Electron pencil-beam redefinition algorithm dose calculations in the presence of heterogeneities.

The electron pencil-beam redefinition algorithm (PBRA) is currently being refined and evaluated for clinical use. The purpose of this work was to evaluate the accuracy of PBRA-calculated dose in the presence of heterogeneities and to benchmark PBRA dose accuracy for future improvements to the algorithm. The PBRA was evaluated using a measured electron beam dose algorithm verification data set developed at The University of Texas M. D. Anderson Cancer Center. The data set consists of measurements made using 9 and 20 MeV beams in a water phantom with air gaps, internal air and bone heterogeneities, and irregular surfaces. Refinements to the PBRA have enhanced the speed of the dose calculations by a factor of approximately 7 compared to speeds previously reported in published data; a 20 MeV, 15 x 15 cm2 field electron-beam dose distribution took approximately 10 minutes to calculate. The PBRA showed better than 4% accuracy in most experiments. However, experiments involving the low-energy (9 MeV) electron beam and irregular surfaces showed dose differences as great as 22%, in albeit a small fractional region. The geometries used in this study, particularly those in the irregular surface experiments, were extreme in the sense that they are not seen clinically. A more appropriate clinical evaluation in the future will involve comparisons to Monte Carlo generated patient dose distributions using actual computed tomography scan data. The present data also serve as a benchmark against which future enhancements to the PBRA can be evaluated.     

The use of an extra-focal electron source to model collimator-scattered electrons using the pencil-beam redefinition algorithm

Currently, the pencil-beam redefinition algorithm (PBRA) utilizes a single electron source to model clinical electron beams. In the single-source model, the electrons appear to originate from a virtual source located near the scattering foils. Although this approach may be acceptable for most treatment machines, previous studies have shown dose differences as high as 8% relative to the given dose for small fields for some machines such as the Varian Clinac 1800. In such machines collimation-scattered electrons originating from the photon jaws and the applicator give rise to extra-focal electron sources. In this study, we examined the impact of modeling an additional electron source to better account for the collimator-scattered electrons. The desired dose calculation accuracy in water throughout the dose distribution is 3% or better relative to the given dose. We present here a methodology for determining the electron-source parameters for the dual-source model using a minimal set of data, that is, two central-axis depth-dose curves and two off-axis profiles. A Varian Clinac 1800 accelerator was modeled for beam energies of 20 and 9 MeV and applicator sizes of 15 x 15 and 6 x 6 cm2. The improvement in the accuracy of PBRA-calculated dose, evaluated using measured two-dimensional dose distributions in water, was characterized using the figure of merit, FA3%, which represents the fractional area containing dose differences greater than 3%. For the 15 x 15 cm2 field the evaluation was restricted to the penumbral region, and for the 6 x 6 cm2 field the central region of the beam was included as it was impacted by the penumbra. The greatest improvement in dose accuracy was for the 6 x 6 cm2 applicator. At 9 MeV, FA3% decreased from 15% to 0% at 100 cm SSD and from 34% to 4% at 110 cm SSD. At 20 MeV, FA3% decreased from 17% to 2% at 100 cm SSD and from 41% to 10% at 110 cm SSD. In the penumbra of the 15 x 15 cm2 applicator, the improvement was less, but still significant. At 9 MeV, FA3% changed from 11% to 1% at 100 cm SSD and from 10% to 12% at 110 cm SSD. At 20 MeV, FA3% decreased from 12% to 8% at 100 cm SSD and from 14% to 5% at 110 cm SSD. Results demonstrate that use of a dual-source beam model can provide significantly improved accuracy in the PBRA-calculated dose distribution that was not achievable with a single-source beam model when modeling the Varian Clinac 1800 electron beams. Time of PBRA dose calculation was approximately doubled; however, dual-source beam modeling of newer accelerators (e.g., the Varian Clinac 2100) may not be necessary because of less impact of collimator-scattered electrons on dosimetry.     

A three-dimensional electron pencil-beam algorithm

We describe the implementation of a three-dimensional electron-dose algorithm based on a Gaussian pencil-beam model. The algorithm calculates dose to an arbitrarily distributed set of points in a heterogeneous volume. Multiple non-coplanar beams can be positioned relative to the volume. The algorithm consists of three basic components: (i) the transport of a pencil-beam through a heterogeneous volume, (ii) the evaluation of the pencil-beam fluence at a given depth in the volume in the presence of irregular fields, and (iii) the matching of points in the volume receiving a significant fluence contribution from a pencil-beam at a given depth in the volume and the calculation of dose to those points. An efficient point-matching algorithm reduces the computation time to the level of conventional two-dimensional implementations. The algorithm uses an optimised subdivision for irregular fields, and accurately predicts output factors for irregular fields placed between the final collimators and the patient. We show comparisons between the new algorithm and conventional two-dimensional calculations using measurements and calculations for finite heterogeneities, irregular fields and output factors.     

Application of the electron pencil beam redefinition algorithm to electron arc therapy

This project investigated the potential of summing fixed-beam dose distributions calculated using the pencil-beam redefinition algorithm (PBRA) at small angular steps (1 degree) to model an electron arc therapy beam. The PRBA, previously modified to model skin collimation, was modified further by incorporating two correction factors. One correction factor that is energy, SSD (source-to-surface distance), and field-width dependent constrained the calculated dose output to be the same as the measured dose output for fixed-beam geometries within the range of field widths and SSDs encountered in arc therapy. Another correction factor (single field-width correction factor for each energy) compensated for large-angle scattering not being modeled, allowing a more accurate calculation of dose output at mid arc. The PBRA was commissioned to accurately calculate dose in a water phantom for fixed-beam geometries typical of electron arc therapy. Calculated central-axis depth doses agreed with measured doses to within 2% in the low-dose gradient regions and within 1-mm in the high-dose gradient regions. Off-axis doses agreed to within 2 mm in the high-dose gradient regions and within 3% in the low-dose gradient regions. Arced-beam calculations of dose output and depth dose at mid arc were evaluated by comparing to data measured using two cylindrical water phantoms with radii of 12 and 15 cm at 10 and 15 MeV. Dose output was measured for all combinations of phantom radii of curvature, collimator widths (4, 5, and 6 cm), and arc angles (0 degrees, 20 degrees, 40 degrees, 60 degrees, 80 degrees, and 90 degrees) for both beam energies. Results showed the calculated mid-arc dose output to agree within 2% of measurement for all combinations. For a 90 degree arc angle and 5 x 20 cm2 field size, the calculated mid-arc depth dose in the low-dose gradient region agreed to within 2% of measurement for all depths at 10 MeV and for depths greater than depth of dose maximum R100 at 15 MeV. For depths in the buildup region at 15 MeV the calculations overestimated the measured dose by as much as 3.4%. Mid-arc depth dose in the high-dose gradient region agreed to within 2.2 mm of measured dose. Calculated two-dimensional relative dose distributions in the plane of rotation were compared to dose measurements using film in a cylindrical polystyrene phantom for a 90 degree arc angle and field widths of 4, 5, and 6 cm at 10 and 15 MeV. Results showed that off-axis dose at the ends of arc (without skin collimation) agreed to within 2% in the low-dose gradient region and to within 1.2 mm in the high-dose gradient region. This work showed that the accuracy of the PBRA arced-beam dose model met the criteria specified by Van Dyk et al. [Int. J. Radiat. Oncol. Biol. Phys. 26, 261-273 (1993)] with the exception of the buildup region of the 15 MeV beam. Based on the present results, results of a previous study showing acceptable accuracy in the presence of skin collimation, and results of a previous study showing acceptable accuracy in the presence of internal heterogeneities, it is concluded that the PBRA arced-beam dose model should be adequate for planning electron arc therapy.     

Modeling skin collimation using the electron pencil beam redefinition algorithm

Skin collimation is an important tool for electron beam therapy that is used to minimize the penumbra when treating near critical structures, at extended treatment distances, with bolus, or using arc therapy. It is usually made of lead or lead alloy material that conforms to and is placed on patient surface. Presently, commercially available treatment-planning systems lack the ability to model skin collimation and to accurately calculate dose in its presence. The purpose of the present work was to evaluate the use of the pencil beam redefinition algorithm (PBRA) in calculating dose in the presence of skin collimation. Skin collimation was incorporated into the PBRA by terminating the transport of electrons once they enter the skin collimator. Both fixed- and arced-beam dose calculations for arced-beam geometries were evaluated by comparing them with measured dose distributions for 10- and 15-MeV beams. Fixed-beam dose distributions were measured in water at 88-cm source-to-surface distance with an air gap of 32 cm. The 6 x 20-cm2 field (dimensions projected to isocenter) had a 10-mm thick lead collimator placed on the surface of the water with its edge 5 cm inside the field's edge located at +10 cm. Arced-beam dose distributions were measured in a 13.5-cm radius polystyrene circular phantom. The beam was arced 90 degrees (-45 degrees to +45 degrees), and 10-mm thick lead collimation was placed at +/- 30 degrees. For the fixed beam at 10 MeV, the PBRA- calculated dose agreed with measured dose to within 2.0-mm distance to agreement (DTA) in the regions of high-dose gradient and 2.0% in regions of low dose gradient. At 15 MeV, the PBRA agreed to within a 2.0-mm DTA in the regions of high-dose gradient; however, the PBRA underestimated the dose by as much as 5.3% over small regions at depths less than 2 cm because it did not model electrons scattered from the edge of the skin collimation. For arced beams at 10 MeV, the agreement was 1-mm DTA in the high-dose gradient regions, and 2% in the low-dose gradient regions. For arced beams at 15 MeV, the agreement was 1 mm in the high-dose gradient regions, and in the low-dose gradient region at depth less than 2 cm, as much as 5% dose difference was observed. This study demonstrated the ease with which skin collimation can be incorporated into the PBRA. The good agreement of PBRA calculated with measured dose shows that the PBRA is likely sufficiently accurate for clinical use in the presence of skin collimation for electron arc therapy. To further improve the accuracy of the PBRA in regions having significant electrons scattered from the edge of the skin collimation would require transporting the electrons through the lead skin collimation near its edges.     

Dosimetric evaluation of a two-dimensional, arc electron, pencil-beam algorithm in water and PMMA.

The accuracy of dose calculations from a pencil-beam algorithm developed specifically for arc electron beam therapy was evaluated at 10 and 15 MeV. Mid-arc depth-doses were measured for 0 degrees and 90 degrees arcs using 12 and 15 cm radius cylindrical water phantoms. Calculated depth-doses for the 90 degrees arced beams in the build-up region were as much as 3% less than measured values; the maximum dose was similar in magnitude but at a greater depth; and the therapeutic depth, R80, was 2-4 mm deeper. Calculated values of output (dose per monitor unit) at the depth of the maximum calculated dose were compared with measured values; for arcs ranging from 0-90 degrees, 12 and 15 cm radius water phantoms, and collimator widths of 4, 5 and 6 cm, results showed differences as great as 7%. Isodose countours for a 90 degrees arc were also measured in a 15 cm radius PMMA phantom. At the depth of maximum dose the algorithm predicted doses in the penumbral regions, both with and without collimation, which agreed within a few per cent of measured values. The largest discrepancies were 5%, which occurred in the penumbral portion of the depth-dose fall-off region. Differences between measurement and calculation are not believed to be clinically significant and are believed to be primarily due to the fact that the algorithm models neither large-angle scattering nor the effects of range straggling on the pencil-beam dose distribution.     

A two-dimensional pencil-beam algorithm for calculation of arc electron dose distributions

A two-dimensional pencil-beam algorithm is presented for the calculation of arc electron dose distributions in any plane that is perpendicular to the axis of rotation. The dose distributions are calculated by modelling the arced beam as a single broad beam defined by the irradiated surface of the patient. The algorithm is two-dimensional in that the anatomical cross section of the patient and the skin collimators are assumed identical in parallel planes outside the plane of calculation. The broad beam is modelled as a collection of strip beams, each strip beam being characterised by its planar fluence, mean projected angular direction and a root-mean-square spread about the mean direction. Using these parameters, the dose distribution is calculated using pencil-beam theory. Examples of strip-beam parameters and resulting dose distributions for patient geometries are presented. Features of the algorithm, which include (1) incorporation of pencil-beam theory for the calculation of dose in heterogeneous tissue, (2) run times of only about twice that of comparable-sized fixed electron fields and (3) the input requirement of only a single depth dose and four off-axis dose profiles of measured data, make the algorithm practical for clinical use.     

Modeling of beam customization devices in the pencil-beam splitting algorithm for heavy charged particle radiotherapy

A broad-beam-delivery system for radiotherapy with protons or ions often employs multiple collimators and a range-compensating filter, which offer complex and potentially useful beam customization. It is however difficult for conventional pencil-beam algorithms to deal with fine structures of these devices due to beam-size growth during transport. This study aims to avoid the difficulty with a novel computational model. The pencil beams are initially defined at the range-compensating filter with angular-acceptance correction for upstream collimation followed by stopping and scattering. They are individually transported with possible splitting near the aperture edge of a downstream collimator to form a sharp field edge. The dose distribution for a carbon-ion beam was calculated and compared with existing experimental data. The penumbra sizes of various collimator edges agreed between them to a submillimeter level. This beam-customization model will be used in the greater framework of the pencil-beam splitting algorithm for accurate and efficient patient dose calculation.     

Electron beam characteristics of the 50-MeV racetrack microtron.

Electron beams in the MM50 racetrack microtron are generated by computer controlled scanning of a well-focused electron pencil beam. The treatment head is optimized to give a minimum of scatter between the source position and the collimator plane by a general minimization of all scattering material in the beam and by replacement of the air in the treatment head by helium, which has a much lower linear scattering power than air. A double-focused multileaf collimator with a 31-cm collimator to patient distance is used both for electron and photon collimation. In general, no extra electron collimation is needed for the standard SSD of 100 cm. To make irregular field collimation at a distance this far from the patient possible, a number of requirements have to be fulfilled regarding the virtual source position and the spatial and angular distribution of the initial electron beam. The virtual source position has been found to be at a fixed position for different irradiation parameters. This is important for the use of the light field in electron beam treatment but also for achieving a high degree of accuracy in the dosimetry. Scatter from the multileaf collimator has not been found to give any significant contribution to the radiation field or to the monitor output factor of the MM50. Experimental dose distribution data on the MM50 have been compared to data both from other types of treatment units and to Monte Carlo simulations.     

Accuracy of the phase space evolution dose calculation model for clinical 25 MeV electron beams

The phase space evolution (PSE) model is a dose calculation model for electron beams in radiation oncology developed with the aim of a higher accuracy than the commonly used pencil beam (PB) models and with shorter calculation times than needed for Monte Carlo (MC) calculations. In this paper the accuracy of the PSE model has been investigated for 25 MeV electron beams of a MM50 racetrack microtron (Scanditronix Medical AB, Sweden) and compared with the results of a PB model. Measurements have been performed for tests like non-standard SSD, irregularly shaped fields, oblique incidence and in phantoms with heterogeneities of air, bone and lung. MC calculations have been performed as well, to reveal possible errors in the measurements and/or possible inaccuracies in the interaction data used for the bone and lung substitute materials. Results show a good agreement between PSE calculated dose distributions and measurements. For all points the differences--in absolute dose--were generally well within 3% and 3 mm. However, the PSE model was found to be less accurate in large regions of low-density material and errors of up to 6% were found for the lung phantom. Results of the PB model show larger deviations, with differences of up to 6% and 6 mm and of up to 10% for the lung phantom; at shortened SSDs the dose was overestimated by up to 6%. The agreement between MC calculations and measurement was good. For the bone and the lung phantom maximum deviations of 4% and 3% were found, caused by uncertainties about the actual interaction data. In conclusion, using the phase space evolution model, absolute 3D dose distributions of 25 MeV electron beams can be calculated with sufficient accuracy in most cases. The accuracy is significantly better than for a pencil beam model. In regions of lung tissue, a Monte Carlo model yields more accurate results than the current implementation of the PSE model.     

The use of film dosimetry of the penumbra region to improve the accuracy of intensity modulated radiotherapy

Accurate measurements of the penumbra region are important for the proper modeling of the radiation beam for linear accelerator-based intensity modulated radiation therapy. The usual data collection technique with a standard ionization chamber artificially broadens the measured beam penumbrae due to volume effects. The larger the chamber, the greater is the spurious increase in penumbra width. This leads to inaccuracies in dose calculations of small fields, including small fields or beam segments used in IMRT. This source of error can be rectified by the use of film dosimetry for penumbra measurements because of its high spatial resolution. The accuracy of IMRT calculations with a pencil beam convolution model in a commercial treatment planning system was examined using commissioning data with and without the benefit of film dosimetry of the beam penumbrae. A set of dose-spread kernels of the pencil beam model was calculated based on commissioning data that included beam profiles gathered with a 0.6-cm-i.d. ionization chamber. A second set of dose-spread kernels was calculated using the same commissioning data with the exception of the penumbrae, which were measured with radiographic film. The average decrease in the measured width of the 80%-20% penumbrae of various square fields of size 3-40 cm, at 5 cm depth in water-equivalent plastic was 0.27 cm. Calculations using the pencil beam model after it was re-commissioned using film dosimetry of the penumbrae gave better agreement with measurements of IMRT fields, including superior reproduction of high dose gradient regions and dose extrema. These results show that accurately measuring the beam penumbrae improves the accuracy of the dose distributions predicted by the treatment planning system and thus is important when commissioning beam models used for IMRT.     

Dosimetric evaluation in heterogeneous tissue of anterior electron beam irradiation for treatment of retinoblastoma

A dosimetric study of anterior electron beam irradiation for treatment of retinoblastoma was performed to evaluate the influence of tissue heterogeneities on the dose distribution within the eye and the accuracy of the dose calculated by a pencil beam algorithm. Film measurements were made in a variety of polystyrene phantoms and in a removable polystyrene eye incorporated into a tissue substitute phantom constructed from a human skull. Measurements in polystyrene phantoms were used to demonstrate the algorithm's ability to predict the effect of a lens block placed in the beam, as well as the eye's irregular surface shape. The eye phantom was used to measure dose distributions within the eye in both the sagittal and transverse planes in order to test the algorithm's ability to predict the dose distribution when bony heterogeneities are present. Results show (1) that previous treatment planning conclusions based on flat, uniform phantoms for central-axis depth dose are adequate; (2) that a three-dimensional heterogeneity correction is required for accurate dose calculations; and (3) that if only a two-dimensional heterogeneity correction is used in calculating the dose, it is more accurate for the sagittal than the transverse plane.     

Pencil-beam redefinition algorithm for electron dose distributions

A pencil-beam redefinition algorithm has been developed for the calculation of electron-beam dose distributions on a three-dimensional grid utilizing 3-D inhomogeneity correction. The concept of redefinition was first used for both fixed and arced electron beams by Hogstrom et al. but was limited to a single redefinition. The success of those works stimulated the development of the pencil-beam redefinition algorithm, the aim of which is to solve the dosimetry problems presented by deep inhomogeneities through development of a model that redefines the pencil beams continuously with depth. This type of algorithm was developed independently by Storchi and Huizenga who termed it the "moments method." Such a pencil beam within the patient is characterized by a complex angular distribution, which is approximated by a Gaussian distribution having the same first three moments as the actual distribution. Three physical quantities required for dose calculation and subsequent radiation transport--namely planar fluence, mean direction, and root-mean-square spread about the mean direction--are obtained from these moments. The primary difference between the moments method and the redefinition algorithm is that the latter subdivides the pencil beams into multiple energy bins. The algorithm then becomes a macroscopic method for transporting the complete phase space of the beam and allows the calculation of physical quantities such as fluence, dose, and energy distribution. Comparison of calculated dose distributions with measured dose distributions for a homogeneous water phantom, and for phantoms with inhomogeneities deep relative to the surface, show agreement superior to that achieved with the pencil-beam algorithm of Hogstrom et al. in the penumbral region and beneath the edges of air and bone inhomogeneities. The accuracy of the redefinition algorithm is within 4% and appears sufficient for clinical use, and the algorithm is structured for further expansion of the physical model if required for site-specific treatment planning problems.     

Two-dimensional pencil beam scaling: an improved proton dose algorithm for heterogeneous media

New dose delivery techniques with proton beams, such as beam spot scanning or raster scanning, require fast and accurate dose algorithms which can be applied for treatment plan optimization in clinically acceptable timescales. The clinically required accuracy is particularly difficult to achieve for the irradiation of complex, heterogeneous regions of the patient's anatomy. Currently applied fast pencil beam dose calculations based on the standard inhomogeneity correction of pathlength scaling often cannot provide the accuracy required for clinically acceptable dose distributions. This could be achieved with sophisticated Monte Carlo simulations which are still unacceptably time consuming for use as dose engines in optimization calculations. We therefore present a new algorithm for proton dose calculations which aims to resolve the inherent problem between calculation speed and required clinical accuracy. First, a detailed derivation of the new concept, which is based on an additional scaling of the lateral proton fluence is provided. Then, the newly devised two-dimensional (2D) scaling method is tested for various geometries of different phantom materials. These include standard biological tissues such as bone, muscle and fat as well as air. A detailed comparison of the new 2D pencil beam scaling with the current standard pencil beam approach and Monte Carlo simulations, performed with GEANT, is presented. It was found that the new concept proposed allows calculation of absorbed dose with an accuracy almost equal to that achievable with Monte Carlo simulations while requiring only modestly increased calculation times in comparison to the standard pencil beam approach. It is believed that this new proton dose algorithm has the potential to significantly improve the treatment planning outcome for many clinical cases encountered in highly conformal proton therapy.     

Incorporation of the aperture thickness in proton pencil-beam dose calculations

Field-specific apertures, of sufficient range-absorbing thickness, are used in the majority of proton-therapy treatments today. In current practice, these apertures are modelled as objects of infinitesimal thickness. Such an approximation, however, is not accurate if the aperture edge is close to, or extends over, the beam axis. Practical situations in which this occurs include off-axis patch fields, small apertures, and fields shaped with a multileaf collimator. We develop an extension of the pencil-beam dose model to incorporate the aperture thickness. We derive an exact solution as well as a computationally simpler approximate implementation. The model is validated using measurements of the lateral penumbra. For a set-up with a source size of 2.76 cm, a source-to-axis distance of 227 cm, and a aperture-to-axis distance of 35 cm, the maximum increase in penumbra for a 6 cm thick aperture compared to the thin-aperture model is about 2 mm. The maximum shift in the 95% isodose contour line is larger. The overall effect depends on the aperture thickness, the position of the aperture edge and the intrinsic source size and SAD, but is fairly insensitive to aperture-to-skin distance and depth in patient.     

Modelling lateral beam quality variations in pencil kernel based photon dose calculations

Standard treatment machines for external radiotherapy are designed to yield flat dose distributions at a representative treatment depth. The common method to reach this goal is to use a flattening filter to decrease the fluence in the centre of the beam. A side effect of this filtering is that the average energy of the beam is generally lower at a distance from the central axis, a phenomenon commonly referred to as off-axis softening. The off-axis softening results in a relative change in beam quality that is almost independent of machine brand and model. Central axis dose calculations using pencil beam kernels show no drastic loss in accuracy when the off-axis beam quality variations are neglected. However, for dose calculated at off-axis positions the effect should be considered, otherwise errors of several per cent can be introduced. This work proposes a method to explicitly include the effect of off-axis softening in pencil kernel based photon dose calculations for arbitrary positions in a radiation field. Variations of pencil kernel values are modelled through a generic relation between half value layer (HVL) thickness and off-axis position for standard treatment machines. The pencil kernel integration for dose calculation is performed through sampling of energy fluence and beam quality in sectors of concentric circles around the calculation point. The method is fully based on generic data and therefore does not require any specific measurements for characterization of the off-axis softening effect, provided that the machine performance is in agreement with the assumed HVL variations. The model is verified versus profile measurements at different depths and through a model self-consistency check, using the dose calculation model to estimate HVL values at off-axis positions. A comparison between calculated and measured profiles at different depths showed a maximum relative error of 4% without explicit modelling of off-axis softening. The maximum relative error was reduced to 1% when the off-axis softening was accounted for in the calculations.     

A finite-size pencil beam model for photon dose calculations in three dimensions.

A three-dimensional dose computation model employing a finite-size, diverging, pencil beam has been developed and is demonstrated for Cobalt-60 gamma rays. The square cross-section pencil beam is simulated in a semi-infinite water phantom by convolving the pencil beam photon fluence with the Monte Carlo point dose kernel for Cobalt-60. This finite-size pencil beam is calculated one time and becomes a new data base with which to build larger beams by two-dimensional superposition. The pencil beam fluence profile, angle correction for beam divergence, the Mayneord inverse square correction, radial and angular sampling rates, error propagation, and computation time have been investigated and are reported. Radial and angular sampling rates have a great effect on accuracy and their appropriate selection is important. Percent depth doses calculated by finite-size pencil beam superposition are within 1% of values calculated by full convolution and the agreement with values from the literature is within 6%. The latter disagreement is shown to be due to a low-energy photon component which is not modeled in other calculations. Computation time measurements show the pencil beam method to be faster than full convolution and one implementation of the differential-scatter-air-ratio (dSAR) method.     

Dose calculation models for proton treatment planning using a dynamic beam delivery system: an attempt to include density heterogeneity effects in the analytical dose calculation

The gantry for proton radiotherapy at the Paul Scherrer Institute (PSI) is designed specifically for the spot-scanning technique. Use of this technique to its full potential requires dose calculation algorithms which are capable of precisely simulating each scanned beam individually. Different specialized analytical dose calculations have been developed, which attempt to model the effects of density heterogeneities in the patient's body on the dose. Their accuracy has been evaluated by a comparison with Monte Carlo calculated dose distributions in the case of a simple geometrical density interface parallel to the beam and typical anatomical situations. A specialized ray casting model which takes range dilution effects (broadening of the spectrum of proton ranges) into account has been found to produce results of good accuracy. This algorithm can easily be implemented in the iterative optimization procedure used for the calculation of the optimal contribution of each individual scanned pencil beam. In most cases an elemental pencil beam dose calculation has been found to be most accurate. Due to the long computing time, this model is currently used only after the optimization procedure as an alternative method of calculating the dose.     

Application of an inverse kernel concept to Monte Carlo based IMRT

Inverse treatment planning by means of pencil beam algorithms can lead to errors in the calculation of dose in areas without secondary electron equilibrium. Monte Carlo (MC) simulations give accurate results in such areas but result in increased computation times. We present a new, so-called inverse kernel concept that offers MC precision in inverse treatment planning with acceptable computation times and memory consumption. Inverse kernels are matrices that describe the dose contribution from all bixels of a beam to a distinct voxel of the patient phantom. The concept is similar to other generalized pencil-beam concepts, except that inverse kernel elements are precalculated using a single MC simulation and stored as binary trees. In this procedure a modified MC code (XVMC) is applied to trace the photon history for each dose deposition. Iterative optimization is then applied in a second step. The inverse process is separated into (i) a slower MC simulation and (ii) a faster iterative optimization, followed by (iii) the segmentation procedure, and (iv) a final MC dose calculation step including a segment weight reoptimization. Inverse kernel optimization, or IKO, with segmentation and reoptimization steps is demonstrated by means of a lung cancer case. To demonstrate the superiority of an inverse MC system over pencil-beam or collapsed-cone based systems, the final result of the IKO is compared to plans where all segments have been calculated by pencil beam or collapsed cone, respectively. Dose-volume histograms and dose-difference histograms show remarkable differences, which can be attributed to systematic errors in both algorithms. IKO is a precise, nonhybrid, inverse MC treatment planning system which suits current clinical needs, as several optimization steps can follow one single MC-simulation step for a distinct beam setup.     

On the initial angular variances of clinical electron beams

Electron beam radiotherapy treatment planning systems need to be fed with the characteristics of the high-energy electron beams (4-50 MeV) from the specifically applied accelerator. Beams can be characterized by their mean initial energy, effective initial angular variance, virtual source position and the resulting central axis depth dose distribution in water. This information is the only input to pencil beam dose calculation models. Newer calculation models like macro Monte Carlo, voxel Monte Carlo and phase space evolution require as input the full initial phase space or a parametrization of that initial phase space, generally consisting of a primary beam component and one or more scatter components. This primary beam component is often characterized by initial energy, primary beam initial angular variance and virtual source distance. The purpose of the present investigation was to investigate to what extent standard values can be used both for the effective initial angular variance as input to pencil beam models and for the primary beam initial angular variance. Comprehensive benchmark data were obtained on the initial angular variance of various types of accelerator, for various energies and field sizes. The initial angular variance sigma2theta(x) has been derived from penumbra measurements in air by means of film dosimetry at various distances from the lower collimator. For the types of accelerator used in radiotherapy nowadays the measurements show values for sigma2theta(x)/T(E) of around 13 cm where T(E) is the ICRU-35 linear angular scattering power in air. This value can be chosen as standard value for the primary beam initial angular variance, only slightly compromising the dose calculation accuracy. As input to pencil beam models, an effective sigma2theta(x)/T(E) should be used incorporating the scatter from the lower collimator. For the case that the air gaps between lower collimator and patient are small (5-10 cm) an effective sigma2theata(x)/T(E) of 20 cm has been found and is recommended as the standard input for pencil beam models. Of the accelerators investigated, a different value was found only for the Elekta SL15, i.e. 50% higher for the effective sigma2theta(x)/T(E).