A solute gradient in the tear meniscus I. A hypothesis to explain Marx's line

Marx's line is a line of mucosal staining behind the mucocutaneous junction. It can be demonstrated throughout life in all normal lids by staining with lissamine green and related dyes. Of all the body orifices, only the mucosae of the eye and mouth are directly exposed to the atmosphere. In this paper, we suggest that for the eye, this exposure leads to the formation of Marx's line. The tear meniscus thins progressively toward its apex, where it is pinned at the mucocutaneous junction of the lid. It also thins toward the black line, which segregates the meniscus from the tear film after the blink. We predict that, because of the geometry of the tear meniscus, evaporation generates a solute gradient across the meniscus profile in the anteroposterior plane, which peaks at the meniscus apices at the end of the interblink. One outcome would be to amplify the level of tear molarity at these sites so that they reach hyperosmolar proportions. Preliminary mathematical modeling suggests that dilution of this effect by advection and diffusion of solute away from the meniscus apex at the mucocutaneous junction will be restricted by spatial constraints, the presence of tear and surface mucins at this site, and limited fluid flow. We conclude that evaporative water loss from the tear meniscus may result in a physiological zone of hyperosmolar and related stresses to the occlusal conjunctiva, directly behind the mucocutaneous junction. We hypothesize that this stimulates a high epithelial cell turnover at this site, incomplete epithelial maturation, and a failure to express key molecules such as MUC 16 and galectin-3, which, with the tight junctions between surface epithelial cells, are necessary to seal the ocular surface and prevent penetration of dyes and other molecules into the epithelium. This is proposed as the basis for Marx's line. In Part II of this paper (also published in this issue of The Ocular Surface), we address additional pathophysiological consequences of this mechanism, affecting lid margins

A solute gradient in the tear meniscus II. implications for lid margin disease, including meibomian gland dysfunction

We have hypothesized previously that evaporation from the tears generates a solute gradient across the tear meniscus, which delivers hyperosmolar stress to the mucocutaneous junction (MCJ) of the lid margin. This is proposed as the basis for Marx's line, a line of staining with topically applied dyes that lies directly behind the MCJ. In this article, we consider the implications of this hypothesis for progressive damage to the lid margin as an age-related phenomenon, its amplification in dry eye states, and its possible role in the etiology of meibomian gland dysfunction (MGD). It is suggested that a hyperosmolar or related stimulus, acting behind the MCJ over a lifetime, promotes the anterior migration of the MCJ, which is a feature of the aging lid margin. This mechanism would be amplified in dry eye states, not only by reason of increased tear molarity at the meniscus apex but also by raising the concentration of inflammatory peptides at this site. This could explain the increased width and irregularity of Marx's line in dry eye. While the presence of stem cells at the lid margin may equip this region to respond to such stress, their depletion could be the basis of irreversible lid margin damage. It is further proposed, given the proximity of the MCJ to the meibomian gland orifices, that the solute gradient mechanism could play a role in the initiation of MGD by delivering hyperosmolar and inflammatory stresses to the terminal ducts and orifices of the glands. By the same token, the presence of a zone of increased epithelial permeability in this region may provide a back door route for the delivery of drugs in the treatment of MGD

A mass and solute balance model for tear volume & osmolarity in the normal and the dry eye

Tear hyperosmolarity is thought to play a key role in the mechanism of dry eye, a common symptomatic condition accompanied by visual disturbance, tear film instability, inflammation and damage to the ocular surface. We have constructed a model for the mass and solute balance of the tears, with parameter estimation based on extensive data from the literature which permits the influence of tear evaporation, lacrimal flux and blink rate on tear osmolarity to be explored. In particular the nature of compensatory events has been estimated in aqueous-deficient (ADDE) and evaporative (EDE) dry eye.\ud \ud The model reproduces observed osmolarities of the tear meniscus for the healthy eye and predicts a higher concentration in the tear film than meniscus in normal and dry eye states. The differential is small in the normal eye, but is significantly increased in dry eye, especially for the simultaneous presence of high meniscus concentration and low meniscus radius. This may influence the interpretation of osmolarity values obtained from meniscus samples since they need not fully reflect potential damage to the ocular surface caused by tear film hyperosmolarity.\ud \ud Interrogation of the model suggests that increases in blink rate may play a limited role in compensating for a rise in tear osmolarity in ADDE but that an increase in lacrimal flux, together with an increase in blink rate, may delay the development of hyperosmolarity in EDE. Nonetheless, it is predicted that tear osmolarity may rise to much higher levels in EDE than ADDE before the onset of tear film breakup, in the absence of events at the ocular surface which would independently compromise tear film stability. Differences in the predicted responses of the pre-ocular tears in ADDE compared to EDE or hybrid disease to defined conditions suggest that no single, empirically-accessible variable can act as a surrogate for tear film concentration and the potential for ocular surface damage. This emphasises the need to measure and integrate multiple diagnostic indicators to determine outcomes and prognosis. Modelling predictions in addition show that further studies concerning the possibility of a high lacrimal flux phenotype in EDE are likely to be profitable

Central connections of the lacrimal functional unit

Purpose: To study the contribution of each eye to the reflex tear response, after unilateral and bilateral topical anaesthesia. Method: A closed eye, modified Schirmer test was performed bilaterally in 8 normal subjects, in a controlled environment chamber set to 23°C, 45% relative humidity and 0.08m/s airflow. Eye drops were instilled into each eye 10 minutes before the Schirmer test. Experiments were: a) bilateral saline (control) b) unilateral anaesthesia (ipsilateral anaesthetic; contralateral saline) and c) bilateral anaesthesia. Results: There was no difference in between-eye wetting lengths in the saline control eyes (p = 0.394) or the bilaterally anaesthetised eyes (p = 0.171). Wetting length was reduced in both eyes after bilateral anaesthesia compared to saline controls (p = 0.001; p = <0.0005). After unilateral anaesthesia, wetting length was reduced in the anaesthetised eye compared to its saline control by 51.4% (p = <0.0005) and compared to its fellow, unanaesthetised eye (p = 0.005). The fellow eye value was also reduced compared to its saline control (p = 0.06). Conclusions: Wetting length was reduced by topical anaesthesia, when instilled bilaterally and ipsilaterally. The latter response implies an ipsilateral, reflex sensory drive to lacrimal secretion. In the unanaesthetised fellow eye the reduction compared to its saline control was not quite significant. This implies a relative lack of central, sensory, reflex cross-innervation, although the possibility cannot entirely be ruled out. These results are relevant to the possibility of reflex lacrimal compensation from a normal, fellow eye, in cases of unilateral corneal anaesthesia

Event-Based Modeling with High-Dimensional Imaging Biomarkers for Estimating Spatial Progression of Dementia

Event-based models (EBM) are a class of disease progression models that can be used to estimate temporal ordering of neuropathological changes from cross-sectional data. Current EBMs only handle scalar biomarkers, such as regional volumes, as inputs. However, regional aggregates are a crude summary of the underlying high-resolution images, potentially limiting the accuracy of EBM. Therefore, we propose a novel method that exploits high-dimensional voxel-wise imaging biomarkers: n-dimensional discriminative EBM (nDEBM). nDEBM is based on an insight that mixture modeling, which is a key element of conventional EBMs, can be replaced by a more scalable semi-supervised support vector machine (SVM) approach. This SVM is used to estimate the degree of abnormality of each region which is then used to obtain subject-specific disease progression patterns. These patterns are in turn used for estimating the mean ordering by fitting a generalized Mallows model. In order to validate the biomarker ordering obtained using nDEBM, we also present a framework for Simulation of Imaging Biomarkers' Temporal Evolution (SImBioTE) that mimics neurodegeneration in brain regions. SImBioTE trains variational auto-encoders (VAE) in different brain regions independently to simulate images at varying stages of disease progression. We also validate nDEBM clinically using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). In both experiments, nDEBM using high-dimensional features gave better performance than state-of-the-art EBM methods using regional volume biomarkers. This suggests that nDEBM is a promising approach for disease progression modeling.Comment: IPMI 201

Density Field Reconstruction of an Overexpanded Supersonic Jet using Tomographic Background-Oriented Schlieren

A Tomographic Background-Oriented Schlieren (TBOS) technique is developed to aid in the visualization of compressible flows. An experimental setup was devised around a sub-scale rocket nozzle, in which four cameras were set up in a circular configuration with 30{\deg} angular spacing in azimuth. Measurements were taken of the overexpanded supersonic jet plume at various nozzle pressure ratios (NPR), corresponding to different flow regimes during the start-up and shut-down of rocket nozzles. Measurements were also performed for different camera parameters using different exposure times and f-stops in order to study the effect of measurement accuracy. Density gradients and subsequently two-dimensional line-of-sight integrated density fields for each of the camera projections are recovered from the index of refraction field by solving a Poisson equation. The results of this stage are then used to reconstruct two-dimensional slices of the (time-averaged) density field using a tomographic reconstruction algorithm employing the filtered back-projection and the simultaneous algebraic reconstruction technique. By stacking these two-dimensional slices, the (quasi-) three-dimensional density field is obtained. The accuracy of the implemented method with a relatively low number of sparse cameras is briefly assessed and basic flow features are extracted such as the shock spacing in the overexpanded jet plume

A Computational Comparison of Optimization Methods for the Golomb Ruler Problem

The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. The Golomb ruler problem has applications in information theory, astronomy and communications, and it can be seen as a challenge for combinatorial optimization algorithms. Although constructing high quality rulers is well-studied, proving optimality is a far more challenging task. In this paper, we provide a computational comparison of different optimization paradigms, each using a different model (linear integer, constraint programming and quadratic integer) to certify that a given Golomb ruler is optimal. We propose several enhancements to improve the computational performance of each method by exploring bound tightening, valid inequalities, cutting planes and branching strategies. We conclude that a certain quadratic integer programming model solved through a Benders decomposition and strengthened by two types of valid inequalities performs the best in terms of solution time for small-sized Golomb ruler problem instances. On the other hand, a constraint programming model improved by range reduction and a particular branching strategy could have more potential to solve larger size instances due to its promising parallelization features