Trapezoid Area Research Articles

Kambin's triangle-related data based on magnetic resonance neurography and its role in percutaneous transforaminal endoscopic lumbar interbody fusion

BackgroundThe percutaneous transforaminal endoscopic lumbar interbody fusion (PETLIF) has many advantages as a new minimally invasive surgical technique, and its surgical approach passes through the Kambin's triangle. One of the greatest challenges in completing PETLIF is avoiding nerve root damage. In previous studies, the relevant anatomic data do not correspond well with current surgical techniques, and there is a paucity of studies based on magnetic resonance neurography (MRN), which is the clearest imaging method for nerve roots. The purpose of this study was to analyze the safety of the PETLIF at each lumbar segment based on measured results from the MRN imaging data and to propose a novel method of intraoperative positioning.MethodsThe coronal images with the clearest course of nerve roots were chosen for retrospective observation. During the PETLIF, the secure region of the operation was considered to be a trapezium. The following parameters were measured, respectively: trapezoid area, height, and median line length, as well as the relevant parameters of the positional relation between the point “O,” the most secure operating center point of the secure region, and each osseous anatomic landmark. And the data were compared with the size of the cage to obtain safety.ResultsAt L1-S1, with the downward motion of the target intervertebral space, the area increased from (67.94 ± 15.22) mm2 to (140.99 ± 26.06) mm2, and the height increased from (7.23 ± 1.17) mm to (12.59 ± 1.63) mm. At L1–L5, the length of the median line was increased from (9.42 ± 1.70) mm to (12.70 ± 1.88) mm. Even though it was reduced to (11.59 ± 1.99) mm at L5–S1, it was still longer than that at L3–L4. The safety obtained by the primary observational indicator was 34.52%, 33.33%, 53.57%, 96.43%, and 77.38%, respectively, at L1–S1. The safety obtained by the two secondary observational indicators was 77.38% and 95.24% at L3–L4 and 100% at L4–S1. There was no point “O” outside the anatomic mark line. The intraoperative positioning method of the point “O” was as follows: It was located medially and horizontally approximately 3/5 of the anatomic mark line at L1–L5; the horizontal distances were (0.48 ± 0.67) mm, (1.20 ± 0.89) mm, (2.72 ± 1.01) mm, and (3.69 ± 1.47) mm, respectively. In addition, it was necessary to locate (3.43 ± 1.41) mm inward at about 4/5 of the anatomic mark line at L5–S1.ConclusionsThe MRN allows clearer and more accurate visualization of the nerve roots, and the basic anatomic study of the Kambin's triangle based on this technology is of practical clinical significance. In the current study, it is believed that, during the PETLIF, cage implantation is the safest at L4–L5, followed by L5–S1; L1–L3 is more likely to cause nerve root injury, and L3–L4 is not less likely. To improve safety, a comprehensive individualized imaging assessment should be performed before surgery. This study also provides an easy method of intraoperative localization, which helps avoid nerve root injury.

ANALISIS PENGARUH SUHU TERHADAP SENSITIVITAS SENSOR PADA HIDUNG ELEKTRONIK UNTUK KEMATANGAN BUAH KELAPA SAWIT

Electronic noses have been developed for decades in many fields. Recently, electronic nose has been used in agriculture to detect the ripeness of fruits because fruits also produce volatile gas during ripening. Oil palm fresh fruit bunches (FFB) is the main source of crude palm oil, its quality depends on the ripeness levels of oil palm FFB. Therefore, electronic detections of oil palm FFB ripeness need to be developed. This study was aimed to investigate the effect of temperature variation on the sensitivity of gas sensors in an electronic nose designed for detecting the ripeness of oil palm FFB. The electronic nose used in this study consisted of 4 sensors which were TGS 2611, TGS 2620, TGS 813 and TGS 822. Samples were peeled fruitlets of ripe oil palm FFB which were heated to temperatures of 30°C, 45°C, and 60°C. Response of each sensor was represented as a trapezoid area of voltage versus time for convenience. The results showed that there was a significant difference in the output voltage of each sensor when the sample temperatures were varied. Fruitlets of oil palm FFB heated at 60°C resulted in higher trapezoid area which mean more volatile gas released. Based on the resulted trapezoid area for each sensor. Sensors of TGS 2611 and TGS 822 are the most sensitive which have higher trapezoid area for the variation of the temperatures.

Rancang Bangun Sistem Hidung Elektronik Berbasis Sensor Gas MQ untuk Mengevaluasi Kualitas Madu

Honeys come in many varieties based on quality attributes and region origin. Electronic nose systems have been adopted and used to classify honey types based on physicochemical parameters. This study was aimed to build a low cost electronic nose (e-nose) based on metal oxide semiconductor (MOS) gas sensors, and then used to evaluate the qualities of two types of honeys and one non honey based on sugar contents and pH values. Six gas sensors of MQ modules namely MQ2, MQ3, MQ4, MQ5, MQ6, MQ9, and an Arduino microcontroller were used in this system. Software of Arduino IDE, PLX-DAQ, and Python were applied to record output voltages of each sensor, saved in Excel format, and to calculate trapezoid areas respectively. Honey samples were named as A, B, and C which were. a national brand honey, a local forest honey, and date syrup respectively. The results show higher output voltages for MQ 3, MQ 4, and MQ 6 sensors. The six sensors are able to differentiate between the two honey types and non honey. Sample A has the highest trapezoid area while sample C has the lowest area. This could be caused by higher pH value of sample C.

A time-varying grey Riccati model based on interval grey numbers for China's clean energy generation predicting

PurposeIn order to accurately predict the uncertain and nonlinear characteristics of China's three clean energy generation, this paper presents a novel time-varying grey Riccati model (TGRM(1,1)) based on interval grey number sequences.Design/methodology/approachBy combining grey Verhulst model and a special kind of Riccati equation and introducing a time-varying parameter and random disturbance term the authors advance a TGRM(1,1) based on interval grey number sequences. Additionally, interval grey number sequences are converted into middle value sequences and trapezoid area sequences by using geometric characteristics. Then the predicted formula is obtained by using differential equation principle. Finally, the proposed model's predictive effect is evaluated by three numerical examples of China's clean energy generation.FindingsBased on the interval grey number sequences, the TGRM(1,1) is applied to predict the development trend of China's wind power generation, China's hydropower generation and China's nuclear power generation, respectively, to verify the effectiveness of the novel model. The results show that the proposed model has better simulated and predicted performance than compared models.Practical implicationsDue to the uncertain information and continuous changing of clean energy generation in the past decade, interval grey number sequences are introduced to characterize full information of the annual clean energy generation data. And the novel TGRM(1,1) is applied to predict upper and lower bound values of China's clean energy generation, which is significant to give directions for energy policy improvements and modifications.Originality/valueThe main contribution of this paper is to propose a novel TGRM(1,1) based on interval grey number sequences, which considers the changes of parameters over time by introducing a time-varying parameter and random disturbance term. In addition, the model introduces the Riccati equation into classic Verhulst, which has higher practicability and prediction accuracy.

Teachers Using GeoGebra to Visualize and Verify Conjectures About Trapezoids

This paper describes outcomes from a project conducted at a small US university where 23 secondary school mathematics teachers participated in the study. Based on sketches created in a dynamic geometry software (DGS) and written responses to an assignment related to developing the trapezoid area formula, we explored how teachers used DGS when visualizing and verifying geometrical conjectures. We found that teachers used a combination of four strategies—eye-balling, measurement, constructions, and written statements—in their DGS sketches. Some teachers used DGS as paint software and their DGS files did not pass the dragging test. Teachers’ misconceptions became obvious while they were visualizing conjectures in the software, which were mediated by the skill for use of technology. Also, some used shortcuts that disagreed with conjectures and distorted their solutions, thus employing practices that could be damaging in teaching situations. These results and the methodological approach used in this study will be of interest to mathematics teacher educators, facilitators of professional development programs, and mathematics teachers.

Anatomical location of the abducens nerves (VI) in the ventral approach of clival tumors.

The aim of this work was to determine reliable anatomical landmarks for locating and preserving the abducens nerves (6th cranial nerves) during trans-facial or trans-nasal endoscopic approaches of skull base tumors involving the clivus and the petrous apex. In order to describe this specific anatomy, we carefully dissected 10 cadaveric heads under optic magnification. Several measurements were taken between the two petro-sphénoidal foramina, from the bottom of the sella and the dorsum sellae. The close relationship between the nerves and the internal carotid artery were taken into account. We defined a trapezoid area that allowed drilling the clivus safely, preserving the 6th cranial nerve while being attentive to the internal carotid artery. The caudal part of this trapezium is, on average, 20mm long at mi-distance between the two petro-sphenoidal foramina. The cranial part is at the sella level, a line between both paraclival internal carotid arteries. Oblique lateral edges between the cranial and caudal parts completed the trapezium.

Comparison of detection percentage and morphology of myocardial bridge between conventional coronary angiography and coronary CT angiography

Introduction: Myocardial bridge (MB) is a congenital anomaly in which a segment of a coronary artery is surrounded by myocardium. In our study, we want to use conventional coronary angiography (CCA) to describe morphologic characteristics of MB (unidentified or identified) in the patients with documented evidence of MB in coronary computed tomography angiography (CCTA). Methods: The present study was designed as cross-sectional and was conducted on 47 patients with documented evidence of MB in CCTA, who were referred to Nemazee and Faghihi hospitals for performing coronary angiography during a one year period. We compared the morphologic characteristics of tunneled segments, which were missed at CCA (unidentified), and the tunneled segments which were identified with CCA. Results: In sum, MB was found in 16 (34%) patients at CCA (identified), and it was not found in 31 (66%) patients (unidentified) based on compression sign. No significant correlation was found between the percentage of systolic compression and the length and depth of the tunneled segment in identified group (r=0.73, P = 0.18; r=1.09, P = 0.15; respectively). Degree of atherosclerotic plaque formation (diameter stenosis, percentage) (mean, 0.25 (25%) ±0.29; range, 0-0.98) of the tunneled segments in unidentified group was significantly more than the same degree (mean, 0.07 (7%) ±0.13; range, 0-0.41) of the identified group (P = 0.03). The measurement of the trapezoid area under the tunneled segment with this formula [(MB length+ intramyocardial segment) ×depth/2] had significant relation with systolic compression (r=0.304, P = 0.03) and defined the cut-off value of 250 mm2 as the value of significant difference in detecting myocardial bridging with CCA. Conclusion: Our results showed that in most of identified MBs in CCA the tunneled segment area was equal and more than 250 mm2. In addition, the degree of atherosclerotic plaque of the tunneled segments at CCA was significantly more in unidentified group.

Mathematical Language Skills of Mathematics Prospective Teachers

Effective mathematics teaching can be actualized only with correct use of the mathematical content language which comprises mathematical rules, concepts, symbols and terms. In this research, it was aimed to examine the mathematics prospective teachers' content language skills in some basic geometric concepts which are ray, angle, polygon, Pythagorean Theorem, area formula of trapezoid and surface area formula of the cone. Participants of the present study were constituted of third grade students in university. From results, it was determined that participants were not able to use the mathematical language adequately and usually not able to explain the concepts using symbols. It was also determined that there were some mistakes on the verbal level that the prospective teachers used to explain the concepts in the research.

Does thermal time for germination vary among populations of a tree legume (Peltophorum dubium)?

Few works report the use of degree-days (DD) - used in crops to predict events and schedule management activities - to describe the germination of tropical trees. The cardinal temperatures (base, optimum and ceiling temperature) for germination of the species may vary depending on the seed provenance. Peltophorum dubium (Spreng.) Taub. is an early successional leguminous tree widely distributed in South America, often occurring as cultivated or naturalized trees, thus considered to be a good example for testing DD model in tree species. The main objective of this study was to describe the seed germination response of different populations of P. dubium as function of DD accumulation during germination assays in semi-controlled (fluctuating temperatures) conditions. Germination assays with manually scarified seeds sown in aluminum sheet trays filled with a composed substrate were performed under greenhouse conditions at different times. Three methods were employed in order to describe the accumulation of thermal time throughout the assays and, considering the seed lot and sowing time, a trapezoid area method was relatively more effective in describing the germination. The germination curves of P. dubium seeds from different populations, expressed in degree-days estimated directly from temperature records schedules, tend to be more clustered suggesting little variation among thermal time requirements in different seed provenances. Otherwise, the thermal time requirement can vary depending on the time of sowing, and any increase in DD requirement when the assays were performed under higher mean temperatures can be related to a thermal effect on the germination of scarified seeds.

The Differential Measurement Model that under the Equal Principle and its Application

According to the equal principle, to establish the relationship between function and curved trapezoid area, designed the fluid differential measurement model, analysis of main parameters, introduced working principle, combining with the different forms of curve, depicting the derived function curve measurement method is given.

Measuring aortic valve coaptation surface area using three-dimensional transesophageal echocardiography

As aortic valve (AV) repairs become more sophisticated, surgeons need increasingly detailed information about the structure and function of this valve. Unlike two-dimensional transesophageal echocardiography (2D-TEE), using three-dimensional (3D)-TEE makes it possible to image the entire AV. We hypothesized that measuring coaptation surface area (CoapSA) would be feasible and reproducible, and CoapSA would decrease in patients with aortic insufficiency. We developed a new technique to calculate the AV-CoapSA using 3D-TEE. We measured the coaptation surfaces between the right coronary cusp/left coronary cusp, right coronary cusp/non-coronary cusp, and left coronary cusp/non-coronary cusp in ten normal AVs and ten AVs with moderate-severe aortic insufficiency (AI). Since computer models have previously shown that CoapSA is trapezoidal, we used the formula: trapezoid area = length × (medial coaptation height + lateral coaptation height)/2. The total CoapSA was calculated by adding all three areas. To adjust for valve size, we indexed the value to the diameter of the ventricular aortic junction (VAJ). Measurements were performed by two observers. The intra-observer correlation was 0.84 for one observer (P < 0.0001) and 0.93 for the other (P < 0.0001). The inter-observer correlation was 0.87 (P < 0.0001). In normal valves, the CoapSA [mean total (standard deviation)] was significantly greater than in the insufficient valves [1.61 (0.31) cm(2) vs 1.03 (0.22) cm(2), respectively; P < 0.001]. After indexing for the VAJ diameter, the total CoapSA remained significantly greater in normal valves than in insufficient valves. In this proof of concept study, we present a new and innovative technique to measure AV-CoapSA using 3D-TEE. It is reproducible and shows decreased CoapSA in patients with AI. Coaptation surface area may provide insight into mechanisms of AI and may have predictive value following AV repair.

Transcutaneous electrical nerve stimulation in the prevention of postoperative nausea and vomiting after elective laparoscopic cholecystectomy

Study Objective To examine the effectiveness of transcutaneous electrical nerve stimulation (TENS) on postoperative nausea and vomiting (PONV). Design Randomized, prospective, controlled study. Setting Gazi University Medical School Hospital. Patients 40 ASA physical status I-II patients who underwent elective laparoscopic cholecystectomy. Interventions Patients were randomly divided into two equal groups. Group I received TENS (stimulation group), whereas group II served as the control group (nonstimulation group). In group I, one electrode was applied to the hairless skin on the neck as anode, and the other 2 (electrodes) were applied to the mastoid area. The stimulator at a frequency of 5 Hz, 50 milliseconds, with a current density of 0.5 to 4 mA was applied on the trapezoid area for 6 hours to all patients postoperatively. Measurements All patients in both groups were evaluated for side effects, antiemetic effects, and analgesic and antiemetic need for 24 hours. Main Results Postoperative nausea and vomiting, frequency of dizziness, additional antiemetic and analgesic need, and PONV scores were lower in group I than group II. Conclusions Electrical stimulation of the vestibular system may be useful in the prevention of PONV.

Evaluation of functional diversity of soil microbial communities - a case study

In our case study, we measured the functional diversity of the microbial communities of twelve soils from the small natural area to assess if this assay is suitable for routine monitoring of soil biological quality. We found the BIOLOG assay meets especially practical benefits in routine monitoring of soils being simple and quick assay. However, we confirmed the ambiguity about the most appropriate analysis of the BIOLOG multivariate data and about the best parameter, which can be derived from the assay. The different analyses of the data were examined and various parameters derived from the BIOLOG assay were comparatively used to contribute to the discussion of how the data should be evaluated. We showed that not-normalized raw absorbances or trapezoid areas should be used for calculation of diversity index if the inoculum was standardized. There was no single answer to what parameter provided more correct results in the multivariate statistical analysis. Evaluating at least one not-normalized (e.g. trapezoid area) and one normalized parameter (e.g. absorbances read in fixed AWCD) was strongly suggested keeping in mind that they reveal different information.

Terminology of the prostate and related structures.

The various studies of J.E. McNeal (1968ndash;1977) established with precision the different sites of predilection for prostatic carcinomas, benign prostatic hypertrophy (BPH), and inflammation, making the division of the prostate into right, left, and middle lobes and isthmus inadequate for their description. Unfortunately, his positional terms for the sites (peripheral, central, transition, and preprostatic) are not based on the usual parameters and cannot be directly related to those of other workers. Nevertheless, the International Federation of Associations of Anatomists' Federative Committee on Anatomical Terminology has made recommendations in Terminologia Anatomica, based on his findings but modified to take some account of those of Tisell and Salander (1975 Scand J Urol Nephrol 1975 9:185-191). The use of the term lobe is confined to the right and left lobes and the variable middle lobe. The term lobule is used for the subdivisions, which are named from the anatomical position. Thus each side has a superomedial, an anteromedial, an inferoposterior, and an inferolateral lobule. Also necessary to describe a site of predilection is a peri-urethral gland zone. In ultrasound diagnosis, the trapezoid area is important: its upper limit is the rectoperinealis, its anterior limit is the intermediate part of the urethra, its lower limit is the anoperinealis, and its posterior limit is the anorectal junction. Confusion at the bladder neck is resolved by recognizing that the position of the internal urethral orifice varies with functional state of the bladder: while it is filling the orifice lies above the base of the prostate; when voiding begins, the orifice descends to the base of the prostate; between the filling internal orifice and the emptying internal orifice is the bladder neck part of the urethra.

A very simple method for true elemental mapping using the scanning proton microprobe

An elemental map by means of SPM is traditionally obtained by total counts entering an energy window (TCEW) corresponding to a characteristic X-ray of that element. Besides the characteristic X-ray signals of the element, the total counts contain the contribution of continuum background and overlapping peaks of the interfering elements as well. A method called NCEW (net counts entering an energy window) has been developed for off-line true elemental mapping. The continuum background is calculated with a trapezoid area determined by the counts within border gates and is subtracted from the total counts of the peak. The branch ratios of the characteristic X-rays of the interfering elements are used to correct their overlapping peaks. Because the net counts eliminate the contribution of the background and the overlapping peaks from the total counts, the map obtained by the NCEW is free of artifacts due to the continuum background and the peak overlapping. This method was tested by scanning a microbeam over a multi-foil target. Applications of the NCEW method to some environmental and geological samples are described.

Prenatal development of cranial base in normal Korean fetuses.

The cranial base is not only an end result of complex segmental growth of rostral end of axial skeleton but also has a tremendous impact on the development of the brain and facial structure. However, little is known about the method for the systematic analysis of the shape of the cranial base in the developing human fetus. We used roentgenograms of the cranial base and eviscerated bones for the assessment of the development of the cranial bony complex. The cranial base was removed from 64 normal human fetuses after 18-40 weeks of gestation. Roentgenograms were taken perpendicular to the cranial base. Major anatomical landmarks are defined as follows: the center of pituitary fossa of sphenoid bone (point S), the growth center of zygomatic bone, the anterior point of nasal septum, otic cartilage, and anterior and posterior growth centers of maxilla. The anterior cranial base angle, the middle cranial base angle, the posterior cranial base angle, the maxillary trapezoid area, the horizontal middle face area, and the occipital cranial base triangle area are defined from the landmarks, and the growth of each parameter was analyzed by gestational age. The proportional growth of the anterior, middle, and posterior cranial fossae could be assessed by the angles around the center of the pituitary fossa (point S) and by the anterior, middle, and posterior cranial base angles. The anterior cranial base angle was relatively constant during the fetal period at 107.4-112.5 degrees, whereas the middle cranial base angle gradually increased, and the posterior cranial base angle decreased. With increasing gestational age, the horizontal middle face area increased rapidly, in contrast to those of the maxillary trapezoid area, occipital cranial base triangle area, or foramen magnum area. The important keys in the structural development of the normal human cranial base are anterior, middle, and posterior cranial base angles. We could define the developmental pattern of human cranial base, which in turn provides a model of a standard growth pattern applicable to the study of the different malformations in the craniofacial structure.

Full‐wave analysis using a tangential vector finite‐element formulation of arbitrary cross‐section transmission lines for millimeter and microwave applications

AbstractA tangential vector finite‐element formulation is implemented to deal with arbitrary cross section and metallic strip shape. Classical planar transmission lines as well as nonconventional cross‐section waveguides such as the new microshield line are treated. Effects on propagation characteristics for these lines are studied when the metallization shape is approximated by a lossy trapezoid area. © 1994 John Wiley &amp; Sons, Inc.

Localization of the prostatic apex for radiation therapy using implanted markers

Purpose : This report concentrates on the localization of the prostatic apex using implantable markers, and a comparison to localization defined by computed tomography (CT) and retrograde urethrography. Methods and Materials : Fifteen patients were entered into a prospective trial and scheduled to undergo (a) pelvic CT, (b) retrograde urethrogram, and (c) transrectal ultrasound with placement of radiodense markers. Three markers were implanted: one was placed at the trapezoid area (prostatic apex), and the others placed lateral to the base of each seminal vesicle. The retrograde urethrogram was performed using standard technique. The superior-inferior distance between the apex identified by the marker placed at the prostatic apex and the other studies was measured. Results : CT and urethrogram overestimated the inferior extent of the prostatic apex when compared to the location as defined by the implanted marker. With CT, the average distance from the marker to the Cr-defined apex was 0.6 cm (95% C.I.-0.4-0.8 cm). With urethrogram, the average distance from the marker to the urethrogramdefined apex was 1.3 cm (95% C.I.-0.7-1.9 cm). When CT and urethrogram were compared, Cr was more accurate in identifying the prostatic apex. Conclusion : Under ultrasound guidance, radiodense markers have been implanted into the prostate. This has revealed that the apex is localized superior to the apical margin as defined by retrograde urethrogram and CT, and that CT may be more accurate than retrograde urethrogram. In addition, the placement of multiple markers yields spatial information on prostatic position that can be extracted from megavoltage portal images.

The Number and Size of the Follicular Epithelium (FE) and Follicles in the Bursa of Fabricius

In a four-week-old chicken .1 ml carbon solution was deposited on the vent. The carbon was sucked into the lumen of the bursa and absorbed by the follicular epithelium which appeared as black dots on the surface of the folds. The number of black dots on the surface of a fold represents the number of follicles per fold. The average nummber of follicles per fold was 820. Since the number of folds per bursa ranges between 10–15, we were able to calculate 8000–12000 follicles per bursa. The volumetric mathematical analysis of the follicles and folds confirmed our calculated number of follicles. On a stereomicrograph from a randomly selected area of a fold surface, a trapezoid was outlined and measured. The surface analysis of the black dots within a trapezoid area revealed that about 10% of the bursal surface was covered by follicular epithelium which is immunologically oriented.