Hausdorff dimension of operator semistable L\'evy processes

Let $X=\{X(t)\}_{t\geq0}$ be an operator semistable L\'evy process in \rd with exponent $E$, where $E$ is an invertible linear operator on \rd and $X$ is semi-selfsimilar with respect to $E$. By refining arguments given in Meerschaert and Xiao \cite{MX} for the special case of an operator stable (selfsimilar) L\'evy process, for an arbitrary Borel set B\subseteq\rr_+ we determine the Hausdorff dimension of the partial range $X(B)$ in terms of the real parts of the eigenvalues of $E$ and the Hausdorff dimension of $B$.Comment: 23 page

Choriocapillaris and Choroidal Microvasculature Imaging with Ultrahigh Speed OCT Angiography

We demonstrate in vivo choriocapillaris and choroidal microvasculature imaging in normal human subjects using optical coherence tomography (OCT). An ultrahigh speed swept source OCT prototype at 1060 nm wavelengths with a 400 kHz A-scan rate is developed for three-dimensional ultrahigh speed imaging of the posterior eye. OCT angiography is used to image three-dimensional vascular structure without the need for exogenous fluorophores by detecting erythrocyte motion contrast between OCT intensity cross-sectional images acquired rapidly and repeatedly from the same location on the retina. En face OCT angiograms of the choriocapillaris and choroidal vasculature are visualized by acquiring cross-sectional OCT angiograms volumetrically via raster scanning and segmenting the three-dimensional angiographic data at multiple depths below the retinal pigment epithelium (RPE). Fine microvasculature of the choriocapillaris, as well as tightly packed networks of feeding arterioles and draining venules, can be visualized at different en face depths. Panoramic ultra-wide field stitched OCT angiograms of the choriocapillaris spanning ~32 mm on the retina show distinct vascular structures at different fundus locations. Isolated smaller fields at the central fovea and ~6 mm nasal to the fovea at the depths of the choriocapillaris and Sattler's layer show vasculature structures consistent with established architectural morphology from histological and electron micrograph corrosion casting studies. Choriocapillaris imaging was performed in eight healthy volunteers with OCT angiograms successfully acquired from all subjects. These results demonstrate the feasibility of ultrahigh speed OCT for in vivo dye-free choriocapillaris and choroidal vasculature imaging, in addition to conventional structural imaging.National Institutes of Health (U.S.) (NIH R01-EY011289-27)National Institutes of Health (U.S.) (NIH R01-EY013178-12)National Institutes of Health (U.S.) (NIH R44-EY022864-01)National Institutes of Health (U.S.) (NIH R01-CA075289-16)United States. Air Force Office of Scientific Research (AFOSR FA9550-10-1-0551)United States. Air Force Office of Scientific Research (AFOSR FA9550-12-1-0499

Proof of concept, randomized, placebo-controlled study of the effect of simvastatin on the course of age-related macular degeneration

BACKGROUND: HMG Co-A reductase inhibitors are ubiquitous in our community yet their potential role in age-related macular degeneration (AMD) remains to be determined. METHODOLOGY/PRINCIPAL FINDINGS: OBJECTIVES: To evaluate the effect of simvastatin on AMD progression and the effect modification by polymorphism in apolipoprotein E (ApoE) and complement factor H (CFH) genes. DESIGN: A proof of concept double-masked randomized controlled study. PARTICIPANTS: 114 participants aged 53 to 91 years, with either bilateral intermediate AMD or unilateral non-advanced AMD (with advanced AMD in fellow eye), BCVA ≥ 20/60 in at least one eye, and a normal lipid profile. INTERVENTION: Simvastatin 40 mg/day or placebo, allocated 1:1. MAIN OUTCOME MEASURES: Progression of AMD either to advanced AMD or in severity of non-advanced AMD. Results. The cumulative AMD progression rates were 70% in the placebo and 54% in the simvastatin group. Intent to treat multivariable logistic regression analysis, adjusted for age, sex, smoking and baseline AMD severity, showed a significant 2-fold decrease in the risk of progression in the simvastatin group: OR 0.43 (0.18-0.99), p = 0.047. Post-hoc analysis stratified by baseline AMD severity showed no benefit from treatment in those who had advanced AMD in the fellow eye before enrolment: OR 0.97 (0.27-3.52), p = 0.96, after adjusting for age, sex and smoking. However, there was a significant reduction in the risk of progression in the bilateral intermediate AMD group compared to placebo [adjusted OR 0.23 (0.07-0.75), p = 0.015]. The most prominent effect was observed amongst those who had the CC (Y402H) at risk genotype of the CFH gene [OR 0.08 (0.02-0.45), p = 0.004]. No evidence of harm from simvastatin intervention was detected. CONCLUSION/SIGNIFICANCE: Simvastatin may slow progression of non-advanced AMD, especially for those with the at risk CFH genotype CC (Y402H). Further exploration of the potential use of statins for AMD, with emphasis on genetic subgroups, is warranted. TRIAL REGISTRATION: Australian New Zealand Clinical Trial Registry (ANZCTR) ACTRN1260500032065

The role of the carotenoids, lutein and zeaxanthin, in protecting against age-related macular degeneration: A review based on controversial evidence

PURPOSE: A review of the role of the carotenoids, lutein and zeaxanthin, and their function in altering the pathogenesis of age-related macular degeneration (AMD). METHODS: Medline and Embase search. RESULTS: Recent evidence introduces the possibility that lutein and zeaxanthin, carotenoids found in a variety of fruits and vegetables may protect against the common eye disease of macular degeneration. This potential and the lack to slow the progression of macular degeneration, has fueled high public interest in the health benefits of these carotenoids and prompted their inclusion in various supplements. The body of evidence supporting a role in this disease ranges from basic studies in experimental animals to various other clinical and epidemiological studies. Whilst some epidemiological studies suggest a beneficial role for carotenoids in the prevention of AMD, others are found to be unrelated to it. Results of some clinical studies indicate that the risk for AMD is reduced when levels of the carotenoids are elevated in the serum or diet, but this correlation is not observed in other studies. Published data concerning the toxicity of the carotenoids or the optimum dosage of these supplements is lacking. CONCLUSION: An intake of dietary supplied nutrients rich in the carotenoids, lutein and zeaxanthin, appears to be beneficial in protecting retinal tissues, but this is not proven. Until scientifically sound knowledge is available we recommend for patients judged to be at risk for AMD to: alter their diet to more dark green leafy vegetables, wear UV protective lenses and a hat when outdoors. Future investigations on the role of nutrition, light exposure, genetics, and combinations of photodynamic therapy with intravitreal steroid (triamcinolone-acetonide) injections hold potential for future treatment possibilities

Comparing polymethylmethacrylate implant with collagen implant in deep sclerectomy: a randomized controlled trial

PURPOSE: To compare the intraocular pressure (IOP) lowering effect and safety of a new rigid, nonabsorbable polymethylmethacrylate implant (PMMA) with the commercially available cylindrical collagen implant used in deep sclerectomy procedure. INTERVENTION: Nonpenetrating deep sclerectomy was performed on all patients. Patients were randomly assigned to receive either a PMMA implant or a collagen implant. METHODS: The trial involved 60 patients (60 eyes) with medically uncontrolled primary and secondary open-angle glaucoma who were randomized to receive either a PMMA implant (30 eyes) or the collagen implant (30 eyes). The patients were examined before and after the operation 1 day before surgery and at day 1; weeks 1, 2 and 3; and months 1, 2, 3, 6, 9, 12, 18, 24, and 30. At each visit, the following examinations were performed: slit lamp examination, tonometry, visual acuity, and fundoscopy. RESULTS: The mean follow-up period was 20.4 (SD 12.4) months (PMMA) and 15.1 (SD 7.7) months (collagen) (P=NS). The mean preoperative IOP was 21.4 (SD 7.1) mm Hg (PMMA) and 21.0 mm Hg (SD 5.4) (collagen). The mean postoperative IOP was 7.4 (SD 4.5) mm Hg (PMMA) and 5.4 (SD 4.4) mm Hg (collagen) at day 1 (P=NS), 15.7 (SD 5.0) mm Hg (PMMA) and 14.7 (SD 5.0) mm Hg (collagen) at month 1 (P=NS), and 13.8 (SD 4.8) mm Hg (PMMA) and 13.3 (SD 2.4) mm Hg (collagen) at month 12 (P=NS). Seven patients had perforations of the trabeculo-Descemet membrane and were excluded from the analysis. At the last follow-up visit, 42% of PMMA patients and 44% of collagen patients achieved an IOP of 21 mm Hg or less without medication (P=NS). The number of medications was reduced from 2.4 (SD 1.0) to 0.6 (SD 0.6) (P<0.001) in the PMMA group, and from 2.4 (SD 1.1) to 0.7 (SD 0.8) (P<0.001) in the collagen group. There were no significant differences between the 2 groups in postoperative and transient complications. CONCLUSIONS: The new PMMA implant offered success and complication rates equal to those of the collagen implant. The new PMMA implant could serve as a low-cost alternative to the collagen implant and render the use of deep sclerectomy with an implant affordable for settings with limited financial resources