Dose Distribution Function Research Articles

Distribution of natural beta dose to individual grains in sediments

In luminescence dating using single grains of quartz, statistical protocols are used to compute the most appropriate dose from the distribution of palaeodoses. The distribution of palaeodoses arises due to, (1) heterogeneity (at grain level) in bleaching at the time of deposition, (2) heterogeneous distribution of beta emitters present as randomly distributed feldspars (Mayya et al. in Radiat Meas 41:1032–1039, 2006) and, (3) heterogeneous distribution of grainsizes (Guérin et al. in Radiat Meas 47:778–785, 2015). Mayya et al. (Radiat Meas 41:1032–1039, 2006) demonstrated that random distribution of feldspar grains(with up to 14% stoichiometric K) and shorter range of beta particles (~ 2.3 mm in quartz) lead to significant variation in dose received by individual grains of quartz. This study improves upon Mayya et al. (Radiat Meas 41:1032–1039, 2006) by, (1) using a more realistic energy deposition function that was estimated using Monte Carlo simulations and (2) computing the effects of porosity of the sediment and beta straggling on the dose distribution function. It additionally concludes that effects of beta straggling are small and can be ignored. Ages based on new calculations led to improved concordance with control ages.

Dose distribution to a random walker moving in a two-dimensional surface around a radioactive source.

Modeling of dose distribution of randomly moving population around a radioactive source is a complex problem. The objective is to develop a model and solution techniques to estimate radiation absorbed dose to the population randomly moving around a radioactive source. The problem is formulated using a second-order partial differential equation; different moments of the dose distribution function are defined related to physically realizable quantities, and solutions are obtained using standard moments methods. Alternatively, numerical simulations are performed to estimate the radiation doses using Monte Carlo approach for individual positions and random motions of the people around the source. A good agreement is found between average doses obtained from moments method and numerical simulations. A typical application of this model to different exposure conditions shows that the average dose is highly dependent on the population density. The study results show that average dose decreases with increase in the population density and movement area of random walker. This mathematical model can be used as a rapid assessment tool by the emergency planners in resource optimization by providing quick estimates of likely exposures for triage and emergency response.

SU‐E‐I‐16: Scan Length Dependency of the Radial Dose Distribution in a Long Polyethylene Cylinder

Purpose:The area‐averaged dose in the central plane of a long cylinder following a CT scan depends upon the radial dose distribution and the length of the scan. The ICRU/TG200 phantom, a polyethylene cylinder 30 cm in diameter and 60 cm long, was the subject of this study. The purpose was to develop an analytic function that could determine the dose for a scan length L at any point in the central plane of this phantom.Methods:Monte Carlo calculations were performed on a simulated ICRU/TG200 phantom under conditions of cylindrically symmetric conditions of irradiation. Thus, the radial dose distribution function must be an even function that accounts for two competing effects: The direct beam makes its weakest contribution at the center while the scatter begins abruptly at the outer radius and grows as the center is approached. The scatter contribution also increases with scan length with the increase approaching its limiting value at the periphery faster than along the central axis. An analytic function was developed that fit the data and possessed these features.Results:Symmetry and continuity dictate a local extremum at the center which is a minimum for the ICRU/TG200 phantom. The relative depth of the minimum decreases as the scan length grows and an absolute maximum can occur between the center and outer edge of the cylinders. As the scan length grows, the relative dip in the center decreases so that for very long scan lengths, the dose profile is relatively flat.Conclusion:An analytic function characterizes the radial and scan length dependency of dose for long cylindrical phantoms. The function can be integrated with the results expressed in closed form. One use for this is to help determine average dose distribution over the central cylinder plane for any scan length.

Development of the radial dose distribution function relevant to the treatment planning system for heavy particle cancer therapy

This paper presents a study of the radial dose due to the irradiation of a heavy ion, through simulations using a selection of types of atomic and molecular (AM) data. In order to widely spread our radial dose simulation results, a simple radial dose distribution function is proposed. This required a comparison of our results with the available conventional radial dose distributions. It is also shown that the treatment planning system for heavy particle cancer therapy is expected to become one of the most important applications of AM data to biological and medical science.

Development and validation of a fast voxel-based dose evaluation system in nuclear medicine

Abstract PET imaging has been widely used in the detection and staging of malignancies and the evaluation of patient-specific dosimetry for PET scans is important in nuclear medicine. However, patient-specific dosimetry can be estimated only by Monte Carlo methods which are usually time-consuming. The purpose of this study is to develop a fast dose evaluation system namely SimDOSE. SimDOSE is a Monte Carlo code embedded in SimSET with a dose scoring routine to record the deposited energy of the photons and electrons. Fluorine-18 is one of the most commonly used radionuclides that decay predominantly by positron emission. Only a 635 keV (Emax) positron and two annihilation photons should be concerned in F-18 radiation dosimetry, hence simulation is relatively simple. To evaluate the effects of resolution, an F-18 point source placed in a 20 cm diameter sphere filled with water was simulated by SimDOSE and GATE v6.1. Grid sizes of 1 mm, 3 mm, and 5 mm were tested and each was simulated with a total of 10 7 decays. The resultant dose distribution functions were compared. Dose evaluation on ORNL phantom was also performed to validate the accuracy of SimDOSE. The grid size of phantom was set as 3 mm and the number of decays was 10 7 . The S -values of liver computed by SimDOSE were compared with GATE and OLINDA (Organ Level INternal Dose Assessment) for 11 C, 15 O, and 18 F.Finally, the CPU time of simulations was compared between SimDOSE and GATE. The dose profiles show the absorption doses located 3 mm outside the center are similar between SimDOSE and GATE. However, 71% (19%) difference of the center dose between SimDOSE and GATE are observed for 1 mm (3 mm) grid. The differences of the profile lie in the assumption in SimDOSE that all kinetic energies of electrons are locally absorbed. The ratios of S values of (SimDOSE/OLINDA) range from 0.95 to 1.11 with a mean value of 1.02±0.043. To compare simulation time from SimDOSE to GATE for calculation of 1 mm, 3 mm, 5 mm gird point source and S values of ORNL phantom are 1.3%, 1.2%, 1.2% and 1.2%, respectively. In conclusion, SimDOSE is an efficient and accurate toolkit to generate patient-specific dose distribution in clinical PET application.

Inverse Planning Optimization Method for Intensity Modulated Radiation Therapy

In order to facilitate the leaf sequencing process in intensity modulated radiation therapy (IMRT), and design of a practical leaf sequencing algorithm, it is an important issue to smooth the planned fluence maps. The objective is to achieve both high-efficiency and high-precision dose delivering by considering characteristics of leaf sequencing process. The key factor which affects total number of monitor units for the leaf sequencing optimization process is the max flow value of the digraph which formulated from the fluence maps. Therefore, we believe that one strategy for compromising dose conformity and total number of monitor units in dose delivery is to balance the dose distribution function and the max flow value mentioned above. However, there are too many paths in the digraph, and we don't know the flow value of which path is the maximum. The maximum flow value among the horizontal paths was selected and used in the objective function of the fluence map optimization to formulate the model. The model is a traditional linear constrained quadratic optimization model which can be solved by interior point method easily. We believe that the smoothed maps from this model are more suitable for leaf sequencing optimization process than other smoothing models. A clinical head-neck case and a prostate case were tested and compared using our proposed model and the smoothing model which is based on the minimization of total variance. The optimization results with the same level of total number of monitor units (TNMU) show that the fluence maps obtained from our model have much better dose performance for the target/non-target region than the maps from total variance based on the smoothing model. This indicates that our model achieves better dose distribution when the algorithm suppresses the TNMU at the same level. Although we have just used the max flow value of the horizontal paths in the diagraph in the objective function, a good balance has been achieved between the dose conformity and the total number of monitor units. This idea can be extended to other fluence map optimization model, and we believe it can also achieve good performance.

Analytical modeling of relative luminescence efficiency of Al2O3:C optically stimulated luminescence detectors exposed to high-energy heavy charged particles

The objective of this work is to test analytical models to calculate the luminescence efficiency of Al2O3:C optically stimulated luminescence detectors (OSLDs) exposed to heavy charged particles with energies relevant to space dosimetry and particle therapy. We used the track structure model to obtain an analytical expression for the relative luminescence efficiency based on the average radial dose distribution produced by the heavy charged particle. We compared the relative luminescence efficiency calculated using seven different radial dose distribution models, including a modified model introduced in this work, with experimental data. The results obtained using the modified radial dose distribution function agreed within 20% with experimental data from Al2O3:C OSLDs relative luminescence efficiency for particles with atomic number ranging from 1 to 54 and linear energy transfer in water from 0.2 up to 1368 keV µm−1. In spite of the significant improvement over other radial dose distribution models, understanding of the underlying physical processes associated with these radial dose distribution models remain elusive and may represent a limitation of the track structure model.

Hypofractionated Stereotactic Body Radiotherapy for Primary and Metastatic Liver Tumors Using the Novalis Image-Guided System: Preliminary Results regarding Efficacy and Toxicity

www.tcrt.org The purpose of this study was to evaluate the efficacy and toxicity of stereotactic body radiotherapy (SBRT) for primary and metastatic liver tumors using the Novalis image-guided radiotherapy system. After preliminarily treating liver tumors using the Novalis system from July 2006, we started a protocol-based study in February 2008. Eighteen patients (6 with primary hepatocellular carcinoma and 12 with metastatic liver tumor) were treated with 55 or 50 Gy, depending upon their planned dose distribution and liver function, delivered in 10 fractions over 2 weeks. Four non-coplanar and three coplanar static beams were used. Patient age ranged from 54 to 84 years (median: 72 years). The Child-Pugh classification was Grade A in 17 patients and Grade B in 1. Tumor diameter ranged from 12 to 35 mm (median: 23 mm). Toxicities were evaluated according to the Common Terminology Criteria of Adverse Events version 4.0, and radiation-induced liver disease (RILD) was defined by Lawrence's criterion. The median follow-up period was 14.5 months. For all patients, the 1-year overall survival and local control rates were 94% and 86%, respectively. A Grade 1 liver enzyme change was observed in 5 patients, but no RILD or chronic liver dysfunction was observed. SBRT using the Novalis image-guided system is safe and effective for treating primary and metastatic liver tumors. Further investigation of SBRT for liver tumors is warranted. In view of the acceptable toxicity observed with this protocol, we have moved to a new protocol to shorten the overall treatment time and escalate the dose.

MONTE CARLO SYMULATION CHARACTERISTICS OF MODEL 6711 BRACHYTHERAPY SEED: EFFECTS OF ENERGY SPECTRUM AND PHANTOM DIMENSIONS

It is important to determine specified dose distributions of radioactive seed sources of brachytherapy in both phantom material and treated tissues. Dosimetric features and specific dose distribution functions of Model 6711 brachytherapy seed which is frequently used in prostate cancer treatments, have been given in literature. In the present study decay spectrum of radioactive material and variations of phantom dimensions which are foreseen to affect dosimetric specifications of the seed, were investigated and results were performed by Monte Carlo simulation. In simulation using separate decay spectrum and mono energy, differences were noted between interval of 1-68 percent. Also in calculations of phantom dimensions variations, deviations were not observed more than 0.1 percent by normalization to 1 as expected.

The effects of energy-loss straggling and elastic scattering models on Monte Carlo calculations of dose distribution functions for 10 keV to 1 MeV incident electrons in water

Accurate simulation of the transport and energy-loss of energetic electrons is an important step in modeling ion-induced effects in materials. Dose distribution functions (or so-called dose point kernels, DPKs) represent one of the most basic and useful quantities for characterizing the spatial distribution of energy deposition in matter. In the present work we investigate the effect on DPK of various models for the elastic scattering cross-section and energy-loss straggling distribution widely used in Monte Carlo simulation of electron transport above a few keV. Our findings indicate that, overall, the DPK is not very sensitive to the examined physical models, except at the tail of the distribution where a strong dependence is observed. The present comparison can be useful for avoiding systematic errors in the simulation of electron transport at primary energies from several keV to a few MeV and to suggest further improvement in the existing codes.

SU‐GG‐T‐03: Dosimetric Study of HDR 192Ir and LDR 125I Brachytherapy Sources Using the Penelope Monte Carlo Code

Purpose: To determine the dosimetric parameters of two HDR models 192Ir (microSelectron, and M‐19), and LDR 125I brachytherapy sources. Method and Materials: In this study we used the microSelectron and M‐19 models, and also source (Amersham OncoSeed model 6711). Penelope Monte Carlo transport code was used. All the photonic interactions were taking into account. AAPM TG‐43 was followed to determine the dosimetric properties1. 2D dose distribution, dose rate constant, anisotropy and radial dose functions were determined. Results: For both Iridium models, the 2D‐dose distribution agrees very well with published data for radius 1 ⩽ r ⩽ 5 cm, the difference was less than 3 %. The dose rate constant is 1.11654 cGy h−1 U−1 for microSelectron and 1.12456 cGy h−1 U−1 M‐19 model. Less than 3 % difference was observed for the radial dose function for radius 1 < r < 5 cm for both Iridium models. The DRC for was found to be 0.984 cGy h−1 U−1, and less than 3 % difference for the radial dose function in comparison with published data in TG‐43. Conclusion: Extensive work had been done on and brachytherapy sources. Daskalov et al2, Medich et al3, and Granero et al4, used different source models and different Monte Carlo transport codes, but the difference for the dosimetric parameters between all these studies was less than 5 %. In this study we used Penelope Monte Carlo code to determine the dosimetric parameters. The results showed 3 % difference for 2D dose distribution, DRC, and radial dose function for Iridium sources and 3 % difference for Iodine source.

Background correction of personal dose distributions by a novel unfolding algorithm

The dosimetry service Seibersdorf monitors more than 20,000 persons with typical monitoring period of one month. The use of thermoluminescence (TL)-dosemeters during the last 30 years allows measurements of even low dose values (some 10 muSv) with sufficient uncertainty. Consideration of the natural background contribution or transport dose which needs to be subtracted from the measured dose requires special protocols which differ significantly from country to country. The chosen protocol has not only a strong influence on the individual dose values (especially for low doses) but changes significantly the whole dose distribution function, as well as the corresponding statistical describing parameters (mean doses, median values, etc.) of these distributions. On the basis of the measured (uncorrected) distribution function the attempt was made to extract both the background doses as well as the remaining occupationally caused dose contribution. For this approach the uncorrected dose values of all customers from several years were analysed and a superposition of two independent log-normal distributions was assumed. By means of a new unfolding algorithm both components were isolated and the corresponding parameters were calculated. The paper gives a detailed description of the procedure and summarises the resulting dose distributions.

Dosimetric characterization of radioactive sources employed in prostate cancer therapy

Purpose Three types of radiation sources are employed currently in the radiation treatment of prostate cancer, namely, external, implant, and high-dose-rate (HDR) sources using an afterloader method. The present article provides a detailed dosimetric characterization of several commercially available implant sources and an HDR source employing the same stochastic code and dataset. Methods and materials The radioactive implants considered are 125I seeds: models 6701, 6702 and 6711, 103Pd seed: model 200, and a high-dose-rate 192Ir source: microSelectron-HDR model V7.0x. Detailed modeling of the sources and their associated X-rays and gamma rays has been carried out using the stochastic code MCNP4C. A sensitivity study has been conducted to quantify effects of varying the composition and density of the tissue equivalent material, and a dosimetric comparison is made for different media (tissue equivalent, solid-water, water, and air). Furthermore, a set of measurements using thermoluminescent dosimeters has been done to provide experimental validation of some of the calculational results obtained. Results Effectively, high-precision dosimetric values (Monte-Carlo statistical 1-sigma error <1%) are provided in tabulated form over a wide range to enable therapy planning as well as to check numerical values calculated by other methods. A subset of calculated dosimetric values has been experimentally validated by using thermoluminescent dosimeters. Conclusions A detailed comparison of results obtained for the radial dose distribution function, anisotropy factor, and dose rate constant as defined in the TG-43 protocol has indicated reasonable agreement with the values reported in the literature.

Radiation dose rate estimates to marine biota resulting from the routine radioactive releases of the nuclear power plants in Daya Bay

Five marine organisms in Daya Bay are selected for estimating the dose rates. Internal exposure and its 5 pathways are also considered. The concentrations of 43 kinds of background and additional radionuclides in seawater are from the survey of background radioactivity and the prediction of routine radioactive releases of the 4 reactors. Point source dose distribution functions are used to estimate the dose rates to various organisms from α and β radiation. Monte-Carlo method is used to determine the absorbed fractions in the organisms from γ radiation. Results indicate that the background dose rates are 2.72 mGya · a-1 to phytoplankton and 1.75 mGy · a-1 to zooplankton. The dose rates to other organisms are in the range of 0.31–0. 49 mGy · a-1. The additional dose rates from the routine releases are varied to different organisms. They reach the range of 5.7–6.1 times of the background dose rates to benthic crustaceans and mollusks, which are 8.3%–15.3% to fishes, and only 0.2% to plankton. β internal irradiation from additional radionuclides is the critical pathway to plankton.131I and60Co are the major contributors to zooplankton, while103Ru,60Co and58Co are the main contributors to phytoplankton. γ external irradiation from sediment is the critical pathway to benthic organisms.58Co and60Co are the main contributors. The main pathways to fishes are internal β and γ irradiation.124Sb is the critical radionuclide.

Effect of UV System Modifications on Disinfection Performance

Numerical simulations have been performed to gain a better understanding of ultraviolet (UV) disinfection process performance. Similar simulations in previous studies revealed critical paths through which particles moved and experienced low UV doses. In vertical UV systems, these paths generally are found near the channel walls with characteristics of high velocity and low turbulence intensity. Moreover, these paths generally coincide with low UV intensity zones and appear to represent the primary limitation of process performance. Reactor modifications have been designed to eliminate or modify these trajectories, thereby improving process performance. In a pilot-scale open-channel system with a vertical lamp orientation, two geometric modifications with “wave” and “baffle” shapes have been developed and examined. The results of these pilot tests confirmed the improvement of process performance when compared with an unmodified UV system. As in the case of the unmodified UV systems, a numerical model that combines kinetic information from a well-mixed batch reactor with a dose-distribution function was used to predict process performance of the UV system with the wave-shaped modification. A dose-distribution function that incorporates the effects of spatial nonuniformities in both hydrodynamics (through a random-walk model) and UV intensity (through a point-source-summation model) was developed. The dose-response function for microorganisms was obtained from completely mixed batch reactor experiments with a collimated beam. Predictions of disinfection efficacy confirmed the ability of the modified systems to improve microbial inactivation.

Integrated UV Disinfection Model Based on Particle Tracking

A general probabilistic particle-centered model is developed that combines kinetic information (dose-response function) from a well-mixed batch reactor with a dose-distribution function to predict disinfection efficacy in practical ultraviolet (UV) systems. An interpretation in terms of a generalized segregated-flow model also is given. The particular case of disinfection using vertical (perpendicular to the direction of the open-channel flow) UV lamps in a staggered configuration is studied. A dose-distribution function that incorporates the effects of spatial nonuniformities in both hydrodynamics (through a random-walk model) and UV intensity (through a point-source summation model) is estimated. The flow-field information necessary for the random-walk model was obtained from laboratory measurements of the turbulent flow using laser Doppler velocimetry. The dose-response function for microorganisms was obtained from completely mixed batch reactor experiments with a collimated beam. Predictions of disinfection efficacy based on the developed dose-distribution function and the laboratory kinetic data compared well with measurements from a pilot-scale vertical UV system. The results also suggest that the regions near the channel sidewalls where UV intensity is low represent a limiting factor in the process performance of continuous-flow UV disinfection systems.

A potential application to the study of microscopic energy deposition in a solid by means of heavy charged-particle induced photochromic alterations in a tissue-equivalent matrix

A theoretical study was carried out to investigate the feasibility of using the radiation-induced colour decay of photochromic molecules embedded in a polymer matrix as a probe for studying the microscopic energy deposition of heavy charged particles (HCPs) in a tissue-equivalent solid. The theoretical treatment makes use of the radial dose distribution function as derived from gas-phase physics, together with the effects of the increase in temperature and of matrix degradation on the colour-decay kinetics of the photochromic molecules, according to empirical models derived for the solid state. Bearing in mind the non-stochastic nature of the model, the use of gas-phase physics at the level of radiation interaction, and the fact that some empirical quantities used have been established macroscopically, all factors which signify that extra caution is required in the interpretation of the results, it is shown that when the optimum information retrieval time (after track formation) is considered the technique may be able to resolve differences in the energy deposition pattern by different HCPs in the nanometre range (1-10 nm; material's mass density ) from the track axis. Most importantly, though, the present study aims to erect a theoretical framework for the possible application of the technique and to highlight those aspects which are likely to be critical to its practical usage, such as particle type and energy range, and spatial scale and magnitude of the expected effect together with its dependence on time, the physical characteristics of the matrix, and the kinetic behaviour of the type of photochromic molecule studied. Furthermore, it establishes a rationale for interpreting the experimentally observed (if available) colour changes in the HCP track in terms of the microscopic distribution of energy deposition in it.

Skin Dose from Radionuclide Contamination on Clothing

Skin dose due to radionuclide contamination on clothing is calculated by Monte Carlo simulation of electron and photon radiation transport. Contamination due to a hot particle on some selected clothing geometries of cotton garment is simulated. The effect of backscattering in the surrounding air is taken into account. For each combination of source-clothing geometry, the dose distribution function in the skin, including the dose at tissue depths of 7 mg cm(-2) and 1,000 mg cm(-2), is calculated by simulating monoenergetic photon and electron sources. Skin dose due to contamination by a radionuclide is then determined by proper weighting of the monoenergetic dose distribution functions. The results are compared with the VARSKIN point-kernel code for some radionuclides, indicating that the latter code tends to underestimate the dose for gamma and high energy beta sources while it overestimates skin dose for low energy beta sources.

Microdosimetric Approach to Calculation of Dose Dependences of Radiation Induced Effects Under Heavy Charged Particles

General expressions which allow calculation of dose dependence of radiation-induced effects for any given distribution of tracks created in irradiated crystal are derived. The dose distribution function in ionising particle tracks, the distribution functions of tracks in a volume of crystal and widely applied in microdosimetry passage from the dose distribution in the track to the dose distribution in the crystal, are used as a basis. The expressions obtained are used for calculation of dose dependences of TL yield for the crystal LiF:Mg,Ti, irradiated with a parallel beam of 4 MeV alpha particles.

Calculation of three‐dimensional photon primary absorbed dose using forward and backward spread dose‐distribution functions

This paper describes a method of calculating three-dimensional (3-D) photon primary absorbed dose in a homogeneous or heterogeneous medium. The method is based on a technique of convolving a pair of forward and backward spread dose-distribution functions with the primary water collision kerma distribution. Both spread dose-distribution functions can be constructed by analyzing the zero-area tissue-maximum ratio, the primary absorbed dose near the beam exit surface, and the laterally spread dose distribution. Primary absorbed dose calculations are performed along the beam axis for 10-MV x rays. The characteristic patterns of primary dose in heterogeneous phantoms containing an aluminum or lunglike material slab can be obtained.