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.     

Application of measured pencil beam parameters for electron beam model evaluation

Most current electron beam models, as are used in commercial treatment planning systems, combine measured broad beam central axis depth dose data with measured or modeled functions to approximate radial scatter and heterogeneity effects. In this paper, we extend a recently developed pencil beam model to calculate doses outside the field edge and doses in heterogeneous media. We have also explored use of this model as a tool for evaluating commercial electron planning programs. The algorithm we have developed, based on the concept of the lateral buildup ratio (LBR), enables calculation of dose at any point in an irregular electron field, and is capable of generating both on- and off-axis depth dose curves and isodose profiles. This model includes the effects of density and mass-angular scattering power in measured broad beam central axis depth dose data, which when combined with small field reference data, can be used to generate LBR ratios. From these ratios one can infer the depth dependent, effective pencil beam radial spread parameter a in water or other materials, which can be used to model any arbitrary field. We have used this approach to calculate fractional depth doses for small fields incident on aluminum and cork, which we have then compared against measurements and the calculations of several commercial planning systems.     

Calculation of a pencil beam kernel from measured photon beam data

Usually, pencil beam kernels for photon beam calculations are obtained by Monte Carlo calculations. In this paper, we present a method to derive a pencil beam kernel from measured beam data, i.e. central axis depth doses, phantom scatter factors and off-axis ratios. These data are usually available in a radiotherapy planning system. The differences from other similar works are: (a) the central part of the pencil beam is derived from the measured penumbra of large fields and (b) the dependence of the primary photon fluence on the depth caused by beam hardening in the phantom is taken into account. The calculated pencil beam will evidently be influenced by the methods and instruments used for measurement of the basic data set. This is of particular importance for an accurate prediction of the absorbed dose delivered by small fields. Comparisons with measurements show that the accuracy of the calculated dose distributions fits well in a 2% error interval in the open part of the field, and in a 2 mm isodose shift in the penumbra region.     

The energy-dependent electron loss model for pencil beam dose kernels

The 'monoenergetic' electron loss model was derived in a previous work to account for pathlength straggling in the Fermi-Eyges pencil beam problem. In this paper, we extend this model to account for energy-loss straggling and secondary knock-on electron transport in order to adequately predict a depth dose curve. To model energy-loss straggling, we use a weighted superposition of a discrete number of monoenergetic pencil beams with different initial energies where electrons travel along the depth-energy characteristics in the continuous slowing down approximation (CSDA). The energy straggling spectrum at depth determines the weighting assigned to each monoenergetic pencil beam. Supplemented by a simple transport model for the secondary knock-on electrons, the 'energy-dependent' electron loss model predicts both lateral and depth dose distributions from the electron pencil beams in good agreement with Monte Carlo calculations and measurements. The calculation of dose distribution from a pencil beam takes 0.2 s on a Pentium III 500 MHz computer. Being computationally fast, the 'energy-dependent' electron loss model can be used for the calculation of 3D energy deposition kernels in dose optimization schemes without using precalculated or measured data.     

CT calibration for two-dimensional scaling of proton pencil beams

For proton dose calculations in heterogeneous media, it was shown in a previous work that the conventional pencil beam approach based on pathlength scaling does not properly account for scattering effects in nonwater media (Szymanowski and Oelfke 2002 Phys. Med. Biol. 47 3313-30). A two-dimensional scaling method was therefore introduced, which is able to predict with high accuracy the propagation of proton pencil beams both along the depth and the lateral directions in inhomogeneous media. In order to integrate this improved pencil beam algorithm in a CT based treatment planning system, two CT calibration curves are needed. The first one relates the Hounsfield numbers to the relative stopping powers, as for the conventional pencil beam approach. The second curve is to relate the Hounsfield numbers to the material-specific lateral scaling factors. The purpose of this work is to provide the CT calibration curves needed for the integration of the pencil beam algorithm featuring the two-dimensional scaling method. Similarly to as suggested by Schneider et al (1996 Phys. Med. Biol. 41 111-24) for the calibration curve in terms of stopping powers, we follow a stoichiometric procedure to get the calibration curve in terms of material-specific lateral scaling factors. The calibration curves for a CT scanner of the type Siemens Somatom Plus 4 are obtained from the analytical calculation of the CT Hounsfield numbers, relative stopping powers and material-specific lateral scaling factors for human biological tissues.     

Dose uncertainties in photon pencil kernel calculations at off-axis positions

The purpose of this study was to investigate the specific problems associated with photon dose calculations in points located at a distance from the central beam axis. These problems are related to laterally inhomogeneous energy fluence distributions and spectral variations causing a lateral shift in the beam quality, commonly referred to as off-axis softening (OAS). We have examined how the dose calculation accuracy is affected when enabling and disabling explicit modeling of these two effects. The calculations were performed using a pencil kernel dose calculation algorithm that facilitates modeling of OAS through laterally varying kernel properties. Together with a multi-source model that provides the lateral energy fluence distribution this generates the total dose output, i.e., the dose per monitor unit, at an arbitrary point of interest. The dose calculation accuracy was evaluated through comparisons with 264 measured output factors acquired at 5, 10, and 20 cm depth in four different megavoltage photon beams. The measurements were performed up to 18 cm from the central beam axis, inside square fields of varying size and position. The results show that calculations including explicit modeling of OAS were considerably more accurate, up to 4%, than those ignoring the lateral beam quality shift. The deviations caused by simplified head scatter modeling were smaller, but near the field edges additional errors close to 1% occurred. When enabling full physics modeling in the dose calculations the deviations display a mean value of -0.1%, a standard deviation of 0.7%, and a maximum deviation of -2.2%. Finally, the results were analyzed in order to quantify and model the inherent uncertainties that are present when leaving the central beam axis. The off-axis uncertainty component showed to increase with both off-axis distance and depth, reaching 1% (1 standard deviation) at 20 cm depth.     

Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters

The BEAM code is used to simulate nine photon beams from three major manufacturers of medical linear accelerators (Varian, Elekta, and Siemens), to derive and evaluate estimates for the parameters of the electron beam incident on the target, and to study the effects of some mechanical parameters like target width, primary collimator opening, flattening filter material and density. The mean energy and the FWHM of the incident electron beam intensity distributions (assumed Gaussian and cylindrically symmetric) are derived by matching calculated percentage depth-dose curves past the depth of maximum dose (within 1% of maximum dose) and off-axis factors (within 2sigma at 1% statistics or less) with measured data from the AAPM RTC TG-46 compilation. The off-axis factors are found to be very sensitive to the mean energy of the electron beam, the FWHM of its intensity distribution, its angle of incidence, the dimensions of the upper opening of the primary collimator, the material of the flattening filter and its density. The off-axis factors are relatively insensitive to the FWHM of the electron beam energy distribution, its divergence and the lateral dimensions of the target. The depth-dose curves are sensitive to the electron beam energy, and to its energy distribution, but they show no sensitivity to the FWHM of the electron beam intensity distribution. The electron beam incident energy can be estimated within 0.2 MeV when matching either the measured off-axis factors or the central-axis depth-dose curves when the calculated uncertainties are about 0.7% at the 1 sigma level. The derived FWHM (+/-0.1 mm) of the electron beam intensity distributions all fall within 1 mm of the manufacturer specifications except in one case where the difference is 1.2 mm.     

Performance of a fluorescent screen and CCD camera as a two-dimensional dosimetry system for dynamic treatment techniques

A two-dimensionally position sensitive dosimetry system has been tested for different dosimetric applications in a radiation therapy facility with a scanning proton beam. The system consists of a scintillating (fluorescent) screen, mounted at the beam-exit side of a phantom and it is observed by a charge coupled device (CCD) camera. The observed light distribution at the screen is equivalent to the two-dimensional (2D)-dose distribution at the screen position. It has been found that the dosimetric properties of the system, measured in a scanning proton beam, are equal to those measured in a proton beam broadened by a scattering system. Measurements of the transversal dose distribution of a single pencil beam are consistent with dose measurements as well as with dose calculations in clinically relevant fields made with multiple pencil beams. Measurements of inhomogeneous dose distributions have shown to be of sufficient accuracy to be suitable for the verification of dose calculation algorithms. The good sensitivity and sub-mm spatial resolution of the system allows for the detection of deviations of a few percent in dose from the expected (intended or calculated) dose distribution. Its dosimetric properties and the immediate availability of the data make this device a useful tool in the quality control of scanning proton beams.     

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.     

Monte Carlo simulation of small electron fields collimated by the integrated photon MLC

In this study, a Monte Carlo (MC)-based beam model for an ELEKTA linear accelerator was established. The beam model is based on the EGSnrc Monte Carlo code, whereby electron beams with nominal energies of 10, 12 and 15?MeV were considered. For collimation of the electron beam, only the integrated photon multi-leaf-collimators (MLCs) were used. No additional secondary or tertiary add-ons like applicators, cutouts or dedicated electron MLCs were included. The source parameters of the initial electron beam were derived semi-automatically from measurements of depth-dose curves and lateral profiles in a water phantom. A routine to determine the initial electron energy spectra was developed which fits a Gaussian spectrum to the most prominent features of depth-dose curves. The comparisons of calculated and measured depth-dose curves demonstrated agreement within 1%/1?mm. The source divergence angle of initial electrons was fitted to lateral dose profiles beyond the range of electrons, where the imparted dose is mainly due to bremsstrahlung produced in the scattering foils. For accurate modelling of narrow beam segments, the influence of air density on dose calculation was studied. The air density for simulations was adjusted to local values (433?m above sea level) and compared with the standard air supplied by the ICRU data set. The results indicate that the air density is an influential parameter for dose calculations. Furthermore, the default value of the BEAMnrc parameter 'skin depth' for the boundary crossing algorithm was found to be inadequate for the modelling of small electron fields. A higher value for this parameter eliminated discrepancies in too broad dose profiles and an increased dose along the central axis. The beam model was validated with measurements, whereby an agreement mostly within 3%/3?mm was found.     

Benchmarking analytical calculations of proton doses in heterogeneous matter

A proton dose computational algorithm, performing an analytical superposition of infinitely narrow proton beamlets (ASPB) is introduced. The algorithm uses the standard pencil beam technique of laterally distributing the central axis broad beam doses according to the Moliere scattering theory extended to slablike varying density media. The purpose of this study was to determine the accuracy of our computational tool by comparing it with experimental and Monte Carlo (MC) simulation data as benchmarks. In the tests, parallel wide beams of protons were scattered in water phantoms containing embedded air and bone materials with simple geometrical forms and spatial dimensions of a few centimeters. For homogeneous water and bone phantoms, the proton doses we calculated with the ASPB algorithm were found very comparable to experimental and MC data. For layered bone slab inhomogeneity in water, the comparison between our analytical calculation and the MC simulation showed reasonable agreement, even when the inhomogeneity was placed at the Bragg peak depth. There also was reasonable agreement for the parallelepiped bone block inhomogeneity placed at various depths, except for cases in which the bone was located in the region of the Bragg peak, when discrepancies were as large as more than 10%. When the inhomogeneity was in the form of abutting air-bone slabs, discrepancies of as much as 8% occurred in the lateral dose profiles on the air cavity side of the phantom. Additionally, the analytical depth-dose calculations disagreed with the MC calculations within 3% of the Bragg peak dose, at the entry and midway depths in the phantom. The distal depth-dose 20%-80% fall-off widths and ranges calculated with our algorithm and the MC simulation were generally within 0.1 cm of agreement. The analytical lateral-dose profile calculations showed smaller (by less than 0.1 cm) 20%-80% penumbra widths and shorter fall-off tails than did those calculated by the MC simulations. Overall, this work validates the usefulness of our ASPB algorithm as a reasonably fast and accurate tool for quality assurance in planning wide beam proton therapy treatment of clinical sites either composed of homogeneous materials or containing laterally extended inhomogeneities that are comparable in density and located away from the Bragg peak depths.     

A consistent formalism for the application of phantom and collimator scatter factors

A coherent system for the use of scatter correction factors, determined at 10 cm depth, is described for dose calculations on the central axis of arbitrarily shaped photon beams. The system is suitable for application in both the fixed source-surface distance (SSD) and in the isocentric treatment set-up. This is in contrast to some other proposals where only one of these approaches forms the basis of the calculation system or where distinct quantities and data sets are needed. In order to derive the relations in the formalism, we introduced a separation of the phenomena related to the energy fluence in air and to the phantom scatter contribution to the dose. Both are used relative to quantities defined for the reference irradiation set-up. It is shown that dose calculations can be performed with only one set of basic beam data, obtained at a reference depth of 10 cm. These data consist for each photon beam quality of measured collimator and phantom scatter correction factors, in combination with a set of (percentage/relative) depth-dose or tissue-phantom ratio values measured along the central axis of the beam. Problems related to measurements performed at the depth of maximum absorbed dose, due to the electron contamination of the beam, are avoided in this way. Collimator scatter correction factors are obtained by using a mini-phantom, while phantom scatter correction factors are derived from measurements in a full scatter phantom in combination with the results of the mini-phantom measurements. For practical reasons the fixed SSD system was chosen to determine the data. Then, dose calculations in a fixed SSD treatment set-up itself are straightforward. Application in the isocentric treatment set-up needs simple conversion steps, while the inverse approach, from isocentric to fixed SSD, is described as well. Differences between the two approaches are discussed and the equations for the conversions are given.     

Modelling pencil-beam divergence with the electron pencil-beam redefinition algorithm.

The electron pencil-beam redefinition algorithm (PBRA), which is used to calculate electron beam dose distributions, assumes that the virtual source of each pencil beam is identical to that of the broad beam incident on the patient. In the present work, a virtual source specific for each pencil beam is modelled by including the source distance as a pencil-beam parameter to be redefined with depth. To incorporate a variable pencil-beam source distance parameter, the transport equation was reformulated to explicitly model divergence resulting in the algorithm divPBRA. Allowing the virtual source position to vary with individual pencil beams is expected to better model the effects of heterogeneities on local electron fluence divergence (or convergence). Selected experiments from a measured data set developed at The University of Texas M D Anderson Cancer Center were used to evaluate the accuracy of the dose calculated using divPBRA. Results of the calculation showed that the theory accurately predicted the virtual source position in regions of side-scatter equilibrium and predicted reasonable virtual source positions in regions lacking side-scatter equilibrium (i.e. penumbra and in the vicinity and shadow of internal heterogeneities). Results of the evaluation showed the dose accuracy of divPBRA to be marginally better to that of PBRA, except in regions of extremely sharp dose perturbations, where the divPBRA calculations were significantly greater than the measured data. Dose calculations using divPBRA took 45% longer than those using PBRA. Therefore, we concluded that divPBRA offers no significant advantage over PBRA for the purposes of clinical treatment planning. However, the results were promising and divPBRA might prove useful if further modelling were to include large-angle scattering, low-energy delta rays and brehmsstrahlung.     

An analytical model for light ion pencil beam dose distributions: multiple scattering of primary and secondary ions

An analytical algorithm based on the generalized Fermi-Eyges theory, amended for multiple Coulomb scattering and energy loss straggling, is used for calculation of the dose distribution of light ion beams in water. Pencil beam energy deposition distributions are derived for light ions by weighting a Monte Carlo (MC) calculated planar integral dose distribution with analytically calculated multiple scattering and range straggling distributions. The planar integral dose distributions are calculated using the MC code SHIELD-HIT07, in which multiple scattering and energy loss straggling processes are excluded. The contribution from nuclear reactions is included in the MC calculations. Multiple scattering processes are calculated separately for primary and secondary ions and parameters of the initial angular and radial spreads, and the covariance of these are derived by a least-square parameterization of the SHIELD-HIT07 data. The results from this analytical algorithm are compared to pencil beam dose distributions obtained from SHIELD-HIT07, where all processes are included, as well as to experimental data. The presented analytical approach allows for the accurate calculation of the spatial energy deposition distributions of ions of atomic numbers Z = 1 - 8.     

Calculation of electron beam dose distributions for arbitrarily shaped fields

A method for the calculation of absorbed dose distributions of arbitrarily shaped electron beams is presented. Isodose distributions and output factors of treatment fields can be predicted with good accuracy, without the need for any dose measurement in the actual field. A Gaussian pencil beam model is employed with two different pencil beams for each electron beam energy. The values of the parameters of the pencil beam dose distributions are determined from a set of measurements of broad beam distributions; in this way the influence of electrons scattered by the applicator walls is taken into account. The dose distribution of electrons scattered from high atomic number metal frames, which define the treatment field contour at the skin, is calculated separately and added. This calculation is based on experimentally derived data. The method has been tested for beams with 6, 10, 14 and 20 MeV electron energy. The distance between calculated and measured isodose lines with values between 10 and 90% is under 0.3 cm. The difference between calculated and measured output factors does not exceed 2%.     

Proton loss model for therapeutic beam dose calculations

A transport algorithm called the proton loss (PL) model is developed for proton pencil beams of therapeutic energies. The PL model takes into account inelastic nuclear reactions, pathlength straggling, and energy-loss straggling and predicts the 3D dose distribution from a proton pencil beam. In proton beams, the multiple scattering and ionizational energy loss processes approach their diffusional limit where scattering and energy loss probability densities become Gaussian. Therefore we chose to derive the PL model from the Fermi-Eyges diffusional multiple scattering theory and the Gaussian theory of energy straggling. We first introduce a generalization of the Fermi-Eyges equation for proton pencil beams, labeled the proton loss (PL) transport equation. This new equation includes terms that model inelastic nuclear reactions as a depth-dependent absorption and pathlength straggling as a quasi-absorption. Then energy straggling is taken into account by using a weighted superposition of a discrete number of elementary pencil beams. These elementary pencil beams have different initial energies and lose energy according to the CSDA, thus they have different ranges of penetration. A final solution for the proton beam transport is obtained as a linear combination of elementary pencil beam solutions with weights defined by the Gaussian evolution of the proton energy spectrum with depth. A numerical comparison of the dose distribution predictions of the PL model with measurements and PTRAN Monte Carlo simulations indicates the model is both computational fast and accurate.     

A beam source model for scanned proton beams

A beam source model, i.e. a model for the initial phase space of the beam, for scanned proton beams has been developed. The beam source model is based on parameterized particle sources with characteristics found by fitting towards measured data per individual beam line. A specific aim for this beam source model is to make it applicable to the majority of the various proton beam systems currently available or under development, with the overall purpose to drive dose calculations in proton beam treatment planning. The proton beam phase space is characterized by an energy spectrum, radial and angular distributions and deflections for the non-modulated elementary pencil beam. The beam propagation through the scanning magnets is modelled by applying experimentally determined focal points for each scanning dimension. The radial and angular distribution parameters are deduced from measured two-dimensional fluence distributions of the elementary beam in air. The energy spectrum is extracted from a depth dose distribution for a fixed broad beam scan pattern measured in water. The impact of a multi-slab range shifter for energy modulation is calculated with an own Monte Carlo code taking multiple scattering, energy loss and straggling, non-elastic and elastic nuclear interactions in the slab assembly into account. Measurements for characterization and verification have been performed with the scanning proton beam system at The Svedberg Laboratory in Uppsala. Both in-air fluence patterns and dose points located in a water phantom were used. For verification, dose-in-water was calculated with the Monte Carlo code GEANT 3.21 instead of using a clinical dose engine with approximations of its own. For a set of four individual pencil beams, both with the full energy and range shifted, 96.5% (99.8%) of the tested dose points satisfied the 1%/1 mm (2%/2 mm) gamma criterion.     

Implementation of pencil kernel and depth penetration algorithms for treatment planning of proton beams

The implementation of two algorithms for calculating dose distributions for radiation therapy treatment planning of intermediate energy proton beams is described. A pencil kernel algorithm and a depth penetration algorithm have been incorporated into a commercial three dimensional treatment planning system (Helax-TMS, Helax AB, Sweden) to allow conformal planning techniques using irregularly shaped fields, proton range modulation, range modification and dose calculation for non-coplanar beams. The pencil kernel algorithm is developed from the Fermi Eyges formalism and Molière multiple-scattering theory with range straggling corrections applied. The depth penetration algorithm is based on the energy loss in the continuous slowing down approximation with simple correction factors applied to the beam penumbra region and has been implemented for fast, interactive treatment planning. Modelling of the effects of air gaps and range modifying device thickness and position are implicit to both algorithms. Measured and calculated dose values are compared for a therapeutic proton beam in both homogeneous and heterogeneous phantoms of varying complexity. Both algorithms model the beam penumbra as a function of depth in a homogeneous phantom with acceptable accuracy. Results show that the pencil kernel algorithm is required for modelling the dose perturbation effects from scattering in heterogeneous media.     

Beam modeling and verification of a photon beam multisource model

Dose calculations for treatment planning of photon beam radiotherapy require a model of the beam to drive the dose calculation models. The beam shaping process involves scattering and filtering that yield radiation components which vary with collimator settings. The necessity to model these components has motivated the development of multisource beam models. We describe and evaluate clinical photon beam modeling based on multisource models, including lateral beam quality variations. The evaluation is based on user data for a pencil kernel algorithm and a point kernel algorithm (collapsed cone) used in the clinical treatment planning systems Helax-TMS and Nucletron-Oncentra. The pencil kernel implementations treat the beam spectrum as lateral invariant while the collapsed cone involves off axis softening of the spectrum. Both algorithms include modeling of head scatter components. The parameters of the beam model are derived from measured beam data in a semiautomatic process called RDH (radiation data handling) that, in sequential steps, minimizes the deviations in calculated dose versus the measured data. The RDH procedure is reviewed and the results of processing data from a large number of treatment units are analyzed for the two dose calculation algorithms. The results for both algorithms are similar, with slightly better results for the collapsed cone implementations. For open beams, 87% of the machines have maximum errors less than 2.5%. For wedged beams the errors were found to increase with increasing wedge angle. Internal, motorized wedges did yield slightly larger errors than external wedges. These results reflect the increased complexity, both experimentally and computationally, when wedges are used compared to open beams.     

Determination of the relative linear collision stopping power and linear scattering power of electron bolus material

The linear collision stopping power and linear scattering power for machineable wax relative to water have been determined for electron energies between 2 and 20 MeV. Knowledge of these quantities is necessary for the use of this wax as bolus in electron pencil-beam dose algorithms. The atomic composition of the wax (rho = 0.920 +/- 0.001 g cm(-3)) was obtained by having the wax assayed. The formalisms expressed in the ICRU Report 35 were used to calculate the relative linear collision stopping and linear scattering powers of the wax. The calculated relative linear collision stopping powers of 2 to 20 MeV electrons in the wax ranged from 0.949 +/- 0.005 to 0.952 +/- 0.005, and the calculated relative linear scattering powers ranged from 0.734 +/- 0.004 to 0.729 +/- 0.004. As a check of the calculation method, the relative linear collision stopping power was measured by determining the shift in electron central-axis depth-ionization curves when varying thicknesses of water were replaced by wax. These measurements, made using 10, 12, 15 and 18 MeV electron beams with wax thicknesses from 1.0 - 4.0 cm, resulted in a mean value of 0.931 +/- 0.008. Determination of the relative linear stopping power and the linear scattering power by using the measured CT number to extract values from patient data tables resulted in values of 0.933 +/- 0.009 and 0.746 +/- 0.016, respectively, indicating that it should be acceptable to use the Hounsfield values obtained with CT scans for treatment planning dose calculations.