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Fabrication imperfections strongly influence the functioning of Micro-Electro-Mechanical Systems (MEMS) if not taken into account during the design process. They must be indeed identified or precisely predicted to guarantee a proper compensation during the calibration phase or directly in operation. In this work, we propose an efficient approach for the identification of geometric uncertainties of MEMS, exploiting the asymptotic homogenization technique. In particular, the proposed strategy is experimentally validated on a MEMS filter, a device constituted by a complex periodic geometry, which would require high computational costs if simulated through full-order models. The complex periodic structure is replaced by an equivalent homogeneous medium, allowing a fast optimization procedure to identify imperfections by comparing a simplified analytical model with the experimental data available for the MEMS filter. The actual over-etch, obtained after the release phase, and the electrode offset of a fabricated MEMS filter are effectively identified through the proposed strategy. [ABSTRACT FROM AUTHOR]

• For respiratory-gated radiotherapy near end-exhalation and irradiation fields involving the liver dome, components of geometric uncertainties originate from temporospatial diaphragm segment movements. • The displacements in a caudal direction of the diaphragm in dorsal/medial segments are significantly larger than those in ventral/right segments. • Personalized irradiating strategies, including inhalation phases of irradiation and beam angles of incidence, are required to reduce the temporospatial geometric uncertainties. The technique of gating near end-exhalation is commonly adopted to reduce respiration-associated geometric uncertainties for particle beam therapy. However, for irradiation fields involving the liver dome, how diaphragm movements generating liver–lung interface change, alongside geometric uncertainties, remain unspecified. Patients receiving respiratory-gated computed tomography (RGCT) with four-dimensional computed tomography (4DCT) scans during simulation were retrospectively reviewed. Differences (Δ) between RGCT and 4DCT images, including diaphragm displacements and liver–lung interface changes, were investigated to specify geometric uncertainties during early inhalation phases. Craniocaudal displacements (Δy, in sagittal/coronal planes) of diaphragm segments (dorsal/ventral/right lateral/medial), liver area changes (ΔA, in axial planes), and liver extent changes in specific directions of incidence (Δr, in axial planes) were analyzed. Altogether, 162 patients received simulating RGCT and 4DCT scans. In 22 of them, both images involved the liver dome. For most cases during early inhalation phases, the Δy values in the dorsal diaphragm were significantly greater than those in the ventral diaphragm (p < 0.05), the ΔA values were significantly enlarged with inhalation progressing (p < 0.05), and the Δr values in the dorsal direction were significantly larger than those in the ventral direction (p < 0.05). These results suggested that the dorsal diaphragm moves earlier and more in a caudal direction than the ventral diaphragm during early inhalation phases. For respiratory-gated radiotherapy near end-exhalation and irradiation fields involving the liver dome, components of geometric uncertainties are temporospatial, including diaphragm segment movements, inhalation phases of irradiation, and beam angles of incidence. [ABSTRACT FROM AUTHOR]

This study evaluated unexpected dosimetric errors caused by machine control accuracy, patient setup errors, and patient weight changes/internal organ deformations. Trajectory log files for 13 gynecologic plans with seven‐ or nine‐beam dynamic multileaf collimator (MLC) intensity‐modulated radiation therapy (IMRT), and differences between expected and actual MLC positions and MUs were evaluated. Effects of patient setup errors on dosimetry were estimated by in‐house software. To simulate residual patient setup errors after image‐guided patient repositioning, planned dose distributions were recalculated (blurred dose) after the positions were randomly moved in three dimensions 0–2 mm (translation) and 0°–2° (rotation) 28 times per patient. Differences between planned and blurred doses in the clinical target volume (CTV) D98% and D2% were evaluated. Daily delivered doses were calculated from cone‐beam computed tomography by the Hounsfield unit‐to‐density conversion method. Fractional and accumulated dose differences between original plans and actual delivery were evaluated by CTV D98% and D2%. The significance of accumulated doses was tested by the paired t test. Trajectory log file analysis showed that MLC positional errors were −0.01 ± 0.02 mm and MU delivery errors were 0.10 ± 0.10 MU. Differences in CTV D98% and D2% were <0.5% for simulated patient setup errors. Differences in CTV D98% and D2% were 2.4% or less between the fractional planned and delivered doses, but were 1.7% or less for the accumulated dose. Dosimetric errors were primarily caused by patient weight changes and internal organ deformation in gynecologic radiation therapy. [ABSTRACT FROM AUTHOR]

Background: The internal target volume (ITV) approach and the mid-ventilation (MidV) concept are the two main respiratory motion-management strategies under free breathing. The purpose of this work was to compare the actual in-treatment target coverage during volumetric modulated arctherapy (VMAT) delivered through both ITV-based and MidV-based planning target volume (PTV) and to provide knowledge in choosing the optimal PTV for stereotactic body radiotherapy (SBRT) for lung lesions.Methods and Materials: Thirty-two lung cancer patients treated by a VMAT technique were included in the study. For each fraction, the mean time-weighted position of the target was localized by using a 4-dimensional cone-beam CT (4D-CBCT)-based image guidance procedure. The respiratory-correlated location of the gross tumor volume (GTV) during treatment delivery was determined for each fraction by using in-treatment 4D-CBCT images acquired concurrently with VMAT delivery (4D-CBCTin-treat). The GTV was delineated from each of the ten respiratory phase-sorted 4D-CBCTin-treat datasets for each fraction. We defined target coverage as the average percentage of the GTV included within the PTV during the patient's breathing cycle averaged over the treatment course. Target coverage and PTVs were reported for a MidV-based PTV (PTVMidV) using dose-probabilistic margins and three ITV-based PTVs using isotropic margins of 5 mm (PTVITV + 5mm), 4 mm (PTVITV + 4mm) and 3 mm (PTVITV + 3mm). The in-treatment baseline displacements and target motion amplitudes were reported to evaluate the impact of both parameters on target coverage.Results: Overall, 100 4D-CBCTin-treat images were analyzed. The mean target coverage was 98.6, 99.6, 98.9 and 97.2% for PTVMidV, PTVITV + 5mm, PTVITV + 4mm and PTVITV + 3mm, respectively. All the PTV margins led to a target coverage per treatment higher than 95% in at least 90% of the evaluated cases. Compared to PTVITV + 5mm, PTVMidV, PTVITV + 4mm and PTVITV + 3mm had mean PTV reductions of 16, 19 and 33%, respectively.Conclusion: When implementing VMAT with 4D-CBCT-based image guidance, an ITV-based approach with a tighter margin than the commonly used 5 mm margin remains an alternative to the MidV-based approach for reducing healthy tissue exposure in lung SBRT. Compared to PTVMidV, PTVITV + 3mm significantly reduced the PTV while still maintaining an adequate in-treatment target coverage. [ABSTRACT FROM AUTHOR]

Axial compressors are susceptible to uncertainties during their manufacturing and operation, resulting in reduced efficiency and performance dispersion. However, uncertainty quantification and robust design of compressors remains challenging due to the complexity of structure and internal flow. In this study, an automated framework for uncertainty quantification and robustness optimization of micro axial compressors is proposed. Ten geometrical uncertainties are propagated for the nominal design point and two off-design points, i.e., near stall and choke conditions, respectively. The main objective of this paper is to optimize the aerodynamic robustness performance at these operating points. The sparse grid-based probabilistic collocation method is used to propagate these uncertainties, and a multi-objective genetic algorithm is employed to perform robust optimization based on a novel constructed surrogate model. The results show that the optimal configuration achieves an improvement in aerodynamic robustness and mean performance across the entire characteristic map, with greater improvement at the design working point than at the off-design points. At the design working point, the mean isentropic efficiency and pressure ratio of the optimal configuration increase by 0.6% and 0.5%, respectively, while the standard deviation of isentropic efficiency, pressure ratio, and mass flow rate decreases by 32.4%, 41.2%, and 25.1%, respectively. This optimization framework proves to be both feasible and efficient and can be applied to aerodynamic robust optimization of turbomachinery. In the future, we will apply this framework to different aspects of the gas turbine life cycle to model and analyze uncertainties of larger orders of magnitude. • A framework for uncertainty qualification and robust optimization of a micro compressor is established. • The SOM model visualizes the correlations between uncertain variables and performance responses. • The constructed SOM-RBF-NSGA-III successfully achieves multi-objective robust optimization. • Optimizing the performance parameters of a micro compressor at three working conditions. [ABSTRACT FROM AUTHOR]

The uncertainties present in a variety of electromagnetic (EM) problems may have important effects on the output parameters of interest. Unfortunately, deterministic schemes are not applicable in such cases, as they only utilize the nominal value of each random variable. In this work, a two-dimensional (2D) finite-difference time-domain (FDTD) algorithm is presented, which is suitable for assessing randomness in the electrical properties, as well as in the dimensions of orthogonal objects. The proposed technique is based on the stochastic FDTD method and manages to extract the mean and the standard deviation of the involved field quantities in one realization. This approach is applied to three test cases, where uncertainty exists in the electrical and geometrical parameters of various materials. The numerical results demonstrate the validity of our scheme, as similar outcomes are extracted compared to the Monte Carlo (MC) algorithm.

Wind flow in urban areas is strongly affected by the urban geometry. In the last decades most of the geometries used to reproduce urban areas, both in wind-tunnel (WT) tests and Computational Fluid Dynamics (CFD) simulations, were simplified compared to reality in order to limit experimental effort and computational costs. However, it is unclear to which extent these geometrical simplifications can affect the reliability of the numerical and experimental results. The goal of this paper is to quantify the deviations caused by geometrical simplifications. The case under study is the district of Livorno city (Italy), called “Quartiere La Venezia”. The 3D steady Reynolds-averaged Navier-Stokes (RANS) simulations are solved, first for a single block of the district, then for the whole district. The CFD simulations are validated with WT tests at scale 1:300. Comparisons are made of mean wind velocity profiles between WT tests and CFD simulations, and the agreement is quantified using four validation metrics ( FB , NMSE , R and FAC1.3 ). The results show that the most detailed geometry provides improved performance, especially for wind direction α = 240° (22% difference in terms of FAC1.3 ). [ABSTRACT FROM AUTHOR]

In this paper, we highlight the influence of geometrical uncertainties (winding pattern and wire diameter) on the $RLC$ parameters of wound magnetic components. To that end, the finite-element method is embedded in a Monte Carlo simulation in order to compute probability distributions of the parameters. An algorithm to randomly generate realistic winding configurations is also proposed. [ABSTRACT FROM AUTHOR]

When geometric uncertainties arising from manufacturing errors are comparable with the characteristic length or the product responses are sensitive to such uncertainties, the products of deterministic design cannot perform robustly. This paper presents a new level set-based framework for robust shape and topology optimization against geometric uncertainties. We first propose a stochastic level set perturbation model of uncertain topology/shape to characterize manufacturing errors in conjunction with Karhunen-Loève (K-L) expansion. We then utilize polynomial chaos expansion to implement the stochastic response analysis. In this context, the mathematical formulation of the considered robust shape and topology optimization problem is developed, and the adjoint-variable shape sensitivity scheme is derived. An advantage of this method is that relatively large shape variations and even topological changes can be accounted for with desired accuracy and efficiency. Numerical examples are given to demonstrate the validity of the present formulation and numerical techniques. In particular, this method is justified by the observations in minimum compliance problems, where slender bars vanish when the manufacturing errors become comparable with the characteristic length of the structures. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Probabilistic topology optimization has gained significant research attention recently. This interest stems from the realization that the achieved high-performance designs resulted from deterministic topology optimization algorithms may become suboptimal under real-world conditions that are often accompanied with uncertainties. Among sources of these uncertainties, the ones that define structural characteristics, such as geometry, are numerically challenging to treat as they lead to stochastic structural stiffness. To date, research on developing efficient probabilistic topology optimization under stochastic stiffness is mainly focused on displacement-based objectives. However, in the design of structures, stress is also a primary design criterion that needs to be directly controlled for. A robust stress-based topology optimization methodology for frame structures under geometric uncertainty is proposed in this work. Assuming that such uncertainties are small relative to frame member lengths, the proposed methodology uses stochastic perturbation method to propagate these uncertainties up to the response level, which is expressed by the maximum of expected values of von Mises stresses throughout the domain. Sensitivities of the response with respect to design variables are derived analytically, which allows using efficient gradient-based optimizers. The proposed algorithm is examined with stress-based design of three frame structures under geometric uncertainty. Changes in the topology of these new designs are discussed, and they are shown to outperform deterministic designs when subjected to geometric uncertainties. Moreover, predictions and the resulting designs from the proposed methodology are found to be in excellent agreement with Monte Carlo simulation results. [ABSTRACT FROM AUTHOR]

The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanics to geometric uncertainties was investigated by comparing polynomial-based and image-based knee models and varying the size of meniscus. The results suggested that the geometric uncertainties in cartilage and meniscus resulting from the resolution of MRI and the accuracy of segmentation caused considerable effects on the predicted knee mechanics. Moreover, even if the mathematical geometric descriptors can be very close to the imaged-based articular surfaces, the detailed contact pressure distribution produced by the mathematical geometric descriptors was not the same as that of the image-based model. However, the trends predicted by the models based on mathematical geometric descriptors were similar to those of the imaged-based models.

The impact of microscopic disease extension (MDE), extra-CTV tumour islets (TIs), incidental dose and dose conformity on tumour control probability (TCP) is analyzed using insilico simulations in this study. MDE in the region in between GTV and CTV is simulated inclusive of geometric uncertainties (GE) using spherical targets and spherical dose distribution. To study the effect of incidental dose on TIs and the effect of dose-response curve (DRC) on tumour control, islets were randomly distributed and TCP was calculated for various dose levels by rescaling the dose. Further, the impact of dose conformity on required PTV margins is also studied. The required PTV margins are ~2 mm lesser than assuming a uniform clonogen density if an exponential clonogen density fall off in the GTV-CTV is assumed. However, margins are almost equal if GE is higher in both cases. This shows that GE has a profound impact on margins. The effect of TIs showed a bi-phasic relation with increasing dose, indicating that patients with islets not in the beam paths do not benefit from dose escalation. Increasing dose conformity is also found to have considerable effect on TCP loss especially for larger GE. Further, smaller margins in IGRT should be used with caution where uncertainty in CTV definition is of concern. [ABSTRACT FROM AUTHOR]

Abstract: Purpose: To compare the mid-position (MidP) strategy to the conventional internal target volume (ITV) for lung tumor management in helical TomoTherapy, using 4D Monte Carlo (MC) plan simulations. Materials and methods: For NSCLC patients treated by SBRT (n =8) or SIB-IMRT (n =7), target volumes and OARs were delineated on a contrast-enhanced CT, while 4D-CT was used to generate either ITV or MidP volumes with deformable registrations. PTV margins were added. Conformity indexes, volumetric and dosimetric parameters were compared for both strategies. Dose distributions were also computed using a 4D MC model (TomoPen) to assess how intra-fraction tumor motion affects tumor coverage, with and without interplay effect. Results: PTVs derived from MidP were on average 1.2 times smaller than those from ITV, leading to lower doses to OARs. Planned dose conformity to TVs was similar for both strategies. 4D MC computation showed that ITV ensured adequate TV coverage (D 95 within 1% of clinical requirements), while MidP failed in 3 patients of the SBRT group (D 95 to the TV lowered by 4.35%, 2.16% and 2.61%) due to interplay effect in one case and to breathing motion alone in the others. Conclusions: Compared to the ITV, the MidP significantly reduced PTV and doses to OARs. MidP is safe for helical delivery except for very small tumors (<5cc) with large-amplitude motion (>10mm) where the ITV might remain the most adequate approach. [Copyright &y& Elsevier]

Abstract: Purpose: Large tumor motion leads to large treatment volumes with an Internal Target Volume (ITV) based approach, whereas mid-ventilation (MidV) based Planning Target Volumes (PTV) margins typically lead to smaller treatment volumes. The purpose of this study was to evaluate the MidV approach on clinical outcome data of Stereotactic Body Radiotherapy (SBRT) in NSCLC. Methods and materials: 297 patients with 314 peripheral tumors treated from 2006 to 2012 were retrospectively analyzed. In all patients a 4D-CT was acquired and the MidV-CT-scan was selected. Tumor amplitudes were determined in left–right (LR), cranio–caudal (CC) and anterior–posterior (AP) direction, to calculate patient specific PTV margins. Results: The median LR, CC and AP tumor amplitudes were 2mm (0–16mm), 4mm (0–39mm) and 3mm (0–18mm), respectively, yielding a median CTV-to-PTV margin of 8mm. An ITV+5mm based PTV margin would have been bigger in 47% of the patients. After a median follow up of 22months, local recurrence occurred in six patients (2%). Two year LC and OS were 98% and 67%, respectively. Conclusions: Using the MidV approach combined with online image guidance an excellent LC of 98% was established with SBRT. This provides clinical support that incorporating respiratory motion into the PTV margin is a safe approach. [Copyright &y& Elsevier]

The aim of this paper is to introduce the stochastic collocation methods in topology optimization for mechanical systems with material and geometric uncertainties. The random variations are modeled by a memory-less transformation of spatially varying Gaussian random fields which ensures their physical admissibility. The stochastic collocation method combined with the proposed material and geometry uncertainty models provides robust designs by utilizing already developed deterministic solvers. The computational cost is discussed in details and solutions to decrease it, like sparse grids and discretization refinement are proposed and demonstrated as well. The method is utilized in the design of compliant mechanisms. [ABSTRACT FROM AUTHOR]

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Purpose: When one is performing online setup correction for prostate positioning displacements prior to daily dose delivery, intrafraction motion can become a limiting factor to prostate targeting accuracy. The aim of this study was to quantify and characterize prostate intrafraction motion assessed by multiple kilovoltage (kV) and megavoltage (MV) imaging of implanted markers during treatment in a large patient group. Methods and Materials: Intrafraction motion in the sagittal plane was studied by retrospective analysis of displacements of implanted gold markers on (nearly) lateral kV and MV images obtained at various time points during the treatment fractions (mean, 27 per patient) in 108 consecutive patients. The effective prostate motion in a fraction was defined as the time-weighted mean displacement. Results: Prostate displacements in the sagittal plane increased during the fraction (mean, 0.2 ± 0.2 mm/min). Forty percent of patients had a systematic (i.e., appearing in all fractions) effective displacement in the sagittal plane greater than 2 mm. Observed effective population mean-of-means (μeff) +/− systematic (Σeff) intrafraction motion (μeff ± Σeff) was 0.9 ± 1.1 mm and 0.6 ± 1.0 mm for the anterior–posterior and superior inferior directions, respectively. Corresponding random motion (σeff) was 1.2 mm and 1.1 mm. Mean effective prostate motion in the first 5 fractions was predictive for mean effective displacement in the remaining fractions (p < 0.001). Conclusion: For a large subgroup of patients, the systematic component of intrafraction prostate motion was substantial. Intrafraction motion correction prior to each beam delivery or offline corrections could likely be beneficial for the subgroup of patients with significant motion. The systematic component is well predicted by measurements in the initial fractions. [Copyright &y& Elsevier]

Background and purpose: To compare setup uncertainties at two different institutions by using identical imaging and analysis techniques for thoracic patients with different fixation equipments. Methods and materials: Patient registration results from Cone-Beam CT (CBCT) scans of 174 patients were evaluated (1068 CBCT scans). Patients were fixated using a standard or custom made fixation at Royal Marsden Hospital and Odense University Hospital, respectively. Five imaging protocols were retrospectively simulated to compare the fixation equipments. Systematic and random setup uncertainties were calculated to estimate sufficient treatment margins. Results: The setup uncertainties are of similar sizes at the two institutions and there is no observable drift in the precision of the fixation equipments during the treatment course. When a correcting imaging protocol is performed there is a significant increase of the systematic setup uncertainties in between imaging fractions. A margin reduction of ⩾0.2cm can be achieved for patients with peak-to-peak respiration amplitudes of ⩾1.2cm when changing from 4D-CT to Active Breathing Coordinator™ (ABC). Conclusions: The setup uncertainties at the two institutions are the same despite different fixation equipments. Hence margins cannot be reduced by changing fixating equipment. [ABSTRACT FROM AUTHOR]

Abstract: A topology optimization method is proposed for the design of trusses with random geometric imperfections due to fabrication errors. This method is a generalization of a previously developed perturbation approach to topology optimization under geometric uncertainties. The main novelty in the present paper is that the objective function includes the nonlinear effects of potential buckling due to misaligned structural members. Solutions are therefore dependent on the magnitude of applied loads and the direction of resulting internal member forces (whether they are compression or tension). Direct differentiation is used in the sensitivity analysis, and analytical expressions for the associated derivatives are derived in a form that is computationally efficient. A series of examples illustrate how the effects of geometric imperfections and buckling may have substantial influence on truss design. Monte Carlo simulation together with second-order elastic analysis is used to verify that solutions offer improved performance in the presence of geometric uncertainties. [Copyright &y& Elsevier]

Purpose: To determine the effect of interfractional changes in anatomy on the target and normal tissue dose distributions during course of radiotherapy in non–small-cell lung cancer patients. Methods and Materials: Weekly respiration-correlated four-dimensional computed tomography scans were acquired for 10 patients. Original beam arrangements from conventional and inverse treatment plans were transferred into each of the weekly four-dimensional computed tomography data sets, and the dose distributions were recalculated. Dosimetric changes to the target volumes and relevant normal structures relative to the baseline treatment plans were analyzed by dose–volume histograms. Results: The overall difference in the mean ± standard deviation of the doses to 95% of the planning target volume and internal target volume between the initial and weekly treatment plans was −11.9% ± 12.1% and −2.5% ± 3.9%, respectively. The mean ± standard deviation change in the internal target volume receiving 95% of the prescribed dose was −2.3% ± 4.1%. The overall differences in the mean ± standard deviation between the initial and weekly treatment plans was 3.1% ± 6.8% for the total lung volume exceeding 20 Gy, 2.2% ± 4.8% for mean total lung dose, and 34.3% ± 43.0% for the spinal cord maximal dose. Conclusion: Serial four-dimensional computed tomography scans provided useful anatomic information and dosimetric changes during radiotherapy. Although the observed dosimetric variations were small, on average, the interfractional changes in tumor volume, mobility, and patient setup was sometimes associated with dramatic dosimetric consequences. Therefore, for locally advanced lung cancer patients, efforts to include image-guided treatment and to perform repeated imaging during the treatment course are recommended. [Copyright &y& Elsevier]

Purpose: To discuss planning target volumes (PTVs) based on internal target volume (PTVITV), exhale-gated radiotherapy (PTVGating), and a new proposed midposition (PTVMidP; time-weighted mean tumor position) and compare them with the conventional free-breathing CT scan PTV (PTVConv). Methods and Materials: Respiratory motion induces systematic and random geometric uncertainties. Their contribution to the clinical target volume (CTV)-to-PTV margins differs for each PTV approach. The uncertainty margins were calculated using a dose–probability-based margin recipe (based on patient statistics). Tumor motion in four-dimensional CT scans was determined using a local rigid registration of the tumor. Geometric uncertainties for interfractional setup errors and tumor baseline variation were included. For PTVGating, the residual motion within a 30% gating (time) window was determined. The concepts were evaluated in terms of required CTV-to-PTV margin and PTV volume for 45 patients. Results: Over the patient group, the PTVITV was on average larger (+6%) and the PTVGating and PTVMidP smaller (−10%) than the PTVConv using an off-line (bony anatomy) setup correction protocol. With an on-line (soft tissue) protocol the differences in PTV compared with PTVConv were +33%, −4%, and 0, respectively. Conclusions: The internal target volume method resulted in a significantly larger PTV than conventional CT scanning. The exhale-gated and mid-position approaches were comparable in terms of PTV. However, mid-position (or mid-ventilation) is easier to use in the clinic because it only affects the planning part of treatment and not the delivery. [Copyright &y& Elsevier]

Purpose: To quantify the interfractional variability in lung tumor trajectory and mean position during the course of radiation therapy. Methods and Materials: Repeat four-dimensional (4D) cone-beam computed tomography (CBCT) scans (median, nine scans/patient) routinely acquired during the course of treatment were analyzed for 56 patients with lung cancer. Tumor motion was assessed by using local rigid registration of a region of interest in the 3D planning CT to each phase in the 4D CBCT. Displacements of the mean tumor position relative to the planned position (baseline variations) were obtained by using time-weighted averaging of the motion curve. Results: The tumor trajectory shape was found to be stable interfractionally, with mean variability not exceeding 1 mm (1 SD) in each direction for the inhale and exhale phases. Interfractional baseline variations, however, were large, with 1.6- (left-right), 3.9- (cranial-caudal), and 2.8-mm (anterior-posterior) systematic variations (1 SD) and 1.2- (left-right), 2.4- (cranial-caudal) and 2.2-mm (anterior-posterior) random variations. Eliminating baseline variations by using soft-tissue guidance decreases planning target volume margins by approximately 50% compared with bony anatomy–driven protocols for conventional fractionation schemes. Conclusions: Systematic and random baseline variations constitute a substantial portion of the geometric variability present in the treatment of patients with lung cancer and require generous safety margins when relying on accurate setup/immobilization or bony anatomy–driven correction strategies. The 4D-CBCT has the ability to accurately monitor tumor trajectory shape and baseline variations and drive image-guided correction strategies that allows safe margin reduction. [Copyright &y& Elsevier]

Purpose: To develop and evaluate a correction strategy for prostate rotation using gantry and collimator angle adjustments. Methods and Materials: Gantry and collimator angle adjustments were used to correct for prostate rotation without rotating the table. A formula to partially correct for left-right (LR) rotations was derived through geometric analysis of rotation-induced clinical target volume (CTV) beam's-eye-view shape changes. For 10 prostate patients, intensity-modulated radiotherapy (IMRT) plans with different margins were created. Simulating CTV LR rotation and correcting each beam by a collimator rotation, the corrected CTV dose was compared with the original and uncorrected dose. Effects of residual geometric uncertainties were assessed using a Monte Carlo technique. A large number of treatments representative for prostate patients were simulated. Dose probability histograms of the minimum CTV dose (D min) were derived, with and without online correction, resulting in a more realistic margin estimate. Results: Dosimetric analysis of all IMRT plans showed that, with rotational correction and a 2-mm margin, D min was constant to within 3% for LR rotations up to +/-15 degrees . The Monte Carlo dose probability histograms showed that, with correction, a margin of 4 mm ensured that 90% of patients received a D min >or=95% of the prescribed dose. Without correction a margin of 6 mm was required. Conclusions: We developed and tested a practical method for (online) correction of prostate rotation, allowing safe and straightforward implementation of margin reduction and dose escalation. [ABSTRACT FROM AUTHOR]

The purpose of this study is to evaluate a geometric image guidance strategy that simultaneously correct for various inter-fractional rigid and nonrigid geometric uncertainties in an on-line environment, using field shape corrections (called the “MU-MLC” technique). The effectiveness of this strategy was compared with two other simpler on-line image guidance strategies that are more commonly used in the clinic. To this end, five prostate cancer patients, with at least 15 treatment CT studies each, were analyzed. The prescription dose was set to the maximum dose that did not violate the rectum and bladder dose-volume constraints, and hence, was unique to each patient. Deformable image registration and dose-tracking was performed on each CT image to obtain the cumulative treatment dose distributions. From this, maximum, minimum, and mean dose, as well as generalized equivalent uniform dose (gEUD) were calculated for each image guidance strategy. As expected, some dosimetric differences in the clinical target volume (CTV) were observed between the three image guidance strategies investigated. For example, up to ±2% discrepancy in prostate minimum dose were observed among the techniques. Of them, only the “MU-MLC” technique did not reduce the prostate minimum dose for all patients (i.e., >=100%). However, the differences were clinically not significant to indicate the preference of one strategy over another, when using a uniform 5 mm margin size. For the organ-at-risks (OARs), the large rectum sparing effect (<=5.7 Gy, gEUD) and bladder overdosing effect (<=16 Gy, gEUD) were observed. This was likely due to the use of bladder contrast during CT simulation studies which was not done during the treatment CT studies. Therefore, ultimately, strategies to maintain relatively constant rectum and bladder volumes, throughout the treatment course, are required to minimize this effect. In conclusion, the results here suggest that simple translational corrections based on three-dimensional (3D) images is adequate to maintain target coverage, for margin sizes at least as large as 5 mm. In addition, due to large fluctuations in OAR volumes, innovative image guidance strategies are needed to minimize dose and maintain consistent sparing during the whole course of radiation therapy. [ABSTRACT FROM AUTHOR]

Background. Computational fluid dynamics (CFD) simulations using medical-image- based anatomical vascular geometry are now gaining clinical relevance. This study aimed at validating the CFD methodology for studying cerebral aneurysms by using particle image velocimetry (PIV) measurements, with a focus on the effects of small geometric variations in aneurysm models on the flow dynamics obtained with CFD. Method of Approach. An experimental phantom was fabricated out of silicone elastomer to best mimic a spherical aneurysm model. PIV measurements were obtained from the phantom and compared with the CFD results from an ideal spherical aneurysm model (S1). These measurements were also compared with CFD results, based on the geometry reconstructed from three-dimensional images of the experimental phantom. We further performed CFD analysis on two geometric variations, S2 and S3, of the phantom to investigate the effects of small geometric variations on the aneurysmal flow field. Results. We found poor agreement between the CFD results from the ideal spherical aneurysm model and the PIV measurements from the phantom, including inconsistent secondary flow patterns. The CFD results based on the actual phantom geometry, however matched well with the PIV measurements. CFD of models S2 and S3 produced qualitatively similar flow fields to that of the phantom but quantitatively significant changes in key hemodynamic parameters such as vorticity, positive circulation, and wall shear stress. Conclusion. CFD simulation results can closely match experimental measurements as long as both are performed on the same model geometry. Small geometric variations on the aneurysm model can significantly alter the flow-field and key hemodynamic parameters. Since medical images are subjected to geometric uncertainties, image-based patient-specific CFD results must be carefully scrutinized before providing clinical feedback. [ABSTRACT FROM AUTHOR]

Purpose: To correctly evaluate realistic treatment plans in terms of absorbed dose to the clinical target volume (CTV), equivalent uniform dose (EUD), and tumor control probability (TCP) in the presence of execution (random) and preparation (systematic) geometric errors.Materials and Methods: The dose matrix is blurred with all execution errors to estimate the total dose distribution of all fractions. To include preparation errors, the CTV is randomly displaced (and optionally rotated) many times with respect to its planned position while computing the dose, EUD, and TCP for the CTV using the blurred dose matrix. Probability distributions of these parameters are computed by combining the results with the probability of each particular preparation error. We verified the method by comparing it with an analytic solution. Next, idealized and realistic prostate plans were tested with varying margins and varying execution and preparation error levels.Results: Probability levels for the minimum dose, computed with the new method, are within 1% of the analytic solution. The impact of rotations depends strongly on the CTV shape. A margin of 10 mm between the CTV and planning target volume is adequate for three-field prostate treatments given the accuracy level in our department; i.e., the TCP in a population of patients, TCPpop, is reduced by less than 1% due to geometric errors. When reducing the margin to 6 mm, the dose must be increased from 80 to 87 Gy to maintain the same TCPpop. Only in regions with a high-dose gradient does such a margin reduction lead to a decrease in normal tissue dose for the same TCPpop. Based on a rough correspondence of 84% minimum dose with 98% EUD, a margin recipe was defined. To give 90% of patients at least 98% EUD, the planning target volume margin must be approximately 2.5 Σ + 0.7 σ − 3 mm, where Σ and σ are the combined standard deviations of the preparation and execution errors. This recipe corresponds accurately with 1% TCPpop loss for prostate plans with clinically reasonable values of Σ and σ.Conclusion: The new method computes in a few minutes the influence of geometric errors on the statistics of target dose and TCPpop in clinical treatment plans. Too small margins lead to a significant loss of TCPpop that is difficult to compensate for by dose escalation. [Copyright &y& Elsevier]

The uncertainties present in a variety of electromagnetic (EM) problems may have important effects on the output parameters of interest. Unfortunately, deterministic schemes are not applicable in such cases, as they only utilize the nominal value of each random variable. In this work, a two-dimensional (2D) finite-difference time-domain (FDTD) algorithm is presented, which is suitable for assessing randomness in the electrical properties, as well as in the dimensions of orthogonal objects. The proposed technique is based on the stochastic FDTD method and manages to extract the mean and the standard deviation of the involved field quantities in one realization. This approach is applied to three test cases, where uncertainty exists in the electrical and geometrical parameters of various materials. The numerical results demonstrate the validity of our scheme, as similar outcomes are extracted compared to the Monte Carlo (MC) algorithm. [ABSTRACT FROM AUTHOR]

Purpose: Geometric uncertainties are inevitable in radiotherapy. To account for these uncertainties, a margin is added to the clinical target volume (CTV) to create the planning target volume (PTV), and its size is critical for obtaining an optimal treatment plan. Dose-based (i.e., physical) margin recipes have been published and widely used, but it is important to consider fractionation and the radiobiological characteristics of the tumor when deriving margins. Hence a tumor control probability (TCP)-based margin is arguably more appropriate. Methods: Margins required for ≤1% loss in mean population TCP (relative to a static tumor) for varying numbers of fractions, varying slope of the dose-response curve (γ50) and varying degrees of dose distribution conformity are investigated for spherical and four-field (4F)-brick dose distributions. To simulate geometric uncertainties, systematic (Σ) and random (σ) tumor displacements were sampled from Gaussian distributions and applied to each fraction for a spherical CTV. Interfraction tumor motion was simulated and the dose accumulated from fraction to fraction on a voxel-by-voxel basis to calculate TCP. PTV margins derived from this work for various fraction numbers and dose-response slopes (γ50) for different degrees of geometric uncertainties are compared with margins calculated using published physical-dose- and TCP-based recipes. Results: Larger margins are required for a decrease in the number of fractions and for an increase in γ50 for both spherical and 4F-brick dose distributions. However, the margins can be close to zero for the 4F-brick distribution for small geometric uncertainties (Σ = 1, σ = 1 mm) irrespective of the number of fractions and the magnitude of γ50 due to the higher 'incidental' dose outside the tumor. For Σ = 1 mm and σ = 3 mm, physical-dose-based recipes underestimate the margin only for the combination of hypofractionated treatments and tumors with a high γ50. For all other situations TCP-based margins are smaller than physical-dose-based recipes. Conclusions: Margins depend on the number of fractions and γ50 in addition to Σ and σ. Dose conformity should also be considered since the required margin increases with increasing dose conformity. Ideally margins should be anisotropic and individualized, taking into account γ50, number of fractions, and the dose distribution, as well as estimates of Σ and σ. No single 'recipe' can adequately account for all these variables. [ABSTRACT FROM AUTHOR]

Purpose: To quantify the variability of diaphragm motion during free-breathing radiotherapy of lung patients and its effect on treatment margins to account for geometric uncertainties. Methods and Materials: Thirty-three lung cancer patients were analyzed. Each patient had 5–19 cone-beam scans acquired during different treatment fractions. The craniocaudal position of the diaphragm dome on the same side as the tumor was tracked over 2 min in the projection images, because it is both easily visible and a suitable surrogate to study the variability of the tumor motion and its impact on treatment margins. Intra-acquisition, inter-acquisition, and inter-patient variability of the respiratory cycles were quantified separately, as were the probability density functions (PDFs) of the diaphragm position over each cycle, each acquisition, and each patient. Asymmetric margins were simulated using each patient PDF and compared to symmetric margins computed from a margin recipe. Results: The peak-to-peak amplitude variability (1 SD) was 3.3 mm, 2.4 mm, and 6.1 mm for the intra-acquisition, inter-acquisition, and inter-patient variability, respectively. The average PDF of each cycle was similar to the sin4 function but the PDF of each acquisition was closer to a skew-normal distribution because of the motion variability. Despite large interfraction baseline variability, the PDF of each patient was generally asymmetric with a longer end-inhale tail because the end-exhale position was more stable than the end-inhale position. The asymmetry of the PDF required asymmetric margins around the time-averaged position to account for the position uncertainty but the average difference was 1.0 mm (range, 0.0–4.4 mm) for a sharp penumbra and an idealized online setup correction protocol. Conclusion: The respiratory motion is more irregular during the fractions than between the fractions. The PDF of the respiratory motion is asymmetrically distributed. Both the intra-acquisition variability and the PDF asymmetry have a limited impact on dose distributions and inferred margins. The use of a margin recipe to account for respiratory motion with an estimate of the average motion amplitude was adequate in almost all patients. [ABSTRACT FROM AUTHOR]

Background: The aim of this study was to compare setup accuracy and reproducibility of a stereotactic head and a head-and-neck fixation system, both based on thermoplastic material. Methods and Material: Ten patients were immobilized with a head and a head-and-neck fixation system (both BrainLAB, Germany). Both mask systems were modified with a custom-made mouthpiece and a strip of thermoplastic material attached to the lower part of the mask. During the first treatment session, after positioning patients using room lasers, two orthogonal portal images were taken as reference. Later on, at least five sets of orthogonal portal images were acquired for each patient. The isocentric setup accuracy was determined by comparing field edges and anatomic landmarks and the repositioning accuracy in the mask was obtained by comparing individual anatomic landmarks with respect to the metal balls, fixed on the masks. Systematic and random deviations and resulting three-dimensional (3D) vectors were calculated. Additionally, margins were derived from the systematic and random component of the isocentric setup accuracy. Finally, inter- and intraobserver variations were analyzed. Results: The systematic variation of the isocentric setup accuracy was very similar for the two mask systems, but the random variations were slightly larger for the head-and-neck system, resulting in a 0.4-mm larger 3D vector. The repositioning variations for the head mask were smaller compared with the head-and-neck mask, resulting in smaller 3D vectors for the random (∼0.4 mm) and systematic variations (∼0.6 mm). For both mask systems, a 2-mm margin can be used in lateral and anteroposterior direction, whereas in craniocaudal direction, this margin should be extended to 2.5 mm for the head mask and to 3 mm for the head-and-neck mask. The average absolute differences between two observers were within 0.5 mm, maximum deviations around 1 mm. Conclusion: Thermoplastic mask–based stereotactic head-and-neck fixation allows accurate and reproducible fixation of patients. For intensity-modulated radiation therapy in the upper head-and-neck region, the application of reduced margins around 2–3 mm, which has an implication on organ sparing, is enabled by such an immobilization device. [Copyright &y& Elsevier]