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At least 1,729 records · Page 96

A TCP model for external beam treatment of intermediate-risk prostate cancer

Purpose: Biological models offer the ability to predict clinical outcomes. The authors describe a model to predict the clinical response of intermediate-risk prostate cancer to external beam radiotherapy for a variety of fractionation regimes. Methods: A fully heterogeneous population averaged tumor control probability model was fit to clinical outcome data for hyper, standard, and hypofractionated treatments. The tumor control probability model was then employed to predict the clinical outcome of extreme hypofractionation regimes, as utilized in stereotactic body radiotherapy. Results: The tumor control probability model achieves an excellent level of fit, R{sup 2} value of 0.93 and a root mean squared error of 1.31%, to the clinical outcome data for hyper, standard, and hypofractionated treatments using realistic values for biological input parameters. Residuals Less-Than-Or-Slanted-Equal-To 1.0% are produced by the tumor control probability model when compared to clinical outcome data for stereotactic body radiotherapy. Conclusions: The authors conclude that this tumor control probability model, used with the optimized radiosensitivity values obtained from the fit, is an appropriate mechanistic model for the analysis and evaluation of external beam RT plans with regard to tumor control for these clinical conditions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Exploration of Use of Copulas in Analysing the Relationship between Precipitation and Meteorological Drought in Beijing, China

Drought risk analysis is essential for regional water resource management. In this study, the probabilistic relationship between precipitation and meteorological drought in Beijing, China, was calculated under three different precipitation conditions (precipitation equal to, greater than, or less than a threshold) based on copulas. The Standardized Precipitation Evapotranspiration Index (SPEI) was calculated based on monthly total precipitation and monthly mean temperature data. The trends and variations in the SPEI were analysed using Hilbert-Huang Transform (HHT) and Mann-Kendall (MK) trend tests with a running approach. The results of the HHT and MK test indicated a significant decreasing trend in the SPEI. The copula-based conditional probability indicated that the probability of meteorological drought decreased as monthly precipitation increased and that 10 mm can be regarded as the threshold for triggering extreme drought. From a quantitative perspective, when R ≤ mm, the probabilities of moderate drought, severe drought, and extreme drought were 22.1%, 18%, and 13.6%, respectively. This conditional probability distribution not only revealed the occurrence of meteorological drought in Beijing but also provided a quantitative way to analyse the probability of drought under different precipitation conditions. Furthermore, the results provide a useful reference for future drought prediction.

54 ENVIRONMENTAL SCIENCES↗

ROBO-AO KEPLER PLANETARY CANDIDATE SURVEY. II. ADAPTIVE OPTICS IMAGING OF 969 KEPLER EXOPLANET CANDIDATE HOST STARS

We initiated the Robo-AO Kepler Planetary Candidate Survey in 2012 to observe each Kepler exoplanet candidate host star with high angular resolution, visible light, laser adaptive optics (AOs) imaging. Our goal is to find nearby stars lying in Kepler's photometric apertures that are responsible for the relatively high probability of false-positive exoplanet detections and that cause underestimates of the size of transit radii. Our comprehensive survey will also shed light on the effects of stellar multiplicity on exoplanet properties and will identify rare exoplanetary architectures. In this second part of our ongoing survey, we observed an additional 969 Kepler planet candidate hosts and we report blended stellar companions up to Δm≈6 that contribute to Kepler's measured light curves. We found 203 companions within ∼4″ of 181 of the Kepler stars, of which 141 are new discoveries. We measure the nearby star probability for this sample of Kepler planet candidate host stars to be 10.6% ± 1.1% at angular separations up to 2.″5, significantly higher than the 7.4% ± 1.0% probability discovered in our initial sample of 715 stars; we find the probability increases to 17.6% ± 1.5% out to a separation of 4.″0. The median position of Kepler Objects of Interest (KOIs) observed in this survey are 1.°1 closer to the galactic plane, which may account for some of the nearby star probability enhancement. We additionally detail 50 Keck AO images of Robo-AO observed KOIs in order to confirm 37 companions detected at a <5σ significance level and to obtain additional infrared photometry on higher significance detected companions.

79 ASTRONOMY AND ASTROPHYSICS↗

A Proper Motions Study of the Globular Cluster NGC 3201

With a high value of heliocentric radial velocity, a retrograde orbit, and suspected to have an extragalactic origin, NGC 3201 is an interesting globular cluster for kinematical studies. Our purpose is to calculate the relative proper motions (PMs) and membership probability for the stars in the wide region of globular cluster NGC 3201. PM based membership probabilities are used to isolate the cluster sample from the field stars. The membership catalog will help address the question of chemical inhomogeneity in the cluster. Archive CCD data taken with a wide-field imager (WFI) mounted on the ESO 2.2 m telescope are reduced using the high-precision astrometric software developed by Anderson et al. for the WFI images. The epoch gap between the two observational runs is ∼14.3 years. To standardize the BVI photometry, Stetson’s secondary standard stars are used. The CCD data with an epoch gap of ∼14.3 years enables us to decontaminate the cluster stars from field stars efficiently. The median precision of PMs is better than ∼0.8 mas yr{sup −1} for stars having V<18 mag that increases up to ∼1.5 mas yr{sup −1} for stars with 18<V<20 mag. Kinematic membership probabilities are calculated using PMs for stars brighter than V∼20 mag. An electronic catalog of positions, relative PMs, BVI magnitudes, and membership probabilities in the ∼19.7 × 17 arcmin{sup 2} region of NGC 3201 is presented. We use our membership catalog to identify probable cluster members among the known variables and X-ray sources in the direction of NGC 3201.

79 ASTRONOMY AND ASTROPHYSICS↗

Fault isolation and fault-tolerant control for nonlinear stochastic distribution control systems with multiplicative faults

Here, in this paper, a fault isolation, diagnosis and fault tolerant control algorithm is proposed for nonlinear multiple multiplicative faults stochastic distribution control systems employing Takagi–Sugeno fuzzy system. To obtain the detailed fault information, a fault detection algorithm is introduced to discover the fault occurrence time. Then a fault isolation observer is built to produce the residual, and the error system is separated to subsystems affected only by disturbance and multiplicative faults. Moreover, a fault estimation scheme is presented to obtain the fault magnitude information. When faults occur, the system output probability density function will deviate from the desired distribution. So the model predictive control fault tolerant control scheme is needed to minimize the impact of faults as much as possible to make sure that the post fault output probability density function track the desired probability density function. The validity of the designed algorithm is demonstrated through a simulation example, where the fault tolerant control algorithm ensures that the system output probability density function still track the given output probability density function despite the complex case of multiple multiplicative faults occurring simultaneously.

42 ENGINEERING↗

Influence of lure choice and survey duration on scent stations for carnivore surveys

Abstract Noninvasive, camera‐based, scent station surveys have become a common approach to estimate population parameters for mammalian carnivores. Many carnivores are particularly sensitive to olfactory cues; and, as such, the quality and quantity of odor attractant used during surveys can significantly affect the accuracy and precision of the survey. Additionally, survey length is also an important consideration because many mammalian predators are highly mobile and elusive in nature. Using scent station surveys in autumn 2013 and 2014 on the Savannah River Site, Aiken, South Carolina, USA, we tested the effects of 5 lures: fatty acid, fish oil, synthetic fermented egg, beaver castor, and skunk essence on visitation rates, visitation probability, and latency to visitation of multiple predator species. We also estimated occupancy probability for 2 carnivore species using different survey lengths to determine the effect of survey period on the precision of occupancy estimates. We found that skunk essence had greater visitation probability and visits than other lures evaluated. Species‐specific bait‐preference models revealed that raccoons ( Procyon lotor ) were more likely to visit skunk essence, and coyotes ( Canis latrans ) were less likely to visit fish oil as compared with fatty acid. Latency to visitation ranged from 104.7 to 112.1 hours and did not vary among scents. Longer survey durations resulted in more precise estimates of occupancy and detection probability. Our results suggest a wide range of scents commonly used for carnivore capture may perform as well as, or better than, fatty acid for noninvasive carnivore surveys. Further, study designs should carefully consider the duration of scent‐station surveys depending on the level of precision desired in estimates of occupancy and detection probability. © 2019 The Wildlife Society.

Webster, Sarah C.↗

The relative influence of climate and housing development on current and projected future fire patterns and structure loss across three California landscapes

Climate and land use patterns are expected to change dramatically in the coming century, raising concern about their effects on wildfire patterns and subsequent impacts to human communities. The relative influence of climate versus land use on fires and their impacts, however, remains unclear, particularly given the substantial geographical variability in fire-prone places like California. Here, we developed a modeling framework to compare the importance of climatic and human variables for explaining fire patterns and structure loss for three diverse California landscapes, then projected future large fire and structure loss probability under two different climate (hot-dry or warm-wet) and two different land use (rural or urban residential growth) scenarios. The relative importance of climate and housing pattern varied across regions and according to fire size or whether the model was for large fires or structure loss. The differing strengths of these relationships, in addition to differences in the nature and magnitude of projected climate or land use change, dictated the extent to which large fires or structure loss were projected to change in the future. Despite this variability, housing and human infrastructure were consistently more responsible for explaining fire ignitions and structure loss probability, whereas climate, topography, and fuel variables were more important for explaining large fire patterns. For all study areas, most structure loss occurred in areas with low housing density (from 0.08 to 2.01 units/ha), and expansion of rural residential land use increased structure loss probability in the future. Regardless of future climate scenario, large fire probability was only projected to increase in the northern and interior parts of the state, whereas climate change had no projected impact on fire probability in southern California. Given the variation in fire-climate relationships and land use effects, policy and management decision-making should be customized for specific geographical regions.

54 ENVIRONMENTAL SCIENCES↗

Dose Escalated Liver Stereotactic Body Radiation Therapy at the Mean Respiratory Position

Purpose: The dosimetric impact of dose probability based planning target volume (PTV) margins for liver cancer patients receiving stereotactic body radiation therapy (SBRT) was compared with standard PTV based on the internal target volume (ITV). Plan robustness was evaluated by accumulating the treatment dose to ensure delivery of the intended plan. Methods and Materials: Twenty patients planned on exhale CT for 27 to 50 Gy in 6 fractions using an ITV-based PTV and treated free-breathing were retrospectively evaluated. Isotoxic, dose escalated plans were created on midposition computed tomography (CT), representing the mean breathing position, using a dose probability PTV. The delivered doses were accumulated using biomechanical deformable registration of the daily cone beam CT based on liver targeting at the exhale or mean breathing position, for the exhale and midposition CT plans, respectively. Results: The dose probability PTVs were on average 38% smaller than the ITV-based PTV, enabling an average ± standard deviation increase in the planned dose to 95% of the PTV of 4.0 ± 2.8 Gy (9 ± 5%) on the midposition CT (P<.01). For both plans, the delivered minimum gross tumor volume (GTV) doses were greater than the planned nominal prescribed dose in all 20 patients and greater than the planned dose to 95% of the PTV in 18 (90%) patients. Nine patients (45%) had 1 or more GTVs with a delivered minimum dose more than 5 Gy higher with the midposition CT plan using dose probability PTV, compared with the delivered dose with the exhale CT plan using ITV-based PTV. Conclusions: For isotoxic liver SBRT planned and delivered at the mean respiratory, reduced dose probability PTV enables a mean escalation of 4 Gy (9%) in 6 fractions over ITV-based PTV. This may potentially improve local control without increasing the risk of tumor underdosing.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Mesh objective stochastic simulations of quasibrittle fracture

Continuum finite element (FE) modeling of damage and failure of quasibrittle structures suffers from the spurious mesh sensitivity due to strain localization. Here this issue has been addressed for deterministic analysis through the development of localization limiters. Here this study proposes a mechanism-based model to mitigate the mesh sensitivity in stochastic FE simulations of quasibrittle fracture. The interest is placed on the analysis of large-size structures, where the mesh size is conveniently chosen to be larger than the width of the fracture process zone as well as the correlation length of the random fields of constitutive properties. The present model is formulated within the framework of continuum damage mechanics. Two localization parameters are introduced to describe the evolution of the damage pattern of each finite element. These parameters are used to guide the energy regularization of the constitutive law, as well as to formulate the mesh-dependent probability distributions of constitutive properties. Depending on the prevailing damage pattern, different energy regularization schemes and mesh dependence of the probability distribution functions are used in the constitutive law. The model is applied to simulate the stochastic failure behavior of quasibrittle structures of different geometries featuring different failure processes including damage initiation, localization, and propagation. It is shown that using fixed probability distribution functions of constitutive properties could lead to strong mesh dependence of the prediction of the mean and variance of the structural load capacity. The probability distribution functions of constitutive properties must be linked to the damage pattern, which may evolve during the failure process. Such a mechanism-based modeling of the probability distributions of constitutive properties is essential for mitigating the spurious mesh sensitivity in stochastic FE analysis of quasibrittle fracture.

42 ENGINEERING↗

Network Algorithms for Detection of Radiation Sources

In support of national defense, Domestic Nuclear Detection Office’s (DNDO) Intelligent Radiation Sensor Systems (IRSS) program supported the development of networks of radiation counters for detecting, localizing and identifying low-level, hazardous radiation sources. Industry teams developed the first generation of such networks with tens of counters, and demonstrated several of their capabilities in indoor and outdoor characterization tests. Subsequently, these test measurements have been used in algorithm replays using various sub-networks of counters. Test measurements combined with algorithm outputs are used to extract Key Measurements and Benchmark (KMB) datasets. We present two selective analyses of these datasets: (a) a notional border monitoring scenario that highlights the benefits of a network of counters compared to individual detectors, and (b) new insights into the Sequential Probability Ratio Test (SPRT) detection method, which lead to its adaptations for improved detection. Using KMB datasets from an outdoor test, we construct a notional border monitoring scenario, wherein twelve 2”*2” NaI detectors are deployed on the periphery of 21*21meter square region. A Cs-137 (175 uCi) source is moved across this region, starting several meters from outside and finally moving away. The measurements from individual counters and the network were processed using replays of a particle filter algorithm developed under IRSS program. The algorithm outputs from KMB datasets clearly illustrate the benefits of combining measurements from all networked counters: the source was detected before it entered the region, during its trajectory inside, and until it moved several meters away. When individual counters are used for detection, the source was detected for much shorter durations, and sometimes was missed in the interior region. The application of SPRT for detecting radiation sources requires choosing the detection threshold, which in turn requires a source strength estimate, typically specified as a multiplier of the background radiation level. A judicious selection of this source multiplier is essential to achieve optimal detection probability at a specified false alarm rate. Typically, this threshold is chosen from the Receiver Operating Characteristic (ROC) by varying the source multiplier estimate. ROC is expected to have a monotonically increasing profile between the detection probability and false alarm rate. We derived ROCs for multiple indoor tests using KMB datasets, which revealed an unexpected loop shape: as the multiplier increases, detection probability and false alarm rate both increase until a limit, and then both contract. Consequently, two detection probabilities correspond to the same false alarm rate, and the higher is achieved at a lower multiplier, which is the desired operating point. Using the Chebyshev’s inequality we analytically confirm this shape. Then, we present two improved network-SPRT methods by (a) using the threshold off-set as a weighting factor for the binary decisions from individual detectors in a weighted majority voting fusion rule, and (b) applying a composite SPRT derived using measurements from all counters.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Application of Bayes' theorem for pulse shape discrimination

A Bayesian approach is proposed for pulse shape discrimination of photons and neutrons in liquid organic scinitillators. Instead of drawing a decision boundary, each pulse is assigned a photon or neutron confidence probability. In addition, this allows for photon and neutron classification on an event-by-event basis. The sum of those confidence probabilities is used to estimate the number of photon and neutron instances in the data. An iterative scheme, similar to an expectation-maximization algorithm for Gaussian mixtures, is used to infer the ratio of photons-to-neutrons in each measurement. Therefore, the probability space adapts to data with varying photon-to-neutron ratios. A time-correlated measurement of Am–Be and separate measurements of 137 Cs, 60 Co and 232 Th photon sources were used to construct libraries of neutrons and photons. These libraries were then used to produce synthetic data sets with varying ratios of photons-to-neutrons. Probability weighted method that we implemented was found to maintain neutron acceptance rate of up to 90% up to photon-to-neutron ratio of 2000, and performed 9% better than the decision boundary approach. Furthermore, the iterative approach appropriately changed the probability space with an increasing number of photons which kept the neutron population estimate from unrealistically increasing.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Uniform-in-phase-space data selection with iterative normalizing flows

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that are routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data are available.

97 MATHEMATICS AND COMPUTING↗

Copacabana: a probabilistic membership assignment method for galaxy clusters

Cosmological analyses using galaxy clusters in optical/near-infrared photometric surveys require robust characterization of their galaxy content. Precisely determining which galaxies belong to a cluster is crucial. In this paper, we present the COlor Probabilistic Assignment of Clusters And BAyesiaN Analysis (Copacabana) algorithm. Copacabana computes membership probabilities for all galaxies within an aperture centred on the cluster using photometric redshifts, colours, and projected radial probability density functions. We use simulations to validate Copacabana and we show that it achieves up to 89 per cent membership accuracy with a mild dependence on photometric redshift uncertainties and choice of aperture size. We find that the precision of the photometric redshifts has the largest impact on the determination of the membership probabilities followed by the choice of the cluster aperture size. We also quantify how much these uncertainties in the membership probabilities affect the stellar mass–cluster mass scaling relation, a relation that directly impacts cosmology. Using the sum of the stellar masses weighted by membership probabilities (⁠μ * ⁠) as the observable, we find that Copacabana can reach an accuracy of 0.06 dex in the measurement of the scaling relation at low redshift for a Legacy Survey of Space and Time type survey. These results indicate the potential of Copacabana and μ * to be used in cosmological analyses of optically selected clusters in the future.

79 ASTRONOMY AND ASTROPHYSICS↗

Neutrino mass priors for cosmology from random matrices

Cosmological measurements of structure are placing increasingly strong constraints on the sum of the neutrino masses, Σm ν , through Bayesian inference. Because these constraints depend on the choice for the prior probability π(Σm ν ), we argue that this prior should be motivated by fundamental physical principles rather than the ad hoc choices that are common in the literature. The first step in this direction is to specify the prior directly at the level of the neutrino mass matrix M ν , since this is the parameter appearing in the Lagrangian of the particle physics theory. Thus by specifying a probability distribution over M ν , and by including the known squared mass splittings, we predict a theoretical probability distribution over Σm ν that we interpret as a Bayesian prior probability π(Σm ν ). Assuming a basis-invariant probability distribution on M ν , also known as the anarchy hypothesis, we find that π(Σm ν ) peaks close to the smallest Σm ν allowed by the measured mass splittings, roughly 0.06 eV (0.1 eV) for normal (inverted) ordering, due to the phenomenon of eigenvalue repulsion in random matrices. We consider three models for neutrino mass generation: Dirac, Majorana, and Majorana via the seesaw mechanism; differences in the predicted priors π(Σm ν ) allow for the possibility of having indications about the physical origin of neutrino masses once sufficient experimental sensitivity is achieved. In conclusion, we present fitting functions for π(Σm ν ), which provide a simple means for applying these priors to cosmological constraints on the neutrino masses or marginalizing over their impact on other cosmological parameters.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Analysis of TPA Pulsed-Laser-Induced Single-Event Latchup Sensitive-Area

Two-photon absorption (TPA) testing is employed to analyze the laser-induced latchup sensitive-volume (SV) of a specially designed test structure. This method takes into account the existence of an onset region in which the probability of triggering latchup transitions from zero to one as the laser pulse energy increases. This variability is attributed to pulse-to-pulse variability, uncertainty in measurement of the pulse energy, and variation in local carrier density and temperature. For each spatial position, the latchup probability associated with a given energy is calculated from multiple pulses. The latchup probability data are well-described by a Weibull distribution. The results show that the area between p-n-p-n cell structures is more sensitive than the p+ and n+ source areas, and locations far from the well contacts are more sensitive than those near the contact region. The transition from low probability of latchup to high probability is more abrupt near the source contacts than it is for the surrounding areas.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Technical Note: On the proton range and nuclear interactions in compounds and mixtures

Purpose: Range and probability of nonelastic nuclear interactions (NNIs) for protons can be found only for a limited number of compounds and mixtures in nuclear data tables, and the proton-related analytical studies are therefore restricted to those materials for which the data are provided in these documents. In this paper, the authors present general solutions for calculating the proton range and probability of NNIs for desired compounds and mixtures. Methods: Benefiting from the Bragg–Kleeman approximation of mass stopping power, the authors derive a concise formula for calculating the proton range in materials with arbitrary number of constituent elements. Additionally, the authors propose another relation for obtaining the probability of undergoing NNIs which is suggested to be additive. Results: The examination of the formula presented shows that the authors’ method can be considered as general solutions for analytical evaluation of the range in compounds and mixtures. The formula proposed for probability of NNIs is valid for almost every compound except for those materials containing H. It is shown that this formula can be modified so that it covers these materials. Conclusions: The authors present a general analytical method for calculating the range and probability of NNIs for protons which are mathematically easy to handle and valid for desired compounds or mixtures composed of an arbitrary number of constituent elements, including materials of interest for proton radiotherapy purposes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

TU-AB-BRB-00: New Methods to Ensure Target Coverage

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

TU-AB-BRB-01: Coverage Evaluation and Probabilistic Treatment Planning as a Margin Alternative

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗