Monte Carlo computed machine-specific correction factors for reference dosimetry of TomoTherapy static beam for several ion chambers.

PURPOSE: To determine k(Q(msr),Q(o) ) (f(msr),f(o) ) correction factors for machine-specific reference (msr) conditions by Monte Carlo (MC) simulations for reference dosimetry of TomoTherapy static beams for ion chambers Exradin A1SL, A12; PTW 30006, 31010 Semiflex, 31014 PinPoint, 31018 microLion; NE 2571. METHODS: For the calibration of TomoTherapy units, reference conditions specified in current codes of practice like IAEA∕TRS-398 and AAPM∕TG-51 cannot be realized. To cope with this issue, Alfonso et al. [Med. Phys. 35, 5179-5186 (2008)] described a new formalism introducing msr factors k(Q(msr),Q(o) ) (f(msr),f(o) ) for reference dosimetry, applicable to static TomoTherapy beams. In this study, those factors were computed directly using MC simulations for Q(0) corresponding to a simplified (60)Co beam in TRS-398 reference conditions (at 10 cm depth). The msr conditions were a 10 × 5 cm(2) TomoTherapy beam, source-surface distance of 85 cm and 10 cm depth. The chambers were modeled according to technical drawings using the egs++ package and the MC simulations were run with the egs_chamber user code. Phase-space files used as the source input were produced using PENELOPE after simulation of a simplified (60)Co beam and the TomoTherapy treatment head modeled according to technical drawings. Correlated sampling, intermediate phase-space storage, and photon cross-section enhancement variance reduction techniques were used. The simulations were stopped when the combined standard uncertainty was below 0.2%. RESULTS: Computed k(Q(msr),Q(o) ) (f(msr),f(o) ) values were all close to one, in a range from 0.991 for the PinPoint chamber to 1.000 for the Exradin A12 with a statistical uncertainty below 0.2%. Considering a beam quality Q defined as the TPR(20,10) for a 6 MV Elekta photon beam (0.661), the additional correction k(Q(msr,)Q) (f(msr,)f(ref) ) to k(Q,Q(o) ) defined in Alfonso et al. [Med. Phys. 35, 5179-5186 (2008)] formalism was in a range from 0.997 to 1.004. CONCLUSION: The MC computed factors in this study are in agreement with measured factors for chamber types already studied in literature. This work provides msr correction factors for additional chambers used in reference dosimetry. All of them were close to one (within 1%).

Monte Carlo-based simulation of dynamic jaws tomotherapy.

PURPOSE: Original TomoTherapy systems may involve a trade-off between conformity and treatment speed, the user being limited to three slice widths (1.0, 2.5, and 5.0 cm). This could be overcome by allowing the jaws to define arbitrary fields, including very small slice widths (<1 cm), which are challenging for a beam model. The aim of this work was to incorporate the dynamic jaws feature into a Monte Carlo (MC) model called TomoPen, based on the MC code PENELOPE, previously validated for the original TomoTherapy system. METHODS: To keep the general structure of TomoPen and its efficiency, the simulation strategy introduces several techniques: (1) weight modifiers to account for any jaw settings using only the 5 cm phase-space file; (2) a simplified MC based model called FastStatic to compute the modifiers faster than pure MC; (3) actual simulation of dynamic jaws. Weight modifiers computed with both FastStatic and pure MC were compared. Dynamic jaws simulations were compared with the convolution∕superposition (C∕S) of TomoTherapy in the "cheese" phantom for a plan with two targets longitudinally separated by a gap of 3 cm. Optimization was performed in two modes: asymmetric jaws-constant couch speed ("running start stop," RSS) and symmetric jaws-variable couch speed ("symmetric running start stop," SRSS). Measurements with EDR2 films were also performed for RSS for the formal validation of TomoPen with dynamic jaws. RESULTS: Weight modifiers computed with FastStatic were equivalent to pure MC within statistical uncertainties (0.5% for three standard deviations). Excellent agreement was achieved between TomoPen and C∕S for both asymmetric jaw opening∕constant couch speed and symmetric jaw opening∕variable couch speed, with deviations well within 2%∕2 mm. For RSS procedure, agreement between C∕S and measurements was within 2%∕2 mm for 95% of the points and 3%∕3 mm for 98% of the points, where dose is greater than 30% of the prescription dose (gamma analysis). Dose profiles acquired in transverse and longitudinal directions through the center of the phantom were also compared with excellent agreement (2%∕2 mm) between all modalities. CONCLUSIONS: The combination of weights modifiers and interpolation allowed implementing efficiently dynamic jaws and dynamic couch features into TomoPen at a minimal cost in terms of efficiency (simulation around 8 h on a single CPU).

On the relationships between electron spot size, focal spot size, and virtual source position in Monte Carlo simulations.

PURPOSE: Every year, new radiotherapy techniques including stereotactic radiosurgery using linear accelerators give rise to new applications of Monte Carlo (MC) modeling. Accurate modeling requires knowing the size of the electron spot, one of the few parameters to tune in MC models. The resolution of integrated megavoltage imaging systems, such as the tomotherapy system, strongly depends on the photon spot size which is closely related to the electron spot. The aim of this article is to clarify the relationship between the electron spot size and the photon spot size (i.e., the focal spot size) for typical incident electron beam energies and target thicknesses. METHODS: Three electron energies (3, 5.5, and 18 MeV), four electron spot sizes (FWHM = 0, 0.5, 1, and 1.5 mm), and two tungsten target thicknesses (0.15 and 1 cm) were considered. The formation of the photon beam within the target was analyzed through electron energy deposition with depth, as well as photon production at several phase-space planes placed perpendicular to the beam axis, where only photons recorded for the first time were accounted for. Photon production was considered for "newborn" photons intersecting a 45 x 45 cm2 plane at the isocenter (85 cm from source). Finally, virtual source position and "effective" focal spot size were computed by back-projecting all the photons from the bottom of the target intersecting a 45 x 45 cm2 plane. The virtual source position and focal spot size were estimated at the plane position where the latter is minimal. RESULTS: In the relevant case of considering only photons intersecting the 45 x 45 cm2 plane, the results unambiguously showed that the effective photon spot is created within the first 0.25 mm of the target and that electron and focal spots may be assumed to be equal within 3-4%. CONCLUSIONS: In a good approximation photon spot size equals electron spot size for high energy X-ray treatments delivered by linear accelerators.

Design of adaptive treatment margins for non-negligible measurement uncertainty: application to ultrasound-guided prostate radiation therapy.

Daily imaging during the course of a fractionated radiotherapy treatment has the potential for frequent intervention and therefore effective adaptation of the treatment to the individual patient. The treatment information gained from such images can be analysed and updated daily to obtain a set of patient individualized parameters. However, in many situations, the uncertainty with which these parameters are estimated cannot be neglected. In this work this methodology is applied to the adaptive estimation of setup errors, the derivation of a daily optimal pre-treatment correction strategy, and the daily update of the treatment margins after application of these corrections. For this purpose a dataset of 19 prostate cancer patients was analysed retrospectively. The position of the prostate was measured daily with an optically guided 3D ultrasound localization system. The measurement uncertainty of this system is approximately 2 mm. The algorithm finds the most likely position of the target maximizing an a posteriori probability given the set of measurements. These estimates are used for the optimal corrections applied to the target volume. The results show that the application of the optimal correction strategy allows a reduction in the treatment margins in a systematic way with increasing progression of the treatment. This is not the case using corrections based only on the measured values that do not take the measurement uncertainty into account.

On the accuracy and effectiveness of dose reconstruction for tomotherapy.

Dose reconstruction is a process that re-creates the treatment-time dose deposited in a patient provided there is knowledge of the delivered energy fluence and the patient's anatomy at the time of treatment. A method for reconstructing dose is presented. The process starts with delivery verification, in which the incident energy fluence from a treatment is computed using the exit detector signal and a transfer matrix to convert the detector signal to energy fluence. With the verified energy fluence and a CT image of the patient in the treatment position, the treatment-time dose distribution is computed using any model-based algorithm such as convolution/superposition or Monte Carlo. The accuracy of dose reconstruction and the ability of the process to reveal delivery errors are presented. Regarding accuracy, a reconstructed dose distribution was compared with a measured film distribution for a simulated breast treatment carried out on a thorax phantom. It was found that the reconstructed dose distribution agreed well with the dose distribution measured using film: the majority of the voxels were within the low and high dose-gradient tolerances of 3% and 3 mm respectively. Concerning delivery errors, it was found that errors associated with the accelerator, the multileaf collimator and patient positioning might be detected in the verified energy fluence and are readily apparent in the reconstructed dose. For the cases in which errors appear in the reconstructed dose, the possibility for adaptive radiotherapy is discussed.

Modeling photon output caused by backscattered radiation into the monitor chamber from collimator jaws using a Monte Carlo technique.

Dose per monitor unit in photon fields generated by clinical linear accelerators can be affected by the backscattered radiation into the monitor chamber from collimator jaws. Thus, it is necessary to account for the backscattered radiation in computing monitor unit setting for a treatment field. In this work, we investigated effects of the backscatter from collimator jaws based on Monte Carlo simulations of a clinical linear accelerator. The backscattered radiation scored within the monitor chamber was identified as originating either from the upper jaws (Y jaws), or from the lower jaws (X jaws). From the results of Monte Carlo simulations, ratios of the monitor-chamber-scored dose caused by the backscatter to the dose caused by the forward radiation, R(x,y), were modeled as functions of the individual X and Y jaw positions. The amount of the backscattered radiation for any field setting was then computed as a compound contribution from both the X and Y jaws. The dose ratios of R(x,y) were then used to calculate the change in photon output caused by the backscatter, Scb(x,y). Results of these calculations were compared with available measured data based on counting the electron pulses or charge from the electron target of an accelerator. Data from this study showed that the backscattered radiation contributes approximately 3% to the monitor-chamber-scored dose. A majority of the backscattered radiation comes from the upper jaws, which are located closer to the monitor chamber. The amount of the backscatter decreases approximately in a linear fashion with the jaw opening. This results in about a 2% increase of photon output from a 10 cm x 10 cm field to a 40 cm x 40 cm field. The off-axis location of the jaw opening does not have a significant effect on the magnitude of the backscatter. The backscatter effect is significant for monitor chambers using kapton windows, particularly for treatment fields using moving jaws. Applying the backscatter correction improves the accuracy of monitor-unit calculation using a model-based dose calculation algorithm such as the convolution method.

Monte Carlo investigation of electron beam output factors versus size of square cutout.

A major task in commissioning an electron accelerator is to measure relative output factors versus cutout size (i.e., cutout factors) for various electron beam energies and applicator sizes. We use the BEAM Monte Carlo code [Med Phys. 22, 503-524 (1995)] to stimulate clinical electron beams and to calculate the relative output factors for square cutouts. Calculations are performed for a Siemens MD2 linear accelerator with beam energies, 6, 9, 11, and 13 MeV. The calculated cutout factors for square cutouts in 10 X 10 cm2, 15 X 15 cm2, and 20 X 20 cm2 applicators at SSDs of 100 and 115 cm agree with the measurements made using a silicon diode within about 1% except for the smallest cutouts at SSD= 115 cm where they agree within 0.015. The details of each component of the dose, such as the dose from particles scattered off the jaws and the applicator, the dose from contaminant photons, the dose from direct electrons, etc., are also analyzed. The calculations show that inphantom side-scatter equilibrium is a major factor for the contribution from the direct component which usually dominates the output of a beam. It takes about 6 h of CPU time on a Pentium Pro 200 MHz computer to simulate an accelerator and additional 2 h to calculate the relative output factor for each cutout with a statistical uncertainty of 1%.

A comparison of Monte Carlo and analytic first scatter dose spread arrays.

We compare first scattered point dose spread arrays generated by Monte Carlo and an analytic method. The analytic method models energy deposition using Klein-Nishina cross sections for Compton scatter and approximations for electron transport. Assumptions in the analytic method are shown to be valid within a region of the point dose spread kernel in which meaningful comparisons can be made. Differences between the models are less than 10% for the forward scatter directions for radii greater than the electron range associated with the first scattered Compton photon. Differences in the backscatter region are discussed and indicate that the analytic model is useful for identifying large errors that might be present in numerically generated first scatter point dose spread arrays. The analytic method is simple and useful for validating first scatter kernels.

Multileaf collimator interleaf transmission.

Multileaf collimators (MLCs) have advanced past their original design purpose as a replacement for field shaping cerrobend blocks. Typically, MLCs incorporate an interlocking tongue-and-groove design between adjacent leaves to minimize leakage between leaves. They are beginning to be used to provide intensity modulation for conformal three-dimensional radiation therapy. It is possible that a critical target volume may receive an underdose due to the region of overlap if adjacent leaves are allowed to alternate between the open and closed positions, as they might if intensity modulation is employed. This work demonstrates the magnitude of that effect for a commercially available one-dimensional temporally modulated MLC. The magnitude of the transmission between leaves as a function of leaf separation was also studied, as well as the transmission as a function of leaf rotation away from the source. The results of this work were used for the design of a tomotherapy MLC. The radiation leakage considerations for a tomotherapy MLC are discussed.

Effects of changes in stopping-power ratios with field size on electron beam relative output factors.

Stopping-power ratios are a function of field size and vary with accelerators. To investigate how these variations affect relative output factor measurements made using ion chambers for electron beams, especially for small fields, (L/rho)air(water) is calculated using the Monte Carlo technique for different field sizes, beam energies, and accelerators and is compared to the data in TG-21 or TG-25, which are for mono-energetic broad beams. For very small field sizes defined by cutouts, if the change in (L/rho)air(water) with dmax is ignored (i.e., TG-25 is not carefully followed), there is an overestimate of relative output factors by up to 3%. Ignoring the field-size effect on stopping-power ratio adds an additional overestimate of up to one-half percent, and using mono-energetic stopping-power ratio data instead of realistic beam data gives another error, but in the opposite direction, of up to 0.7%. Due to the cancellation of these latter two errors, following TG-25 with (L/rho)air(water) data for broad mono-energetic beams will give the correct answer for the ROF measurement within 0.4% compared to using (L/rho)air(water) data for which the field-size effect is considered for realistic electron beams.

Calculating dose and output factors for wedged photon radiotherapy fields using a convolution/superposition method.

We have developed a convolution/superposition method to calculate dose distributions in photon treatment fields with beam modifiers such as physical wedges. The dose component due to wedge generated radiation was accounted for by using an extended phantom model, which integrated a wedge, an air gap, and a patient phantom as the calculation phantom. The inhomogeneities in the extended phantom and the effect of beam hardening by the wedge were both corrected for in the convolution dose calculation. The calculated dose was verified by Monte Carlo simulation of the same extended phantom. A new dual photon source model was also used in the convolution method to account for both primary photons from the target and extra-focal photons from the primary collimator and flattening filter. Thus, realistic photon energy fluence distributions in the extended phantom were used for the dose calculation. The calculated dose distributions and the wedge factors agreed with the measured data within 2% for a variety of treatment fields including asymmetric fields. Our results showed that the wedge-generated radiation could contribute a significant fraction of the total dose in patients. This dose component depends on a specific field configuration, thus wedge factor changes with photon energy, wedge angle, field size, depth, and patient phantom SSD. The variation of the wedge factor can be predicted accurately by our convolution approach with the extended phantom model, which allows for more accurate dose or monitor unit computation for photon fields with beam modifiers.

Correcting kernel tilting and hardening in convolution/superposition dose calculations for clinical divergent and polychromatic photon beams.

To account for clinical divergent and polychromatic photon beams, we have developed kernel tilting and kernel hardening correction methods for convolution dose calculation algorithms. The new correction methods were validated by Monte Carlo simulation. The accuracy and computation time of the our kernel tilting and kernel hardening correction methods were also compared to the existing approaches including terma divergence correction, dose divergence correction methods, and the effective mean kernel method with no kernel hardening correction. Treatment fields of 10 x 10-40 x 40 cm2 (field size at source to axis distance (SAD)) with source to source distances (SSDs) of 60, 80, and 100 cm, and photon energies of 6, 10, and 18 MV have been studied. Our results showed that based on the relative dose errors at a depth of 15 cm along the central axis, the terma divergence correction may be used for fields smaller than 10 x 10 cm2 with a SSD larger than 80 cm; the dose divergence correction with an additional kernel hardening correction can reduce dose error and may be more applicable than the terma divergence correction. For both these methods, the dose error increased linearly with the depth in the phantom; the 90% isodose lines at the depth of 15 cm were shifted by about 2%-5% of the field width due to significant underestimation of the penumbra dose. The kernel hardening effect was less prominent than the kernel tilting effect for clinical photon beams. The dose error by using nonhardening corrected kernel is less than 2.0% at a depth of 15 cm along the central axis, yet it increased with a smaller field size and lower photon energy. The kernel hardening correction could be more important to compute dose in the fields with beam modifiers such as wedges when beam hardening is more significant. The kernel tilting correction and kernel hardening correction increased computation time by about 3 times, and 0.5-1 times, respectively. This can be justified by more accurate dose calculations for the majority of clinical treatments.

Accurate characterization of Monte Carlo calculated electron beams for radiotherapy.

Monte Carlo studies of dose distributions in patients treated with radiotherapy electron beams would benefit from generalized models of clinical beams if such models introduce little error into the dose calculations. Methodology is presented for the design of beam models, including their evaluation in terms of how well they preserve the character of the clinical beam, and the effect of the beam models on the accuracy of dose distributions calculated with Monte Carlo. This methodology has been used to design beam models for electron beams from two linear accelerators, with either a scanned beam or a scattered beam. Monte Carlo simulations of the accelerator heads are done in which a record is kept of the particle phase-space, including the charge, energy, direction, and position of every particle that emerges from the treatment head, along with a tag regarding the details of the particle history. The character of the simulated beams are studied in detail and used to design various beam models from a simple point source to a sophisticated multiple-source model which treats particles from different parts of a linear accelerator as from different sub-sources. Dose distributions calculated using both the phase-space data and the multiple-source model agree within 2%, demonstrating that the model is adequate for the purpose of Monte Carlo treatment planning for the beams studied. Benefits of the beam models over phase-space data for dose calculation are shown to include shorter computation time in the treatment head simulation and a smaller disk space requirement, both of which impact on the clinical utility of Monte Carlo treatment planning.

Electron fluence correction factors for conversion of dose in plastic to dose in water.

In radiation dosimetry protocols, plastic is allowed as a phantom material for the determination of absorbed dose to water in electron beams. The electron fluence correction factor is needed in conversion of dose measured in plastic to dose in water. There are large discrepancies among recommended values as well as measured values of electron fluence correction factors when polystyrene is used as a phantom material. Using the Monte Carlo technique, we have calculated electron fluence correction factors for incident clinical beam energies between 5 and 50 MeV as a function of depth for clear polystyrene, white polystyrene and PMMA phantom materials and compared the results with those recommended in protocols as well as experimental values from published data. In the Monte Carlo calculations, clinical beams are simulated using the EGS4 user-code BEAM for a variety of medical accelerators. The study shows that our calculated fluence correction factor, phi pw, is a function of depth and incident beam energy Eo with little dependence on other aspects of beam quality. However the phi pw values at dmax are indirectly influenced by the beam quality since they vary with depth and dmax also varies with the beam quality. Calculated phi pw values at dmax are in a range of 1.005-1.045 for a clear polystyrene phantom, 1.005-1.038 for a white polystyrene phantom and 0.996-1.016 for a PMMA phantom. Our values of phi pw are about 1-2% higher than those determined according to the AAPM TG-25 protocol at dmax for clear or white polystyrene. Our calculated values of phi pw also explain some of the variations of measured data because of its depth dependence. A simple formula is derived which gives the electron fluence correction factor phi pw as a function of R50 at dmax or at the depth of 0.6R50-0.1 for any clinical electron beam with energy between 5 and 25 MeV for three plastics: clear polystyrene, white polystyrene and PMMA. The study also makes a careful distinction between phi pw and the corresponding IAEA Code of Practice quantity, hm.

A dual source photon beam model used in convolution/superposition dose calculations for clinical megavoltage x-ray beams.

A realistic model of photon beams generated by clinical linear accelerators has been incorporated in a convolution/superposition method to compute dose distributions in photon treatment fields. In this beam model, a primary photon source represents photons directly from the target, and an extra-focal photon source represents scattered photons from the primary collimator and the flattening filter. Monte Carlo simulation was used to study clinical linear accelerators producing photon beams. From the output of the Monte Carlo simulation, the fluence and spectral distributions of each photon component, as well as the geometrical characteristics of each photon source with respect to its distance to the isocenter and its source distribution, were analyzed. These quantities were used to reproduce realistic photon distributions in treatment fields, and thus to compute dose distributions using the convolution method. Our results showed that compared to the primary photon fluence, the extra-focal photon fluence from the primary collimator and the flattening filter was 11%-16% at the isocenter, among which 70% was contributed by the flattening filter. The variation of extra-focal photons in different treatment fields was predicted accurately by accounting for the finite size of the extra-focal source. Compared to measurements, dose distributions in photon treatment fields, including those of asymmetric jaw settings and at different SSDs were calculated accurately, particularly in the penumbral region, by using the convolution method with the new dual source photon beam model.

Calculating output factors for photon beam radiotherapy using a convolution/superposition method based on a dual source photon beam model.

A realistic photon beam model based on Monte Carlo simulation of clinical linear accelerators was implemented in a convolution/superposition dose calculation algorithm. A primary and an extra-focal sources were used in this beam model to represent the direct photons from the target and the scattered photons from other head structures, respectively. The effect of the finite size of the extra-focal source was modeled by a convolution of the source fluence distribution with the collimator aperture function. Relative photon output in air (Sc) and in phantom (Scp) were computed using the convolution method with this new photon beam model. Our results showed that in a 10 MV photon beam, the Sc, Sp (phantom scatter factor), and Scp factors increased by 11%, 10%, and 22%, respectively, as the field size changed from 3 x 3 cm2 to 40 x 40 cm2. The variation of the Sc factor was contributed mostly by an increase of the extra-focal radiation with field size. The radiation backscattered into the monitor chamber inside the accelerator head affected the Sc by about 2% in the same field range. The output factors in elongated fields, asymmetric fields, and blocked fields were also investigated in this study. Our results showed that if the effect of the backscattered radiation was taken into account, output factors in these treatment fields can be predicted accurately by our convolution algorithm using the dual source photon beam model.

Modeling dose distributions from portal dose images using the convolution/superposition method.

Post-treatment dose verification refers to the process of reconstructing delivered dose distributions internal to a patient from information obtained during the treatment. The exit dose is commonly used to describe the dose beyond the exit surface of the patient from a megavoltage photon beam. Portal imaging provides a method of determining the dose in a plane distal to a patient from a megavoltage therapeutic beam. This exit dose enables reconstruction of the dose distribution from external beam radiation throughout the patient utilizing the convolution/superposition method and an extended phantom. An iterative convolution/superposition algorithm has been created to reconstruct dose distributions in patients from exit dose measurements during a radiotherapy treatment. The method is based on an extended phantom that includes the patient CT representation and an electronic portal imaging device (EPID). The convolution/superposition method computes the dose throughout the extended phantom, which allows the portal dose image to be predicted in the EPID. The process is then reversed to take the portal dose measurement and infer what the dose distribution must have been to produce the measured portal dose. The dose distribution is modeled without knowledge of the incident intensity distribution, and includes the effects of scatter in the computation. The iterative method begins by assuming that the primary energy fluence (PEF) at the portal image plane is equal to the portal dose image, the PEF is then back-projected through the extended phantom and convolved with the dose deposition kernel to determine a new prediction of the portal dose image. The image of the ratio of the computed PEF to the computed portal dose is then multiplied by the measured portal dose image to produce a better representation of the PEF. Successive iterations of this process then converge to the exiting PEF image that would produce the measured portal dose image. Once convergence is established, the dose distribution is determined by back-projecting the PEF and convolving with the dose deposition kernel. The method is accurate, provided the patient representation during treatment is known. The method was used on three phantoms with a photon energy of 6 MV to verify convergence and accuracy of the algorithm. The reconstructed dose volumes agree to within 3% of the forward computation dose volumes. Furthermore, this technique assumes no prior knowledge of the incident fluence and therefore may better represent the dose actually delivered.

Calculation of portal dose using the convolution/superposition method.

The convolution/superposition method was used to predict the dose throughout an extended volume, which includes a phantom and a portal imaging device. From the calculated dose volume, the dose delivered in the portal image plane was extracted and compared to a portal dose image. This comparison aids in verifying the beam configuration or patient setup after delivery of the radiation. The phantoms used to test the accuracy of this method include a solid water cube, a Nuclear Associates CT phantom, and an Alderson Rando thorax phantom. The dose distribution in the image plane was measured with film and an electronic portal imaging device in each case. The calculated portal dose images were within 4% of the measured images for most voxels in the central portion of the field for all of the extended volumes. The convolution/superposition method also enables the determination of the scatter and primary dose contributions using the particular dose deposition kernels for each contribution. The ratio of primary dose to total dose was used to extract the primary dose from the detected portal image, which enhances the megavoltage portal images by removing scatter blurring. By also predicting the primary energy fluence, we can find the ratio of computed primary energy fluence to total dose. Multiplying this ratio by the measured dose image estimates the relative primary energy fluence at the portal imager. The image of primary energy fluence possesses higher contrast and may be used for further quantitative image processing and dose modeling.

Photon dose calculation incorporating explicit electron transport.

Significant advances have been made in recent years to improve photon dose calculation. However, accurate prediction of dose perturbation effects near the interfaces of different media, where charged particle equilibrium is not established, remain unsolved. Furthermore, changes in atomic number, which affect the multiple Coulomb scattering of the secondary electrons, are not accounted for by current photon dose calculation algorithms. As local interface effects are mainly due to the perturbation of secondary electrons, a photon-electron cascade model is proposed which incorporates explicit electron transport in the calculation of the primary photon dose component in heterogeneous media. The primary photon beam is treated as the source of many electron pencil beams. The latter are transported using the Fermi-Eyges theory. The scattered photon dose contribution is calculated with the dose spread array [T.R. Mackie, J.W. Scrimger, and J.J. Battista, Med. Phys. 12, 188-196 (1985)] approach. Comparisons of the calculation with Monte Carlo simulation and TLD measurements show good agreement for positions near the polystyrene-aluminum interfaces.

Calculation of stopping-power ratios using realistic clinical electron beams.

The Spencer-Attix water/air restricted mass collision stopping-power ratio is calculated in realistic electron beams in the energy range from 5-50 MeV for a variety of clinical accelerators including the Varian Clinac 2100C, the Philips SL75-20, the Siemens KD2, the AECL Therac 20, and the Scanditronix Medical Microtron 50. The realistic clinical beams are obtained from full Monte Carlo simulations of the clinical linear accelerators using the code BEAM. The stopping-power ratios calculated using clinical beams are compared with those determined according to the AAPM and the IAEA protocols which were calculated by using monoenergetic parallel beams. Using the energy-range relationship of Rogers and Bielajew [Med. Phys. 13, 687-694 (1986)] leads to the most consistent picture in which the stopping-power ratios at dmax derived from mono-energetic calculations underestimate the stopping-power ratios calculated with the realistic beam by 0.3% at 5 MeV and up to 1.4% at 20 MeV. The stopping-power ratios at dmax determined according to the AAPM TG-21 protocol (1983) are shown to overestimate the realistic stopping-power ratios by up to 0.6% for a 5-MeV beam and underestimate them by up to 1.2% for a 20-MeV beam. Those determined according to the IAEA (1987) protocol overestimate the realistic stopping-power ratios by up to 0.3% for a 5-MeV beam and underestimate them by up to a 1.1% for a 20-MeV beam at reference depth. The causes of the differences in the stopping-power ratios between the realistic clinical mono-energetic beams are analyzed quantitatively. The changes in the stopping-power ratios at dmax are mainly due to the energy spread of the electron beam and the contaminant photons in the clinical beams. The effect of the angular spread of electrons is rather small except at the surface. Data are presented which give the corrected stopping-power ratios at dmax or reference depth starting from those determined according to protocols for any energy of clinical electron beams with scattering foils. For scanned clinical electron beams the correction to stopping-power ratios determined according to protocols is found to be less than 0.5% at dmax or reference depth for all beam energies studied. We quantify the differences in the stopping-power ratios determined using the depth of 50% ionization level and the depth of 50% dose level. The differences are very small except for very-high-energy beams (50 MeV) where they can be up to 0.8%.