Collimated electron beams and their associated penumbra widths

The Fermi-Eyges multiple-scattering theory for electrons is applied to calculate profiles of collimated electron beams. The dose profile below the collimator is a convolution of the intensity distribution of the electrons at the level of the collimator and the distribution arising from the propagation of a Gaussian point source from the collimator to the level of the calculation. The electrons at the level of the collimator possess an angular distribution characteristic of the configuration of the electron beam at the vacuum window. Hence, the dose profile and its associated penumbra width can be expressed in terms of the angular moments of the distribution of the electrons at the collimator. The dependence of the penumbra width on the configuration-dependent angular spread of the electrons at the collimator accounts for differences in the size of the penumbra between two broad-beam configurations. These differences are also seen experimentally. We have also studied the dependence of the angular moments of the electrons upon scattering foils present above the collimator and the position of the beam-broadening device in the accelerator head.     

Field equivalence for clinical electron beams

The concept of field equivalence for electron beams is examined using a pencil beam theory applied to circular fields. It is shown that a circular field can be found for a field of any size, shape and energy for which the depth dose distribution is approximately equivalent. The usefulness of the concept in clinical dosimetry is discussed.     

Experimental evaluation of analytical penumbra calculation model for wobbled beams

The goal of radiotherapy is not only to apply a high radiation dose to a tumor, but also to avoid side effects in the surrounding healthy tissue. Therefore, it is important for carbon-ion treatment planning to calculate accurately the effects of the lateral penumbra. In this article, for wobbled beams under various irradiation conditions, we focus on the lateral penumbras at several aperture positions of one side leaf of the multileaf collimator. The penumbras predicted by an analytical penumbra calculation model were compared with the measured results. The results calculated by the model for various conditions agreed well with the experimental ones. In conclusion, we found that the analytical penumbra calculation model could predict accurately the measured results for wobbled beams and it was useful for carbon-ion treatment planning to apply the model.     

Effects on electron beam penumbra using the photon MLC to reduce bremsstrahlung leakage for an add-on electron MLC

Electron IMRT treatments have the potential to reduce the integral dose due to the limited range of the electrons. However, bremsstrahlung produced in the scattering foils could penetrate an added electron MLC (eMLC), thus producing an unmodulated dose contribution that could become unacceptable in electron IMRT treatments. To limit this bremsstrahlung contribution, the photon MLC (xMLC) was used to track the eMLC, but with a margin to avoid penumbra widening through partial screening of the effective electron source. The purpose of this work was to study the effect of the photon-electron MLC tracking on the electron beam penumbra for different treatment head designs. Both isocentric designs and designs where the eMLC is used close to the patient (proximity geometry) have been analysed using Monte Carlo simulations. At 22.5 MeV energy, a tracking margin of 1 cm was enough to avoid penumbra degradation for a helium-filled isocentric geometry, while air-filled geometries (including proximity geometries) require a 2-3 cm margin. Illustrated by an example of a chest wall treatment by electron IMRT, the use of 1 cm tracking margin will reduce the collimator leakage contribution by a factor of 36 as compared to using a static setting of the photon collimator.     

Measurement of dose distributions using film in therapeutic electron beams

The feasibility of using film dosimetry data as the input data for patient treatment planning was evaluated. The central-axis depth dose and the off-axis ratios obtained from film measurements in a solid phantom were compared with those of ion-chamber measurements in water. Two techniques were used to generate isodose distributions. The first technique used only the film data, i.e., the central-axis depth dose and the off-axis ratios used for the reconstruction were determined from the film optical density (corrected for film nonlinearity). In the second technique, the central-axis depth dose measured by an ion chamber in a water phantom was combined with the off-axis ratios measured using film in the "solid water" phantom. The resulting isodose distributions from both techniques were compared with the ion-chamber measurements in water for 7-, 12-, and 18-MeV electrons, and the second technique showed better agreement with the ion-chamber measurements than did the first technique. The differences were within a clinically acceptable range.     

Field size dependence of wedge factors

The radiation output in the presence of wedge filters is characterized by the wedge transmission factor and open beam field size factors. Conventionally, the wedge factor for high-energy photons is measured in a water phantom at depth of maximum dose for a reference field size. Experimental measurements on different wedges indicate that the wedge factors are a function of field size. An analysis of these data show that this is primarily caused by the change in scattered radiation from the treatment head in the presence of wedge filters. The change in phantom scatter and radiation backscattered to the monitor chamber are minimal. For 4- or 6-MV x rays with a 60 degrees wedge, the use of a single wedge factor measured for 10 cm X 10 cm field introduces errors of up to 3.5%, for a 16-cm-wide field. For a 20-cm-wide field with this wedge, the error is 7%. Thinner wedges exhibit less differences.     

Direct measurement of electron contamination in cobalt beams using a charge detector

A method is described in some detail for measuring the magnitude and penetration of the electron contamination in photon beams using a pancake charge detector. It is shown that the response of the detector to a photon beam can be separated from the component due to the electron contamination. In the present work, the detector is used to measure the electron fluence in a 60Co photon beam. This fluence is subsequently converted to dose by comparison with the fluence and dose measured from a pure electron beam (90Sr). This study proves, within experimental error, that the observed changes in the buildup region, with the collimator opening for both filtered and unfiltered 60Co beams, are due to electron, rather than photon, contamination.     

Monte Carlo simulation of electron beams from an accelerator head using PENELOPE

The Monte Carlo code PENELOPE has been used to simulate electron beams from a Siemens Mevatron KDS linac with nominal energies of 6, 12 and 18 MeV. Owing to its accuracy, which stems from that of the underlying physical interaction models, PENELOPE is suitable for simulating problems of interest to the medical physics community. It includes a geometry package that allows the definition of complex quadric geometries, such as those of irradiation instruments, in a straightforward manner. Dose distributions in water simulated with PENELOPE agree well with experimental measurements using a silicon detector and a monitoring ionization chamber. Insertion of a lead slab in the incident beam at the surface of the water phantom produces sharp variations in the dose distributions, which are correctly reproduced by the simulation code. Results from PENELOPE are also compared with those of equivalent simulations with the EGS4-based user codes BEAM and DOSXYZ. Angular and energy distributions of electrons and photons in the phase-space plane (at the downstream end of the applicator) obtained from both simulation codes are similar, although significant differences do appear in some cases. These differences, however, are shown to have a negligible effect on the calculated dose distributions. Various practical aspects of the simulations, such as the calculation of statistical uncertainties and the effect of the 'latent' variance in the phase-space file, are discussed in detail.     

Central axis depth dose curve for electron beams.

In this article an analytical equation for electron depth dose is proposed electron energies from 6-20 MeV. The equation contains four parameters and it fits the build-up region, fall-off region as well as the bremsstrahlung background region. The calculated values from this equation fit within 1,5% of the measured data in the build-up region and in the fall-off region within 0,5 mm for the energy range 5-10 MeV and within 1 mm for the range 12-20 MeV. This equation can be applied beyond the practical range.     

Intraoperative radiation therapy using a mobile electron linear accelerator: field matching for large-field electron irradiation

Intraoperative radiation therapy (IORT) consists of delivering a large, single-fraction dose of radiation to a surgically exposed tumour or tumour bed at the time of surgery. With the availability of a mobile linear accelerator in the OR, IORT procedures have become more feasible for medical centres and more accessible to cancer patients. Often the area requiring irradiation is larger than what the treatment applicators will allow, and therefore, two or more adjoining fields are used. Unfortunately, the divergence and scattering of the electron beams may cause significant dose variations in the region of the field junction. Furthermore, because IORT treatments are delivered in a large single fraction, the effects of underdosing or overdosing could be more critical when compared to fractionated external beam therapy. Proper matching of the fields is therefore an important technical aspect of treatment delivery. We have studied the matching region using the largest flat applicator available for three different possibilities: abutting the fields, leaving a small gap or creating an overlap. Measurements were done using film dosimetry for the available energies of 4, 6, 9 and 12 MeV. Our results show the presence of clinically significant cold spots for the low-energy beams when the fields are either gapped or abutted, suggesting that the fields should be overlapped. No fields should be gapped. The results suggest that an optimal dose distribution may be obtained by overlapping the fields at 4 and 6 MeV and simply abutting the fields at 9 and 12 MeV. However, due to uncertainties in the placement of lead shields during treatment delivery, one may wish to consider overlapping the higher energy fields as well.     

Determination of percentage depth-dose curves for electron beams using different types of detectors

According to the new AAPM TG-51 dosimetry protocol, reference dosimetry for electron beams is performed at depth of d(ref)=0.6R50-0.1 (cm) instead of d(max) recommended in TG-21. In clinical practice most electron beams are normalized at d(max). Therefore it becomes more important to get an accurate percentage-depth-dose (%dd) curve particularly for higher-energy electron beams in which the depth d(ref) is away from d(max). When ionization chambers are used in determining %dd curves the water-to-air stopping-power ratios and the fluence correction factors are required. The TG-51 recommends that the stopping-power ratios for realistic electron beams be used instead of the monoenergetic stopping-power ratios used in TG-21. This investigation aims to study the effects of those correction factors on the determination of %dd curves. We observed 1% deviations in the value of %dd at d(ref) for 15 and 18 MeV beams between a plane-parallel NACP and a cylindrical IC-10 chamber without considering the fluence correction factors P(fl). We explored a method to derive the fluence correction factors at any depth by using the existing fluence correction data at d(max) and tested its feasibility. We compared %dd curves measured by a diode detector and a NACP chamber with stopping-power ratios recommended by TG-51 and those recommended by TG-21. We found that for 15 and 18 MeV beams the difference in the values of %dd at d(ref) between using those two different stopping-power ratios is about 0.5%. Excellent agreement is found between %dd curves measured by the diode and by the NACP chamber when the stopping-power ratios recommended by TG-51 are used.     

A new approach to film dosimetry for high-energy photon beams using organic plastic scintillators

This study is concerned with dose measurement of photon beams, both dynamic and static, by using x-ray film. As discussed in our last study (Burch et al 1997, Yeo et al 1997), x-ray film, as an integrating dosimeter, can be an ideal candidate if the over-response problem to low-energy photons (energies below 400 keV) is solved. In summary, the problem of the over-response can be explained as follows. Because the mass energy absorption coefficient of x-ray film increases as photon energy decreases, softening of the photon spectra with depth in a phantom makes the extent of film over-response a function of phantom depth (Burch et al 1997, Yeo et al 1997). Film dosimetry is based upon (a) calibration of the film response (i.e. optical density) at some specific depth in a phantom and (b) conversion of the film density which can cover whole depths in a phantom to dose by using the calibration curve. In megavoltage dosimetry, this normally causes over-response in doses at depths greater than the calibration depth.     

Magnetic fields with photon beams: dose calculation using electron multiple-scattering theory

Strong transverse magnetic fields can produce large dose enhancements and reductions in localized regions of a patient under irradiation by a photon beam. We have developed a new equation of motion for the transport of charged particles in an arbitrary magnetic field, incorporating both energy loss and multiple scattering. Key to modeling the latter process is a new concept, that of "typical scattered particles." The formulas which we have arrived at are particularly applicable to the transport of, and deposition of energy by, Compton electrons and pair-production electrons and positrons generated within a medium by a photon beam, and we have shown qualitatively how large dose enhancements and reductions can occur. A companion article examines this dose modification effect through systematic Monte Carlo simulations.     

Characteristics of bremsstrahlung in electron beams

Clinical electron beams contain an admixture of bremsstrahlung produced in structures in the accelerator head, in field-defining cerrobend or lead cutouts, and in the irradiated patient or water phantom. Accurate knowledge of these components is important for dose calculations and treatment planning. In this study, the bremsstrahlung components are separated for electron beams (energy 6-22 MeV, diameter 0-5 cm) using measurements in water and calculations. The results show that bremsstrahlung from the accelerator head dominates and increases with field size for electron beams generated by accelerators equipped with scattering foils. The bremsstrahlung from the field-defining cerrobend accounts for 10% to 30% of the total bremsstrahlung and decreases with increasing beam radius. The bremsstrahlung is softer than the x-ray beams of corresponding nominal energy since the latter are hardened by the flattening filter. For the 6, 12, and 22 MeV electron beams, the effective attenuation coefficients in water for the bremsstrahlung are 0.058, 0.050, and 0.043 cm(-1). The depths of maximum dose at 100 cm SSD are 0.8, 1.7, and 3.0 cm. The position of the virtual source of the bremsstrahlung shifts downstream from the nominal source position by 20, 13, 5.6 cm, respectively. The lateral bremsstrahlung dose distribution is more forward-peaked for higher electron energy. The bremsstrahlung components could be described for any machine by a set of simple measurements and can be modeled by an analytical expression.     

Monte Carlo simulation of backscatter from lead for clinical electron beams using EGSnrc

In electron radiotherapy of superficial lesions in the eyelid, lip, buccal mucosa, ear, and nose, backscattered electrons are produced from the lead shield used to protect the critical tissue underneath the tumor. In this study, the backscattered electrons, produced by clinical electron beams using a Varian 21 EX linear accelerator, were studied using Monte Carlo simulations. The electron backscatter factor (EBF), defined as the ratio of dose at the tissue-lead interface to the dose at the same point without the presence of backscatter, was calculated using the Monte Carlo EGSnrc-based code. The calculated EBFs were verified with measurements using metal-oxide-semiconductor field effect transistor detectors. The effect of the (1) initial electron beam energy, (2) thickness of bolus over the lead shield, (3) beam's angle of incidence, and (4) presence of an aluminum sheet used to absorb backscattered electrons, on the EBF, were studied. It is found that for lead shielding positioned at any fixed depth, the EBF decreases with an increase in initial electron beam energy (4-16 MeV). In addition, for depths within the electron practical range, Rp, and at a particular beam energy, the EBF increases with depth (or thickness of the treatment volume). When the electron beam angle increases from 0 degrees to 5 degrees, the EBF only decreases slightly (<4%) for all energies. The influence of the beam obliquity on the EBF is important when the treatment surface is not flat and perpendicular to the central beam axis. The use of an aluminum sheet to reduce backscattered electrons was also investigated. For a relatively low electron beam energy (4 MeV), a 2 mm aluminum sheet can reduce backscattering by 31%. While the electron beam energy increased, less backscattered electrons were produced and therefore removed by the same thickness of aluminum (only about 6% for 16 MeV). The Monte Carlo calculated EBFs from this study, characterized by the electron beam energy, depth of bolus above the lead shield, beam obliquity, and presence of an aluminum sheet, may provide important clinical information for radiation oncology staff when considering the effect of electron backscatter on radiotherapy using internal shielding.     

Improvement of field matching in segmented-field electron conformal therapy using a variable-SCD applicator

The purpose of the present study is to demonstrate that the use of an electron applicator with energy-dependent source-to-collimator distances (SCDs) will significantly improve the dose homogeneity for abutted electron fields in segmented-field electron conformal therapy (ECT). Multiple Coulomb scattering theory was used to calculate and study the P(80-20) penumbra width of off-axis dose profiles as a function of air gap and depth. Collimating insert locations with air gaps (collimator-to-isocenter distance) of 5.0, 7.5, 11.5, 17.5 and 19.5 cm were selected to provide equal P(80-20) at a depth of 1.5 cm in water for energies of 6, 9, 12, 16 and 20 MeV, respectively, for a Varian 2100EX radiation therapy accelerator. A 15 x 15 cm(2) applicator was modified accordingly, and collimating inserts used in the variable-SCD applicator for segmented-field ECT were constructed with diverging edges using a computer-controlled hot-wire cutter, which resulted in 0.27 mm accuracy in the abutted edges. The resulting electron beams were commissioned for the pencil-beam algorithm (PBA) on the Pinnacle(3) treatment planning system. Four hypothetical planning target volumes (PTVs) and one patient were planned for segmented-field ECT using the new variable-SCD applicator, and the resulting dose distributions were compared with those calculated for the identical plans using the conventional 95 cm SCD applicator. Also, a method for quality assurance of segmented-field ECT dose plans using the variable-SCD applicator was evaluated by irradiating a polystyrene phantom using the treatment plans for the hypothetical PTVs. Treatment plans for all four of the hypothetical PTVs using the variable-SCD applicator showed significantly improved dose homogeneity in the abutment regions of the segmented-field ECT plans. This resulted in the dose spread (maximum dose-minimum dose), sigma, and D(90-10) in the PTV being reduced by an average of 32%, 29% and 32%, respectively. Reductions were most significant for abutted fields of nonadjacent energies. Planning segmented-field ECT using the variable-SCD applicator for a patient with recurrent squamous cell carcinoma of the left ear showed the dose spread, sigma, and D(90-10) of the dose distribution in the PTV being reduced by an average of 38%, 22% and 22%, respectively. The measured and calculated dose in a polystyrene phantom resulting from the variable-SCD, segmented-field ECT plans for the hypothetical PTVs showed good agreement; however, isolated differences between dose calculation and measurement indicated the need for a more accurate dose algorithm than the PBA for segmented-field ECT. These results confirmed our hypothesis that using the variable-SCD applicator for segmented-field ECT results in the PTV dose distribution becoming more homogenous and being within the range of 85-105% of the 'given dose'. Clinical implementation of this method requires variable-SCD applicators, and the design used in the present work should be acceptable, as should our methods for construction of the inserts. Dose verification measurements in a polystyrene phantom and the recommended improvements in dose calculation should be appropriate for quality assurance of segmented-field ECT.