Energy Fluence Distribution Research Articles

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

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

SU-FF-T-41: A Novel Tomotherapy Design for the Breast

Purpose: Previous work on partial breast irradiation in the prone position has lead to the development of a new treatment modality made specifically for the breast. Current methods often utilize a modified two‐tangent approach meaning beams are delivered around the body. This device, on the other hand, takes advantage of the unique geometry of the prone breast by rotating around it to deliver a highly targeted dose to the PTV, while sparing the normal breast tissue and other non‐breast structures. This device will involve helical tomotherapy but on a rotated axis. This will allow many more angles to be utilized compared to the standard methods. Method and Materials: Several technical and clinical aspects of this device have been explored. The technical aspects include the design of a new target, shielding requirements, and energy fluence distributions. The clinical aspects researched include dose distribution comparisons from several different potential energies and the determination of patient selection criteria. Results: These investigations have shown that a 4MV x‐ray beam created from a beryllium target would be the optimal design. Since the breast is a thin structure, a higher energy is not need. However if the energy is any lower, the skindose will increase. Beryllium targets are ideal for this machine since the forward output is roughly 70% that of tungsten for field sizes up to 10 cm, but the lateral energy fluence is significantly less. Conclusions: This machine is able to produce brachytherapy like PBI dose distributions that consist of highly conformal doses to the target and low doses to the non‐target structures. It is also able to achieve this without the additional surgery required for brachytherapy procedures. In addition, a large percentage of breast patients would be eligible for this treatment, since it is able to deliver dose close to the chestwall.

A software tool for 2D/3D visualization and analysis of phase-space data generated by Monte Carlo modelling of medical linear accelerators

A computer program has been developed for novel 2D/3D visualization and analysis of the phase-space parameters of Monte Carlo simulations of medical accelerator radiation beams. The software is written in the IDL language and reads the phase-space data generated in the BEAMnrc/BEAM Monte Carlo code format. Contour and colour-wash plots of the fluence, mean energy, energy fluence, mean angle, spectra distribution, energy fluence distribution, angular distribution, and slices and projections of the 3D ZLAST distribution can be calculated and displayed. Based on our experience of using it at Massachusetts General Hospital, the software has proven to be a useful tool for analysis and verification of the Monte Carlo generated phase-space files. The software is in the public domain.

SU-FF-T-357: Modeling Thick-Target Bremsstrahlung Production by Compound-Poisson-Process Electron Multiple Scatter

Purpose: To develop an accurate analytic algorithm to model bremsstrahlung production in a linac target and to calculate the angular distribution of the primary photon energy spectrum. This provides an alternative to Monte Carlo calculation of the primary photon spectrum. Method and Materials: The Compound-Poisson-Process (CPP) method is used to calculate the directional distribution of electrons in the target at each depth, explicitly including multiple scatters at large angles. This CPP method is modified to include the electron loss of energy at depth in the thick target. The Schiff integral formula is used to compute the bremsstrahlung spectrum produced at each angle and depth, and the contributions are integrated over depth to yield the photon energy fluence spectrum as a function of polar angle. This formula makes no small-angle approximations, so it should be accurate at all angles. Results: The primary (and attenuated first-scatter) photon energy fluence distribution was computed for a 15 MeV electron beam incident on a thick lead target and compared to a measurement in the same geometry. Conclusion: It is hoped that an accurate analytic calculation of the bremsstrahlung energy fluence distribution emerging from a linear accelerator treatment head will provide a quick and useful alternative to Monte Carlo calculations of this same distribution.

SU‐FF‐T‐155: Monte Carlo Dosimetric Verification for IMRT QA Using MLC Log Files and EPID

Purpose: EPID is a useful tool for pre‐treatment patient setup and target localization and post‐treatment dosimetry verification. However, EPID images are significantly affected by photon attenuation and scattering in the patient and the detector and therefore cannot be used directly for dose reconstruction. This work investigates a Monte Carlo dosimetric verification method based on MLC log files and the electronic portal imaging device (EPID) for IMRT quality assurance (QA). Method and Materials: We have developed Monte Carlo based software to derive accurate intensity‐modulated fluence maps behind the patient using MLC log files, which take into account the accelerator head geometry, the MLC leaf movement accuracy and the patient attenuation and scatter. Patient initial simulation and pre‐treatment CT data were used to simulate the patient anatomy for interfraction dose comparison. The phase space data behind the patient were used in the EPID response simulation and compared with measured EPID images to investigate patient setup accuracy and dose reconstruction uncertainty. Results: Ten previously treated prostate IMRT plans and patient CT data are included in this study. The MLC leaf position accuracy of the dynalog files from a Varian 21Ex accelerator is verified to within 1mm. The dose distributions based on the leaf sequences from the treatment planning system and the fluence maps rebuilt from the dynalog files are consistent to within 2%, validating our software implementation. The primary photons and scatters are recorded separately behind the patient for different applications as described above. Energy spectrum, fluence distribution and angular distribution are derived to facilitate dose calculation in the EPID. Conclusion: We have developed a log file based Monte Carlo method to generate phase space and fluence maps for pre‐treatment patient setup and post‐treatment dose verification with EPID. This work is implemented as part of our IMRT QA procedure.

Photon‐beam subsource sensitivity to the initial electron‐beam parameters

One limitation to the widespread implementation of Monte Carlo (MC) patient dose-calculation algorithms for radiotherapy is the lack of a general and accurate source model of the accelerator radiation source. Our aim in this work is to investigate the sensitivity of the photon-beam subsource distributions in a MC source model (with target, primary collimator, and flattening filter photon subsources and an electron subsource) for 6- and 18-MV photon beams when the energy and radial distributions of initial electrons striking a linac target change. For this purpose, phase-space data (PSD) was calculated for various mean electron energies striking the target, various normally distributed electron energy spread, and various normally distributed electron radial intensity distributions. All PSD was analyzed in terms of energy, fluence, and energy fluence distributions, which were compared between the different parameter sets. The energy spread was found to have a negligible influence on the subsource distributions. The mean energy and radial intensity significantly changed the target subsource distribution shapes and intensities. For the primary collimator and flattening filter subsources, the distribution shapes of the fluence and energy fluence changed little for different mean electron energies striking the target, however, their relative intensity compared with the target subsource change, which can be accounted for by a scaling factor. This study indicates that adjustments to MC source models can likely be limited to adjusting the target subsource in conjunction with scaling the relative intensity and energy spectrum of the primary collimator, flattening filter, and electron subsources when the energy and radial distributions of the initial electron-beam change.

Monte Carlo calculation of entire in situ gamma-ray spectra

We present a method for the synthesis of entire in situ gamma-ray spectra based on Monte Carlo calculations and measured data that characterize the detector properties. The method can serve for the determination of the effective depth of 137Cs in soil based on the information contained in the low-energy part of an in situ spectrum. Effective depth is defined as the depth of a plane distribution of 137Cs beneath the surface that reproduces the fluence energy and angular distribution at 1 m above the ground of gamma rays belonging to the real 137Cs distributions. We managed to reproduce the measured in situ spectra with our method and to demonstrate that the method allows the determination of the effective depth of 137Cs with a precision of 10 –2 m. The method requires minimal experimental characterization of the detector and is not sensitive to the details of the detector model and the soil composition and density employed in the Monte Carlo calculations.

Total skin electron therapy treatment verification: Monte Carlo simulation and beam characteristics of large non-standard electron fields

Total skin electron therapy (TSET) is a complex technique which requires non-standard measurements and dosimetric procedures. This paper investigates an essential first step towards TSET Monte Carlo (MC) verification. The non-standard 6 MeV 40 × 40 cm2 electron beam at a source to surface distance (SSD) of 100 cm as well as its horizontal projection behind a polymethylmethacrylate (PMMA) screen to SSD = 380 cm were evaluated. The EGS4 OMEGA-BEAM code package running on a Linux home made 47 PCs cluster was used for the MC simulations. Percentage depth–dose curves and profiles were calculated and measured experimentally for the 40 × 40 cm2 field at both SSD = 100 cm and patient surface SSD = 380 cm. The output factor (OF) between the reference 40 × 40 cm2 open field and its horizontal projection as TSET beam at SSD = 380 cm was also measured for comparison with MC results. The accuracy of the simulated beam was validated by the good agreement to within 2% between measured relative dose distributions, including the beam characteristic parameters (R50, R80, R100, Rp, E0) and the MC calculated results. The energy spectrum, fluence and angular distribution at different stages of the beam (at SSD = 100 cm, at SSD = 364.2 cm, behind the PMMA beam spoiler screen and at treatment surface SSD = 380 cm) were derived from MC simulations. Results showed a final decrease in mean energy of almost 56% from the exit window to the treatment surface. A broader angular distribution (FWHM of the angular distribution increased from 13° at SSD = 100 cm to more than 30° at the treatment surface) was fully attributable to the PMMA beam spoiler screen. OF calculations and measurements agreed to less than 1%. The effect of changing the electron energy cut-off from 0.7 MeV to 0.521 MeV and air density fluctuations in the bunker which could affect the MC results were shown to have a negligible impact on the beam fluence distributions. Results proved the applicability of using MC as a treatment verification tool for complex radiotherapy techniques.

Investigations on absolute portal dosimetry for the verification of static and dynamic dose delivery in radiotherapy (in English)

New in vivo dosimetry procedures using electronic portal imaging devices (EPIDs) either compare measured to predicted transmission dose, or infer patient dose from measured transmission dose images. These procedures demand a careful calibration of the portal imager. The EPID used in this research was a scanning liquid ionization chamber (SLIC). The first investigation was to see if a dose calibration of the EPID, performed on the central axis, is sufficiently accurate to estimate the dose for off‐axis points. The incident photon energy fluence distribution generated from the phase space of a linear accelerator was first convolved with Monte Carlo calculated dose spread kernels in water, which serves as the reference medium, and then in the detector. The kernels in water and the detector differ considerably at photon energies lower than 1 MeV or higher than 6 MeV. Transmission doses were then calculated in the SLIC‐EPID and in water. The dose differences are due to changing beam quality. It is shown that depending on the type of calibration, the difference can be as large as 5%, which is unacceptable for accurate transmission dose measurements. To investigate the applicability of the EPID for dynamic dose delivery techniques, the dose response to a photon beam with variable intensity was measured and theoretically modeled. It was found that the accuracy using the detector for verification of the dose from intensity modulated treatment fields delivered by a dynamically modulated multileaf technique is limited. This is due to the detector's nonlinear response. However, under certain acquisition conditions, the leaf movement during delivery can be precisely verified.

Measurement of neutrons produced in an intermediate energy heavy ion reaction using an activation technique.

The fluence rate, energy, and angular distributions of neutrons produced by the reaction of 50 MeV/u 12C ions on a thick copper target around the experimental target in the physics experimental hall of Heavy Ion Research Facility of Lanzhou were studied. The neutrons were measured with threshold activation detectors. Aluminum, fluorine, carbon, aluminum, and indium activation samples were used to measure neutrons with energies greater than 7 MeV, 11 MeV, 20 MeV, 50 MeV, and thermal neutrons, respectively. The fluence rate, energy and angular distributions of neutrons, total neutron yield of 12C ions, and the emission rate in the forward direction of neutrons with energies over 11 MeV and 20 MeV were obtained.

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.

Effective source size, yield and beam profile from multi-layered bremsstrahlung targets

Modern conformal radiotherapy benefits from heterogeneous dose delivery using scanned narrow bremsstrahlung beams of high energy in combination with dynamic double focused multi-leaf collimation and purging magnets. When using a purging magnet to remove electrons and positrons the target space is limited and unorthodox thin multi-layered targets are needed. A computational technique has therefore been developed to determine the forward yield and the angular distributions of the bremsstrahlung beam as well as the size and location of the effective and the virtual photon point source for arbitrary multi-layer bremsstrahlung targets. The Gaussian approximation of the diffusion equation for the electrons has been used and convolved with the bremsstrahlung production process. For electrons with arbitrary emittance impinging on targets of any multi-layer and atomic number combination, the model is well applicable, at least for energies in the range 1 - 100 MeV. The intrinsic bremsstrahlung photon profile has been determined accurately by deconvolving the electron multiple scattering process from thin experimental beryllium target profiles. For electron pencil beams incident on a target of high density and atomic number such as tungsten, the size of the effective photon source stays at around a tenth of a millimetre. The effective photon source for low-Z materials such as Be, C and Al is located at depths from 3 - 7 mm in the target, decreasing with increasing atomic number. The effective photon source at off-axis positions then moves out considerably from the central axis, which should be considered when aligning collimators. For high-Z materials such as tungsten, the location of the effective photon source is at a few tenths of a millimetre deep. The virtual photon point source is located only a few tenths of a millimetre upstream of the effective photon source both for high- and low-Z materials. For 50 MeV electrons incident on multi-layered full range targets the radial energy fluence distributions will have a full width at half maximum (FWHM) of 80 to 100 mm at 1 m from the target. The best target composition made of two layers when the space is limited to 15 mm was found to be 9 mm Be followed by 6 mm W. A thin beryllium target () results in a high-intensity bremsstrahlung lobe with a FWHM of about 35 mm at the isocentre. Interestingly, the forward dose rate in such a beam is as high as 62% of the maximum achievable with an optimal target design, even if on average only 1 MeV is lost by the electrons.

Verification and implementation of dynamic wedge calculations in a treatment planning system based on a dose-to-energy-fluence formalism.

The use of dynamic movements on linear accelerators during irradiation has found a revised interest lately due to the integration of computers to control the accelerator. In this paper, dynamic wedge fields that are produced by moving one of the collimator blocks during irradiation are studied. Since these wedge fields differ from those of mechanical wedges, certain requirements are to be met on the treatment planning system. A pencil-beam-based treatment planning system that uses the resultant energy fluence distribution from the dynamic collimator movement has been extensively reviewed. In calculations, the system treats the dynamic collimated field as a single, modulated field that yields calculation times close to those for open beams. Details are given on the theoretical model used for the calculation of dynamically generated dose distributions. Measurements of depth doses, profiles, and output factors in dynamic wedge fields indicate that calculations accurately predict the outcome from dynamic wedges without any additional measurements other than those used for characterization of static open beams.

Analysis of grating formation with excimer laser irradiated phase masks

Excimer laser irradiated phase masks provide a convenient and effective method for writing micron-scale gratings for optoelectronic device applications. Here we analyze the interference field produced by a periodic mask and assess the near-field energy density and fluence distribution for varying degrees of order content when exposed using an excimer laser with finite spatial and temporal coherence. Results are compared with experimental findings for gratings produced on ablated polymers and in optical fibres.

Laser ablation of polymethylmethacrylate and polystyrene at 308 nm: Demonstration of thermal and photothermal mechanisms by a time-of-flight mass spectroscopic study

Laser ablation of polymethylmethacrylate and polystyrene films by an excimer laser at 308 nm was studied by detecting the fragments by time-of-flight mass spectroscopy after multiphoton ionization. Neutral fragments ablating from the polymer surface were predominantly monomer and dimer methylmethacrylate and monomer styrene, as deduced from the mass spectra. Thus, ‘‘unzipping’’ of these polymers occurs. The dependence of fragment yields on ablating laser fluence and kinetic energy distributions of ablating species demonstrates thermal and photothermal dissociation of these polymers under the experimental conditions.

An analytical solution for the dynamic control of multileaf collimators

General analytical expressions are derived for the required motion of the collimator leaves to achieve a desired energy fluence distribution or collimator opening density in the patient in the shortest possible time. By simplification of the general expressions the equations of motion have been derived for both the shrinking field and the curtain shutter techniques with the associated approximations clearly quantified. The mechanical limitations on leaf motion, caused by the finite velocity and acceleration, are taken into account. It is shown that almost any desired energy fluence distribution can be created even when the limitations on velocity and acceleration are considered. The basic rule with the curtain shutter technique is that when the energy fluence gradient along the direction of motion of the leaves is positive, the leading leaf should move at maximum speed and the lagging leaf should modulate the field. In regions where the gradient is negative the lagging leaf should instead move at full speed and the leading leaf should modulate the field. The overall treatment time is then proportional to the total increment in energy fluence of opening density between consecutive minima and maxima. For energy fluence profiles with numerous high peaks the treatment time may therefore increase considerably over that for conventional uniform dose delivery. However, in general the treatment time is prolonged by a factor of about two compared to a traditional uniform treatment. Obviously the method developed here for multileaf collimators is also suitable for simple block collimators.

Two accurate algorithms for calculating the energy fluence profile in inverse radiation therapy planning

Two accurate algorithms for calculating the required incident energy fluence distributions from the optimal irradiation density distribution in inverse radiation therapy planning have been developed. The algorithms are characterized by a high speed and accuracy and an ability to handle both divergent and parallel beams even for extremely heterogeneous target volumes. The fastest algorithm is based on a longitudinal distance weighting method, whereas the slower but more accurate algorithm uses an area weighting method which has the advantage that it also works very well at low spatial resolutions. Both algorithms have been inverted for forward calculation of the delivered absorbed dose distribution from known fluence profiles. This is essential for the validation of the resultant dose distributions since the projected irradiation density has been determined from dose distributions calculated with convolution methods. A shortcoming of the longitudinal distance weighting algorithm for forward calculation is that it requires a higher spatial resolution in the energy fluence to minimize the discretization noise caused by interpolation. The area weighting algorithm on the other hand requires a longer calculation time. When the forward calculation time is also taken into account, the more accurate area weighting method is the most advantageous algorithm from the point of view of total calculation time.

OPTIMIZATION OF MULTIFIBER LIGHT DELIVERY FOR THE PHOTODYNAMIC THERAPY OF LOCALIZED PROSTATE CANCER

The understanding of light distribution within the target organ is essential in ensuring efficacy and safety in photodynamic therapy (PDT). A computer simulator of light distribution in prostatic tissue was employed for optimizing dosimetry for PDT in localized prostatic cancer. The program was based on empirically determined light distributions and optical constants and an assumed fluence rate differential from fiber source to necrosis periphery. The diffusion theory approximation to the Boltzmann transport equation was the applicable formulation relevant to prostatic tissue, which has a high albedo with forward-scattering characteristics. Solving this equation of diffusive transfer for the appropriate fiber geometry yielded the energy fluence distributions for cleaved fiber and cylindrical diffuser light delivery. These distributions, confirmed by our measurements, show a 1/r and 1/square root of r dependency (r = distance from light source) of the fluence phi (r) for the cleaved fiber and diffuser, respectively. This manifests itself by the tighter spacing of energy fluence isodoses in the case of the cleaved fiber. It was predicted that for a typical PDT regime a single interstitially placed cleaved fiber would treat 0.05-0.72 cm3. Four parallel fibers improved the uniformity of light distribution and treatment volume, and an interfiber separation of 12 mm would be necessary to provide optimal overlap of PDT necrosis, treating 0.26-3.6 cm3. The cylindrical diffuser, however, could treat larger volumes, and it was predicted that four 3 cm long diffusers at an optimal separation of 25 mm would treat 25-88 cm3 of prostatic tissue.

Acquisition of the effective lateral energy fluence distribution for photon beam dose calculations by convolution models

A method is described for acquiring the lateral energy fluence distribution of therapeutic photon beams. The method is designed for characterization of clinical accelerators for the convolution/superposition methods of photon dose calculations. Radial dose profiles, measured in a water phantom at a reference depth for the largest field size of the machine, are used to construct a discrete Cartesian dose matrix. A corresponding pencil beam energy deposition kernel is calculated from a database of Monte Carlo calculated kernels for monoenergetic photons by using the energy bin data of an effective spectrum as weights. The lateral kernel distribution at the depth of measurement is filtered and resampled into a discrete matrix, similar to that of the measured dose distribution. The dose matrix is then deconvolved by the kernel matrix, using fast Fourier transforms and Wiener filtering, to yield the effective energy fluence distribution. The method is tested by using the acquired energy fluence for convolution dose calculations and comparing the result with measured dose distributions.