top of page
guicocodtosi

Diameters and Circumferences: The Basics of Geometry



Background/Purpose. Recent findings suggest that an objective assessment of retinal vessel caliber from fundus photographs provide information about the association of microvascular characteristics with macrovascular disease. Current methods used to quantify retinal vessel caliber, introduced by Parr(1,2) and Hubbard,(3) are not independent of scale and are affected by the number of vessels. To improve upon these methods we introduce revised formulas for quantifying vessel caliber. Methods. Revised formulas were estimated using retinal vessel measurements from 44 young adults free of hypertension and diabetes. Comparisons between the two methods were done using digitized photographs from 4926 participants at the baseline examination of the Beaver Dam Eye Study (BDES), an ongoing population-based cohort study initiated in 1987. Individual arterioles and venules were measured using semi-automated computer software from which summary measures were calculated. Results. Correlation coefficients between the Parr-Hubbard and revised formulas were high (Pearson correlation coefficients ranging from 0.94 to 0.98). Both arteriolar and venular caliber significantly increased with an increasing number of vessels measured using the Parr-Hubbard formulas (p 0.50). Conclusions. We describe revised formulas for summarizing retinal vessel diameters measured from fundus photographs to be used in future studies and analyses. The revised formulas correlate highly with the previously used Parr-Hubbard formulas, but offer the advantages of being more robust against variability in the number of vessels observed, being independent of image scale, and being easier to implement.


Current screening and detection of asymptomatic aortic aneurysms is based largely on uniform cut-point diameters. The aims of this study were to define normal aortic diameters in asymptomatic men and women in a community-based cohort and to determine the association between aortic diameters and traditional risk factors for cardiovascular disease. Measurements of the diameters of the ascending thoracic aorta (AA), descending thoracic aorta (DTA), infrarenal abdominal aorta (IRA), and lower abdominal aorta (LAA) were acquired from 3,431 Framingham Heart Study (FHS) participants. Mean diameters were stratified by gender, age, and body surface area. Univariate associations with risk factor levels were examined, and multivariate linear regression analysis was used to assess the significance of covariate-adjusted relations with aortic diameters. For men, the average diameters were 34.1 mm for the AA, 25.8 mm for the DTA, 19.3 mm for the IRA, and 18.7 mm for the LAA. For women, the average diameters were 31.9 mm for the AA, 23.1 mm for the DTA, 16.7 mm for the IRA, and 16.0 mm for the LAA. The mean aortic diameters were strongly correlated (p




diameters



In more modern usage, the length d \displaystyle d of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice the radius r . \displaystyle r.


For an ellipse, the standard terminology is different. A diameter of an ellipse is any chord passing through the centre of the ellipse.[2] For example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one diameter is parallel to the conjugate diameter. The longest diameter is called the major axis.


In planar geometry, a diameter of a conic section is typically defined as any chord which passes through the conic's centre; such diameters are not necessarily of uniform length, except in the case of the circle, which has eccentricity e = 0. \displaystyle e=0.


Contrast-enhanced CMR angiography (CE-CMRA) is being increasingly used for diagnosing aortic arch anomalies, planning interventions and follow-up assessment. We sought to establish normal values for the diameters of the thoracic aorta and reference curves related to body growth in children using CE-CMRA.


This study provides normative values for aortic diameters in children measured by CE-CMRA. These data may serve for making the diagnosis of pediatric arch anomalies, assessing the need for treatment and planning interventions.


The aortic diameters were measured at nine standardised sites, consisting of the aortic sinus (AS), sinotubular junction (STJ), ascending aorta at the level of the right pulmonary artery (AA), proximal to the brachiocephalic artery (BCA), first transverse segment (T1), second transverse segment (T2), isthmic region (IR), descending aorta at the level of the left pulmonary artery (DA) and the thoracoabdominal aorta at the level of the diaphragm (D) (figure 1). Each aortic segment was first reconstructed in two double oblique planes. The first plane was set through the longitudinal axis of the vessel corresponding to a left anterior view, as performed in conventional angiograms during catheterization. The second plane was set perpendicularly to the first one along the longitudinal axis of the vessel. Both planes were chosen to be as thick as the vessel itself, in order to assure inclusion of the vessel at its maximal diameter. Finally, a plane perpendicular to both longitudinal views was created and a true cross-section of the vessel obtained with the minimum possible slice thickness (figure 2). Two perpendicular aortic diameters were measured on both the longitudinal images and the cross-sectional images at the corresponding vessel sites.


Measurements from longitudinal MIP images and cross-sectional planes were compared using Bland-Altman analysis [13]. The variability of the measurements was assessed by calculating coefficients of variability (i.e. the standard deviation of the difference divided by their mean). Since aortic cross-sections were observed to be often slightly oval shaped, the shortest diameter passing the centre of the vessel was considered to accurately represent the vessel diameter. The aortic diameters were displayed in relation to BSA0.5 for each measurement site. The best statistical model was defined by a small R2 and analysis of residuals, when comparing the results of regression analysis using linear functions (diameter = a + b*bsa), power functions (diameter = b*bsa^c) (diameter = a + b*bsa^c) and second order polynomial functions (diameter = a+b*bsa + c*bsa^2).


The range of the diameters for each aortic segment is presented in table 1. A common origin of the brachiocephalic and the left common carotid arteries was observed as a normal anatomical variant in 9 patients (20%). Thus the diameter of the first transversal segment could only be measured in 44 subjects. No additional anatomical variants were observed.


A linear relationship between aortic diameters and the square root of BSA was found to be the best model for regression (diameter = a + b*BSA0.5). The correlation curves between aortic diameters and BSA for each aortic segment are shown in figure 3. The regression equations and the corresponding standard deviation of residuals are presented in table 2. Z-values for each aortic diameter can be calculated from the values reported in table 2 as follows:


This study provides normative values for the diameters of the thoracic aorta in children and adolescents measured in 9 different segments in vivo using CE-CMRA. These represent the first normal data published for this technique in pediatric patients.


For this study we utilized similar measurement sites and statistical model as Sluysmans, who performed echocardiographic measurements of the aorta in a large pediatric population. We found minimally larger diameters for small children, but the values for adolescents were consistent in both studies [7].


Body growth is a complex and variable process and its description always represents a simplification. The extensive work done so far for understanding the relationship between somatic growth and development of the cardiac structures suggests that growth of vascular diameters is best described by using a linear relationship between the diameter and the square-root of BSA [7, 20]. The different statistical analyses that we performed on our data confirmed this observation; therefore we chose to represent the results graphically as a linear regression between the aortic diameters and BSA0.5. Among several formulas than can be used for the calculation of BSA, the one described by Mosteller is known to be accurate for children and is convenient for clinical use [14].


By using an adequate slice thickness for the MIP reconstruction in a longitudinal plane at the aortic root, atrial structures may partially superimpose the aorta and make proper visualization of the vascular border difficult. On the basis of these observations, we decided to use cross-sectional measurements for calculation of linear regression in all locations. Measurements of the diameters in both, cross-sectional and longitudinal imaging planes, demonstrated a negligible mean difference of 1% and a limited variability. Moreover, we found most reconstructed cross sections of the aorta to be slightly oval. For clinical use and considering all potential factors which may limit the accuracy of the measurements, including slightly oblique transsection of the vessel when reconstructing, repeatability of the measurements and vessel pulsation, we considered the short diameters to best represent the diameter of the vessel. Analysis of the difference between short diameters and the geometrical means of the short and long diameter resulted in a difference smaller than 1 mm (percentual smaller than 5%), which has to be considered as not significant.


The most important limitation of our study is the lack of data acquired in small children with a BSA smaller than 0.5 m2. Sluysmans et al described a linear correlation between the aortic diameters and BSA0.5 for small children with a body size within this range [7]. Although an extrapolation from our data for smaller children would be possible, such extrapolation may potentially increase errors in the calculated regression coefficients. Therefore, we do not recommend the use of our normograms for children smaller than BSA 0.5 m2. 2ff7e9595c


0 views0 comments

Recent Posts

See All

Nswhatsapp 3 orange apk

NSWhatsApp 3 Orange APK: uma nova maneira de aproveitar o WhatsApp Você está entediado com o mesmo velho aplicativo WhatsApp no seu...

Comments


bottom of page