Perimeter Measurements Research Articles

A Synergetic Approach to Burned Area Mapping Using Maximum Entropy Modeling Trained with Hyperspectral Data and VIIRS Hotspots

Southern European countries, particularly Spain, are greatly affected by forest fires each year. Quantification of burned area is essential to assess wildfire consequences (both ecological and socioeconomic) and to support decision making in land management. Our study proposed a new synergetic approach based on hotspots and reflectance data to map burned areas from remote sensing data in Mediterranean countries. It was based on a widely used species distribution modeling algorithm, in particular the Maximum Entropy (MaxEnt) one-class classifier. Additionally, MaxEnt identifies variables with the highest contribution to the final model. MaxEnt was trained with hyperspectral indexes (from Earth-Observing One (EO-1) Hyperion data) and hotspot information (from Visible Infrared Imaging Radiometer Suite Near Real-Time 375 m active fire product). Official fire perimeter measurements by Global Positioning System acted as a ground reference. A highly accurate burned area estimation (overall accuracy = 0.99%) was obtained, and the indexes which most contributed to identifying burned areas included Simple Ratio (SR), Red Edge Normalized Difference Vegetation Index (NDVI750), Normalized Difference Water Index (NDWI), Plant Senescence Reflectance Index (PSRI), and Normalized Burn Ratio (NBR). We concluded that the presented methodology enables accurate burned area mapping in Mediterranean ecosystems and may easily be automated and generalized to other ecosystems and satellite sensors.

Indecomposable sets of finite perimeter in doubling metric measure spaces

We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak (1,1)-Poincaré inequality. The two main results we obtain are a decomposition theorem into indecomposable sets and a characterisation of extreme points in the space of BV functions. In both cases, the proof we propose requires an additional assumption on the space, which is called isotropicity and concerns the Hausdorff-type representation of the perimeter measure.

Space Point Target Ranging System Based on Laser Beam Triangulation

With the rapid development of ranging technology, people’s requirements for ranging technology are more and more high. In some special occasions, such as live, high temperature, explosive and other inconvenient scenes, the importance of non-contact ranging technology is highlighted. As a non-contact measurement technology, laser ranging technology has faster measurement speed, higher measurement accuracy, longer measurement distance and stronger anti-interference ability compared with other measurement methods. However, at present, the measurement accuracy of laser ranging technology in China is not very high, and the design is relatively complex. Aiming at the above problems, this paper designs a spatial point target ranging system based on laser beam triangulation. The system uses the combination of laser ranging module and angle sensor module to measure the distance, uses the laser axis angle algorithm based on triangle method to calculate the distance, and uses the pyboard development platform to design the simultaneous acceptance and processing of multiple serial port data, and finally displays the measured data through the display. The experimental results show that the system can measure the distance between two points in space with relative error less than 1%, and it has the functions of circle and quadrilateral perimeter measurement, continuous measurement distance and data storage, which can meet the ranging requirements in various fields of engineering.

RELATIVE AGE IN FEMALE FUTSAL ATHLETES: IMPLICATIONS ON ANTHROPOMETRIC PROFILE AND STARTER STATUS

ABSTRACT Introduction: Evidence suggests that a higher distribution of elite athletes have birth dates in the first few months of the year. However, the advantages of birth month on performance related to starter status, structure and body composition in female futsal (5-a-side football played on a hard court, mainly indoors), are unknown. Objective: To determine the effect of relative age (ERA) on competitive female futsal athletes, and its influence on anthropometric profile and starter status. Methods: One hundred and fifteen athletes, participants in the 20th Brazilian Cup of Adult Futsal Clubs, special division, were submitted to measurements of body mass, height, skinfold thickness, body perimeters and bone diameters, in order to characterize the anthropometric profile and determine the body somatotype. The athletes were distributed in semesters and quartiles of the months of the year, according to their birth dates. Differences in the distribution of expected and observed birth dates were tested using Chi-square tests (χ2). Comparisons between semesters and birth quartiles were performed using parametric and non-parametric tests. Results: There was no ERA in distribution (p=0.248), anthropometric profile (p=0.872 to 0.912), or starter status between athletes born from January to June (p=0.352) and those born between July and December (p=0.744). On the other hand, those born in the first months of the year showed longer practice times than those born in the latter months of the year. Conclusion: Although the ERA in this study reveals longer practice times favoring female futsal athletes born in the first quartile of the year, it did not influence the starter status, the distribution in the teams, or any advantage in anthropometric profile. Level of evidence III, Case-Control Study.

An In-Service Primary Teacher’s Responses to Unexpected Moments in the Mathematics Classroom

The purpose of this case study is to investigate the triggers of unexpected (contingent) moments during one in-service primary teacher’s teaching of the measurement of length and perimeter, to identify this teacher’s responses to these moments, and to examine how these responses change the flow of the measurement of length and perimeter instruction. Ten lessons were recorded: the triggers of the contingent moments during these lessons were analyzed according to Rowland, Thwaites and Jared’s (2015) framework and the teacher’s responses were analyzed according to Stockero and Van Zoest’s (Journal of Mathematics Teacher Education, 16(2), 125–147, 2013) response types. The findings of this study showed that the contingent moments in these lessons resulted from the students’ incorrect answers, questions, and ideas, and the availability of materials. Moreover, the analysis of the teacher’s responses indicated that there were differences in the teacher’s spontaneous responses during the lessons, both in terms of the different types and the depth of the given responses. In addition, the teacher’s way of responding affected the flow of the measurement of length and perimeter instruction.

THE PERSONAL TRAINNER ON THE PERFORMANCE OF MUSCULATION PRACTITORS: A CASE STUDY

The Physical Education Professional responsible for prescribing and monitoring personalized activities in order to serve each client in a specific way, using a methodology in their training program, capable of providing the best results is the Personal Trainner. This research was conducted before and after through a physical evaluation followed by individualized intervention over a period of 3 months, with a weekly frequency of 3 days, and reevaluation analyzing and comparing data obtained in the measurements of perimeters, BMI, skinfolds and physical tests as the sit and reach test (Wells Bank), abdominal muscle strength test, abdominal and pectoral muscular endurance test, and the VO2 max test. Individual records were also made in the evaluation and reassessment for possible comparisons. The results obtained assure the truth reported above, because the client obtained improvement in all evaluated items, despite being an athletic subject. Theoretical and practical foundations for excellence in practical application by Personal Trainers, generating subsidies to rationalize and verify which conduct is most effective with your student.

Effect of Juvenile Idiopathic Arthritis on the Temporomandibular Joint and Occlusion in Children and Young Adolescents: A Descriptive Cross-sectional Study

Introduction: Juvenile Idiopathic Arthritis (JIA) is a chronic rheumatic disease, with a prevalence of 1 in 1000 children under the age of 16 years. The clinical symptoms include inflammation of joints, swelling of synovial membrane resulting in growth disturbances and loss of bone density. Aim: To assess the effect of JIA on the development of Temporomandibular Joint (TMJ) and occlusion in children and young adolescents in the age group of 8-16 years and to evaluate the effect of TMJ arthritis on the growth of maxilla and mandible. Materials and Methods: This is a descriptive cross-sectional study with a study and control group. A total of 44 children with JIA attending the Department of Rheumatology, Nizam Institute of Medical Sciences (NIMS), within the age group of 8-16 years were screened and enrolled in study from May-July 2014. A gender and sex-matched healthy control group were enrolled from Paediatric Dentistry outpatient specialty. For the measurement and comparison of arch perimeters of mandible and maxilla, the JIA and control group were divided into sub-groups 1 (8-10 y), 2 (11-13 y), and 3 (14-16 y). All the parameters were recorded and subjected to statistical analysis. An Independent sample t-test was used to find a significant difference for maxillary and mandibular arch perimeters among both the groups. Chi-square test was used to know the difference for TMJ parameters, occlusion and occlusal abnormalities. The level of significance was set at p<0.05 for all tests. Results: Children in the JIA group had reported TMJ pain on movement (40.9%), clicking sounds (36.4%), and dislocation (22.7%). Angle’s class II malocclusion was seen in 36.4% compared to the control group (4.5%). The mean arch perimeter of the mandible was significantly less among JIA children in subgroups 2 (73.00±3.03 mm), and 3 (71.77±6.27 mm) when compared to healthy controls. Other occlusal abnormalities such as increased overjet (34.1%), decreased overbite (31.8%), and crowding (54.5%) were reported in significant percentages compared to healthy controls. Conclusion: The mean arch perimeter of the mandible in the JIA group is less when compared to children of the same age in the control group. There is increased predilection of developing Angle’s class II Malocclusion in the JIA group. From a paediatric dentist perspective, it’s important to understand the overall impact of JIA on stomatognathic system, and an early intervention is recommended.

Intra and inter-rater agreement of inflammatory choroidal neovascular membrane measurements using optical coherence tomography angiography.

Automated measurement algorithm software is not routinely available in optical coherence tomography angiography (OCTA) devices and manual measurement of choroidal neovascular membrane (CNVM) size is necessary. Our aim was to determine intra- and inter-rater agreement of inflammatory CNVM manual measurements obtained with OCTA. OCTA (Triton® Topcon Corporation) images in patients with inflammatory CNVM were imported into ImageJ software v1.50 (NIH image). Two experienced observers performed manual area and perimeter measurements independently, and one of the observers performed the same measurements twice. Agreement was evaluated with intraclass correlation coefficients (ICC) and concordance correlation coefficients (CCC). Bland-Altman plots were plotted to graphically assess concordance. Statistical analysis was performed using STATA v13.0. Sixteen eyes of 16 subjects, with a mean age of 39.0 ± 16.6 years (range 13-71), were included. Mean CNVM area and perimeter was 124.83 ± 117.80 and 4.20 ± 2.00 mm, respectively. Intra-rater ICC for both area and perimeter measured was 0.99 (95% confidence interval (CI) 0.99-0.99). Inter-rater ICC for area and perimeter measured was 0.95 (95%CI 0.87-0.98) and 0.81 (95%CI 0.17-0.94), respectively. Intra-rater CCC for both area and perimeter measured was 0.99 (95%CI 0.99-0.99). Inter-rater CCC for both area and perimeter measured was 0.91 (95%CI 0.81-0.99) and 0.66 (95%CI 0.44-0.88), respectively. Inflammatory CNVM manual measurement showed high intra-rater agreement and moderate inter-rater agreement. Repeatability and reproducibility studies are essential in manual analysis to establish thresholds that can distinguish measurements variation from true clinical change. An automatic algorithm may be helpful to accurately grade lesions and monitor disease activity and response to treatment.

Evaluation of Spheroid 3D Culture Methods to Study a Pancreatic Neuroendocrine Neoplasm Cell Line.

Pancreatic Neuroendocrine Neoplasms (pNEN) are rare tumors which treatment still represent an important clinical problem, due to the paucity of medical treatments. Due to tumor complexity, techniques as 3D cultures are important to study drug activity in a more realistic model. This study aims to compare three different 3D culture methods in order to understand which one can be considered the best option in terms of experimental easiness and reproducibility in studying the efficacy of a target drug on pNEN. The BON1 cell line was used as a pNEN model and the well-known Receptor Tyrosine Kinase inhibitor Sunitinib was used in order to better investigate the different features of each method. The investigated methods are: (1) 96-well hanging drop plates (HD plates), (2) 24-well plates with a cell-repellent surface, and (3) ultra-low attachment 96-well plates with clear round bottom (ULA plates). The evaluated parameters during the study were: cell seeding, easiness in spheroids formation, morphology, culture maintenance, medium change, spheroids monitoring, picture quality, spheroid perimeter measurement reproducibility error, possibility to perform assays into the seeding plate, overall time of the experiment. Moreover, we investigated how culture methods can influence experimental outcomes evaluating perimeter changes, cell viability and immunohistochemistry of spheroids treated with different Sunitinib concentrations. Results showed that each method has weak and strong points but, considering the easiness of spheroids maintenance and reproducibility results, ULA plates method appears to be the best approach to culture BON1 spheroids and, therefore, to study pNEN.

A341 How Does Body Composition Change Measured by Bioimpedanciometry When the Patient Loses Weight, Whether with Medical or Pharmacological Management? Preliminary Results Clinic of Obesity in Colombia

Part of the parameters to determine weight reduction are BMI and body weight. But there are more precise measurements that demonstrate adherences to patterns and changes in body composition that directly affect the metabolic behavior of certain diseases such as the measurement of visceral fat, phase angle, body fat and skeletal muscle and the measurement of the abdominal perimeter. Aim: Determine how body composition changes after medical and surgical management in a group of patients enrolled in the same bariatric clinic

P3730Left atrial appendage perimeter measurement by cardiac CT is superior to transesophageal echocardiography for Watchman device sizing

Abstract Background Left atrial appendage occlusion with Watchman device traditionally relies on accurate left atrial appendage (LAA) ostium diameter measurement by 2D or 3D transesophageal echocardiogram (TEE). Alternate methods of ostium measurement including area-derived diameter and perimeter-derived diameter using cardiac computed tomography (CT) have been proposed. Purpose We aim to use CT technology with an advanced medical imaging application to measure LAA ostium perimeter for improved pre-procedural device sizing. Methods We performed a retrospective analysis of 92 patients with atrial fibrillation (Afib) who underwent Watchman implantation with pre-procedural TEE and cardiac CT between May 2015 and December 2018. LAA characteristics including ostial or landing zone perimeter, minimum and maximum diameters were acquired utilizing 3mensio Structural Heart Imaging Program. Proposed Watchman device size was estimated utilizing ostium perimeter by CT and compared to the current standard utilizing ostium diameter by 2D-TEE. Both measurements were then compared to actual implanted Watchman device size which met the P.A.S.S. criteria of position, anchor, size and seal. Results Watchman device sizing based on novel LAA landing zone perimeter size by CT had a very high correlation with the actual implanted Watchman size (Pearson coefficient r=0.94, p<0.001). Traditional TEE based Watchman sizing only had a modest correlation with the implanted Watchman size (Pearson coefficient r=0.66, p<0.001). CT predicted Watchman size had a significantly higher agreement compared to current standard TEE based sizing (93.4% vs 47.8%), inter-rater agreement was very high for CT based Watchman sizing compared to current standard TEE based sizing (Cohen's kappa = 0.91 vs Cohen's kappa = 0.32, p<0.001, p<0.001 respectively). Bland-Altman analysis also showed better correlation with CT based sizing compared to TEE (see Figure 1). Figure 1 Conclusion CT LAA perimeter sizing is superior to the current standard TEE based Watchman sizing. Larger, multi-center studies may be necessary to further validate our results.

Three-Dimensional Echocardiography for Transcatheter Aortic Valve Replacement Sizing: A Systematic Review and Meta-Analysis.

BackgroundTranscatheter aortic valve replacement (TAVR) is the standard of care for many patients with severe symptomatic aortic stenosis and relies on accurate sizing of the aortic annulus. It has been suggested that 3‐dimensional transesophageal echocardiography (3D TEE) may be used instead of multidetector computed tomography (MDCT) for TAVR planning. This systematic review and meta‐analysis compared 3D TEE and MDCT for pre‐TAVR measurements.Methods and ResultsA systematic literature search was performed. The primary outcome was the correlation coefficient between 3D TEE– and MDCT‐measured annular area. Secondary outcomes were correlation coefficients for mean annular diameter, annular perimeter, and left ventricular outflow tract area; interobserver and intraobserver agreements; mean differences between 3D TEE and MDCT measurements; and pooled sensitivities, specificities, and receiver operating characteristic area under curve values of 3D TEE and MDCT for discriminating post‐TAVR paravalvular aortic regurgitation. A random effects model was used. Meta‐regression and leave‐one‐out analysis for the primary outcome were performed. Nineteen studies with a total of 1599 patients were included. Correlations between 3D TEE and MDCT annular area, annular perimeter, annular diameter, and left ventricular outflow tract area measurements were strong (0.86 [95% CI, 0.80–0.90]; 0.89 [CI, 0.82–0.93]; 0.80 [CI, 0.70–0.87]; and 0.78 [CI, 0.61–0.88], respectively). Mean differences between 3D TEE and MDCT between measurements were small and nonsignificant. Interobserver and intraobserver agreement and discriminatory abilities for paravalvular aortic regurgitation were good for both 3D TEE and MDCT.ConclusionsFor pre‐TAVR planning, 3D TEE is comparable to MDCT. In patients with renal dysfunction, 3D TEE may be potentially advantageous for TAVR measurements because of the lack of contrast exposure.

Plug and play perimetry: Evaluating the use of a self-calibrating digital display for screen-based threshold perimetry

This study evaluated the feasibility of using a ‘self-calibrating’ display (EIZO CG277) to perform screen-based threshold perimetry. Such displays incorporate their own integrated photometer, so could potentially be used ‘straight out of the box’, without the need for time-consuming and costly luminance calibration by skilled experts. Concerns remain, however, due to the fact that the internal calibration of such devices is imperfect, and lingering doubts regarding the accuracy of screen-based perimetry in general. To evaluate such a system, automated static threshold perimetry was performed in thirty-two normal-sighted adults. In one condition, participants performed a novel screen-based perimetry test, for which the screen was calibrated extensively using traditional photometric techniques/equipment. In a second condition, the same test was performed, but the display was calibrated using only the screen’s integrated photometer (and assuming uniformity across the display). For reference, participants also completed a traditional visual-field assessment using a Humphrey Field Analyzer (HFA). All three tests were performed twice to assess test-retest repeatability (six tests total). The results showed no differences when comparing screen-based perimetric measurements made with internal self-calibration vs full manual calibration (either in terms of mean sensitivity, pointwise sensitivity, test-retest repeatability, or test duration). Furthermore, the accuracy and precision of both were indistinguishable from the current gold standard (HFA), although the HFA was approximately two minutes (~30%) faster. These results indicate that self-calibrating commercial monitors can be used to perform screen-based perimetry almost as well as current clinical devices, and without the need for any specialized knowledge or equipment to setup or maintain. This could facilitate perimetric testing in currently hard-to-reach settings, such as community centers, stroke wards, homes, rural locations, or developing countries.

A trace theorem for Martinet-type vector fields

In [Formula: see text] we consider the vector fields [Formula: see text] where [Formula: see text]. Let [Formula: see text] be the (closed) upper half-space and let [Formula: see text] be a function such that [Formula: see text] for some [Formula: see text]. In this paper, we prove that the restriction of [Formula: see text] to the plane [Formula: see text] belongs to a suitable Besov space that is defined using the Carnot–Carathéodory metric associated with [Formula: see text] and [Formula: see text] and the related perimeter measure.

Dual-Energy CT and Radiation Dose

As dual-energy CT scanners become more common, it is worth revisiting their benefits over conventional CT. The promises to increase the conspicuity of pathology and assist in differentiating tissue are much touted, but how can we realize the benefits of radiation dose reduction [1Grajo J.R. Sahani D.V. Dual-energy CT of the abdomen and pelvis: radiation dose considerations.J Am Coll Radiol. 2018; 15: 1128-1132Abstract Full Text Full Text PDF PubMed Scopus (12) Google Scholar]? This article will briefly discuss the technology of dual-energy CT scanners, review some of the practical applications, and discuss the potential benefits and shortcomings of dose reduction. The principle behind dual-energy CT is that scanning at two different kilovoltage peaks allows determination of attenuation curves of tissue. This can be accomplished through several different methods, including fast kilovoltage switching with single-source and single-detector, dual-layer detectors with one source, or dual detectors with dual-source, or dual-detector offset 90° from each other. The spectral information can be used to generate standard CT images in addition to mono-energetic reformats (often chosen slightly higher than the k-edge of iodine to increase conspicuity of enhancement; Fig. 1), virtual noncontrast images (Fig. 2), perfusion-like imaging (iodine-only images) [2Weidman E.K. Plodkowski A.J. Halpenny D.F. et al.Dual-energy CT angiography for detection of pulmonary emboli: incremental benefit of iodine maps.Radiology. 2018; 289: 546-553Crossref PubMed Scopus (53) Google Scholar], as well as other niche benefits to identify elements by k-edge and z-effective techniques (such as uric acid in gout) [3Glazebrook K.N. Guimaraes L.S. Murthy N.S. et al.Identification of intraarticular and periarticular uric acid crystals with dual-energy CT: initial evaluation.Radiology. 2011; 261: 516-524Crossref PubMed Scopus (189) Google Scholar]. Further applications of mono-energetic selection at higher kilovoltage may allow for reduced streak artifact from beam hardening in the case of orthopedic prostheses or other hardware [4Bamberg F. Dierks A. Nikolaou K. Reiser M.F. Becker C.R. Johnson T.R. Metal artifact reduction by dual energy computed tomography using monoenergetic extrapolation.Eur Radiol. 2011; 21: 1424-1429Crossref PubMed Scopus (423) Google Scholar].Fig 2Traditional (A), virtual noncontrast (B), and iodine-only (C) reformats of a CT abdomen/pelvis with intravenous contrast. Indeterminate density right renal lesion (arrows). Circle region of interest on lesion with measurements of Area (A/Ar), Perimeter (P/Perim), Mean attenuation (M/Av), and Standard Deviation of attenuation (SD). Virtual noncontrast image shows similar density to traditional scan and iodine-only image shows no enhancement, confirming benign cyst.View Large Image Figure ViewerDownload Hi-res image Download (PPT) Some of these benefits translate well into radiation dose reduction. The virtual noncontrast imaging at times permits removing a whole phase of imaging, as with renal or angiographic imaging. This could cut the dose in half for some studies. Furthermore, if the mono-energetic imaging is sufficient to salvage a poorly timed contrast bolus, this may spare a patient from needing to return for repeat imaging, reducing dose to the patient and delay in care. Yet, in other ways, the dual-energy CT scanner is similar to a traditional scanner. Simply substituting a dual-energy CT scanner for a conventional scanner will not reduce dose. Automatic exposure compensation works in the same way as on a traditional scanner, and though there are additional tools at the radiologist’s disposal as described previously, the intrinsic radiation exposure will be similar. The responsibility remains with the radiologist to act as steward of diagnostic medical radiation and determine if the advantages of dual-energy CT permit a dose reduction. If protocols are not adapted to remove the noncontrast phase, optimal dose savings will not be realized. If practices do not elect to reduce dose to offset the other benefits of dual-energy imaging, dose will remain the same. The responsibility falls to the radiologist to decide conscientiously how to reduce radiation dose in keeping with the principles of “as low as reasonably allowable” and the efforts of groups like Image Wisely and Image Gently. Dual-energy CT empowers us to re-assess imaging protocols in a new light and optimize patient care.

Notions of Dirichlet problem for functions of least gradient in metric measure spaces

We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazón-Rossi–De León, solutions by considering the Dirichlet problem for p -harmonic functions, p > 1 , and letting p \to 1 . Tools developed and used in this paper include the inner perimeter measure of a domain.

Histological and histomorphometric analysis of bone tissue after guided bone regeneration with non-resorbable membranes vs resorbable membranes and titanium mesh.

Guided bone regeneration (GBR) allows to achieve vertical ridge augmentation whether with nonresorbable membranes or resorbable membranes with Ti-mesh, but till now no studies are published comparing histological and histomorphometrical outcomes of these two procedures. Forty partially edentulous patients required vertical bone regeneration to place implants in the posterior mandible: 20 patients were randomly assigned to group A (Ti-PTFE); while 20 patients to group B (Collagen plus Ti-mesh). For both groups, graft material was a 50:50 mixture of autogenous bone and bone allograft. After 9 months, tissue biopsies were taken from augmented sites (regenerated bone ROI-1; native bone ROI-2) and undergone to histological and histomorphometric analysis. Percentages of bone tissue (B.Ar), biomaterial (Mat. Ar), and soft tissue (St.Ar) were measured; measurements of perimeters were calculated too. ROI-1 values were also compared to ROI-2 in both groups. Twenty-five samples were collected and analyzed consecutively: 13 in group A and 12 in group B. The mean B.Ar, Mat.Ar, and St.Ar were 39.7%, 8.6%, and 52.1% in group A; similar results were obtained in group B, with mean values of 42.1%, 9.6%, and 48.3%, respectively. No significant statistically differences were observed. Differences were observed between ROI-1 and ROI-2 in both group. Finally, bone structure index of ROI-1 and ROI-2 showed statistical differences. The preliminary results of this study suggest that GBR using nonresorbable membranes and Ti-mesh with resorbable membranes in combination with autogenous bone and bone allograft provide similar histological and histomorphometric results.

Rigidity of the 1-Bakry–Émery Inequality and Sets of Finite Perimeter in RCD Spaces

This note is dedicated to the study of the asymptotic behaviour of sets of finite perimeter over $${{\,\mathrm{RCD}\,}}(K,N)$$ metric measure spaces. Our main result asserts existence of a Euclidean tangent half-space almost everywhere with respect to the perimeter measure and it can be improved to an existence and uniqueness statement when the ambient is non collapsed. As an intermediate tool, we provide a complete characterization of the class of $${{\,\mathrm{RCD}\,}}(0,N)$$ spaces for which there exists a nontrivial function satisfying the equality in the 1-Bakry–Emery inequality. This result is of independent interest and it is new, up to our knowledge, even in the smooth framework.

The value of the left atrial appendage orifice perimeter of 3D model based on 3D TEE data in the choice of device size of LAmbre™ occluder.

Preoperative optimal selection of the occluder size is crucial in percutaneous left atrial appendage (LAA) occlusion, and the maximal width of the LAA orifice is the main reference index, however it can not fully meet the practical operation requirements. We retrospectively analyzed three-dimensional (3D) transesophageal echocardiography (TEE) and computed tomography (CT) imaging dataset of the 41 patients who underwent LAA occlusion with LAmbre™ system. The LAA orifice parameters were overall evaluated to determine their role in device size selection. Eight LAA 3D models of the four cases who had been replaced their device during the procedure based on TEE and CT were printed out to verify the optimal parameter decision strategy. There was a significant concordance of the results between 3D TEE and CT in the LAA orifice evaluation. The correlations between the perimeter and maximal width measurements by 3D TEE and the closure disk of the device were stronger than that between the area measurements and the closure disk (r = 0.93, 0.95, 0.86, respectively and p < 0.001 all), and the result was similar to that by CT (r = 0.92, 0.93, 0.84, respectively and p < 0.001 all). The ratios of the maximal width to the minimal width of the four cases were all > 1.4, however the rest 37 cases were all ≤ 1.4. Based on the comprehensive assessment of the LAA orifice perimeter and maximal width of the 3D printed models, the experiments were all succeed just for one try. The LAA orifice perimeter of 3D printed model based on 3D TEE may help in choosing the optimal device size of LAmbre™, especially for the LAA with flater ostial shape.

Elementary Students' Understanding of Geometrical Measurement in Three Dimensions

In this study, we investigated the potential of a hypothesized geometrical measurement learning progression (LP) to examine students' thinking and understanding in this domain. We interviewed 30 third to fifth graders using 3 LP‐based cognitive tasks that asked the students to find the length, perimeter, area, surface area, and volume measurement of a given object. We analyzed the students' responses to the tasks to examine variation in levels of the students' geometrical measurement understanding and found evidence of understanding at 5 successive levels of a geometrical measurement LP in 1, 2, and 3 dimensions. From these findings, we concluded that an LP can be a practical tool for understanding students' existing thinking and understanding in a targeted domain and has the potential to support students' further learning in the domain.