Biofluids and Biotransport Laboratory

Location: RRB 107B

Investigators: Drs S.S. Sadhal & Anita N. Penkova


Ocular Drug Delivery

Retinal Diseases and Transport Processes: Retinal diseases affect the neurosensory tissue in the posterior segment of the eye. Two of the most prevalent retinal diseases include macular edema from diabetic retinopathy and neovascular age-related macular degeneration, are significant causes of visual impairment worldwide, especially among the elderly population. Approximately 15 million people in the United States have AMD, and more than 1.7 million Americans suffer from advance stages of this disease.

This number is expected to grow to nearly 3 million by 2020. With the ocular system, as for most other physiological systems, fluid transport is a common parameter participating in maintaining health and nutrition as well as an active drug transporter for disease-related intervention. Delivering drugs to the posterior segment of the eye requires detailed information about the transport mechanisms and major diffusion barriers present in the eye. While advances have been made in the area of drug delivery, several open questions relating to the feasibility, maintenance of drug levels within a desired optimum concentration range and achievement of more effective therapies still remain. Mathematical and computational models and analysis on mass transport mechanisms of the drug have proven to be effective tools for better understanding and predicting the transport process in the posterior part of the eye.




While topical eye-drop administration is considered among the least invasive, its effectiveness for retinal absorption is limited accompanying side-effects arising from systemic absorption are high. Intravitreal and transscleral administration have therefore gained favor. Systemic therapy and topical eye drop administration deliver low drug levels to the retina and the potential for systemic drug absorption and the accompanying side effects are high. Due to the effectiveness of intravitreal delivery methods in delivering the required dose levels ranges without the expense of systemic exposure, we have focused on this treatment method for vitreoretinal diseases. In addition to the side effects, there are several limitations of many of the drugs used for the treatment of vitreoretinal diseases. While the development of these drugs indeed required the expertise of biochemists and pharmacologists, the delivery mechanisms to focused targets demands understanding and knowledge of transport phenomena, together with the fluid mechanics. In order to control the drug delivery rate for achieving maximum effectiveness, it is vital that we develop the capability to predict the drug concentration distribution. The predictive model needs to take into consideration the various transport mechanisms such as diffusion and convection, as well as saccadic motion. One of the important outcomes from successful predictive models (accompanied by sound experiments) will be the drug distribution to the entire vitreous, including the delivery rate to the back of the eye, particularly the retina, in terms of the input parameters.


There are numerous challenges concerning drug delivery to the posterior of the eye resulting from the various physiological and anatomical transport barriers that affect the concentration distribution of the drug. Optimal levels of localized drug concentration are highly desirable since low concentrations are often insufficient for the treatment of retinal disease, and with high concentrations toxicity can be an issue. Therefore, the minimization of unnecessary drug concentration in healthy tissues is imperative. Although delivery via the vitreous provides the mechanism for high concentrations in the retina, the relevant surgical procedure (injection or implant) carries with it the risks of side effects such as cataract, retinal detachment, and endophthalmitis. However, the use of intravitreal corticosteroids for DME and intravitreal injections of anti-vascular endothelial growth factor (VEGF) for CNV have revolutionized the treatment of these diseases.


Mathematical Modeling of Fluid Transport and Ocular Drug Delivery (NEI/NIH Grant No.: 1R01EY026599 - 01A1)

Under the current project, extensive experimental and analytical work is underway on the development of a comprehensive eye model for fluid mechanics and transport phenomena. For such a model, while the differential equations describing the transport processes can be implemented, the biophysical properties for ocular tissue require accurate measurement. We have embarked upon this task, and in the present phase of this work, the following tasks are underway:


1.     Hydraulic Conductivity Measurement of the Vitreous Humor and the Hyaloid Membrane.

The hydraulic conductivity of the vitreous humor and the hyaloid membrane have been measured for the bovine eye. In a forthcoming publication, we have taken on the novel approach of measuring the combined hydraulic conductivity of the vitreous with the hyaloid intact, as well as with the vitreous broken. This method, applied to fresh bovine eyes (Manning Beef, Pico Rivera, CA), has allowed us to obtain the permeability of the hyaloid membrane which is otherwise extremely difficult to isolate and carry out measurements on. For the hydraulic conductivity measurement of the vitreous alone, we proposed and applied the drainage technique whereby the vitreous, placed in an upright cylindrical chamber, was allowed to drain its liquid content. Hydrostatic back-pressure  was applied at the exit by a vertical tube running about 80cm below the exit of the chamber. The height  of the vitreous body was recorded as a function of time, and theoretical model for this history was developed. Specifically, we obtained following new result,

where  represents the hyaluronic acid and collagen volume fraction in the vitreous at start,  is the initial height,  is the viscosity of the liquid phase is the vitreous,   is the gel viscosity, and  is the hydraulic conductivity of the fully hydrated vitreous. The least-squares best fit (see Figure 1) for the experimental values of  with this equation, with  floating, gave the value of m2/s. The novel features here include the implementation of rigorously-established variation of the Darcy parameter  with diminishing liquid volume and thus increasing hyaluronic acid, and collagen volume fraction .


For the hydraulic resistance of the vitreous with the hyaloid membrane intact, the carefully-extracted whole bovine vitreous was placed in the cylindrical chamber (the cell) with the flat ends supported by 20 nylon filters with 14% open area. Hydrostatically pressurized saline (20-120 cm head) was fed in at one end and allowed to percolate through the cylindrically-shaped vitreous body. The exiting saline was collected over recorded periods and the flowrates were measured and implemented into the Darcy’s equation to yield the effective hydraulic conductivity of the intact vitreous. The data are being collected to be analyzed.


2.     Diffusion Coefficient of the Vitreous Humor

As a part of the overall goal of the development of a comprehensive mathematical model for ocular fluid dynamics and drug delivery, we are measuring the diffusion coefficient of the vitreous humor to various surrogate drugs. The accuracy afforded by MRI visualization has been demonstrated to be quite remarkable (see Penkova et al., Int. J. Heat Mass Transfer 70, 504-514, 2014). Since the development of the technique, we have instituted substantial improvements for application to Gd-Albumin (galbumin) and Immunoglobulin (IgG), besides on Gd-DTPA (Magnavist) and Prohance. Galbumin and IgG are available as MRI contrast agents (Biopal, Inc.), and have molecular weights 74, and 149 kDa, respectively, as representative sizes of macromolecules. The measurement technique entails injection of the contrast agent into the middle vitreous of an ex vivo bovine eye and tracking the diffusion of the agent. The imaging data provides information to construct concentration contours around the injected region, and quantitative comparison and least-squares best fit of these with theoretically predicted contours provides the value of the diffusion coefficient. The main new feature is the implementation of a finite-element code to better fit irregularly-shaped boluses, as is the case for many of the larger molecules. The theoretical and the experimental diffusion-front contours are exhibited in Figure 2.

Figure 2: An example of the theoretical and experimental concentration-front contours. The drug surrogate is Immunoglobulin-Gd (IgG, 149 kDa) at  169 min after injection (─── : measurement,   ---- : finite element analysis)


Figure 3: A comparative chart of the Diffusion coefficient values measured by MRI for (1) Gd-DTPA ); (2) Prohance; (3) Galbumin; (4) Immunoglobulin-Gd.


A comparison of the diffusion-coefficient values is given in Figure 3 where we see that the large molecules (Galbumin and IgG) have a factor of 10 lower diffusion coefficient compared with Gd-DTPA and Prohance. This goal has been met to the extent defined in the timeline. See draft manuscript of the publication in preparation


3.     Permeability Measurements

See details at:


4.     Hindrance Coefficient

The proper implementation of convective transport in gel portion of the vitreous requires the introduction of a resistive parameter (known as the Staverman filtration coefficient). We shall refer to it as the hindrance coefficient. This is necessary since without it the theory assumes the convective transport of the large molecule solute to be at the same rate as the solvent, aside from diffusion, and can overestimate the transport rate depending on the sizes of macromolecules. We have demonstrated in earlier studies that with very high water flow rates in ex vivo bovine eyes, while the water pushes the surrogate, significant residue of the latter remains.  For more details see



5.      Simulation of drug transport in the eye

Finite-difference modeling for the non-syneretic eye has been initiated with full implementation of the boundary conditions in the vitreous region using Matlab. At the same time, a preliminary code based on estimated flow conditions has been developed using STAR-CCM+. Both models are based on Darcy flow in the vitreous, with water source at the hyaloid region and the RPE-choroid as the sink. The STAR-CCM+ is a packaged solver and offers less flexibility for the rigor, numerical accuracy and control. The in-house code development with Matlab affords greater flexibility in this regard and will be the one eventually in place for this project. With the developments based on STAR-CCM+, we have been able to provide animation of the drug-delivery process. More details and animations of numerical work are available at


The water flowrate is set artificially set much higher than the physiological rate in order to obtain a quick visual of the drug transport process. For the animation setup, this has the same effect as speeding the clock.