The differential on operator S(Γ).

Consider a simple graph $ \Gamma = (V(\Gamma), E(\Gamma)) $ with $ n $ vertices and $ m $ edges. Let $ P $ be a subset of $ V(\Gamma) $ and $ B(P) $ the set of neighbors of $ P $ in $ V(\Gamma)\backslash P $. In the study of graphs, the concept of differential refers to a measure of how much the number of edges leaving a set of vertices exceeds the size of that set. Specifically, given a subset $ P $ of vertices, the differential of $ P $, denoted by $ \partial(P) $, is defined as $ |B(P)|-|P| $. The differential of $ \Gamma $, denoted by $ \partial(\Gamma) $, is then defined as the maximum differential over all possible subsets of $ V(\Gamma) $. Additionally, the subdivision operator $ {{\mathcal{S}}({\Gamma})} $ is defined as the graph obtained from $ \Gamma $ by inserting a new vertex on each edge of $ \Gamma $. In this paper, we present results for the differential of graphs on the subdivision operator $ {{\mathcal{S}}({\Gamma})} $ where some of these show exact values of $ \partial({{\mathcal{S}}({\Gamma})}) $ if $ \Gamma $ belongs to a classical family of graphs. We obtain bounds for $ \partial({{\mathcal{S}}({\Gamma})}) $ involving invariants of a graph such as order $ n $, size $ m $ and maximum degree $ \Delta $, and we study the realizability of the graph $ \Gamma $ for any value of $ \partial({{\mathcal{S}}({\Gamma})}) $ in the interval $ \left[n-2, \frac{n(n-1)}{2}-n+2\right] $. Moreover, we give a characterization for $ \partial({{\mathcal{S}}({\Gamma})}) $ using the notion of edge star packing.

Definition, prevalence, clinical relevance and treatment of T-shaped uterus: systematic review.

OBJECTIVES: To summarize in a systematic review the current evidence regarding definitions, diagnosis, prevalence, etiology, clinical relevance and impact of surgical treatment for T-shaped uterus not related to diethylstilbestrol (DES) exposure, and to highlight areas on which future research should focus. METHODS: A search of PubMed, Scopus and EMBASE was performed on 9 April 2020 using the search terms 't-shaped OR t-shape OR infantile OR (lateral indentation) OR (diethylstilbestrol OR DES) AND (uterus OR uterine OR uteri) AND (anomaly OR anomalies OR malformation OR malformations)'. Additionally, the reference lists of the included studies were searched manually for other relevant publications. All studies presenting data on T-shaped uterus not associated with DES exposure and including at least 10 women were considered eligible. Studies regarding DES-related T-shaped uterus were excluded because DES has not been used since 1971. There were no restrictions on language, date of publication or status of publication. RESULTS: Of 2504 records identified by the electronic search, 20 studies were included in the systematic review. The majority of studies were of poor quality. In 11 of 16 studies reporting on the diagnosis of T-shaped uterus, the diagnostic method used was three-dimensional ultrasound. There is no consensus on the definition of T-shaped uterus, but the most cited criteria (4/16 studies) were of the European Society of Human Reproduction and Embryology and the European Society for Gynaecological Endoscopy (ESHRE/ESGE; 2013). The prevalence of T-shaped uterus varied from 0.2% to 10% in the four included studies reporting such data. With respect to etiology (except for DES), T-shaped uterus was considered a primary condition in three studies and secondary to adhesions in five and adenomyosis in one. T-shaped uterus was related to worse reproductive outcome based on subfertility (nine studies), miscarriage (seven studies), preterm delivery (two studies), ectopic pregnancy (one study) and repeat implantation failure (seven studies). Of the 12 studies that reported on the effects of surgical treatment of T-shaped uterus by hysteroscopic metroplasty, some mentioned an improvement in pregnancy rate (rates ranging from 49.6% to 88%; eight studies), live-birth rate (rates ranging from 35.1% to 76%; seven studies) and term-delivery rate (four studies) and a reduction in miscarriage (rates ranging from 7% to 49.6%; five studies) and ectopic pregnancy (one study). However, the evidence is of very low quality with serious/critical risk of bias toward overestimating the intervention effect. Some authors reported no complications related to the procedure, while others mentioned persistence of the dysmorphism (rates ranging from 1.4% to 11%; three studies), bleeding (1.3%; one study), infection (2.6%; one study) and adhesions (11.1% and 16.8%; two studies). CONCLUSIONS: The prevalence, etiology and clinical relevance, with respect to reproductive outcome, of T-shaped uterus remain unclear and there is no consensus on the definition and diagnostic method for this condition. Expectant management should be considered the most appropriate choice for everyday practice until randomized controlled trials show a benefit of intervention. © 2020 International Society of Ultrasound in Obstetrics and Gynecology.

Rickettsia parkeri strain Atlantic rainforest in ticks (Acari: Ixodidae) of wild birds in Arauca, Orinoquia region of Colombia.

Birds are important hosts for the development of the immature stages of several tick species that are vectors for disease-causing microorganisms in animals and humans. Colombia has the highest number of bird species worldwide; however, there is scarce data on the role of birds in the circulation of ticks and their associated pathogens, such as rickettsiae. The department of Arauca has a high diversity of resident and migratory (boreal and austral) birds and ticks associated with the transmission of Rickettsia. The objective of this research was to identify tick species parasitizing birds and to detect Rickettsia species in these ectoparasites. We conducted samplings in the municipalities of Arauca, Cravo Norte, and Tame between November of 2018 and August of 2019. Birds were captured using mist nets and examined for the presence of tick species. The collected ticks were morphologically and molecularly identified. Furthermore, we detected rickettsiae in ticks by amplifying fragments of the citrate synthase (gltA) and outer membrane protein (ompB) genes. We captured 606 birds belonging to 25 families and 115 species. Tick infestation rate was 3.3% (20/606) in the birds captured and eight new associations between wild birds and ticks are reported for the American continent. We identified four tick species: Amblyomma nodosum, Amblyomma longirostre, Amblyomma mixtum, and Amblyomma sp.. Moreover, we confirmed the presence of Rickettsia parkeri strain Atlantic rainforest in A. nodosum, a medically-relevant rickettsia due to cases of rickettsiosis in the American continent. This finding manifests the importance of wild birds as hosts and dispersal agents of ticks infected with pathogenic rickettsiae, as well as the need to monitor migratory birds in the Orinoquia and other regions of Colombia and America.

Removal of uterine polyps: clinical management and surgical approach.

Endometrial polyps have a reported prevalence from 7.8% up to 30% and are one of the most cost-consuming gynecological conditions for our specialty. There are strong practitioner beliefs that surgical removal of endometrial polyps is highly beneficial, particularly for those with abnormal uterine bleeding and infertility. Additionally, polypectomy is indicated to reduce the risk of malignancy. Transvaginal ultrasound is the first-line diagnostic option for detection of endometrial polyps, while sonohysterography has similar accuracy as hysteroscopy in the diagnostic confirmation. Blind dilatation and curettage is not recommended for polyp removal; rather, hysteroscopy in the operating room and office setting using small-diameter hysteroscopic equipment is the standard approach. This can be performed without anesthesia in most women. While hysteroscopy is an effective method for polypectomy with a low complication rate, it is unknown whether this is truly beneficial for reproductive-age women with infertility and prior assisted reproduction therapy. The risk of malignancy in women with postmenopausal bleeding justifies the necessity of polypectomy with histologic tissue examination. In asymptomatic women, the risk of malignancy is low, and there are no known benefits of polyp removal in the prevention of malignant transformation. Cost-effective studies remain to be done to provide us with the optimal approach to endometrial polyps including the management of asymptomatic and/or infertile women, ideal location including office-based or the operating room setting, complication prevention including intrauterine adhesions, and recurrence issues.

Congenital Uterine Malformation by Experts (CUME): diagnostic criteria for T-shaped uterus.

OBJECTIVES: To identify uterine measurements that are reliable and accurate to distinguish between T-shaped and normal/arcuate uterus, and define T-shaped uterus, using Congenital Uterine Malformation by Experts (CUME) methodology, which uses as reference standard the decision made most often by several independent experts. METHODS: This was a prospectively planned multirater reliability/agreement and diagnostic accuracy study, performed between November 2017 and December 2018, using a sample of 100 three-dimensional (3D) datasets of different uteri with lateral uterine cavity indentations, acquired from consecutive women between 2014 and 2016. Fifteen representative experts (five clinicians, five surgeons and five sonologists), blinded to each others' opinions, examined anonymized images of the coronal plane of each uterus and provided their independent opinion as to whether it was T-shaped or normal/arcuate; this formed the basis of the CUME reference standard, with the decision made most often (i.e. that chosen by eight or more of the 15 experts) for each uterus being considered the correct diagnosis for that uterus. Two other experienced observers, also blinded to the opinions of the other experts, then performed independently 15 sonographic measurements, using the original 3D datasets of each uterus. Agreement between the diagnoses made by the 15 experts was assessed using kappa and percent agreement. The interobserver reliability of measurements was assessed using the concordance correlation coefficient (CCC). The diagnostic test accuracy was assessed using the area under the receiver-operating-characteristics curve (AUC) and the best cut-off value was assessed by calculating Youden's index, according to the CUME reference standard. Sensitivity, specificity, negative and positive likelihood ratios (LR- and LR+) and post-test probability were calculated. RESULTS: According to the CUME reference standard, there were 20 T-shaped and 80 normal/arcuate uteri. Individual experts recognized between 5 and 35 (median, 19) T-shaped uteri on subjective judgment. The agreement among experts was 82% (kappa = 0.43). Three of the 15 sonographic measurements were identified as having good diagnostic test accuracy, according to the CUME reference standard: lateral indentation angle (AUC = 0.95), lateral internal indentation depth (AUC = 0.92) and T-angle (AUC = 0.87). Of these, T-angle had the best interobserver reproducibility (CCC = 0.87 vs 0.82 vs 0.62 for T-angle vs lateral indentation depth vs lateral indentation angle). The best cut-off values for these measurements were: lateral indentation angle ≤ 130° (sensitivity, 80%; specificity, 96%; LR+, 21.3; LR-, 0.21), lateral indentation depth ≥ 7 mm (sensitivity, 95%; specificity, 77.5%; LR+, 4.2; LR-, 0.06) and T-angle ≤ 40° (sensitivity, 80%; specificity, 87.5%; LR+, 6.4; LR-, 0.23). Most of the experts diagnosed the uterus as being T-shaped in 0% (0/56) of cases when none of these three criteria was met, in 10% (2/20) of cases when only one criterion was met, in 50% (5/10) of cases when two of the three criteria were met, and in 93% (13/14) of cases when all three criteria were met. CONCLUSIONS: The diagnosis of T-shaped uterus is not easy; the agreement among experts was only moderate and the judgement of individual experts was commonly insufficient for accurate diagnosis. The three sonographic measurements with cut-offs that we identified (lateral internal indentation depth ≥ 7 mm, lateral indentation angle ≤ 130° and T-angle ≤ 40°) had good diagnostic test accuracy and fair-to-moderate reliability and, when applied in combination, they provided high post-test probability for T-shaped uterus. In the absence of other anomalies, we suggest considering a uterus to be normal when none or only one criterion is met, borderline when two criteria are met, and T-shaped when all three criteria are met. These three CUME criteria for defining T-shaped uterus may aid in determination of its prevalence, clinical implications and best management and in the assessment of post-surgical morphologic outcome. The CUME definition of T-shaped uterus may help in the development of interventional randomized controlled trials and observational studies and in the diagnosis of uterine morphology in everyday practice, and could be adopted by guidelines on uterine anomalies to enrich their classification systems. Copyright © 2019 ISUOG. Published by John Wiley & Sons Ltd.

Cutaneous small-vessel vasculitis following hysterosalpingo-foam sonography (HyFoSy).

We present a case of diffuse skin immune reaction, diagnosed as cutaneous small-vessel vasculitis, following assessment of tubal patency by contrast ultrasound, which appears to be the first reported case of hypersensitivity reaction to sonographic tubal patency testing, based on a literature search. A 32-year-old woman presented with non-thrombocytopenic palpable purpura the day after assessment of tubal patency by two-/three-dimensional hysterosalpingo-foam sonography (HyFoSy) using ExEm® Foam. During real-time ultrasound, the observer identified flow in only the right tube when using saline with air as contrast medium; however, the same observer identified flow in both tubes after injecting ExEm Foam and the woman left the clinic without any complications. The next day, the patient was admitted with a complaint of a red-purple skin rash noticed the same morning, associated with moderate leg pain. Slow-motion analysis of the recorded videos and three-dimensional ultrasound datasets showed previously unnoticed venous intravasation of ExEm Foam into the myometrial vessels. Palpable purpura is typically found in vasculitis as a result of extravasation of red cells outside the inflamed blood vessel. This previously unreported side effect of tubal patency testing by HyFoSy, its potential rare organ consequences, as well as unknown consequences of venous intravasation by foam, should be included in the informed consent prior to the examination. Copyright © 2019 ISUOG. Published by John Wiley & Sons Ltd.

Septate uterus according to ESHRE/ESGE, ASRM and CUME definitions: association with infertility and miscarriage, cost and warnings for women and healthcare systems.

OBJECTIVES: To estimate the differences in frequency of diagnosis of septate uterus using three different definitions and determine whether these differences are significant in clinical practice, and to examine the association between diagnosis of septate uterus, using each of the three definitions, and infertility and/or previous miscarriage as well as the cost of allocation to surgery. METHODS: This was a secondary analysis of data from a prospective study of 261 consecutive women of reproductive age attending a private clinic focused on the diagnosis and treatment of congenital uterine malformations. Reanalysis of the datasets was performed according to three different means of defining septate uterus: following the recommendations of the American Society for Reproductive Medicine (ASRM), a 2016 update of those of the American Fertility Society from 1988 (ASRM-2016: internal fundal indentation depth ≥ 1.5 cm, angle of internal indentation < 90° and external indentation depth < 1 cm); following the recommendations of the European Society of Human Reproduction and Embryology/European Society for Gynaecological Endoscopy (ESHRE/ESGE), published in 2013 and reaffirmed in 2016 (ESHRE/ESGE-2016: internal fundal/uterine indentation depth > 50% of uterine-wall thickness and external indentation depth < 50% of uterine-wall thickness, with uterine-wall thickness measured above interostial/intercornual line); and using a definition published last year which was based on the decision made most often by a group of experts (Congenital Uterine Malformation by Experts; CUME) (CUME-2018: internal fundal indentation depth ≥ 1 cm and external fundal indentation depth < 1 cm). We compared the rate of diagnosis of septate uterus using each of these three definitions and, for each, we estimated the association between the diagnosis and infertility and/or previous miscarriage, and anticipated the costs associated with their implementation using a guesstimation method. RESULTS: Although 32.6% (85/261) of the subjects met the criteria for one of the three definitions of septate uterus, only 2.7% (7/261) of them were defined as having septate uterus according to all three definitions. We diagnosed significantly more cases of septate uterus using ESHRE/ESGE-2016 than using ASRM-2016 (31% vs 5%, relative risk (RR) = 6.7, P < 0.0001) or CUME-2018 (31% vs 12%, RR = 2.6, P < 0.0001) criteria. We also observed frequent cases that could not be classified definitively by ASRM-2016 (gray zone: neither normal/arcuate nor septate; 6.5%). There were no significant differences (P > 0.05) in the prevalence of septate uterus in women with vs those without infertility according to ASRM-2016 (5% vs 4%), ESHRE/ESGE-2016 (35% vs 28%) or CUME-2018 (11% vs 12%). Septate uterus was diagnosed significantly more frequently in women with vs those without previous miscarriage according to ASRM-2016 (11% vs 3%; P = 0.04) and CUME-2018 (22 vs 10%; P = 0.04), but not according to ESHRE/ESGE-2016 (42% vs 28%; P = 0.8) criteria. Our calculations showed that global costs to the healthcare system would be highly dependent on the criteria used in the clinical setting to define septate uterus, with the costs associated with the ESHRE/ESGE-2016 definition potentially being an extra US$ 100-200 billion over 5 years in comparison to ASRM-2016 and CUME-2018 definitions. CONCLUSIONS: The prevalence of septate uterus according to ESHRE/ESGE-2016, ASRM-2016 and CUME-2018 definitions differs considerably. An important limitation of the ASRM classification, which needs to be addressed, is the high proportion of unclassifiable cases originally named, by us, the 'gray zone'. The high rate of overdiagnosis of septate uterus according to ESHRE/ESGE-2016 may lead to unnecessary surgery and therefore unnecessary risk in these women and may impose a considerable financial burden on healthcare systems. Efforts to define clinically meaningful and universally applicable criteria for the diagnosis of septate uterus should be encouraged. Copyright © 2019 ISUOG. Published by John Wiley & Sons Ltd.

Útero septo según las definiciones de ESHRE/ESGE, ASRM y CUME: la relación con la infertilidad y el aborto espontáneo, el costo y advertencias para las mujeres y los sistemas de salud OBJETIVO: Evaluar el rendimiento de la velocidad sistólica máxima de la arteria cerebral media fetal (MCA-PSV, por sus siglas en inglés) ≥1,5 múltiplos de la mediana (MdM) para la predicción de la anemia moderada-severa en fetos sometidos a transfusión y no sometidos. MÉTODOS: Se realizó una búsqueda sistemática para identificar estudios observacionales relevantes reportados en el período 2008-2018 que evaluaron el rendimiento de la MCA-PSV, utilizando un umbral de 1,5MdM para la predicción de la anemia fetal. El diagnóstico de la anemia fetal mediante la toma de muestras de sangre fue el estándar de referencia. Se utilizaron modelos de efectos aleatorios para la elaboración de una curva jerárquica resumen de las características operativas del receptor (hSROC, por sus siglas en inglés). Se realizaron análisis de subgrupos y metarregresión, según el número de transfusiones intrauterinas previas. RESULTADOS: En el metaanálisis se incluyeron doce estudios y 696 fetos. El área bajo la curva (ABC) hSROC para la anemia moderada-severa fue del 83%. La sensibilidad y especificidad agrupadas (IC 95%) fueron del 79% (70-86%) y 73% (62-82%), respectivamente, y los cocientes de verosimilitud positivos y negativos fueron 2,94 (IC 95%: 2,13-4,00) y 0,272 (IC 95%: 0,188-0,371). Cuando solo se consideraron los fetos no sometidos a transfusión, la predicción mejoró, pues se logró un ABC del 87%, una sensibilidad del 86% (IC 95%: 75-93%) y una especificidad del 71% (IC 95%: 49-87%). Se observó una disminución en la sensibilidad de la predicción de la anemia moderada-severa mediante la MCA-PSV ≥1.5MdM (estimación, -5,5% (IC 95%: -10,7 a -0,3%), P=0,039) en función del aumento del número de transfusiones previas. CONCLUSIONES: El uso de la MCA-PSV ≥1.5MdM para la predicción de la anemia moderada-severa en fetos no sometidos a transfusión muestra una precisión moderada (86% de sensibilidad y 71% de especificidad), que disminuye con el aumento del número de transfusiones intrauterinas.

Congenital Uterine Malformation by Experts (CUME): better criteria for distinguishing between normal/arcuate and septate uterus?

OBJECTIVES: To assess the level of agreement between experts in distinguishing between septate and normal/arcuate uterus using their subjective judgment when reviewing the coronal view of the uterus from three-dimensional ultrasound. Another aim was to determine the interobserver reliability and diagnostic test accuracy of three measurements suggested by recent guidelines, using as reference standard the decision made most often by experts (Congenital Uterine Malformation by Experts (CUME)). METHODS: Images of the coronal plane of the uterus from 100 women with suspected fundal internal indentation were anonymized and provided to 15 experts (five clinicians, five surgeons and five sonologists). They were instructed to indicate whether they believed the uterus to be normal/arcuate (defined as normal uterine morphology or not clinically relevant degree of distortion caused by internal indentation) or septate (clinically relevant degree of distortion caused by internal indentation). Two other observers independently measured indentation depth, indentation angle and indentation-to-wall-thickness (I:WT) ratio. The agreement between experts was assessed using kappa, the interobserver reliability was assessed using the concordance correlation coefficient (CCC), the diagnostic test accuracy was assessed using the area under the receiver-operating characteristics curve (AUC) and the best cut-off value was assessed using Youden's index, considering as the reference standard the choice made most often by the experts (CUME). RESULTS: There was good agreement between all experts (kappa, 0.62). There were 18 septate and 82 normal/arcuate uteri according to CUME; European Society of Human Reproduction and Embryology (ESHRE)-European Society for Gynaecological Endoscopy (ESGE) criteria (I:WT ratio > 50%) defined 80 septate and 20 normal/arcuate uteri, while American Society for Reproductive Medicine (ASRM) criteria defined five septate (depth > 15 mm and angle < 90°), 82 normal/arcuate (depth < 10 mm and angle > 90°) and 13 uteri that could not be classified (referred to as the gray-zone). The agreement between ESHRE-ESGE and CUME was 38% (kappa, 0.1); the agreement between ASRM criteria and CUME for septate was 87% (kappa, 0.39), and considering both septate and gray-zone as septate, the agreement was 98% (kappa, 0.93). Among the three measurements, the interobserver reproducibility of indentation depth (CCC, 0.99; 95% CI, 0.98-0.99) was better than both indentation angle (CCC, 0.96; 95% CI, 0.94-0.97) and I:WT ratio (CCC, 0.92; 95% CI, 0.90-0.94). The diagnostic test accuracy of these three measurements using CUME as reference standard was very good, with AUC between 0.96 and 1.00. The best cut-off values for these measurements to define septate uterus were: indentation depth ≥ 10 mm, indentation angle < 140° and I:WT ratio > 110% . CONCLUSIONS: The suggested ESHRE-ESGE cut-off value overestimates the prevalence of septate uterus while that of ASRM underestimates this prevalence, leaving in the gray-zone most of the uteri that experts considered as septate. We recommend considering indentation depth ≥ 10 mm as septate, since the measurement is simple and reliable and this criterion is in agreement with expert opinion. Copyright © 2017 ISUOG. Published by John Wiley & Sons Ltd.

Counting ovarian antral follicles by ultrasound: a practical guide.

This Consensus Opinion summarizes the main aspects of several techniques for performing ovarian antral follicle count (AFC), proposes a standardized report and provides recommendations for future research. AFC should be performed using a transvaginal ultrasound (US) probe with frequency ≥ 7 MHz. For training, we suggest a minimum of 20-40 supervised examinations. The operator should be able to adjust the machine settings in order to achieve the best contrast between follicular fluid and ovarian stroma. AFC may be evaluated using real-time two-dimensional (2D) US, stored 2D-US cine-loops and stored three-dimensional (3D) US datasets. Real-time 2D-US has the advantage of permitting additional maneuvers to determine whether an anechoic structure is a follicle, but may require a longer scanning time, particularly when there is a large number of follicles, resulting in more discomfort to the patient. 2D-US cine-loops have the advantages of reduced scanning time and the possibility for other observers to perform the count. The 3D-US technique requires US machines with 3D capability and the operators to receive additional training for acquisition/analysis, but has the same advantages as cine-loop and also allows application of different imaging techniques, such as volume contrast imaging, inversion mode and semi-automated techniques such as sonography-based automated volume calculation. In this Consensus Opinion, we make certain recommendations based on the available evidence. However, there is no strong evidence that any one method is better than another; the operator should choose the best method for counting ovarian follicles based on availability of resources and on their own preference and skill. More studies evaluating how to improve the reliability of AFC should be encouraged. Copyright © 2017 ISUOG. Published by John Wiley & Sons Ltd.