MODELLING OCULAR DELIVERY USING COMPUTATIONAL FLUID DYNAMICS
Alcon Research / ANSYS, IncMODELLING OCULAR DELIVERYUSING COMPUTATIONALFLUID DYNAMICSIn this piece, Paul Missel, PhD, Therapeutic Area Modeller, Modelling & Simulation,Global Clinical and Regulatory Affairs, Alcon Research Ltd, and Marc Horner, PhD, LeadTechnical Services Engineer, Healthcare, ANSYS, Inc, describe the use of computationalfluid dynamics simulations to predict drug flow and temperature inside the eye, andprovide examples of applications modelling: delivery following topical application;delivery from an intra-ocular depot; and delivery from juxtascleral devices.INTRODUCTIONEffective drug delivery to internal oculartissues must overcome significant barriersimposed by fluid flow and clearance withinthe eye. Fluid flow processes include production, circulation and elimination of bothtear fluid and aqueous humour, and hydraulic-assisted flow through porous media suchas the vitreous humour, iris root, and outersheath tissues. Clearance occurs as dissolveddrug flows past or percolates through vascular tissues such as the conjunctiva, iris,ciliary body, retina and choroid or intothe lymphatic system. Computer modelling is helping pharmaceutical scientistsunderstand the interplay between drug formulation, fluid flow and clearance, which isleading to the development of more effectiveocular drug delivery systems.Classical pharmacokinetic (PK) modelswere among the first models developed forpredicting ocular drug disposition. Thesemodels are comprised of well-mixed compartments representing specific ocular tissues withvarious interconnections. A series of firstorder transfer equations describes transportbetween and elimination from each compartment. Physiologically-based pharmacokinetic(PBPK) approaches improve on PK models byincorporating the flow processes that facilitatedrug distribution within the eye and drugclearance through vascular tissues. This isaccomplished by constructing model compartments explicitly reflecting the volumes of thetissues they represent, by replicating the physiological production and elimination of tearfluid and aqueous humour and by assigningtransfer coefficients between compartmentsreflecting physicochemical drug properties.112The PBPK approach can be more powerfully applied using computational fluiddynamics (CFD), which uses numericalmethods to provide approximate solutionsto the differential equations that describefluid flow, heat transfer, and species transport. Today’s CFD software tools are general enough such that the same softwareused to model product performance in suchdiverse fields as automotive, nautical, aeronautical, civil, and petroleum engineeringcan be applied to predict the flow of fluid,heat and drug in the eye. A primary advantage over compartmental approaches is thatCFD models the spatial distribution of drugwithin each compartment through time.Such detailed numerical experimentationcan help establish the safety and efficacy ofa delivery system while reducing the numberand/or size of clinical studies required.Dr Paul MisselTherapeutic Area ModellerModelling & SimulationGlobal Clinical and Regulatory AffairsT: 1 817 551 4926E: paul.missel@alcon.comAlcon Research, LtdTC-47, 6201 South FreewayFort Worth, TX 76134United Stateswww.alcon.comOCULAR CFD MODEL SUMMARYThis section provides an introductionto the physical processes that govern fluidflow, heat transfer, and drug motion in theeye and their implementation into a CFDmodel, please see Missel et al, 2010 for acomplete description.2A CFD simulation begins with the construction of a geometric model that includesall structures involved in fluid, heat, anddrug transport. The geometry is typicallyconstructed in CAD or a geometry toolspecific to the CFD software. Figure 1shows anatomical human and rabbit ocularmodels. The rabbit is frequently used as apreclinical model for evaluating ophthalmicdrug products before human clinical testing. Conducting simulations in both ocularwww.ondrugdelivery.comDr Marc HornerLead Technical Services Engineer,HealthcareT: 1 847 491 0200F: 1 847 869 6495E: marc.horner@ansys.comANSYS, Inc2600 Ansys DriveCanonsburg, PA 15317United Stateswww.ansys.comCopyright 2015 Frederick Furness Publishing Ltd
Alcon Research / ANSYS, Incgeometries enables translating results frompreclinical experiments in rabbits into predictions for clinical outcomes in humans.The aqueous humour region consistsof the fluid zones between the cornea andvitreous, excluding the iris and ciliary body.Aqueous humour is a clear, non-viscous,water-like fluid that is secreted by cells onthe outer lining of the ciliary body. Aqueoushumour flows around the iris and exits theeye through the trabecular meshwork, aring-shaped structure of connective tissue.Aqueous humour following this path eventually returns to the blood via a fine venousnetwork surrounding the outer layer of thesclera, the shell encasing most of the eye. Asmall fraction of aqueous humour percolatesthrough the sclera and cornea. The resistance of the sclera to fluid permeation produces the intra-ocular pressure. The trabecular meshwork also provides some resistanceto fluid flow and in glaucoma this resistanceincreases, thus increasing the pressure.All structures apart from aqueoushumour were treated as porous media.Experimental measurements have established the hydraulic resistance of the sclerais about 15,000 times higher than that ofthe vitreous. All other porous media tissues,apart from the trabecular meshwork and thevitreous, are assigned the same resistance asthe sclera. The hydraulic resistance of thetrabecular meshwork was a parameter inthe model whose value was adjusted suchthat the maximum pressure inside the eyematched an intraocular pressure of 15 Torr.A band along the ciliary body behind theiris produces aqueous humour at a rateappropriate for each species. The pressureboundary condition on the outer sclera andthe surface behind the trabecular meshworkwas specified as 10 Torr, matching the episcleral venous pressure, whereas there waszero (atmospheric) pressure applied on theouter cornea. The sclera, choroid, retina,iris and ciliary body were set to a fixedtemperature of 37 C and the cornea was setto 34 C. The thermal gradient between thecornea and internal tissues creates densitygradients in the aqueous humour, whichsignificantly impact aqueous flow patterns.The fluidic and thermal transport processes were simulated using the ANSYSFluent CFD solver. Figure 2 shows simulation results of pressure, temperature andfluid flow in the rabbit ocular model. InFigure 2a, most of the ocular interior isat the maximum pressure of 15 Torr; thepressure drop occurs almost entirely acrossa)b)Figure 1: Comparison of geometric ocular models for human and rabbit, shown onthe same scale; the horizontal bar below each panel corresponds to 1 cm.8c)Figure 2: CFD simulation results in the rabbit eye model. a) Pressure (Torr). b)Temperature (Kelvin). c) Vector velocity, arrows show direction of flow and arecolour-coded to match the scale for the superimposed contour plot (m/s).Copyright 2015 Frederick Furness Publishing Ltdthe outer sheath surfaces. Figure 2b showsthe variation of temperature within the eye.Since the aqueous humour density is allowedto vary with temperature, density gradientsgive rise to thermal convection, which creates a circulating flow pattern with a maximum fluid velocity on the order of 10-4 m/s,as illustrated in Figure 2c. The maximumvelocity for the hydraulic flow in the vitreous is four orders of magnitude lower thanthe maximum velocity within the aqueoushumour region. This fluid-thermal solutionforms the baseline convective flow patternupon which the modes of drug delivery presented in the next three sections occur.MODEL APPLICATION:PK FOLLOWING TOPICAL DELIVERYTopical dosing is commonly used totreat glaucoma. The target of anti-glaucomadrugs is typically the iris / ciliary body.Mechanisms of action include reducing theproduction rate for aqueous humour andreducing the hydraulic resistance of theiris root to facilitate outflow. Topicallyadministered anti-inflammatory drugs alsotarget the iris / ciliary body to reducepain and inflammation following cataractsurgery. These drugs can also exert animportant influence on deeper ocular tissuessuch as the retina and macula to preventedema, which occurs occasionally in diabetic patients following surgery.Drug transport in the eye was also simulated using ANSYS Fluent, which can modelthe interaction between drug convection,diffusion and elimination. Convection is themotion of drug due to bulk flow of aqueous humour; diffusion is the rate of passivemass transport through the medium downwww.ondrugdelivery.com13
Alcon Research / ANSYS, Inca)or vascular circulation pathways capableof transporting drug between tissue compartments may be at work. Identifying andincorporating these missing fluidic and circulatory currents could improve the model.b)MODEL APPLICATION: DELIVERYFROM INTRAOCULAR DEPOTSFigure 3: Simulated advection of drug into ocular tissue following topical dosingwith timolol maleate (concentration plotted on a logarithmic scale where 1corresponds to the concentration of drug in the topical dose). a) Three minutesafter instillation of a topical dose. b) Four hours after instillation.a concentration gradient, and sink termsaccount for removal of drug by vascular orlymphatic clearance. Chemical partitioning,which gives rise to discontinuities in drugconcentration at boundaries between tissues having different lipophilic / hydrophilicproperties, is also included in the modelthrough the use of jump conditions at tissueinterfaces. Each tissue is assigned its ownunique set of values for the partition coefficient, diffusion coefficient, sink term, andequilibrium drug concentration.Drug application to the outer cornealsurface can be modelled by a time-varyingfunction approximating the tear concentration resulting from instillation of a topicaldose. The tear film concentration decaysexponentially with time, the concentrationdynamics being influenced by the initialrapid decrease in pre-corneal fluid volumeafter dosing and by the continuous influx offresh tears. Since our models do not includetissues outside the eye such as the conjunctiva and eyelids, our drug input functionwill most likely overestimate the flux ofdrug into the eye. Thus we include a singleadjustable parameter to enable tuning theamplitude of the drug input function. Themodel predicts that rapid mixing of aqueoushumour in the anterior chamber creates awisp of higher drug concentration just a fewminutes after drug instillation (Figure 3a).Mixing has rendered the aqueous humourdrug concentration to be approximatelyuniform four hours later (Figure 3b).Figure 4 compares simulation results withexperimental measurements of mean tissueconcentrations following the topical dosingof a drug solution. The concentrations inthe anterior compartments initially increasewith time, then decrease as drug distributesthroughout the remaining tissues. Applyingan amplitude prefactor of one quarter forour drug input function, the simulationaccurately predicts the time dependence ofthe concentrations for anterior tissues suchas the iris / ciliary body, the tissue affectedby the drug. Thus, CFD is quite useful forpredicting the time course of drug distribution. Simulated concentrations in the vitreous and lens lag behind the experimentalvalues, however. Additional fluid currents1. E-01Concentration (mg/g)1. E-021. E-031. E-041. E-051. E-060123Time (Hours)Figure 4: Comparison of simulated & experimental mean tissue compartmentconcentrations following topical instillation of 25 μL 0.65% timolol maleate.914www.ondrugdelivery.com4Much effort has been expended indevelopment of bio-erodible dosage formsthat will sustain drug release over time.However, a suspension may perform suitably as a sustained release depot if injectedin a region of quiescent vitreous which hasretained its gel-like consistency, providedthat the drug solubility is low enough todissolve slowly but high enough to delivera therapeutic level of drug. Drug releaserate and duration can be controlled byadjusting the suspension drug concentration. This behaviouur is a consequence ofa local concentration effect, in which drugdissolved from one particle suppresses thedissolution of drug from nearby particles.The formulation will need to be engineeredto immobilise the particles until they arecompletely dissolved for this approach to bemost effective.Figures 5 and 6 show simulation resultsfrom various model suspensions of triamcinolone acetonide (TAC). In each simulation, identically sized particles are initiallyarranged in an evenly spaced array inside aspherically shaped depot.Figure 5 illustrates how the duration ofthe suspension (defined as the time afterinjection at which all solid drug has dissolved) varies with particle size. Figure 6shows the time dependence of drug contentfor two different suspensions. These simulations utilised the volume of fluid (VOF)method in ANSYS Fluent, which enablesthe tracking of phase boundaries througha stationary mesh. In this case, the VOFmethod tracks the boundary between solid,undissolved drug crystals and drug dissolved in solution. The concentration at thedissolving surface was set to 36 ppm, thedrug solubility limit.The insets in Figure 5 show the quasisteady-state drug distributions a few days afterintravitreal injection. The contours show thedrug concentration in the region containingthe particles is very close to the solubility limit(denoted by the red colour). The concentration decreases at a rate that is approximatelyinversely proportional to distance outside thesuspension depot. If the therapeutic window(the difference between the minimum effectiveCopyright 2015 Frederick Furness Publishing Ltd
Alcon Research / ANSYS, IncMODEL APPLICATION:JUXTASCLERAL DEVICESOur last example is a juxtascleral devicefor anecortave acetate (AAc), a low-molecular-weight lipophilic compound which atone time was being developed to treat macular degeneration. The prototype device,shown in Figure 7a, is a silicone holder forplacing a drug tablet adjacent to the sclera.A simulation for steady-state drug distribution in ocular tissue is shown in Figure7b. Drug partition and diffusion coefficients were obtained from in vitro experiments equilibrating ocular tissues with drugsolution and measuring drug permeabilitythrough excised tissues.6 Partition coefficients for drug are 2.2 and 4 for sclera andCopyright 2015 Frederick Furness Publishing LtdDuration (Months)128401234Total Particle Surface Area RatioFigure 5: Influence of particle size on duration of suspensions of 16 mg TACconfined to a 100 μL spherical vitreous depot. The units of the horizontal axisdenote the ratio in total particle surface area compared to the model suspensionwith the largest particle size simulated. The insets show model suspensions dividingthe drug into either 21 (left) or 588 (right) equally sized spherical particles. Thecolour spectrum denotes drug concentration, red corresponding to the solubilitylimit and blue corresponding to zero drug concentration. Duration becomes quiteinsensitive to particle size when the size falls below 428 μm in diameter. Thissimulation used an earlier rendition of the rabbit eye geometry in which the lenswas represented by an appropriately shaped void.2retina/choroid respectively; this partitioning is apparent in the figure contours. Thestrength of the choroidal drug sink wasadjusted to match drug clearance rate afterintravitreal injection of a dilute AAc solution. This sink localises delivery to a regionimmediately beneath the tablet.Juxtascleral devices containing AAc16Amount Remaining (mg)concentration and the maximum concentration allowable before toxic side effects aremanifested) is wide enough, the entire eye maybe treated effectively.For an oral suspension dissolving in thestomach, drug particles dissolve at a rateproportional to the total particle surfacearea, as specified by the Noyes-Whitneyequation.3 This strong dependence of dissolution rate on particle surface area isobserved in certain in vitro dissolutionexperiments which expose drug particlesto copious amounts of dissolution mediumunder substantial agitation.4 Each particle isuniformly accessible to the release mediumin these methods. This is not the case forthe intravitreal depot, because the particleson the exterior shield interior particlesfrom dissolution. Instead, the dependenceof dissolution rate on particle size exhibitsan asymptote. The arrow in Figure 5 at428 μm identifies the diameter at which thedissolution rate is within 1% of the valuein the limit of infinitesimally small particlesize. Since this diameter is 30-100 times thediameter of particles in a typical ophthalmicsuspension, dissolution rate of an intravitreal depot will not depend on particle size.Figure 6 shows a comparison betweensimulated dissolution-versus-time profiles forsuspensions containing either 4 or 16 mgTAC confined to a 100 μL spherical depotversus simulations in the infinitesimally smallparticle size limit. The predictions match theexperimental data fairly well for the 16 mgdepots, but under-predict the duration of the4 mg depots. If we allow for the depot tocondense to a smaller volume after day 10, aswas observed in the 2006 study by Kim et al,5the simulation curve for 4 mg comes in closeragreement with the data.1284002468Time (Months)Figure 6: Dissolution versus time profiles for 4 mg and 16 mg TAC confined to a100 μL spherical vitreous depot compared with experimental data from Kim 2006(diamonds).5 Curves represent simulation predictions in the limit of infinitesimallysmall particles. The appearance of the 276-particle suspension model at varioustimes is shown in the insets. The dashed curve for 4 mg restarts the simulation bydistributing 2.7 mg of drug in a 25 μL depot on day 10 to approximate the influenceof depot condensation observed in vivo.2www.ondrugdelivery.com15
Alcon Research / ANSYS, Inca)b)c)Figure 7: a) Upper panel: Schematic for juxtascleral device 10: 102 – cavity; 106 –drug source; 104 – exposed opening; 108 – circumferential rim to retain the drugsource. Lower panel: photo of prototype device. b) Simulated steady-state drugconcentration in ocular tissue resulting from delivery of AAc from the device. c)Comparison between experimental and simulated average concentrations in themeasured tissues at the one year following implantation of juxtascleral devicescontaining AAc in rabbits.7,11implanted in rabbits maintained constantocular tissue drug levels for two years.Figure 7c shows average drug levels inretina, choroid and sclera in a 10 mm circular dissection beneath the depot one yearafter insertion. Since the device providesfor unidirectional release of drug towardsthe ocular interior, and shields from nonproductive loss behind the eye, the payloadduration is extended. The simulated tissueconcentration is ranked Sclera Choroid Retina Vitreous. Using no additionaladjustable parameters, simulations predictthe appropriate rank order and come closeto the values measured in the retina andchoroid. The values for sclera match lesswell, but less is known about the exteriorscleral sinks.The number of publications utilisingmethods similar to what is described hereare increasing. Many additional aspectshave been explored, such as the effectsof age and disease on liquefaction of thevitreous, eye movements, and variabilityin permeability of the outer tissue layers.Simulations may also provide insights intoin the effect of various disease states ondrug delivery. Such work needs to be guidedand qualified by appropriate preclinicaland clinical observations to maximise theinsights provided.The design of ophthalmic drug deliverytherapies can be improved as the fluidic andvascular clearance barriers are better understood through careful in vivo experimentsilluminated through simulation.CONCLUSIONACKNOWLEDGE
fluid dynamics simulations to predict drug flow and temperature inside the eye, and provide examples of applications modelling: delivery following topical application; delivery from an intra-ocular depot; and delivery from juxtascleral devices.
with Ocular Surface Disorders describes contemporary and appropriate examination, treatment and management protocols to reduce the risk for visual discomfort and disability. The most common ocular surface disorders stem from tear-film abnormalities and lid-gland dysfunction ("blepharitis"), either of which may lead to ocular surface disorders.
The calibration procedure for the ocular micrometer requires that the graduations on both micrometers be superimposed on each other . This is accomplished by rotating the ocular lens. A determination is then made of the number of ocular divisions per known distance on the stage micrometer. Finally, the calibration factor for one ocular division .
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Computational fluid dynamics modelling of the air movement in an environmental test chamber with a respiring manikin Article Accepted Version Mahyuddin, N., Awbi, H. B. and Essah, E. A. (2015) Computational fluid dynamics modelling of the air movement in
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