R. D. Franich

Robust calculation of effective atomic numbers: The Auto‐Zeff software

PURPOSE The most appropriate method of evaluating the effective atomic number necessitates consideration of energy-dependent behavior. Previously, this required quite laborious calculation, which is why many scientists revert to over-simplistic power-law methods. The purpose of this work is to develop user-friendly software for the robust, energy-dependent computation of effective atomic numbers relevant within the context of medical physics, superseding the commonly employed simplistic power law approaches. METHOD Visual Basic was used to develop a GUI allowing the straightforward calculation of effective atomic numbers. Photon interaction cross section matrices are constructed for energies spanning 10 keV to 10 GeV and elements Z = 1-100. Coefficients for composite media are constructed via linear additivity of the fractional constituents and contrasted against the precalculated matrices at each energy, thereby associating an effective atomic number through interpolation of adjacent cross section data. Uncertainties are of the order of 1-2%. RESULTS Auto-Z(eff) allows rapid (∼0.6 s) calculation of effective atomic numbers for a range of predefined or user-specified media, allowing estimation of radiological properties and comparison of different media (for instance assessment of water equivalence). The accuracy of Auto-Z(eff) has been validated against numerous published theoretical and experimental predictions, demonstrating good agreement. The results also show that commonly employed power-law approaches are inaccurate, even in their intended regime of applicability (i.e., photoelectric regime). Furthermore, comparing the effective atomic numbers of composite materials using power-law approaches even in a relative fashion is shown to be inappropriate. CONCLUSION Auto-Z(eff) facilitates easy computation of effective atomic numbers as a function of energy, as well as average and spectral-weighted means. The results are significantly more accurate than normal power-law predictions. The software is freely available to interested readers, who are encouraged to contact the authors.

The Effective Atomic Number of Dosimetric Gels

Radiological properties of gel dosimeters and phantom materials are often compared against each other and against water or tissue by consideration parameters including their effective atomic number, Zeff. Effective atomic numbers have been calculated for a range of ferrous-sulphate and polymeric gel dosimeters using mass attenuation coefficient data over the energy range 10 keV to 10 MeV. Data is presented relative to water to allow direct comparison over a range of energies. These data provide energy specific values of Zeff which improves on the practice of applying a power-law based formula to estimate an energy independent value. For applications that require a single value of Zeff, the data presented here allows the choice of a value appropriate to the energy of the photon source or a spectrum-weighted average. Studying the variation of Zeff, which is equivalent to taking into account the variation of mass attenuation coefficients with photon energy, it is found that gels typically match water better than water matches human tissues. As such, the subtle differences in effective atomic number between water and gels are small and may be considered negligible. Consideration of the mean disparity over a large energy range shows, broadly, BANG-1 to be the most water equivalent gel.

A contemporary review of stereotactic radiotherapy: Inherent dosimetric complexities and the potential for detriment

Abstract Objective. The advantages of highly localised, conformal treatments achievable with stereotactic radiotherapy (SRT) are increasingly being extended to extracranial sites as stereotactic body radiotherapy with advancements in imaging and beam collimation. One of the challenges in stereotactic treatment lies in the significant complexities associated with small field dosimetry and dose calculation. This review provides a comprehensive overview of the complexities associated with stereotactic radiotherapy and the potential for detriment. Methods. This study is based on a comprehensive review of literature accessible via PubMed and other sources, covering stereotactic radiotherapy, small-field dosimetry and dose calculation. Findings. Several key issues were identified in the literature. They pertain to dose prescription, dose measurement and dose calculation within and beyond the treatment field. Field-edge regions and penumbrae occupy a significant portion of the total field size. Spectral and dosimetric characteristics are difficult to determine and are compounded by effects of tissue inhomogeneity. Measurement of small-fields is made difficult by detector volume averaging and energy response. Available dosimeters are compared, and emphasis is given to gel dosimetry which offers the greatest potential for three-dimensional small-field dosimetry. The limitations of treatment planning system algorithms as applied to small-fields (particularly in the presence of heterogeneities) is explained, and a review of Monte Carlo dose calculation is provided, including simplified treatment planning implementations. Not incorporated into treatment planning, there is evidence that far from the primary field, doses to patients (and corresponding risks of radiocarcinogenesis) from leakage/scatter in SRT are similar to large fields. Conclusions. Improved knowledge of dosimetric issues is essential to the accurate measurement and calculation of dose as well as the interpretation and assessment of planned and delivered treatments. This review highlights such issues and the potential benefit that may be gained from Monte Carlo dose calculation and verification via three-dimensional dosimetric methods (such as gel dosimetry) being introduced into routine clinical practice.

A novel methodology for 3D deformable dosimetry.

PURPOSE Interfraction and intrafraction variation in anatomic structures is a significant challenge in contemporary radiotherapy. The objective of this work is to develop a novel tool for deformable structure dosimetry, using a tissue-equivalent deformable gel dosimeter that can reproducibly simulate targets subject to deformation. This will enable direct measurement of integrated doses delivered in different deformation states, and the verification of dose deforming algorithms. METHODS A modified version of the nPAG polymer gel has been used as a deformable 3D dosimeter and phantom to investigate doses delivered to deforming tissue-equivalent geometry. The deformable gel (DEFGEL) dosimeter/phantom is comprised of polymer gel in a latex membrane, moulded (in this case) into a cylindrical geometry, and deformed with an acrylic compressor. Fifteen aluminium fiducial markers (FM) were implanted into DEFGEL phantoms and the reproducibility of deformation was determined via multiple computed tomography (CT) scans in deformed and nondeformed states before and after multiple (up to 150) deformations. Dose was delivered to the DEFGEL phantom in three arrangements: (i) without deformation, (ii) with deformation, and (iii) cumulative exposures with and without deformation, i.e., dose integration. Irradiations included both square field and a stereotactic multiple dynamic arc treatment adapted from a patient plan. Doses delivered to the DEFGEL phantom were read out using cone beam optical CT. RESULTS Reproducibility was verified by observation of interscan shifts of FM locations (as determined via CT), measured from an absolute reference point and in terms of inter-FM distance. The majority (76%) of points exhibited zero shift, with others shifting by one pixel size consistent with setup error as confirmed with a control sample. Comparison of dose profiles and 2D isodose distributions from the three arrangements illustrated complex spatial redistribution of dose in all three dimensions occurring as a result of the change in shape of the target between irradiations, even for a relatively simple deformation. Discrepancies of up to 30% of the maximum dose were evident from dose difference maps for three orthogonal planes taken through the isocenter of a stereotactic field. CONCLUSIONS This paper describes the first use of a tissue-equivalent, 3D dose-integrating deformable phantom that yields integrated or redistributed dosimetric information. The proposed methodology readily yields three-dimensional (3D) dosimetric data from radiation delivery to the DEFGEL phantom in deformed and undeformed states. The impacts of deformation on dose distributions were readily seen in the isodose contours and line profiles from the three arrangements. It is demonstrated that the system is potentially capable of reproducibly emulating the physical deformation of an organ, and therefore can be used to evaluate absorbed doses to deformable targets and organs at risk in three dimensions and to validate deformation algorithms applied to dose distributions.

An in vivo investigative protocol for HDR prostate brachytherapy using urethral and rectal thermoluminescence dosimetry

PURPOSE To develop an in vivo dosimetry based investigative action level relevant for a corrective protocol for HDR brachytherapy boost treatment. METHODS AND MATERIALS The dose delivered to points within the urethra and rectum was measured using TLD in vivo dosimetry in 56 patients. Comparisons between the urethral and rectal measurements and TPS calculations showed differences, which are related to the relative position of the implant and TLD trains, and allowed shifts of implant position relative to the prostate to be estimated. RESULTS AND CONCLUSIONS Analysis of rectal dose measurements is consistent with implant movement, which was previously only identified with the urethral data. Shift corrected doses were compared with results from the TPS. Comparison of peak doses to the urethra and rectum has been assessed against the proposed corrective protocol to limit overdosing these critical structures. An initial investigative level of 20% difference between measured and TPS peak dose was established, which corresponds to 1/3 of patients which was practical for the caseload. These patients were assessed resulting in corrective action being applied for one patient. Multiple triggering for selective investigative action is outlined. The use of a single in vivo measurement in the first fraction optimizes patient benefit at acceptable cost.

Electron Interaction with Gel Dosimeters: Effective Atomic Numbers for Collisional, Radiative and Total Interaction Processes

Abstract Taylor, M. L., Franich, R. D., Trapp, J. V. and Johnston, P. N. Electron Interaction with Gel Dosimeters: Effective Atomic Numbers for Collisional, Radiative and Total Interaction Processes. Radiat. Res. 171, 123–126 (2009). The effective atomic number is widely employed in radiation studies, particularly for the characterization of interaction processes in dosimeters, biological tissues and substitute materials. Gel dosimeters are unique in that they comprise both the phantom and dosimeter material. In this work, effective atomic numbers for total and partial electron interaction processes have been calculated for the first time for a Fricke gel dosimeter, five hypoxic and nine normally oxygenated polymer gel dosimeters. A range of biological materials are also presented for comparison. The spectrum of energies studied spans 10 keV to 100 MeV, over which the effective atomic number varies by 30%. The effective atomic numbers of gels match those of soft tissue closely over the full energy range studied; greater disparities exist at higher energies but are typically within 4%.

Technical Note: Modeling a complex micro‐multileaf collimator using the standard BEAMnrc distribution

PURPOSE The component modules in the standard BEAMnrc istribution may appear to be insufficient to model micro-multileaf collimators that have trifaceted leaf ends and complex leaf profiles. This note indicates, however, that accurate Monte Carlo simulations of radiotherapy beams defined by a complex collimation device can be completed using BEAMnrcs standard VARMLC component module. METHODS That this simple collimator model can produce spatially and dosimetrically accurate microcollimated fields is illustrated using comparisons with ion chamber and film measurements of the dose deposited by square and irregular fields incident on planar, homogeneous water phantoms. RESULTS Monte Carlo dose calculations for on-axis and off-axis fields are shown to produce good agreement with experimental values, even on close examination of the penumbrae. CONCLUSIONS The use of a VARMLC model of the micro-multileaf collimator, along with a commissioned model of the associated linear accelerator, is therefore recommended as an alternative to the development or use of in-house or third-party component modules for simulating stereotactic radiotherapy and radiosurgery treatments. Simulation parameters for the VARMLC model are provided which should allow other researchers to adapt and use this model to study clinical stereotactic radiotherapy treatments.

ASSESSMENT OF OUT-OF-FIELD DOSES IN RADIOTHERAPY OF BRAIN LESIONS IN CHILDREN

PURPOSE To characterize the out-of-field doses in pediatric radiotherapy and to identify simple methods by which out-of-field dose might be minimized, with a view to reducing the risk of secondary cancers. METHODS AND MATERIALS With the aim of characterizing the peripheral doses under different treatment conditions, the dose measurements in an anthropomorphic child phantom were taken in various organs and critical structures outside the primary field using thermoluminescent dosimetry. The doses from a Varian 600C and Varian Trilogy linear accelerator, both at 6 MV, were investigated. RESULTS Larger field sizes have been shown to result in greater peripheral doses close to the primary beam, with the difference becoming less significant at large distances, indicating that most of out-of-field doses result from head leakage and collimator scatter>40 cm from the primary field. The use of lead shields has been shown to reduce the absorbed dose resulting from leakage. Aligning the craniocaudal axis of the patient with the x-plane of the collimator resulted in a dose reduction of 40%, for both machines. Out-of-field doses from the Varian Trilogy were shown to be approximately 40% greater than those from the 600C linear accelerator, despite being operated at the same energy. CONCLUSION Out-of-field doses to pediatric patients can be minimized by using simple treatment options, such as using the single-energy mode linear accelerator rather than the multimode, orienting the couch and collimator such that the patient lies along the x-plane and avoiding fields directed along the trunk of the body.

Systematic variations in polymer gel dosimeter calibration due to container influence and deviations from water equivalence.

There are a number of gel dosimeter calibration methods in contemporary usage. The present study is a detailed Monte Carlo investigation into the accuracy of several calibration techniques. Results show that for most arrangements the dose to gel accurately reflects the dose to water, with the most accurate method involving the use of a large diameter flask of gel into which multiple small fields of varying dose are directed. The least accurate method was found to be that of a long test tube in a water phantom, coaxial with the beam. The large flask method is also the most straightforward and least likely to introduce errors during the set-up, though, to its detriment, the volume of gel required is much more than other methods.

Source position verification and dosimetry in HDR brachytherapy using an EPID

PURPOSE Accurate treatment delivery in high dose rate (HDR) brachytherapy requires correct source dwell positions and dwell times to be administered relative to each other and to the surrounding anatomy. Treatment delivery inaccuracies predominantly occur for two reasons: (i) anatomical movement or (ii) as a result of human errors that are usually related to incorrect implementation of the planned treatment. Electronic portal imaging devices (EPIDs) were originally developed for patient position verification in external beam radiotherapy and their application has been extended to provide dosimetric information. The authors have characterized the response of an EPID for use with an (192)Ir brachytherapy source to demonstrate its use as a verification device, providing both source position and dosimetric information. METHODS Characterization of the EPID response using an (192)Ir brachytherapy source included investigations of reproducibility, linearity with dose rate, photon energy dependence, and charge build-up effects associated with exposure time and image acquisition time. Source position resolution in three dimensions was determined. To illustrate treatment verification, a simple treatment plan was delivered to a phantom and the measured EPID dose distribution compared with the planned dose. RESULTS The mean absolute source position error in the plane parallel to the EPID, for dwells measured at 50, 100, and 150 mm source to detector distances (SDD), was determined to be 0.26 mm. The resolution of the z coordinate (perpendicular distance from detector plane) is SDD dependent with 95% confidence intervals of ± 0.1, ± 0.5, and ± 2.0 mm at SDDs of 50, 100, and 150 mm, respectively. The response of the EPID is highly linear to dose rate. The EPID exhibits an over-response to low energy incident photons and this nonlinearity is incorporated into the dose calibration procedure. A distance (spectral) dependent dose rate calibration procedure has been developed. The difference between measured and planned dose is less than 2% for 98.0% of pixels in a two-dimensional plane at an SDD of 100 mm. CONCLUSIONS Our application of EPID dosimetry to HDR brachytherapy provides a quality assurance measure of the geometrical distribution of the delivered dose as well as the source positions, which is not possible with any current HDR brachytherapy verification system.