effect of retinal permeability, diffusivity, and aqueous …€¦ · effect of retinal...

JOURNAL OF OCULAR PHARMACOLOGY AND THERAPEUTICSVolume 24, Number 3, 2008© Mary Ann Liebert, Inc.DOI: 10.1089/jop.2007.0111

Effect of Retinal Permeability, Diffusivity, and AqueousHumor Hydrodynamics on Pharmacokinetics of

Drugs in the Eye

MAHESH K. KRISHNAMOORTHY,1 JUYOUNG PARK,1 JAMES J. AUGSBURGER,3and RUPAK K. BANERJEE1,2

ABSTRACT

Aim: Retinal permeability is one of the important parameters that determine drug distrib-ution during diseased retinal conditions, whose effect is still unclear. Thus, the main aim ofthis study was to understand the influence of varying retinal permeability (P) on drug dis-tribution under normal (F1) and elevated vitreous outflow pathophysiologic conditions (F10)for a wide variety of drug diffusivities—high: D(-5) and low: D(-7).

Method: A computational model of the rabbit eye was developed that took into account thevarying effects of convection during normal and pathophysiologic conditions.

Results: High retinal permeability, P(-5), is associated with low peak macular concentrationand a rapid clearance from the ocular chambers, with the retina as the major route of elimi-nation. For low permeability, P(-7), there is very high peak macular concentration, slow elim-ination, and a buildup of drug concentration, which depends on vitreous outflow. The vari-ation of t1/2 with P was found to be of linear and nonlinear trends for F1 and F10 flow cases,respectively. Moreover, for D(-5) diffusivity, there was a 1.5-fold increase and a 1.6-fold de-crease in t1/2 values when the retinal permeability values were P(-5) and P(-7). On the con-trary, for D(-7) diffusivity, there was a 2.5-fold decrease and a 1.4-fold increase in t1/2 valuesfor P(-5) and P(-7), with t1/2 increasing for P(-6) during both high and low diffusivities.

Conclusions: Thus, the combined effect of variables P, D, and F are important factors thatshould be considered in order to determine drug dosage. This study could be used to esti-mate the drug distribution and elimination for (1) wide range of physicochemical propertiesof drugs and (2) normal and abnormally elevated vitreous flows during the diseased condi-tion of the eye. These results could help in obtaining essential information about the treat-ment protocol for targeted retinal diseases while simultaneously avoiding the toxic effects ofthese drugs.

255

INTRODUCTION

POSTERIOR-SEGMENT EYE DISEASES, such as age-re-lated macular degeneration (AMD), diabetic

retinopathy, and retinitis pigmentosa, account for

most cases of irreversible blindness world-wide.1–4 A wide variety of drugs, with varyingphysicochemical properties, are being used totreat these diseases. A number of in vivo studies5–8

and clinical studies9,10 have been performed to

Departments of 1Mechanical Engineering, 2Biomedical Engineering, and 3Ophthalmology, University of Cincinnati,Cincinnati, OH.

study the pharmacokinetics of drugs. However,it is still difficult to understand the behavior ofdrugs with varying physicochemical propertiesinside the ocular chambers as a result of a patho-physiologic condition.

Of all the factors affecting drug distributionand elimination, the main ones are the physico-chemical properties of drugs and the pathophys-iologic conditions. Physicochemical properties,such as drug diffusivity (D) and permeability (P)of the retina to the drugs, are constant for a par-ticular drug; however, the permeability of theretina could change as a result of a diseased con-dition, which is unknown. Though many re-searchers have neglected the effect of convectiveflow inside the vitreous on drug distribution,11–13

there is strong evidence that a fraction of fluidgenerated from the ciliary processes flowsthrough the vitreous and across the retina in thehealthy eye as vitreous outflow.14 The vitreousoutflow increases during abnormalities, such asglaucoma and retinal detachment.15,16

From the drug-delivery perspective, intravit-real injection (IJ) and controlled release implant(IP) are the most common modes of administra-tion, as they can overcome the blood-retinal bar-rier. Thus, the IJ and IP have the ability to attainthe necessary therapeutic range to cure the dis-eases. Most previous works on the numeric cal-culation of drug distribution and elimination inthe eye have focused on the combined effects ofpermeability and diffusivity changes and the ef-fects of varying coupled diffusion and convec-tion.11,17–19 Recently, Park et al.20 have numeri-cally shown only the effect of drug diffusivity andconvection in the vitreous on drug distribution inthe rabbit eye by using a computational eyemodel. However, there is no study that has fo-cused on the combined effects of all the three fac-tors (P, D, and F) on drug distribution not onlywithin the vitreous, but also the entire anteriorand posterior segments of the eye.

In this study, the retinal permeability (P), dif-fusivity (D), and vitreous outflow (F) values werevaried to simulate the drug distribution and elim-ination from the ocular chambers when drugswere administered by IJ and IP. The variation ofP, D, and F covers a wide range of drugs, whichhave different physicochemical properties (P andD) and pathophysiologic conditions (P and F).Also, many drugs that are used to treat suchdiseases have a narrow concentration range, inwhich they are effective and may be toxic at

higher concentrations.21–25 Therefore, a priorknowledge of drug distribution not only for aparticular physicochemical property, but also thebehavior under the influence of pathophysiologiccondition is absolutely critical to develop the ef-fective treatment protocol for targeted retinal dis-eases while simultaneously avoiding the toxic ef-fects of these drugs. As a result, the effect ofretinal-permeability variation on drug behaviorinside the eye could be delineated and the drugdistribution that maximizes the therapeutic effectof drugs can be predicted.

METHODS

Computational model

The three-dimensional (3D) eye model, whichis comprised of the cornea, sclera, retina-choroid, vitreous, posterior and anterior cham-bers, iris, ciliary processes, hyaloid membrane,lens, Schemm’s canal, and a drug source (whichgives the drug-delivery location for either an IJor IP) is shown in Figure 1. Since the drug sourcewas positioned closer to the hyaloid membrane,half of the eye was modeled, with the symme-try plane passing through the middle of the drugsource as well as all other eye compartments.The drug source was represented as a sphere ofa 0.1-cm radius that was administered by IJ andIP. The drug delivered from the drug source waseliminated from the eye by convection and dif-fusion through two pathways: the aqueous out-flow pathway and the vitreous outflow path-way, as shown in Figure 1. In addition, thismodel also took into account the varying effectsof convection during normal and pathophysio-logic conditions. To validate this numeric model,the in vivo data of spatial concentration profilefrom the lens to the retina at 15 h after IJ werecompared with the numeric data. The differencewas less than 5% between the numerical and ex-perimental data.20

Numerical method, governing equations, andinitial and boundary conditions

The Navier–Stokes equations (Eqs. 1 and 2)were used to solve the flow field first for the vit-reous outflow; then, the output of the flow wascoupled with the species transport equation (Eq.3) to calculate the drug distribution in the eye for

KRISHNAMOORTHY ET AL.256

changing permeability and diffusivity (Fidap;Ansys Inc., ver 8.6):

��.(U) � 0 (1)

�U.�U � ��P � ��2U (2)

� U.�C � D�2C (3)

where, U: Velocity, 2: Density of medium, C: Drugconcentration, D: Diffusivity

The fluid velocity of the generation of aqueoushumor was modeled as a fluid source with a con-stant flow rate of 2.2 �L/min from the ciliaryprocesses.20 The fluid velocity of aqueous humorwas set to zero in the iris, lens, and cornea. The ve-locity component normal to the symmetric surfacesof the various compartments of the eye was set tozero. Vitreous outflow was modeled by assigninga velocity normal to the outer surface of the retina-choroid compartment. The two tangential velocitycomponents were set to zero at the outer surface ofthe retina-choroid compartment.

At the surface of the lens and cornea, and at allsymmetric surfaces, a zero-species flux-boundarycondition was used. Species concentration at theouter surface of the sclera is a perfect sink; thus, theconcentration was set to zero to model completeclearance by the blood. The initial concentration was

�C��t

specified at the spheric location of the injected bolusof the drug within the vitreous. An initial concen-tration of 15 �g of drug was specified throughoutthe hemispheric volume for IJ. In contrast, for the IP,an equivalent amount of the drug was deliveredwith a constant flux at the outer surface of the drugover a time period of 15 h. Elsewhere, the initial con-centration was set to zero for both IJ and IP.

Model parameters: Retinal permeability,diffusivity, and convective flow

In this study, the retinal-permeability value hasbeen varied between 1 � 10�5 cm/sec: P(-5) and1 � 10�7 cm/sec: P(-7).26,27 P(-5) represents goodpermeation through the retina and, hence,lipophilicity, whereas P(-7) represents poor per-meation through the retina and hydrophilicity.26

This retinal-permeability range includes both theeffect of passive and active transport processes. Anequivalent amount of bulk diffusivity (retinal per-meability � thickness of retina) was applied overthe retinal volume to signify retinal permeabilityinstead of retinal-surface permeability.20 Two ex-treme values of vitreous drug diffusivity, 1 � 10�5

cm2/sec: D(-5) and 1 � 10�7 cm2/sec: D(-7), signi-fying high- and low molecular weights, respec-tively, were used in this study.11 In order to seethe effect of convective species transfer on drugdistribution in the eye, two vitreous flow rates

INFLUENCE OF PHYSIOCHEMICAL PROPERTIES ON PHARMACOKINETICS 257

FIG. 1. Computational model of rabbit eye.

were assumed: 0.1 �L/min (F1) and 1 �L/min(F10). These flow rates signify the normal (F1) andthe abnormal conditions (F10) caused as a resultof glaucoma or retinal detachment conditions.

RESULTS

In this section, we delineate the effects of reti-nal-permeability change along with the change indiffusivity on drug distribution in the vitreousand aqueous chambers. Also, the combined ef-fects of normal and pathophysiologic flow con-ditions, retinal permeability, and drug diffusivityon the pharmacokinetics of the drugs are dis-cussed.

Effect of retinal permeability on spatial distribution

Figure 2 shows the spatial distribution of drugsinjected intravitreally (IJ) in the vitreous along the

center line joining the axis from the lens (x � 0cm) to the retina (x � 0.78 cm) following a druginjection. Figure 2A and 2B shows the spatial dis-tribution at different times for normal flow con-ditions (F1), when the retinal permeability variesfrom P(-5) to P(-7) for D(-5) (Fig. 2A) and D(-7)(Fig. 2B) diffusivities. The spatial distribution forabnormal flow (F10) is provided in Fig. 2C and2D. Flow has a significant impact on drug distri-bution when there is low diffusivity in the vitre-ous (Fig. 2B and 2D). For IP, the distribution isshown in Figure 3 A–D for normal flow: F1 (Fig.3A and 3B) and abnormal flow: F10 (Fig. 3C and3D). The trend of drug distribution for the IP wassimilar to that of IJ, but the magnitude was lowerthan that of IJ for the same release rate.

Effect of retinal permeability and drug diffusivityon macular temporal distribution

Figure 4 shows the temporal variation of theconcentration at the center of the retina for dif-


FIG. 2. Spatial distribution for varying permeability of the retina for intravitreal injection (IJ). (A) Spatial distribu-tion for D-5 drug diffusivity when the flow is F1 and the retinal permeability changes from P-5 to P-7. (B) Spatial dis-tribution for D-7 drug diffusivity when the flow is F1 and the retinal permeability changes from P-5 to P-7. (C, D)Spatial distribution of drugs when the flow is F10 and the drug diffusivities are D-5 and D-7, respectively, when theretinal permeability varies from P-5 to P-7 under each case.

ferent retinal permeability values when the drugwas administered through IJ and IP. The plots areshown until 500 h after the administration of thedrugs by IJ and IP.

Figure 4A and 4B describes the temporal vari-ation of concentration at the center of the retinafor varying P and D for drugs that were ad-ministered through IJ for F1 and F10, respec-tively. For F1 flow and D(-5) diffusivity, the de-crease in retinal permeability from P(-5) to P(-7)caused an increase in the peak concentrationvalue by 1.4-fold (Fig. 4A, arrow #1), whereas itcaused a sixtyfold increase for F1 flow and D(-7) (Fig. 4A, arrow 2). Thus, for F1 flow, thecombined effect of P and D increased the peakconcentration at the center of the retina for D(-7), as compared to D(-5). Higher diffusivity, forexample, D(-5) encountered lower resistance inthe vitreous for drug transport as compared toD(-7) case.

For F10 flow and D(-5) diffusivity, when theretinal permeability changes from P(-5) to P(-7),

there was a threefold increase in peak concentra-tion values at the center of the retina (Fig. 4B, ar-row 1). However, for F10 flow and D(-7) diffu-sivity, the change in retinal permeability fromP(-5) to P(-7) caused the concentration at the cen-ter of the retina to double in magnitude (Fig. 4B,arrow 2). Thus, compared to F1, for F10 flow, thecombined effect of P and D tended to result in anoverall decreased peak concentration at the cen-ter of the retina. It is also evident from Figure 4Aand 4B that the change in magnitude of peak-flowvalue for extreme cases, that is, from P(-5) D(-5)case to P(-7) D(-7) case, was a 54% increase fornormal flow: F1 [27.1 �g/mL for P(-5) D(-5) to41.8 �g/mL for P(-7) D(-7)] and a 18.75% decreasefor abnormal flow: F10 [16.2 �g/mL for P(-5) D(-5) to 13.1 �g/mL for P(-7) D(-7 )]. Thus, whenthe diffusivity was fixed, flow had a significanteffect on peak concentration, particularly whenthe retinal permeability was low. This effect wasmore pronounced when the drug had the lowestdiffusivity value.


FIG. 3. Spatial distribution for varying permeability of the retina for implant (IP). (A) Spatial distribution for D-5 drug diffusivity when the flow is F1 and the retinal permeability changes from P-5 to P-7. (B) Spatial distribu-tion for D-7 drug diffusivity when the flow is F1 and the retinal permeability changes from P-5 to P-7. (C, D) Spatialdistribution of drugs when the flow is F10 and the drug diffusivities are D-5 and D-7, respectively, when the retinalpermeability varies from P-5 to P-7 under each case.

Figure 4C and 4D shows the temporal varia-tion in the concentration at the center of the retinafor IP. The trend was similar to that of IJ, exceptthat IP reduced the overall peak concentrationand delayed the time to achieve these levels.Thus, in order to show the effect of change inphysicochemical factors on elimination and meandistribution, only the results pertaining to IJ werediscussed from this point forward and the varia-tion for IP for the following cases could be ob-tained in a similar fashion.

Effect of retinal permeability change and vitreousoutflow on clearance

Figure 5 illustrates the percentage cumulativeamount of drugs that reach the retina and theSchemm’s canal for F1 (Fig. 5A) and F10 (Fig. 5B).Since it was desired to study the effect of changein retinal permeability and flow on drug clear-ance, only the trend pertaining to high diffusiv-

ity of drugs are shown in this illustration. Theplots are shown until the first 200 h. It can be ob-served from the Figure 5A and 5B that P(-5) elim-inates the fastest under F1 as well as F10 condi-tions, predominantly getting eliminated throughthe retina (70%). As a result of a flow change toF10, the cumulative concentration reached at theretina increases for all the retinal permeabilityvalues. The increase is significant particularly forthe case of F10 flow and P(-6) permeability. It isalso evident that more amount of drug clearsthrough the retina for F10 flow and P(-6) case(38%, as shown in Fig. 5B) than F1 flow and P(-6) case (22%, as shown in Fig. 5A). There is alsoa simultaneous decrease in the clearance throughthe Schemm’s canal. Figure 5B also shows thatthe trend for P(-5) and P(-6) reaches a constantvalue after a certain time point. Thus, flow has asignificant effect on clearance in the first 200 h forfixed drug diffusivity in the vitreous, especiallywhen the retinal permeability is low. As men-


FIG. 4. Temporal variation of the concentration at the center of the retina for varying permeability of the retina—intravitreal injection (IJ) and implant (IP). (A, B) Concentration profiles at the center of the retina for varying retinalpermeability and drug diffusivity for F1 and F10 flow conditions, respectively, that are administered through IJ. (C,D) Concentration profiles at the center of the retina for varying retinal permeability and drug diffusivity for F1 andF10 flow conditions, respectively, that are administered through IP. As permeability decreases, peak concentrationincreases.

tioned earlier, the effect of flow is more pro-nounced when both the drug diffusivity in thevitreous and retinal permeability values are low.

Combined effects of physicochemical andpathophysiologic properties on distribution and elimination

Vitreous and aqueous humor drug distribution.Figure 6 discusses the trend of volume of aver-aged mean concentration of drugs inside the vit-reous administered through IJ. The trend during

the first 300 h after IJ is displayed by Figure 6Aand 6B for normal flow: F1 and abnormal flow:F10, respectively. For a particular flow rate anddrug diffusivity, as the retinal permeability de-creases from P(-5) to P(-7), the slope of the meanconcentration versus time curve decreases. Theelimination rates can be calculated from the slopeof the mean concentration of drugs inside the vit-reous, assuming the elimination occurs throughthe first-order process. It can be observed thatduring F1 flow, the effect of low drug diffusivity,D(-7), decreases the slope for P(-5) and P(-6) by


FIG. 5. Cumulative amount of drugs reaching the retina and Schemm’s canal for varying permeability of the retina.(A) Cumulative amount of drugs reaching the retina when the retinal permeability changes from P-5 to P-7. (B) Cu-mulative amount of drugs reaching the Schemm’s canal when the retinal permeability changes from P-5 to P-7.

fourteen- and 1.7-fold (arrows 1 and 2, respec-tively, shown in Fig. 6A), as compared to highdrug diffusivity, D(-5). However, for F1 flow, theslope of P(-7) D(-7) is increased by 3.4-fold, ascompared to P(-7) D(-5) (arrow 3, Fig. 6A). ForF10 flow, the effect of D(-7) diffusivity decreasesthe slope for P(-5) D(-7) by 3.5-fold, as shown byarrow 1 in Figure 6B, and increases the slope forP(-6) D(-7) and P(-7) D(-7) by 1.3- and 1.7-fold, re-spectively (shown by arrows 2 and 3, respec-tively, in Fig. 6B), as compared to the slopes for

D(-5) drugs. Thus, the abnormal (F10) flow has asignificant effect when there is low retinal per-meability.

Figure 7A and 7B shows the ratio of aqueousto vitreous humor concentrations (Caq/Cvit) forhigh- and low-diffusivity drugs injected into thevitreous chamber for F1 and F10 flow conditions.For D(-5), for both F1 and F10, the Caq/Cvit val-ues have a similar profile by attaining the peakvalue and, thereafter, attaining a constant valueafter a sharp decrease. However, the profiles for


FIG. 6. Variation of mean concentration of the drugs in the vitreous with time for different flows. Volume of aver-aged mean concentration of drugs in the vitreous humor for different combinations of retinal permeability (P-5, P-6,and P-7) and diffusivity (D-5, D-7) for F1 (A) and for F10 (B).

D(-7) differ from that of D(-5) by having a grad-ual increase, followed by a decrease. Overall, dur-ing normal (F1) flow and high-diffusivity drugs,D(-5), P(-5) results in vitreous elimination,whereas P(-6) and P(-7) result in effective elimi-nation through the Schemm’s canal. For normalflow and low-diffusivity drugs, D(-7), all the reti-nal permeability values showed similar trends,with P(-6) achieving the highest peak among thethree retinal permeability values (0.91), and there-

after, the concentration ratio decreased with time.Also, it can be seen from Figure 7A and 7B thatfor both normal and abnormal flows, the drugeliminated rapidly through the vitreous in thecase of P(-5), whereas in the case of P(-6), the par-tition of the drug between the aqueous and thevitreous took place in such a way that there wasmore of an amount of the drug reaching the aque-ous humor during the initial IJ phase (peak at t �3 h for P(-6) D(-5) in Fig. 7A).


FIG. 7. Ratio of aqueous to vitreous concentration variation with time—normal and pathophysiologic flow. Ratiosof the volume of averaged mean concentration of drugs in the aqueous and vitreous humor for different combina-tions of retinal permeability (P-5, P-6, and P-7) and diffusivity (D-5, D-7) for F1 (A) and for F10 (B.

Elimination characteristics from the vitreous hu-mor. Half-life of drugs (t1/2) in the vitreous for thevarying retinal permeability and diffusivity, fordifferent vitreous outflows, are discussed in Fig-ure 8. The elimination from the vitreous is as-sumed to occur through a first-order process,whose t1/2 is given by the formula, t1/2 �0.693/kel, where kel (elimination constant) is theslope of the mean concentration curve with time(Fig. 6). The calculated t1/2 values are listed inTable 1. Overall, as retinal permeability decreasesfrom P(-5) to P(-7), t1/2 increases for a particularflow and diffusivity of the drug, with the increasebeing linear for normal (F1) and nonlinear for ab-normal (F10) flow cases.

When the diffusivity was fixed at D(-5), at highretinal permeability, P(-5), increase in flow re-

sulted in an increase in the value of t1/2 (�47%;arrow 1). However, a low permeability, P(-7), re-sulted in a 30% decrease (arrow 2) in t1/2 whenthere was an elevation in the vitreous outflowfrom F1 to F10. When the diffusivity was fixed atD(-7), at P(-5) the increase in flow resulted in thedecrease in t1/2 by 60% (arrow 3), whereas at P(-7) it led to a 40% increase; thus, the effects of con-vection and the influence of change in retinal per-meability on drug distribution were significant.The t1/2 for P(-6) increased as flow changed fromnormal (F1) to abnormal (F10) for both high andlow diffusivities, with the increase for high dif-fusivity (3.3-fold) being much higher than duringthe low-diffusivity case (1.5-fold; arrow 4).

DISCUSSION

A computational model has been developed topredict the drug distribution and eliminationcharacteristics of varying physicochemical prop-erties of drugs, namely the retinal permeabilityand diffusivity during normal and pathophysio-logic conditions. The results obtained from thisstudy have importance in determining the drug-delivery protocol for targeted diseases by usingspecific or combinations of drugs with particularphysicochemical properties.


TABLE 1. HALF LIFE VALUES FOR DIFFERENT

RETINAL PERMEABILITIES, DRUG DIFFUSIVITIES

AND VITREOUS CUTFLOWS

Normal flow (F1) Abnormal flow (F10)

D-5 D-7 D-5 D-7

P-5 5.41 76.15 7.98 30P-6 58.24 99 182.37 141.43P-7 770 223.55 533.08 315

Note. All values are expressed in hours.

FIG. 8. Half-life of drugs in the vitreous versus retinal permeability.

First, this study provides significant informa-tion about the effect of change in retinal perme-ability on spatial and temporal concentrations in-side the vitreous, particularly at the center of theretina, which otherwise is difficult to measure ex-perimentally. The macula is the region of high-acuity vision and the target point of most of thedrugs for treating retinal diseases, such as AMD,which is one of the leading causes of blindness inthe United States.4 The temporal variation fromFigure 4 shows that drugs with low retinal per-meability result in very high local drug concen-trations near the macula. Also, the combined ef-fect of retinal permeability and drug diffusivitywas more pronounced in the case of low drug dif-fusivity. For lower retinal permeability and F1flow, the drug concentration for the low-drug-dif-fusivity case was significantly higher than thehigh-drug-diffusivity case. This trend reversedfor the F10 flow.

Second, the knowledge of the cumulative con-centration at the retina and mode of clearance (theretina or the Schemm’s canal28,29) for varying reti-nal permeability is essential to estimate the ther-apeutic range for administering the drugs. Themode of clearance would provide informationabout how much drug would reach the target site(retina) and how much would clear through theSchemm’s canal. Thus, from the drug-dosage per-spective, it would be helpful if an appropriatecombination of physicochemical properties areknown for specific drugs. Drugs with a high-reti-nal-permeability value eliminate faster throughthe vitreous and aqueous chambers and are mod-erately influenced by flow rates. As a result of aflow change from F1 to F10, the cumulative con-centration reached at the retina increases for allthe permeability values, with more of an amountclearing through the retina for the F10P(-6) case(Fig. 5B) than the F1P(-6) case and a simultane-ous decrease in the clearance through theSchemm’s canal.

Finally, this study obtained the drug-concen-tration values in both the aqueous and vitreouschambers (Fig. 7), which is important from theperspective of drug partitioning that takes placebetween the vitreous and aqueous chambers. Avery high value of aqueous to vitreous concen-trations at the beginning of the elimination phaseimplies that the drugs preferentially eliminatethrough the aqueous chamber. It has been shownthat in the case of F1, for high retinal permeabil-ity, vitreous elimination is independent of diffu-

sivity, whereas for low retinal permeability, it isdependent on diffusivity. On the contrary, for F10flow, for both high and low retinal permeabili-ties, vitreous elimination is dependent on drugdiffusivity.

Pharmacokinetics explain a lot about the drug-elimination rates and the path that each categoryof drugs takes to clear itself from the ocular cham-bers (Figs. 6 and 8). For F1, the effect of low drugdiffusivity tends to decrease the slope for P(-5)and P(-6) and increase the slope for P(-7). On thecontrary, for F10, it tends to decrease the slopefor P(-5) and increase the slope for P(-6) and P(-7). Thus, it has been shown that the combinedeffect of retinal permeability, drug diffusivity,and pathophysiologic condition (flow) signifi-cantly affects the t1/2 of drugs inside the vitreous.

Clinically, there are several drugs and beta-blocker molecules with varying physicochemicalproperties that are used therapeutically in thetreatment of retinal degeneration and glau-coma.30 The retinal pigment epithelium (RPE)-choroid permeability values for the beta blockershave been estimated in vitro by Pitkanen et al.26

Thus, the lipophilic blockers, such as betaxaloland timolol, would eliminate predominantlythrough the vitreous retina pathway. Also, theyhave low molecular weights of around 250–320Da. This would correspond to very high diffu-sivities in the vitreous. However, there is a lackof knowledge of the complete permeability of theretina and RPE. Though we cannot completely at-tribute the characteristics seen by P(-5) and D(-5)to these molecules, we could reasonably estimatethe drug distribution inside the vitreous.

CONCLUSIONS

The main limitations of this study were that theeffect of local drug metabolism, the drug bindingto intraocular proteins, and the influence of thelocation of the site of IJ and IP have not been eval-uated. Also, the phrase “diseased condition”could imply the change in retinal permeability,abnormal vitreous outflow,14,31 or both. Disrup-tion of retina owing to a large number of retinaldiseases simultaneously alters the pattern of drugmovement and its distribution inside the ocularchambers.5,31,32 Although retinal-permeabilitychanges are both owing to the physicochemicalproperties of drugs and the pathophysiologicconditions, this study assumed the retinal per-


meability only as a function of the physicochem-ical property of the drug. The diseased conditionwas taken care of by the elevated vitreous out-flow condition (F10). The retinal permeabilityvariation with various vitreo-retinal diseases, aswell as the adoption of a porous model approachfor the retinal membrane, could be included inthe future. Further study is required to delineatethese effects. With the induction of release-ratevariations for different implants, the effect of reti-nal-permeability change on drug distributioncould be studied in the future. This study had alot of application in areas to estimate the drugdistribution for a wide range of physicochemicalproperties of drugs, such as lipophilicity or hy-drophilicity,33 and diffusivity of drugs that aresubjected to normal and pathophysiologic flowsduring the diseased condition of the eye. Theseresults could yield essential information aboutthe treatment protocol for targeted retinal dis-eases.

REFERENCES

1. Bressler, N.M., Bressler, S.B., and Fine, S.L. Age-re-lated macular degeneration. Surv. Opthalmol. 32:375–413, 1988.

2. Leibowitz, H.M., Krueger, D.E., Maunder, L.R., et al.The Framingham Eye Study monograph: An oph-thalmological and epidemiological study of cataract,glaucoma, diabetic retinopathy, macular degenera-tion, and visual acuity in a general population of 2631adults, 1973–1975. Surv. Ophthalmol. 24:335–610, 1980.

3. D’Amico, D.J. Diseases of the retina. N. Engl. J. Med.331:95–106, 1994.

4. Geroski, D.H., and Edelhauser, H.F. Drug delivery forposterior segment eye disease. Invest. Ophthalmol. Vis.Sci. 41:961–964, 2000.

5. Coco, R.M., Lopez, M.I., Pastor, J.C., et al. Pharmaco-kinetics of intravitreal vancomycin in normal and in-fected rabbit eyes. J. Ocul. Pharmacol. Ther. 14:555–563,1998.

6. Fauser, S., Kalbacher, H., Alteheld, N., et al. Pharma-cokinetics and safety of intravitreally delivered etan-ercept. Graefe’s Arch. Clin. Exp. Ophthalmol. 242:582–586, 2004.

7. Gaudreault, J., Fei, D., Rusit, J., et al. Preclinical phar-macokinetics of ranibizumab (rhuFabV2) after a sin-gle intravitreal administration. Invest. Ophthalmol. Vis.Sci. 46:726–733, 2005.

8. Robinson, M.R., Baffi, J., Yuan, P., et al. Safety andpharmacokinetics of intravitreal 2-methoxyestradiolimplants in normal rabbit and pharmacodynamics ina rat model of choroidal neovascularization. Exp. Eye.Res. 74:309–317, 2002

9. Audren, F., Tod, M., Massin, P., et al. Pharmacoki-netic-pharmacodynamic modeling of the effect of tri-amcinolone acetonide on central macular thickness inpatients with diabetic macular edema. Invest. Oph-thalmol. Vis. Sci. 45:3435–3441, 2004.

10. Beer, P.M., Bakri, S.J., Singh, R.J., et al. Intraocularconcentration and pharmacokinetics of triamcinoloneacetonide after a single intravitreal injection. Ophthal-mology 110:681–686, 2003.

11. Friedrich, S., Saville, B., and Cheng, Y.L. Drug distri-bution in the vitreous humor of the human eye: Theeffects of aphakia and changes in retinal permeabil-ity and vitreous diffusivity. J. Ocul. Pharmacol. Ther.13:445–459, 1997.

12. Friedrich, S., Cheng, Y.L., and Saville, B. Finite ele-ment modeling of drug distribution in the vitreoushumor of the rabbit eye. Ann. Biomed. Eng. 25:303–314,1997.

13. Yoshida, A., Ishiko, S., and Kojima, M. Outward per-meability of the blood retinal barrier. In: Cunha-Vaz,J., and Leite, E., eds. Ocular Fluorophotometry and theFuture. Amsterdam: Kugler and Ghedini, 1989:89–97.

14. Araie, M., and Maurice, D.M. The loss of fluorescein,fluorescein glucuronide, and fluorescein isothio-cyanate dextran from the vitreous by the anterior andretinal pathways. Exp. Eye. Res 52:27–39, 1991.

15. Kaufman, P.L., and Alm, A. Adler’s Physiology of theEye, 10th ed. Mosby, yearbook, 2003.

16. Flocks, M., Littwin, C.S., and Zimmerman, L.E. Pha-colytic glaucoma. A clinicopathologic study of onehundred thirty-eight cases of glaucoma associatedwith hypermature cataract. Arch. Ophthalmol. 54:37–45, 1955.

17. Stay, M.S., Xu, J., Randolph, T.W., et al. Computersimulation of convective and diffusive transport ofcontrolled-release drugs in the vitreous humor.Pharm. Res. 20:96–102, 2003.

18. Kim, H., Lizak, M.J., Tansey, G., et al. Study of ocu-lar transport of drugs released from an intravitrealimplant using magnetic resonance imaging. Ann. Bio-med. Eng. 33:150–164, 2005.

19. Xu, J., Heys, J.J., Barocas, V.H., et al. Permeability anddiffusion in vitreous humor: Implications for drug de-livery. Pharm. Res. 17: 664–669, 2000.

20. Park, J., Bungay, P.M., Lutz, R.J., et al. Evaluation ofcoupled convective-diffusive transport of drugs ad-ministered by intravitreal injection and controlled re-lease implant. J. Contr. Rel. 105: 279–295, 2005.

21. Forster, R.K., Abbott, R.L., and Gelender, H. Man-agement of infectious endophthalmitis. Ophthalmol-ogy 87:313–319, 1980.

22. Pflugfelder, S.C., Hernandez, E., Fliesler, S.J., et al. In-travitreal vancomycin. Retinal toxicity, clearance, andinteraction with gentamicin. Arch. Opthalmol. 105:831–837, 1987.

23. Stainer, G.A., Peyman, G.A., Meisels, H., et al. Toxic-ity of selected antibiotics in vitreous replacementfluid. Ann. Opthalmol. 9:615–618, 1977.

24. Tabatabay, C.A., D’Amico, D.J., Hanninen, L.A., et al.Experimental drusen formation induced by intra-


vitreal aminoglycoside injection. Arch. Opthalmol. 105:826–830, 1987.

25. Talamo, J.H., D’Amico, D.J., Hanninen, L.A., et al. Theinfluence of aphakia and vitrectomy on experimentalretinal toxicity of aminoglycoside antibiotics. Am.J.Opthalmol. 100:840–847, 1985.

26. Pitkanen, L., Ranta, V.P., Moilanen, H., et al. Perme-ability of retinal pigment epithelium: Effects of per-meant molecular weight and lipophilicity. Invest.Ophthalmol. Vis. Sci. 46:641–646, 2005.

27. Streuer, H., Jaworkski, A., Stoll, D., et al. In vitromodel of the outer blood-retina barrier. Brain Res.Brain Res. Protoc. 13:26–36, 2004.

28. Kane, A., Barza, M., Baum, J. Intravitreal injection ofgentamicin in rabbits. Effect of inflammation and pig-mentation on half-life and ocular distribution. Invest.Ophthalmol. Vis. Sci. 20:593–597, 1981.

29. Johnson, M.C., and Kamm, R.D. The role of Schemm’scanal in aqueous outflow from the human eye. Invest.Ophthalmol. Vis. Sci. 24:320–325, 1983.

30. Niemeyer, G., Cottier, D., and Gerber, U. Effects ofbeta-agonists on b- and c-waves implicit for adrener-gic mechanisms in cat retina. Doc. Ophthalmol. 66:373–381, 1987.

31. Pederson, J.E., and Cantrill, H.L. Experimental retinaldetachment. Arch. Ophthalmol. 102:136–139, 1984.

32. Goldberg, M.F. Diseases affecting the inner blood-retinal barrier. In: Cunha-Vaz, J.G., ed. The Blood-Reti-nal Barriers. New York: Plenum Press, 1979:309–363.

33. Prausnitz, M.R., and Noonan, J.S. Permeability ofcornea, sclera, and conjuctiva: A literature analysis fordrug delivery to the eye. J. Pharm. Sci. 87:1479–1488,1998.

Reprint Requests: Rupak K. BanerjeeDepartment of Mechanical, Industrial and

Nuclear EngineeringUniversity of Cincinnati

598 Rhodes HallP.O. Box 210072

Cincinnati, OH 45221-0072

E-mail: [email protected]

Received: September 24, 2007Accepted: February 25, 2008


effect of retinal permeability, diffusivity, and aqueous …€¦ · effect of retinal...

Documents