Conjugate Diameters Research Articles

A survey of pelvic types on computed tomography images

BackgroundIn the medical literature several classifications of the pelvis according to its shape can be found. The most common classification distinguishes four general pelvis types: gynecoid, android, anthropoid and platypelloid. Natural childbirth may be significantly prolonged, difficult or even impossible if the pelvis shape is not in proportion to the size of the fetus. The objectives of our study were to calculate major diameters and conjugate diameters of the female bony pelvic ring and to determine the major pelvic types according to their shape. Based on the parameters obtained, we aimed to establish a relationship between some pelvic types and difficult childbirth. MethodsThe study was prospective in design and included 54 female subjects of various ages who had been referred for computed tomography of the pelvis, as part of the diagnosis of an underlying condition. In each patient, five most important parameters in two planes were measured and the pelvic type was determined by using the brim index and a special formula for android type. All measurements were performed using the Vue PACS v 12.1.6.1005 program. The description of the pelvic inlet was used to confirm all pelvic types. Data on previous births were taken from the questionnaire filled out by the subjects during the radiological examination. ResultsGynecoid pelvic type was the most common in our sample (28 pelvises – 52%), followed by platypelloid type (11 pelvises – 20%), anthropoid type (8 pelvises – 15%) and finally android type (7 pelvises – 13%). There was a statistically significant difference in the diameter bispinous length (p < 0.05) between the platypelloid and anthropoid pelvic types. Pathological degree of stenosis was present in seven pelvises (the first degree in six pelvises and the second degree in one pelvis). The frequency of cesarean section was 31.82% and this technique was most frequently used in the subjects with a gynecoid pelvic type. The duration of natural labor ranged from 4 to 18 h. There was no statistically significant difference in the duration of labor between subjects with different pelvic types. ConclusionsGynecoid pelvic type was present in more than half of our subjects. Although this type is considered ideal for labor, we have not established that it has a great influence on whether the labor will be performed naturally or by cesarean section, neither that it significantly affects the length of birth. The gross narrowing of the pelvic ring is present in non-gynecoid pelvic types. The data obtained will certainly be useful to the obstetrician when planning the labor and considering all the factors that may affect the course of birth.

Conics in Place

A method is presented for creating a problem, solving it, and confirming that the solution is correct. The problem is to analyze a second-degree polynomial equation in two variables, in order to identify and draw the defined conic section, with its axes, without changing coordinates. One creates the problemby choosing conjugate diameters that are not axes.

Neonatal Size and Birth Canal Dimensions

The limitation of the fetal growth process during pregnancy is supposed to be an adaptative response to a physical or a physiological constraint: the pelvic size or the maternal resources and metabolism. In this study 131 mother-infant dyads were recruited. We investigate correlation between maternal traits (height, BMI) pelvic variables (conjugate diameter, inter-spinous diameter, sub-pubic angle) and neonatal traits (gestational age, birthweight, head, suboccipito-brematic and abdominal girth). We found that the three neonatal variables are significantly inter-correlated. Among maternal traits, height is highly correlated with conjugate and inter-spinous diameters. Subpubic angle is correlated with inter-spinous diameter. Among neonatal and pelvimetry correlations, conjugate diameter is highly correlated with suboccipito-bregmatic girth. The pelvic size seems to be the primary constraint to the fetal growth process. This adjustement of fetus size to the birth canal dimensions limits the risk of dystocia. But the way this adjustement occurs at the end of pregnancy is unclear. We assume that the uterus expansion limitation may be an intermediate mechanism explaining the high correlation between pelvic and neonatal traits.

Кривые второго порядка на экране компьютера

Modern computer graphics is based on methods of computational geometry. The curves and surfaces’ description is based on apparatus of spline functions, which became the main tool for geometric modeling. Methods of projective geometry are almost not applying. One of the reasons for this is impossibility to exactly construct a second-order curve passing through given points and tangent to given straight lines. To eliminate this defect a computer program for second order curves construction has been developed. The program performs the construction of second-order curve’s metric (center, vertices, asymptotes, foci) for following combinations: • The second-order curve is given by five points; • The second-order curve is given by five tangent lines; • The second-order curve is given by a point and two tangent lines with points of contact indicated on them; • The parabola is given by four tangent lines; • The parabola is given by four points. In this paper are presented algorithms for construction a metric for each combination. After construction the metric the computer program written in AutoLISP language and using geometrically exact projective algorithms which don’t require algebraic computations draws a second-order curve. For example, to construct vertices and foci of two parabolas passing through four given points, it is only necessary to draw an arbitrary circle and several straight lines. To construct a conic metric passing through five given points, it is necessary to perform only three geometrically exact operations: to construct an involution of conjugate diameters, to find the main axes and asymptotes; to note the vertices of desired second-order curve. Has been considered the architectural appearance of a new airport in Simferopol. It has been demonstrated that a terminal facade’s wavelike form can be obtained with a curve line consisting of conic sections’ areas with common tangent lines at junction points. The developed computer program allows draw second-order curves. The program application will promote the development of computer graphics’ tools and techniques.

Central quadrics in Euclidean n-space - metric and focal properties

In this paper metric properties of central quadrics and cones in n-dimensional Euclidean space are discussed. Basic statements on the system of confocal regular quadrics are proved, and some interesting analogues of famous three-dimensional theorems are given for higher dimension, such as the Apollonian theorem on pedal curves. We also investigate systems of focal cones, and in particular we determine the common lines of focal cones in any dimension. As further applications of our approach and of our formulas we give a detailed description of the construction of Chasles on conjugate diameters, and the wire model of Staude is also given.

On the constructibility of the axes of an ellipsoid: the construction of Chasles in practice

In this paper we discuss Chasles’s construction on ellipsoid to draw the semi-axes from a complete system of conjugate diameters. We prove that there is such situation when the construction is not planar (the needed points cannot be constructed with compasses and ruler) and give some others in which the construction is planar.

Heat transfer and turbulent flow characteristics over pocket cavity in the junction part of an outlet guide vane in a gas turbine

A pocket cavity is generated when the Low Pressure Turbine (LPT) is connected to the Outlet Guide Vane (OGV) in the rear part of a gas turbine engine due to the different conjugate diameters. This kind of pocket cavities, due to the high Reynolds number and the specific shapes, are hardly investigated in previous researches. The heat transfer distribution and fluid flow over the pocket cavity have significant effects on the incoming flow of the OGV in the downstream distribution. In the present work, the specified triangular pocket cavities are built in a high aspect ratio channel and heat transfer and fluid flow over the pocket surface are investigated experimentally and numerically. These pocket cavities are built with different radii to find out optimized heat transfer distributions and flow patterns. Liquid Crystal Thermography (LCT) is employed to measure heat transfer over the pocket surfaces at Reynolds number ranging from 87,600 to 219,000. Flow details are provided by numerical calculations with a suitable turbulence model. In this study, the largest heat transfer regions over a pocket cavity are found to be at the downstream edge where strong flow impingement occurs. The peak values are influenced by the size of the fillet radius. The smaller fillet radius provides a higher heat transfer peak value with a stronger recirculating flow inside the pocket cavity. However, the pocket cavity with the larger fillet radius can reduce the peak heat transfer values but increase the overall averaged heat transfer value of the pocket surface with weakened strength of the recirculating flows. Accordingly, the larger fillet radius is recommended for the design of the pocket cavity in the rear part of a gas turbine engine.

Influence of pelvic volume on surgical outcome after low anterior resection for rectal cancer.

Low anterior resection (LAR) for rectal cancer is a potentially challenging operation due to limited space in the pelvis. CT pelvimetry allows to quantify pelvic space, so that its relationship with outcome after LAR may be assessed. Studies investigating this, however, yielded conflicting results. We hypothesized that a small pelvis is associated with a higher rate of incomplete mesorectal excision, anastomotic leakages, and increased rate of urinary dysfunction in patients operated for rectal cancer. In a single-center retrospective analysis, we studied 74 patients that underwent LAR for rectal cancer with primary anastomosis. Thin-layered multi-slice CT datasets were used for slice by slice depiction of the inner pelvic surface, and the inner pelvic volume was automatically compounded. The primary outcome was quality of total mesorectal excision (TME; Mercury grading); secondary outcomes were anastomotic leakage and urinary dysfunction with regard to pelvic dimensions. Univariate analyses and multiple logistic regression analyses were performed for the primary and the secondary outcomes. Shorter obstetric conjugate diameters were associated with a higher probability of a worse TME quality (110.8±10.2 vs. 105.0±8.6mm; OR 0.85; 95% CI 0.73-0.99; p=0.038). Short interspinous distance showed a trend towards an increased risk for deteriorated TME quality (OR 0.88; 95% CI 0.76-1.0; p=0.06). Anastomotic leakage was associated with anemia (OR 2.77; 95% CI 1.0-7.7; p=0.047). Association between pelvic diameters or pelvic volume and anastomotic leakage or urinary dysfunction was not observed. Perioperative blood transfusions were administered more often in patients with postoperative urinary dysfunction (OR 17.67; 95% CI 2.44-127.7; p=0.004). Shorter obstetric conjugate diameter might be a risk factor for incompleteness of total mesorectal excision. Anastomotic leakage seems to be influenced more by clinical factors such as anemia rather than pelvic dimensions. Further studies have to prove the influence of pelvic diameter on local recurrence of rectal cancer after LAR.

Maternal pelvic dimensions and neonatal size: Implications for growth plasticity in early life as adaptation.

Patterns of fetal growth predict non-communicable disease risk in adult life, but fetal growth variability appears to have a relatively weak association with maternal nutritional dynamics during pregnancy. This challenges the interpretation of fetal growth variability as ‘adaptation’. We hypothesized that associations of maternal size and nutritional status with neonatal size are mediated by the dimensions of the maternal pelvis. We analysed data on maternal height, body mass index (BMI) and pelvic dimensions (conjugate, inter-spinous and inter-cristal diameters) and neonatal gestational age, weight, length, thorax girth and head girth (n = 224). Multiple regression analysis was used to identify independent maternal predictors of neonatal size, and the mediating role of neonatal head girth in these associations. Pelvic dimensions displaced maternal BMI as a predictor of birth weight, explaining 11.6% of the variance. Maternal conjugate and inter-spinous diameters predicted neonatal length, thorax girth and head girth, whereas inter-cristal diameter only predicted neonatal length. Associations of pelvic dimensions with birth length, but not birth weight, were mediated by neonatal head girth. Pelvic dimensions predicted neonatal size better than maternal BMI, and these associations were mostly independent of maternal height. Sensitivity of fetal growth to pelvic dimensions reduces the risk of cephalo-pelvic disproportion, potentially a strong selective pressure during secular trends in height. Selection on fetal adaptation to relatively inflexible components of maternal phenotype, rather than directly to external ecological conditions, may help explain high levels of growth plasticity during late fetal life and early infancy.

Geometric construction of an ellipse from its moments

This paper oers a trio of Euclidean constructions of an ellipse given its rst moments and second central moments. The crux of these constructions lies in the graphical construction of Carlyle [4, p. 99] and Lill [2] for the roots of a quadratic and the Pappus-Euler problem [12] of the construction of the principal axes of an ellipse from a pair of its conjugate diameters. Mathematics Subject Classication : 51M15, 51N20

A matrix-vector analytic demonstration of Pappus' construction of an ellipse from a pair of conjugate diameters

A matrix-vector analytic demonstration is provided for Pappus’ construction of the principal axes of an ellipse from a pair of its conjugate diameters. Mathematics Subject Classification: 15A72, 51M15, 51N20

A three-dimensional reconstructive study of pelvic cavity in the New Zealand rabbit (Oryctolagus cuniculus).

The present study has been performed to reveal biometrical aspects and diameter-related differences in terms of sexes regarding pelvic cavity via three-dimensional (3D) reconstruction by using multidetector computed tomography (MDCT) images of pelvic cavity of the New Zealand rabbit. A total of 16 adult New Zealand rabbits, including 8 males and 8 females, were used in this study. Under anesthesia, the images obtained from MDCT were stacked and overlaid to reconstruct the 3D model of the pelvic cavity using 3D modeling software (Mimics 13.1). Measurements, such as the conjugate, transverse, and vertical diameters of the pelvic cavity, and the pelvic inclination were calculated and analyzed statistically. Biometrical differences of the pelvic diameters in New Zealand rabbits of both sexes were shown clearly. It was concluded that the pelvic diameters revealed by 3D modeling techniques can shed light on medical students who take both anatomy training and gynecological applications. The authors hope that the synchronization of medical approaches may give rise to novel diagnostic and therapeutic developments related to pelvic cavity.

A vector analytic demonstration of Pappus' construction of an ellipse from a pair of conjugate diameters

A vector analytic demonstration of Pappus' construction of an ellipse from a pair of conjugate diameters

Smaller pelvic size in pregnant adolescents contributes to lower birth weight

Adolescent pregnancy is associated with low birth weight. This has been explained by socioeconomic or emotional factors. However, an adolescent's pelvis may not be completely developed and this can contribute to impairing fetal growth. Our aim was to compare the relationship between pelvic size and birth weight among adolescents and adult mothers. A cross-sectional study was carried out at Instituto de Medicina Infantil Professor Fernando Figueira (IMIP), Brazil. We studied 125 healthy adolescents and 207 healthy adult women, all of whom were primiparous with a singleton term and low-risk pregnancy. The conjugate, intercristal and interspinous diameters were assessed by the Collins pelvimeter. The effect of pelvic size on the birth weight was evaluated using principal component analysis and multiple linear regression model. The mean pelvic size was smaller in adolescent mothers compared to adult ones (35.1 cm vs. 37.5 cm; p<0.001; t-test). After adjusting for other confounding variables, the predicted birth weights corresponding to these mean values of pelvic size were: 3020±27 g for adolescent mothers and 3145±26 g for adult mothers and showed a significant difference (p<0.001). We concluded that a pelvis that is less than fully developed in adolescents, as assessed by pelvic size, may contribute to lower birth weight in adolescent mothers.

A matrix analytic approach to conjugate diameters of an ellipse

Herein, problems pertaining to the conjugate diameters of a nondegenerate ellipse are studied within a matrix analytic framework. Pride of place is reserved for the construction of the matrix associated with the positive definite quadratic form defining a nondegenerate ellipse from a pair of its conjugate diameters. Mathematics Subject Classification: 15A18, 15A23, 15A24, 51N20

On Euler's synthetic demonstration of Pappus' construction of an ellipse from a pair of conjugate diameters

On Euler's synthetic demonstration of Pappus' construction of an ellipse from a pair of conjugate diameters

An experimentally validated and parameterized periodic unit-cell reconstruction of open-cell foams

The physical behavior of open-cell foams depends on their microscopic structure. An open-cell geometrical model is proposed, which can serve as the basis for a future macroscopic analysis. The strut geometry is of particular interest, as it is reported to have substantial influence on the occurring thermo-hydraulic and mechanical phenomena. Axial strut size variation, as well as the porosity dependence of shape is quantified and included in a geometrical model. The foam is generated by placing the struts on an elongated tetrakaidecahedron. The required input parameters for the model are two cell dimensions, corresponding to the mean transverse and conjugate diameters of the ellipse encompassing a cell, and the strut cross-sectional surface area at its midpoint between two nodes. The foam geometry is generated iteratively, as porosity is used as validation. A high resolution micro-computed tomography scan is performed to measure the three parameters, the resulting porosity and surface-to-volume ratio. This allows to validate the model. The predictions are found to be within measurement accuracy. A numerical implementation of the model in the preprocessor of a commercial CFD package is demonstrated.

Factors Affecting the Outcome of Extraperitoneal Laparoscopic Radical Prostatectomy: Pelvic Arch Interference and Depth of the Pelvic Cavity

PurposeTo determine the effect of pelvic arch interference and the depth of the pelvic cavity, as shown on preoperative magnetic resonance imaging (MRI), on the performance of extraperitoneal laparoscopic radical prostatectomy (ELRP).Materials and MethodsIn 115 patients, pelvic bone images were obtained at the time of prostate MRI before ELRP. In the reconstructed sagittal plane, we measured the true conjugate diameter, the obstetric conjugate diameter, the difference between the true and obstetric diameters, and the distance between the true conjugate and the prostate apex (pelvic depth). We analyzed which factors were associated with operative time (OT), estimated blood loss (EBL), and positive surgical margins (PSMs).ResultsThe difference between the true and obstetric conjugate diameters was 12.7±3.7 mm, and the pelvic depth was 59.9±6.0 mm. The OT, EBL, and the rate of PSMs were 260.1±91.1 minutes, 633.3±524.7 ml, and 19% (22/115), respectively. According to multiple linear regression analysis, predictors of a higher EBL included pelvic depth (3.0% higher per 1 mm increase in diameter difference, p=0.01) and prostate volume (1.5% higher per 1 cc increase in prostate volume, p=0.002). Factors associated with a longer OT were pelvic depth (p=0.04), serum prostate-specific antigen (p=0.04), prostate volume (p=0.02), and Gleason score (p=0.001). For PSMs, only pT2 was an independent factor.ConclusionsOur results suggest that the depth of the pelvic cavity and prostate volume may increase surgical difficulty in patients undergoing ELRP.

Maternal and Social Origins of Hypertension

We previously reported that in 2003 people from the Helsinki birth cohort whose blood pressures were measured, 2 different paths of growth preceded the development of hypertension. People already diagnosed with hypertension were small at birth but of average body size at age 11 years. People newly diagnosed with hypertension grew slowly in utero and through childhood. We have now examined how the mother's body size, placental size, and living conditions after birth, 3 influences that affect growth, affect hypertension. Diagnosed hypertension was associated with low placental weight and poor living conditions after birth. The odds ratios were 1.6 (95% CI, 1.1 to 2.3) in people with placental weights <550 g, compared with those with weights >750 g, and 2.2 (95% CI, 1.5 to 3.3) in people whose fathers were laborers compared with those in upper middle-class families. Newly diagnosed hypertension was associated with a small anteroposterior diameter of the mother's bony pelvis, a known consequence of rickets or lesser degrees of malnutrition in infancy. The odds ratio was 2.2 (95% CI, 1.4 to 3.5) in people whose mothers' pelvic external conjugate diameters were <18 cm when compared with people whose mothers' diameters were >/=19 cm. We conclude that one path of growth that leads to hypertension is initiated by fetal undernutrition, which may make a baby vulnerable to postnatal stress, whereas the other originates in a functional incapacity in the mother's metabolism, possibly protein metabolism, which she acquired through undernutrition during her infancy.

Changes in anthropometric and metabolic parameters in pregnancy and neonatal physical development during last decades

To evaluate changes in anthropometric and biochemical parameters in pregnancy and their dynamics during last two decades and to determine the association between anthropometric and biochemical parameters, their influence on fetal and neonatal development. In 1985-2005, anthropometric (height, body mass, weight gain during pregnancy, pelvic measurements, skinfold thicknesses, passive body mass) and biochemical (cholesterol, triglyceride, protein, and iron levels) parameters, their correlation, changes in pregnancy were examined; also the correlations between these parameters and neonatal body mass indices were evaluated. In 1986-1987, 383 pregnant women were examined, in 1998--130, and in 2003-2005--133. During 20 years, the height of examined women increased on an average of 2.5 cm; they became thinner; body mass index decreased. The body composition became similar to "cylinder" shape due to decreased thickness of adipose tissue in the limbs. The dimensions of bony pelvis--external conjugate and bicristal diameters--decreased. Primiparous women became older (1995--22.5 years of age, 2004--27.6). At the beginning of investigation, the weight gain was on an average of 21.9% of body mass before pregnancy (13.3 kg) and at the end--23.9% (14.2 kg). The values of anthropometric parameters vary in a consistent pattern during pregnancy: the lower body mass and body mass index at the beginning of pregnancy, the higher weight gain at the end of pregnancy. Blood serum levels of cholesterol, triglycerides, and especially iron were decreased during the study. An inverse correlation between body mass index and lipid metabolism in pregnancy was revealed: the higher body mass index was at the beginning of pregnancy, the lower increase in lipid concentration was during pregnancy. At the beginning of investigation as well as after 20 years, women with low body mass index showed the most significant anthropometric and lipid metabolic changes in pregnancy.