to 240 keV).

CONCLUSIONS

The corrected spectrum demonstrates that using a FLUKA Monte Carlo code and an algorithm based on the Poisson distribution are effective methods in removing the distortion due to the pile-up in LINAC spectra when measuring with NaI and plastic scintillation detectors. The agreement between the corrected and measured spectra indicates that Monte Carlo modeling can accurately determine the spectrum of a LINAC machine at the maze entrance.

Fifty years of Monte Carlo simulations for medical physics

Monte Carlo techniques have become ubiquitous in medical physics over the last 50 years with a doubling of papers on the subject every 5 years between the first PMB paper in 1967 and 2000 when the numbers levelled off. While recognizing the many other roles that Monte Carlo techniques have played in medical physics, this review emphasizes techniques for electron-photon transport simulations. The broad range of codes available is mentioned but there is special emphasis on the EGS4/EGSnrc code system which the author has helped develop for 25 years. The importance of the 1987 Erice Summer School on Monte Carlo techniques is highlighted. As an illustrative example of the role Monte Carlo techniques have played, the history of the correction for wall attenuation and scatter in an ion chamber is presented as it demonstrates the interplay between a specific problem and the development of tools to solve the problem which in turn leads to applications in other areas.

Reconstruction of megavoltage photon spectra from electronic portal imager derived transmission measurements

Three variants of the Schiff equation are investigated to model the spectra produced by megavoltage linear accelerators. These models are tested against well-validated Monte Carlo (MC) generated spectra on the central axis of large-area fields, and show excellent agreement. Numerical reconstructions of 6 and 10 MV spectra using the same models are then presented, using experimental attenuation data derived from an electronic portal imager. The process of deriving spectra from experimental attenuation data is shown to be inherently badly constrained mathematically, with the derived spectrum being highly sensitive to noise in the source data, and non-unique. By placing a priori constraints on the Schiff model from both physical knowledge of the construction of the accelerator and MC data, physically useful results are gained and presented for both the energy dependence and off-axis behaviour of photon spectra.

Reconstruction of megavoltage photon spectra by attenuation analysis

A simple analytical model for reconstructing photon spectra from the indirect measurement of transmission or depth-dose curves is presented, based on the Schiff expression for forward-directed bremsstrahlung differential in photon energy with added inherent filtration. Calculated transmission curves for 21 simulated and measured bremsstrahlung spectra with maximum photon energies in the range 4 to 30 MeV covering a broad range of filtration conditions were used to assess the model's ability to represent megavoltage spectra. Input data were reproduced to within 0.1 per cent in all cases, which is the same order of magnitude as the uncertainty involved in its calculation. Inclusion of a fourth parameter in the model is shown to allow the effective maximum photon energy present in the spectrum to be derived to an accuracy of approximately 3 per cent.

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.

Stopping power data for high-energy photon beams

Spencer-Attix stopping power ratios for the dosimetry of high-energy photon beams used in radiation therapy have been calculated using the Monte Carlo method. The stopping power ratios are calculated in a more consistent way than previously and are given as a function of the attenuation properties of the beam. The dependence of the stopping power ratio on the electron contamination of the beam as well as on depth and field size has also been investigated. Results are compared with stopping power ratios recommended in different dosimetry protocols and to experimental results. The agreement with most dosimetry protocols is within about one per cent and with recent experimental data is better than half a per cent.

Dosimetry and quality specification of high energy photon beams

A number of quality descriptors are defined characterizing the photon attenuation and lepton contamination properties of high energy photon beams for radiation therapy. The dependence of the quality parameters on the design of the clinical beams such as the incident electron energy, target and filter thicknesses, field size and depth in the phantom are analyzed in some detail using analytical and Monte Carlo techniques. It is shown that the mean attenuation coefficient of the beam for a standard field size of 10 cm X 10 cm is related very accurately to the mean stopping power ratio for ionizing chamber dosimetry but also approximately to the equilibrium absorbed dose in the beam for a given photon energy fluence. This means that accurate photon dosimetry can be performed without knowing the acceleration potential, target design or filter thickness for the beam in use. Furthermore, the mechanism behind beam hardening and softening in the phantom are quantitized and suitable quality parameters for the lepton contamination are identified. The latter allow a determination of the lepton contamination for correction of the stopping power ratio near the surface if the contamination is large.

Water/air mass stopping power ratios for megavoltage photon and electron beams

Water/air mass stopping power ratios have been calculated for 5, 10, 20 and 30 MeV electron beams and various photon beams from 60Co to 31 MV betatron. The stopping power ratios have been evaluated by applying a modified version of the Spencer-Attix theory to depth-dependent electron flux spectra computed by the Monte Carlo method. Results are presented for three values of the cavity size parameter delta, 0.001, 0.01 and 0.1 MeV, and also for a Bragg-Gray cavity. For the electron beams, the results are compared to Berger's comprehensive computations. In the case of the photon beams, such a rigorous evaluation of the stopping power ratio has not been carried out previously. It is shown that the currently used approximate Bragg-Gray ratios are as much as 2% too low for high energy photon beams, and that there is a difference of about 1% between values for betatron (thin target) and linac (thick target) beams of the same maximum photon energy.

Secondary radiation from a spherical tissue-equivalent phantom irradiated with 60Co gamma radiation and 6 MV X-rays

The angular dependence and the dependence on the phantom mass of the secondary exposure rate from spherical tissue-equivalent phantoms irradiated with 60Co gamma radiation and 6 MV X-rays have been investigated both by measurement and by calculation using the Monte Carlo method and approximate methods. A nonlinear dependence on the phantom mass was found. Calculation of the differential photon fluence was also made. These measurements and calculations can be used when calculating the required barrier thickness for walls which are not hit by primary radiation.