Simulation of Vitreous Traction Force and Flow Rate of High Speed Dual-Pneumatic 7500 Cuts Per Minute Vitrectomy Probes.

Purpose: To develop methods to simulate vitreous flow and traction during vitrectomy and qualify these methods using laboratory measurements. Methods: Medium viscosity and phase treatment were adjusted to represent vitreous (Eulerian two-phase flow) or saline solution (single-phase Navier-Stokes flow). Retinal traction was approximated using a one-way fluid-structure interaction simulating cut vitreous volume coupled to a structural simulation of elastic stretching of a cylinder representing vitreous fibers entrained in the flow. Results: Simulated saline solution flow decreased, but vitreous flow increased with increasing cut rate, consistent with experimental trends observed for the 50/50 duty cycle mode. Traction simulations reproduced all trends in variation of traction force with changes in conditions. Simulations reproduced the majority of traction measurements within experimental error. Conclusions: A scientific basis is provided for understanding how flow and traction vary with operational parameters. This model-based analysis serves as a "virtual lab" to determine optimal system settings to maximize flow efficiency while reducing traction. Translational Relevance: The model provides a better understanding regarding how instrument settings can help control a vitrectomy procedure so that it can be made as efficient as possible (maximizing the rate of vitreous removal) while at the same time being made as safe as possible (minimizing retinal traction).

Physiologically based ocular pharmacokinetic modeling using computational methods.

By explicitly representing ocular anatomy, computational fluid dynamic simulation methods model drug mass transport both within and between ocular tissue regions, providing reliable animal-to-human translation of bioavailability. Here, we apply physiologically based models to simulate ocular drug administration. A non-anatomical model is used that applies a simple theorem for calculating ocular bioavailability from a topical dose. A computational fluid dynamic model is also described that incorporates ocular physiology in anatomical models for rabbit, monkey and man. This second method applies material properties and boundary conditions for various tissues enabling simulation of fluid flows, pressures, temperatures, convection, and drug advection following various modes of administration. The method provides a regional distribution with a given tissue not available using standard compartmental models, and enables translation of results from animal experiments into predictions for human ocular pharmacokinetics (PK).

Simulating intravitreal injections in anatomically accurate models for rabbit, monkey, and human eyes.

PURPOSE: To develop models for rabbit, monkey, and human that enable prediction of the clearance after intravitreal (IVT) injections in one species from experimental results obtained in another species. METHODS: Anatomically accurate geometric models were constructed for rabbit, monkey, and human that enabled computational fluid dynamic simulation of clearance of an IVT injected bolus. Models were constructed with and without the retrozonular space of Petit. Literature data on clearance after IVT injection of substances spanning a range of molecular weight up to 157 kDa were used to validate the rabbit model. RESULTS: The space of Petit had a significant increase on the clearance of slowly diffusing substances cleared by the anterior pathway by reducing the bottleneck for drug efflux. Models that did not include this zone could not accurately predict the clearance of slowly diffusing substances whose clearance was accelerated by intraocular pressure-driven convection. CONCLUSIONS: The ocular anatomy must be carefully reconstructed in the model to enable accurate predictions of clearance. This method offers an alternative means for scaling experimental data from one species to another that may be more appropriate than other simple approaches based entirely upon scaling of compartment volumes and flow rates.

Simulating dissolution of intravitreal triamcinolone acetonide suspensions in an anatomically accurate rabbit eye model.

PURPOSE: A computational fluid dynamics (CFD) study examined the impact of particle size on dissolution rate and residence of intravitreal suspension depots of Triamcinolone Acetonide (TAC). METHODS: A model for the rabbit eye was constructed using insights from high-resolution NMR imaging studies (Sawada 2002). The current model was compared to other published simulations in its ability to predict clearance of various intravitreally injected materials. Suspension depots were constructed explicitly rendering individual particles in various configurations: 4 or 16 mg drug confined to a 100 microL spherical depot, or 4 mg exploded to fill the entire vitreous. Particle size was reduced systematically in each configuration. The convective diffusion/dissolution process was simulated using a multiphase model. RESULTS: Release rate became independent of particle diameter below a certain value. The size-independent limits occurred for particle diameters ranging from 77 to 428 microM depending upon the depot configuration. Residence time predicted for the spherical depots in the size-independent limit was comparable to that observed in vivo. CONCLUSIONS: Since the size-independent limit was several-fold greater than the particle size of commercially available pharmaceutical TAC suspensions, differences in particle size amongst such products are predicted to be immaterial to their duration or performance.

In vitro transport and partitioning of AL-4940, active metabolite of angiostatic agent anecortave acetate, in ocular tissues of the posterior segment.

PURPOSE: The purpose of this study was to evaluate partitioning into and transport across posterior segment tissues (sclera, retinal pigment epithelium (RPE)-choroid) of AL-4940, the active metabolite of angiostatic cortisene anecortave acetate (AL-3789). METHODS: Transport of [(14)C]-AL-4940 was measured through RPE-choroid-sclera (RCS) and sclera, excised from Dutch Belted pigmented rabbits' eyes, in the directions of scleral to vitreal (S-->V) and vitreal to scleral (V-->S) for 3 h at 37 degrees C using Ussing chambers. Tissue integrity was monitored by transepithelial electrical resistance (TEER), potential difference (PD), and biochemical assay (LDH). Partitioning in RPE-choroid and sclera was determined separately for both [(14)C]-AL-4940 and [(14)C]-AL-3789. Mathematical analysis for bilaminate membranes used partitioning and transport data to derive diffusion coefficients for 2 tissue layers sclera and RPE-choroid. RESULTS: Partitioning of drug in tissue was comparable for both [(14)C]-AL-4940 and [(14)C]-AL-3789. Partition coefficients of drug in tissue were 2.2 for sclera and about 4 for RPE-choroid. Permeability through sclera alone was about 3 x 10(-5) cm/s and about 1 x 10(-5) cm/s through the RCS tissue, irrespective of the direction of transport (S-->V) or (V-->S). Results from bioelectrical and biochemical evaluation of tissue with modified LDH assay provided evidence that the RCS tissue preparation remained viable during the period of transport study. CONCLUSIONS: The thin RPE-choroid layer contributes significantly to resistance to drug transport, and diffusivity in this layer is 10 times less than in sclera. This experimental scheme is proposed as an important component for the development of a general ocular physiologically based pharmacokinetic model.

Controlled flow-through dissolution methodology: a high-performance system.

Measuring release rates using compendial systems, especially for sparingly soluble compounds, often produces complex results with less than desired precision and lacks relevance to key formulation or biological parameters. A flow-through approach was used by focusing on convective diffusion and controlling certain key physical-chemical factors. Results are presented for an automated multisample flow-through system that displays significant advantages over compendial (1) stirred and (2) flow-through systems. Advantages include precision, physicochemical, and in vivo relevance, along with analytical and formulation sensitivity. The convective diffusion/dissolution process was also simulated by using finite element modeling with predictions agreeing with measurements to within a few percent.

Impact of density gradients on flow-through dissolution in a cylindrical flow cell.

Measuring release rates for sparingly soluble compounds requires slow flow rates to achieve measurable eluent levels. However, flow rate cannot be reduced indefinitely because density gradients could measurably alter the drug release rate. Finite element simulations of convective diffusion/dissolution with an applied concentration-dependent density gradient reproduced the trends of the changes in dissolution rate on eluent flow rate which occur upon switching flow direction and sample cell orientation relative to gravitational field as observed in the literature employing a rectangular flow cell. The situation was experimentally reproduced using an implant obstruction placed centrally in a cylindrical flow cell.

Dissolution of anecortave acetate in a cylindrical flow cell: re-evaluation of convective diffusion/drug dissolution for sparingly soluble drugs.

Steady-state drug release rates were measured from a model cylindrical implant, comprised mainly of the sparingly soluble drug anecortave acetate, suspended as an obstacle in a cylindrical flow cell. Dissolution medium was delivered at a steady, slow flow rate (0.05-0.7 mLs/min) using an HPLC pump, and samples from the outflow were analyzed by direct injection onto an HPLC column. Release rates were determined as a function of flow rate for three different implant orientations--vertical, elevated to the center of the dissolution cell; horizontal, elevated; and horizontal, resting directly upon the flat porous inlet frit. Release rates were ranked as follows: horizontal, floor >> horizontal, elevated>vertical, elevated. The steady, laminar flow enabled use of the finite element method (FEM) to simulate the dissolution process using convective diffusion/drug dissolution theory. Simulations predicted the absolute magnitude of the release rate to within < 10% for all situations, and predicted the power law exponent of the dependence of release rate on flow rate with great accuracy. The current method is more general than compendial methods that provide a dissolving surface that is uniformly accessible to the dissolution medium, or a shear rate that is uniform across the entire dissolving surface. The current approach may be utilized to provide estimates of dissolution rates for any geometry and set of hydrodynamic conditions that can be numerically calculated.

Reexamination of convective diffusion/drug dissolution in a laminar flow channel: accurate prediction of dissolution rate.

PURPOSE: The convective diffusion/dissolution theory applied to flowthrough dissolution in a laminar channel was reexamined to evaluate how closely it can predict release rate for a model compound on an absolute basis--a comparison that was lacking from the original literature observations reported from this technique. METHODS: The theory was extended to allow for a finite flux of dissolving material, replacing the fixed concentration by a flux condition on the dissolving surface. The derivation introduces a new parameter, k(s), an area-independent analog of the dissolution rate constant defined in the USP intrinsic dissolution procedure. RESULTS: The release rate for ethyl-p-aminobenzoate originally observed fell within 10% of the absolute prediction assuming a solubility limited situation, and deviated from this prediction in a manner possibly consistent with a finite flux-limited condition, with k(s) approximately 10(-4) M s(-1). For materials exhibiting lower k(s) values, the derivation suggests that at high flow rates, a limit occurs where dissolution rate becomes independent of shear rate and merely a function of solubility and surface area. CONCLUSIONS: The new parameter k(s) may be deduced from any set of geometric and flow conditions, provided the fluid velocity can be determined everywhere in the domain.

Hydraulic flow and vascular clearance influences on intravitreal drug delivery.

PURPOSE: A recent paper proposed a model for hydraulic flow inthe eye, claiming this could affect intravitreal drug administration. The impact of flow on various modes of administration was investigated in a physiologically accurate ocular model of the rabbit eye. METHODS: Hydraulic flow initiated at the hyaloid was simulated in a three-dimensional finite element model including effects of convection and episcleral efflux. The interrelation between hydraulic and vascular clearance was treated using a method in which choroidal clearance is effected by simple boundary conditions, diminishing computing requirements. Drug diffusion coefficient and clearance rates for the choroid and anterior chamber were varied. RESULTS: Volumes and velocities of fluid flow permeating the vitreous agreed with literature values. Hydraulic flow impacted clearance of compounds not eliminated by the choroid; agreement with experimental data justified assuming perfect aqueous humor mixing. Hypertensive pressure produced up to a maximum 4-fold change in vitreal drug content from an intravitreal device depending upon location, orientation of the releasing surface, but was less important than vascular clearance strength and diffusion coefficient. CONCLUSIONS: The influence of intraocular pressure ([OP)-induced hydraulic flow is not likely to be of clinical significance for low molecular weight drugs that are efficiently cleared by the choroid.

Finite and infinitesimal representations of the vasculature: ocular drug clearance by vascular and hydraulic effects.

New methods are presented for simulating steady-state drug concentration in vitreous, choroid, and sclera from an intravitreal device. Clearance by choroidal flow and intraocular pressure (IOP) -induced Darcy hydraulic flow are included. Two methods are proposed for modeling the vasculature using simple one-dimensional models for simulating drug concentration profiles from intravitreal devices. The finite choroid method adds a concentration-dependent sink term to the convective diffusion equation, allowing for a continuous but rapid decrease in concentration throughout the choroid region. The infinitesimal choroid method uses a combination of a simple flux boundary condition and a redefinition of the dependent variable to account for the impact of the vascular drain by a discontinuous drop in concentration across the exterior vitreous boundary. This eliminates the need for a choroidal region, reducing finite element memory requirements, enabling the choroid to be made arbitrarily thin. The impact of permeating fluid induced by IOP on convection was examined, using hydraulic coefficients for ocular tissue recently made available [Xu, J. et al., Pharm. Res. 17:664-669 (2000)], allowing for drug efflux through the outer sclera. Transport becomes diffusion limited at high vascular clearance. Hydraulic flow restricts the range in concentration predicted in the vitreous compared to zero flow. Hydraulic influences for small, rapidly cleared drugs can be neglected.