Uniform Margin Research Articles

The topological structures of the spaces of copulas and subcopulas

The (sub)copulas play a central role in statistics for capturing the stochastic dependence structure of random variables. A subcopula is a map from the Cartesian product of two closed subsets of the unit closed interval containing zero and one to the unit closed interval, which is grounded, 2-increasing and has uniform margins. A copula is a subcopula whose domain is the Cartesian product of the unit closed interval and itself. The uniform metric on the set of all copulas can be extended to a metric on the set of all subcopulas. In this work, we investigate topological structures of these spaces by using tools from infinite-dimensional topology. Our main result is as follows: there exists a homeomorphism from the space of subcopulas onto the Hilbert cube which sends the space of all copulas onto an end of the Hilbert cube and sends the space of exchangeable copulas onto an end of the end of the Hilbert cube. As a consequence, we obtain that the spaces of subcopulas, copulas and exchangeable copulas are homeomorphic to the Hilbert cube and hence have the fixed point property.

Asymptotic Properties of Random Contingency Tables with Uniform Margin

Let $C\geq 2$ be a positive integer. Consider the set of $n\times n$ non-negative integer matrices whose row sums and column sums are all equal to $Cn$ and let $X=(X_{ij})_{1\leq i,j\leq n}$ be uniformly distributed on this set. This $X$ is called the random contingency table with uniform margin. In this paper, we study various asymptotic properties of $X=(X_{ij})_{1\leq i,j\leq n}$ as $n\to\infty$.

A factor of i.i.d. with uniform marginals and infinite clusters spanned by equal labels

AbstractWe give an example of an FIID vertex-labeling of${\mathbb T}_3$whose marginals are uniform on$[0,1]$, and if we delete the edges between those vertices whose labels are different, then some of the remaining clusters are infinite. We also show that no such process can be finitary.

Generative quantum learning of joint probability distribution functions

Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling joint distributions via copulas is well understood, it gets practically challenging to accurately model real data with many variables. In this work, we design quantum machine learning algorithms to model copulas. We show that any copula can be naturally mapped to a multipartite maximally entangled state. A variational ansatz we christen as a `qopula' creates arbitrary correlations between variables while maintaining the copula structure starting from a set of Bell pairs for two variables, or GHZ states for multiple variables. As an application, we train a Quantum Generative Adversarial Network (QGAN) and a Quantum Circuit Born Machine (QCBM) using this variational ansatz to generate samples from joint distributions of two variables for historical data from the stock market. We demonstrate our generative learning algorithms on trapped ion quantum computers from IonQ for up to 8 qubits and show that our results outperform those obtained through equivalent classical generative learning. Further, we present theoretical arguments for exponential advantage in our model's expressivity over classical models based on communication and computational complexity arguments.

A copula-based set-variant association test for bivariate continuous, binary or mixed phenotypes.

In genome wide association studies (GWAS), researchers are often dealing with dichotomous and non-normally distributed traits, or a mixture of discrete-continuous traits. However, most of the current region-based methods rely on multivariate linear mixed models (mvLMMs) and assume a multivariate normal distribution for the phenotypes of interest. Hence, these methods are not applicable to disease or non-normally distributed traits. Therefore, there is a need to develop unified and flexible methods to study association between a set of (possibly rare) genetic variants and non-normal multivariate phenotypes. Copulas are multivariate distribution functions with uniform margins on the [0, 1] interval and they provide suitable models to deal with non-normality of errors in multivariate association studies. We propose a novel unified and flexible copula-based multivariate association test (CBMAT) for discovering association between a genetic region and a bivariate continuous, binary or mixed phenotype. We also derive a data-driven analytic p-value procedure of the proposed region-based score-type test. Through simulation studies, we demonstrate that CBMAT has well controlled type I error rates and higher power to detect associations compared with other existing methods, for discrete and non-normally distributed traits. At last, we apply CBMAT to detect the association between two genes located on chromosome 11 and several lipid levels measured on 1477 subjects from the ASLPAC study.

Baire category results for stochastic orders

In the sense of Baire categories, we prove that the elements of a typical pair of univariate distribution functions (defined on a bounded subset of {mathbb {R}}) cannot be compared in the sense of the usual stochastic order, the increasing convex order and the mean residual lifetime order. A similar result is also proved in the class of copulas, i.e. multivariate distribution functions with standard uniform marginals, equipped with the orthant order.

Preclinical validation and treatment of volumetric modulated arc therapy based total bone marrow irradiation in Halcyon™ ring gantry linear accelerator

AimThis study aims​ to report preclinical validation, and the first clinical treatment of total bone marrow irradiation (TMI) and total bone marrow and lymph nodal irradiation (TMLI) using Volumetric modulated arc therapy in Halcyon-E ring gantry linear accelerator. Preclinical validation includes simulation, planning, patient-specific QA, and dry run.Material and methodFour patients, two female and two male, with body weights of 116 kg, 52 kg, 64 kg, and 62 kg; with two with chronic myeloid leukemia, one each with acute lymphoblastic leukemia and acute myeloid leukemia (AML) were simulated and planned for TMI/TMLI. Patients were immobilized with a full-body vacuum bag. Head first supine (HFS) and Feet first supine (FFS) CT scans were acquired from head to knee and knee to toe. Planning target volume (PTV) was created with a uniform margin of 6 mm over the total bone marrow/bone marrow + lymph nodes. HFS and FFS PTVs were optimized independently using 6MV unflatten energy for 12 Gy in 6 fractions. Plans were merged to create the resultant dose distribution using a junction bias dose matching technique. The total number of isocenters was ≤ 10 per CT set, and two to four full arcs were used for each isocenter. A junction dose gradient technique was used for dose feathering between arcs between adjacent isocenters.ResultOnly one female patient diagnosed as AML received the TMLI treatment, while the other three patients dropped out due to clinical complications and comorbidities that developed in the time between simulation and treatment. The result presented has been averaged over all four patients. For PTV, 95% dose was normalised to 95% volume, PTV_V107% receiving 3.3 ± 3.1%. Total lung mean and V12Gy were 1048.6 ± 107.1 cGy and 19.5 ± 12.1%. Maximum lens doses were 489.5 ± 35.5 cGy (left: L) and 497 ± 69.2 cGy (right: R). The mean cardiac and bilateral kidney doses were 921.75 ± 89.2 cGy, 917.9 ± 63.2 cGy (L), and 805.9 ± 9.7 cGy (R). Average Monitor Unit was 7738.25 ± 1056.6. The median number of isocenters was 17(HFS+FFS), average MU/Dose (cGy) ratio per isocenter was 2.28 ± 0.3.ConclusionHalcyon-E ring gantry linear accelerator capable of planning and delivering TMI/TMLI.​​

Approximate Bayesian conditional copulas

Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem, any multidimensional absolutely continuous distribution function can be uniquely represented as a copula, i.e. a joint cumulative distribution function on the unit hypercube with uniform marginals, which captures the dependence structure among the vector components. In real data applications, the interest of the analyses often lies on specific functionals of the dependence, which quantify aspects of it in a few numerical values. A broad literature exists on such functionals, however extensions to include covariates are still limited. This is mainly due to the lack of unbiased estimators of the conditional copula, especially when one does not have enough information to select the copula model. Several Bayesian methods to approximate the posterior distribution of functionals of the dependence varying according covariates are presented and compared; the main advantage of the investigated methods is that they use nonparametric models, avoiding the selection of the copula, which is usually a delicate aspect of copula modelling. These methods are compared in simulation studies and in two realistic applications, from civil engineering and astrophysics.

Effect of total body irradiation lung block parameters on lung doses using three-dimensional dosimetry.

PurposeTotal body irradiation (TBI) is an integral part of stem cell transplant. However, patients are at risk of treatment‐related toxicities, including radiation pneumonitis. While lung dose is one of the most crucial aspects of TBI dosimetry, currently available data are based on point doses. As volumetric dose distribution could be substantially altered by lung block parameters, we used 3D dosimetry in our treatment planning system to estimate volumetric lung dose and measure the impact of various lung block designs.Materials and methodsWe commissioned a TBI beam model in RayStation that matches the measured tissue‐phantom ratio under our clinical TBI setup. Cerrobend blocks were automatically generated in RayStation on thoracic Computed Tomography (CT) scans from three anonymized patients using the lung, clavicle, spine, and diaphragmatic contours. The margin for block edge was varied to 0, 1, or 2 cm from the superior, lateral, and inferior thoracic borders, with a uniform margin 2.5 cm lateral to the vertebral bodies. The lung dose was calculated and compared with a prescription dose of 1200 cGy in six fractions (three with blocks and three without).ResultThe point dose at midplane under the block and the average lung dose are at the range of 73%–76% and 80%–88% of prescription dose respectively regardless of the block margins. In contrast, the percent lung volume receiving 10 Gy increased by nearly two‐fold, from 31% to 60% over the margins from 0 to 2 cm.ConclusionsThe TPS‐derived 3D lung dose is substantially different from the nominal dose assumed with HVL lung blocks. Point doses under the block are insufficient to accurately gauge the relationship between dose and pneumonitis, and TBI dosimetry could be highly variable between patients and institutions as more descriptive parameters are not included in protocols. Much progress remains to be made to optimize and standardize technical aspects of TBI, and better dosimetry could provide more precise dosimetric predictors for pneumonitis risk.

Optimization of treatment isocenter location in single-isocenter LINAC-based stereotactic radiosurgery for management of multiple brain metastases.

Single-isocenter linear accelerator (LINAC)-based stereotactic radiosurgery (SRS) has become a promising treatment technique for the management of multiple brain metastases. Because of the high prescription dose and steep dose gradient, SRS plans are sensitive to geometric errors, resulting in loss of target coverage and suboptimal local tumor control. Current planning techniques rely on adding a uniform and isotropic setup margin to all gross tumor volumes (GTVs) to account for rotational uncertainties. However, this setup margin may be insufficient, since the magnitude of rotational uncertainties varies and is dependent upon the distance between a GTV and the isocenter. In this study, we designed a framework to determine the optimal isocenter of a single-isocenter SRS plan for multiple brain metastases using stochastic optimization to mitigate potential errors resulting from rotational uncertainties. Planning target volumes (PTVs), defined as GTVs plus a 1-mm margin following common SRS planning convention, were assumed to be originally treated with a prescription dose and therefore covered by the prescription isodose cloud. The dose distribution, including the prescription isodose, was considered invariant assuming small rotations throughout the study. A stochastic optimization scheme was developed to determine the location of the optimal isocenter, so that the prescription dose coverage of rotated GTVs, equivalent to the intersecting volumes between the rotated GTVs and original PTVs, was maximized for any random small rotations about the isocenter. To evaluate the coverage of GTVs, the expected undergoing random rotations was approximated as the sample average undergoing a predetermined number of rotations. The expected of each individual GTV and total GTVs was then compared between the plans using the optimal isocenter and the center-of-mass (CoM), respectively. Twenty-two patients previously treated for multiple brain metastases in a single institute were included in this retrospective study. Each patient was initially treated for more than three brain metastases (mean: 7.6; range: 3-15) with the average GTV volume of 0.89 cc (range: 0.03-11.78 cc). The optimal isocenter found for each patient was significantly different from the CoM, with the average Euclidean distance between the optimal isocenter and the CoM being 4.36±2.59cm. The dose coverage to GTVs was also significantly improved (paired t-test; p<0.001) when the optimal isocenter was used, with the average of total GTVs increasing from 87.1% (standard deviation as std: 11.7%; range: 39.9-98.2%) to 94.2% (std: 5.4%; range: 77.7-99.4%). The volume of a GTV was positively correlated with the expected regardless of the isocenter used (Spearman coefficient: ; p<0.001). The distance between a GTV and the isocenter was negatively correlated with the expected when the CoM was used ( ; p=0.004), however no significant correlation was found when the optimal isocenter was used ( ; p=0.137). The proposed framework provides an effective approach to determine the optimal isocenter of single-isocenter LINAC-based SRS plans for multiple brain metastases. The implementation of the optimal isocenter results in SRS plans with consistently higher target coverage despite potential rotational uncertainties, and therefore significantly improves SRS plan robustness against random rotational uncertainties.

Setup Accuracy of Accelerated Partial Breast Irradiation Using Surgical Clips and Anatomical Surrogates

Accuracy of patient setup for accelerated partial breast irradiation (APBI) using intensity modulated radiation therapy (IMRT) is challenging due to the low visibility of the lumpectomy cavity in planar X-ray images and CBCT. Surgical clips, chest wall, or skin surface are typically used as surrogates of the lumpectomy cavity. The correlation of these three surrogates with the lumpectomy cavity needs to be validated.Twenty-five patients (12 left-sided and 13 right-sided) who underwent IMRT-APBI at our institution were included in the study. Daily CT-on-rail images were acquired. Sixteen patients had surgical clips. A total of 125 setup CT images were retrospectively analyzed, comparing the isocenter shifts aligning to the ipsilateral chest wall-lung interface, skin surface, and surgical clips with the isocenter shifts directly aligning to the lumpectomy cavity. The alignment differences (setup errors) in lateral, longitudinal, and vertical directions and 3D vector differences were reported. Two-sided, paired t-test was used for statistical analysis. The correlation of the setup errors with the volume of the ipsilateral breast, the lateral distance of the lumpectomy cavity center to the body midline, the minimum distance from the lumpectomy cavity to the chest wall, and the minimum distance to skin was analyzed using Pearson's correlation.3D vector errors for the surgical clips, chest wall, and skin surface-based alignment were 1.8+/-1.0, 4.7+/-2.9, and 3.6+/-2.1 mm, respectively. Alignment using surgical clips outperformed alignment using the chest wall (P < 0.001) and skin surface (P < 0.001). The alignment using skin surface outperformed the alignment using chest wall (P < 0.001). The 95% confidence interval for the surgical clip-based alignment was (-2.5, 2.9) mm in lateral, (-2.1, 1.6) mm in vertical, and (-2.5, 3.2) mm in longitudinal directions. For chest wall-based alignment, the 95% confidence interval was (-8.3, 5.1) mm in lateral, (-14.4, 6.7) mm in vertical, and (-6.4, 7.7) mm in longitudinal directions. For skin surface-based alignment, the 95% confidence interval was (-7.8, 6.1) mm in lateral, (-3.9, 4.2) mm in vertical, and (-5.8, 5.6) mm in longitudinal directions. To ensure coverage for 99% of the treatment fractions, a uniform setup margin of 5, 15, and 10 mm was needed for the surgical clips, chest wall, and skin surface-based alignment, respectively. Setup error using chest wall alignment has a moderate correlation (R2 = 0.45) with the minimum distance from the lumpectomy cavity to the chest wall. Breast volume, lateral distance to the midline, and minimum distance to skin all had low correlation (R2 < 0.3) with setup errors.For accelerated partial breast irradiation, patient setup is most accurate by using surgical clips with a mean residual error of 1.8 mm due to deformation of the lumpectomy cavity. Using skin surface or chest wall as surrogates for setup requires larger planning margins than the surgical clips.

Pathology reporting of margin status in locally advanced pancreatic cancer: challenges and uncertainties.

Chemo(radio)therapy is becoming the new standard for patients with locally advanced pancreatic cancer. In case of tumor regression on imaging, surgical resection can be undertaken, albeit often with the need for extended procedures. Reevaluation of the current routine pathology procedures is required to establish the appropriate histopathological approach of the resulting specimens. This review focusses on margin status, which is universally considered a core data item of the pathology report, of relevance to both the management of the individual patient and the evaluation of the result of surgery in this particular patient group. As explained in this review, due to the cytoreductive effect of neoadjuvant therapy, the conventional definition of a tumor-free margin ("R0") based on 1 mm clearance is not adequate. Furthermore, the complexity of many of the specimens following extended or multivisceral en bloc surgical resection make margin assessment challenging. These large specimens require extensive sampling, which is not always easily implemented in daily practice. At present, there is marked divergence in pathology practice, and consequently, neither the true R0-rate nor the exact prognostic effect of the margin status have been definitively established for resected locally advanced pancreatic cancer. A concerted effort towards uniform and optimal margin assessment is unfortunately still lacking.

Does the protocol-required uniform margin around the CTV adequately account for setup inaccuracies in whole breast irradiation?

PurposeTo use cone-beam computed tomography (CBCT) imaging to determine the impacts of patient characteristics on the magnitude of geometric setup errors and obtain patient-specific planning target volume (PTV) margins from the correlated patient characteristics in whole breast irradiation (WBI).MethodsBetween January 2019 and December 2019, a total of 97 patients who underwent breast-conserving surgery, followed by intensity-modulated radiation therapy in WBI, were scanned with pre-treatment CBCT for the first three treatment fractions and weekly for the subsequent fractions. Setup errors in the left–right (LR), superior–inferior (SI) and anterior–posterior (AP) directions were recorded and analyzed with patient characteristics—including age, tumor location, body mass index (BMI), chest circumference (CC) and breast volume (BV)—to examine the predictors for setup errors and obtain specific PTV margins.ResultsA total of 679 CBCT images from 97 patients were acquired for analysis. The mean setup errors for the whole group were 2.32 ± 1.21 mm, 3.71 ± 2.21 mm and 2.75 ± 1.56 mm in the LR, SI and AP directions, respectively. Patients’ BMI, CC and BV were moderately associated with setup errors, especially in the SI directions (R = 0.40, 0.43 and 0.22, respectively). Setup errors in the SI directions for patients with BMI > 23.8 kg/m2, CC > 89 cm and BV > 657 cm3 were 4.56 ± 2.59 mm, 4.77 ± 2.42 mm and 4.30 ± 2.43 mm, respectively, which were significantly greater than those of patients with BMI ≤ 23.8 kg/m2, CC ≤ 89 cm and BV ≤ 657 cm3 (P < 0.05). Correspondingly, the calculated PTV margins in patients with BMI > 23.8 kg/m2, CC > 89 cm and BV > 657 cm3 were 4.25/7.95/4.93 mm, 4.37/7.66/5.24 mm and 4.22/7.54/5.29 mm in the LR/SI/AP directions, respectively, compared with 3.64/4.64/5.09 mm, 3.31/4.50/4.82 mm and 3.29/5.74/4.73 mm for BMI ≤ 23.8 kg/m2, CC ≤ 89 cm and BV ≤ 657 cm3, respectively.ConclusionsThe magnitude of geometric setup errors was moderately correlated with BMI, CC and BV. It was recommended to set patient-specific PTV margins according to patient characteristics in the absence of daily image-guided treatment setup.

Dose escalation guided by 18F-FDG PET/CT for esophageal cancer

ObjectiveTo assess the feasibility of dose escalation guided by 18F-deoxyglucose positron emission tomography/computer tomography (18F-FDG PET/CT) for esophageal cancer (EC). Methods and materialsTen random patients treated with definitive chemoradiotherapy and pre-therapeutic 18F-FDG PET/CT were included in this study. Retrospectively, a threshold of 50% of SUVmax was used to define the high FDG uptake region of the GTV (GTVPET). Three intensity-modulated radiation therapy (IMRT) plans were generated, delivering three dose levels to three different planning target volumes (PTVs). 50.4 ​Gy delivered to PTV50.4 was defined on computed tomography (CT) as Plan50.4, 63 ​Gy was delivered to PTV63 was defined as GTV plus a uniform margin of 0.5 ​cm as Plan63, and 70 ​Gy delivered to PTV70 was defined as GTVPET plus a 0.5 ​cm margin as Plan70. A dosimetric comparison was performed based on normal tissue complication probability (NTCP) for the lung and heart. ResultsClinically acceptable dose escalation failed for 2 of 10 patients in Plan63 due to heart dose constraints. One patient failed heart dose constraint for Plan70. Two patients failed spinal cord constraint for Plan63. Three patients failed lung dose constraints for both Plan63 and Plan70, two of which were even not suitable for Plan50.4 for the same reason.NTCP modeling for lung showed increased risk for Plan63 and Plan70 compared to Plan50.4. The difference between Plan63 and Plan70 was insignificant. NTCP modeling for heart showed an increased risk from 6.38% of Plan50.4 to 8.88% of Plan70 (P ​= ​0.009) or 9.79% of Plan63 (P ​= ​0.007). The risk of heart mortality was significantly higher for Plan63 than Plan70 (P ​= ​0.047). ConclusionsSelective boosting of sub-volumes based on 18F-FDG PET/CT is feasible way with a modest increase in the risk of cardiac and lung toxicities.

Right-truncated Archimedean and related copulas

The copulas of random vectors with standard uniform univariate margins truncated from the right are considered and a general formula for such right-truncated conditional copulas is derived. This formula is analytical for copulas that can be inverted analytically as functions of each single argument. This is the case for Archimedean and related copulas. The resulting right-truncated Archimedean copulas are not only analytically tractable but can also be characterized as tilted Archimedean copulas, one of the main contributions of this work. This characterization now allows one to not only immediately obtain a limiting Clayton copula for a general vector of truncation points converging to zero (an extension of a result known in the special case of equal truncation points), but to work with an exact model instead of an approximate limiting model in the first place. As tilted Archimedean copulas have been studied in the literature, the characterization allows one to obtain various analytical and stochastic properties of right-truncated Archimedean copulas. Further contributions include the characterization of right-truncated Archimax copulas with logistic stable tail dependence functions as tilted outer power Archimedean copulas, and an analytical form of right-truncated nested Archimedean copulas.

Application of seismic stratigraphy in reservoir characterisation: a case study of the passive margin deposits of the northern Orange Basin, South Africa

The Barremian-Cenozoic depositional sequences in the northern Orange Basin, SW, South Africa, were investigated using the principles of seismic stratigraphy to understand the interplay of tectonics and sedimentary processes in the distribution of potential hydrocarbon reservoirs. A seismic stratigraphic workflow (seismic sequence, seismic facies and lithofacies analysis) was completed by utilising three seismic lines (L1, L2 and L3) tied to Wireline data (gamma, checkshots and sonic) in two exploration wells (A1 and A2). Seven depositional sequences were mapped followed by the creation of lithofacies log interpreted from the gamma-ray log (GR) by setting maximum GR value at 60 API for Sandstone, 60–100 API for Siltstone and above 100 API for Shale. Six seismic facies units are recognised based on internal geometry and configurations of the seismic reflectors; Tangential-Oblique (SF1), Hummocky (SF2), Wavy-Parallel (SF3), Chaotic (SF4), Sub-parallel/parallel (SF5) and Divergent (SF6). SF4 is dominant within the Barremian-Aptian sequence and expressed in an incised valley fill, suggesting mass transport deposition accompanied by strong hydrodynamic conditions. Evidence of sedimentary basins progradation is seen within the Late-Albian-Turonian sequences, because of the occurrences of SF2, SF6 and SF 4 facies. SF5 facies is prominent in the Maastrichtian/Campanian sequence, indicating that the deposition of sediments may have been accompanied by uniform margin subsidence after the Late-Cretaceous uplift of the Africa margin. The occurrence of SF1 and SF4 facies within the Cenozoic sequence indicates terrigenous pro-deltaic deposits and mass transport deposits, respectively. Further results from seismic-lithofacies modelling reveal that sand deposits of Barremian-Aptian (SF4 facies unit) and Albian sequences (SF2 and SF6 facies units) are potential stratigraphic reservoirs in this part of the basin.

Improved Independent and Uniform Multivariable Gain and Phase Margins in $\mathcal {H}_{\infty }$/LTR Control

In this article, we presented guaranteed independent and uniform multivariable stability margins for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> /LTR control, both in continuous and discrete time. In previous works, it was shown that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> /LTR control generalizes the linear quadratic Gaussian (LQG)/LTR setup, allowing the designer to better impose bounds on the complementary sensitivity frequency peak in the loop-shaping procedure. In this article, we extend this result by showing that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> /LTR control is able to recover better robustness properties than those recovered in the LQG/LTR case. Numerical examples are presented for multivariable and monovariable cases.

Data-Driven Margin Determination for Online Adaptive Radiotherapy Using Batch Automated Planning

To fully realize the potential benefits of adaptive radiotherapy (ART), target margins must be reduced. The purpose of this study was to develop a data-driven methodology to determine minimum clinical target volume (CTV) to planning target volume (PTV) margin expansions in daily online ART scenarios. To empirically determine the minimum allowable CTV-to-PTV margins for various adaptive scenarios, we seek to measure the frequency at which the minimum dose (Dmin) to the daily CTV falls below 100% prescription dose in both the non-adaptive and varied margin adaptive scenarios. By measuring across many treatment observations in a disease site, an adaptive strategy that holds fixed this frequency ensures equivalent outcomes to existing non-adaptive scenarios. The intended adaptive system can create auto-segmented targets (CTVauto) and organs-at-risk (OARs) for previously captured on-treatment images. Each daily CTVauto is edited to establish ground truth (CTVtrue) for dosimetric evaluation. Without manual intervention, batch automated planning can generate adapted plans with varied spatial margins for both CTVauto-to-PTVauto (fully automated adaptive scenario) and CTVtrue-to-PTVtrue (daily edited CTV scenario).To demonstrate this framework in prostate radiotherapy, we examined volumetric modulated arc therapy delivered on a linear accelerator with kilovoltage cone-beam CT and adaptive contours from the Ethos platform. Batch automated treatment planning was conducted with a clinically-validated knowledge-based planning routine. Every fraction from a single prostate case was analyzed for the two adaptive scenarios and uniform margins ranging from 2-5mm. The volumes of bladder and rectum receiving prescription dose (V100%) relative to the non-adaptive scenario were measured to quantify the normal tissue benefit of each margin reduction. In a 27-fraction test case with institutional margins (3mm post, 5mm ant/right/left, 7mm sup/inf), CTVtrue Dmin <100% was observed in 22% of fractions. ART with unedited auto-segmentation allowed a 4mm uniform PTV margin with only 11% of fractions where CTVtrue Dmin<100%, with a 45±3% and 16±5% reduction in bladder and rectum V100%, respectively. If ART includes CTVauto correction, a 3mm uniform PTV margin resulted in 0% of fractions where CTVtrue Dmin<100% with a 63±2% and 45±4% reduction in bladder and rectum V100%, respectively. This framework allows for an intuitive methodology to empirically determine margins for daily ART, tuned to auto-segmentation and auto-planning performance in intended disease sites.Tabled 1Abstract 2836; TableNo adaptation (% CTVtrue Dmin<100%)Adapted to CTVauto+margin (% CTVtrue Dmin<100%)Adapted to CTVtrue+margin (% CTVtrue Dmin<100%)V100% bladderV100% rectum3mm P, 5mm A/R/L, 7mm S/I22%----5mm symmetric-4%0%-22% ± 2%+14% ± 5%4mm symmetric-11%0%-45% ± 3%-16% ± 5%3mm symmetric-30%0%-63% ± 2%-45% ± 4%2mm symmetric-67%41%-80% ± 8%-70% ± 4% Open table in a new tab

Thoracic Reirradiation with Stereotactic Body Radiation Therapy (SBRT) for Recurrent Advanced Non-Small Cell Lung Cancer (NSCLC)

Locoregional failure is common among patients with advanced non-small cell lung cancer (NSCLC) treated with definitive chemoradiation +/- immunotherapy, and palliative systemic therapy is the most common treatment for locoregional failure. SBRT with ≤5 fractions have been described for small volume local recurrences, but may not be amenable to recurrences that are large or centrally located near critical structures. The purpose of this study is to evaluate the safety and efficacy of hypofractionated RT with 60 Gy in 8 using SBRT treatment techniques as salvage therapy for local failure for patients with advanced NSCLC previously treated with external beam radiation therapy (EBRT). Between July 2013 and February 2020, 5 patients were re-irradiated with SBRT of 60 Gy in 8 fractions for recurrence in the lung parenchyma after previous EBRT delivered to the same site. Patients with lymph node recurrence were excluded from analysis. Internal target volume (ITV) was created on 4D-CT with +0.5cm uniform margin to create the planning target volume (PTV). LINAC-based SBRT was delivered on non-consecutive days. Toxicity was assessed by CTCAE v5.0. Median follow-up from re-irradiation was 36 months (5.9 – 55.3 months). Median age was 67 years (range, 63 – 80 years), with KPS > 70. Patients were previously treated with a median dose of 60 Gy in median number of 30 fractions (59.4 – 66 Gy in 30 – 33 fractions). Median time to re-irradiation was 15 months (7.3 – 28.6 months). Median re-treated tumor size was 4.8 cm, with median re-treated ITV of 58.3 cc (18.3 – 344.6 cc) and median re-treated PTV of 121.3 cc (44.3 – 506.9 cc). Local control was 100%, and 60% patients remained free of any progression of disease at time of analysis. All patients remain alive at follow-up. One patient experienced grade 3 rib fracture as late toxicity for a chest wall invasive recurrence. Our institutional experience shows that SBRT-like 60 Gy in 8 fractions appears to be a safe and effective means of salvaging recurrent advanced NSCLC that was previously irradiated.Abstract 2415; TablePatient NumberInitial StageTime to re-irradiation (months)ITV of re-irradiation (cc)PTV of re-irradiation (cc)Follow-up after re-irradiation (months)Disease StatusAdditional treatment rendered1IIB, T3 N0 M07.3133.822918.1Locally controlled but metastatic disease in spinePembrolizumab and SBRT to oligometastatic adrenal gland2IIIA, T4 N0 M011.657.9113.655.3No evidence of diseaseNone3Recurrence at suture line after wedge resection for IA128.658.3121.350.3Locally controlled but metastatic disease in bilateral lungs, adrenal, and ribCarboplatin, Pemetrexed, and Pembrolizumab followed by SBRT to 3 oligoprogressive lung metastases and maintenance Pemetrexed/Pembrolizumab4IIIA, T2a N2 M018.3344.6506.936.0No evidence of diseaseNone5IIIB, T3 N2 M015.018.344.35.9No evidence of diseaseNone Open table in a new tab

Tunnel Ventilation Analysis Using a Probabilistic Approach: Case Study, Fire in Road Tunnels with Longitudinal Ventilation

Tunnels are nowadays key elements in transport networks worldwide. To achieve a safe and efficient operation, a proper integration and design of Mechanical, Electrical and Intelligent Transportation Systems is required. Among these systems, tunnel ventilation is one of the most critical ones from the Fire Life Safety perspective, being smoke control to maintain safe conditions during self-evacuation and rescue operations one of its main objectives. Traditionally tunnel ventilation systems are sized following a deterministic approach. Designers, based on requirements and design criteria from Standards and Recommendations, focus on a limited number of fire scenarios and design parameters to reach a solution considered acceptable from a fire safety perspective. This paper proposes the use of a probabilistic approach to assess, in terms of probability of failure, the capacity of a tunnel ventilation system for fire scenarios. The model applied in the proposed process uses a 1D steady state model based on pressure losses, where critical design variables are considered random (unlike with the deterministic approach) to calculate a failure probability associated to an installed ventilation thrust. A case study example is used to analyse results using both, the traditional deterministic approach and the proposed probabilistic one. Results obtained with the deterministic approach show how, under the same design requirements, tunnels with similar characteristics allow different safety margins for the capacity of the ventilation system. These results are confirmed numerically using the probabilistic approach by evaluating failure probabilities. To avoid this, the paper proposes the use of the probabilistic approach to allow a definition of an equivalent uniform safety margin (to achieve a certain probability of failure) which would be of significant help for designers, administrations and tunnel operators. It is not the aim of the study to define the limit for the probability of failure or to characterise the design variables, but to present a useful tool with which important conclusions about the design criteria can be obtained.