The effect of dose calculation uncertainty on the evaluation of radiotherapy plans

Monte Carlo dose calculations will potentially reduce systematic errors that may be present in currently used dose calculation algorithms. However, Monte Carlo calculations inherently contain random errors, or statistical uncertainty, the level of which decreases inversely with the square root of computation time. Our purpose in this study was to determine the level of uncertainty at which a lung treatment plan is clinically acceptable. The evaluation methods to decide acceptability were visual examination of both isodose lines on CT scans and dose volume histograms (DVHs), and reviewing calculated biological indices. To study the effect of systematic and/or random errors on treatment plan evaluation, a simulated "error-free" reference plan was used as a benchmark. The relationship between Monte Carlo statistical uncertainty and dose was found to be approximately proportional to the square root of the dose. Random and systematic errors were applied to a calculated lung plan, creating dose distributions with statistical uncertainties of between 0% and 16% (1 s.d.) at the maximum dose point and also distributions with systematic errors of -16% to 16% at the maximum dose point. Critical structure DVHs and biological indices are less sensitive to calculation uncertainty than those of the target. Systematic errors affect plan evaluation accuracy significantly more than random errors, suggesting that Monte Carlo dose calculation will improve outcomes in radiotherapy. A statistical uncertainty of 2% or less does not significantly affect isodose lines, DVHs, or biological indices.

Comparison of EGS4 and MCNP4b Monte Carlo codes for generation of photon phase space distributions for a Varian 2100C

Monte Carlo based dose calculation algorithms require input data or distributions describing the phase space of the photons and secondary electrons prior to the patient-dependent part of the beam-line geometry. The accuracy of the treatment plan itself is dependent upon the accuracy of this distribution. The purpose of this work is to compare phase space distributions (PSDs) generated with the MCNP4b and EGS4 Monte Carlo codes for the 6 and 18 MV photon modes of the Varian 2100C and determine if differences relevant to Monte Carlo based patient dose calculations exist. Calculations are performed with the same energy transport cut-off values. At 6 MV, target bremsstrahlung production for MCNP4b is approximately 10% less than for EGS4, while at 18 MV the difference is about 5%. These differences are due to the different bremsstrahlung cross sections used in the codes. Although the absolute bremsstrahlung production differs between MCNP4b and EGS4, normalized PSDs agree at the end of the patient-independent geometry (prior to the jaws), resulting in similar dose distributions in a homogeneous phantom. EGS4 and MCNP4b are equally suitable for the generation of PSDs for Monte Carlo based dose computations.

A method to predict the effect of organ motion and set-up variations on treatment plans

Dose distributions calculated by commercial treatment planning systems do not allow incorporation of the effects of patient position variation or organ motion throughout the course of radiation therapy treatment. We have established a convolution-based method, which enables us to display dose distributions using a commercial treatment planning system that can take into account target movement. An example of the method applied to a prostate treatment plan is presented. For the method to be of clinical use it requires assessment of the parameters leading to target movement in a scientific manner in the same treatment department that it is to be used. It is not sufficient to rely on published data especially that relating to set-up accuracy as this has been shown to vary widely from centre to centre. We believe that with appropriate movement data, a convolution-based approach can lead to more optimal radiation margins around clinical target volumes (CTV). Optimal margins will help prevent geometric misses as well as ensure that the amount of critical late reacting normal tissues surrounding the CTV irradiated is minimised. Optimal margins cannot be guaranteed with the more conventionally used "rule of thumb" techniques for placing a planning target volume around the CTV.

Comparisons between MCNP, EGS4 and experiment for clinical electron beams

Understanding the limitations of Monte Carlo codes is essential in order to avoid systematic errors in simulations, and to suggest further improvement of the codes. MCNP and EGS4, Monte Carlo codes commonly used in medical physics, were compared and evaluated against electron depth dose data and experimental backscatter results obtained using clinical radiotherapy beams. Different physical models and algorithms used in the codes give significantly different depth dose curves and electron backscattering factors. The default version of MCNP calculates electron depth dose curves which are too penetrating. The MCNP results agree better with experiment if the ITS-style energy-indexing algorithm is used. EGS4 underpredicts electron backscattering for high-Z materials. The results slightly improve if optimal PRESTA-I parameters are used. MCNP simulates backscattering well even for high-Z materials. To conclude the comparison, a timing study was performed. EGS4 is generally faster than MCNP and use of a large number of scoring voxels dramatically slows down the MCNP calculation. However, use of a large number of geometry voxels in MCNP only slightly affects the speed of the calculation.

Bremsstrahlung production from a linac target in the presence of external magnetic fields

A method to increase the photon fluence of the linac is to apply a magnetic field to the bremsstrahlung producing electrons in the target. This field changes the electron paths, and therefore the photon trajectories. In this research Monte Carlo techniques are used to model the effect of three separate magnetic field configurations applied to a tungsten target, on the forward projection of bremsstrahlung created from incident 6 MeV electrons. A radial fluence spectrum is produced for each magnetic field. The maximum increase in fluence is shown to be around 10% for a physically possible field. We conclude that the cost of constructing and installing such magnets (currently) outweighs the small increase in fluence yield.

Photon buildup in orthovoltage X-ray beams

Orthovoltage x-ray beams exhibit the characteristic of depth dose buildup which is not well described in the literature. The principal reason for this phenomenon is the increase in dose deposited due to electrons set in motion by secondary (Compton) scattered photons within the phantom, as depth is increased until longitudinal equilibrium is reached. This happens within a few millimetres of the surface and has been demonstrated both experimentally and by Monte Carlo methods. The Monte Carlo technique also enabled description of a second order primary dose buildup effect (due to longitudinal electronic disequilibrium) that would be impossible to detect with conventional detectors due to the short range of the electrons. The magnitude of buildup was observed to alter with various combinations of beam parameters. Variations will also occur with detectors used to measure buildup. It is recommended that radiation oncology departments assess this effect in the context of their clinical data in current use to ensure that there are not doses higher than prescribed being applied a few millimetres below the skin surface, especially if data was collected with a thin windowed, parallel plate ionisation chamber and/or that coarse steps for depth dose data collection were used along the beam central axis.

Super-Monte Carlo: a 3-D electron beam dose calculation algorithm

An electron beam dose calculation algorithm has been developed which is based on a superposition of pregenerated Monte Carlo electron track kernels. Electrons are transported through media of varying density and atomic number using electron tracks produced in water. The perturbation of the electron fluence due to each material encountered by the electrons is explicitly accounted for by considering the effect of (i) varying stopping power, (ii) scattering power, and (iii) radiation yield. For each step of every electron track, these parameters affect the step length, the step direction, and for energy deposited in that step respectively. Dose distributions in both homogeneous water and nonwaterlike phantoms, and heterogeneous phantoms show consistent agreement with "standard" Monte Carlo results. For the same statistical uncertainty in broad beam geometries, this new calculation method uses a factor of 9 less computation time than a full Monte Carlo simulation.

A review of electron beam dose calculation algorithms

The advantage of accurate dose calculation in radiotherapy is the availability of better quality information with which to prescribe treatments, and also increased confidence when optimisation procedures are applied in the planning process. Due to the continual increase in computation speed through improvements in technology, a number of advanced electron beam dose calculation algorithms have recently been developed which incorporate physically rigorous modelling of the scattering and interaction processes involved in electron transport. These algorithms are significantly more accurate than those employed by commercially available radiotherapy planning systems. The advantages and disadvantages of the 3D Pencil beam method, the Pencil Beam Redefinition Method, the Multi-ray model, theoretical perturbative methods, the Phase Space Evolution model, Monte Carlo techniques, the Superposition/Convolution method, the Macro-Monte Carlo algorithm, the Super-Monte Carlo method and the Voxel-based Monte Carlo method are discussed in this review.

Modelling clinical accelerator beams: a review

Radiotherapy dose calculation algorithms currently under development (and some in use) require knowledge of the characteristics of particles in linear accelerator-generated radiation beams. A range of techniques have been developed which allow determination of those characteristics requiring minimal interaction with the physical beam. Such techniques may be analytical in nature, making use of analytical transport results and cross sections, or they may be numerical, employing the increasing utility of Monte Carlo techniques. These techniques provide us with an extensive description of clinical beams and the ability to refine beam production and collimation systems. This review details several published analytical and numerical approaches to megavoltage photon and electron beam modelling, the characteristics that they provide, and their relative accuracy and utility.

Calculating the angular standard deviation of electron beams using Fermi-Eyges theory

Knowledge of the angular distribution of an electron beam at the applicator face is a necessary parameter in defining a beam when the Hogstrom pencil beam method of dose calculation is used. The angular spread can be found experimentally using penumbra widths measured at various distances from the applicator face. Using knowledge of the geometry and composition of the scattering foils of the linear accelerator, the angular standard deviation was calculated theoretically using Fermi-Eyges theory. The obtained angular spread values agree with experimentally derived values to within experimental error for electron energies from 6 to 21 MeV. The Fermi-Eyges calculation is fast, and can be used as a quick check to validate experimental angular spread values.

Superposition dose calculation incorporating Monte Carlo generated electron track kernels

The superposition/convolution method and the transport of pregenerated Monte Carlo electron track data have been combined into the Super-Monte Carlo (SMC) method, an accurate 3-D x-ray dose calculation algorithm. The primary dose (dose due to electrons ejected by primary photons) is calculated by transporting pregenerated (in water) Monte Carlo electron tracks from each primary photon interaction site, weighted by the terma for that site. The length of each electron step is scaled by the inverse of the density of the medium at the beginning of the step. Because the density scaling of the electron tracks is performed for each individual transport step, the limitations of the macroscopic scaling of kernels (in the superposition algorithm) are overcome. This time-consuming step-by-step transport is only performed for the primary dose calculation, where current superposition methods are most lacking. The scattered dose (dose due to electrons set in motion by scattered photons) is calculated by superposition. In both a water-lung-water phantom and a two lung-block phantom, SMC dose distributions are more consistent with Monte Carlo generated dose distributions than are superposition dose distributions, especially for small fields and high energies-for an 18-MV, 5 X 5-cm(2) beam, the central axis dose discrepancy from Monte Carlo is reduced from 4.5% using superposition to 1.5% using SMC. The computation time for this technique is approximately 2 h (depending on the simulation history), 20 times slower than superposition, but 15 times faster than a full Monte Carlo simulation (on our platform).

The angular and energy distribution of the primary electron beam

The angular distribution for electron beams produced by the Siemens KD-2 linear accelerator has been found by simulating electron transport through the scattering foils and air using two methods: Fermi-Eyges multiple Coulomb scattering calculations, and EGS4 Monte Carlo simulations. Fermi-Eyges theory gives solutions where both the angular and spatial fluence distributions are Gaussian, with the angular standard deviation being invariant with off-axis distance. The EGS4 results show slightly non-Gaussian angular and lateral distributions as a result of the use of Moliére theory rather than Fermi-Eyges multiple scattering theory, as well as the simulation of discrete bremsstrahlung and Møller interactions. However, the results from both methods are very similar. The angular standard deviations obtained by these methods agree very closely with those found experimentally. The similar shape of the Monte Carlo and Fermi-Eyges results indicate that a Gaussian approximation to the incident angular distribution will be adequate for use in treatment planning algorithms. Furthermore, the angular standard deviation may be determined using Fermi-Eyges theory as an alternative to experimental methods. Both Monte Carlo simulations, and Fermi-Eyges theory predict that the mean electron angle is proportional to off axis distance for all useful field sizes. For a 15 MeV electron beam, an effective source position of 99 cm and 98 cm from the nominal 100 SSD plane was obtained from Fermi-Eyges and Monte Carlo results respectively for a 15 MeV beam. The effective source position found experimentally for this energy was 98 cm.(ABSTRACT TRUNCATED AT 250 WORDS)