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Purpose: To investigate the effects of 1% atropine eye drops on the choroidal thickness and structure of amblyopic and fellow eyes in children with hyperopic anisometropic amblyopia. Methods: This study included 16 children with hypermetropic anisometropic amblyopia. All patients received 1% atropine eye drops in both eyes twice a day for 7 days. In the subfoveal choroidal region, choroidal thickness, total choroidal area, luminal area, and stromal area were measured quantitatively using swept-source optical coherence tomography. The choroidal parameters of the amblyopic and fellow eyes were compared between the baseline and atropine conditions. Results: There were no significant differences in all choroidal parameters of the amblyopic eye between baseline and atropine conditions. However, the subfoveal choroidal thickness in the fellow eye was significantly higher for the atropine condition than the baseline condition. This change was accompanied by a significant increase in both the luminal and stromal areas of the choroid. The median differences of subfoveal choroidal thickness between the conditions were larger for the fellow eye (6.46%) than the amblyopic eye (0.26%). Conclusions: The choroidal structural change induced by 1% atropine instillation was smaller for the amblyopic eye than the fellow eye in children with hyperopic anisometropic amblyopia. Mechanisms of choroidal thickness changes could be inhibited in amblyopic eyes. [ J Pediatr Ophthalmol Strabismus . 2023;60(1):39–45.]

We consider the 3D incompressible Navier–Stokes equations under the following 2 + 1 2 2+\frac {1}{2} -dimensional situation: vertical vortex blob (quasi-streamwise vortices) being stretched by two-dimensional shear flow. We prove enhanced dissipation induced by such quasi-streamwise vortices.

Two fluid configurations along a flow are conjugate if there is a one parameter family of geodesics (fluid flows) joining them to infinitesimal order. Geometrically, they can be seen as a consequence of the (infinite dimensional) group of volume preserving diffeomorphisms having sufficiently strong positive curvatures which ‘pull’ nearby flows together. Physically, they indicate a form of (transient) stability in the configuration space of particle positions: a family of flows starting with the same configuration deviate initially and subsequently re-converge (resonate) with each other at some later moment in time. Here, we first establish existence of conjugate points in an infinite family of Kolmogorov flows—a class of stationary solutions of the Euler equations—on the rectangular flat torus of any aspect ratio. The analysis is facilitated by a general criterion for identifying conjugate points in the group of volume preserving diffeomorphisms. Next, we show non-existence of conjugate points along Arnold stable steady states on the annulus, disk and channel. Finally, we discuss cut points, their relation to non-injectivity of the exponential map (impossibility of determining a flow from a particle configuration at a given instant) and show that the closest cut point to the identity is either a conjugate point or the midpoint of a time periodic Lagrangian fluid flow.

We consider enstrophy dissipation in two-dimensional (2D) Navier-Stokes flows and focus on how this quantity behaves in thelimit of vanishing viscosity. After recalling a number of a priori estimates providing lower and upper bounds on this quantity, we state an optimization problem aimed at probing the sharpness of these estimates as functions of viscosity. More precisely, solutions of this problem are the initial conditions with fixed palinstrophy and possessing the property that the resulting 2D Navier-Stokes flows locally maximize the enstrophy dissipation over a given time window. This problem is solved numerically with an adjoint-based gradient ascent method and solutions obtained for a broad range of viscosities and lengths of the time window reveal the presence of multiple branches of local maximizers, each associated with a distinct mechanism for the amplification of palinstrophy. The dependence of the maximum enstrophy dissipation on viscosity is shown to be in quantitative agreement with the estimate due to Ciampa, Crippa & Spirito (2021), demonstrating the sharpness of this bound., 20 pages, 4 figures

Vortex thinning is one of the main mechanisms of two-dimensional turbulence. By direct numerical simulation to the two-dimensional Navier–Stokes equations with small-scale forcing and large-scale damping, Xiao et al (2009 J. Fluid Mech. 619 1–44) found an evidence that inverse energy cascade may proceed with the vortex thinning mechanism. On the other hand, Alexakis and Doering (2006 Phys. Lett. A 359 652–657) calculated the upper bound of the bulk averaged enstrophy dissipation rate of the steady-state two dimensional turbulence. In this paper, we show that vortex thinning induces enhanced dissipation with strictly slower vanishing order of the enstrophy dissipation than Re−1.

We studied the latitudinal and altitudinal variations in composition and species richness of trees in 24 plots across temperate to subtropical regions from southern Kyushu to the northern Ryukyu Ar...

We consider the 3D incompressible Navier–Stokes equations under the following $$2+\frac{1}{2}$$ -dimensional situation: small-scale horizontal vortex blob being stretched by large-scale, anti-parallel pairs of vertical vortex tubes. We prove enhanced dissipation induced by such vortex-stretching.

To investigate the treatment policy for amblyopia in Japan as of 2017 through a survey of multiple facilities and to compare the findings with those obtained by the Amblyopia Treatment Study (ATS) of the Pediatric Eye Disease Investigator Group.Questionnaire survey study.A questionnaire was sent to 181 facilities where patients with amblyopia are being treated. The outcomes of the present survey were compared with the results of the ATS study, and the coincidence rates were evaluated.The questionnaire response rate was 68.0%. The treatment plan that showed the highest agreement between the outcomes of the ATS study and the present study was whether or not treatment was to be given to patients aged 10-15 years who had received no previous treatment; 90% of the facilities answered that they would provide treatment to such patients as well. The next highest agreement was the future treatment of amblyopia with stable visual acuity in the affected eye; 82.6% of the facilities responded that they would reduce the occlusion time. On the other hand, the lowest agreement rate was the follow-up period of the refractive correction for moderate anisometropic amblyopia. The ATS showed "4 months," whereas most of the facilities in the present survey replied "3 months." The agreement rate was 10.8%.The amblyopia treatment in Japan survey did not always agree with the research results of the ATS. Japanese ophthalmologists tend to make treatment plans for amblyopia according to their clinical experience.

Energy transfers from larger to smaller scales in turbulence. This energy cascade is a process of the creation of smaller-scale coherent vortices by larger ones. In our recent study (Yoneda, Goto and Tsuruhashi 2022 Nonlinearity 35 , 1380-1401), we reformulated the energy cascade in terms of this stretching process and derived the − 5 / 3 law of the energy spectrum under physically reasonable assumptions. In the present study, we provide a quantitative verification of these assumptions by using direct numerical simulations. We decompose developed turbulence in a periodic cube into scales by using the band-pass filter and identify the axes of coherent tubular vortices by the low-pressure method. Even when the turbulent kinetic energy and its dissipation rate temporally fluctuate about their temporal means, the total length of the vortices at each scale varies little with time. This result is consistent with our assumption of the temporal stationarity on the vorticity decomposition. The present numerical analysis also shows that the hierarchy of vortex axes is self-similar in a wide range of scales, i.e. in the inertial range and a lower part of the dissipation range and that the volume fraction occupied by the tubular vortices at each scale is independent of the scale. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.

Glaucoma leads to irreversible blindness. Numerous anti-glaucoma eye drops have been developed. Unfortunately, many patients with glaucoma still suffer from progressive visual disorders. Recently, ripasudil hydrochloride hydrate, a selective Rho-associated protein kinase inhibitor, was launched for the treatment of glaucoma. However, adverse events, such as conjunctival hyperemia, are often noted in clinical trials using healthy subjects. Therefore, we investigated the onset, offset, and kinetic changes of conjunctival hyperemia induced by ripasudil ophthalmic solution in patients with open-angle glaucoma or ocular hypertension who had already been treated with anti-glaucoma eye drops other than ripasudil. Conjunctival hyperemia was evaluated by both clinical grading by 3 ophthalmic physicians and pixel coverage of conjunctival blood vessels determined by conjunctival hyperemia-analyzing software. Conjunctival hyperemia appeared within 10 min post-instillation in most of the participants. Clinical grade and pixel coverage increased significantly 10 min post-instillation and then decreased. In most of the participants, hyperemia resolved within 2 h. Median conjunctival hyperemia offset was 90 min. A tendency of monotonic increase was observed between clinical grade and pixel coverage. Taken altogether, hyperemia induced by ripasudil was transient in glaucoma patients who had already been treated with anti-glaucoma eye drops other than ripasudil.

In this paper, with the aid of direct numerical simulations (DNS) of forced turbulence in a periodic domain, we mathematically reformulate the Kolmogorov–Richardson energy cascade in terms of vortex stretching. By using the description, we prove that if the Navier–Stokes flow satisfies a new regularity criterion in terms of the enstrophy production rate, then the flow does not blow up. Our DNS results seem to support this regularity criterion. Next, we mathematically construct the hierarchy of tubular vortices, which is statistically self-similar in the inertial range. Under the assumptions of the scale-locally of the vortex stretching/compressing (i.e. energy cascade) process and the statistical independence between vortices that are not directly stretched or compressed, we can derive the −5/3 power law of the energy spectrum of statistically stationary turbulence without directly using the Kolmogorov hypotheses.

We investigate the geometry of the central extension $\widehat{\mathcal D}_{\mu}(S^{2})$ of the group of volume-preserving diffeomorphisms of the 2-sphere equipped with an $L^{2}$-metric, for which geodesics correspond to solutions of the incompressible Euler equation with Coriolis force. In particular, we calculate the Misiołek curvature of this group. This value is related to the existence of a conjugate point and its positivity directly implies the positivity of the sectional curvature.

In a method evaluating conjunctival hyperemia using rabbits, it is common to visually grade the degree of vasodilation. However, this method is limited in evaluating consecutive value and in reproducibility. We quantified the degree of conjunctival hyperemia in rabbits as the area ratio of blood vessels by image analysis, and compared the vascular area percentage calculated by image analysis with the hyperemia score.The conjunctiva was photographed before and after the instillation of 0.1% arachidonic acid using a digital medical scope VersaCamFifteen minutes after the instillation of arachidonic acid, the area ratio of the blood vessels in the conjunctiva increased significantly and gradually decreased over time. This trend correlated with the hyperemia score.We found that the degree of conjunctival hyperemia in rabbits can be evaluated numerically and quantitatively. This method is considered to be useful for evaluating conjunctival hyperemia in allergic conjunctival diseases.

BackgroundStructural changes of the choroid, such as choroidal thickening, have been indicated in amblyopic eyes with hyperopic anisometropia as compared to fellow or healthy eyes. The purpose of the present study was to investigate choroidal vascular density (CVD) in children with unilateral hyperopic amblyopia.MethodsThis study included 88 eyes of 44 patients with unilateral amblyopia due to hyperopic anisometropia with or without strabismus and 29 eyes of 29 age-matched normal controls. The CVD of Haller’s layer was quantified from en-face images constructed by 3-dimensional swept-source optical coherence tomography images flattened relative to Bruch’s membrane. The analysis area was a 3 × 3-mm square of macula after magnification correction. Relationships between CVD and other parameters [best-corrected visual acuity (BCVA), refractive error and subfoveal choroidal thickness (SFCT)] were investigated, and CVDs were compared between amblyopic, fellow, and normal control eyes.ResultsMean CVD was 59.11 ± 0.66% in amblyopic eyes, 59.23 ± 0.81% in fellow eyes, and 59.29 ± 0.74% in normal control eyes. CVD showed a significant positive relationship with SFCT (p = 0.004), but no relationships with other parameters. No significant differences in CVD were evident among amblyopic, fellow, and normal control eyes after adjusting for SFCT (p = 0.502).ConclusionsCVD was unrelated to BCVA, and CVD did not differ significantly among amblyopic, fellow and normal control eyes. These results suggest that the local CVD of Haller’s layer is unaffected in unilateral hyperopic amblyopic eyes.

Objective We investigated the detailed time course of conjunctival hyperemia induced by omidenepag isopropyl ophthalmic solution 0.002% (omidenepag), a selective prostaglandin E2 receptor 2 agonist. Methods and analysis We recruited 34 healthy subjects and administered omidenepag in the right eye and ripasudil 0.4% in the left eye. We evaluated conjunctival hyperemia using slit-lamp photography at baseline and after 15, 30, 60, 120, 180 and 360 min. The conjunctival hyperemia score was graded by three independent observers using a scale from 0 (none) to 3 (severe). We also evaluated conjunctival hyperemia by the pixel coverage of conjunctival blood vessels (per cent coverage) determined using a conjunctival hyperemia-analysing software. Results In omidenepag, the conjunctival hyperemia score and per cent coverage peaked at both 30 min (mean score±SD: 1.57±0.67 and 11.90%±3.66%, respectively) and then gradually decreased at 60 min (10.79%±3.32%) and 120 min (1.10±0.52) when they reached a level that was not significantly different from the baseline values. For ripasudil 0.4%, the peak time of the conjunctival hyperemia score and per cent coverage were both at 15 min (score: 2.42±0.54 and 15.26%±3.38%). The degree of conjunctival hyperemia was significantly higher for ripasudil 0.4% than that for omidenepag from 15 to 30 min in both the conjunctival hyperemia score and per cent coverage (p, The article has been presented at the 30th Annual Meeting of the Japanese Glaucoma Society on 7 September 2019.

We developed a hyperemia analysis software, which can quantitatively assess the degree of conjunctival hyperemia, and evaluated the reproducibility and reliability of its percent coverage. In addition, we compared the clinical grading and the percent coverage to examine the applicability of the software analysis.We took images of the temporal conjunctiva with slit lamp microscopes. We used our hyperemia analysis software to detect blood vessels in the region of interest using its image processing capabilities and obtained a ratio of the area occupied by blood vessels to the rest of the area. In addition, we used the clinical evaluation criteria of the Japanese guidelines for allergic conjunctival diseases 2017 to clinically grade the hyperemia in each eye. Nine evaluators examined the images and graded the severity of hyperemia into four stages. We looked for a statistical correlation between the results of the hyperemia analysis software and the clinical grading.The percent coverage of the blood vessels in the region of interest calculated by the hyperemia analysis software correlated with the arithmetic average of our clinical grading (r = 0.953; 95% CI, 0.8470340-0.9862136).The percent coverage from our hyperemia analysis software reflects the clinical grading score, suggesting that our software can be used to obtain a detailed analysis of conjunctival hyperemia.

[Purpose] This study aimed to assess the influence of ultrasound (US) transducer tilt on muscle thickness and echo intensity of the rectus femoris muscle (RF) in healthy subjects. [Subjects and Methods] Fourteen healthy male subjects (20.8 ± 0.8 years) participated in this study. Transducer tilt was measured during US, with a digital angle gauge. Muscle thickness and echo intensity were measured in 4 transducer tilt conditions: reference angle; +3°; +6°; and +9° cranial from the reference angle. [Results] All differences in transducer tilt relative to the reference condition were larger than the minimal detectable change (MDC) of the reference condition. All differences in muscle thickness relative to the reference condition were not larger than the MDC of the reference condition. All differences in the echo intensity relative to the reference condition, except between the reference and the +3° condition, were larger than the MDC of the reference condition. [Conclusion] Our results indicated that an examiner should maintain a precise transducer tilt during repeated US measurements to quantify the minimal change in the echo intensity of the RF.

Using numerical simulations of the axisymmetric Navier–Stokes equations with swirl on a no-slip flat boundary, Hsu et al. (J Fluid Mech 794:444–459, 2016) observed the creation of a high-vorticity region on the boundary near the axis of symmetry. In this paper, using a differential geometric approach, we prove that such flows indeed have a destabilizing effect, which is formulated in terms of a lower bound on the $$L^\infty $$ -norm of derivatives of the velocity field on the boundary.

In this paper, we consider the two–dimensional Euler flow under a simple symmetry condition, with hyperbolic structure in a unit square \({D = \{(x_1,x_2):0 < x_1+x_2 < \sqrt{2},0 < -x_1+x_2 < \sqrt{2}\}}\). It is shown that the Lipschitz estimate of the vorticity on the boundary is at most a single exponential growth near the stagnation point.

We give new viewpoints of Campanato spaces with variable growth condition for applications to the Navier-Stokes equation. Namely, we formulate a blowup criteria along maximum points of the 3D-Navier-Stokes flow in terms of stationary Euler flows and show that the properties of Campanato spaces with variable growth condition are very useful for this formulation, since variable growth condition can control the continuity and integrability of functions on the neighborhood at each point. Our criterion is different from the Beale-Kato-Majda type and Constantin-Fefferman type criterion. If geometric behavior of the velocity vector field near the maximum point has a kind of stationary Euler flow configuration up to a possible blowup time, then the solution can be extended to be the strong solution beyond the possible blowup time. As another application we also mention the Cauchy problem for the Navier-Stokes equation.

Background Recent studies using optical coherence tomography (OCT) have indicated that choroidal thickness (CT) in the anisometropic amblyopic eye is thicker than that of the fellow and normal control eyes. However, it has not yet been established as to how amblyopia affects the choroid thickening. The purpose of the present study was to investigate the effect of amblyopia treatment on macular CT in eyes with anisometropic amblyopia using swept-source OCT. Methods Thirteen patients (mean age: 6.2 ± 2.4 years) with hypermetropic anisometropic amblyopia were included in this study. Visual acuity (VA), axial length (AL), and CT were measured at the enrollment visit and at the final visit, after at least 6 months of treatment. CT measurements were corrected for magnification error and were automatically analyzed using built-in software and divided into three macular regions (subfoveal choroidal thickness (SFCT), center 1 mm, and center 6 mm). A one-way analysis of covariance using AL as a covariate was performed to determine whether CT in amblyopic eyes changed after amblyopia treatment. Results The average observation period was 22.2 ± 11.0 months. After treatment, VA (logMAR) improvement in the amblyopic eyes was 0.41 ± 0.19 (p

We used an image analysis software program to quantitatively investigate conjunctival injection in patients treated with eye drops for glaucoma.We compared 169 patients (89 men and 80 women) with a diagnosis of glaucoma. Photographs of the conjunctiva were taken on the temporal side of each patient's right eye using a slit lamp. We determined the mean pixel frequencies of the conjunctival blood vessels from the photographs.The ocular hyperemia of the patients being treated with prostaglandins was more severe than that of the patients being treated with beta-blockers or no eye drops. In multiple comparisons of each of the eye drops, the control group had a significantly lower degree of hyperemia than did the patients being treated with each of the various prostaglandin analogs (latanoprost, travoprost, tafluprost, and bimatoprost). Among the patients receiving prostaglandin, the percentage of those with hyperemia was highest in the bimatoprost users, followed in order by the travoprost, latanoprost, and tafluprost users. However, no significant differences were found among the different prostaglandin analogs in terms of the percentage of patients with hyperemia.Our software program may be useful for evaluating the hyperemic effects of eye drops used for glaucoma. The particular type of prostaglandin analog seems to determine the level of conjunctival hyperemia during ocular hypotensive medical treatment.

We show that the 2D Euler equations are not locally well-posed in the sense of Hadamard in the \(C^1\) space and in the Besov space \(B^1_{\infty ,1}\). Our approach relies on the technique of Lagrangian deformations of Bourgain and Li (Strong ill-posedness of the incompressible Euler equations in borderline Sobolev spaces. arXiv:1307.7090). We show that the assumption that the data-to-solution map is continuous in either \(C^1\) or \(B^1_{\infty ,1}\) leads to a contradiction with a result in \(W^{1,p}\) of Kato and Ponce (Rev Mat Iberoam 2:73–88, 1986).

Digitization of clinical observation is necessary for assessing the severity of superior limbic keratoconjunctivitis (SLK). This study aimed to use a novel quantitative marker to examine hyperemia in patients with SLK.We included six eyes of six patients with both dry eye disease and SLK (SLK group) and eight eyes of eight patients with Sjögren syndrome (SS group). We simultaneously obtained the objective finding scores by using slit-lamp examination and calculated the superior hyperemia index (SHI) with an automated conjunctival hyperemia analysis software by using photographs of the anterior segment. Three objective finding scores, including papillary formation of the superior palpebral conjunctiva, superior limbal hyperemia and swelling, and superior corneal epitheliopathy, were determined. The SHI was calculated as the superior/temporal ratio of bulbar conjunctival hyperemia by using the software. Fisher's exact test was used to compare a high SHI (≥1.07) ratio between the SLK and SS groups. P-Values0.05 were considered statistically significant.The SHI (mean ± standard deviation) in the SLK and SS groups was 1.19 ± 0.50 and 0.69 ± 0.24, respectively. The number of patients with a high SHI (≥1.07) was significantly higher in the SLK group than in the SS group (p 0.05). The sensitivity and specificity of the SHI in the differential diagnosis between SS and SLK were 66.7% and 87.5%, respectively. An analysis of the association between the objective finding scores and SHI showed that the SHI had a tendency to indicate the severity of superior limbal hyperemia and swelling score in the SLK group.The SHI calculated using the automated conjunctival hyperemia analysis software could successfully quantify superior bulbar conjunctival hyperemia and may be a useful tool for the differential diagnosis between SS and SLK and for the quantitative follow-up of patients with SLK.

Ma and Wang derived an equation linking the separation location and times for the boundary layer separation of incompressible fluid flows. The equation gave a necessary condition for the separation (bifurcation) point. The purpose of this paper is to generalize the equation to other geometries, and to phrase it as a simple ODE. Moreover we consider the Navier-Stokes equation with the Coriolis effect, which is related to the presence of trade winds on Earth., 10 pages, submitted

Conjunctival hyperemia is observed in a variety of ocular inflammatory conditions. The evaluation of hyperemia is indispensable for the treatment of patients with ocular inflammation. However, the major methods currently available for evaluation are based on nonquantitative and subjective methods. Therefore, we developed novel software to evaluate bulbar hyperemia quantitatively and objectively. First, we investigated whether the histamine-induced hyperemia of guinea pigs could be quantified by image analysis. Bulbar conjunctival images were taken by means of a digital camera, followed by the binarization of the images and the selection of regions of interest (ROIs) for evaluation. The ROIs were evaluated by counting the number of absolute pixel values. Pixel values peaked significantly 1 minute after histamine challenge was performed and were still increased after 5 minutes. Second, we applied the same method to antigen (ovalbumin)-induced hyperemia of sensitized guinea pigs, acquiring similar results except for the substantial upregulation in the first 5 minutes after challenge. Finally, we analyzed human bulbar hyperemia using the new software we developed especially for human usage. The new software allows the automatic calculation of pixel values once the ROIs have been selected. In our clinical trials, the percentage of blood vessel coverage of ROIs was significantly higher in the images of hyperemia caused by allergic conjunctival diseases and hyperemia induced by Bimatoprost, compared with those of healthy volunteers. We propose that this newly developed automated hyperemia analysis software will be an objective clinical tool for the evaluation of ocular hyperemia.

In this paper we prove the Liouville type theorem for the stationary Navier–Stokes equations on R 3 . More specifically, if a solution u ∈ H 1 ( R 3 ) to the stationary Navier–Stokes system satisfies additional conditions characterized by the decays near infinity and by the oscillation, then we show that u = 0 .

Aim Large trees (d.b.h. 70 cm) store large amounts of biomass. Several studies suggest that large trees may be vulnerable to changing climate, poten- tially leading to declining forest biomass storage. Here we determine the importance of large trees for tropical forest biomass storage and explore which intrinsic (species trait) and extrinsic (environment) variables are associated with the density of large trees and forest biomass at continental and pan-tropical scales. Location Pan-tropical.

We consider existence of global solutions to equations for three-dimensional rotating fluids in a periodic frame provided by a sufficiently large Coriolis force. The Coriolis force appears in almost all of the models of meteorology and geophysics dealing with large-scale phenomena. In the spatially decaying case, Koh, Lee and Takada (2014) showed existence for the large times of solutions of the rotating Euler equations provided by the large Coriolis force. In this case the resonant equation does not appear anymore. In the periodic case, however, the resonant equation appears, and thus the main subject in this case is to show existence of global solutions to the resonant equation. Research in this direction was initiated by Babin, Mahalov and Nicolaenko (1999) who treated the rotating Navier-Stokes equations on general periodic domains. On the other hand, Golse, Mahalov and Nicolaenko (2008) considered bursting dynamics of the resonant equation in the case of a cylinder with no viscosity. Thus we may not expect to show global existence of solutions to the resonant equation without viscosity in the periodic case. In this paper we show existence of global solutions for fractional Laplacian case (with its power strictly less than the usual Laplacian) in the periodic domain with the same period in each direction. The main ingredient is an improved estimate on resonant three-wave interactions, which is based on a combinatorial argument., Comment: In this revised version, the main theorem has been slightly improved and part of its proof (Section 6) has been simplified