Central Axis Depth Dose Curves Research Articles

SU‐FF‐T‐135: Commissioning of Multi‐Leaf Collimator for Fast Neutron Therapy

Purpose: To collect and analyze data required for modeling of d(48.5)+Be fast neutron beam and shaped by newly installed multi‐leaf collimator (MLC) replacing previously used multi‐rod collimator (MRC). Method and Materials: The MLC is of semi‐focused design and consists of 60 leaf pairs operated under vision control. The leaf ends are straight, while the sides of the leaves are tapered to match the beam divergence and project 5 mm at isocenter plane. The leaf thickness is 300 mm of steel, and the MLC is the primary beam shaping device. The measurements along the central axis as well as lateral profiles were done in a water phantom. In the build‐up region the central axis depth dose curves were combined with data obtained from the measurements using thin window extrapolation ionization chamber. The output factors were defined at 0.9 cm depth in phantom and in free air by means of small volume Tissue Equivalent (TE) ionization chamber and miniature pin diode. In addition TE/Mg(Ag) paired ionization chambers were used to separate the neutron and gamma components in phantom as well as in free air. Results: No significant variations of the central axis depth doses were observed compared to MRC. Penumbra measured between tapered leaf sides was smaller than penumbra measured between straight leaf ends. The differences were largest at shallow depths and for large field sizes: 7 mm for 25 × 25 cm2 field decreasing to less than1 mm for fields smaller than 15 × 15 cm2. Linear relationship between the actual leaf end position and field size was observed. The gamma component at 0.9 cm depth in phantom increased with the field size from 1.5% to 3% and from 0.4% to 0.74% in air. Conclusion: A set of beam data measured for neutron MLC was used in beam modeling.

SU‐FF‐T‐426: The Response of RadioChromic EBT Film in High‐Energy Electron Beams

Purpose: To describe the response of a new radiochromic film to highenergy clinical electron beams. GAFChromic® EBT film was designed primarily for verification of high energy photon IMRT treatments. It has been shown to be a very accurate and convenient photon detector. However, there is no literature on this film's response to high‐energy electron beams. We initiated a study to characterize the response and utility of this film for routine electron beam dosimetry. Method and Materials: The linac was first calibrated to ensure that the delivered dose was known accurately. We exposed a series of EBT films at dmax in polystyrene to 6, 9, 12, 16, and 20 MeV electrons to develop standard characteristic curves. All films were from the same batch. We also exposed the EBT films in a solid water phantom to produce central axis depth dose curves. These data were compared against percent depth dose curves measured with either Kodak XV2 film in a solid water cassette, or in a water phantom using an IC‐10 ion chamber or a PTW electron diode. Results: Results showed that the characteristic curve for this film was the same for electron energies from 6–20 MeV. Also, the response of the EBT film along the central axis of the beam matched the central axis percentage depth dose characteristics (R50, Rp) determined using Kodak XV2 film, electron diodes, and corrected ionization chamber measurements. Conclusion: GAFChromic® EBT film is shown to be an accurate detector for clinical electron beam applications. It is convenient to use since the solid water film cassette can be loaded in the linac room and requires no post‐irradiation processing. It gives the same results for electron dosimetry as silver halide films, diodes, and ionization chambers. Research sponsored by International Specialty Products corporation.

Design tools for proton therapy nozzles based on the double-scattering foil technique

Proton therapy has been increasing over the past several years, with several new treatment facilities being built in Europe, Japan and the United States. In this work, analytical and Monte Carlo tools were combined to model the passively scattered neurosurgery treatment beamline of the Harvard Cyclotron Laboratory (Cambridge, MA). The predicted three-dimensional dose distributions agree with actual measurements to within 0.1 mm for all quantities considered in central-axis depth-dose curve and to within 2.1 mm for all quantities considered in the absorbed dose cross-field profile. The predicted neutron dose equivalent per therapeutic absorbed dose, H/D, was calculated at various locations representing clinically significant anatomical sites. Under typical treatment conditions, the average ratio of predicted-to-measured H/D is 1.8 in the gonadal region (50 cm from isocentre) and 3.4 in the thyroid region (21 cm from isocentre). The global ratio of predicted-to-measured H/D is 2.6.

SU-FF-T-260: A Higher Accuracy Electron Beam Model Based On Large Field Measurements

Purpose: To commission the beam model for electron treatment planning with Monte Carlo using measurements made with the jaws wide open (with no applicator) along with state-of-the-art Monte Carlo simulation. Method and Materials: Central axis depth dose curves and dose profiles of 6–21 MeV Primus electron beams were measured for the 40×40 cm field. Monte Carlo treatment head and water phantom simulations were done with the EGSnrc system using the BEAM and DOSXYZNRC user codes, respectively. The measured data was used to estimate source and geometry parameters, some previously inaccessible in treatment head simulation, including incident beam direction, scattering foil thickness, offset of the secondary scattering foil and monitor chamber from the beam axis, and the distance separating the monitor chamber from the primary scattering foil. Parameter estimation relied on a published, comprehensive analysis of the sensitivity of the measured quantities to source and geometry parameters. Results: Dose distributions calculated with this large-field commissioning approach generally compared to 2%/2 mm with diode measurement. Larger discrepancies, as large as 5 mm present at a couple beam energies, were limited to the beam edge, well outside the region collimated with an applicator. The match to dose in the bremsstrahlung region was considerably better than previously published results for EGS4. Conclusion: This method gives more accurate estimates of source and geometry parameters than simulation of fields defined with an applicator. EGSnrc provides a better match than EGS4. This approach simplifies the commissioning procedure, relying on a single beam model, with parameters derived from a relatively small data set, to model all applicators. In addition, the beam has few energy-degraded, scattered electrons, relative to fields collimated with an applicator. A clean beam is much easier to model, opening up the possibility of achieving high accuracy in fluence estimation with a simple, experimentally-based beam model.

Application of a radiophotoluminescent glass plate dosimeter for small field dosimetry

We have recently developed a prototypical radiophotoluminescent glass plate dosimeter (GPD) system as a device for small field dosimetry. The purpose of this study is to examine the usefulness of the GPD system for small field dosimetry. The profiles measured with the GPD were evaluated by comparing them to those from Kodak X-Omat V and GAFCROMIC XR type R film dosimeters for 2, 5, 9, and 15 mm circular collimators created by a linear accelerator-based radiosurgery system. The GPD output factors were compared with those of various detectors including an ion chamber, a p-type silicon diode detector, a glass rod dosimeter (GRD), and a diamond detector. The results measured with the GPD were also confirmed by comparing them to those from Monte Carlo simulations. The accuracy of a simulated beam is validated by the excellent agreement between Monte Carlo calculated and measured central axis depth-dose curves for 9- and 15 mm circular collimators using 4- and 10 MV photon beams. The GPD profiles show almost the same full width at half maximum as those of film dosimeters and Monte Carlo simulations at 4- and 10 MV photon beams, but a little narrower penumbrae than the film dosimeters and Monte Carlo simulations. The output factors measured with the GPD are in good agreement with those from a diode detector, a diamond detector, and the GRD with a small active volume and Monte Carlo simulations, except for a very small 2 mm circular collimator. It was found that the GPD is a very useful detector for small field dosimetry.

Monte Carlo simulation of large electron fields

Accurate simulation of large electron fields may lead to improved accuracy in Monte Carlo treatment planning while simplifying the commissioning procedure. We have used measurements made with wide-open jaws and no electron applicator to adjust simulation parameters. Central axis depth dose curves and profiles of 6–21 MeV electron beams measured in this geometry were used to estimate source and geometry parameters, including those that affect beam symmetry: incident beam direction and offset of the secondary scattering foil and monitor chamber from the beam axis. Parameter estimation relied on a comprehensive analysis of the sensitivity of the measured quantities, in the large field, to source and geometry parameters. Results demonstrate that the EGS4 Monte Carlo system is capable of matching dose distributions in the largest electron field to the least restrictive of 1 cGy or 1 mm, with Dmax of 100 cGy, over the full energy range. This match results in an underestimation of the bremsstrahlung dose of 10–20% at 15–21 MeV, exceeding the combined experimental and calculational uncertainty in this quantity of 3%. The simulation of electron scattering at energies of 15–21 MeV in EGS4 may be in error. The recently released EGSnrc/BEAMnrc system may provide a better match to measurement.

Large efficiency improvements in BEAMnrc using directional bremsstrahlung splitting

The introduction into the BEAMnrc code of a new variance reduction technique, called directional bremsstrahlung splitting (DBS), is described. DBS uses a combination of interaction splitting for bremsstrahlung, annihilation, Compton scattering, pair production and photoabsorption, and Russian Roulette to achieve a much better efficiency of photon beam treatment head simulations compared to the splitting techniques already available in BEAMnrc (selective bremsstrahlung splitting, SBS, and uniform bremsstrahlung splitting, UBS). In a simulated 6 MV photon beam (10 x 10 cm2 field) photon fluence efficiency in the beam using DBS is over 8 times higher than with optimized SBS and over 20 times higher than with UBS, with a similar improvement in electron fluence efficiency in the beam. Total dose efficiency in a central-axis depth-dose curve improves by a factor of 6.4 over SBS at all depths in the phantom. The performance of DBS depends on the details of the accelerator being simulated. At higher energies, the relative improvement in efficiency due to DBS decreases somewhat, but is still a factor of 3.5 improvement over SBS for total dose efficiency using DBS in a simulated 18 MV photon beam. Increasing the field size of the simulated 6 MV beam to 40 x 40 cm2 (broad beam) causes the relative efficiency improvement of DBS to decrease by a factor of approximately 1.7 but is still up to 7 times more efficient than with SBS.

The response of Kodak EDR2 film in high-energy electron beams.

Kodak XV2 film has been a key dosimeter in radiation therapy for many years. The advantages of the recently introduced Kodak EDR2 film for photon beam dosimetry have been the focus of several IMRT verification dosimetry publications. However, no description of this film's response to electron beams exists in the literature. We initiated a study to characterize the response and utility of this film for electron beam dosimetry. We exposed a series of EDR2 films to 6, 9, 12, 16, and 20 MeV electrons in addition to 6 and 18 MV x rays to develop standard characteristic curves. The linac was first calibrated to ensure that the delivered dose was known accurately. All irradiations were done at dmax in polystyrene for both photons and electrons, all films were from the same batch, and were developed at the same time. We also exposed the EDR2 films in a solid water phantom to produce central axis depth dose curves. These data were compared against percent depth dose curves measured in a water phantom using an IC-10 ion chamber, Kodak XV2 film, and a PTW electron diode. The response of this film was the same for both 6 and 18 MV x rays, but showed an apparent energy-dependent enhancement for electron beams. The response of the film also increased with increasing electron energy. This caused the percent depth dose curves using film to be shifted toward the surface compared to the ion chamber data.

Scattered radiation from applicators in clinical electron beams

In radiotherapy with high-energy (4–25 MeV) electron beams, scattered radiation from the electron applicator influences the dose distribution in the patient. In most currently available treatment planning systems for radiotherapy this component is not explicitly included and handled only by a slight change of the intensity of the primary beam. The scattered radiation from an applicator changes with the field size and distance from the applicator. The amount of scattered radiation is dependent on the applicator design and on the formation of the electron beam in the treatment head. Electron applicators currently applied in most treatment machines are essentially a set of diaphragms, but still do produce scattered radiation. This paper investigates the present level of scattered dose from electron applicators, and as such provides an extensive set of measured data. The data provided could for instance serve as example input data or benchmark data for advanced treatment planning algorithms which employ a parametrized initial phase space to characterize the clinical electron beam.Central axis depth dose curves of the electron beams have been measured with and without applicators in place, for various applicator sizes and energies, for a Siemens Primus, a Varian 2300 C/D and an Elekta SLi accelerator. Scattered radiation generated by the applicator has been found by subtraction of the central axis depth dose curves, obtained with and without applicator.Scattered radiation from Siemens, Varian and Elekta electron applicators is still significant and cannot be neglected in advanced treatment planning. Scattered radiation at the surface of a water phantom can be as high as 12%. Scattered radiation decreases almost linearly with depth. Scattered radiation from Varian applicators shows clear dependence on beam energy. The Elekta applicators produce less scattered radiation than those of Varian and Siemens, but feature a higher effective angular variance. The scattered radiation decreases somewhat with increasing field size and is spread uniformly over the aperture. Experimental results comply with the results of simulations of the treatment head and electron applicator, using the BEAM Monte Carlo code.

Alternative effective modality of Leipzig applicator with an electron beam for the treatment of superficial malignancies

Object: The project was designed to study the effect of the same aperture high-energy electron beams from a dual photon-energy linear accelerator with the Leipzig applicator being a successful method of treating superficial malignancy in achieving a maximum relative surface dose. Methods: Leipzig applicator with its protective cap beams and small field electron beams from a Varian Clinac 2100CD linear accelerator were used. Circular fields at 100 cm SSD were obtained from cadmium-free cerrobend shields attached to the bottom face of a 6×6 cm 2 open wall electron cone. The central axis depth–dose curves, profiles and isodose curves measurement were carried out in a water phantom (NWP, Nucletron, The Netherlands) with a pair of silicon p-type diode electron detectors (Scanditronix, Sweden) with cross-section facing the source. The output factors, central-axis depth–dose curves, 90% isodose curve depth and area, flatness at depth of maximum dose were compared and the sagittal plane leakage of the Leipzig applicator were examined. Results: The data show that the maximum dose of Leipzig applicator and all 1 cm diameters electron beam are all located at the surface. The central-axis depth–dose curve of the Ir-192 beam is attenuated in an inverse square law manner. The surface to maximum dose ratio of the electron field decreases when the aperture size increases. The specified dose depths of Leipzig applicators are at least 3–6-fold less, and the area are at least 2–5-fold less than those of same aperture electron beams. The hot spot of a Leipzig applicator is located at the top and surrounding the source for both types of applicator with a leakage dose of up to 30% of D max. Conclusions: The Leipzig applicator with 192Ir high-dose-rate brachytherapy source can be used as an alternative method to electron beam irradiation in the treatment of superficial malignancies when the bulky electron applicator is difficult to set-up and approach.

Electron beam therapy at extended SSDs: an analysis of output correction factors for a Mitsubishi linear accelerator

The effects of extended source-to-surface distance (SSD) on the electron beam dose profiles were evaluated for various electron beam energies—6, 9, 12, 15 and 20 MeV—and the accuracy of various output correction methods was analysed on a Mitsubishi linear accelerator using a radiation field analyser (RFA). The dose fall-off region of the central axis depth–dose curves was nearly independent for SSDs up to 120 cm where as in the build-up region, a marginal reduction of surface dose was observed, particularly for lower energies and for smaller field sizes. Effective SSDs and virtual source distances were evaluated for field sizes ranging from 5 × 5 to 15 × 15 cm2 for various energies. Curve fitting was done with the measured outputs with various equations and coefficients were evaluated. The accuracy of the derived output correction factors by effective SSD, virtual source distance and curve-fit methods was assessed by evaluating correlation coefficients between the calculated and the measured values. The correlation coefficient was best with the linear-quadratic equation followed by the effective SSD method and the virtual source method. The output correction based on the linear-quadratic equation showed the best estimate of electron beam output at extended SSDs with an accuracy well within ±1%. The rapid reduction of dose due to the applicator-scattered component at dmax point with an extended SSD was significant for the 5 × 5 cm2 applicator and lower energies.

Are neutrons responsible for the dose discrepancies between Monte Carlo calculations and measurements in the build-up region for a high-energy photon beam?

This study presents measured neutron dose using a neutron dosimeter in a water phantom and investigates a hypothesis that neutrons in a high-energy photon beam may be responsible for the reported significant dose discrepancies between Monte Carlo calculations and measurements at the build-up region in large fields. Borated polyethylene slabs were inserted between the accelerator head and the phantom in order to remove neutrons generated in the accelerator head. The thickness of the slab ranged from 2.5 cm to 10 cm. A lead slab of 3 mm thickness was also used in the study. The superheated drop neutron dosimeter was used to measure the depth–dose curve of neutrons in a high-energy photon beam and to verify the effectiveness of the slab to remove these neutrons. Total dose measurements were performed in water using a WELLHOFER WP700 beam scanner with an IC-10 ionization chamber. The Monte Carlo code BEAM was used to simulate an 18 MV photon beam from a Varian Clinac-2100EX accelerator. Both EGS4/DOSXYZ and EGSnrc/DOSRZnrc were used in the dose calculations. Measured neutron dose equivalents as a function of depth per unit total dose in water were presented for 10 × 10 and 40 × 40 cm2 fields. The measured results have shown that a 5–10 cm thick borated polyethylene slab can reduce the neutron dose by a factor of 2 when inserted between the accelerator head and the detector. In all cases the measured neutron dose equivalent was less than 0.5% of the photon dose. In order to study if the ion chamber was highly sensitive to the neutron dose, we have investigated the disagreement between the Monte Carlo calculated and measured central-axis depth–dose curves in the build-up region when different shielding materials were used. The result indicated that the IC-10 chamber was not highly sensitive to the neutron dose. Therefore, neutrons present in a high-energy photon beam were unlikely to be responsible for the reported discrepancies in the build-up region for large fields.

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.

Experimental determination of depth-scaling factors and central axis depth dose for clinical electron beams.

Depth-scaling factors rho(eff) for clear polystyrene and polymethylmethacrylate (PMMA) phantoms have been determined experimentally as a function of nominal electron-beam energy in the range 6 to 22 MeV. Values of rho(eff) have been calculated from the ratio rho(eff) = R(wat)(50) / R(med)(50), where R(wat)(50) and R(med)(50) are the measured depths of 50% ionization in electron solid water and plastic (clear polystyrene and PMMA) phantoms, respectively. Measurements were made using an Attix chamber in an electron solid water phantom, a Holt chamber in a clear polystyrene phantom, and a Markus chamber in a PMMA phantom. The average value of measured rho(poly)(eff) was found to be 0.999 +/- 0.009. This is higher than the value of 0.975 recommended by Task Group 25 (TG-25) of the American Association of Physicists in Medicine (AAPM) by 2.5%. Depending on energy, the maximum differences between the AAPM TG-25-recommended and the measured values lie in the range 1% to 3.5%. Similarly, the average value of measured rho(PMMA)(eff) was found to be 1.168 +/- 0.023. This is higher than the AAPM TG-25-recommended value of 1.115, by 5%. Depending on energy, the maximum differences between the AAPM TG-25-recommended and the measured values lie in the range 3% to 8%. Central axis depth dose curves in water were generated for 6, 15, and 20 MeV electron beams from measured depth-ionization data in PMMA and clear polystyrene phantoms following the recommendations of the AAPM TG-25 report and using both TG-25-recommended and experimentally determined values of depth-scaling factors rho(eff). For both phantoms, either the TG-25-recommended value or the experimentally determined values of rho(eff) yielded agreement to within about 2 mm among all depth doses in water at the depths of clinical relevance.

Derivation of electron and photon energy spectra from electron beamcentral axis depth dose curves

A method for deriving the electron and photon energy spectra from electronbeam central axis percentage depth dose (PDD) curves has been investigated. ThePDD curves of 6, 12 and 20 MeV electron beams obtained from the Monte Carlofull phase space simulations of the Varian linear accelerator treatment headhave been used to test the method. We have employed a `random creep' algorithmto determine the energy spectra of electrons and photons in a clinicalelectron beam. The fitted electron and photon energy spectra have beencompared with the corresponding spectra obtained from the Monte Carlo fullphase space simulations. Our fitted energy spectra are in good agreement withthe Monte Carlo simulated spectra in terms of peak location, peak width,amplitude and smoothness of the spectrum. In addition, the derived depth dosecurves of head-generated photons agree well in both shape and amplitude withthose calculated using the full phase space data. The central axis depth dosecurves and dose profiles at various depths have been compared using anautomated electron beam commissioning procedure. The comparison hasdemonstrated that our method is capable of deriving the energy spectra for theVarian accelerator electron beams investigated. We have implemented thismethod in the electron beam commissioning procedure for Monte Carlo electronbeam dose calculations.

A strategy for selecting measurement points in the determination of depth-dose curves and dose profiles

Knowledge of the central-axis depth-dose curve and the dose profiles of a radiotherapy treatment unit are essential for setting up an external system for planning radiotherapy treatment. Estimates for these are usually found with the aid of a measurement probe with which the dose is measured at equally spaced measurement points. In this paper a strategy for selecting the measurement points for determination of the depth-dose curve and dose profile is proposed. The performance of the method is evaluated with real 6 MV photon depth-dose data and real 18 MV dose-profile data. The studies show that the proposed method allows the estimation of the depth-dose curve with adequate accuracy typically from 10 - 14 measurements at this energy instead of approximately 120 measurements, which is a common number of measurements. Thus the measurements protocol decreases about tenfold the number of measurements required. The studies also show that a fivefold decrease can be achieved in the dose-profile measurement.

A proton dose calculation algorithm for conformal therapy simulations based on Molière's theory of lateral deflections.

An algorithm is developed for computing proton dose distributions in the therapeutic energy range (100-250 MeV). The goal is to provide accurate pencil beam dose distributions for two-dimensional or three-dimensional simulations of possible intensity-modulated proton therapy delivery schemes. The algorithm is based on Molière's theory of lateral deflections, which accurately describes the distribution of lateral deflections suffered by incident charged particles. The theory is applied to nonuniform targets through the usual pencil beam approximation which assumes that all protons from a given pencil beam pass through the same material at each depth. Fluence-to-dose conversion is made via Monte Carlo calculated broad-field central-axis depth-dose curves, which accounts for attenuation due to nuclear collisions and range straggling. Calculation speed is enhanced by using a best-fit Gaussian approximation of the radial distribution function at depth. Representative pencil beam and spread-out Bragg-peak computations are presented at 250 MeV and 160 MeV in water. Computed lateral full-widths-at-half-maximum's in water, at the Bragg peak, agree with the expected theoretical lateral values to within 1% at 160 MeV and to within 3% at 250 MeV. This algorithm differs from convolution methods in that the effect of the depth of any inhomogeneities in density or atomic composition are accounted for in a rigorous fashion. The algorithm differs from Fermi-Eyges based methods by accounting in a rigorous way for the effect of nonsmall-angle scattering and screening due to atomic electrons. The computational burden is only slightly greater than that expected using the less-rigorous Fermi-Eyges theory.

An evaluation of the recommendations of the TG-25 protocol for determination of depth dose curves for electron beams using ionization chambers.

AAPM Radiation Therapy Committee Task Group 25 has recently outlined a protocol for the determination of relative dose curves for electron beams [Med. Phys. 18, 73-109 (1991)]. We have performed an evaluation of this protocol by comparing the central axis depth dose curves determined from measurements using two different ionization chambers and three different phantom materials. Measurements were made with a Farmer-type PTW and Capintec ionization chamber in solid water, PMMA, and clear polystyrene phantoms irradiated by 6- and 15-MeV electron beams. Central axis depth dose curves were generated from the measured depth-ionization data using the new protocol. For both the chambers and energies investigated in this study, excellent agreement was observed among all the depth doses in water obtained from measurements in all of the three phantoms studied.

The spectral dependence of electron central‐axis depth‐dose curves

Electron linac fields are usually characterized by the central-axis practical range in water, Rp, and the depth of half maximum dose, R50, for dosimetry, quality assurance, and treatment planning. The quantitative relations between the range parameters and the intrinsic linac beam's energy structure are critically reviewed. The spectral quantity <E0>* is introduced which is defined as the mean energy of the incident spectral peak, termed the "peak mean energy." An analytical model is constructed to demonstrate the predicted relation between polyenergetic spectral shapes and the resulting depth-dose curves. The model shows that, in the absence of electrons at the patient plane with energies outside about <E0>* +/- 0.1 <E0>*, Rp and R50 are both determined by <E0>*. This analytical approximation is confirmed by a Monte Carlo calculation comparing two different idealized incident spectra. The effect of contaminant lower energy or wide-angle scattered electrons is also discussed. The effect of the width of the intrinsic energy spread on the shape of the depth-dose curve is investigated using Monte Carlo depth-dose simulations based on measured linac energy spectra having energy spreads (full width at half maximum) as large as 20%. These simulations show that the energy spread has only a small effect on the shape of the central-axis depth-dose curve.

The effect of strong longitudinal magnetic fields on dose deposition from electron and photon beams.

The use of strong, uniform, longitudinal magnetic fields for external electron and photon beam irradiation is considered. Using the EGS4 Monte Carlo code modified to account for the presence of magnetic fields, dramatic narrowing of penumbra for photon and electron irradiations is demonstrated. In the vicinity of heterogeneities, "hot" and "cold" spots due to multiple scattering in electron beams are reduced substantially. However, in the presence of strong magnetic fields, the effect of inhomogeneities can be observed far from the location of the inhomogeneity due to reduced "washout" caused by lateral multiple scattering. The enhanced "Bragg peak," proposed or calculated by other authors, is not observed on the central axis of broad beams, owing to lateral equilibrium. It is proven that for broad parallel beams, the central axis depth-dose curve is independent of the strength of the external longitudinal magnetic field, as long as it is uniform. However, strong longitudinal magnetic fields can induce enhancements by redirection of the electron fields coming from point sources. Strong uniform longitudinal magnetic fields provide a way of controlling the spreading of electron beams due to multiple scattering, making the electron beams more "geometrical" in character, simplifying dose-deposition patterns, possibly allowing electron beams to be used in new ways for radiotherapy. Photon therapy also benefits from strong uniform longitudinal magnetic fields since the penumbra or other lateral disequilibrium effects associated with lateral electron transport can be eliminated.