Multi-scale modeling of follicular ovulation as a reachability problem

During each ovarian cycle, only a definite number of follicles ovulate, while the others undergo a degeneration process called atresia. We have designed a multi-scale mathematical model where ovulation and atresia result from a hormonal controlled selection process. A 2D-conservation law describes the age and maturity structuration of the follicular cell population. In this paper, we focus on the operating mode of the control, through the study of the characteristics of the conservation law. We describe in particular the set of microscopic initial conditions leading to the macroscopic phenomenon of either ovulation or atresia, in the framework of backwards reachable sets theory

The Evolution of Central Retinal and Choroidal Thickness in Acute Anterior Uveitic Patients with Spondyloarthropathy

Purpose. To describe and correlate the degree of anterior segment inflammation with central retinal and choroidal thickness throughout the treatment period (in the course of follow-up) in the eyes affected with acute anterior uveitis in the patients with seronegative spondyloarthropathy (subgroup: ankylosing spondylitis). Methods. Thirty eyes of 30 consecutive Caucasian patients with HLA-B27-associated acute anterior uveitis were included in this study. The flare, AC cell number, and central retinal/choroidal thickness were determined at each visit by optical coherence tomography and laser flare photometry. Treatment consisted of topical corticosteroids. Statistical analysis was performed by MathWorks Matlab software. Results. In the follow-up period, central retinal thickness was increased in the first 9-10 days and then decreased until stabilization (after 5-6 weeks). The flare and AC cell number decreased rapidly at the beginning of the treatment, in the first 10 days, and thereafter, slower decrease could be observed until complete resolution of inflammation. Statistically significant, positive correlation was found between initial laser flare value and maximal central retinal thickness (r = 0.881, p < 0.001). Positive correlation between flare and retinal thickening was observable throughout the treatment period. Central choroidal thickness was decreased also significantly during the follow-up (p < 0.001). Conclusions. The retina and choroid may play a biomarker function in the anterior segment inflammation of the eye in the patients with seronegative spondyloarthropathy

On Nonlinear Stochastic Balance Laws

We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal equicontinuity in $L^1$ of the approximations, uniformly in the viscosity coefficient. Using these estimates, we supply a multidimensional existence theory of stochastic entropy solutions. In addition, we establish an error estimate for the stochastic viscosity method, as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions. Various further generalizations of the results are discussed

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

Construction of a Mean Square Error Adaptive Euler--Maruyama Method with Applications in Multilevel Monte Carlo

A formal mean square error expansion (MSE) is derived for Euler--Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a pathwise a posteriori adaptive time stepping Euler--Maruyama method for numerical solutions of SDE, and the resulting method is incorporated into a multilevel Monte Carlo (MLMC) method for weak approximations of SDE. This gives an efficient MSE adaptive MLMC method for handling a number of low-regularity approximation problems. In low-regularity numerical example problems, the developed adaptive MLMC method is shown to outperform the uniform time stepping MLMC method by orders of magnitude, producing output whose error with high probability is bounded by TOL>0 at the near-optimal MLMC cost rate O(TOL^{-2}log(TOL)^4).Comment: 43 pages, 12 figure

Guidance on noncorticosteroid systemic immunomodulatory therapy in noninfectious uveitis: fundamentals of care for uveitis (focus) initiative

Topic: An international, expert-led consensus initiative to develop systematic, evidence-based recommendations for the treatment of noninfectious uveitis in the era of biologics. Clinical Relevance: The availability of biologic agents for the treatment of human eye disease has altered practice patterns for the management of noninfectious uveitis. Current guidelines are insufficient to assure optimal use of noncorticosteroid systemic immunomodulatory agents. Methods: An international expert steering committee comprising 9 uveitis specialists (including both ophthalmologists and rheumatologists) identified clinical questions and, together with 6 bibliographic fellows trained in uveitis, conducted a Preferred Reporting Items for Systematic Reviews and Meta-Analyses protocol systematic reviewof the literature (English language studies from January 1996 through June 2016; Medline [OVID], the Central Cochrane library, EMBASE,CINAHL,SCOPUS,BIOSIS, andWeb of Science). Publications included randomized controlled trials, prospective and retrospective studies with sufficient follow-up, case series with 15 cases or more, peer-reviewed articles, and hand-searched conference abstracts from key conferences. The proposed statements were circulated among 130 international uveitis experts for review.Atotal of 44 globally representativegroupmembersmet in late 2016 to refine these guidelines using a modified Delphi technique and assigned Oxford levels of evidence. Results: In total, 10 questions were addressed resulting in 21 evidence-based guidance statements covering the following topics: when to start noncorticosteroid immunomodulatory therapy, including both biologic and nonbiologic agents; what data to collect before treatment; when to modify or withdraw treatment; how to select agents based on individual efficacy and safety profiles; and evidence in specific uveitic conditions. Shared decision-making, communication among providers and safety monitoring also were addressed as part of the recommendations. Pharmacoeconomic considerations were not addressed. Conclusions: Consensus guidelines were developed based on published literature, expert opinion, and practical experience to bridge the gap between clinical needs and medical evidence to support the treatment of patients with noninfectious uveitis with noncorticosteroid immunomodulatory agents

The Effect of Tear Supplementation on Ocular Surface Sensations during the Interblink Interval in Patients with Dry Eye.

PURPOSE: To investigate the characteristics of ocular surface sensations and corneal sensitivity during the interblink interval before and after tear supplementation in dry eye patients. METHODS: Twenty subjects (41.88+/-14.37 years) with dry eye symptoms were included in the dry eye group. Fourteen subjects (39.13+/-11.27 years) without any clinical signs and/or symptoms of dry eye were included in the control group. Tear film dynamics was assessed by non-invasive tear film breakup time (NI-BUT) in parallel with continuous recordings of ocular sensations during forced blinking. Corneal sensitivity to selective stimulation of corneal mechano-, cold and chemical receptors was assessed using a gas esthesiometer. All the measurements were made before and 5 min after saline and hydroxypropyl-guar (HP-guar) drops. RESULTS: In dry eye patients the intensity of irritation increased rapidly after the last blink during forced blinking, while in controls there was no alteration in the intensity during the first 10 sec followed by an exponential increase. Irritation scores were significantly higher in dry eye patients throughout the entire interblink interval compared to controls (p0.05). CONCLUSION: Ocular surface irritation responses due to tear film drying are considerably increased in dry eye patients compared to normal subjects. Although tear supplementation improves the protective tear film layer, and thus reduce unpleasant sensory responses, the rapid rise in discomfort is still maintained and might be responsible for the remaining complaints of dry eye patients despite the treatment

Guidance on Noncorticosteroid Systemic Immunomodulatory Therapy in Noninfectious Uveitis: Fundamentals Of Care for UveitiS (FOCUS) Initiative

Topic: An international, expert-led consensus initiative to develop systematic, evidence-based recommendations for the treatment of noninfectious uveitis in the era of biologics. Clinical Relevance: The availability of biologic agents for the treatment of human eye disease has altered practice patterns for the management of noninfectious uveitis. Current guidelines are insufficient to assure optimal use of noncorticosteroid systemic immunomodulatory agents. Methods: An international expert steering committee comprising 9 uveitis specialists (including both ophthalmologists and rheumatologists) identified clinical questions and, together with 6 bibliographic fellows trained in uveitis, conducted a Preferred Reporting Items for Systematic Reviews and Meta-Analyses protocol systematic review of the literature (English language studies from January 1996 through June 2016; Medline [OVID], the Central Cochrane library, EMBASE, CINAHL, SCOPUS, BIOSIS, and Web of Science). Publications included randomized controlled trials, prospective and retrospective studies with sufficient follow-up, case series with 15 cases or more, peer-reviewed articles, and hand-searched conference abstracts from key conferences. The proposed statements were circulated among 130 international uveitis experts for review. A total of 44 globally representative group members met in late 2016 to refine these guidelines using a modified Delphi technique and assigned Oxford levels of evidence. Results: In total, 10 questions were addressed resulting in 21 evidence-based guidance statements covering the following topics: when to start noncorticosteroid immunomodulatory therapy, including both biologic and nonbiologic agents; what data to collect before treatment; when to modify or withdraw treatment; how to select agents based on individual efficacy and safety profiles; and evidence in specific uveitic conditions. Shared decision-making, communication among providers and safety monitoring also were addressed as part of the recommendations. Pharmacoeconomic considerations were not addressed. Conclusions: Consensus guidelines were developed based on published literature, expert opinion, and practical experience to bridge the gap between clinical needs and medical evidence to support the treatment of patients with noninfectious uveitis with noncorticosteroid immunomodulatory agents