Simultaneous tectonic Descemet stripping endothelial keratoplasty and tectonic Bowman layer transplant for the management of corneal perforation.

AIM: To report the outcomes of three cases of corneal perforation managed with simultaneous tectonic Descemet stripping endothelial keratoplasty (t-DSEK) and tectonic Bowman layer transplant (t-BLT) as an alternative to tectonic penetrating keratoplasty (t-PKP). METHODS: Three eyes of three patients receiving simultaneous t-DSEK and t-BLT for corneal perforation were included. The technique for DSEK was modified depending on individual requirements. The t-BLT technique was standardised using an 8 mm graft and fixated with a running suture. Success was measured by the ability of this procedure to close a corneal perforation. RESULTS: All three cases achieved tectonic eye globe restoration and remained stable during the minimum 3-month observation period. Reinterventions were relatively common: 2 cases required amniotic membrane transplant for persistent epithelial defects. One case required DSEK rebubbling. One case developed angle closure glaucoma requiring surgical peripheral iridectomy. CONCLUSION: Simultaneous t-DSEK and t-BLT may be a useful strategy for the management of corneal perforation as an alternative management to t-PKP for selected cases.

Stochastic Reaction Networks Within Interacting Compartments.

Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on [Formula: see text], and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes, chemical and otherwise, in homogeneous environments. There are multiple avenues for generalizing away from the assumption that the environment is homogeneous, with the proper modeling choice dependent upon the context of the problem being considered. One such generalization was recently introduced in Duso and Zechner (Proc Nat Acad Sci 117(37):22674-22683 , Duso and Zechner (2020)), where the proposed model includes a varying number of interacting compartments, or cells, each of which contains an evolving copy of the stochastic reaction system. The novelty of the model is that these compartments also interact via the merging of two compartments (including their contents), the splitting of one compartment into two, and the appearance and destruction of compartments. In this paper we begin a systematic exploration of the mathematical properties of this model. We (i) obtain basic/foundational results pertaining to explosivity, transience, recurrence, and positive recurrence of the model, (ii) explore a number of examples demonstrating some possible non-intuitive behaviors of the model, and (iii) identify the limiting distribution of the model in a special case that generalizes three formulas from an example in Duso and Zechner (Proc Nat Acad Sci 117(37):22674-22683 , Duso and Zechner (2020)).

Mixing times for two classes of stochastically modeled reaction networks.

The past few decades have seen robust research on questions regarding the existence, form, and properties of stationary distributions of stochastically modeled reaction networks. When a stochastic model admits a stationary distribution an important practical question is: what is the rate of convergence of the distribution of the process to the stationary distribution? With the exception of [1] pertaining to models whose state space is restricted to the non-negative integers, there has been a notable lack of results related to this rate of convergence in the reaction network literature. This paper begins the process of filling that hole in our understanding. In this paper, we characterize this rate of convergence, via the mixing times of the processes, for two classes of stochastically modeled reaction networks. Specifically, by applying a Foster-Lyapunov criteria we establish exponential ergodicity for two classes of reaction networks introduced in [2]. Moreover, we show that for one of the classes the convergence is uniform over the initial state.

Case series of staged lamellar corneal grafting with thin manual Descemet's stripping endothelial keratoplasty, followed by manual deep anterior lamellar keratoplasty, as an alternative to penetrating keratoplasty.

The purpose of this report is to present the outcomes of Descemet's stripping endothelial keratoplasty (DSEK), followed by deep anterior lamellar keratoplasty (DALK), as an alternative to penetrating keratoplasty (PKP) for different indications. Patients in this retrospective case series underwent manual DSEK, followed by manual DALK, for tectonic and/or visual reasons. It includes three cases that underwent DSEK followed by DALK as an alternative to PKP for the following conditions: failed PKP and stromal scarring, aphakic bullous keratopathy and herpetic stromal scarring, and herpetic corneal perforation. All cases had successful anatomical repair with visual improvement. Many corneal conditions involving endothelium and stroma have been traditionally managed with PKP. However, in certain settings with high risk of complications, this might not be an appropriate option. Therefore, for these cases, we propose management with DSEK followed by DALK as an alternative approach in a 'closed anterior chamber' fashion, which can reduce the risk of significant, sometimes irreversible, complications.

1 year posterior corneal changes after Bowman Layer Transplant for keratoconus.

INTRODUCTION: To report the posterior corneal changes after Bowman Layer Transplant for keratoconus in a tertiary hospital in the UK. METHODS: 5 eyes of 5 patients receiving Bowman Layer Transplant for advanced keratoconus in Royal Gwent Hospital (Newport, UK) were included. Pre and postoperative posterior corneal astigmatism, posterior Kmean, and back surface elevation were analysed. RESULTS: No significant changes were seen in the posterior corneal astigmatism, posterior Kmean, or back surface elevation between the pre- and postoperative period. CONCLUSION: This results would support the idea that the corneal changes seen after Bowman Layer Transplant are mainly in the anterior corneal surface.

One-Year Front Versus Central and Paracentral Corneal Changes After Bowman Layer Transplantation for Keratoconus.

PURPOSE: To report the front corneal versus central and paracentral corneal changes after Bowman layer transplantation for keratoconus in a tertiary hospital in the United Kingdom. METHODS: Five eyes of 5 patients receiving Bowman layer transplant for advanced keratoconus in Royal Gwent Hospital (Newport, United Kingdom) were included. Preoperative and postoperative visual acuity; Kmax; Kmean, and corneal cylinder in the front cornea, 4.5 mm central, and 6 mm central; and corneal thickness were analyzed. RESULTS: Corneal flattening and reduction in corneal astigmatism was observed, more marked in the central and paracentral zone, allowing for improvement in best-corrected visual acuity with the aid of visual correction in 4 eyes. CONCLUSIONS: These results support previous data reporting Bowman layer transplantation as a useful strategy in the treatment of advanced keratoconus and suggest greater attention may be focused on central or paracentral corneal changes.

On reaction network implementations of neural networks.

This paper is concerned with the utilization of deterministically modelled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary differential equations (ODEs) associated with certain reaction network implementations of neural networks have desirable properties including (i) existence of unique positive fixed points that are smooth in the parameters of the model (necessary for gradient descent) and (ii) fast convergence to the fixed point regardless of initial condition (necessary for efficient implementation). We do so by first making a connection between neural networks and fixed points for systems of ODEs, and then by constructing reaction networks with the correct associated set of ODEs. We demonstrate the theory by constructing a reaction network that implements a neural network with a smoothed ReLU activation function, though we also demonstrate how to generalize the construction to allow for other activation functions (each with the desirable properties listed previously). As there are multiple types of 'networks' used in this paper, we also give a careful introduction to both reaction networks and neural networks, in order to disambiguate the overlapping vocabulary in the two settings and to clearly highlight the role of each network's properties.

Tectonic Descemet Stripping Endothelial Keratoplasty for the Management of Corneal Perforation: A Case Series.

PURPOSE: Corneal perforations pose a considerable challenge for ophthalmic surgeons. The aim remains restoring the anatomical integrity of eye while attempting to preserve as much visual function as possible. To our knowledge, we report the first case series of 4 successful tectonic Descemet stripping endothelial keratoplasty (DSEK) grafts completed for acute corneal perforation. In all cases, restoration of globe integrity was achieved. In cases where visual potential remained, deep anterior lamellar keratoplasty over DSEK was offered. METHODS: Four patients presenting to Royal Gwent Hospital (Newport, Wales) with corneal perforation were included. Etiological origins included exposure keratopathy, corneal hydrops secondary to pellucid marginal degeneration with fistulization-associated aqueous leak, and herpetic keratitis. Patients were treated with initial temporary therapies, including glue patch, the use of bandage contact lenses, amniotic membrane transplant, and antibiotic cover, depending on the size and location of the perforation. Subsequent DSEK was subsequently performed under local anesthesia. RESULTS: All patients had successful tectonic grafts (3 DSEKs and 1 hemi-DSEK) up to 4 months postoperatively. In the case involving a hemi-DSEK, the patient underwent 2 refloating attempts of the graft before anchoring suture placement because of repeated graft detachment. Successful graft placement and tectonic globe restoration was confirmed by anterior segment imaging. CONCLUSIONS: Tectonic DSEK provides corneal surgeons with a new modality of treating corneal perforations. It provides clinicians an additional tool in their armamentarium in complex cases where anterior lamellar or penetrating keratoplasty may be contraindicated or deemed high risk of complications.

Time-dependent product-form Poisson distributions for reaction networks with higher order complexes.

It is well known that stochastically modeled reaction networks that are complex balanced admit a stationary distribution that is a product of Poisson distributions. In this paper, we consider the following related question: supposing that the initial distribution of a stochastically modeled reaction network is a product of Poissons, under what conditions will the distribution remain a product of Poissons for all time? By drawing inspiration from Crispin Gardiner's "Poisson representation" for the solution to the chemical master equation, we provide a necessary and sufficient condition for such a product-form distribution to hold for all time. Interestingly, the condition is a dynamical "complex-balancing" for only those complexes that have multiplicity greater than or equal to two (i.e. the higher order complexes that yield non-linear terms to the dynamics). We term this new condition the "dynamical and restricted complex balance" condition (DR for short).

Modified thin manual Descemet stripping endothelial keratoplasty with air-guided, non-pachymetric donor lenticule dissection: outcomes of graft thickness and complication rate.

AIM: To describe a modified technique of donor lenticule dissection for thin manual Descemet stripping endothelial keratoplasty (TM-DSEK). METHODS: Donor material was soaked in balanced salt solution (BSS) for 30min, before being mounted on an artificial anterior chamber (AAC). Rather than BSS, the AAC was filled with filtered air, resulting in a visible reflection at the corneal endothelium-air interface. This reflection served as a landmark for the depth of the dissection, facilitating the creation of a thin lenticule with low risk of perforation. Dissection was commenced at a standardized depth of 500 microns, with no initial pachymetry necessary. Totally 29 donor corneas were dissected by a novice TM-DSEK surgeon. Dissection time, central graft thickness at 2mo and complications were analysed. RESULTS: Results were similar to other endothelial keratoplasty techniques, despite the cases being performed by a novice DSEK surgeon. Mean dissection time was 7min (range 6-10). One graft perforation occurred (3.45%), but the air tamponaded the break and enabled dissection to be restarted and completed from a different location. Mean central graft thickness after at least two months follow-up was 106 microns (range 25-170). CONCLUSION: A problem with manual DSEK is the risk of graft perforation by attempting to dissect too thin a lenticule, or creating a thick graft due to fear of perforating. This modified air-guided technique addresses this problem, and is recommended for surgeons either embarking on the learning curve, or who wish to achieve more consistently thin grafts while reducing perforation rates.

Discrepancies between extinction events and boundary equilibria in reaction networks.

Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In particular, the deterministic model consists of an autonomous system of differential equations, whereas the stochastic system is a continuous-time Markov chain. Connections between the two modeling regimes have been studied since the seminal paper by Kurtz (J Chem Phys 57(7):2976-2978, 1972), where the deterministic model is shown to be a limit of a properly rescaled stochastic model over compact time intervals. Further, more recent studies have connected the long-term behaviors of the two models when the reaction network satisfies certain graphical properties, such as weak reversibility and a deficiency of zero. These connections have led some to conjecture a link between the long-term behavior of the two models exists, in some sense. In particular, one is tempted to believe that positive recurrence of all states for the stochastic model implies the existence of positive equilibria in the deterministic setting, and that boundary equilibria of the deterministic model imply the occurrence of an extinction event in the stochastic setting. We prove in this paper that these implications do not hold in general, even if restricting the analysis to networks that are bimolecular and that conserve the total mass. In particular, we disprove the implications in the special case of models that have absolute concentration robustness, thus answering in the negative a conjecture stated in the literature in 2014.

Results on stochastic reaction networks with non-mass action kinetics.

In 2010, Anderson, Craciun, and Kurtz showed that if a deterministically modeled reaction network is complex balanced, then the associated stochastic model admits a stationary distribution that is a product of Poissons [1]. That work spurred a number of followup analyses. In 2015, Anderson, Craciun, Gopalkrishnan, and Wiuf considered a particular scaling limit of the stationary distribution detailed in [1], and proved it is a well known Lyapunov function [2]. In 2016, Cappelletti and Wiuf showed the converse of the main result in [1]: if a reaction network with stochastic mass action kinetics admits a stationary distribution that is a product of Poissons, then the deterministic model is complex balanced [3]. In 2017, Anderson, Koyama, Cappelletti, and Kurtz showed that the mass action models considered in [1] are non-explosive (so the stationary distribution characterizes the limiting behavior). In this paper, we generalize each of the three followup results detailed above to the case when the stochastic model has a particular form of non-mass action kinetics.

Distribution of preoperative and postoperative astigmatism in a large population of patients undergoing cataract surgery in the UK.

PURPOSE: To assess the prevalence and severity of preoperative and postoperative astigmatism in patients with cataract in the UK. SETTING: Data from 8 UK National Health Service ophthalmology clinics using MediSoft electronic medical records (EMRs). DESIGN: Retrospective cohort study. METHODS: Eyes from patients aged ≥65 years undergoing cataract surgery were analysed. For all eyes, preoperative (corneal) astigmatism was evaluated using the most recent keratometry measure within 2 years prior to surgery. For eyes receiving standard monofocal intraocular lens (IOLs), postoperative refractive astigmatism was evaluated using the most recent refraction measure within 2-12 months postsurgery. A power vector analysis compared changes in the astigmatic 2-dimensional vector (J0, J45) before and after surgery, for the subgroup of eyes with both preoperative and postoperative astigmatism measurements. Visual acuity was also assessed preoperatively and postoperatively. RESULTS: Eligible eyes included in the analysis were 110 468. Of these, 78% (n=85 650) had preoperative (corneal) astigmatism ≥0.5 dioptres (D), 42% (n=46 003) ≥1.0 D, 21% (n=22 899) ≥1.5 D and 11% (n=11 651) ≥2.0 D. After surgery, the refraction cylinder was available for 39 744 (36%) eyes receiving standard monofocal IOLs, of which 90% (n=35 907) had postoperative astigmatism ≥0.5 D and 58% (n=22 886) ≥1.0 D. Visual acuity tended to worsen postoperatively with increased astigmatism (ρ=-0.44, P<0.01). CONCLUSIONS: There is a significant burden of preoperative astigmatism in the UK cataract population. The available refraction data indicate that this burden is not reduced after surgery with implantation of standard monofocal IOLs. Measures should be taken to improve visual outcomes of patients with astigmatic cataract by simultaneously correcting astigmatism during cataract surgery.

Low Variance Couplings for Stochastic Models of Intracellular Processes with Time-Dependent Rate Functions.

A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an exceptionally low variance between the generated paths. This coupling will be useful in the numerical computation of parametric sensitivities and the fast estimation of expectations via multilevel Monte Carlo methods. We provide the requisite estimators in both cases.

Non-explosivity of Stochastically Modeled Reaction Networks that are Complex Balanced.

We consider stochastically modeled reaction networks and prove that if a constant solution to the Kolmogorov forward equation decays fast enough relatively to the transition rates, then the model is non-explosive. In particular, complex-balanced reaction networks are non-explosive.

Noise control for molecular computing.

Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement in nucleic-acid-based technology in general, and strand-displacement DNA computing in particular, a large class of abstract biochemical networks may be physically realized using nucleic acids. Methods for systematic design of the abstract systems with prescribed behaviours have been predominantly developed at the (less-detailed) deterministic level. However, stochastic effects, neglected at the deterministic level, are increasingly found to play an important role in biochemistry. In such circumstances, methods for controlling the intrinsic noise in the system are necessary for a successful network design at the (more-detailed) stochastic level. To bridge the gap, the noise-control algorithm for designing biochemical networks is developed in this paper. The algorithm structurally modifies any given reaction network under mass-action kinetics, in such a way that (i) controllable state-dependent noise is introduced into the stochastic dynamics, while (ii) the deterministic dynamics are preserved. The capabilities of the algorithm are demonstrated on a production-decay reaction system, and on an exotic system displaying bistability. For the production-decay system, it is shown that the algorithm may be used to redesign the network to achieve noise-induced multistability. For the exotic system, the algorithm is used to redesign the network to control the stochastic switching, and achieve noise-induced oscillations.

Global prevalence and economic and humanistic burden of astigmatism in cataract patients: a systematic literature review.

PURPOSE: To systematically review the published evidence on the prevalence and economic and humanistic burden of astigmatism in cataract patients. MATERIALS AND METHODS: For this systematic literature review, the Medline, PubMed, Embase, and Cochrane databases were searched from 1996 to September 2015 for available scientific literature that met the inclusion criteria. Studies published in the English language reporting prevalence and humanistic and economic burden in patients diagnosed with cataract and astigmatism were included. RESULTS: Of 3,649 papers reviewed, 31 studies from 32 publications met the inclusion criteria of this review. Preexisting astigmatism ≥1 D was present in up to 47% of cataract eyes. The cost burden of residual uncorrected astigmatism after cataract surgery was driven by the cost of spectacles, which was estimated to range from $2,151 to $3,440 in the US and $1,786 to $4,629 in Europe over a lifetime. In cataract patients, both preexisting and postoperative residual astigmatism were associated with poor vision-related patient satisfaction and quality of life, as well as higher spectacle burden. Astigmatism correction during cataract surgery appears to improve visual outcomes and results in overall lifetime cost savings compared to astigmatism correction with postoperative vision correction. CONCLUSION: There is a high prevalence of preexisting astigmatism in cataract patients. Although published data are limited, both preoperative astigmatism and postoperative residual astigmatism affect visual function and vision-related quality of life, resulting in increased humanistic burden. Suboptimal correction of astigmatism during cataract surgery drives the continuous need for vision correction with spectacles in the postoperative period. Patients must bear the out-of-pocket expenses, since payers often do not reimburse the cost of spectacles. Greater access to astigmatism correction during cataract surgery could improve visual outcomes and quality of life in patients. More research is required to gain a better understanding of the disease burden of astigmatism in cataract patients.

Conditions for extinction events in chemical reaction networks with discrete state spaces.

We study chemical reaction networks with discrete state spaces and present sufficient conditions on the structure of the network that guarantee the system exhibits an extinction event. The conditions we derive involve creating a modified chemical reaction network called a domination-expanded reaction network and then checking properties of this network. Unlike previous results, our analysis allows algorithmic implementation via systems of equalities and inequalities and suggests sequences of reactions which may lead to extinction events. We apply the results to several networks including an EnvZ-OmpR signaling pathway in Escherichia coli.