Standard Deviation Of Random Error Research Articles

Trends analysis of Evapotranspiration and responses to soil moisture and wind speed over the Taklimakan Desert, China

The Tarim Basin is a typical hyper-arid area, 57% of which is occupied by the Taklimakan desert. Because evapotranspiration (ET) is a key factor in determining water demand, accurate estimation of ET is critical for efficient water management in arid regions. In this study, the spatiotemporal dynamics of ET across the Tarim Basin from 2001 to 2020 were simulated based on a revised Surface Energy Balance System (SEBS) algorithm, and the impacts of driving factors on ET trends in the Taklimakan desert were quantified. The findings indicated that the mean annual ET in the entire basin was slightly greater than that in the desert (302 mm vs. 295 mm), although the decreasing rate of annual ET across the entire basin was slower than that in the desert (−0.27 mm/year vs. −0.50 mm/year). Strong increasing trends were found in croplands, whereas decreasing trends, which accounted for 56.5% of the basin, were primarily concentrated in the central and southern parts of the desert. Correlation analysis revealed that wind speed (WS) and soil moisture (SM) were the dominant factors, with a negative contribution of more than 35% and a positive contribution of more than 45%, respectively, to ET trends. Compared with the ERA5-Land and complementary relationship ET using the extended triple collocation method, SEBS ET provided detailed information and a lower random error standard deviation. Our findings contribute to the understanding of how dominant factors impact ET in hyper-arid regions and provide a reference for water management.

Assessments of Doppler Velocity Errors of EarthCARE Cloud Profiling Radar Using Global Cloud System Resolving Simulations: Effects of Doppler Broadening and Folding

The Earth Clouds, Aerosol, and Radiation Explorer (EarthCARE) is a satellite mission jointly developed by the Japan Aerospace Exploration Agency (JAXA) and the European Space Agency (ESA). One challenging feature of this mission is the observation of Doppler velocity by the Cloud Profiling Radar (EC-CPR). The Doppler measurement accuracy is affected by random errors induced by Doppler broadening due to the finite beamwidth and Doppler folding caused by the finite pulse repetition frequency. We investigated the impact of horizontal (along-track) integration and unfolding methods on the reduction of Doppler errors, in order to improve Doppler data processing in the JAXA standard algorithm. We simulated EC-CPR-observed Doppler velocities from pulse-pair covariances with the latest EC-CPR specifications using the radar reflectivity factor and Doppler velocity fields simulated by a satellite data simulator and a global cloud system resolving simulation. Two representative cases of a cirrus cloud and precipitation were examined. In the cirrus cloud case, the standard deviation of random error was decreased to 0.5 m/s for −10 dB <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Z} _{\mathbf {e}}$ </tex-math></inline-formula> after 10-km horizontal integration. In the precipitation case, large falling speeds of precipitation caused Doppler folding errors due to larger Doppler velocities than that in the cirrus cloud case. When <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Z} _{\mathbf {e}}$ </tex-math></inline-formula> is larger than −15 dB <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Z} _{\mathbf {e}}$ </tex-math></inline-formula> , the standard deviations of random error were less than 1.0 m/s after 10-km horizontal integration and unfolding.

The impact of Aeolus wind retrievals on ECMWF global weather forecasts

AbstractAeolus is the world's first spaceborne Doppler Wind Lidar, providing profiles of horizontal line‐of‐sight (HLOS) wind retrievals. Numerical weather prediction (NWP) impact and error statistics of Aeolus Level‐2B (L2B) wind statistics have been assessed using the European Centre for Medium‐range Weather Forecasts (ECMWF) global data assimilation system. Random and systematic error estimates were derived from observation minus background departure statistics. The HLOS wind random error standard deviation is estimated to be in the range 4.0–7.0 m·s−1 for the Rayleigh‐clear and 2.8–3.6 m·s−1 for the Mie‐cloudy, depending on atmospheric signal levels which in turn depend on instrument performance, atmospheric backscatter properties and the processing algorithms. Complex systematic HLOS wind error variations on time‐scales less than one orbit were identified, most strongly affecting the Rayleigh‐clear winds. NWP departures and instrument housekeeping data confirmed that it is caused by temperature gradients across the primary mirror. A successful bias correction scheme was implemented in the operational processing chain in April 2020. In Observing System Experiments (OSEs), Aeolus provides statistically significant improvement in short‐range forecasts as verified by observations sensitive to temperature, wind and humidity. Longer forecast range verification shows positive impact that is strongest at the day two to three forecast range: ∼2% improvement in root‐mean‐square error for vector wind and temperature in the tropical upper troposphere and lower stratosphere, and polar troposphere. Positive impact up to 9 days is found in the tropical lower stratosphere. Both Rayleigh‐clear and Mie‐cloudy winds provide positive impact, but the Rayleigh accounts for most tropical impact. The Forecast Sensitivity Observation Impact (FSOI) metric is available since 9 January 2020, when Aeolus was operationally assimilated, which confirms Aeolus is a useful contribution to the global observing system, with the Rayleigh‐clear and Mie‐cloudy winds providing similar overall short‐range impact in 2020.

Influence of intra- and interfraction motion on planning target volume margin in liver stereotactic body radiation therapy using breath hold

PurposeThis study aimed to investigate intra- and interfraction motion during liver stereotactic body radiation therapy for the purpose of planning target volume (PTV) margin estimation, comparing deep inspiration breath hold (DIBH) and deep expiration breath hold (DEBH). Methods and materialsPre- and posttreatment kV cone beam computed tomography (CT) images were acquired for patients with liver cancer who were treated using stereotactic body radiation therapy with DIBH or DEBH. A total of 188 images were analyzed from 18 patients. Positioning errors were determined based on a comparison with planning CT images and matching to the liver. Treatment did not proceed until errors were ≤3 mm. Standard deviations of random and systematic errors resulting from this image matching process were used to calculate PTV margin estimates. ResultsDIBH errors are generally larger than DEBH errors, especially in the anterior–posterior and superior–inferior directions. Posttreatment errors tend to be larger than pretreatment errors, especially for DIBH. Standard deviations of random errors are larger than those of systematic errors. Considering both pre- and posttreatment cone beam CT images, PTV margins for DIBH and DEBH are estimated as anterior–posterior, superior–inferior, right–left = (5.7, 6.3, 3.0) mm and (3.1, 3.4, 2.8) mm, respectively. ConclusionsThis study suggests that DEBH results in more reproducible target positioning, which could in turn justify the use of smaller PTV margins.

Error Modeling Radar Rainfall Estimation Through Incorporating Rain Gauge Data Over Upper Blue Nile Basin, Ethiopia

Accurate and precise measurements of rainfall from weather radar reflectivity data is essential to supplement the limited characterization of spatial and temporal measurements provided by insufficient network and density of rain gauges. While weather radar has high spatial and temporal resolution, it contaminated with various sources of errors due to the conversion of reflectivity to rain rate and the projectile rainfall motion. Error modeling improvement with the application of projectile rainfall motion correction is essential to improve the radar data. However, stile is not well documented for over the world as well as Ethiopia. Therefore, the aim of this study was to generate an error model for weather radar rainfall estimation by incorporating gauge rainfall data over upper Blue Nile basin, Ethiopia. Projectile rainfall motion correction is considered on the data of reflectivity and rain rate to determine empirical error model parameter values. The model parameter values are found, multiplicative factor (a) was 55, the exponent factor (b) was 1.12, standard deviation of proportional error was 0.08 and standard deviation of random error was 0.07. The value of the total error varied from -0.45 to 1.16 mm and the domain of proportional error was greater than random error. After applying the projectile rainfall motion correction, the total error is reduced by 12%. In general, the assumption of projectile method is quite useful for improving the radar data over upper Blue Nile basin in Ethiopia as well as over the world. Hence, we wish to extend this method for other regions.

Analysis of Variance for Item Differences in Verification Data with Unknown Groups

For sequentially collected data, this paper introduces a lag-one differencing method to estimate the random error standard deviation δR and then uses the estimate δ^R to calculate a change detection threshold in a moving window method to detect shifts in the short-term systematic error. Performance results on simulated and real data are presented. Fortunately, the impact of having to perform change detection on the estimated short-term systematic and random error variances is anticipated to be modest or small. The motivating example arises from facilities under nuclear safeguards agreements, where inspector data collected during International Atomic Energy Agency (IAEA) verifications are compared to corresponding operator data. The differences between the operator and inspector values are evaluated using an application of analysis of variance (ANOVA). Typically, it is assumed that short-term systematic errors change across inspection periods, so inspection periods form the groups used in the ANOVA. In some data sets, it appears that the short-term errors have changed at other times, so change detection methods could be used to detect the actual change times.

Analysis and Modeling of Imperfections in Multi-Bit Per Stage Pipelined ADCs

In this paper, an approach to estimate signal to noise ratio (SNR) and effective number of bits (ENOB) in nonideal multi-bit stages of pipelined analog to digital converters (ADCs) is presented. The most significant error sources in multistage ADCs are the capacitor mismatch and the finite and imprecise gain of amplifier. Output voltage of each stage in pipelined ADC is modeled by an ideal and a nonideal output, where nonideal output is the error due to circuit imperfections in each stage. Using an appropriate model, the SNR and ENOB due to circuit nonidealities and in terms of standard deviation of random errors are calculated. Simulation results show the accuracy of the analytical proposed approach in estimation of SNR and ENOB in multi-bit per stage pipelined converters.

Evaluation of random errors in Williams’ series coefficients obtained with digital image correlation

The use of the Williams’ series parameters for fracture analysis requires valid information about their error values. The aim of this investigation is the development of the method for estimation of the standard deviation of random errors of the Williams’ series parameters, obtained from the measured components of the stress field. Also, the criteria for choosing the optimal number of terms in the truncated Williams’ series for derivation of their parameters with minimal errors is proposed. The method was used for the evaluation of the Williams’ parameters, obtained from the data, and measured by the digital image correlation technique for testing a three-point bending specimen.

A Suggestion on Uncertainty Correction of Ground Motion Attenuation in Probabilistic Seismic Hazard Assessment

The uncertainty of ground motion attenuation and its correction in PSHA is deal with in this paper. Mean values and standard deviations of random errors of three attenuation relationships of NGA-west1 are analyzed statistically from the data base released by the project. The dependences of the mean and deviation on magnitude, distance and peak ground acceleration are checked by the data base. The fact of mean values varying with acceleration is revealed obviously. Ground motion parameter Y is adopted into the probability density function of random error in a form of subsection. Finally, a suggestion to improve the correction is presented as subsection correction in the paper. The result of a case study by suggested procedure shows that the corrected acceleration is slightly higher than that of the traditional correction at the start of hazard curve, and is significantly lower than that of the traditional correction at the end of the curve, if the mean of random error decreases with acceleration.

Assessment of Digital Image Correlation Measurement Accuracy in the Ultimate Error Regime: Main Results of a Collaborative Benchmark

ABSTRACTWe report on the main results of a collaborative work devoted to the study of the uncertainties associated with Digital image correlation techniques (DIC). More specifically, the dependence of displacement measurement uncertainties with both image characteristics and DIC parameters is emphasised. A previous work [Bornert et al. (2009) Assessment of digital image correlation measurement errors: methodology and results. Exp. Mech. 49, 353–370] dedicated to situations with spatially fluctuating displacement fields demonstrated the existence of an ‘ultimate error’ regime, insensitive to the mismatch between the shape function and the real displacement field. The present work is focused on this ultimate error. To ensure that there is no mismatch error, synthetic images of in‐plane rigid body translation have been analysed. Several DIC softwares developed by or in use in the French community have been used to explore the effects of a large number of settings. The discrepancies between DIC evaluated displacements and prescribed ones have been statistically analysed in terms of random errors and systematic bias, in correlation with the fractional part τ of the displacement component expressed in pixels. Main results are as follows: (i) bias amplitude is almost always insensitive to subset size, (ii) standard deviation of random error increases with noise level and decreases with subset size and (iii) DIC formulations can be split up into two main families regarding bias sensitivity to noise. For the first one, bias amplitude increases with noise while it remains nearly constant for the second one. In addition, for the first family, a strong dependence of random error with τ is observed for noisy images.

Stiffness of sands through a laboratory test database

Deformations of sandy soils around geotechnical structures generally involve strains in the range small (0·01%) to medium (0·5%). In this strain range the soil exhibits non-linear stress–strain behaviour, which should be incorporated in any deformation analysis. In order to capture the possible variability in the non-linear behaviour of various sands, a database was constructed including the secant shear modulus degradation curves of 454 tests from the literature. By obtaining a unique S-shaped curve of shear modulus degradation, a modified hyperbolic relationship was fitted. The three curve-fitting parameters are: an elastic threshold strain γe, up to which the elastic shear modulus is effectively constant at G0; a reference strain γr, defined as the shear strain at which the secant modulus has reduced to 0·5G0; and a curvature parameter a, which controls the rate of modulus reduction. The two characteristic strains γeand γrwere found to vary with sand type (i.e. uniformity coefficient), soil state (i.e. void ratio, relative density) and mean effective stress. The new empirical expression for shear modulus reduction G/G0is shown to make predictions that are accurate within a factor of 1·13 for one standard deviation of random error, as determined from 3860 data points. The initial elastic shear modulus, G0, should always be measured if possible, but a new empirical relation is shown to provide estimates within a factor of 1·6 for one standard deviation of random error, as determined from 379 tests. The new expressions for non-linear deformation are easy to apply in practice, and should be useful in the analysis of geotechnical structures under static loading.

Poster - Thur Eve - 62: Assessing the clinical application of the van Herk margin formula for lung radiotherapy.

According to a margin recipe developed by van Herk et al. the Planning Target Volume (PTV) margin to ensure the Clinical Target Volume is covered by at least 95% of the prescribed dose can be calculated by applying the following formula: M = 2.5Σ + 1.64σ2 - 1.64σp. In the van Herk Margin formula (VHMF), Σ is the standard deviation (SD) of all systematic errors; σ is the SD of random errors and σp is the width of the penumbra. This formula is based on an idealized dose profile model that may not account for factors that vary significantly in lung radiotherapy such as tumour size and tissue density. The purpose of this study was to use accurate dose calculation algorithms and respiratory motion modeling to investigate the validity of the VHMF for lung radiotherapy. Random and systematic errors were simulated in treatment planning software using dose accumulation techniques for clinically relevant 3DCRT and IMRT treatment plans constructed on virtual phantoms. Phantom parameters such as target size, peak-to-peak motion amplitude and tissue density were varied to investigate their impact on the systematic and random error components of the margin formula. The VHMF was found to provide adequate dose coverage for all plans generated on different target sizes and motion amplitudes. Although discrepancies existed between idealized and realistic dose profiles in water and lung, the dose coverage defined by the V95 was not affected. The margin formula was found to be robust; however, further investigation of the influence of plan conformity is needed.

Rounding error effects in the presence of underlying measurement error

A previous related paper considered rounding error effects in the presence of underlying measurement error and presented a Bayesian approach to estimate instrument input random error standard deviation. This addendum to the previous paper emphasizes that the effects of random error depend on the true (and usually unknown) value of the measurand, in terms of both the variance and the item-specific bias. However, it is shown that if we assume that the true values are uniformly distributed, then instrument variance and item-specific bias can be combined into an “effective random error variance” and a strategy to estimate the effective random error variance is provided.

TU-E-BRB-10: Dosimetric Consequences of Setup Errors Using CBCT for SBRT Localization.

Steep dose gradients and high dose per fraction in stereotactic ablative radiation therapy (SABR or SBRT) necessitate highly accurate tumor localization. This study evaluates inter-fraction shifts, as defined by couch correction analysis, and investigates the effect of tumor location and internal target volume (ITV) on these shifts. In addition, residual errors associated with post-CBCT correction and their dosimetric consequences were quantified. Daily free-breathing (FB) CBCT images used for daily localization of 78 patients with non-small cell lung cancer were retrospectively evaluated. Among the population, 39 patients also received pre-treatment kV images after CBCT alignment. ITV inter-fraction displacement was evaluated by matching the CBCT and the FB helical CT images, and setup errors were quantified using orthogonal kV images. Associations between ITV location and inter-fraction motion were studied by categorizing tumors into the following locations: chest-wall seated (CWS) and island, peripheral, central, or upper, middle and lower. Dosimetric consequences for the patient with the largest setup error were explored. ITV inter-fraction motion included the mean of the systematic error, ?inter=(-1.4, 2.0, 1.6) mm, standard deviation (SD) of the systematic error, Σinter=(2.1, 4.2, 2.9) mm, and SD of random errors, sinter=(2.2, 3.2, 3.6) mm. No significant associations were observed between inter-fraction shifts and tumor location or volume. Using CBCT for image guidance reduced the observed errors to μsetup=(-0.3, 0.1, 0.0) mm, Σsetup=(0.6, 0.6, 0.4) mm and ssetup=(1.2, 0.7, 0.7) mm. Dosimetric consequences for the patient with the largest setup error were explored. It was shown that a 3.0 mm setup margin was sufficient to provide greater than 95% dose coverage to the ITV. CBCT image guidance reduced setup errors significantly such that 2-3 mm, population-based, setup margins provided proper dose coverage to the ITV. Further investigation of inter-and intrafraction error classification by tumor location is warranted.

TH-E-BRA-11: Real-Time Tumor Localization with Kilovoltage Intrafraction Monitoring: First Clinical Implementation for Prostate Intensity Modulated Arc Therapy

Purpose: We have proposed a novel real-time tumor localization method, kilovoltage (kV) intrafraction monitoring (KIM), in which the intrafraction 3D tumor position is continuously measured during intensity modulated arc therapy (IMAT) by a gantry-mounted kV x-ray imager. This study reports the first clinical implementation of this method in patients with localized prostate cancer. Methods: In an ethics-approved study, 10 prostate cancer patients with implanted fiducial markers underwent conventionally fractionated IMAT. During treatment, intrafraction prostate motions were tracked using KIM at a rate of 5 or 10Hz. The kV imager acquired 2D projections of the prostate markers. Post-treatment, markers in the images were segmented to obtain 2D positions. 3D positions were reconstructed by maximum likelihood estimation of a 3D probability density function. Trajectories were analyzed to determine the motion type and the percentage of time the prostate was displaced for more than 3mm, 5mm, 7mm and 10mm. Results: Various prostate trajectories were observed (e.g. continuous target drift, transient excursion, stable target position, persistent excursion, high-frequency excursions and erratic behaviour). Over all patients, 3D displacements exceeding 3mm, 5mm, 7mm and 10mm were observed 5.6%, 2.2%, 0.7% and 0.4% of the time respectively. For individual patients, 3D displacements exceeding 3mm over all fractions ranged from 0.0% to 23.8% and 3D displacements exceeding 5mm ranged from 0.0% to 10.0%. For all patients, the left-right (LR), superior-inferior (SI) and anterior-posterior (AP) standard deviation of systematic setup error was 0.3mm, 0.2mm and 0.2mm, respectively. The LR, SI and AP standard deviation of random error was 0.7mm, 1.1mm and 1.1mm, respectively. Conclusions: Our results demonstrate that KIM is a clinically viable and objective method for monitoring prostate motion during treatment. KIM only requires a single kV imager, which is commonly available, enabling its widespread implementation. Research supported by NIH/NCI R01 93626

Interfraction Prostate Rotation Determined from In-Room Computerized Tomography Images

Fiducial markers (FMs) are commonly used as a correction technique for interfraction translations of the prostate. The aim of this investigation was to determine the magnitude of prostate rotations using 2 methods: FM coordinates and the anatomical border of the prostate and rectum. Daily computed tomography (CT) scans ( n = 346) of 10 prostate cancer patients with 3 implanted FMs were acquired using the CT on rails. FM coordinates were used to determine rotation in the sagittal, transverse, and coronal planes, and CT contours of the prostate and rectum were used to determine rotation along the sagittal plane. An adaptive technique based on a subset of images ( n = 6; planning and first 5 treatment CTs) to reduce systematic rotation errors in the sagittal plane was tested. The standard deviation (SD) of systematic rotation from FM coordinates was 7.6°, 7.7°, and 5.0° in the sagittal, transverse and coronal planes. The corresponding SD of random error was 10.2°, 15.8°, and 6.5°. Errors in the sagittal plane, determined from prostate and rectal contours, were 10.1° (systematic) and 7.7° (random). These results did not correlate with rotation computed from FM coordinates (r = −0.017; p = 0.753, n = 337). The systematic error could be reduced by 43% to 5.6° when the mean prostate position was estimated from 6 CT scans. Prostate rotation is a significant source of error that appears to be more accurately determined using the anatomical border of the prostate and rectum rather than FMs, thus highlighting the utility of CT image guidance.

Measuring Interfractional and Intrafractional Motion With Cone Beam Computed Tomography and an Optical Localization System for Lower Extremity Soft Tissue Sarcoma Patients Treated With Preoperative Intensity-Modulated Radiation Therapy

To evaluate inter- and intrafractional motion and rotational error for lower extremity soft tissue sarcoma patients by using cone beam computed tomography (CBCT) and an optical localization system. Thirty-one immobilized patients received CBCT image-guided intensity-modulated radiation therapy. Setup deviations of >3 mm from the planned isocenter were corrected. A second CBCT acquired before treatment delivery was registered to the planning CT to estimate interfractional setup error retrospectively. Interfractional error and rotational error were calculated in the left-right (LR), superoinferior (SI), and anteroposterior (AP) dimensions. Intrafractional motion was assessed by calculating the maximum relative displacement of optical localization system reflective markers placed on the patient's surface, combined with pre- and postfraction CBCT performed for 17 of the 31 patients once per week. The overall systematic error (SE) and random error (RE) were calculated for the interfractional and intrafractional motion for planning target volume margin calculation. The standard deviation (SD) of the interfractional RE was 1.9 mm LR, 2.1 mm SI, and 1.8 mm AP, and the SE SD was 0.6 mm, 1.2 mm, and 0.7 mm in each dimension, respectively. The overall rotation (inter- and intrafractional) had an RE SD of 0.8° LR, 1.7° SI, and 0.7° AP and an SE SD of 1.1° LR, 1.3° SI, and 0.3° AP. The SD of the overall intrafractional RE was 1.6 mm LR, 1.6 mm SI, and 1.4 mm AP, and the SE SD was 0.7 mm AP, 0.6 mm SI, and 0.6 mm AP. A uniform 5-mm planning target volume margin was quantified for lower extremity soft tissue sarcoma patients and has been implemented clinically for image-guided intensity-modulated radiation therapy.

Influences of observation errors in eddy flux data on inverse model parameter estimation

Abstract. Eddy covariance data are increasingly used to estimate parameters of ecosystem models. For proper maximum likelihood parameter estimates the error structure in the observed data has to be fully characterized. In this study we propose a method to characterize the random error of the eddy covariance flux data, and analyse error distribution, standard deviation, cross- and autocorrelation of CO2 and H2O flux errors at four different European eddy covariance flux sites. Moreover, we examine how the treatment of those errors and additional systematic errors influence statistical estimates of parameters and their associated uncertainties with three models of increasing complexity – a hyperbolic light response curve, a light response curve coupled to water fluxes and the SVAT scheme BETHY. In agreement with previous studies we find that the error standard deviation scales with the flux magnitude. The previously found strongly leptokurtic error distribution is revealed to be largely due to a superposition of almost Gaussian distributions with standard deviations varying by flux magnitude. The crosscorrelations of CO2 and H2O fluxes were in all cases negligible (R2 below 0.2), while the autocorrelation is usually below 0.6 at a lag of 0.5 h and decays rapidly at larger time lags. This implies that in these cases the weighted least squares criterion yields maximum likelihood estimates. To study the influence of the observation errors on model parameter estimates we used synthetic datasets, based on observations of two different sites. We first fitted the respective models to observations and then added the random error estimates described above and the systematic error, respectively, to the model output. This strategy enables us to compare the estimated parameters with true parameters. We illustrate that the correct implementation of the random error standard deviation scaling with flux magnitude significantly reduces the parameter uncertainty and often yields parameter retrievals that are closer to the true value, than by using ordinary least squares. The systematic error leads to systematically biased parameter estimates, but its impact varies by parameter. The parameter uncertainty slightly increases, but the true parameter is not within the uncertainty range of the estimate. This means that the uncertainty is underestimated with current approaches that neglect selective systematic errors in flux data. Hence, we conclude that potential systematic errors in flux data need to be addressed more thoroughly in data assimilation approaches since otherwise uncertainties will be vastly underestimated.

The Impact of Prostate and Seminal Vesicle Motion during Prostate Cancer Radiotherapy on Planning Margins

The seminal vesicles (SVs) form part of the target in the radiotherapy (RT) treatment of prostate cancer, either because of their significant risk of involvement in locally advanced disease or because of overt clinical invasion. While prostate motion and appropriate margins have been documented, there is little information on SV motion. Movement of the SVs compared to the prostate, if uncorrected, can lead to geometrical target miss. The aim of this prospective study was to assess and compare SV motion with respect to prostate motion to ascertain the appropriate margins for each target. The study population consisted of 10 patients with locally advanced prostate cancer and considered to be at risk of SV invasion or with clinically T3b disease. The average age was 71 years, with average PSA and median Gleason scores of 10 μg/L and 8, respectively, and T stages from T2a to T3b. Following consent, 5 gold seeds were inserted trans-rectally into each patient. Of the 5 seeds, 3 were inserted into the prostate (right base, left mid gland, right apex), and 1 into each of the left and right SVs. All patients were treated to a dose of 78 Gy in 39 fractions with IMRT. Daily orthogonal 2D Electronic Portal Images (EPIs) were taken of each patient in treatment position prior to RT. Elekta I-View GT template matching software was used to verify EPIs with the reference image (CT-derived Digitally Reconstructed Radiograph). Online verification was performed for each fraction using the 3 prostate seeds. Matches of the left and right SV seeds were performed offline for each of the 39 fractions of all 10 patients. The total standard deviation (SD) of systematic errors (∑tot) and SD of random errors (σtot) were calculated, and the CTV-PTV margins for both the prostate and SVs were generated using a previously published formula (2.5∑tot + 0.7σtot). The average correctional shifts (with ranges) for the prostate and SVs in mm were: Prostate: Right-Left (RL) 0.9 (−4.6 to 6.5), Superior-Inferior (SI) −0.3 (−9.8 to 6.3), Anterior-Posterior (AP) −0.3 (−8.6 to 9.1) Left SV: RL 0.9 (−10.5 to 10.4), SI -1.4 (−10.8 to 8.8), AP -2.2 (−16.6 to 8.3) Right SV: RL 0.1 (−9.0 to 5.3), SI -1.1 (−9.4 to 6.3), AP -2.1 (−13.2 to 10.9). Required CTV-PTV margins in mm in the RL, SI and AP planes were: Prostate: 4.2, 6.1, 3.3 Left SV: 9.1, 5.4, 6.9 Right SV: 5.5, 5.4, 6.7. Positional variation of the prostate and SVs was observed during RT. We have found that SV motion is greater in the RL and AP directions than prostate motion. Consequently, the calculated PTV margins for the SVs were greater than the prostate margins, indicating that differential margins may be warranted.

A Stochastic Expected Utility Theory

This paper proposes a new model that explains the violations of expected utility theory through the role of random errors. The paper analyzes decision making under risk when individuals make random errors when they compute expected utilities. Errors are drawn from the normal distribution, which is truncated so that the stochastic utility of a lottery cannot be greater (lower) than the utility of the highest (lowest) possible outcome. The standard deviation of random errors is higher for lotteries with a wider range of possible outcomes. It converges to zero for lotteries converging to a degenerate lottery. The model explains all major stylized empirical facts such as the Allais paradox and the fourfold pattern of risk attitudes. The model fits the data from ten well-known experimental studies at least as good as cumulative prospect theory.