Convex and toric geometry to analyze complex dynamics in chemical reaction systems

Convex cone, toric variety, graph theory, electrochemical catalysis, oxidation of formic acid, feedback-loopsbifurcations, enzymatic catalysis, Peroxidase reaction, Shil'nikov chaos

Rescue technique for salvaging toric intraocular lens alignment

Accurate alignment of a toric intraocular lens (IOL) is a requisite to achieving the intended reduction in astigmatism at the time of cataract surgery. However, it requires a reasonably clear view of the limbal vascular anatomy, which is sometimes altered by chemosis from a subconjunctival anesthetic injection or a hemorrhage. We describe a technique that can quickly restore vascular anatomy and facilitate toric IOL alignment.

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.

From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code

We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)-symmetric variant of Kitaev’s toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.

The algebraic density property for affine toric varieties

In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.

Toric implantable collamer lens for moderate to high myopic astigmatism: 3-year follow-up

Background To evaluate the 3-year clinical outcomes after toric implantable collamer lens (ICL) implantation for the management of moderate to high myopic astigmatism. Methods Thirty-four eyes of 20 patients who underwent toric ICL implantation were reviewed. All eyes completed 3-year follow-up. Uncorrected (UDVA) and corrected (CDVA) distance LogMAR visual acuities, refraction, endothelial cell density (ECD), and surgical complications were evaluated. Vectorial analysis of astigmatic correction was also done. Results A significant improvement in UDVA, CDVA, manifest spherical and cylindrical refraction was observed at 1 week and remained stable after 3 years. Twenty-six eyes (76.5 %) gained lines of CDVA, and two eyes (5.9 %) showed a loss of 1 line of CDVA. The spherical equivalent (SE) was within ±0.50 D of emmetropia in 18 eyes (52.9 %) and within ±1.00 D in 28 eyes (82.4 %). Differences between target-induced astigmatism (TIA) and surgically-induced astigmatism (SIA) were statistically significant (p < 0.01), and a trend to undercorrection of the refractive astigmatism was present after 3 years. The magnitude of flattening effect (FE) was found to be significantly lower than the magnitude of TIA (p < 0.01). The magnitude of the torque vector was always positive, with a value below 0.50 D in all cases. No vision-threatening complications were observed during the follow-up. Conclusion Toric ICL implantation is an effective and safe surgical option that provides a relatively predictable and stable refractive correction of myopic astigmatism. Further improvements are needed to minimize the degree of undercorrection.

Analysis of internal astigmatism and higher order aberrations in eyes implanted with a new diffractive multifocal toric intraocular lens

Background To evaluate the intraocular lens (IOL) position by analyzing the postoperative axis of internal astigmatism as well as the higher-order aberration (HOA) profile after cataract surgery following the implantation of a diffractive multifocal toric IOL. Methods Prospective study including 51 eyes with corneal astigmatism of 1.25D or higher of 29 patients with ages ranging between 20 and 61 years old. All cases underwent uneventful cataract surgery with implantation of the AT LISA 909 M toric IOL (Zeiss). Visual, refractive and corneal topograpy changes were evaluated during a 12-month follow-up. In addition, the axis of internal astigmatism as well as ocular, corneal, and internal HOA (5-mm pupil) were evaluated postoperatively by means of an integrated aberrometer (OPD Scan II, Nidek). Results A significant improvement in uncorrected distance and near visual acuities (p < 0.01) was found, which was consistent with a significant correction of manifest astigmatism (p < 0.01). No significant changes were observed in corneal astigmatism (p = 0.32). With regard to IOL alignment, the difference between the axes of postoperative internal and preoperative corneal astigmatisms was close to perpendicularity (12 months, 87.16° ± 7.14), without significant changes during the first 6 months (p ≥ 0.46). Small but significant changes were detected afterwards (p = 0.01). Additionally, this angular difference correlated with the postoperative magnitude of manifest cylinder (r = 0.31, p = 0.03). Minimal contribution of intraocular optics to the global magnitude of HOA was observed. Conclusions The diffractive multifocal toric IOL evaluated is able to provide a predictable astigmatic correction with apparent excellent levels of optical quality during the first year after implantation.

Objective analysis of toric intraocular lens rotation and centration

PURPOSE: To assess the repeatability of an objective image analysis technique to determine intraocular lens (IOL) rotation and centration. SETTING: Six ophthalmology clinics across Europe. METHODS: One-hundred seven patients implanted with Akreos AO aspheric IOLs with orientation marks were imaged. Image quality was rated by a masked observer. The axis of rotation was determined from a line bisecting the IOL orientation marks. This was normalized for rotation of the eye between visits using the axis bisecting 2 consistent conjunctival vessels or iris features. The center of ovals overlaid to circumscribe the IOL optic edge and the pupil or limbus were compared to determine IOL centration. Intrasession repeatability was assessed in 40 eyes and the variability of repeated analysis examined. RESULTS: Intrasession rotational stability of the IOL was ±0.79 degrees (SD) and centration was ±0.10 mm horizontally and ±0.10 mm vertically. Repeated analysis variability of the same image was ±0.70 degrees for rotation and ±0.20 mm horizontally and ±0.31 mm vertically for centration. Eye rotation (absolute) between visits was 2.23 ± 1.84 degrees (10%>5 degrees rotation) using one set of consistent conjunctival vessels or iris features and 2.03 ± 1.66 degrees (7%>5 degrees rotation) using the average of 2 sets (P =.13). Poorer image quality resulted in larger apparent absolute IOL rotation (r =-0.45,P<.001). CONCLUSIONS: Objective analysis of digital retroillumination images allows sensitive assessment of IOL rotation and centration stability. Eye rotation between images can lead to significant errors if not taken into account. Image quality is important to analysis accuracy.

Rotational and centration stability of an aspheric intraocular lens with a simulated toric design

Purpose: To assess the stability of the Akreos AO intraocular lens (IOL) platform with a simulated toric design using objective image analysis. Setting: Six hospital eye clinics across Europe. Methods: After implantation in 1 eye of patients, IOLs with orientation marks were imaged at 1 to 2 days, 7 to 14 days, 30 to 60 days, and 120 to 180 days. The axis of rotation and IOL centration were objectively assessed using validated image analysis. Results: The study enrolled 107 patients with a mean age of 69.9 years ± 7.7 (SD). The image quality was sufficient for IOL rotation analysis in 91% of eyes. The mean rotation between the first day postoperatively and 120 to 180 days was 1.93 ± 2.33 degrees, with 96% of IOLs rotating fewer than 5 degrees and 99% rotating fewer than 10 degrees. There was no significant rotation between visits and no clear bias in the direction of rotation. In 71% of eyes, the dilation and image quality was sufficient for image analysis of centration. The mean change in centration between 1 day and 120 to 180 days was 0.21 ± 0.11 mm, with all IOLs decentering less than 0.5 mm. There was no significant decentration between visits and no clear bias in the direction of the decentration. Conclusion: Objective analysis of digital retroillumination images taken at different postoperative periods shows the aspheric IOL platform was stable in the eye and is therefore suitable for the application of a toric surface to correct corneal astigmatism.

Clinical outcomes after implantation of a new hydrophobic acrylic toric IOL during routine cataract surgery

PURPOSE: To assess the clinical outcomes after implantation of a new hydrophobic acrylic toric intraocular lens (IOL) to correct preexisting corneal astigmatism in patients having routine cataract surgery. SETTING: Four hospital eye clinics throughout Europe. DESIGN: Cohort study. METHODS: This study included eyes with at least 0.75 diopter (D) of preexisting corneal astigmatism having routine cataract surgery. Phacoemulsification was performed followed by insertion and alignment of a Tecnis toric IOL. Patients were examined 4 to 8 weeks postoperatively; uncorrected distance visual acuity (UDVA), corrected distance visual acuity, manifest refraction, and keratometry were measured. Individual patient satisfaction with uncorrected vision and the surgeon’s assessment of ease of handling and performance of the IOL were also documented. The cylinder axis of the toric IOL was determined by dilated slitlamp examination. RESULTS: The study enrolled 67 eyes of 60 patients. Four to 8 weeks postoperatively, the mean UDVA was 0.15 logMAR G 0.17 (SD) and the UDVA was 20/40 or better in 88% of eyes. The mean refractive cylinder decreased significantly postoperatively, from -1.91 +/- 1.07 D to -0.67 +/- 0.54 D. No significant change in keratometric cylinder was observed. The mean absolute IOL misalignment from the intended axis was 3.4 degrees (range 0 to 12 degrees). The good UDVA resulted in high levels of patient satisfaction. CONCLUSION: Implantation of the new toric IOL was an effective, safe, and predictable method to manage corneal astigmatism in patients having routine cataract surgery.

Evaluating the effect of splitting cylindrical power on improving patient tolerance to toric lens misalignment

Purpose: Evaluating the impact of splitting toric power on patient tolerance to misorientation such as with intraocular lens rotation. Setting: University vision clinic. Methods: Healthy, non astigmats had +1.50D astigmatism induced with spectacle lenses at 90°, 135°, 180° and +3.00D at 90°. Two correcting cylindrical lenses of the opposite sign and half the power each were subsequently added to the trial frame misaligned by 0°, 5° or 10° in a random order and misorientated from the initial axis in a clockwise direction by up to 15° in 5° steps. A second group of adapted astigmats with between 1.00 and 3.00DC had their astigmatism corrected with two toric spectacle lenses of half the power separated by 0°, 5° or 10° and misorientated from the initial axis in both directions by up to 15° in 5° steps. Distance, high contrast visual acuity was measured using a computerised test chart at each lens misalignment and misorientation. Results: Misorientation of the split toric lenses caused a statistically significant drop in visual acuity (F= 70.341; p< 0.001). Comparatively better acuities were observed around 180°, as anticipated (F= 3.775; p= 0.035). Misaligning the split toric power produced no benefit in visual acuity retention with axis misorientation when subjects had astigmatism induced with a low (F= 2.190, p= 0.129) or high cylinder (F= 0.491, p= 0.617) or in the adapted astigmats (F= 0.120, p= 0.887). Conclusion: Misalignment of toric lens power split across the front and back lens surfaces had no beneficial effect on distance visual acuity, but also no negative effect. © 2013 British Contact Lens Association.

Comparison of fitting stability of the different soft toric contact lenses

Purpose: To compare lens orientation and rotational recovery of five currently available soft toric lenses. Methods: Twenty subjects were recruited and trialed with each of the study lenses in a random order. Study lenses were PureVision® Toric (B&L), Air Optix® for Astigmatism (Alcon), Biofinity® Toric (CooperVision), Acuvue® Advance for Astigmatism (Vistakon), and Proclear® Toric (CooperVision). Lens orientation in primary position to determine the lens rotation form the vertical position and rotational recovery to primary gaze orientation following a 45° manual misorientation for the different lenses was compared. Results: The Biofinity Toric showed the lowest rotation from the vertical position and the Proclear Toric the highest. Also, the highest and the lowest reorientation speed were related to the Biofinity Toric and the Acuvue Advance for Astigmatism, respectively. The Repeated Measures ANOVA showed a significant difference in the lens rotation (P=. 0.004) and rotational recovery (P<. 0.001) among different contact lenses and the performed multiple comparisons indicated differences in rotation and also in reorientation speed were only seen between the Biofinity Toric when compared to four other lenses (P<. 0.05). Conclusion: Although there was appropriate fitting, based upon lens orientation and reorientation speed, with each of the study lenses it would appear that the optimized ballast technique used in the design of the Biofinity Toric helps reduce lens rotation and improve rotational recovery compared to others.

Computation of some Differential Operators in Toric Coordinates

Toric coordinates and toric vector field have been introduced in [2]. Let A be an arbitrary vector field. We obtain formulae for the divA, rotA and the Laplace operator in toric coordinates.

Light-distortion analysis as a possible indicator of visual quality after refractive lens exchange with diffractive multifocal intraocular lenses

METHODS: Refractive lens exchange was performed with implantation of an AT Lisa 839M (trifocal) or 909MP (bifocal toric) IOL, the latter if corneal astigmatism was more than 0.75 diopter (D). The postoperative visual and refractive outcomes were evaluated. A prototype light-distortion analyzer was used to quantify the postoperative light-distortion indices. A control group of eyes in which a Tecnis ZCB00 1-piece monofocal IOL was implanted had the same examinations. RESULTS: A trifocal or bifocal toric IOL was implanted in 66 eyes. The control IOL was implanted in 18 eyes. All 3 groups obtained a significant improvement in uncorrected distance visual acuity (UDVA) (P < .001) and corrected distance visual acuity (CDVA) (P Z .001). The mean uncorrected near visual acuity (UNVA) was 0.123 logMAR with the trifocal IOL and 0.130 logMAR with the bifocal toric IOL. The residual refractive cylinder was less than 1.00 D in 86.7% of cases with the toric IOL. The mean light-distortion index was significantly higher in the multifocal IOL groups than in the monofocal group (P < .001), although no correlation was found between the light-distortion index and CDVA. CONCLUSIONS: The multifocal IOLs provided excellent UDVA and functional UNVA despite increased light-distortion indices. The light-distortion analyzer reliably quantified a subjective component of vision distinct from visual acuity; it may become a useful adjunct in the evaluation of visual quality obtained with multifocal IOLs.