Angular distribution and yield from bremsstrahlung targets (for radiation therapy)

Low Z target switching to increase tumor endothelial cell dose enhancement during gold nanoparticle-aided radiation therapy

PURPOSE

Previous studies have introduced gold nanoparticles as vascular-disrupting agents during radiation therapy. Crucial to this concept is the low energy photon content of the therapy radiation beam. The authors introduce a new mode of delivery including a linear accelerator target that can toggle between low Z and high Z targets during beam delivery. In this study, the authors examine the potential increase in tumor blood vessel endothelial cell radiation dose enhancement with the low Z target.

METHODS

The authors use Monte Carlo methods to simulate delivery of three different clinical photon beams: (1) a 6 MV standard (Cu/W) beam, (2) a 6 MV flattening filter free (Cu/W), and (3) a 6 MV (carbon) beam. The photon energy spectra for each scenario are generated for depths in tissue-equivalent material: 2, 10, and 20 cm. The endothelial dose enhancement for each target and depth is calculated using a previously published analytic method.

RESULTS

It is found that the carbon target increases the proportion of low energy (<150 keV) photons at 10 cm depth to 28% from 8% for the 6 MV standard (Cu/W) beam. This nearly quadrupling of the low energy photon content incident on a gold nanoparticle results in 7.7 times the endothelial dose enhancement as a 6 MV standard (Cu/W) beam at this depth. Increased surface dose from the low Z target can be mitigated by well-spaced beam arrangements.

CONCLUSIONS

By using the fast-switching target, one can modulate the photon beam during delivery, producing a customized photon energy spectrum for each specific situation.

Simulation of a medical linear accelerator for teaching purposes

Simulation software for medical linear accelerators that can be used in a teaching environment was developed. The components of linear accelerators were modeled to first order accuracy using analytical expressions taken from the literature. The expressions used constants that were empirically set such that realistic response could be expected. These expressions were programmed in a MATLAB environment with a graphical user interface in order to produce an environment similar to that of linear accelerator service mode. The program was evaluated in a systematic fashion, where parameters affecting the clinical properties of medical linear accelerator beams were adjusted independently, and the effects on beam energy and dose rate recorded. These results confirmed that beam tuning adjustments could be simulated in a simple environment. Further, adjustment of service parameters over a large range was possible, and this allows the demonstration of linear accelerator physics in an environment accessible to both medical physicists and linear accelerator service engineers. In conclusion, a software tool, named SIMAC, was developed to improve the teaching of linear accelerator physics in a simulated environment. SIMAC performed in a similar manner to medical linear accelerators. The authors hope that this tool will be valuable as a teaching tool for medical physicists and linear accelerator service engineers.

PACS number: 87.55Gh, 87.56bd

Feasibility of using intermediate x-ray energies for highly conformal extracranial radiotherapy

PURPOSE

To investigate the feasibility of using intermediate energy 2 MV x-rays for extracranial robotic intensity modulated radiation therapy.

METHODS

Two megavolts flattening filter free x-rays were simulated using the Monte Carlo code MCNP (v4c). A convolution/superposition dose calculation program was tuned to match the Monte Carlo calculation. The modeled 2 MV x-rays and actual 6 MV flattened x-rays from existing Varian Linacs were used in integrated beam orientation and fluence optimization for a head and neck, a liver, a lung, and a partial breast treatment. A column generation algorithm was used for the intensity modulation and beam orientation optimization. Identical optimization parameters were applied in three different planning modes for each site: 2, 6 MV, and dual energy 2/6 MV.

RESULTS

Excellent agreement was observed between the convolution/superposition and the Monte Carlo calculated percent depth dose profiles. For the patient plans, overall, the 2/6 MV x-ray plans had the best dosimetry followed by 2 MV only and 6 MV only plans. Between the two single energy plans, the PTV coverage was equivalent but 2 MV x-rays improved organs-at-risk sparing. For the head and neck case, the 2 MV plan reduced lips, mandible, tongue, oral cavity, brain, larynx, left and right parotid gland mean doses by 14%, 8%, 4%, 14%, 24%, 6%, 30% and 16%, respectively. For the liver case, the 2 MV plan reduced the liver and body mean doses by 17% and 18%, respectively. For the lung case, lung V 20, V 10, and V5 were reduced by 13%, 25%, and 30%, respectively. V 10 of heart with 2 MV plan was reduced by 59%. For the partial breast treatment, the 2 MV plan reduced the mean dose to the ipsilateral and contralateral lungs by 27% and 47%, respectively. The mean body dose was reduced by 16%.

CONCLUSIONS

The authors showed the feasibility of using flattening filter free 2 MV x-rays for extracranial treatments as evidenced by equivalent or superior dosimetry compared to 6 MV plans using the same inverse noncoplanar intensity modulated planning method.

Polarization transfer of bremsstrahlung arising from spin-polarized electrons

We report on a study of the polarization transfer between transversely polarized incident electrons and the emitted x rays for electron-atom bremsstrahlung. By means of Compton polarimetry we performed for the first time an energy-differential measurement of the complete properties of bremsstrahlung emission related to linear polarization, i.e., the degree of linear polarization as well as the orientation of the polarization axis. For the high-energy end of the bremsstrahlung continuum the experimental results for both observables show a high sensitivity on the initial electron spin polarization and prove that the polarization orientation is virtually independent of the photon energy.

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

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.

A theoretical model for the production of Ac-225 for cancer therapy by photon-induced transmutation of Ra-226

Radium needles that were once implanted into tumours as a cancer treatment are now obsolete and constitute a radioactive waste problem, as their half-life is 1600 years. We are investigating the reduction of radium by transmutation on a small scale by bombarding Ra-226 with high-energy photons from a medical linear accelerator (linac) to produce Ra-225, which subsequently decays to Ac-225, which can be used as a generator to produce Bi-213 for use in 'targeted alpha therapy' for cancer. This paper examines the possibility of producing Ac-225 with a linac using an accurate theoretical model in which the bremsstrahlung photon spectrum at 18 MV linac electron energy is convoluted with the corresponding photonuclear cross sections of Ra-226. The total integrated yield can then be obtained and is compared with a computer simulation. This study shows that at 18 MV, the photonuclear reaction on Ra-226 can produce low activities of Ac-225 with a linac. However, a high power linac with high current, pulse length and frequency is needed to produce practical amounts of Ac-225 and a useful reduction of Ra-226.

Monte Carlo modelling of external radiotherapy photon beams

An essential requirement for successful radiation therapy is that the discrepancies between dose distributions calculated at the treatment planning stage and those delivered to the patient are minimized. An important component in the treatment planning process is the accurate calculation of dose distributions. The most accurate way to do this is by Monte Carlo calculation of particle transport, first in the geometry of the external or internal source followed by tracking the transport and energy deposition in the tissues of interest. Additionally, Monte Carlo simulations allow one to investigate the influence of source components on beams of a particular type and their contaminant particles. Since the mid 1990s, there has been an enormous increase in Monte Carlo studies dealing specifically with the subject of the present review, i.e., external photon beam Monte Carlo calculations, aided by the advent of new codes and fast computers. The foundations for this work were laid from the late 1970s until the early 1990s. In this paper we will review the progress made in this field over the last 25 years. The review will be focused mainly on Monte Carlo modelling of linear accelerator treatment heads but sections will also be devoted to kilovoltage x-ray units and 60Co teletherapy sources.

Dose calculations for external photon beams in radiotherapy

Dose calculation methods for photon beams are reviewed in the context of radiation therapy treatment planning. Following introductory summaries on photon beam characteristics and clinical requirements on dose calculations, calculation methods are described in order of increasing explicitness of particle transport. The simplest are dose ratio factorizations limited to point dose estimates useful for checking other more general, but also more complex, approaches. Some methods incorporate detailed modelling of scatter dose through differentiation of measured data combined with various integration techniques. State-of-the-art methods based on point or pencil kernels, which are derived through Monte Carlo simulations, to characterize secondary particle transport are presented in some detail. Explicit particle transport methods, such as Monte Carlo, are briefly summarized. The extensive literature on beam characterization and handling of treatment head scatter is reviewed in the context of providing phase space data for kernel based and/or direct Monte Carlo dose calculations. Finally, a brief overview of inverse methods for optimization and dose reconstruction is provided.

An accurate energy-range relationship for high-energy electron beams in arbitrary materials

A general analytical energy-range relationship has been derived to relate the practical range, Rp, to the most probable energy, Ep, of incident electron beams in the range 1 to 50 MeV and above, for absorbers of any atomic number. The expression is cubic in energy and requires as input parameters the total stopping power, So, the ratio of the scattering power and the total specific stopping power, T0/epsilon0, both taken at 10 MeV, and the radiation length for the material involved, X0. In addition to these parameters, five of the derived parameters are used to 'fine tune' the equation and minimize the mean square deviation from experimental and/or Monte Carlo data by means of non-linear regression. In the present study only Monte Carlo data determined with the new ITS.3 code have been employed. The standard deviations of the mean deviation from the Monte Carlo data at any energy are about 0.10, 0.12, 0.04, 0.11, 0.04, 0.03, 0.02 mm for Be, C, H2O, Al, Cu, Ag and U, respectively, and the relative standard deviation of the mean is about 0.5% for all materials. The fitting program gives some priority to water-equivalent materials, which explains the low standard deviation for water. A small error in the fall-off slope can give a different value for Rp. We describe a new method which reduces the uncertainty in the Rp determination, by fitting an odd function to the descending portion of the depth-dose curve in order to accurately determine the tangent at the inflection point, and thereby the practical range. An approximate inverse relation is given expressing the most probable energy of an electron beam as a function of the practical range. The resultant relative standard error of the energy is less than 0.7%, and the maximum energy error deltaEp is less than 0.3 MeV.

Scanned intensity modulations for 50 MV photons

Optimization of the dose distributions by individual beam compensation is a useful tool in conformal radiation therapy. Intensity modulation by electromagnetic scanning of a narrow elementary beam allows fast dose delivery and causes little change in beam quality compared with other methods, especially for high energies such as 50 MV. Intensity modulated beams from the MM50 accelerator were measured and compared with calculations based on Monte Carlo simulations. Good agreement between measurements and calculations were found, typically within 1% for central dose profiles. The steepest wedge angle that was produced with the scanning beam technique was of 45 degrees or 3.5% cm(-1) for a 20 cm x 20 cm field, slightly varying with depth. The elementary 50 MV photon 'pencil beam' for a full range, high-z bremsstrahlung target, is a wide dose distribution at 10 cm depth in water which limits the modulation gradient and hence the complexity of the modulation by the scanning of a photon pencil beam only. Scanned wedge beam distributions were modelled in the treatment planning system and a pelvic treatment with three fields was used to illustrate a clinical application. The resulting dose volume data were compared for different radiation qualities but with similar beam portals. 'Energy modulation' by field matching with lower photon energies was performed to sharpen the penumbra towards organs at risk.

Target, purging magnet and electron collector design for scanned high-energy photon beams

A new method for producing very narrow and intense 50 MV bremsstrahlung beams with a half-width as low as 35 mm at a distance of 1 m from the target is presented. Such a beam is well suited for intensity modulation using scanned photon beams. An algorithm has been developed to minimize the width of the bremsstrahlung beam generated in a multilayer target by varying the individual layer thicknesses and atomic numbers under given constraints on the total target thickness and the mean energy of the transmitted electrons. Under such constraints the narrowest possible bremsstrahlung beam is obtained with a target composed of layers of monotonically increasing atomic number starting with the lowest possible value at the entrance side where the electrons impinge. It is also shown that the narrowest photon beam profile is associated with the highest possible forward photon yield. To be able to use the optimized target clinically it is desirable to be able to collect and stop all the electrons that are transmitted through the target. The electrons are most efficiently collected if they are kept close together, i.e. by minimizing the multiple scatter of the electrons and consequently the half-width of the generated bremsstrahlung beam. This is achieved by a thin low-atomic-number target. A dedicated electron stopper has been developed and integrated with the purging magnet. When the electron stopper is combined with a purging magnet, a primary photon collimator and a multileaf collimator, almost all of the transmitted electrons and their associated bremsstrahlung contamination can effectively be collected. The narrow photon beams from thin low-atomic-number targets have the additional advantage of producing the hardest and most penetrative photon spectrum possible, which is ideal for treating large deep-seated tumours.

Calculation of photon energy and dose distributions in a 50 MV scanned photon beam for different target configurations and scan patterns

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.

The role of phantom and treatment head generated bremsstrahlung in high-energy electron beam dosimetry

An analytical expression has been derived for the phantom generated bremsstrahlung photons in plane-parallel monoenergetic electron beams normally incident on material of any atomic number (Be, H2O, Al, Cu and U). The expression is suitable for the energy range from 1 to 50 MeV and it is solely based on known scattering power and radiative and collision stopping power data for the material at the incident electron energy. The depth dose distribution due to the bremsstrahlung generated by the electrons in the phantom is derived by convolving the bremsstrahlung energy fluence produced in the phantom with a simple analytical energy deposition kernel. The kernel accounts for both electrons and photons set in motion by the bremsstrahlung photons. The energy loss by the primary electrons, the build-up of the electron fluence and the generation, attenuation and absorption of bremsstrahlung photons are all taken into account in the analytical formula. The longitudinal energy deposition kernel is derived analytically and it is consistent with both the classical biexponential relation describing the photon depth dose distribution and the exponential attenuation of the primary photons. For comparison Monte Carlo calculated energy deposition distributions using ITS3 code were used. Good agreement was found between the results with the analytical expression and the Monte Carlo calculation. For tissue equivalent materials, the maximum total energy deposition differs by less than 0.2% from Monte Carlo calculated dose distributions. The result can be used to estimate the depth dependence of phantom generated bremsstrahlung in different materials in therapeutic electron beams and the bremsstrahlung production in different electron absorbers such as scattering foils, transmission monitors and photon and electron collimators. By subtracting the phantom generated bremsstrahlung from the total bremsstrahlung background the photon contamination generated in the treatment head can be determined to allow accurate dosimetry of heavily photon contaminated electron beams.

Effective source size, yield and beam profile from multi-layered bremsstrahlung targets

Modern conformal radiotherapy benefits from heterogeneous dose delivery using scanned narrow bremsstrahlung beams of high energy in combination with dynamic double focused multi-leaf collimation and purging magnets. When using a purging magnet to remove electrons and positrons the target space is limited and unorthodox thin multi-layered targets are needed. A computational technique has therefore been developed to determine the forward yield and the angular distributions of the bremsstrahlung beam as well as the size and location of the effective and the virtual photon point source for arbitrary multi-layer bremsstrahlung targets. The Gaussian approximation of the diffusion equation for the electrons has been used and convolved with the bremsstrahlung production process. For electrons with arbitrary emittance impinging on targets of any multi-layer and atomic number combination, the model is well applicable, at least for energies in the range 1-100 MeV. The intrinsic bremsstrahlung photon profile has been determined accurately by deconvolving the electron multiple scattering process from thin experimental beryllium target profiles. For electron pencil beams incident on a target of high density and atomic number such as tungsten, the size of the effective photon source stays at around a tenth of a millimetre. The effective photon source for low-Z materials such as Be, C and Al is located at depths from 3-7 mm in the target, decreasing with increasing atomic number. The effective photon source at off-axis positions then moves out considerably from the central axis, which should be considered when aligning collimators. For high-Z materials such as tungsten, the location of the effective photon source is at a few tenths of a millimetre deep. The virtual photon point source is located only a few tenths of a millimetre upstream of the effective photon source both for high- and low-Z materials. For 50 MeV electrons incident on multi-layered full range targets the radial energy fluence distributions will have a full width at half maximum (FWHM) of 80 to 100 mm at 1 m from the target. The best target composition made of two layers when the space is limited to 15 mm was found to be 9 mm-Be followed by 6 mm W. A thin beryllium target (approximately 3 mm) results in a high-intensity bremsstrahlung lobe with a FWHM of about 35 mm at the isocentre. Interestingly, the forward dose rate in such a beam is as high as 62% of the maximum achievable with an optimal target design, even if on average only 1 MeV is lost by the electrons.

Photon field quantities and units for kernel based radiation therapy planning and treatment optimization

The problem of choosing radiation quantities and units for energy deposition kernels and their associated kernel densities is treated with the aim of making them consistent with related classical radiation quantities and units such as restricted mass stopping powers and mass attenuation coefficients. It is shown that it is very useful to define the kernels h(r), in terms of the quotient of the mean specific energy imparted to the medium by the radiant energy incident on a volume element centred at the origin of the kernel. The basic building block used to generate these kernels is the point energy deposition kernel, h(p), describing the spatial distribution of the energy imparted by a photon interacting at a point in a medium. This will allow the kernels to be regarded as generalizations of the traditional mass stopping and attenuation coefficients, which in detail describe the spatial distribution of the mean energy deposition around an interaction site. As a consequence, the irradiation or kernel density, f(r) should be expressed in terms of the radiant energy incident per unit volume of the medium. It is shown that the kernel density is equal to minus the divergence of the incident unattenuated vectorial energy fluence, and it therefore acts as an irradiation density for the incident vectorial energy fluence. The microscopic kernels or the irradiation density may thus be viewed as a perfect 'sink' distribution to the required incident photon energy fluence which is totally absorbed at f(r), and instead replaced by the kernels which describe the detailed energy deposition in the medium in coordinates centred at the sinks. From these definitions the required incident energy fluence from an external radiation source used for treatment realization can be determined directly by projecting the irradiation density on the relevant positions of the radiation source. This procedure has the valuable property that maximal calculational accuracy is achieved in the tumour because the irradiation density has non-zero values only in the tumour, and the accuracy of the kernel is highest at its origin.

Determination of effective bremsstrahlung spectra and electron contamination for photon dose calculations

A method is described for determining an effective, depth dose consistent bremsstrahlung spectra for high-energy photon beams using depth dose curves measured in water. A simple, analytical model with three parameters together with the nominal accelerating potential is used to characterise the bremsstrahlung spectra. The model is used to compute weights for depth dose curves from monoenergetic photons. These monoenergetic depth doses, calculated with the convolution method from Monte Carlo generated point spread functions (PSF), are added to yield the pure photon depth dose distribution. The parameters of the analytical spectrum model are determined using an iterative technique to minimise the difference between calculated and measured depth dose curves. The influence from contaminant electrons is determined from the difference between the calculated and the measured depth dose.

Design principles and clinical possibilities with a new generation of radiation therapy equipment. A review

The main steps in the development of isocentric megavoltage external beam radiation therapy machines are briefly reviewed identifying three principal types or generations of equipment to date. The new fourth generation of equipment presented here is characterized by considerably increased flexibility in dose delivery through the use of scanned elementary electron and photon beams of very high quality. Furthermore the wide energy range and the possibility of using high resolution multileaf collimation with all beam modalities makes it possible to simplify irradiation techniques and increase the accuracy in dose delivery. The main design features are described including a dual dipole magnet scanning system, a photon beam purging magnet, a helium atmosphere in the treatment head, a beam's eye view video read-out system of the collimator setting and a radiotherapeutic computed tomography facility. Some of the clinical applications of this new type of radiation therapy machine are finally reviewed, such as the ease of performing beam flattening, beam filtering and compensation, and the simplification of many treatment techniques using the wide spectrum of high quality electron and photon beams. Finally the interesting possibility of doing conformation and more general isocentric treatments with non-uniform beams using the multileaf collimator and the scanning system are demonstrated.

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.

Computer assisted dosimetry of scanned electron and photon beams for radiation therapy

A computer controlled beam forming system for energies up to 50 MeV has been developed in order to produce high quality electron and photon beams for radiation therapy. The desired radiation field shape and dose distribution are achieved by programming the scanning pattern of a narrow and unfiltered electron or photon beam. The computer that controls the scanning pattern also performs dosimetric analyses in the resultant radiation beams. The system allows real time display of the measured dose distributions at a rate of up to five discrete dose values per second for a 15 cm square field. Measurements in scanned as well as in stationary electron and photon beams at energies of 10, 20 and 50 MeV are presented. Finally, the consequences of photon generated electrons in the very broad high energy photon beams that can be produced by a scanning system are illustrated and discussed.