Elliptical Annulus Research Articles

Mid-term repair durability after MitraClip implantation in patients with functional mitral regurgitation

The aim of this study was to identify variables that are associated with the durability of percutaneous repair of secondary mitral regurgitation at 6-month follow-up. Thirty-five consecutive patients with functional mitral regurgitation scheduled for MitraClip implant were enrolled. Left ventricular (LV) volumes and function and mitral valve characteristics were assessed before and immediately after MitraClip implantation using three-dimensional transesophageal echocardiography. Five patients with an unsuccessful procedure were excluded. The other patients were subdivided according to repair durability: group 1 with a durable repair (19 patients, 65%) and group 2 with significant mitral regurgitation recurrence (11 patients, 35%). At baseline, group 1 patients had smaller and more elliptical mitral valve annulus (1055 ± 241 vs. 1273 ± 359 mm, P = 0.02 and 125 ± 11 vs. 117 ± 16%, P = 0.02), a smaller left atrial volume (54.1 ± 26 vs. 71.5 ± 20 ml, P = 0.005) and lower systolic pulmonary artery pressure (38 ± 11 vs. 49 ± 12 mmHg, P = 0.03). Baseline LV end systolic volume had a linear correlation with the 3D annulus area (P = 0.048) and an inverse correlation with annulus ellipticity (P = 0.021). Group 1 patients showed an increase in annulus ellipticity after MitraClip (125 ± 17 vs. 141 ± 23%, P = 0.014). Percutaneous mitral valve repair leads to a significant and stable mitral regurgitation reduction in a large number of patients. Annulus dimensions and remodeling as well as left atrial area and pulmonary hypertension seem to be associated with durability of the procedure.

Correlation between laser speckle flowgraphy and optical coherence tomography angiography measurements in normal and glaucomatous eyes.

PurposeTo investigate the relationship between laser speckle flowgraphy (LSFG) and optical coherence tomography angiography (OCTA) measurements of the peripapillary retina and optic nerve head (ONH) in normal eyes and eyes with primary open-angle glaucoma (POAG).Patients and methodsOne eye from each of 46 normal subjects and mild and moderate/advanced POAG patients were included. ONH blood flow acquired by LSFG, circumpapillary vessel density (cpVD, a 250 μm-wide elliptical annulus around the optic disc), and intra-papillary vessel density (ipVD, a 1.5×1.5 mm scan field) acquired by OCTA were measured. Their values were compared among normal controls and patients at each stage of glaucoma using one-way ANOVA, and the correlation between measurements obtained by the two methods was examined by univariate regression analysis.ResultsONH tissue blood flow, tissue mean blur rate (MBR-T), and cpVD in the outer layer of the retina significantly decreased with the progression of glaucoma stage, although the latter showed no significant difference between normal subjects and mild-stage glaucoma patients. MBR-T was significantly correlated with cpVD, but not with ipVD, in the retinal outer layer.ConclusionA correlation was found only between MBR-T and cpVD in the retinal outer layer. A difference in MBR-T, but not in cpVD, was detected between normal controls and mild glaucoma patients.

The relation of left ventricular geometry to left ventricular outflow tract shape and stroke volume index calculations.

Stroke volume (SV) and aortic valve area calculations require the left ventricular (LV) outflow tract (LVOT) or aortic annular area calculations that involve squaring the respective diameters. Area calculation errors became evident with transcatheter aortic valve replacement where areas were underestimated due to an elliptical annulus. We hypothesized that LVOT and annular shape are more elliptical in patients with greater relative LV wall thickness (RWT) leading to underestimation of SV index using 2D Doppler echocardiography. We studied 203 consecutive patients referred to an outpatient noninvasive laboratory for Doppler echocardiograms which included acceptable 3-dimensional images. 3-dimensional assessment of the LVOT at 3-5mm from the valve insertion, at the site of valve insertion, and at the sinus of Valsalva (SOV) was performed with assessment of the minor axis (MN), major axis (MJ), and areas at mid-systole. SV index was calculated from LVOT and annular diameters obtained from 2-dimensional echo and from 3-dimensional LVOT areas. An inverse relation of RWT with MN/MJ at mid-systole for the LVOT (r=0.5812, P<0.0001) and annulus (r=0.6865, P<0.0001) was noted. LVOT and annulus areas were similar among groups at mid-systole. SV index calculated from 2D LVOT dimensions was significantly smaller than using 3D LVOT areas (35.6±8.9 vs 53.6±16.1mL, P<0.0001). There is an inverse relation between MN/MJ and RWT at the LVOT and aortic annulus despite the LVOT and annular areas being similar across most geometries resulting in SV index underestimation calculated using LVOT diameters vs 3D LVOT areas.

Modeling of laminar flow in an eccentric elliptical annulus for YPL fluid

The precise and convenient calculation of bottom hole pressure can provide a guarantee for safe drilling. Most of the existing models for determining the downhole pressure or annular pressure gradient (PG) are applied only to the circular wellbore. Due to the nonuniform in situ stress and the anisotropism of formation rock, the borehole formed by rotary drilling is the closest to the ellipse, that is, the irregular circular borehole. Therefore, it is of importance to research YPL fluid flow through the eccentric elliptical annulus (EEA) for the accurate prediction of bottom hole pressure. In this paper, a numerical model for determining the PG of YPL fluid flow in the EEA is developed on the basis of fluid mechanics. Then, through parameter studies, a new regression model (RM) of the pressure ratio in the EEA is established. The commercial software ANSYS was used to research the laminar flow of yield-power-law fluids through the EEA, and the simulation results are used to verify the numerical model and new regression model. The main conclusions are as follows. (1) The PG increases quasi-linearly or linearly with the mean velocity, fluid consistency index and yield stress and hardly changes with the azimuth of the inner pipe center. The PG decreases with a/b (η) and eccentricity (ε) when the mean velocity is constant. (2) The new regression model is valid for the ranges 0.2≤Kd ≤ 0.8, 0≤ε ≤ 0.95, 0.2 ≤ n ≤ 1.0, and 1.0≤η ≤ 1.2 and shows excellent agreement with existing model and computational fluid dynamics (CFD) simulations, within ±5% error bars. (3) The maximum velocity first increases and then decreases with ε. The results of axial velocity and PG using CFD software are found to be in excellent agreement with the numerical model solutions. (4) Predicting the PG in the EEA using the new regression model has high precision and without complicated numerical computation.

Nanofluid Convective Heat Transfer Enhancement Elliptical Tube inside Circular Tube under Turbulent Flow

Heat transfer enhancement employing an elliptical tube inside a circular tube to increase the heat transfer rate without increasing in pressure drop is investigated. The flow rate inside the narrow is in the range of Reynolds number 10,000 to 100,000. Commercial software is used to solve the governing equations (continuity, momentum, and energy) by adopting a finite volume method (FVM). The electrical heater is connected around the circular tube to apply uniform heat flux (3000 W/m2) as a boundary condition. The volume concentrations are in the range of 0.25% to 1% with different TiO2 nanoparticle diameters in the range of 27 nm to 50 nm dispersed in water. The results indicate that the elliptical annulus tube can enhance heat transfer and friction factor by approximately 19% and 6% than the circular tube respectively. Results show that the heat transfer enhancement is significantly increasing as the volume concentrations increase and the nanoparticles size diameter decrease.

Hydraulically optimal porous liner around a porous lens: Strack’s problem revisited

ABSTRACT A porous barrier bounded by two confocal ellipses is filled with material of a hydraulic conductivity different from the ambient one in order to control the flow rate inside. Optimization problems are solved by describing the flow through a medium consisting of zones of different properties. For three-component composites, viz. three zones demarcated by two confocal ellipses, an explicit rigorous solution of refraction problems for potential fields of Darcian 2-D saturated flows is used. An aquifer, an elliptical ‘core’ and an elliptical annulus, which serves as a liner of the core, have contrasting hydraulic conductivities (control variables). The magnitude of the velocity in the core, total flow rate, travel time along streamlines, hydraulic gradient in the core are objectives in optimization. A single maximum of the magnitude of velocity in the ‘core’ is found at a certain conductivity of the annulus, similarly to the Strack circular annulus refracting a unidirectional flow. This maximum can be higher or lower than the velocity at infinity, i.e. the liner can amplify or lessen the incident flow. Applications to in situ ore leaching, permeable reactive barriers, porous waste repositories, aquifer permeameters and formation damage due to suffusion in the vicinity of pumping wells are discussed. Abbreviations: ISL: in situ leaching; RAF: reduction–amplification factor.

Confocal Annular Josephson Tunnel Junctions with Large Eccentricity

Confocal Annular Josephson Tunnel Junctions (CAJTJs) which are the natural generalization of the circular annular Josephson tunnel junctions, have a rich nonlinear phenomenology due to the intrinsic non-uniformity of their planar tunnel barrier delimited by two closely spaced confocal ellipses. In the presence of a uniform magnetic field in the barrier plane, the periodically changing width of the elliptical annulus generates a asymmetric double-well for a Josephson vortex trapped in a long and narrow CAJTJ. The preparation and readout of the vortex pinned in one of the two potential minima, which are important for the possible realization of a vortex qubit, have been numerically and experimentally investigated for CAJTJs with the moderate aspect ratio 2:1. In this work we focus on the impact of the annulus eccentricity on the properties of the vortex potential profile and study the depinning mechanism of a fluxon in more eccentric samples with aspect ratio 4:1. We also discuss the effects of the temperature-dependent losses as well as the influence of the current and magnetic noise.

Low-Pass FSS for 50–230 GHz Quasi-Optical Demultiplexing for the MetOp Second-Generation Microwave Sounder Instrument

This paper reports the design, manufacture, and characterization of a new frequency selective surface (FSS) structure which meets the demanding requirements for transmission of 50.2–57.7 GHz radiation simultaneously for TE and TM polarizations at 45° incidence, and reflection of signals in four discrete higher frequency bands centered at 89, 165.5, 183.3, and 229 GHz. The FSS is required for a quasi-optical network, which was developed during the preparatory breadboarding of the microwave sounder instrument. The 100 mm diameter ultrawideband FSS must exhibit ≤0.25 dB loss for all signals in the above bands, and has to satisfy the requirements of the space environment. The FSS is formed by a periodic metal film array sandwiched between two 0.83 mm thick, optically flat, fused quartz substrates. It has 19 000 unit cells composed of two compact resonant slot elements, a meandering elliptical annulus and a folded dipole. Spectral transmission and reflection measurements in the 50–230 GHz frequency range yielded results that are in excellent agreement with numerical predictions.

Retinal vessel density from optical coherence tomography angiography to differentiate early glaucoma, pre-perimetric glaucoma and normal eyes

PurposeTo evaluate optic nerve vascular density using swept source optical coherence tomography angiography (OCTA) in patients with early primary open angle glaucoma (POAG), pre-perimetric glaucoma and normal eyes.MethodsThis is a prospective, observational study including 56 eyes in total and divided into 3 groups; 20 eyes with mild POAG, 20 pre-perimetric glaucoma eyes, and 16 age-matched normal eyes as controls. The optic disc region was imaged by a 1050-nm-wavelength swept-source OCT system (DRI OCT Triton, TOPCON). Vessel density was assessed as the ratio of the area occupied by the vessels in 3 distinct regions: 1) within the optic nerve head; 2) in the 3 mm papillary region around the optic disc; and 3) in the peripapillary region, defined as a 700-μm-wide elliptical annulus around the disc. The potential associations between vessel density and structural, functional measures were analyzed.ResultsThere was a statistically significant difference for the peripapillary vessel density, optic nerve head vessel density, and papillary vessel density among all the groups (p<0.001). Control eyes showed a significant difference for all measured vessel densities compared to glaucomatous eyes (p values from 0.001 to 0.024). There was a statistically significant difference between control and pre-perimetric glaucoma eyes for peripapillary, optic nerve head and papillary vessel density values (p values from 0.001 to 0.007). The optic nerve head vessel density, superior and inferior papillary area vessel density (Pearson r = 0.512, 0.436, 0.523 respectively) were highly correlated with mean overall, superior and inferior RNFL thickness in POAG eyes (p = 0.04, p = 0.02 and p = 0.04 respectively). Multiple linear regression analysis of POAG group showed that optic nerve head vessel density in POAG group was more strongly linked to RNFL thickness than to any other variables.ConclusionsEyes with mild POAG could be differentiated from pre-perimetric glaucoma eyes, which also could be differentiated from normal eyes using OCTA-derived retinal vessel density measurements.

Challenging TAVI imaging case with Portico valve

Transcatheter aortic valve implantation is considered as an appropriate alternative to surgical valve replacement in patients with severe symptomatic aortic valve stenosis at moderate to high perioperative risk. There have also been case reports and patient series using TAVI system in patients with predominant or pure symptomatic aortic regurgitation. We report a case of a patient with symptomatic combined aortic valve disease that was successfully treated with selfexpandable Portico system despite extremely elliptical annulus.

Retinal ganglion cell/inner plexiform layer thickness in patients with Parkinson's disease.

<i><b>Introduction: </b> The aim of the paper was to analyze the changes in the macular ganglion cell layer and inner plexiform layer (GCL-IPL) thickness in patients with Parkinson's disease. <b>Material and methods</b>: The study enrolled 46 patients with established diagnosis of Parkinson's disease and 46 healthy subjects. Both groups were age- and gender-matched. An OCT protocol, namely standardized Ganglion Cell Analysis algorithm was used to measure the thickness of the macular GCL-IPL layer. The average, minimum, and six sectoral (superotemporal, superior, superonasal, inferonasal, inferior, inferotemporal) GCL-IPL thicknesses were measured from the elliptical annulus centered on the fovea. <b>Results</b>: The mean value of the clinical severity of Parkinson's disease was between 2 and 3, according to the Hoehn and Yahr scale. Statistically significant thinning of the GCL-IPL layer was registered in average and minimum GCL-IPL thickness, as well as in the sectoral layer thicknesses in patients with Parkinson's disease in comparison to the controls. There was no correlation between structural changes in the retina and disease duration or severity. A statistically significant difference in thickness between the different stages of the disease was registered only in the inferior sector. <b>Conclusions</b>: Parkinson's disease is accompanied by thinning of the GCL-IPL complex of macula even in the earliest stages. This may indicate a possible retinal dopaminergic neurodegeneration. There is no correlation between duration or severity of Parkinson's disease with thinning of the GCL-IPL complex. </i>.

Glaucoma-Diagnostic Ability of Ganglion Cell-Inner Plexiform Layer Thickness Difference Across Temporal Raphe in Highly Myopic Eyes.

To evaluate the glaucoma-diagnostic ability of the ganglion cell-inner plexiform layer (GCIPL) thickness difference across the temporal raphe in highly myopic eyes. We consecutively enrolled a total of 195 highly myopic eyes (axial length [AL] >26.5 mm) of 195 subjects: 93 glaucoma patients along with and 102 nonglaucomatous subjects. Cirrus high-definition optical coherence tomography (OCT) was employed to scan all of the subjects' macular and optic discs. Using a MATLAB-based customized program (the GCIPL hemifield test), a positive test result was automatically declared if the following two conditions were met: (1) the horizontal line is detected for longer than one-half of the distance from the temporal inner elliptical annulus to the outer elliptical annulus, and (2) the average GCIPL thickness difference within 10 pixels of the reference line, both above and below, is 5 μm or more. The glaucoma-diagnostic ability was computed using the area under the receiver operating characteristic curve (AUC). Among the glaucomatous eyes, GCIPL hemifield test positivity was shown in 92.5% (86 of 93), significantly higher than that for the nonglaucomatous eyes (4.90%, 5 of 102; P <0.001). The value of AUC for the GCIPL hemifield test was excellent (0.938; sensitivity 92.50%, specificity 95.10%) and was the best compared with those for any of OCT parameters. In highly myopic eyes, determination of the presence or absence of GCIPL thickness difference across the temporal raphe via OCT macula scan can be a useful means of distinguishing the glaucomatous damage.

Relationship between Optical Coherence Tomography Angiography Vessel Density and Severity of Visual Field Loss in Glaucoma

To evaluate the association between vessel density measurements using optical coherence tomography angiography (OCT-A) and severity of visual field loss in primary open-angle glaucoma. Observational, cross-sectional study. A total of 153 eyes from 31 healthy participants, 48 glaucoma suspects, and 74 glaucoma patients enrolled in the Diagnostic Innovations in Glaucoma Study. All eyes underwent imaging using OCT-A (Angiovue; Optovue, Fremont, CA), spectral-domain OCT (Avanti; Optovue), and standard automated perimetry (SAP). Retinal vasculature information was summarized as vessel density, the percentage of area occupied by flowing blood vessels in the selected region. Two measurements from the retinal nerve fiber layer (RNFL) were used: circumpapillary vessel density (cpVD) (750-μm-wide elliptical annulus around the optic disc) and whole-image vessel density (wiVD) (entire 4.5×4.5-mm scan field). Associations between the severity of visual field loss, reported as SAP mean deviation (MD), and OCT-A vessel density. Compared with glaucoma eyes, normal eyes demonstrated a denser microvascular network within the RNFL. Vessel density was higher in normal eyes followed by glaucoma suspects, mild glaucoma, and moderate to severe glaucoma eyes for wiVD (55.5%, 51.3%, 48.3%, and 41.7%, respectively) and for cpVD (62.8%, 61.0%, 57.5%, 49.6%, respectively) (P < 0.001 for both). The association between SAP MD with cpVD and wiVD was stronger (R2= 0.54 and R2= 0.51, respectively) than the association between SAP MD with RNFL (R2= 0.36) and rim area (R2= 0.19) (P < 0.05 for all). Multivariate regression analysis showed that each 1% decrease in wiVD was associated with 0.66 decibel (dB) loss in MD and each 1% decrease in cpVD was associated with 0.64 dB loss in MD. In addition, the association between vessel density and severity of visual field damage was found to be significant even after controlling for the effect of structural loss. Decreased vessel density was significantly associated with the severity of visual field damage independent of the structural loss. Optical coherence tomography angiography is a promising technology in glaucoma management, potentially enhancing the understanding of the role of vasculature in the pathophysiology of the disease.

Optical Coherence Tomography Angiography Vessel Density in Glaucomatous Eyes with Focal Lamina Cribrosa Defects

To investigate whether vessel density assessed by optical coherence tomography angiography (OCT-A) is reduced in glaucomatous eyes with focal lamina cribrosa (LC) defects. Cross-sectional, case-control study. A total of 82 patients with primary open-angle glaucoma (POAG) from the Diagnostic Innovations in Glaucoma Study (DIGS) with and without focal LC defects (41 eyes of 41 patients in each group) matched by severity of visual field (VF) damage. Optical coherence tomography (OCT) angiography-derived circumpapillary vessel density (cpVD) was calculated as the percentage area occupied by vessels in the measured region extracted from the retinal nerve fiber layer (RNFL) in a 750-μm-wide elliptical annulus around the disc. Focal LC defects were detected using swept-source OCT images. Comparison of global and sectoral (eight 45-degree sectors) cpVDs and circumpapillary RNFL (cpRNFL) thicknesses in eyes with and without LC defects. Age, global, and sectoral cpRNFL thicknesses, VF mean deviation (MD) and pattern standard deviation, presence of optic disc hemorrhage, and mean ocular perfusion pressure did not differ between patients with and without LC defects (P > 0.05 for all comparisons). Mean cpVDs of eyes with LC defects were significantly lower than in eyes without a defect globally (52.9%±5.6% vs. 56.8%±7.7%; P= 0.013) and in the inferotemporal (IT) (49.5%±10.3% vs. 56.8%±12.2%; P= 0.004), superotemporal (ST) (54.3%±8.8% vs. 58.8%±9.6%; P= 0.030), and inferonasal (IN) (52.4%±9.0% vs. 57.6%±9.1%; P= 0.009) sectors. Eyes with LC defects in the IT sector (n= 33) had significantly lower cpVDs than eyes without a defect in the corresponding IT and IN sectors (P < 0.05 for all). Eyes with LC defects in the ST sector (n= 19) had lower cpVDs in the ST, IT, and IN sectors (P < 0.05 for all). In eyes with similar severity of glaucoma, OCT-A-measured vessel density was significantly lower in POAG eyes with focal LC defects than in eyes without an LC defect. Moreover, reduction of vessel density was spatially correlated with the location of the LC defect.

Optical Coherence Tomography Angiography Vessel Density in Healthy, Glaucoma Suspect, and Glaucoma Eyes.

PurposeThe purpose of this study was to compare retinal nerve fiber layer (RNFL) thickness and optical coherence tomography angiography (OCT-A) retinal vasculature measurements in healthy, glaucoma suspect, and glaucoma patients.MethodsTwo hundred sixty-one eyes of 164 healthy, glaucoma suspect, and open-angle glaucoma (OAG) participants from the Diagnostic Innovations in Glaucoma Study with good quality OCT-A images were included. Retinal vasculature information was summarized as a vessel density map and as vessel density (%), which is the proportion of flowing vessel area over the total area evaluated. Two vessel density measurements extracted from the RNFL were analyzed: (1) circumpapillary vessel density (cpVD) measured in a 750-μm-wide elliptical annulus around the disc and (2) whole image vessel density (wiVD) measured over the entire image. Areas under the receiver operating characteristic curves (AUROC) were used to evaluate diagnostic accuracy.ResultsAge-adjusted mean vessel density was significantly lower in OAG eyes compared with glaucoma suspects and healthy eyes. (cpVD: 55.1 ± 7%, 60.3 ± 5%, and 64.2 ± 3%, respectively; P < 0.001; and wiVD: 46.2 ± 6%, 51.3 ± 5%, and 56.6 ± 3%, respectively; P < 0.001). For differentiating between glaucoma and healthy eyes, the age-adjusted AUROC was highest for wiVD (0.94), followed by RNFL thickness (0.92) and cpVD (0.83). The AUROCs for differentiating between healthy and glaucoma suspect eyes were highest for wiVD (0.70), followed by cpVD (0.65) and RNFL thickness (0.65).ConclusionsOptical coherence tomography angiography vessel density had similar diagnostic accuracy to RNFL thickness measurements for differentiating between healthy and glaucoma eyes. These results suggest that OCT-A measurements reflect damage to tissues relevant to the pathophysiology of OAG.

Effect of oversizing and elliptical shape of aortic annulus on transcatheter valve hemodynamics: An in vitro study

BackgroundTranscatheter aortic valve implantation (TAVI) is often performed in patients with non-circular aortic annulus and in oversizing (OS) conditions. The impact of elliptical annulus shape and the consequences of oversizing/underdeployment on the hemodynamic performance are still debated. ObjectiveThis in-vitro study aims to assess and compare the valve hemodynamic performances of the Edwards SAPIEN transcatheter heart valve (THV) in the different current conditions of use: important oversizing in small circular annuli and in elliptical annuli, moderate oversizing in circular and in elliptical annuli of various degrees of eccentricity. MethodsA pulsed cardiovascular simulator was used. Edwards SAPIEN 23 and 26 (mm) were implanted in different circular and elliptical annuli of various sizes and eccentricity. Transvalvular mean pressure gradients (TPGm), effective orifice area (EOA) after implantation of Edwards SAPIEN THV were measured by Doppler-echocardiography and the performance index (PI=100×EOA/Annulus Area) was calculated. Para and transvalvular regurgitation was assessed by color-Doppler and leakage volume was quantified by flowmeter measurement. ResultsFor a given aortic annulus area, EOAs after implantation of Edwards SAPIEN THV were generally larger and TPGms lower with elliptical annuli compared to circular annuli. The PI was higher (p=0.047) for elliptical (48±3%) than for circular annuli (43±5%). Paravalvular regurgitation occurred only in the case of the SAPIEN 26 implanted in the elliptical annulus with highest eccentricity. ConclusionThe results of this in-vitro study suggest that the EOAs of Edwards SAPIEN are better in elliptical than in circular annuli. No transvalvular regurgitation occurred and only one paravalvular regurgitation was observed after implantation of SAPIEN 26 in the highly eccentric annulus.

Optical Coherence Tomography Angiography of the Peripapillary Retina in Glaucoma.

Vascular factors may have important roles in the pathophysiology of glaucoma. A practical method for the clinical evaluation of ocular perfusion is needed to improve glaucoma management. To detect peripapillary retinal perfusion in glaucomatous eyes compared with normal eyes using optical coherence tomography (OCT) angiography. Prospective observational study performed from July 24, 2013, to April 17, 2014. Participants were recruited and tested at Casey Eye Institute, Oregon Health & Science University. In total, 12 glaucomatous eyes and 12 age-matched normal eyes were analyzed. The optic disc region was imaged twice using a 3 × 3-mm scan by a 70-kHz, 840-nm-wavelength spectral OCT system. The split-spectrum amplitude-decorrelation angiography algorithm was used. Peripapillary flow index was calculated as the mean decorrelation value in the peripapillary region, defined as a 700-µm-wide elliptical annulus around the disc. Peripapillary vessel density was the percentage area occupied by vessels. The data statistical analysis was performed from October 30, 2013, to May 30, 2014. Variability was assessed by the coefficient of variation. The Mann-Whitney test was used to compare the 2 groups of eyes. Correlations between vascular and visual field variables were assessed by linear regression analysis. In 12 normal eyes, a dense microvascular network around the disc was visible on OCT angiography. In 12 glaucomatous eyes, this network was visibly attenuated globally and focally. In normal eyes, between-visit reproducibilities of peripapillary flow index and peripapillary vessel density were 4.3% and 2.7% of the coefficient of variation, respectively, while the population variabilities of peripapillary flow index and peripapillary vessel density were 8.2% and 3.0% of the coefficient of variation, respectively. Peripapillary flow index and peripapillary vessel density in glaucomatous eyes were lower than those in normal eyes (P < .001 for both). Peripapillary flow index (Pearson r = -0.808) and peripapillary vessel density (Pearson r = -0.835) were highly correlated with visual field pattern standard deviation in glaucomatous eyes (P = .001 for both). The areas under the receiver operating characteristic curve for normal vs glaucomatous eyes were 0.892 for peripapillary flow index and 0.938 for peripapillary vessel density. Using OCT angiography, reduced peripapillary retinal perfusion in glaucomatous eyes can be visualized as focal defects and quantified as peripapillary flow index and peripapillary vessel density, with high repeatability and reproducibility. Quantitative OCT angiography may have value in future studies to determine its potential usefulness in glaucoma evaluation.

Automated Detection of Hemifield Difference across Horizontal Raphe on Ganglion Cell–Inner Plexiform Layer Thickness Map

A MATLAB-based (The MathWorks, Inc, Natick, MA) computer program (the ganglion cell-inner plexiform layer [GCIPL] hemifield test) for automated detection of GCIPL thickness difference across the horizontal raphe was developed, and its glaucoma diagnostic performance was assessed. Cross-sectional study. A total of 65 eyes of normal, healthy subjects along with 162 eyes of patients with glaucoma (79 preperimetric and 83 early perimetric). Cirrus high-definition optical coherence tomography (HD-OCT) (Carl Zeiss Meditec, Dublin, CA) was used to scan all of the subjects' macular and optic discs. A positive (i.e., "outside normal limits") GCIPL hemifield test result was declared if the following 3 conditions were all met: (1) The reference line (a horizontal line dividing the superior and inferior hemifields) is continuously detected for longer than one-half of the distance from the temporal inner elliptical annulus to the outer elliptical annulus; (2) the average GCIPL thickness difference within 10 pixels of the reference line, both above and below, is ≥5 μm; and (3) the average RGB color ranges of the 10 pixels above and below the reference line display blue in 1 hemifield and red/yellow/white in the other hemifield. Comparison of diagnostic ability using the areas under the receiver operating characteristic curves (AUCs). A positive GCIPL hemifield test result was observed more frequently in the glaucomatous eyes (74/79 preperimetric, 78/83 early perimetric) than in the normal eyes (1/65). In the preperimetric group, the AUC of the GCIPL hemifield test (0.967; sensitivity 94.94%, specificity 98.46%) was greater than that of the minimum GCIPL thickness (0.933), the inferotemporal GCIPL thickness (0.907), and the average GCIPL thickness (0.899) (P=0.09, 0.06, and 0.03, respectively). In the early perimetric group, the AUC of the GCIPL hemifield test (0.962; sensitivity 93.98%, specificity 96.46%) was greater than that of the inferotemporal GCIPL thickness (0.938), the minimum GCIPL thickness (0.919), and the average GCIPL thickness (0.912) (P=0.38, 0.17, and 0.11, respectively). For discrimination of early glaucomatous structural loss, most notably in preperimetric glaucoma cases, identification of the GCIPL thickness difference across the horizontal raphe was effective.

Effect of eccentricity on natural convection in fluid-saturated porous media in an elliptical annulus

In this paper, we summarize a numerical study of two-dimensional natural convection in an annular elliptical space fluid-saturated porous, by solving numerically the mass balance equations, momentum and energy, using Darcy’s law, Boussinesq approximation, vorticity-stream function formulation and the finite volumes method for the discretization of partial derivative equations. Both walls delimiting the annular space are maintained at two uniform different temperatures. The external parameters considered are the eccentricity of the inner elliptic wall (0.55, 0.688, 0.86, 0.9 and 0.999) and Rayleigh-Darcy number (R a m = 500). The results indicate that there are two main modes of natural convection: natural convection with only two cells and with more cells, their description is given in detail. The average equivalent conductivity is presented in terms of external parameters and allows us to see that it increases when the internal wall eccentricity increases.

Generalization of Zernike polynomials for regular portions of circles and ellipses.

Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit circle. Here, we present a generalization of this Zernike basis for a variety of important optical apertures. On the contrary to ad hoc solutions, most of them based on the Gram-Schmidt orthonormalization method, here we apply the diffeomorphism (mapping that has a differentiable inverse mapping) that transforms the unit circle into an angular sector of an elliptical annulus. In this way, other apertures, such as ellipses, rings, angular sectors, etc. are also included as particular cases. This generalization, based on in-plane warping of the basis functions, provides a unique solution and what is more important, it guarantees a reasonable level of invariance of the mathematical properties and the physical meaning of the initial basis functions. Both, the general form and the explicit expressions for most common, elliptical and annular apertures are provided.