Eye rotation induced dynamics of a Newtonian fluid within the vitreous cavity: the effect of the chamber shape

Investigation of crystalline lens overshooting: ex vivo experiment and optomechanical simulation results

Introduction: Crystalline lens overshooting refers to a situation in which the lens momentarily shifts too much from its typical location immediately after stopping the rotational movement of the eye globe. This movement can be observed using an optical technique called Purkinje imaging. Methods: In this work, an experimental setup was designed to reproduce this effect ex vivo using a fresh porcine eye. The sample was rotated 90° around its centroid using a high-velocity rotation stage, and the Purkinje image sequences were recorded, allowing us to quantify the overshooting effect. The numerical part of the study consisted of developing a computational model of the eye, based on the finite element method, that allowed us to understand the biomechanical behavior of the different tissues in this dynamic scenario. A 2D fluid-structure interaction model of the porcine eye globe, considering both the solid parts and humors, was created to reproduce the experimental outcomes. Results: Outputs of the simulation were analyzed using an optical simulation software package to assess whether the mechanical model behaves optically like the real ex vivo eye. The simulation predicted the experimental results by carefully adjusting the mechanical properties of the zonular fibers and the damping factor. Conclusion: This study effectively demonstrates the importance of characterizing the dynamic mechanical properties of the eye tissues to properly comprehend and predict the overshooting effect.

Future research perspective on the interfacial physics of non-invasive glaucoma testing in pathogen transmission from the eyes

Non-contact tonometry (NCT) is a non-invasive ophthalmologic technique to measure intraocular pressure (IOP) using an air puff for routine glaucoma testing. Although IOP measurement using NCT has been perfected over many years, various phenomenological aspects of interfacial physics, fluid structure interaction, waves on corneal surface, and pathogen transmission routes to name a few are inherently unexplored. Research investigating the interdisciplinary physics of the ocular biointerface and of the NCT procedure is sparse and hence remains to be explored in sufficient depth. In this perspective piece, we introduce NCT and propose future research prospects that can be undertaken for a better understanding of the various hydrodynamic processes that occur during NCT from a pathogen transmission viewpoint. In particular, the research directions include the characterization and measurement of the incoming air puff, understanding the complex fluid-solid interactions occurring between the air puff and the human eye for measuring IOP, investigating the various waves that form and travel; tear film breakup and subsequent droplet formation mechanisms at various spatiotemporal length scales. Further, from an ocular disease transmission perspective, the disintegration of the tear film into droplets and aerosols poses a potential pathogen transmission route during NCT for pathogens residing in nasolacrimal and nasopharynx pathways. Adequate precautions by opthalmologist and medical practioners are therefore necessary to conduct the IOP measurements in a clinically safer way to prevent the risk associated with pathogen transmission from ocular diseases like conjunctivitis, keratitis, and COVID-19 during the NCT procedure.

Effects of Flow Hydrodynamics and Eye Movements on Intraocular Drug Clearance

New in vitro prototypes (PK-Eye™) were tested with and without eye movement to understand diffusion and convection effects on intraocular clearance. Port placement in front ((i) ciliary inflow model) and behind the model lens ((ii) posterior inflow model) was used to study bevacizumab (1.25 mg/50 µL) and dexamethasone (0.1 mg/100 µL) in phosphate-buffered saline (PBS, pH 7.4) and simulated vitreal fluid (SVF). Dexamethasone was studied in a (iii) retinal-choroid-sclera (RCS) outflow model (with ciliary inflow and two outflow pathways). Ciliary vs. posterior inflow placement did not affect the half-life for dexamethasone at 2.0 µL/min using PBS (4.7 days vs. 4.8 days) and SVF (4.9 days with ciliary inflow), but it did decrease the half-life for bevacizumab in PBS (20.4 days vs. 2.4 days) and SVF (19.2 days vs. 10.8 days). Eye movement only affected the half-life of dexamethasone in both media. Dexamethasone in the RCS model showed approximately 20% and 75% clearance from the RCS and anterior outflows, respectively. The half-life of the protein was comparable to human data in the posterior inflow model. Shorter half-life values for a protein in a ciliary inflow model can be achieved with other eye movements. The RCS flow model with eye movement was comparable to human half-life data for dexamethasone.

Stability of the Interface Between Two Immiscible Liquids in a Model Eye Subject to Saccadic Motion

The interface between silicone oil and saline layers in a three-dimensional model of the eye chamber was studied under different eye-like saccadic motions in order to determine the stability of the interface and propensity for emulsification in the bulk. The effect of level of fill, saccade amplitude, angular velocity, latency time, and orientation were investigated experimentally in spherical flasks with internal diameters 10, 28, and 40 mm, as well as a 28 mm diameter flask with an indent replicating the lens or the presence of a buckle. The deformation of the interface was quantified in terms of the change in its length in two-dimensional images. The deformation increased with Weber number, We, and was roughly proportional to We for We > 1. The presence of the lens gave rise to higher deformation near this feature. In all cases emulsification was not observed in either bulk fluid. The velocity profile in the spherical configuration was mapped using particle imaging velocimetry and is compared with an analytical solution and a short computational fluid dynamics simulation study. These confirm that the saccadic motion induces flow near the wall in the saline layer and significantly further into the chamber in the silicone oil. Surfactants soluble in the aqueous and oil phases reduced the interfacial tension, increasing deformation but did not lead to emulsification in the bulk.

Ocular Fluid Mechanics and Drug Delivery: A Review of Mathematical and Computational Models

The human eye is a complex biomechanical structure with a range of biomechanical processes involved in various physiological as well as pathological conditions. Fluid flow inside different domains of the eye is one of the most significant biomechanical processes that tend to perform a wide variety of functions and when combined with other biophysical processes play a crucial role in ocular drug delivery. However, it is quite difficult to comprehend the effect of these processes on drug transport and associated treatment experimentally because of ethical constraints and economic feasibility. Computational modeling on the other hand is an excellent means to understand the associated complexity between these aforementioned processes and drug delivery. A wide range of computational models specific to different types of fluids present in different domains of the eye as well as varying drug delivery modes has been established to understand the fluid flow behavior and drug transport phenomenon in an insilico manner. These computational models have been used as a non-invasive tool to aid ophthalmologists in identifying the challenges associated with a particular drug delivery mode while treating particular eye diseases and to advance the understanding of the biomechanical behavior of the eye. In this regard, the author attempts to summarize the existing computational and mathematical approaches proposed in the last two decades for understanding the fluid mechanics and drug transport associated with different domains of the eye, together with their application to modify the existing treatment processes.

Biocompatibility of intraocular liquid tamponade agents: an update

Intraocular liquids tamponade agents, such as perfluorocarbon liquids (PFCLs), semifluorinated alkanes (SFAs), silicone oils (SOs) and heavy silicone oils (HSOs), are a crucial intraoperative and/or postoperative tool in vitreoretinal surgery, in particular for the management of complex vitreoretinal diseases. However, their use is not without complications, which are potentially severe. Consequently, a growing interest has been devoted to the biocompatibility of these compounds and the adequacy of current regulations that should guarantee their safety. Obviously, an updated knowledge on research findings and potential risks associated to the use of intraocular liquid compounds is essential, not only for vitreoretinal surgeons, but also for any ophthalmologist involved in the management of patients receiving intraocular liquid tamponades. In light of this, the review provides a comprehensive characterisation of intraocular liquid tamponades, in terms of physical and chemical properties, current clinical use and possible complications. Moreover, this review focuses on the safety profile of these compounds, summarising the existing regulation and the available evidence on their biocompatibility.

Evaluation of the ocular fluid dynamic effects on intraocular magnesium-based device: A comparison between CFD and FSI approaches

Magnesium is an essential element for the ocular functions and used for the realization of medical devices due to its low corrosion resistance, bioresorbable nature and biocompatibility. Wet age-related macular degeneration is one of the main causes of blindness with patients treated by intravitreal injections of inhibitor drugs. According to the need to reduce the number of injections, the development of new drug delivery devices able to extend the therapeutical outcomes is mandatory and magnesium can be considered as a promising candidate. The aim of the work concerns the evaluation of the ocular fluid dynamic role on a magnesium-based device placed in the vitreous chamber. Particularly, the fluid-induced shear stress field on the surfaces in contact with the liquefied vitreous was studied. Both computational fluid dynamic and fluid-structure interaction approaches were proposed and then compared. Saccadic motion was implemented to recreate the vitreous fluid dynamics. High changes in terms of fluid-induced shear stress field varying the CFD and FSI numerical approaches and kinematic parameters of the saccadic function can be noticed. The comparison between CFD and FSI approaches showed minor significant differences and both implementations suggested the possibility to obtain a uniform and controlled corrosion of the device.

Flow dynamics of vitreous humour during saccadic eye movements

In this work, we reveal the flow dynamics of Vitreous Humour (VH) gel and liquid phases during saccadic movements of the eye, considering the biofluids viscoelastic character as well as realistic eye chamber geometry and taking into account the saccade profile. We quantify the differences in the flow dynamics of VH gel and liquid phases using viscoelastic rheological models that are able to model the VH shear rheology, considering different amplitudes of saccadic movements (10^∘, 20^∘, 30^∘ and 40^∘). For this purpose, the computational fluid dynamics (CFD) open source software OpenFOAM® was used. The results portray a distinct flow behaviour for the VH gel and liquid phases, with inertial effects being more significant for the VH liquid phase. Moreover, the Wall Shear Stress (WSS) values produced by the VH gel phase are more than twice of those generated by the VH liquid phase. Results also show that for different amplitudes of eye movement both the velocity magnitude in the vitreous cavity and the shear stresses on the cavity walls rise with increasing saccadic movement displacement.

A drug delivery analysis of large molecules in ocular vitreous chamber: Dependency on saccadic movements after intravitreal injection

The purpose of this study is to investigate the effect of vitreous sloshing induced by saccades on the intravitreal delivery of large molecule drugs. The vitreous body was considered in its age-related liquefaction condition. Fluid dynamics and large molecule distribution were described by the coupling of mass conservation's and Fick's laws with continuity and momentum equations for a Newtonian incompressible fluid in a 3D unsteady analysis. Two injection sites were analyzed, in both the mixing effect of a 50° periodic saccade leads to uniform drug distribution in 30 s of simulation, the initial bolus site being left after 3 s of simulation. In absence of saccadic movements, the dominant transport contribution is the diffusive one and large molecules hardly reach their uniform distribution inside the vitreous cavity. A model describing the intravitreal distribution of large molecules in presence of saccades was developed, improving the understanding of drug transport mechanism after an intravitreal injection and highlighting how advection contribution enhances its distribution in the vitreous chamber.

Hydrodynamics of Intravitreal Injections into Liquid Vitreous Substitutes

Intravitreal injections have become the cornerstone of retinal care and one of the most commonly performed procedures across all medical specialties. The impact of hydrodynamic forces of intravitreal solutions when injected into vitreous or vitreous substitutes has not been well described. While computational models do exist, they tend to underestimate the starting surface area of an injected bolus of a drug. Here, we report the dispersion profile of a dye bolus (50 µL) injected into different vitreous substitutes of varying viscosities, surface tensions, and volumetric densities. A novel 3D printed in vitro model of the vitreous cavity of the eye was designed to visualize the dispersion profile of solutions when injected into the following vitreous substitutes—balanced salt solution (BSS), sodium hyaluronate (HA), and silicone oils (SO)—using a 30G needle with a Reynolds number (Re) for injection ranging from approximately 189 to 677. Larger bolus surface areas were associated with faster injection speeds, lower viscosity of vitreous substitutes, and smaller difference in interfacial surface tensions. Boluses exhibited buoyancy when injected into standard S1000. The hydrodynamic properties of liquid vitreous substitutes influence the initial injected bolus dispersion profile and should be taken into account when simulating drug dispersion following intravitreal injection at a preclinical stage of development, to better inform formulations and performance.

A study of the mechanical forces on aphakic iris-fixated intraocular lenses

Iris-fixated aphakic intraocular lenses (IFIOL) are used in cataract surgery, when more common intraocular lenses cannot be adopted because of the absence of capsular bag support. These lenses can be implanted either on the poste- rior or the anterior surface of the iris. In this work we study whether one of these options is preferable over the other from the mechanical point of view. In particular, we focus on the forces that the IFIOL transmits to the iris, which are asso- ciated with the risk of lens dislocation. We study the prob- lem numerically and consider aqueous flow induced by sac- cadic rotations in the cases of an IFIOL in the anterior and posterior side of the iris. The IFIOL considered is the Arti- san Aphakia +30.0 D lens (IFIOL) produced by Ophtec BV. We perform the simulations in OpenFOAM. We find that the forces transmitted by the aphakic IFIOL to the iris are sig- nificantly higher in the case of posterior implantation. This suggests that lens implantation on the posterior surface of the iris might be associated with a higher risk of lens disloca- tion, when an inadequate amount of iris tissue is enclavated during implantation.

Principles of pharmacology in the eye

The eye is a highly specialized organ that is subject to a huge range of pathology. Both local and systemic disease may affect different anatomical regions of the eye. The least invasive routes for ocular drug administration are topical (e.g. eye drops) and systemic (e.g. tablets) formulations. Barriers that subserve as protection against pathogen entry also restrict drug permeation. Topically administered drugs often display limited bioavailability due to many physical and biochemical barriers including the pre-corneal tear film, the structure and biophysiological properties of the cornea, the limited volume that can be accommodated by the cul-de-sac, the lacrimal drainage system and reflex tearing. The tissue layers of the cornea and conjunctiva are further key factors that act to restrict drug delivery. Using carriers that enhance viscosity or bind to the ocular surface increases bioavailability. Matching the pH and polarity of drug molecules to the tissue layers allows greater penetration. Drug delivery to the posterior segment is a greater challenge and, currently, the standard route is via intravitreal injection, notwithstanding the risks of endophthalmitis and retinal detachment with frequent injections. Intraocular implants that allow sustained drug release are at different stages of development. Novel exciting therapeutic approaches include methods for promoting transscleral delivery, sustained release devices, nanotechnology and gene therapy.

An experimental model of vitreous motion induced by eye rotations

BACKGROUND

During eye rotations the vitreous humour moves with respect to the eye globe. This relative motion has been suggested to possibly have an important role in inducing degradation of the gel structure, which might lead to vitreous liquefaction and/or posterior vitreous detachment. Aim of the present work is to study the characteristics of vitreous motion induced by eye rotations.

METHODS

We use an experimental setup, consisting of a Perspex model of the vitreous chamber that, for simplicity, is taken to have a spherical shape. The model is filled with an artificial vitreous humour, prepared as a solution of agar powder and hyaluronic acid sodium salt in deionised water, which has viscoelastic mechanical properties similar to those of the real vitreous. The model rotates about an axis passing through the centre of the sphere and velocity measurements are taken on the equatorial plane orthogonal to the axis of rotation, using an optical technique.

RESULTS

The results show that fluid viscoelasticity has a strong influence on flow characteristics. In particular, at certain frequencies of oscillation of the eye model, fluid motion can be resonantly excited. This means that fluid velocity within the domain can be significantly larger than that of the wall.

CONCLUSIONS

The frequencies for which resonant excitation occurs are within the range of possible eye rotations frequencies. Therefore, the present results suggest that resonant excitation of vitreous motion is likely to occur in practice. This, in turn, implies that eye rotations produce large stresses on the retina and within the vitreous that may contribute to the disruption of the vitreous gel structure. The present results also have implications for the choice of the ideal properties for vitreous substitute fluids.

Mechanical models of the dynamics of vitreous substitutes

We discuss some aspects of the fluid dynamics of vitreous substitutes in the vitreous chamber, focussing on the flow induced by rotations of the eye bulb. We use simple, yet not trivial, theoretical models to highlight mechanical concepts that are relevant to understand the dynamics of vitreous substitutes and also to identify ideal properties for vitreous replacement fluids. We first recall results by previous authors, showing that the maximum shear stress on the retina grows with increasing viscosity of the fluid up to a saturation value. We then investigate how the wall shear stress changes if a thin layer of aqueous humour is present in the vitreous chamber, separating the retina from the vitreous replacement fluid. The theoretical predictions show that the existence of a thin layer of aqueous is sufficient to substantially decrease the shear stress on the retina. We finally discuss a theoretical model that predicts the stability conditions of the interface between the aqueous and a vitreous substitute. We discuss the implications of this model to understand the mechanisms leading to the formation of emulsion in the vitreous chamber, showing that instability of the interface is possible in a range of parameters relevant for the human eye.

Tamponade or filling effect: changes of forces in myopic eyes

Myopia is the most common ocular abnormality. Its high and growing prevalence has contributed to a recent surge in surgical interest in the disorder, since retinal detachment in eyes with high myopia differs from that in emmetropic eyes or eyes with low myopia. The myopic eye, because of its specific anatomy, poses special challenges that need to be overcome to ensure the appropriate use of vitreous substitutes. However, intraocular tamponades have shown great potential for revolutionizing retinal detachment surgery and vitreomacular surgery in general in myopic eyes. We provide an updated review of the clinical use of vitreous substitutes in the myopic eye, paying particular attention to analyzing the ideal function of endotamponade agents and comparing the effects of these agents on the physical and biological properties of the eye.

Vitreous deformation during eye movement

Retinal detachment results in visual loss and requires surgical treatment. The risk of retinal detachment depends, among other factors, on the vitreous rheology, which varies with age. To date, the viscoelasticity of the vitreous body has only been measured in cadaver eyes. However, the ex vivo and in vivo viscoelasticity may differ as a result of the effect of intravitreal membranes. Therefore, an MRI method and appropriate postprocessing tools were developed to determine the vitreous deformation and viscoelastic properties in the eyes of living humans. Nineteen subjects (eight women and 11 men; mean age, 33 years; age range, 14-62 years) gazed at a horizontal sinusoidal moving target during the segmented acquisition of complementary spatial modulation of magnetization images. The center of the lens and the scleral insertion of the optic nerve defined the imaging plane. The vitreous deformation was tracked with a dedicated algorithm and fitted with the commonly used viscoelastic model to determine the model parameters: the modified Womersley number a and the phase angle b. The vitreous deformation was successfully quantified in all 17 volunteers having a monophasic vitreous. The mean and standard deviation of the model parameters were determined to be 5.5 ± 1.3 for a and -2.3 ± 0.2 for b. The correlation coefficient (-0.76) between a and b was significant. At the eye movement frequency used, the mean storage and loss moduli of the vitreous were around 3 ± 1 hPa. For two subjects, the vitreous deformation was clearly polyphasic: some compartments of the vitreous were gel-like and others were liquefied. The borders of these compartments corresponded to reported intravitreal membrane patterns. Thus, the deformation of the vitreous can now be determined in situ, leaving the structure of the intravitreal membranes intact. Their effect on vitreous dynamics challenges actual vitreous viscoelastic models. The determination of the vitreous deformation will aid in the quantification of local vitreous stresses and their correlation with retinal detachment.

Contribution of saccadic motion to intravitreal drug transport: theoretical analysis

PURPOSE

The vitreous humor liquefies with age and readily sloshes during eye motion. The objective was to develop a computational model to determine the effect of sloshing on intravitreal drug transport for transscleral and intra-vitreal drug sources at various locations

METHODS

A finite element model based on a telescopic implicit envelope tracking scheme was developed to model drug dispersion. Flow velocities due to saccadic oscillations were solved for and were used to simulate drug dispersion.

RESULTS

Saccades induced a three-dimensional flow field that indicates intense drug dispersion in the vitreous. Model results showed that the time scale for transport decreased for the sloshing vitreous when compared to static vitreous. Macular concentrations for the sloshing vitreous were found be much higher than that for the static vitreous. For low viscosities the position of the intravitreal source did not have a big impact on drug distribution.

CONCLUSION

Model results show that care should be taken when extrapolating animal data, which are mostly done on intact vitreous, to old patients whose vitreous might be a liquid. The decrease in drug transport time scales and changes in localized concentrations should be considered when deciding on treatment modalities and dosing strategies.

Mathematical model of flow in the vitreous humor induced by saccadic eye rotations: effect of geometry

Saccadic eye rotations induce a flow in the vitreous humor of the eye. Any such flow is likely to have a significant influence on the dispersion of drugs injected into the vitreous chamber. The shape of this chamber deviates from a perfect sphere by up to 10-20% of the radius, which is predominantly due to an indentation caused by the lens. In this paper we investigate theoretically the effect of the domain shape upon the flow field generated by saccades by considering an idealized model. The posterior chamber geometry is assumed to be a sphere with a small indentation, undergoing prescribed small-amplitude sinusoidal torsional oscillations, and, as an initial step towards understanding the problem, we treat the vitreous humor as a Newtonian fluid filling the chamber. The latter assumption applies best in the case of a liquefied vitreous or a tamponade fluid introduced in the vitreous chamber after vitrectomy. We find the flow field in terms of vector spherical harmonics, focusing on the deviation from the flow that would be obtained in a perfect sphere. The flow induced by the departure of the domain geometry from the spherical shape has an oscillating component at leading order and a smaller-amplitude steady streaming flow. The oscillating component includes a circulation cell formed every half-period, which migrates from the indentation towards the center of the domain where it disappears. The steady component has two counter-rotating circulations in the anterior part of the domain. These findings are in good qualitative agreement with the experimental results of Stocchino et al. (Phys Med Biol 52:2021-2034, 2007). Our results predict a significant reduction in the expected time for drug dispersal across the eye compared with the situation in which there is no fluid flow present.