Azimuthal particle redistribution for the reduction of latent phase-space variance in Monte Carlo simulations.

It is well known that the use of a phase space in Monte Carlo simulation introduces a baseline level of variance that cannot be suppressed through the use of standard particle recycling techniques. This variance (termed latent phase-space variance by Sempau et al) can be a significant limiting factor in achieving accurate, low-uncertainty dose scoring results, especially near the surface of a phantom. A BEAMnrc component module (MCTWIST) has been developed to reduce the presence of latent variance in phase-space-based Monte Carlo simulations by implementing azimuthal particle redistribution (APR). For each recycled use of a phase-space particle a random rotation about the beam's central axis is applied, effectively utilizing cylindrical symmetry of the particle fluence and therefore providing a more accurate representation of the source. The MCTWIST module is unique in that no physical component is actually added to the accelerator geometry. Beam modifications are made by directly transforming particle characteristics outside of BEAMnrc/EGSnrc particle transport. Using MCTWIST, we have demonstrated a reduction in latent phase-space variance by more than a factor of 20, for a 10 x 10 cm(2) field, when compared to standard phase-space particle recycling techniques. The reduction in latent variance has enabled the achievement of dramatically smoother in-water dose profiles. This paper outlines the use of MCTWIST in Monte Carlo simulation and quantifies for the first time the latent variance reduction resulting from exploiting cylindrical phase-space symmetry.

Absolute dose calculations for Monte Carlo simulations of radiotherapy beams.

Monte Carlo (MC) simulations have traditionally been used for single field relative comparisons with experimental data or commercial treatment planning systems (TPS). However, clinical treatment plans commonly involve more than one field. Since the contribution of each field must be accurately quantified, multiple field MC simulations are only possible by employing absolute dosimetry. Therefore, we have developed a rigorous calibration method that allows the incorporation of monitor units (MU) in MC simulations. This absolute dosimetry formalism can be easily implemented by any BEAMnrc/DOSXYZnrc user, and applies to any configuration of open and blocked fields, including intensity-modulated radiation therapy (IMRT) plans. Our approach involves the relationship between the dose scored in the monitor ionization chamber of a radiotherapy linear accelerator (linac), the number of initial particles incident on the target, and the field size. We found that for a 10 x 10 cm2 field of a 6 MV photon beam, 1 MU corresponds, in our model, to 8.129 x 10(13) +/- 1.0% electrons incident on the target and a total dose of 20.87 cGy +/- 1.0% in the monitor chambers of the virtual linac. We present an extensive experimental verification of our MC results for open and intensity-modulated fields, including a dynamic 7-field IMRT plan simulated on the CT data sets of a cylindrical phantom and of a Rando anthropomorphic phantom, which were validated by measurements using ionization chambers and thermoluminescent dosimeters (TLD). Our simulation results are in excellent agreement with experiment, with percentage differences of less than 2%, in general, demonstrating the accuracy of our Monte Carlo absolute dose calculations.

Optimisation of electron cone design in high energy radiotherapy using the Monte Carlo method.

Cylindrical solid-walled steel electron collimators are used at the Royal Adelaide Hospital with a Siemens KD2 Mevatron accelerator to produce circular fields 2-8 cm in diameter. The cones are used in contact with the patient's skin. A flat treatment field is required at the treatment depth and the beam should also satisfy the uniformity standards as specified by the International Electrotechnical Commission (IEC). However, the seven and eight centimetre diameter cones provided by the manufacturer did not meet these specifications. In particular, the maximum dose relative to the depth-dose maximum on the central axis exceeded 126% as compared with the IEC recommended value of 109%, when used with a 21 MeV electron beam. Cone modifications were previously investigated by others with the results demonstrating some improvement in the 'horn' (as it appears on surface dose profiles) but still not satisfying IEC requirements. In the present paper the EGS4 code was used to model the existing treatment head geometry and cones, as well as new suggested modifications to the cone. The results of the simulation for the existing cone geometry corresponded closely to previously obtained measurements. The suggested collimator modifications involved a plastic insert along the internal wall of the collimator. Variations of the insert width and height were simulated for a 21 MeV electron beam and the results plotted to indicate the optimal insert dimensions. A plastic insert with the dimensions taken from one of the best models was produced and tested. The measurements showed close agreement with the simulation results (for the 'horn' height, dose within 1% and radial position within 2 mm) and improvement of the "maximum ratio of absorbed dose" from 126% before modification to 108% with the plastic insert. The tested insert was also simulated for a 12 MeV electron beam, to see whether permanent fitting of such an insert would have a deleterious effect at lower energies. Neither penetration nor flatness was significantly compromised, with a small penalty being a slight increase in the central axis dose near the surface.

A method for calculating the dose to a multi-storey building due to radiation scattered from the roof of an adjacent radiotherapy facility.

With modern urbanization trends, situations occur where a general-purpose multi-storey building would have to be constructed adjacent to a radiotherapy facility. In cases where the building would not be in the primary x-ray beam, "skyshine" radiation is normally accounted for. The radiation scattered from the roof side-wise towards the building can also be a major contributing factor. However, neither the NCRP reports nor recently published literature considered this. The current paper presents a simple formula to calculate the dose contribution from scattered radiation in such circumstances. This equation includes workload, roof thickness, field size, distance to the reference point and a normalized angular photon distribution function f(theta), where theta is the angle between central axis of the primary beam and photon direction. The latter was calculated by the Monte Carlo method (EGS4 code) for each treatment machine in our department. For angles theta exceeding approximately 20 degrees (i.e., outside the primary beam and its penumbra) the angular distribution function f(theta) was found to have little dependence on the shielding barrier thickness and the beam energy. An analytical approximation of this function has been obtained. Measurements have been performed to verify this calculation technique. An agreement within 40% was found between calculated and measured dose rates. The latter combined the scattered radiation and the dose from "skyshine" radiation. Some overestimation of the dose resulted from uncertainties in the radiotherapy building drawings and in evaluation of the "skyshine" contribution.

Multi-isocenter stereotactic radiotherapy: implications for target dose distributions of systematic and random localization errors.

PURPOSE: This investigation examined the effect of alignment and localization errors on dose distributions in stereotactic radiotherapy (SRT) with arced circular fields. In particular, it was desired to determine the effect of systematic and random localization errors on multi-isocenter treatments. METHODS AND MATERIALS: A research version of the FastPlan system from Surgical Navigation Technologies was used to generate a series of SRT plans of varying complexity. These plans were used to examine the influence of random setup errors by recalculating dose distributions with successive setup errors convolved into the off-axis ratio data tables used in the dose calculation. The influence of systematic errors was investigated by displacing isocenters from their planned positions. RESULTS: For single-isocenter plans, it is found that the influences of setup error are strongly dependent on the size of the target volume, with minimum doses decreasing most significantly with increasing random and systematic alignment error. For multi-isocenter plans, similar variations in target dose are encountered, with this result benefiting from the conventional method of prescribing to a lower isodose value for multi-isocenter treatments relative to single-isocenter treatments. CONCLUSIONS: It is recommended that the systematic errors associated with target localization in SRT be tracked via a thorough quality assurance program, and that random setup errors be minimized by use of a sufficiently robust relocation system. These errors should also be accounted for by incorporating corrections into the treatment planning algorithm or, alternatively, by inclusion of sufficient margins in target definition.

The effects of radiotherapy treatment uncertainties on the delivered dose distribution and tumour control probability.

Uncertainty in the precise quantity of radiation dose delivered to tumours in external beam radiotherapy is present due to many factors, and can result in either spatially uniform (Gaussian) or spatially non-uniform dose errors. These dose errors are incorporated into the calculation of tumour control probability (TCP) and produce a distribution of possible TCP values over a population. We also study the effect of inter-patient cell sensitivity heterogeneity on the population distribution of patient TCPs. This study aims to investigate the relative importance of these three uncertainties (spatially uniform dose uncertainty, spatially non-uniform dose uncertainty, and inter-patient cell sensitivity heterogeneity) on the delivered dose and TCP distribution following a typical course of fractionated external beam radiotherapy. The dose distributions used for patient treatments are modelled in one dimension. Geometric positioning uncertainties during and before treatment are considered as shifts of a pre-calculated dose distribution. Following the simulation of a population of patients, distributions of dose across the patient population are used to calculate mean treatment dose, standard deviation in mean treatment dose, mean TCP, standard deviation in TCP, and TCP mode. These parameters are calculated with each of the three uncertainties included separately. The calculations show that the dose errors in the tumour volume are dominated by the spatially uniform component of dose uncertainty. This could be related to machine specific parameters, such as linear accelerator calibration. TCP calculation is affected dramatically by inter-patient variation in the cell sensitivity and to a lesser extent by the spatially uniform dose errors. The positioning errors with the 1.5 cm margins used cause dose uncertainty outside the tumour volume and have a small effect on mean treatment dose (in the tumour volume) and tumour control.

Modelling the dosimetric consequences of organ motion at CT imaging on radiotherapy treatment planning.

Treatment planning algorithms usually assume that the correct or at least the mean organ position is derived from the CT imaging procedure, and that this position is reproduced throughout the treatment. In reality a mobile organ is unlikely to be in its exact mean position at the time of imaging, causing the treatment to be planned with an organ off-set from its assumed mean position. This introduces an extra 'CT uncertainty' into the treatment. A Monte Carlo (MC) model is used to simulate organ translations at imaging and evaluate the effect of this uncertainty (above the treatment delivery uncertainties) on the dose distribution. An underdose by 4 Gy in a 60 Gy treatment is calculated in the penumbral region of a single-field dose distribution as a result of the CT uncertainty. The effect is reduced to less then 0.5 Gy when the organ position at planning is derived as the average from multiple pretreatment CT scans. It is shown that a convolution method can be applied to predict the effect of CT uncertainty on the dose distribution for a patient population. Additionally, a variation kernel for a convolution method is derived that incorporates uncertainty at both imaging and treatment.

Radiosurgery at the Royal Adelaide Hospital: the first 4 1/2 years' clinical experience.

Radiosurgery refers to the treatment of small lesions localized by stereotactic technology using highly focused radiation. This review utilizes prospectively gathered data from the Royal Adelaide Hospital Radiosurgery unit to summarize experience with the first 62 patients (65 lesions) treated between November 1993 and May 1998. This experience included acoustic neuromas (23 patients), arteriovenous malformations (18), brain metastases (12), meningiomas (6), and glomus tumour, subependymoma, dural arteriovenous fistula (1 each). Although follow up is relatively short, the outcome in terms of morbidity and tumour control is thus far comparable with results reported in the literature. Radiosurgery provides a viable alternative to neurosurgery and conventional external beam radiotherapy for several benign and malignant intracranial lesions.

Treatment planning algorithm corrections accounting for random setup uncertainties in fractionated stereotactic radiotherapy.

A number of relocatable head fixation systems have become commercially available or developed in-house to perform fractionated stereotactic radiotherapy (SRT) treatment. The uncertainty usually quoted for the target repositioning in SRT is over 2 mm, more than twice that of stereotactic radiosurgery (SRS) systems. This setup uncertainty is usually accounted for at treatment planning by outlining extra target margins to form the planning target volume (PTV). It was, however, shown by Lo et al. [Int. J. Radiat. Oncol., Biol., Phys. 34, 1113-1119 (1996)] that these extra margins partly offset the radiobiological advantages of SRT. The present paper considers dose calculations in SRT and shows that the dose predictions could be made at least as accurate as in SRS with no extra margins required. It is shown that the dose distribution from SRT can be calculated using the same algorithms as in SRS, with the measured off-axis ratios (OARs) replaced by "effective" OARs. These are obtained by convolving the probability density distribution of the isocenter positions (assumed to be normal) and the original OARs. An additional output correction factor has also been introduced accounting for the isocenter dose reduction (2.4% for a 7 mm collimator) due to the OARs "blurring." Another correction factor accommodates for the reduced (by 1% for 6 MV beam) dose rate at the isocenter due to x-ray absorption in the relocatable mask. Mean dose profiles and the standard deviations of the dose (STD) were obtained through simulating SRT treatment by a combination of normally distributed isocenters. These dose distributions were compared with those calculated using the convolution approach. Agreement of the dose distributions was within 1%. Since standard deviation reduces with the number of fractions, N, as STD/square root(N), the planning predictions in fractionated stereotactic radiotherapy can be made more accurate than in SRS by increasing N and using "effective" OARs along with corrected dose output.

Modeling dose response in the presence of spatial variations in dose rate.

Nonuniform dose rates are an inevitability in treatments involving internal sources, arising from electronic disequilibrium effects as well as nonuniformity in activity distribution. These dose-rate nonuniformities are of consequence for protracted treatments (when dose-delivery times are of the order of cell-repair times). The influence of nonuniform dose rates on tumor control probability (TCP) has thus been considered. A model for TCP has been developed by merging established (linear-quadratic based) TCP models for dose nonuniformity, with dose-rate effects as influenced by cell repair and proliferation capacities. This model has been examined by considering treatment of spherical tumors of varying sizes filled with uniform distributions of several beta-emitting isotopes. Dose (or dose-rate) volume histograms (DVHs) were calculated for the combinations of tumor size and isotope, and applied to the developed TCP model. Comparison of the results identified several characteristics of the effect of nonuniform dose rate, including the balance between minimum dose and cell number as they vary with tumor size, the dominance of minimum dose (dose rate) on TCP, and the influence of cell-proliferation effects on effective delivered dose (and the effective DVH). The model was also used to determine TCPs for simulated 90Y-labeled microsphere treatments of liver metastases using both uniform and clustered-microsphere models for activity distributions, and for varying tumor size. Despite significantly higher doses being achieved via clustered (nonuniform) activity distributions, the minimum dose for clustered distributions is consistently lower than that of the corresponding uniform distributions, and TCP is always higher for the uniform distributions.

Set-up error & organ motion uncertainty: a review.

Conformal radiotherapy allows improvement in the treatment outcome due to increased targeting accuracy through advanced beam shaping techniques to precisely conform radiation dose to the geometry of the tumour. Treatment set-up and organ motion uncertainties are unavoidable factors that are limiting increases in accuracy and have to be accounted for in conformal treatment planning. The magnitudes of set-up errors and organ motion uncertainties for specific sites, and using various set-up techniques, have been quantified in the literature. However, the parameters used with these measurements and the presentation of the data has differed between studies for the same site. The purpose of this paper is to analyse and combine the published material into a uniform format and to display typical reported values of set-up and organ motion uncertainties. Values measured under similar conditions were averaged across studies. The results of this analysis illustrate (1) variability in the parameters used for measurements across studies, (2) typical motion ranges of the prostate, kidneys, liver and diaphragm, (3) typical means and standard deviations for set-up errors associated with the prostate, pelvis, brain, head and neck, thorax, rectum and breast and (4) a brief review of the common methods to lower or account for these uncertainties.

A method to predict the effect of organ motion and set-up variations on treatment plans.

Dose distributions calculated by commercial treatment planning systems do not allow incorporation of the effects of patient position variation or organ motion throughout the course of radiation therapy treatment. We have established a convolution-based method, which enables us to display dose distributions using a commercial treatment planning system that can take into account target movement. An example of the method applied to a prostate treatment plan is presented. For the method to be of clinical use it requires assessment of the parameters leading to target movement in a scientific manner in the same treatment department that it is to be used. It is not sufficient to rely on published data especially that relating to set-up accuracy as this has been shown to vary widely from centre to centre. We believe that with appropriate movement data, a convolution-based approach can lead to more optimal radiation margins around clinical target volumes (CTV). Optimal margins will help prevent geometric misses as well as ensure that the amount of critical late reacting normal tissues surrounding the CTV irradiated is minimised. Optimal margins cannot be guaranteed with the more conventionally used "rule of thumb" techniques for placing a planning target volume around the CTV.

A model for dose estimation in therapy of liver with intraarterial microspheres.

Therapy with intraarterial microspheres is a technique which involves incorporation of radioisotope-labelled microspheres into a capillary bed of tumour and normal tissue. Betaemitters such as 90Y and 166Ho are used for this purpose. This technique provides tumour to normal tissue (TNT) dose ratios in the range of 2-10 and demonstrates significant clinical benefit, which could potentially be increased with more accurate dose predictions and delivery. However, dose calculations in this modality face the difficulties associated with nonuniform and inhomogeneous activity distribution. Most of the dose calculations used clinically do not account for the nonuniformity and assume uniform activity distribution. This paper is devoted to the development of a model which would allow more accurate prediction of dose distributions from microspheres. The model calculates dose assuming that microspheres are aggregated into randomly distributed clusters, and using precomputed dose kernels for the clusters. The dose kernel due to a microsphere cluster was found by numerical integration of a point source dose kernel over the volume of the cluster. It is shown that a random distribution of clusters produces an intercluster distance distribution which agrees well with the one measured by Pillai et al in liver. Dose volume histograms (DVHs) predicted by the model agree closely with the results of Roberson et al for normal tissue and tumour. Dose distributions for different concentrations and types of radioisotope as well as for tumours of different radii, have been calculated to demonstrate the model's possible applications.

A method for producing uniform dose distributions in the junction regions of large hinge angle electron fields.

PURPOSE: The planning problems presented by abutting electron fields are well recognized. Junctioning electron fields with a large hinge angle compounds the problems because of the creation of closely situated high dose and low-dose regions. METHODS AND MATERIALS: The technique involving a compensated superficial x-ray (SXR) field to treat the junction region between electron fields was developed and used in a particular clinical case (treatment of a squamous cell carcinoma of the forehead/scalp). The superficial x-ray beam parameters were chosen and the compensator was designed to make the SXR field complementary to the electron fields. RESULTS: Application of a compensated SXR field eliminated low dose zones in the junction region and reduced high dose zones to 110%. In the clinical case discussed, the high-dose areas due to the SXR field would not appear because of increased attenuation of the soft X-rays in bone. CONCLUSION: The technique proposed produces uniform dose distribution up to 3 cm deep and can be considered as an additional tool for dealing with electron field junctioning problems.