Reference dosimetry in the presence of magnetic fields: conditions to validate Monte Carlo simulations.

With the advent of MRI-guided radiotherapy, reference dosimetry must be thoroughly addressed to account for the effects of the magnetic field on absorbed dose to water and on detector dose response. While Monte Carlo plays an essential role in reference dosimetry, it is also crucial for determining quality correction factors in these new conditions. The Fano cavity test is recognized as fundamental to validate Monte Carlo transport algorithms. In the presence of magnetic fields, it is necessary to define special conditions under which such a test can be performed. The present theoretical study proposes two conditions in which the validity of Fano's theorem is demonstrated in the presence of a magnetic field and the analytic expression of energy deposition is verified. It is concluded that the proposed conditions form a valid basis for two types of Fano cavity tests in the presence of a magnetic field.

Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms.

To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano's theorem. Additionally, Lewis' approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano's and Lewis' approaches are stated in this new equation. Fano's theorem is found not to apply in the presence of electromagnetic fields. Lewis' theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms.

The inverse-square gamma-irradiation anomaly of the Nuclear Enterprises 2575 large-volume ionisation chamber.

The Nuclear Enterprises (Model 2575) 600 cc ionisation chamber is examined to discover the cause of its anomalous behaviour in inverse-square stability measurements. Measurements and Monte Carlo calculations are employed to isolate the cause of the discrepancy. It is found that most of the effect is due to the long photon attenuation pathlengths in the long side wall of the instrument. A phenomenological procedure, based on measurements, is proposed to correct for the anomaly. The procedure results in inverse-square stability to within 0.5 % over a range of 1-7 m.

Minimizing the 1/r(2) perturbation for ideal fluence detectors in small source γ-irradiation fields.

A technique for analyzing the effect of the geometrical shape of a source or a detector, using a quadrupole expansion, is described herein. It is shown that this method may be exploited to predict, optimize the geometry of a source, or a measurement device, and nearly eliminate, the departure from the 1/r(2) fall-off characteristic due to irradiation from small sources. We have investigated several simple shapes that have a vanishing Q2 quadrupole moment: a right circular cylinder with a diameter to depth ratio of √[2], a cone with a radius to height ratio of unity, and an oblate ellipsoid with a diameter to depth ratio of √[3/2]. These ideal shapes produce optimally small departures in a 1/r(2) field, nearly mimicking a point-like detector. We have also found a rotationally symmetric shape, intermediate to the other three, that has additionally, a vanishing Q4, the hexadecapole moment. This geometry further improves the 1/r(2)-perturbation characteristics and has an additional free parameter that may be adjusted to model the ideal cylinder, cone or oblate spheroid.

Experimental verification of a Monte Carlo-based MLC simulation model for IMRT dose calculation.

Inter- and intra-leaf transmission and head scatter can play significant roles in intensity modulated radiation therapy (IMRT)-based treatment deliveries. In order to accurately calculate the dose in the IMRT planning process, it is therefore important that the detailed geometry of the multi-leaf collimator (MLC), in addition to other components in the accelerator treatment head, be accurately modeled. In this paper, we have used the Monte Carlo method (MC) to develop a comprehensive model of the Varian 120 leaf MLC and have compared it against measurements in homogeneous phantom geometries under different IMRT delivery circumstances. We have developed a geometry module within the DPM MC code to simulate the detailed MLC design and the collimating jaws. Tests consisting of leakage, leaf positioning and static MLC shapes were performed to verify the accuracy of transport within the MLC model. The calculations show agreement within 2% in the high dose region for both film and ion-chamber measurements for these static shapes. Clinical IMRT treatment plans for the breast [both segmental MLC (SMLC) and dynamic MLC (DMLC)], prostate (SMLC) and head and neck split fields (SMLC) were also calculated and compared with film measurements. Such a range of cases were chosen to investigate the accuracy of the model as a function of modulation in the beamlet pattern, beamlet width, and field size. The overall agreement is within 2% /2 mm of the film data for all IMRT beams except the head and neck split field, which showed differences up to 5% in the high dose regions. Various sources of uncertainties in these comparisons are discussed.

Dose comparison of megavoltage cone-beam and orthogonal-pair portal images.

The technique of megavoltage cone-beam computed tomography (MV CBCT) is available for image-guided radiation therapy to improve the accuracy of patient setup and tumor localization. However, development of strategies to efficiently and effectively implement this technique or to replace the current orthogonal portal images technique remains challenging in the clinical environment. It is useful to compare the difference in absorbed dose between the MV CBCT technique and the orthogonal portal images technique, the current standard practice for treatment verification. Our study analyzed the doses generated from these two imaging techniques for six treatment sites (pelvis, abdomen, lung, head and neck, breast, prostate). The analysis was made by simulating the MV CBCT technique with an arc beam and a beam-on time of 9 monitor units (MUs), and the orthogonal pair technique with a double-exposure anterior-posterior and lateral pair and a beam-on time of 4 MUs. The results are presented as dose per MU (cGy/MU) and absolute dose (cGy). The isocenter doses, integral doses, maximum doses, and mean doses to tumor and critical organs, and the two-dimensional isodose distributions and dose-volume histograms of each critical organ were investigated. The absolute dose difference between MV CBCT and orthogonal pair at the isocenter was 4.02 +/- 0.59 cGy. Major differences were seen between the two techniques in critical organs whose locations are away from the tumor. These organs, such as the contralateral breast (difference: 0.17 +/- 0.10 cGy/MU) and lung (difference: 0.15 +/- 0.20 cGy/MU), receive a higher dose from MV CBCT images than from orthogonal portal images. Additionally, higher doses and larger dose areas involving more normal tissues were observed for MV CBCT images than for orthogonal portal images in our analysis methodology, which used 200 beam projections delivered from various angles for the MV CBCT simulation and from just two perpendicular angles for the orthogonal pair simulation. In our selected clinical cases, the high-dose area from the orthogonal pair technique was always located inside the tumor; with MV CBCT, the high-dose area will most likely be outside the tumor. Therefore, the potentially higher doses to critical organs from MV CBCT images should be properly analyzed to ensure that they do not exceed the tolerance dose when therapy is delivered using that technique. On the other hand, to obtain good image quality, the higher MUs with MV CBCT images may be necessary. The absorbed dose for the tumor and for other critical organs should be calculated accordingly in the treatment plans. Images by MV CBCT are a great tool for three-dimensional verification of patient treatment position. The trade-off is that the MV CBCT technique for patient treatment verification might have a higher chance of increasing the dose to normal tissue during image acquisition.

Magnetic confinement of electron and photon radiotherapy dose: a Monte Carlo simulation with a nonuniform longitudinal magnetic field.

It recently has been shown experimentally that the focusing provided by a longitudinal nonuniform high magnetic field can significantly improve electron beam dose profiles. This could permit precise targeting of tumors near critical areas and minimize the radiation dose to surrounding healthy tissue. The experimental results together with Monte Carlo simulations suggest that the magnetic confinement of electron radiotherapy beams may provide an alternative to proton or heavy ion radiation therapy in some cases. In the present work, the external magnetic field capability of the Monte Carlo code PENELOPE was utilized by providing a subroutine that modeled the actual field produced by the solenoid magnet used in the experimental studies. The magnetic field in our simulation covered the region from the vacuum exit window to the phantom including surrounding air. In a longitudinal nonuniform magnetic field, it is observed that the electron dose can be focused in both the transverse and longitudinal directions. The measured dose profiles of the electron beam are generally reproduced in the Monte Carlo simulations to within a few percent in the region of interest provided that the geometry and the energy of the incident electron beam are accurately known. Comparisons for the photon beam dose profiles with and without the magnetic field are also made. The experimental results are qualitatively reproduced in the simulation. Our simulation shows that the excessive dose at the beam entrance is due to the magnetic field trapping and focusing scattered secondary electrons that were produced in the air by the incident photon beam. The simulations also show that the electron dose profile can be manipulated by the appropriate control of the beam energy together with the strength and displacement of the longitudinal magnetic field.

Photon beam relative dose validation of the DPM Monte Carlo code in lung-equivalent media.

Validation experiments have been conducted using 6 and 15 MV photons in inhomogeneous (water/lung/water) media to benchmark the accuracy of the DPM Monte Carlo code for photon beam dose calculations. Small field sizes (down to 2 x 2 cm2) and low-density media were chosen for this investigation because the intent was to test the DPM code under conditions where lateral electronic disequilibrium effects are emphasized. The treatment head components of a Varian 21EX linear accelerator, including the jaws (defining field sizes of 2 x 2, 3 x 3 and 10 x 10 cm2), were simulated using the BEAMnrc code. The phase space files were integrated within the DPM code system, and central axis depth dose and profile calculations were compared against diode measurements in a homogeneous water phantom in order to validate the phase space. Results of the homogeneous phantom study indicated that the relative differences between DPM calculations and measurements were within +/- 1% (based on the rms deviation) for the depth dose curves; relative profile dose differences were on average within +/- 1%/1 mm. Depth dose and profile measurements were carried out using an ion-chamber and film, within an inhomogeneous phantom consisting of a 6 cm slab of lung-equivalent material embedded within solid water. For the inhomogeneous phantom experiment, DPM depth dose calculations were within +/- 1% (based on the rms deviation) of measurements; relative profile differences at depths within and beyond the lung were, on average, within +/- 2% in the inner and outer beam regions, and within 1-2 mm distance-to-agreement within the penumbral region. Relative point differences on the order of 2-3% were within the estimated experimental uncertainties. This work demonstrates that the DPM Monte Carlo code is capable of accurate photon beam dose calculations in situations where lateral electron disequilibrium effects are pronounced.

Benchmarking of the dose planning method (DPM) Monte Carlo code using electron beams from a racetrack microtron.

A comprehensive set of measurements and calculations has been conducted to investigate the accuracy of the Dose Planning Method (DPM) Monte Carlo code for dose calculations from 10 and 50 MeV scanned electron beams produced from a racetrack microtron. Central axis depth dose measurements and a series of profile scans at various depths were acquired in a water phantom using a Scanditronix type RK ion chamber. Source spatial distributions for the Monte Carlo calculations were reconstructed from in-air ion chamber measurements carried out across the two-dimensional beam profile at 100 cm downstream from the source. The in-air spatial distributions were found to have full width at half maximum of 4.7 and 1.3 cm, at 100 cm from the source, for the 10 and 50 MeV beams, respectively. Energy spectra for the 10 and 50 MeV beams were determined by simulating the components of the microtron treatment head using the code MCNP4B. DPM calculations are on average within +/- 2% agreement with measurement for all depth dose and profile comparisons conducted in this study. The accuracy of the DPM code illustrated in this work suggests that DPM may be used as a valuable tool for electron beam dose calculations.

Experimental validation of the DPM Monte Carlo code using minimally scattered electron beams in heterogeneous media.

A comprehensive set of measurements and calculations has been conducted to investigate the accuracy of the Dose Planning Method (DPM) Monte Carlo code for electron beam dose calculations in heterogeneous media. Measurements were made using 10 MeV and 50 MeV minimally scattered, uncollimated electron beams from a racetrack microtron. Source distributions for the Monte Carlo calculations were reconstructed from in-air ion chamber scans and then benchmarked against measurements in a homogeneous water phantom. The in-air spatial distributions were found to have FWHM of 4.7 cm and 1.3 cm, at 100 cm from the source, for the 10 MeV and 50 MeV beams respectively. Energy spectra for the electron beams were determined by simulating the components of the microtron treatment head using the code MCNP4B. Profile measurements were made using an ion chamber in a water phantom with slabs of lung or bone-equivalent materials submerged at various depths. DPM calculations are, on average, within 2% agreement with measurement for all geometries except for the 50 MeV incident on a 6 cm lung-equivalent slab. Measurements using approximately monoenergetic, 50 MeV, 'pencil-beam'-type electrons in heterogeneous media provide conditions for maximum electronic disequilibrium and hence present a stringent test of the code's electron transport physics; the agreement noted between calculation and measurement illustrates that the DPM code is capable of accurate dose calculation even under such conditions.