Correlation of the Corneal Toricity Between Anterior and Posterior Corneal Surfaces in the Normal Human Eye

Purpose: To evaluate the correlation of the magnitude of corneal toricity and power vector components of both corneal surfaces measured with a Scheimpflug photography-based system. Methods: A total of 117 healthy normal eyes of 117 subjects selected randomly with ages ranging from 7 to 80 years were included. All eyes received an anterior segment and corneal analysis with the Sirius system (CSO) evaluating the anterior and posterior mean toricity for 3 and 7 mm (aAST and pAST). The vector components J0 and J45 as well as the overall strength blur (B) were calculated for each keratometric measurement using the procedure defined by Thibos and Horner. Results: The coefficient of correlation between aAST and pAST was 0.52 and 0.62 and the mean anteroposterior ratio for toricity was 0.46 ± 0.39 and 0.57 ± 0.75 for 3 and 7 mm, respectively. These ratios correlated significantly with aAST, anterior corneal J0, and manifest refraction J0 (r ≥ 0.39, P < 0.01). The coefficient of correlation was 0.69 and 0.81 between anterior and posterior J0 for 3 and 7 mm, respectively. For J45, the coefficients were 0.62 and 0.71, respectively. The linear regression analysis revealed that the pAST and power vectors could be predicted from the anterior corneal data (R2 ≥ 0.40, P < 0.01). Conclusions: The toricity and astigmatic power vector components of the posterior corneal surface in the human healthy eye are related to those of the anterior and therefore can be predicted consistently from the anterior toricity and astigmatic power vectors.

Estimation of the Central Corneal Power in Keratoconus: Theoretical and Clinical Assessment of the Error of the Keratometric Approach

Purpose: The aim of this study was to analyze theoretically the errors in the central corneal power calculation in eyes with keratoconus when a keratometric index (nk) is used and to clinically confirm the errors induced by this approach. Methods: Differences (DPc) between central corneal power estimation with the classical nk (Pk) and with the Gaussian equation (PGauss c ) in eyes with keratoconus were simulated and evaluated theoretically, considering the potential range of variation of the central radius of curvature of the anterior (r1c) and posterior (r2c) corneal surfaces. Further, these differences were also studied in a clinical sample including 44 keratoconic eyes (27 patients, age range: 14–73 years). The clinical agreement between Pk and PGauss c (true net power) obtained with a Scheimpflug photography–based topographer was evaluated in such eyes. Results: For nk = 1.3375, an overestimation was observed in most cases in the theoretical simulations, with DPc ranging from an underestimation of 20.1 diopters (D) (r1c = 7.9 mm and r2c = 8.2 mm) to an overestimation of 4.3 D (r1c = 4.7 mm and r2c = 3.1 mm). Clinically, Pk always overestimated the PGauss c given by the topography system in a range between 0.5 and 2.5 D (P , 0.01). The mean clinical DPc was 1.48 D, with limits of agreement of 0.71 and 2.25 D. A very strong statistically significant correlation was found between DPc and r2c (r = 20.93, P , 0.01). Conclusions: The use of a single value for nk for the calculation of corneal power is imprecise in keratoconus and can lead to significant clinical errors.

The role of local luminance amplitude in the interpretation of shape-from-shading in textured surfaces

Luminance changes within a scene are ambiguous; they can indicate reflectance changes, shadows, or shading due to surface undulations. How does vision distinguish between these possibilities? When a surface painted with an albedo texture is shaded, the change in local mean luminance (LM) is accompanied by a similar modulation of the local luminance amplitude (AM) of the texture. This relationship does not necessarily hold for reflectance changes or for shading of a relief texture. Here we concentrate on the role of AM in shape-from-shading. Observers were presented with a noise texture onto which sinusoidal LM and AM signals were superimposed, and were asked to indicate which of two marked locations was closer to them. Shape-from-shading was enhanced when LM and AM co-varied (in-phase), and was disrupted when they were out-of-phase. The perceptual differences between cue types (in-phase vs out-of-phase) were enhanced when the two cues were present at different orientations within a single image. Similar results were found with a haptic matching task. We conclude that vision can use AM to disambiguate luminance changes. LM and AM have a positive relationship for rendered, undulating, albedo textures, and we assess the degree to which this relationship holds in natural images. [Supported by EPSRC grants to AJS and MAG].

Local luminance amplitude modulates the interpretation of shape-from-shading in textured surfaces

The pattern of illumination on an undulating surface can be used to infer its 3-D form (shape-from-shading). But the recovery of shape would be invalid if the luminance changes actually arose from changes in reflectance. So how does vision distinguish variation in illumination from variation in reflectance to avoid illusory depth? When a corrugated surface is painted with an albedo texture, the variation in local mean luminance (LM) due to shading is accompanied by a similar modulation in local luminance amplitude (AM). This is not so for reflectance variation, nor for roughly textured surfaces. We used depth mapping and paired comparison methods to show that modulations of local luminance amplitude play a role in the interpretation of shape-from-shading. The shape-from-shading percept was enhanced when LM and AM co-varied (in-phase) and was disrupted when they were out of phase or (to a lesser degree) when AM was absent. The perceptual differences between cue types (in-phase vs out-of-phase) were enhanced when the two cues were present at different orientations within a single image. Our results suggest that when LM and AM co-vary (in-phase) this indicates that the source of variation is illumination (caused by undulations of the surface), rather than surface reflectance. Hence, the congruence of LM and AM is a cue that supports a shape-from-shading interpretation. © 2006 Elsevier Ltd. All rights reserved.

The effect of corneal thickness and corneal curvature on pneumatonometer measurements

Purpose. The purpose of this study was to investigate the influence of corneal topography and thickness on intraocular pressure (IOP) and pulse amplitude (PA) as measured using the Ocular Blood Flow Analyzer (OBFA) pneumatonometer (Paradigm Medical Industries, Utah, USA). Methods. 47 university students volunteered for this cross-sectional study: mean age 20.4 yrs, range 18 to 28 yrs; 23 male, 24 female. Only the measurements from the right eye of each participant were used. Central corneal thickness and mean corneal radius were measured using Scheimpflug biometry and corneal topographic imaging respectively. IOP and PA measurements were made with the OBFA pneumatonometer. Axial length was measured using A-scan ultrasound, due to its known correlation with these corneal parameters. Stepwise multiple regression analysis was used to identify those components that contributed significant variance to the independent variables of IOP and PA. Results. The mean IOP and PA measurements were 13.1 (SD 3.3) mmHg and 3.0 (SD 1.2) mmHg respectively. IOP measurements made with the OBFA pneumatonometer correlated significantly with central corneal thickness (r = +0.374, p = 0.010), such that a 10 mm change in CCT was equivalent to a 0.30 mmHg change in measured IOP. PA measurements correlated significantly with axial length (part correlate = -0.651, p < 0.001) and mean corneal radius (part correlate = +0.459, p < 0.001) but not corneal thickness. Conclusions. IOP measurements taken with the OBFA pneumatonometer are correlated with corneal thickness, but not axial length or corneal curvature. Conversely, PA measurements are unaffected by corneal thickness, but correlated with axial length and corneal radius. These parameters should be taken into consideration when interpreting IOP and PA measurements made with the OBFA pneumatonometer.

Radial growth and carbohydrate levels in the lichen Parmelia conspersa on north and south facing rock surfaces

Parmelia conspersa (Ehrh. Ex Ach.)Ach. is a foliose lichen found more frequently on south facing compared with north facing rock surfaces in South Gwynedd, Wales, UK. The radial growth of thalli of P. conspersa from a north and a south facing rock surface was measured in situ at intervals of two months for 1 yr during 1990/1991. Mean annual radial growth rates were greater on the south compared with the north facing rock surface. In addition, the pattern of radial growth varied during the year with maximum growth recorded in the Feb/Mar. period especially on the south facing rock surface. The levels of ribitol, arabitol and mannitol were measured in individual lobes of P. conspersa collected from the same rock surfaces on 4 days (2 Jun; 7 July and 30 Nov. 1990 and 29 Mar. 1991) during 1990/1991. The total of the three carbohydrates varied between days; the levels of arbitol and ribitol being significantly lower in the 7 July sample on both north and south facing rock surfaces. In addition, the levels ribitol, arabitol and mannitol were higher on the south facing rock surface especially in the summer samples. The ratio of arabitol plus mannitol to ribitol and the mannitol/arabitol ratio varied more between days sampled than between north and south facing rock surfaces. The level of ribitol in individual thalli was positively correlated with arabitol on the north facing and with mannitol on the south facing slope. These results suggest that differences in the radial growth of P. conspersa thalli with aspect are more likely to reflect higher rates of photosynthesis on the south facing rock surface rather than large difference in the way carbohydrates were partitioned on the different surfaces. Lower radial growth rates may place P. conspersa at a competitive disadvantage on north facing rock surfaces.

Laparoscopic greater curvature plication in morbidly obese women with type 2 diabetes:effects on glucose homeostasis, postprandial triglyceridemia and selected gut hormones

Background: Laparoscopic greater curvature plication (LGCP) is an emerging bariatric procedure that reduces the gastric volume without implantable devices or gastrectomy. The aim of this study was to explore changes in glucose homeostasis, postprandial triglyceridemia, and meal-stimulated secretion of selected gut hormones [glucose-dependent insulinotropic polypeptide (GIP), glucagon-like peptide-1 (GLP-1), ghrelin, and obestatin] in patients with type 2 diabetes mellitus (T2DM) at 1 and 6 months after the procedure. Methods: Thirteen morbidly obese T2DM women (mean age, 53.2 ± 8.76 years; body mass index, 40.1 ± 4.59 kg/m2) were prospectively investigated before the LGCP and at 1- and 6-month follow-up. At these time points, all study patients underwent a standardized liquid mixed-meal test, and blood was sampled for assessment of plasma levels of glucose, insulin, C-peptide, triglycerides, GIP, GLP-1, ghrelin, and obestatin. Results: All patients had significant weight loss both at 1 and 6 months after the LGCP (p≤0.002), with mean percent excess weight loss (%EWL) reaching 29.7 ;plusmn2.9 % at the 6-month follow-up. Fasting hyperglycemia and hyperinsulinemia improved significantly at 6 months after the LGCP (p<0.05), with parallel improvement in insulin sensitivity and HbA1c levels (p<0.0001). Meal-induced glucose plasma levels were significantly lower at 6 months after the LGCP (p<0.0001), and postprandial triglyceridemia was also ameliorated at the 6-month follow-up (p<0.001). Postprandial GIP plasma levels were significantly increased both at 1 and 6 months after the LGCP (p<0.0001), whereas the overall meal-induced GLP-1 response was not significantly changed after the procedure (p ;gt0.05). Postprandial ghrelin plasma levels decreased at 1 and 6 months after the LGCP (p<0.0001) with no significant changes in circulating obestatin levels. Conclusion: During the initial 6-month postoperative period, LGCP induces significant weight loss and improves the metabolic profile of morbidly obese T2DM patients, while it also decreases circulating postprandial ghrelin levels and increases the meal-induced GIP response. © 2013 Springer Science+Business Media New York.

Complex Hyperbolic Surfaces of Abelian Type

2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Investigating wetting characteristics on microstructured surfaces for superhydrophobicity and metal microcasting

The engineering of liquid behavior on surfaces is important for infrastructure, transportation, manufacturing, and sensing. Surfaces can be rendered superhydrophobic by microstructuring, and superhydrophobic devices could lead to practical corrosion inhibition, self-cleaning, fluid flow control, and surface drag reduction. To more fully understand how liquid interacts with microstructured surfaces, this dissertation introduces a direct method for determining droplet solid-liquid-vapor interfacial geometry on microstructured surfaces. The technique performs metrology on molten metal droplets deposited onto microstructured surfaces and then frozen. Unlike other techniques, this visualization technique can be used on large areas of curved and opaque microstructured surfaces to determine contact line. This dissertation also presents measurements and models for how curvature and flexing of microstructured polymers affects hydrophobicity. Increasing curvature of microstructured surfaces leads to decreased slide angle for liquid droplets suspended on the surface asperities. For a surface with regularly spaced asperities, as curvature becomes more positive, droplets suspended on the tops of asperities are suspended on fewer asperities. Curvature affects superhydrophobicity because microscopic curvature changes solid-liquid interaction, pitch is altered, and curvature changes the shape of the three phase contact line. This dissertation presents a model of droplet interactions with curved microstructured surfaces that can be used to design microstructure geometries that maintain the suspension of a droplet when curved surfaces are covered with microstructured polymers. Controlling droplet dynamics could improve microfluidic devices and the shedding of liquids from expensive equipment, preventing corrosion and detrimental performance. This dissertation demonstrates redirection of dynamic droplet spray with anisotropic microstructures. Superhydrophobic microstructured surfaces can be economically fabricated using metal embossing masters, so this dissertation describes casting-based microfabrication of metal microstructures and nanostructures. Low melting temperature metal was cast into flexible silicone molds which were themselves cast from microfabricated silicon templates. The flexibility of the silicone mold permits casting of curved surfaces, which this dissertation demonstrates by fabricating a cylindrical metal roller with microstructures. The metal microstructures can be in turn used as a reusable molding tool. This dissertation also describes an industrial investment casting process to produce aluminum molds having integrated microstructures. Unlike conventional micromolding tools, the aluminum mold was large and had complex curved surfaces. The aluminum was cast into curved microstructured ceramic molds which were themselves cast from curved microstructured rubber. Many structures were successfully cast into the aluminum with excellent replication fidelity, including circular, square, and triangular holes. This dissertation demonstrates molding of large, curved surfaces having surface microstructures using the aluminum mold. This work contributes a more full understanding of the phenomenon of superhydrophobicity and techniques for the economic fabrication of superhydrophobic microstructures.

Triangular mesh parameterization with trimmed surfaces

Given a 2manifold triangular mesh \(M \subset {\mathbb {R}}^3\), with border, a parameterization of \(M\) is a FACE or trimmed surface \(F=\{S,L_0,\ldots, L_m\}\) -- \(F\) is a connected subset or region of a parametric surface \(S\), bounded by a set of LOOPs \(L_0,\ldots ,L_m\) such that each \(L_i \subset S\) is a closed 1manifold having no intersection with the other \(L_j\) LOOPs -- The parametric surface \(S\) is a statistical fit of the mesh \(M\) -- \(L_0\) is the outermost LOOP bounding \(F\) and \(L_i\) is the LOOP of the ith hole in \(F\) (if any) -- The problem of parameterizing triangular meshes is relevant for reverse engineering, tool path planning, feature detection, redesign, etc -- Stateofart mesh procedures parameterize a rectangular mesh \(M\) -- To improve such procedures, we report here the implementation of an algorithm which parameterizes meshes \(M\) presenting holes and concavities -- We synthesize a parametric surface \(S \subset {\mathbb {R}}^3\) which approximates a superset of the mesh \(M\) -- Then, we compute a set of LOOPs trimming \(S\), and therefore completing the FACE \(F=\ {S,L_0,\ldots ,L_m\}\) -- Our algorithm gives satisfactory results for \(M\) having low Gaussian curvature (i.e., \(M\) being quasi-developable or developable) -- This assumption is a reasonable one, since \(M\) is the product of manifold segmentation preprocessing -- Our algorithm computes: (1) a manifold learning mapping \(\phi : M \rightarrow U \subset {\mathbb {R}}^2\), (2) an inverse mapping \(S: W \subset {\mathbb {R}}^2 \rightarrow {\mathbb {R}}^3\), with \ (W\) being a rectangular grid containing and surpassing \(U\) -- To compute \(\phi\) we test IsoMap, Laplacian Eigenmaps and Hessian local linear embedding (best results with HLLE) -- For the back mapping (NURBS) \(S\) the crucial step is to find a control polyhedron \(P\), which is an extrapolation of \(M\) -- We calculate \(P\) by extrapolating radial basis functions that interpolate points inside \(\phi (M)\) -- We successfully test our implementation with several datasets presenting concavities, holes, and are extremely nondevelopable -- Ongoing work is being devoted to manifold segmentation which facilitates mesh parameterization

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.