A γ‐conical position error representation method considering high‐order position relevance of array elements

Precise Point Positioning (PPP) is an increasingly recognized precisely the GPS/GNSS positioning technique. In order to improve the accuracy of PPP, the error sources in PPP measurements should be reduced as much as possible and the ambiguities should be correctly resolved. The correct ambiguity resolution requires a careful control of residual errors that are normally categorized into random and systematic errors. To understand effects from two categorized errors on the PPP ambiguity resolution, those two GPS datasets are simulated by generating in locations in South Korea (denoted as SUWN) and Hong Kong (PolyU). Both simulation cases are studied for each dataset; the first case is that all the satellites are affected by systematic and random errors, and the second case is that only a few satellites are affected. In the first case with random errors only, when the magnitude of random errors is increased, L1 ambiguities have a much higher chance to be incorrectly fixed. However, the size of ambiguity error is not exactly proportional to the magnitude of random error. Satellite geometry has more impacts on the L1 ambiguity resolution than the magnitude of random errors. In the first case when all the satellites have both random and systematic errors, the accuracy of fixed ambiguities is considerably affected by the systematic error. A pseudorange systematic error of 5 cm is the much more detrimental to ambiguity resolutions than carrier phase systematic error of 2 mm. In the 2 nd case when only a portion of satellites have systematic and random errors, the L1 ambiguity resolution in PPP can be still corrected. The number of allowable satellites varies from stations to stations, depending on the geometry of satellites. Through extensive simulation tests under different schemes, this paper sheds light on how the PPP ambiguity resolution (more precisely L1 ambiguity resolution) is affected by the characteristics of the residual errors in PPP observations. The numerical examples recall the PPP data analysts that how accurate the error correction models must achieve in order to get all the ambiguities resolved correctly.

Purpose: To investigate dosimetric effect of the random and systematic errors of MLC leaf positions on the IMRT plans for patients with head and neck cancer. Method and Materials: For six clinical IMRT plans, random errors (from −2 to 2 mm) and systematic errors (±0.5 mm and ±1 mm) MLC positioning errors were introduced into the each segment for these plans, simulating the mechanical uncertainties and potential miscalibration of the MLC. The altered MLC segments for each plan were imported to a commercial treatment planning system to evaluate dosimetric changes of the plan. The altered plans were compared to the original plans, based on DVHs and defined endpoint doses. Results: With the up‐to‐2 mm random errors in MLC positions, the dose changes to the 95% of the tumor volumes were (−1.247± 1.153)%. For serial structures, the dose changes to the 0.1 cc of the brainstem and spinal cord were (0.230±0.794)% and (−0.340±1.254)%, respectively. The dose changes to the 50% of the parotids varied from patient to patient, from 0.536% to 11.333%, (1.641±4.274)% and (4.910±5.322)% overall. With systematic errors in MLC positions up to 1 mm, the dose changes to the 95% of the tumor volumes were (−0.078±1.048)%. The dose changes to the 0.1 cc of the brainstem and spinal cord for all patients except one were (0.591±1.058)%. The dose changes to the 50% of the parotids overall were (7.782±3.111)%, beyond 5% limit. Conclusion: The dosimetric changes introduced by the random errors for each leaf within 2mm were not significant compared to the original plans. The systematic error up to 1mm for each leaf did not significantly changed the target dose and the maximum doses to the serial structures while the doses changes to the parotid could be significant. Conflict of Interest: This project is partly funded by SIEMENS.

Evaluation of errors in the determination of gas chromatographic retention parameters and derivative quantities

A service evaluation of on-line image-guided radiotherapy to lower extremity sarcoma: Investigating the workload implications of a 3 mm action level for image assessment and correction prior to delivery

A common question in movement studies is how the results should be interpreted with respect to systematic and random errors. In this study, simulations are made in order to see how a rigid body's orientation in space (i.e. helical angle between two orientations) is affected by (1) a systematic error added to a single marker (2) a combination of this systematic error and Gaussian white noise. The orientation was estimated after adding a systematic error to one marker within the rigid body. This procedure was repeated with Gaussian noise added to each marker. In conclusion, results show that the systematic error's effect on estimated orientation depends on number of markers in the rigid body and also on which direction the systematic error is added. The systematic error has no effect if the error is added along the radial axis (i.e. the line connecting centre of mass and the affected marker).

To quantify systematic and random patient set-up errors in breast and head and neck conventional irradiation and to evaluate a no-action level (NAL) protocol for systematic set-up error off-line correction in head and neck cancer and breast cancer patients. Verification electronic portal images of orthogonal set-up fields were obtained daily for the initial four consecutive fractions for 20 patients treated for breast cancer and for 20 head and neck cancer patients. The calculated systematic error was used to shift the isocentre accordingly on the fifth treatment day. From then until the end of the treatment course, pair orthogonal portal images of set-up fields were obtained weekly. To assess the impact of the protocol, pre- and post-correction systematic errors were compared and PTV margins were estimated before and after correction using published margin recipes. Population systematic set-up error decreased in the breast cancer patient group after the implementation of NAL protocol from 4.0 to 1.7 mm on the x-axis, from 4.7 to 2.1 mm on the y-axis and from 2.8 to 0.9 mm on the z axis. The percentage of patients with individual systematic set-up error reduction was 80%, 90% and 80% on the x-, y and z-axes respectively. Population systematic set-up error decreased also in the head and neck cancer patient group from 2.3 to 1.1 mm on the x-axis, from 1.6 to 1.4 mm on the y-axis and from 1.7 to 0.7 mm on the z-axis. The percentage of patients with individual systematic set-up error reduction was 70%, 65% and 85% on the x-, y- and z-axes respectively. Margin reduction achievable with NAL protocol implementation on the x-, y- and z-axes was 6.3, 7.2 and 4.8 mm for breast cancer patients and 3.3, 0.6 and 2.8 mm for head and neck cancer patients. NAL off-line protocol is useful for systematic set-up error correction and PTV margin reduction in conventional breast and head and neck irradiation.

Thermodilution cardiac output using a pulmonary artery catheter is the reference method against which all new methods of cardiac output measurement are judged. However, thermodilution lacks precision and has a quoted precision error of ± 20%. There is uncertainty about its true precision and this causes difficulty when validating new cardiac output technology. Our aim in this investigation was to determine the current precision error of thermodilution measurements. A test rig through which water circulated at different constant rates with ports to insert catheters into a flow chamber was assembled. Flow rate was measured by an externally placed transonic flowprobe and meter. The meter was calibrated by timed filling of a cylinder. Arrow and Edwards 7Fr thermodilution catheters, connected to a Siemens SC9000 cardiac output monitor, were tested. Thermodilution readings were made by injecting 5 mL of ice-cold water. Precision error was divided into random and systematic components, which were determined separately. Between-readings (random) variability was determined for each catheter by taking sets of 10 readings at different flow rates. Coefficient of variation (CV) was calculated for each set and averaged. Between-catheter systems (systematic) variability was derived by plotting calibration lines for sets of catheters. Slopes were used to estimate the systematic component. Performances of 3 cardiac output monitors were compared: Siemens SC9000, Siemens Sirecust 1261, and Philips MP50. Five Arrow and 5 Edwards catheters were tested using the Siemens SC9000 monitor. Flow rates between 0.7 and 7.0 L/min were studied. The CV (random error) for Arrow was 5.4% and for Edwards was 4.8%. The random precision error was ± 10.0% (95% confidence limits). CV (systematic error) was 5.8% and 6.0%, respectively. The systematic precision error was ± 11.6%. The total precision error of a single thermodilution reading was ± 15.3% and ± 13.0% for triplicate readings. Precision error increased by 45% when using the Sirecust monitor and 100% when using the Philips monitor. In vitro testing of pulmonary artery catheters enabled us to measure both the random and systematic error components of thermodilution cardiac output measurement, and thus calculate the precision error. Using the Siemens monitor, we established a precision error of ± 15.3% for single and ± 13.0% for triplicate reading, which was similar to the previous estimate of ± 20%. However, this precision error was significantly worsened by using the Sirecust and Philips monitors. Clinicians should recognize that the precision error of thermodilution cardiac output is dependent on the selection of catheter and monitor model.

Purpose: To evaluate two commercially available Head‐and‐Neck immobilization devices for daily treatment setup and their correlations to anatomy changes. The study represents an early implementation experience with the Orfit mask, which was new to our clinic. Method and Materials: Twenty‐one patients enrolled in an in‐house adaptive radiotherapy protocol 3171 using daily CT guided treatment were randomly assigned to one of two different thermoplastic masks: 5‐Point Efficast mask from Orfit (ORFIT Industries, Jericho, NY) or the extended S‐Board mask from Civco (CIVCO/MedTec, Orange City, IA). The daily setup displacements in each of the antero‐posterior(AP), supero‐inferior(SI), and medio‐lateral(ML) direction were determined using a 3D rigid image registration technique with the C2 vertebral body as the bony landmark. Systematic and random setup errors were computed for each group. The Pearson product‐moment correlation coefficient was used to determine the correlation between parotid shrinkage and the magnitudes of 3D displacements. Results: The random errors in AP, SI, and ML directions for Orfit mask (10 patients) were 0.13, 0.12, 0.11cm, and 0.12, 0.16, 0.11cm for the Civco mask (11 patients), respectively. The systematic errors were 0.20, 0.12, 0.16 cm for the Orfit mask, and 0.16, 0.16, 0.13 cm for the Civco mask, respectively. The Orfit mask significantly reduced the setup error in SI direction. However, in the AP and ML directions the systematic error increased with the Orfit mask, although the random errors were similar. The magnitude of the total (3D) shift was found to be correlated with the percent of parotid shrinkage for the Civco mask (p=0.026), but not for the Orfit mask. Conclusion: Although the Orfit mask reduced setup error in SI direction due to its head rest design, setup errors in AP and ML directions increased mainly due to increased systematic mask preparation errors. User training may be important.

Purpose:To empirically derive margin formulas from existing clinical radiotherapy plans accounting for respiratory motion and setup uncertainties.Methods:We simulated realistic treatment scenarios, including respiratory motion and setup errors. Individual probability density functions (PDF) from respiratory data were used to simulate respiratory motion. Random (σ) and systematic (Σ) setup errors were modeled as Gaussian distributions. One‐dimensional dose profiles were extracted from existing radiotherapy plans and convolved with respiratory PDFs and random error distributions to produce blurred dose profiles. Each blurred dose profile was then shifted 1000 times by randomly sampling the simulated systematic error distribution. Margins were determined from the distance between the simulated treatment and the original 95% isodose level. An equation was fit for each (σ, Σ) combination to derive margin formulas for 90% of the population receiving 95% dose. This methodology can be applied to different tumor sites. Here, dose profiles were extracted from partial breast 3DCRT plans in the anterior‐posterior (AP) and superior‐inferior (SI) directions. Respiratory motion data was from healthy volunteers, and a clinically relevant range of random and systematic setup errors (standard deviations 1 – 4 mm) was determined from the literature.Results:The PBI margin formulas in the AP and SI directions for 95% dose coverage for 90% of the population were very similar: M= 0.68σ + 1.54Σ and M= 0.72σ + 1.50Σ, respectively. Systematic setup errors had the largest influence on required margin size, whereas realistic respiratory amplitude had minimal impact. The derived formulas resulted in a smaller systematic component than commonly‐used theoretical margin recipes.Conclusion:We have demonstrated a method to derive empirical margin formulas from existing patient radiotherapy plans, incorporating realistic respiratory motion and appropriate ranges of random and systematic error. Site‐specific margin formulas may be better suited to patient populations than theoretically derived, ideal geometry general margin formulas.

Introduction: Breast radiation therapy in prone position has shown a superior alternative to supine Deep Inspiration Breath Hold (DIBH) technique.Dosimetric parameters, setup error and total treatment time were compared in two approaches.Methods: In this retrospective study, supine DIBH and free-breathing prone position CT simulation was done for 12 patients.Radiation plans were created for both positions to compare dosimetric parameters, namely mean doses of heart and lung, alongside percentage volume of ipsilateral lung receiving 20Gy (V20).Positional errors and differences in total treatment time were also assessed.Results: In this study, 12 patients treated with prone breast radiotherapy were included.In left sided breast cancer (Supine versus prone position): average mean lung dose: 9.38 Gy versus 1.83Gy; Mean lung V20: 16.36% versus 1.34%.In right sided breast cancer (Supine versus prone position): average mean lung dose: 9.76 Gy versus 3.44 Gy; Mean lung V20: 17.57% versus 5.10%.Systematic and random errors were comparable between the prone and supine positions.However, there was no significant differences in heart dose between both positions.The total treatment time was prolonged in prone position as compared to supine DIBH treatment.Conclusion: In our study, there was a reduction in lung doses with prone breast radiation therapy whereas there were no significant differences in heart dose between prone and supine positions.Mean lung dose and lung V20 were lower in prone position whereas overall treatment time was longer.Systematic and random positional setup errors were comparable between the two positions.

Intersection refers to the determination of a point’s position in object space by intersecting the image rays from two or more images. The standard method is application of the collinearity equations, with two equations for each image of the point. Approximate coordinates of the point, calculated by collinearity equations. EOPs are obtained by using space resection. Initial approximations are required for ground coordinate. In this experiment, we use several data types on flat, rugged, and incline terrain. The data has random and systematic error. We create a simulated data of ground coordinate points then we compute the image points using collinearity equations. Finally, we can conclude that the data with systematic error achieves the best precise than data with random error. This is occurred in all of terrain types. The RMS error in data with systematic error achieves constantly after the limitation number 100 control points. Therefore, data with systematic radial lens error can be used in intersection case. The RMSx is more than RMSy in almost all of data types.

Dosimetric comparison of 3-dimensional conformal radiation therapy and intensity modulated radiation therapy and impact of setup errors in lower limb sarcoma radiation therapy

Abstract. A high-fidelity lidar turbulence measurement technique relies on accurate estimates of radial velocity variance that are subject to both systematic and random errors determined by the autocorrelation function of radial velocity, the sampling rate, and the sampling duration. Using both statistically simulated and observed data, this paper quantifies the effect of the volumetric averaging in lidar radial velocity measurements on the autocorrelation function and the dependence of the systematic and random errors on the sampling duration. For current-generation scanning lidars and sampling durations of about 30 min and longer, during which the stationarity assumption is valid for atmospheric flows, the systematic error is negligible but the random error exceeds about 10 %.

The introduction of IMRT poses new challenges for delivering intended target dose and minimizing dose and toxicity to critical normal structures. For head and neck cancer, reproducible patient positioning throughout the whole treatment course is particularly important due to the proximity of many critical organs. Deviations from the planned irradiation geometry during a treatment session may be systematic or random. Systematic errors occur if the mean irradiation geometry in the fractionated treatment differs differs from the geometry in the treatment plan. The mean deviations are then called systematic errors. Fraction-to-fraction variations around the mean deviation are called random errors. The purpose of this study is to measure the interfraction setup variation of patient undergoing IMRT of head and neck cancer. The data is used to define adequate treatment clinical target volume to planning target volume (CTV-to-PTV) margin. During March to November 2006, the data was collected from 9 head and neck cancer patients treated with dynamic IMRT using 6 MV X-ray beam from Varian Clinac 23EX. Weekly portal images of setup fields which were anterior-posterior and lateral portal images were acquired for each patient with an amorphous silicon EPID, Varian aS500. These images were matched with the reference images from Varian Acuity simulator using the VARiS Vision software, version 7.3.10 Six anatomical landmarks were selected for comparison. The displacement of portal image from the reference image was recorded in X (Left-Right, L-R), Y (Superior-Inferior, S-I) direction for anterior field and Z (Anterior-Posterior, A-P), Y (S-I) direction for lateral field. The systematic and random error for individual and population were calculated. Then the population-based margins were obtained. The total of 168 images ( 27 simulation images and 141 portal images) and 564 match points were evaluated. The results showed that the systematic error ranged from 0 to 7.5 mm and the random error ranged from 0.3 to 4.8 mm for all direction. The population-based margin ranged from 2.4 to 4.9 mm (L-R), 3.9 to 5.0 mm (S-I) for anterior field and 3.4 to 4.7 mm (A-P), 2.6 to 3.7 mm (S-I) for the lateral field. The difference in population-based margins along S-I axis between anterior field and lateral field were observed because the clavicles chosen for anterior field at the shoulder level were less stable than anatomical landmarks chosen for lateral field i.e. skull bones, C1 and C4. These margins were comparable to the margin that prescribed at King Chulalongkorn Memorial Hospital (5-10 mm) for head and neck cancer. These results showed that the population-based margin is less than 5 mm, thus the margin provides sufficient coverage for all of the patients.

As a highly complex multi-input and multi-output system, blast furnace plays an important role in industrial development. Although much research has been done in the past few decades, there still exist many problems, such as the modeling and control problems. In view of these reasons, this paper is concerned with developing a Wiener model to predict the silicon content of blast furnace. Unlike traditional Wiener model, this paper avoids the optimization of high number of model parameters. The Wiener model here is composed of a basis filter filter expansion named Laguerre filter and a linear programming support vector regression (LP-SVR). They are used to represent the linear dynamic component and the nonlinear static element. Take the advantages that Laguerre filter can approximate linear systems with a lower model and order and LP-SVR can achieve a sparse solution, the proposed Wiener model not only improves the prediction accuracy but also reduces the computation complexity. Simulation results show that this Wiener model is suitable for the prediction of blast furnace silicon content.