Geometric Index Research Articles

A Predictive Analysis of Wall Stress in Abdominal Aortic Aneurysms Using a Neural Network Model.

Rupture risk assessment of abdominal aortic aneurysms (AAAs) by means of quantifying wall stress is a common biomechanical strategy. However, the clinical translation of this approach has been greatly limited due to the complexity associated with the computational tools required for its implementation. Thus, being able to estimate wall stress using nonbiomechanical markers that can be quantified as a direct outcome of clinical image segmentation would be advantageous in improving the potential implementation of said strategy. In the present work, we investigated the use of geometric indices to predict patient-specific AAA wall stress by means of a novel neural network (NN) modeling approach. We conducted a retrospective review of existing clinical images of two patient groups: 98 asymptomatic and 50 symptomatic AAAs. The images were subject to a protocol consisting of image segmentation, processing, volume meshing, finite element modeling, and geometry quantification, from which 53 geometric indices and the spatially averaged wall stress (SAWS) were calculated. SAWS estimated from finite element analysis was considered the gold standard for the predictions. We developed feed-forward NN models composed of an input layer, two dense layers, and an output layer using Keras, a deep learning library in python. The NN models were trained, tested, and validated independently for both AAA groups using all geometric indices, as well as a reduced set of indices resulting from a variable reduction procedure. We compared the performance of the NN models with two standard machine learning algorithms (MARS: multivariate adaptive regression splines and GAM: generalized additive model) and a linear regression model (GLM: generalized linear model). With the reduced sets of indices, the NN-based approach exhibited the highest mean goodness-of-fit (for the symptomatic group 0.71 and for the asymptomatic group 0.79) and lowest mean relative error (17% for both groups). In contrast, MARS yielded a mean goodness-of-fit of 0.59 for the symptomatic group and 0.77 for the asymptomatic group, with relative errors of 17% for the symptomatic group and 22% for the asymptomatic group. GAM had a mean goodness-of-fit of 0.70 for the symptomatic group and 0.80 for the asymptomatic group, with relative errors of 16% for the symptomatic group and 20% for the asymptomatic group. GLM did not perform as well as the other algorithms, with a mean goodness-of-fit of 0.53 for the symptomatic group and 0.70 for the asymptomatic group, with relative errors of 19% for the symptomatic group and 23% for the asymptomatic group. Nevertheless, the NN models required a reduced set of 15 and 13 geometric indices to predict SAWS for the symptomatic and asymptomatic AAA groups, respectively. This was in contrast to the reduced set of nine and eight geometric indices required to predict SAWS with the MARS and GAM algorithms for each AAA group, respectively. The use of NN modeling represents a promising alternative methodology for the estimation of AAA wall stress using geometric indices as surrogates, in lieu of finite element modeling. The performance metrics of NN models are expected to improve with significantly larger group sizes, given the suitability of NN modeling for "big data" applications.

The geometric arithmetic (GA) index of certain trees and bicyclic graphs

The geometric arithmetic index is one of the recently most investigated degree-based molecular structure descriptors that have applications in chemistry. For a graph , the index is defined as , where denotes the degree of a vertex in . In this paper, we obtain the general formulas of geometric arithmetic index for two types of trees graphs. Also, we provide the general formulas to the bicyclic graphs after attaching branches of for all vertices. Finally, we computed the geometric arithmetic index to the molecular graph representing the molecular structure of the bicyclic chemical graphs.

Evaluation of heat stress tolerance in spring wheat (Triticum aestivum L.) genotypes using stress tolerance indices in western region of Nepal

High temperature coinciding with the anthesis period in wheat is one of the major constraints in wheat production. Appropriate selection criteria help plant breeders to make maximum use of the genetic variation to improve stress tolerant in crops. Thus, the aim of the study was to explore heat stress tolerance indices in spring wheat genotypes to select the heat stress tolerant lines. In this study twenty wheat genotypes were evaluated during wheat growing season (2019–2020) under normal and late sown (heat stress) conditions. The experiment was conducted at Institute of Agriculture and Animal Science, Bhairahawa, Nepal using alpha lattice design with two replications. The results of the study reveal that the mean grain yield of all genotypes was decreased by 47.58% under stress condition as compared to normal sowing condition, suggesting significant effect of heat on grain yield. Tolerance index (TOL) and stress susceptibility index (SSI) had strong negative correlation (−0.804 to −0.945) with grain yield (Ys) of genotypes under stress condition. Similarly, the grain yield of genotypes under both conditions was found strongly and positively correlated (0.899 to 0.965) with mean productivity (MP), geometric mean productivity (GMP) and stress tolerance index (STI). Results suggest that these indices could be used to select high yielding genotypes under both conditions. Based on principal component and biplot analysis Bhrikuti, NL1420, BL4669, NL1350 and NL1368 were found to be superior genotypes with high yielding capacity under both conditions. Thus these genotypes are potential to cultivate in heat prone areas of Nepal and can be used as genetic resources in crop improvement program. • Terminal heat stress is a major abiotic factor that limits wheat productivity. • This study aimed to find the suitable stress tolerance indices to identify heat tolerance in spring wheat genotypes. • Mean productivity (MP), Geometric mean productivity (GMP) and Stress tolerance index (STI) were found to be the most suitable stress indices. • Bhrikuti, NL1420, BL4669, NL1350 and NL1368 were found to be superior spring wheat genotypes under both normal and late sown (heat stress) conditions.

Biomechanical tests: applications and their reliability for the prediction of bone strength in broiler chicken

The poultry industry is considered potent for the economy of any country because chicken production is an important food source now-a-days. However, skeletal abnormalities are one of the major contributing factors to production loss. For decades researchers are trying to make contributions for the diagnosis of these problems effectively and are giving suggestions for the improvement in their skeletal deficiencies. Bone structural and metabolic disturbances (like tibial dyschondroplasia, osteoporosis and osteoarthrosis) are common in broiler chickens and have emerged in past few years. Due to fast growth and high leg to body weight ratio bone suffers excessive stress and loses the strength. Such conditions are manifested with a tendency for fracture. Understanding of bone quality provides deep information of the mechanical and functional aspects of bone tissues. The measurements of the bone strength can be performed with some methods, like the geometrical indices, radiographic or dual-energy X-ray absorptiometric density measurements, ash content measurements or the assays of bone turnover biomarkers. But biomechanical tests are the core diagnostic tools that can measure bone health parameters with reliable indicators. In this review, an overview of the mechanical tests used to test bone quality has been given and the effectiveness of such methods is discussed using different bones of poultry birds. Knowing the basic concepts on biomechanical tests applied in poultry bones and comparing the results to identify suitable testing methods may input improvement in the dialogue between the researchers interested in the assessment of bone strength at both structural and pathophysiological levels.

Topological analysis of para‐line graph of Remdesivir used in the prevention of corona virus

AbstractTopological indices are the molecular descriptors that characterize the formation of chemical compounds and they assist us to predict certain physical–chemical properties like molar refraction, molar volume, chromatographic behavior, boiling point, heat of vaporization and partition coefficient. The computation of the topological index of a drug design enable researchers to have a high quality conception of the physical science and bioorganic characteristics of drugs. Reverse degree based topological indices play important role for calculation of topological descriptor. Para‐line graphs are used to illustrate the molecular structure in another way and these illustrations are valuable in structural chemistry. In this article, we present some reverse degree based topological indices namely, the reverse general Randic index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse forgotten index, the reverse Balaban index and different types of Zagreb indices for the para‐line graph of Remdesivir. The results attained can help in the design of new medicine for the prevention of corona virus.

Indices for exploring information in Lorentz curve of daily precipitation and their application in natural disaster risk assessment

The concentration index (CI) based on the Lorenz curve has been widely used to analyse the temporal structure of daily precipitation. However, two different Lorenz curves may have the same CI, while indicating different distribution information of precipitation. Previous studies have proposed Lorentz asymmetry coefficient, the value of which concentrated around 0.9 without significant distinction. Additional indicators are thus in need to investigate the complete information in Lorenz curves besides CI. In this study, six geometrical indices are defined to characterize a Lorenz curve. Together with the CI, any one of the proposed indices can help determine a unique Lorenz curve. An analysis of the daily precipitation over the Qinghai–Tibet Plateau derived five groups of meteorological stations with identical CIs, but completely different Lorenz curves. The correlation analysis between the CI and proposed indices indicated that there are two parameters independent of the CI, representing the contribution of heavy rain and the position of the transaction point, respectively, thus introducing relatively new information on precipitation beyond the CI. Within the stations with high CIs, these two indices were used to further identify areas in the Qinghai–Tibet Plateau at a high risk for natural disasters, such as rainstorms, debris flows, and aridity, the derived results were consistent with the debris flow prone areas in China designated by China Meteorological Administration. The proposed indices can not only help CI to describe the Lorentz curve of daily rainfall, but can also help identify areas at a high risk for natural disasters.

Determination of geometric reliability index of piles at site-specific scale: case studies

An application of geometric reliability techniques on various pile types based on 67 load–displacement curves obtained from pertinent literature is presented in this paper. These static loading tests were performed at local scale (even building-specific sites) under essentially identical geotechnical conditions. A power-law function with two parameters was used to fit the measured load–settlement curves. For each site, the means and coefficients of variation for the power-law parameters were obtained. Since the number of tests conducted at each site is usually small, it is extremely difficult to identify a certain distribution type for these regression parameters. Thus, for simplicity, a bivariate normal distribution was assumed to represent the set of regression pairs. This joint distribution was incorporated into a geometric reliability method, which offers an estimation of the bearing capacity of piles at the serviceability limit state. Examples are provided to illustrate the application of the proposed reliability method to interpret the visually determined reliability index of the bearing capacity of piles. These case studies showed that the proposed method is a useful and comprehensive tool for capturing the load–displacement response and for evaluating the bearing capacity of piles by considering uncertainties in their load–displacement behaviour.

Hemodynamic Versus Anatomic Assessment of Symptomatic Atherosclerotic Middle Cerebral Artery Stenosis: the Relationship Between Pressure Wire Translesional Gradient and Angiographic Lesion Geometry.

Background: Intracranial cerebral atherosclerosis (ICAS) is a leading etiology of ischemic stroke. The diagnosis and assessment of intracranial stenosis are shifting from anatomic to hemodynamic for better risk stratification. However, the relationships between lesion geometry and translesional pressure gradient have not been clearly elucidated.Methods: Patients with symptomatic unifocal M1 middle cerebral artery (M1-MCA) stenosis were consecutively recruited. The translesional pressure gradient was measured with a pressure wire and was recorded as both mean distal/proximal pressure ratios (Pd/Pa) and translesional pressure difference (Pa–Pd). Lesion geometry measured on angiography was recorded as diameter stenosis, minimal lumen diameter, and lesion length. The correlations between pressure-derived and angiography-derived indices were then analyzed.Results: Forty-three patients were analyzed. A negative correlation was found between Pd/Pa and diameter stenosis (r = −0.371; p = 0.014) and between Pa – Pd and minimal lumen diameter (r = −0.507; p = 0.001). A positive correlation was found between Pd/Pa and minimal lumen diameter (r = 0.411; p = 0.006) and between Pa – Pd and diameter stenosis (r = 0.466; p = 0.002).Conclusions: In a highly selected ICAS subgroup, geometric indices derived from angiography correlate significantly with translesional pressure gradient indices. However, the correlation strength is weak-to-moderate, which implies that anatomic assessment could only partly reflect hemodynamic status. Translesional pressure gradient measured by pressure wire may serve as a more predictive marker of ICAS severity. More factors need to be identified in further studies.

Screening of Wheat Genotypes for Nitrogen Deficiency Tolerance Using Stress Screening Indices

An increased awareness of environmental protection and sustainable production raise the necessity of incorporating the selection of low nitrogen-tolerant winter wheat cultivars for high yield and quality in the breeding process. This selection can be assisted by using stress screening indices. Our study aimed to evaluate and compare a number of stress screening indices and to determine and select the most nitrogen deficiency-tolerant winter wheat cultivars for further breeding. The experiment included forty-eight winter wheat cultivars from eight different countries that were grown for two consecutive years at three different locations under low-nitrogen (LN) and high-nitrogen (HN) conditions. The results emphasized the importance of applying the appropriate stress screening indices in evaluating and selecting nitrogen deficiency-tolerant wheat cultivars. The promising stress screening indices were the mean productivity index (MP), geometric mean productivity index (GMP), harmonic mean index (HM), stress tolerance index (STI) and yield index (YI). They identified cultivars Sofru, BC Opsesija and MV-Nemere as the most tolerant cultivars to LN conditions for grain yield. The same indices classified U-1, OS-Olimpija, Forcali, Viktoria and BC Tena cultivars as the most tolerant to LN conditions for the grain protein content. Using the tolerance index (TOL), yield stability index (YSI) and relative stress index (RSI), the Katarina and Ficko cultivars were denoted as LN-tolerant cultivars in terms of the grain yield and Isengrain, Tosunbey, Vulkan and BC Darija in terms of the grain protein content.

MRI-TRUS registration methodology for TRUS-guided HDR prostate brachytherapy.

PurposeHigh‐dose‐rate (HDR) prostate brachytherapy is an established technique for whole‐gland treatment. For transrectal ultrasound (TRUS)‐guided HDR prostate brachytherapy, image fusion with a magnetic resonance image (MRI) can be performed to make use of its soft‐tissue contrast. The MIM treatment planning system has recently introduced image registration specifically for HDR prostate brachytherapy and has incorporated a Predictive Fusion workflow, which allows clinicians to attempt to compensate for differences in patient positioning between imaging modalities. In this study, we investigate the accuracy of the MIM algorithms for MRI‐TRUS fusion, including the Predictive Fusion workflow.Materials and MethodsA radiation oncologist contoured the prostate gland on both TRUS and MRI. Four registration methodologies to fuse the MRI and the TRUS images were considered: rigid registration (RR), contour‐based (CB) deformable registration, Predictive Fusion followed by RR (pfRR), and Predictive Fusion followed by CB deformable registration (pfCB). Registrations were compared using the mean distance to agreement and the Dice similarity coefficient for the prostate as contoured on TRUS and the registered MRI prostate contour.ResultsTwenty patients treated with HDR prostate brachytherapy at our center were included in this retrospective evaluation. For the cohort, mean distance to agreement was 2.1 ± 0.8 mm, 0.60 ± 0.08 mm, 2.0 ± 0.5 mm, and 0.59 ± 0.06 mm for RR, CB, pfRR, and pfCB, respectively. Dice similarity coefficients were 0.80 ± 0.05, 0.93 ± 0.02, 0.81 ± 0.03, and 0.93 ± 0.01 for RR, CB, pfRR, and pfCB, respectively. The inclusion of the Predictive Fusion workflow did not significantly improve the quality of the registration.ConclusionsThe CB deformable registration algorithm in the MIM treatment planning system yielded the best geometric registration indices. MIM offers a commercial platform allowing for easier access and integration into clinical departments with the potential to play an integral role in future focal therapy applications for prostate cancer.

Topological Study of Line Graph of Remdesivir Compound Used in the Treatment of Corona Virus

Corona virus is a transforming and refastening pandemic that likely transmitting through an affected person in droplet-generated forms that have infected beyond 250 countries and threaten the whole world. There is no clear approach for taking care of corona cases. Besides, scientists around the world are working energetically to develop medicinal or anti-virus drugs. Scientists have developed the potency of Remdesivir to prevent corona virus in vitro. Topological indices are mathematical representations of a molecule developed by an algorithm executed to a given molecular description. Topological indices are used to design different physical, medical, chemical and biological properties of chemical compounds. The idea of line graph for a graph G has found several applications in field of chemical research. In this paper, we present some reverse degree based topological indices namely, the reverse general randic index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse forgotten index, the reverse balaban index and different types of Zagreb indices for the line graph of Remdesivir. The results attained can help in the design of new medicine for the treatment of corona virus.

On Computation of Recently Defined Degree-Based Topological Indices of Some Families of Convex Polytopes via M-Polynomial

Topological indices are of incredible significance in the field of graph theory. Convex polytopes play a significant role both in various branches of mathematics and also in applied areas, most notably in linear programming. We have calculated some topological indices such as atom-bond connectivity index, geometric arithmetic index, K-Banhatti indices, and K-hyper-Banhatti indices and modified K-Banhatti indices from some families of convex polytopes through M-polynomials. The M-polynomials of the graphs provide us with a great help to calculate the topological indices of different structures.

Influence of Geometric Indexes of Escape Routes Over Evacuation of People from Buildings and Facilities

The present work presents the relationship between geometric parameters of escape routes and efficiency of evacuation of people from buildings and facilities. An integrated mathematical approach for providing conditions for successful evacuation is presented. Specific effects of measurements and shapes of escape routes and escape exits on the behavior of the crowd are studied. An assessment of consequences of incorrectly applied architectural and construction measures in the construction of escape routes and escape exits is made. Adequate geometric solutions are proposed to facilitate the rapid and reliable movement of the crowd to a safe area. A concrete example of application of the approach through a calculation procedure is presented.

Topological Indices of Some Classes of Thorn Complete and Wheel Graphs

We have multiple real numbers that describe chemical descriptors in the field of Graph theory. These descriptors constitute the entire structure of a graph, which possesses an actual chemical structure. Among these, the main focus of topological indices is that they are associated with many non-identical physiochemical properties of chemical compounds. Also, the biological properties of chemical compounds can be established by the topological indices. In this analysis, we compute the Reciprocal Randic index〖(R〗^(-1)), Reduced Reciprocal Randic index(〖RR〗^(-1)), Atom-bond Connectivity index(ABC) and the geometric arithmetic index(GA) of thorn graphs are obtained theoretically.

Topological Study of Zeolite Socony Mobil-5 via Degree-Based Topological Indices

Graph theory is a subdivision of discrete mathematics. In graph theory, a graph is made up of vertices connected through edges. Topological indices are numerical parameters or descriptors of graph. Topological index tells the symmetry of compound and helps us to compare those mathematical values, with boiling point, melting point, density, viscosity, hydrophobic surface area, polarity, etc., of that compound. In the present research paper, degree-based topological indices of Zeolite Socony Mobil-5 are calculated. Names of those topological indices are Randić index, first Zagreb index, general sum connectivity index, hyper-Zagreb index, geometric index, ABC index, etc.

Unicyclic graphs with extremal values of arithmetic–geometric index

The n-vertex unicyclic graphs with extreme values of arithmetic–geometric index or AG index are determined for all values of n. The case regarding the extremal values of the AG index in the class of bicyclic graphs has been stated as open problem.

Geometric contour variation in clinical target volume of axillary lymph nodes in breast cancer radiotherapy: an AIRO multi-institutional study.

To determine interobserver variability in axillary nodal contouring in breast cancer (BC) radiotherapy (RT) by comparing the clinical target volume of participating single centres (SC-CTV) with a gold-standard CTV (GS-CTV). The GS-CTV of three patients (P1, P2, P3) with increasing complexity was created in DICOM format from the median contour of axillary CTVs drawn by BC experts, validated using the simultaneous truth and performance-level estimation and peer-reviewed. GS-CTVs were compared with the correspondent SC-CTVs drawn by radiation oncologists, using validated metrics and a total score (TS) integrating all of them. Eighteen RT centres participated in the study. Comparative analyses revealed that, on average, the SC-CTVs were smaller than GS-CTV for P1 and P2 (by -29.25% and -27.83%, respectively) and larger for P3 (by +12.53%). The mean Jaccard index was greater for P1 and P2 compared to P3, but the overlap extent value was around 0.50 or less. Regarding nodal levels, L4 showed the highest concordance with the GS. In the intra-patient comparison, L2 and L3 achieved lower TS than L4. Nodal levels showed discrepancy with GS, which was not statistically significant for P1, and negligible for P2, while P3 had the worst agreement. DICE similarity coefficient did not exceed the minimum threshold for agreement of 0.70 in all the measurements. Substantial differences were observed between SC- and GS-CTV, especially for P3 with altered arm setup. L2 and L3 were the most critical levels. The study highlighted these key points to address. The present study compares, by means of validated geometric indexes, manual segmentations of axillary lymph nodes in breast cancer from different observers and different institutions made on radiotherapy planning CT images. Assessing such variability is of paramount importance, as geometric uncertainties might lead to incorrect dosimetry and compromise oncological outcome.

Synthesis, Spectroscopic, and Theoretical Study of Copper and Cobalt Complexes with Dacarbazine.

Dacarbazine (DAC) 5-(3,3-dimethyl-1-triazenyl)imidazole-4-carboxamide is an imidazole-carboxamide derivative that is structurally related to purines. DAC belongs to the triazene compounds, which are a group of alkylating agents with antitumor and mutagenic properties. DAC is a non-cell cycle specific drug, active in all phases of the cellular cycle. In the frame of this work the 3d metal complexes (cobalt and copper) with dacarbazine were synthesized. Their spectroscopic properties by the use of FT-IR, FT-Raman, and 1HNMR were studied. The structures of dacarbazine and its complexes with copper(II) and cobalt(II) were calculated using DFT methods. The effect of metals on the electronic charge distribution of dacarbazine was discussed on the basis of calculated NBO atomic charges. The reactivity of metal complexes in relation to ligand alone was estimated on the basis of calculated energy of HOMO and LUMO orbitals. The aromaticity of the imidazole ring in dacarbazine and the complexes were compared (on the basis of calculated geometric indices of aromaticity). Thermal stability of the investigated 3d-metal complexes with dacarbazine and the products of their thermal decomposition were analyzed.

Predictors of heart and lung dose in left-sided breast cancer treated with VMAT relative to 3D-CRT: A retrospective study.

BackgroundBefore generating radiotherapy plans for breast cancer patients, the choice of plan techniques (three-dimensional conformal radiation therapy (3D-CRT) and volumetric modulated arc therapy (VMAT)) should be made. This study investigated the performance of two geometric indices in aiding the choice of 3D-CRT and VMAT plans in women undergoing left-sided whole breast radiotherapy.Materials and methods119 patients, previously treated with left-sided breast radiotherapy (61 3D-CRT treatments and 58 VMAT treatments) from a single institution, were retrospectively studied. Two geometric indices, which were cardiac junction (CJ) index and pulmonary junction (PJ) index, were defined and the relationship between these indices and dose of organs at risk (OARs) were evaluated. Two-tailed Student’s t-test was performed to compare patient characteristics between 3D-CRT and VMAT. Linear regressions were calculated to investigate the association between geometric indices and absorbed dose of heart and left lung, including mean dose of heart (MHD), V5, V30 of heart, and mean dose of left lung (MLLD), V5, V10, V20, V30, V40 of left lung.ResultsThe CJ index was strongly correlated with the MHD in 3D-CRT group and VMAT group. The linear regression formulas were MHD = 4826.59 ×CJ Index+310.48 (R = 0.857, F = 163.77, P = 0.000) in 3D-CRT plans and MHD = 1789.29×CJ Index+437.50 (R = 0.45, F = 14.23, P = 0.000) in VMAT plans. The intersection of the two formulas was CJ index = 4.2% and MHD = 512.33 cGy. The PJ index demonstrated a strongly positive correlation with MLLD in 3D-CRT group and VMAT group as well. The linear regression formulas were MLLD = 2879.54×PJ Index+999.79 (R = 0.697, F = 55.86, P = 0.000) in 3D-CRT plans and MLLD = 1411.79×PJ Index+1091.88 (R = 0.676, F = 47.11, P = 0.000) in VMAT plans, the intersection of the two formulas was PJ index = 6.3% and MLLD = 1180.46 cGy.ConclusionsCJ index and PJ index could be used as a practical tool to select 3D-CRT or VMAT before generating plans. We recommend that VMAT plan is preferable when CJ index is greater than 4.2% and/or PJ index is greater than 14.6%, while 3D-CRT plan is the first choice in the opposite.

A novel specific grading standard study of auto-segmentation of organs at risk in thorax: subjective\u2013objective-combined grading standard

BackgroundTo develop a novel subjective–objective-combined (SOC) grading standard for auto-segmentation for each organ at risk (OAR) in the thorax.MethodsA radiation oncologist manually delineated 13 thoracic OARs from computed tomography (CT) images of 40 patients. OAR auto-segmentation accuracy was graded by five geometric objective indexes, including the Dice similarity coefficient (DSC), the difference of the Euclidean distance between centers of mass (ΔCMD), the difference of volume (ΔV), maximum Hausdorff distance (MHD), and average Hausdorff distance (AHD). The grading results were compared with those of the corresponding geometric indexes obtained by geometric objective methods in the other two centers. OAR auto-segmentation accuracy was also graded by our subjective evaluation standard. These grading results were compared with those of DSC. Based on the subjective evaluation standard and the five geometric indexes, the correspondence between the subjective evaluation level and the geometric index range was established for each OAR.ResultsFor ΔCMD, ΔV, and MHD, the grading results of the geometric objective evaluation methods at our center and the other two centers were inconsistent. For DSC and AHD, the grading results of three centers were consistent. Seven OARs’ grading results in the subjective evaluation standard were inconsistent with those of DSC. Six OARs’ grading results in the subjective evaluation standard were consistent with those of DSC. Finally, we proposed a new evaluation method that combined the subjective evaluation level of those OARs with the range of corresponding DSC to determine the grading standard. If the DSC ranges between the adjacent levels did not overlap, the DSC range was used as the grading standard. Otherwise, the mean value of DSC was used as the grading standard.ConclusionsA novel OAR-specific SOC grading standard in thorax was developed. The SOC grading standard provides a possible alternative for evaluation of the auto-segmentation accuracy for thoracic OARs.