Pharmacokinetic Interpretation of Vitreous Fluorophotometry

Transcription

1 Pharmacokinetic Interpretation of Vitreous Fluorophotometry Ran C. Zeimer,* Norman P. Blair,* and Jose G. Cunha-Vazf Vitreous fluorophotometry is producing an increasing amount of clinical and experimental data. In order to interpret these data and obtain quantitative values for the permeability of the blood ocular barriers, there is a need to understand better the basic phenomena governing the transport of fluorescein. We present here a refined mathematical model that we use to interpret a large body of clinical data yielding values for the inward (6.9 X 10~ 6 cm/min) and outward (210 X 10~ 6 cm/min) posterior permeability coefficients, the effective diffusion coefficient in the vitreous (8 X 10~ 4 cm 2 /min), and the plasma fluorescein decay constants (1.17, 0.34, and per hour). Moreover, we utilize the model to make predictions related to kinetic vitreous fluorophotometry and to the reliability of the procedure to calculate the permeability coefficients. Invest Ophthalmol Vis Sci 24: , 1983 There has been an increasing number of reports on the evaluation of the blood-ocular barriers of the posterior segment with the aid of vitreous fluorophotometry. Most reports have been limited to the measurement of the concentration of fluorescein at some point in the vitreous after an intravenous injection of the dye. 1 " 5 Since the penetration of the dye into the vitreous depends on its concentration in the blood as well as on the permeability of the blood-ocular barrier, some authors also have evaluated this concentration. 6 "" In addition, preliminary measurements have been made to follow the penetration of fluorescein into the vitreous with time. 12 Finally, late kinetic readings have been performed to detect and evaluate the outward transport of fluorescein across the blood-ocular barriers. 13 " 17 To interpret the increasing amount of information one needs more than a qualitative description. Palestine and Brubaker 10 have developed a mathematical model for the pharmacokinetics of the blood-retinal barrier (BRB) transport. However, these authors have compared their model with experimental data that were taken under suboptimal instrumental conditions. The axial resolution was not satisfactory and the measurement was performed at only one point. Having recognized this flaw, these authors have had to introduce From the Department of Ophthalmology, University of Illinois Eye and Ear Infirmary, Chicago, Illinois* and the Department of Ophthalmology, University of Coimbra, Portugal.f Supported in part by Public Health Service Research Grants EY03106 and EY03227 and Ophthalmic Research Center Core Grant EY1792 from the National Eye Institute, Bethesda, Maryland. Presented in part at the International Symposium on Ocular Fluorophotometry, Paris, France, April 16-18, Submitted for publication October 26, Reprint requests: Ran C. Zeimer, Ph.D., University of Illinois Eye & Ear Infirmary, 1855 W. Taylor Street, Chicago, IL some arbitrary factors into their calculations, namely a geometrical summation over the whole vitreous. As a result, their theoretical model has not been verified empirically with reliable data. We have gathered experimental data that were shown to be free from any significant artifact. 18 " 20 However, when we tried to fit the data into the model, irreconciliable discrepancies became evident. The purpose of this communication is to refine the model proposed by Palestine and Brubaker and to use it to interpret the diversified body of clinical data that we have gathered. We hope that this model will allow the separation of phenomena that can be explained by simple pharmacokinetic considerations from those that need more elaboration. Materials and Methods Assumptions of the Model The model is based mainly on assumptions of transport similar to those of Palestine and Brubaker, except where stated: (1) The transports across the blood-ocular barriers are first-order processes. This implies that the flux (the mass transported across a unit area per unit of time) is linearly dependent on the concentration. This excludes processes that are saturated in the concentration range used in vitreous fluorophotometry. (2) The inward penetration is determined by the concentration of free fluorescein in the plasma, which bears a constant ratio of 17% to the total plasma concentration. 21 No other form of fluorescein is assumed to contribute to the vitreous concentration. (3) In the vitreous, the dye is transported by diffusion alone, which is oriented radially, ie, from the surface toward the center of the vitreous /83/1000/1374/$ 1.20 Association for Research in Vision and Ophthalmology 1374

2 No. 10 PHARMACOKINETIC INTERPRETATION OF VITREOUS FLUOROPHOTOMETRY / Zeimer er ol (4) The geometry of the vitreous is simplified to two hemispheres. The BRB is assumed to be homogeneous over the posterior surface and the bloodaqueous barrier over the anterior one. These two hemispheres meet at the center where there is mixing over a sphere 4 mm in diameter. These assumptions are an addition to the one-sphere model of Palestine and Brubaker. Using these assumptions a simple computer simulation was developed in which the concentration was calculated for individual shells 1 mm thick, at 1-min intervals. The basic formulas of this model are described in the appendix. The simulation was tested by comparing its prediction for diffusion in a sphere with the computations published by Crank. 22 The results showed an excellent agreement. Experimental Background of the Model Blood fluorescein decay after intravenous injection: We measured the concentrations of fluorescein in plasma obtained by fingerpricks from 15 normal subjects, 22 to 41 years old, at 15 and 60 minutes after intravenous injection of 14 mg/kg. In order to extend the time span of plasma data, we also used the ratio of 5.5 between the first and third hour readings, as published by Palestine and Brubaker. 10 The kinetics of plasma fluorescein concentration after oral administration of 3 g were followed by readings performed at 7 and 10.5 hours after administration in 10 normal subjects, 27 to 38 years old, and at 14 and 38 hours in six normal subjects, 23 to 38 years old. The blood was spun down and the plasma was diluted 100 times in phosphate buffer (ph = 7.5). All the concentration measurements were performed on the Fluorotron (Coherent, Palo Alto, CA). This new commercial instrument was described briefly and evaluated by us. 19 The parameters of a three exponential function were adjusted to fit the data. Vitreal distribution of fluorescein 1 hour after injection: The spatial distribution of fluorescein in the vitreous depends on the diffusion coefficient within the vitreous, as well as on the decay rate of the blood fluorescein. For example, a low diffusion coefficient will produce a steep gradient in fluorescein concentration from the retinal surface to the center of the vitreous. We thus evaluated the diffusion coefficient from the fluorescein concentration profile obtained 1 hour after intravenous injection. A 14-mg/kg intravenous injection was given in 14 eyes of nine normal subjects^: and 17 eyes of 10 diabetic subjects,^ 20 to 38 years old. We purposely selected a group in whom the vitreous was normal and in whom % Appropriate consent was obtained. no retinopathy could be observed. The measurements were performed with the Fluorotron, and the readings were corrected by algorithms that were described elsewhere. 20 This procedure and the axial resolution of the instrument assured that the results were satisfactorily reliable. From the scans we obtained the ratio of the fluorescein. concentration at 3 and 6 mm from the choroid-retina. The mathematical model then was used to generate different ratios by adjusting the diffusion coefficient. Evaluation of the BRB permeability coefficients: The kinetics of fluorescein across the BRB can be described under the above assumptions as: F = P in *Cp - P 0Ut *Cv (eq. 1) where F is the flux, ie, the net mass transported across a 1 cm 2 of BRB in 1 minute, P in and P ou t are the inward and outward permeability coefficients, respectively, Cp is the free fluorescein concentration in the plasma; and Cv is the fluorescein concentration in the posterior vitreous. 26 Three different measurements were obtained to evaluate the inward and outward permeability coefficients. The first measurement, yielding the ratio of the two coefficients, was described in detail. 17 It consisted basically of measuring the vitreous concentration of fluorescein when a maximum was reached after oral administration. Indeed, it is realized from equation 1 that a maximal vitreous concentration is reached when F = 0 or when P in *Cs = P out *Cv (eq. 2) namely, when: Pout/Pin = CS/CV (eq. 3) The second measurement consisted of measuring the decay of the fluorescein concentration in the vitreous of six normal subjects, 23 to 38 years old, 14 to 38 hours after oral administration of 3 g of fluorescein. The plasma fluorescein concentration was measured from fingerpricks at 14 and 38 hours. The third measurement consisted of following the vitreal concentration of fluorescein 1 to 5 hours after intravenous injection of 14 mg/kg fluorescein. 12 The measurements were done before the Fluorotron was available; therefore, we used an instrument described earlier that consisted of a modified slit-lamp microscope. ' The performance of this instrument has been evaluated by us and found to be adequate when and only when it is optimized. 18 Procedure to Calculate the Inward Permeability Coefficient From a Single Scan We will first derive an ideal expression from which the inward permeability can be evaluated, and we will

3 1376 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / October 1983 Vol A (10-" 7t t 0.025»10" 0044t ) Palestine and Brubaker cm 2 at this location, the expression can be simplified to: A(r)/r 2 = 1/R 2 (eq.8) thus: dv = A(r)*dr = l/rvtdr (eq.9) Equation 6 now becomes: J F*dt = 1/R 2 *J Cv(r)*r 2 *dr (eq. 10) Finally, by combining equation 10 with equation 5, one obtains: P in = 1/R 2 *J Cv(r)*r 2 *dr If Cp*dt (eq. 11) TIME (hours) Fig. 1. Plasma fluorescein concentration as a function of time after intravenous injection of 14 mg/kg fluorescein. The dots and bars represent the means and standard deviations of the experimental data. The solid line is the plot of the formula, with t being the time in hours. The broken line represents the curve obtained by Palestine and Brubaker. later attempt to make it conform to more realistic conditions. We have shown that the outward transport contributes little during the first 2 hours, so we can rewrite equation 1: F = P in *Cp (eq.4) If we now integrate over time, J F*dt = P in *J Cp*dt (eq.5) The left-hand side is the total mass that has penetrated a 1 cm 2 of BRB. This mass is now in the vitreous, thus allowing us to write: J F ' dt - J Cv(r)*dv (eq.6) where Cv(r) is the concentration in the vitreous as a function of r, and dv is an element of volume. According to assumption C, the mass that penetrates the vitreous diffuses radially toward the center. In other words, the mass that leaks through a 1 cm 2 will be contained in a cone with its apex at the center of the vitreous; its base is a 1 cm 2 on the retina. We can divide this cone into shells of thickness dr and surface A(r) and, since all these shells sustain the same threedimensional angle, we can write: = A(R)/R 2 (eq.7) where R is the radius at the retina. But since A(R) = 1 This last equation should allow us to determine P in from the experimental data. We have shown that the readings are reliable at distances larger than 2 to 3 mm from the choroid-retina (especially after correction for the spread functions of the chorioretinal peak), 20 but there is a region close to the retina where the vitreous fluorophotometry results are less reliable. Consequently, the integral in equation 11 has to be limited to a radius smaller than R. In addition, it should be limited to the posterior vitreous so not to include any significant contribution from peripheral and anterior leakages. We therefore shall modify equation 11 and write: P inesl = B* 1/R 2 * I Cv(r)*r 2 *dr / f Cp*dt JR-2.5 / J (eq.12) where P inest is now the estimated inward permeability coefficient. The integral is carried out from 2.5 to 6.5 mm from the retina, namely, between radii (R 2.5) and (R 6.5) mm. B is the scaling factor which accounts for the fact that the integral is not carried out over the whole preretinal volume (equation 11) but only limited to the 2.5- to 6.5-mm region. B will be obtained theoretically in the following way: the integral over the whole distance from the retina in (equation 11) will be computed as well as the integral over the 2.5- to 6.5-mm range (equation 12). B will be derived from the ratio of the two integrals. Finally, to test the reliability of equation 12 to predict Pin, we can change the values of parameters that are known to vary between individuals, such as the blood decay and the diffusion coefficient. Results Blood Fluorescein Decay after Intravenous Injection The plasma fluorescein concentration is seen to decrease rapidly for the first hour, and later to gradually reach a constant decay curve (Figs. 1, 2). These data

4 No. 10 PHARMACOKINETIC INTERPRETATION OF VITREOUS FLUOROPHOTOMETRY / Zeimer er ol consist of our 15- and 60-min measurements and data derived from Palestine and Brubaker. By using these latter data we were able to extrapolate the 3-hour value from the 1-hour value. The analytical function shown in the figures was matched to the data. A is a scaling constant that is determined when the function is fitted to the data. The three exponents and their factors in the parentheses account for the time dependence of the fluorescein concentration. They correspond to halftimes of 15 and 53 minutes and 5 hours, respectively. It should be noted that the same function matches the intravenous and oral data. Vitreal Distribution of Fluorescein 1 Hour after Intravenous Injection The ratio between the readings 3 and 6 mm away from the retina were measured. This ratio was expected to vary strongly with the diffusion coefficient as plotted in Figure 3. In this figure we also have indicated the experimental data. The results corresponded to a diffusion coefficient of 8 X 10~ 4 cm 2 /min. We also have shown in the figure the value published by Kaiser and Maurice 25 and used by Palestine and Brubaker. Evaluation of the BRB Permeability Coefficients The ratio between the outward and inward permeabilities obtained at maximum vitreal concentration was 30 ± Thefluoresceinconcentration was found to decrease from 8.8 ± 2.0 ng/ml at 14 hours after oral administration to 4.1 ± 1.0 ng/ml at 38 hours. At both times the fluorescein concentration was distributed evenly in the vitreous. The plasma fluorescein concentration was found to decrease from 800 ±330 ng/ml to 50 ± 20 ng/ml. The vitreous fluorescein concentration followed for 5 hours, taken from a previous publication, 12 is illustrated in Figure 4. The model was adjusted by first fitting the inward permeability, mainly at 2 to 5 hours, and adjusting the ratio with the outward permeability to match the first two experiments. The best results were obtained when P in = ~ 6 cm/min and P ou t = " 4 cm/min. Predictions of the Model The good qualitative correlation of the model with the experimental data allows us to consider some of its predictions. We have plotted the results of computations in which the values of some of the parameters have been changed (Fig. 4). The following conclusions can be drawn from these results: (1) The early kinetic phase is not influenced by outward transport. Curve 3 represents the model's prediction using the values obtained above for P in and A (10" 1 "'* ' 0Mt lo" 0-04 *') TIME (hours) Fig. 2. Plasma fluorescein concentration as a function of time after oral administration of 3 g fluorescein. The dots and bars represent the means and standard deviations of the experimental data obtained in this study. The solid line is the plot of the formula, with t being the time in hours. P out. Curve 2 was obtained by setting the outward permeability to zero. The readings at 3 mm from the choroid-retina are not influenced, until the third hour, by the shut-down of the outward transport; the influence of the outward transport is not very significant until the fifth hour. DIFFUSION COEFFICIENT [10' Fig. 3. Ratio of the fluorescein concentrations 3 and 6 mm away from the retina as a function of the diffusion coefficient of fluorescein in the vitreous. The dot and bar represent the mean and standard deviation of the experimental data. The solid curve is the result of the computer simulation. The open dot is the diffusion coefficient obtained by Kaiser and Maurice.

5 1378 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / October 1983 Vol. 24 Pin cm/min P out cm/min Plasma (15') Plasma (60') Factors Affecting the Determination of the Outward Permeability (1) By varying the inward permeability between 4 X 10" 6 (-30%) and 9 X 10" 6 cm/min (+30%) one obtains, for the outward permeability, values between 208 and 216 X 10~ 6 cm/min, namely a variation less than 3%. (2) By varying the 14-hour plasma value between 1,200 (+25%) and 730 (-25%) ng/ml one obtains an outward permeability between 212 and 209 X 10~ 6 cm/min, namely, a variation of less than 1%. Discussion Assumptions of the Model 2 3 TIME (hours) Fig. 4. Fluorescein concentration 3 mm away from the retina as a function of time. The different curves represent the computer simulations using the different parameters tabulated. The dots represent the experimental data. (2) The plasma fluorescein decay curve influences the results. By comparing curves 1,3, and 4, a change in the ratio of the 15 to 60 minutes plasma values with the same 60-min value yields different results for the vitreous concentration of fluorescein. A change of +30% in the blood ratio (equivalent to its standard deviation in humans) causes a similar change in the 3-mm reading 1 to 2 hours after injection. Factors Affecting the Determination of the Inward Permeability Coefficient We determined the factor B of equation 12 and found a value of 3.3 and 2.5 for the 1 and 2 hour scans, respectively. Moreover, from the results we can realize that: (1) The variation of the blood decay rate in the range observed clinically has less than 5% influence on the accuracy of the estimate of the inward permeability coefficient. (2) The variation of the diffusion coefficient affects the accuracy of the evaluation of P in. When the diffusion coefficient assumes the lower value of 6 X 10~ 4 cm 2 /min (Fig. 3) the error is 17 and 8% for the 1- and 2-hour estimates, respectively. When the diffusion coefficient assumes the higher value of 11 X 10~ 4 cm 2 /min, the error is 13 and 6% for the 1- and 2-hour estimates, respectively. (3) Finally, by comparing the mass in the posterior vitreous to the mass that has penetrated throughout the BRB only, it is realized that the anterior leakage contributes insignificantly in normal eyes to the calculated mass at 2.5 to 6.5 mm from the retina for the first 2 hours. The mathematical model we have used is based on assumptions, some of which are straightforward, whereas others need the validation of more experimental data. The assumption on the nature of the transport across the BRB seems to be justified. The equation of transport across the BRB is general enough to be adequate for passive, nonsaturated active, and even bulk flow transports. As discussed previously, 17 the contribution of transport governed by an electric potential appears to be low. In contrast, the diffusive transport, which is assumed to be present in the vitreous, is not necessarily applicable in all cases. With slit-lamp examination one can observe, occasionally, vitreous motions caused by degenerative changes. Such motions suggest that bulk flow could play an important role in the transport of fluorescein in the vitreous, and could be induced by mechanical motions or by thermal convective currents. Nonetheless, the assumption of radial diffusion provides valuable information because it can help estimate the importance of phenomena other than simple diffusion. This can be achieved by estimating the extent of deviation of the experimental data from the predictions of the model. The assumptions regarding the geometry of the globe seem appropriate for the posterior pole. The approximation of the anterior vitreous and BRB as a homogeneous sphere is more crude. A two-dimensional model taking into account the geometry of the ciliary body, the posterior chamber, and the lens would improve the authenticity of the model as related to the anterior vitreous. Blood Fluorescein Kinetics We have shown that the decay of plasma fluorescein concentration can be described by a three-exponential function. The first two terms govern the early decay while the last one reflects the monoexponential decay

6 No. 10 PHARMACOKINETIC INTERPRETATION OF VITREOUS FLUOROPHOTOMETRY / Zeimer er ol after 5 to 7 hours. Although this function is a phenomenological one, it perhaps reflects three phenomena controlling the kinetics of fluorescein such as the distribution in the interstitial space and the nitration rate in the kidney. These results apply to the plasma fluorescein concentration. However, the important factor is the free fluorescein concentration. There is a need for more experimental data regarding the kinetics of metabolites of fluorescein such as fluorescein glucuronide. This is important when a model such as ours will be applied to clinical conditions in which the free fraction may vary. Moreover, if the kinetics of free fluorescein during the first hour differ from that of whole plasma fluorescein, the results of the model could be affected. In the absence of such data we have assumed, following the work by Araie et al, 21 that 17% of the plasma fluorescein is free. Determination of the Diffusion Coefficient We have shown that to fit the model to the average vitreous fluorophotometry profile at 1 hour, the diffusion coefficient has to be adjusted. The best fit was with a diffusion coefficient of 8 X 10~ 4 cm 2 /min. This is lower than that of oxygen in water (10.8 X 10~ 4 cm 2 /min) and higher than that of acetate in water (4.8 X 10~ 4 cm 2 /min). As shown in the results, it is definitely higher than the value of 3.6 X 10~ 4 cm 2 / min found by Kaiser and Maurice for the diffusion of fluorescein in water. 25 The discrepancy could be caused by several factors. It could result from experimental error in either of the measurements or from the difference in media. For example, one could speculate that the vitreous interacts with the fluorescein anion and causes it to diffuse faster than in water. Finally, and most probably, it could simply result from the presence of mixing in the vitreous. Evaluation of the Permeability Coefficients We have shown that the inward permeability coefficient can be evaluated by fitting the model to the vitreous fluorophotometry data obtained during the first few hours. At this time, the outward transport plays a minor role and the kinetics are dominated by the inward transport. We have shown in Figure 4 that if one adjusts the model to the second and third hours a permeability coefficient of 6.9 X 10~ 6 cm/min is obtained, while adjusting only to the first hour a permeability coefficient of 3.7 X 10~ 6 cm/min is obtained. This discrepancy definitely calls for a revision of the model. It seems that there is at one hour less fluorescein 3 mm away from the retina than is predicted. The discrepancy cannot be attributed to an underestimate of the diffusion coefficient because the experimental data show a higher fluorescein concentration at midvitreous than the model. We believe, however, that before modifying the model a larger body of experimental data should be gathered to define the possible discrepancy better. The value for the inward permeability depends on the scaling factor of equation 12. This factor was derived directly from the model and is thus dependent on the model for its validity. Moreover, according to the model this factor is affected by changes in the diffusion coefficient because the amount of fluorescein reaching the 2.5 to 6.5 integration range of equation 12 is determined by the diffusion rate. This influence of the diffusion on the results will be discussed below. The value we obtained for the permeability coefficient is 12 times lower than the value chosen by Palestine and Brubaker in their model and adopted from the estimations of Maurice 6 in rabbit retinas that were inhibited by probenecid. On the other hand, it is surprisingly similar to the value of 9.6 X 10~ 6 cm/min for the permeability of cerebral capillaries to Na and Cl anions in rabbits and rats. 27 We also have evaluated the outward permeability coefficient by three experiments. The first consisted of measuring the ratio between the fluorescein concentration in the blood and the vitreous, which yielded a predicted ratio of 30 ± 18 between the outward and inward permeability coefficients. The second experiment, which consisted of following the decay of the vitreous concentration between 14 and 38 hours after oral administration of fluorescein, yielded identical results (ratio of 30). The third experiment followed the fluorescein vitreous concentration from three to five hours after intravenous injection. This experiment was used only to test the validity of the values obtained by the first two experiments. As seen in Figure 4, the fit of curve 3, obtained with the derived values for the inward and outward permeability is satisfactory. The experiment was given a lesser importance in the determination of the outward permeability because, as shown in the results and discussed further, the outward permeability has only little influence on the kinetics of the vitreous fluorescein concentration in the first few hours after administration. It is interesting to note that a somewhat similar ratio (50) was extrapolated by Palestine and Brubaker from their model. The presence of a higher outward permeability and of a transport against a concentration gradient suggests that the outward transport is linked to an active process. The elimination of fluorescein through the anterior chamber was ruled out because the anterior chamber concentration was always higher than that in the vitreous.

7 1380 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / October 1983 Vol. 24 It will be of interest to evaluate this transport in different disease states. Predictions of the Model The model first predicts that the outward transport has little influence on the kinetics of fluorescein during the first few hours. This contradicts the predictions of Palestine and Brubaker. The reason for the discrepancy is simply due to the fact that their outward permeability coefficient was too large, although the ratio between the permeability coefficients was similar to ours. This prediction allows us to conclude that the first 2 hours reflect only the inward transport mechanism, which thereby is isolated from the outward one. The calculations of the influence of the blood fluorescein decay rate on the vitreous fluorophotometry results are not surprising because they are a straightforward outcome of the basic equations. We have included this result to emphasize further the importance of determining the blood fluorescein concentration at an early time, such as 10 minutes after injection. Of more interest is the evaluation of the reliability of the estimation of the permeability coefficients. We have shown that if the blood fluorescein curve is integrated, the variations in decay rate have no influence on the accuracy of the calculated inward permeability coefficient. Moreover, the simulation indicates that the calculation can probably be carried out relying only on the information of a 4-mm portion of the posterior vitreous located 2.5 mm away from the retina, provided the model reflects the actual transport in the eye. It also was shown that the model predicts no influence of the anterior leakage during the first 2 hours. The main variation seems to be caused by the diffusion coefficient. If it is allowed to vary over the 30% range calculated from the vitreous fluorescein gradient, the estimate of the permeability coefficient varies by up to 17 and 8% for the scans at 1 and 2 hours, respectively. It appears, therefore, that, under the conditions of the model, which were tailored to the transport in a normal eye, the 2-hour scan is more reliable. At least for this model, it seems that at this time more fluorescein is present between 2.5 and 6.5 mm from the retina, and the posterior and anterior leakages do not mix significantly. More experimental data would be beneficial, especially with older eyes. Finally, it was noticed that the determination of the outward permeability coefficient, by measurements at 14 and 38 hours after oral administration of fluorescein, is influenced minimally by variations of the inward permeability coefficient or the plasma fluorescein concentration. Key words:fluorophotometry,blood ocular barrier, pharmacokinetics, permeability, fluorescein Acknowledgments Appreciation is expressed to Mark M. Rusin for technical assistance, to Marlene Heneghan for secretarial assistance, and to Maxine Gere for editorial services. References 1. Cunha-Vaz J, Faria de Abreu JR, Campos AJ, and Figo GM: Early breakdown of the blood-retinal barrier in diabetes. Br J Ophthalmol 59:649, Krupin T, Waltman SR, Oestrich C, Santiago J, Ratzan S, Kilo C, and Becker B: Vitreous fluorophotometry in juvenile-onset diabetes mellitus. Arch Ophthalmol 96:812, Waltman S, Krupin T, Hanish S, Oestrich C, and Becker B: Alteration of the blood-retinal barrier in experimental diabetes mellitus. Arch Ophthalmol 96:878, Cunha-Vaz JG, Fonseca JR, Abreu JF, and Ruas MA: A followup study by vitreous fluorophotometry of early retinal involvement in diabetes. Am J Ophthalmol 86:467, Waltman SR, Krupin T, Kilo C, and Becker B: Vitreous fluorophotometry in adult-onset diabetes mellitus. Am J Ophthalmol 88:342, Cunha-Vaz JG and Maurice DM: The active transport of fluorescein by the retinal vessels and the retina. J Physiol (Lond) 191:467, Cunha-Vaz J and Maurice D: Fluorescein dynamics in the eye. Doc Ophthalmol 26:61, Cunha-Vaz JG, Goldberg MF, Vygantas C, and Noth J: Early detection of retinal involvement in diabetes by vitreous fluorophotometry. Ophthalmology 86:264, Lund-Andersen HM, Lassen N: Microvascular permeability in diabetic patients. Bibl Anat 20:675, Palestine AG and Brubaker RF: Pharmacokinetics of fluorescein in the vitreous. Invest Ophthalmol Vis Sci 21:542, Jones CW, Cunha-Vaz JG, and Rusin MM: Vitreous fluorophotometry in the alloxan- and streptozocin-treated rat. Arch Ophthalmol 100:1141, Cunha-Vaz JG, Zeimer R, Wong WP, and Kiani R: Kinetic vitreous fluorophotometry in normals and noninsulin dependent diabetics. Ophthalmology 89:751, Jones CW, Cunha-Vaz J, Zweig KO, and Stein M: Kinetic vitreous fluorophotometry in experimental diabetes. Arch Ophthalmol 97:1941, Zweig K, Cunha-Vaz J, Peyman G, Stein M, and Raichand M: Effect of argon laser photocoagulation of fluorescein transport across the blood-retinal barrier. Exp Eye Res 32:323, Krupin T, Waltman SR, Szewczyk P, Koloms B, Farber M, Silverstein B, and Becker B: Fluorometric studies on the bloodretinal barrier in experimental animals. Arch Ophthalmol 100:631, Anstadt B, Blair NP, Rusin M, Cunha-Vaz JG, and Tso MOM: Alteration of the blood-retinal barrier by sodium iodate: kinetic vitreous fluorophotometry^and horseradish peroxidase tracer studies. Exp Eye Res 35:653, Blair NP, Zeimer RC, Rusin MM, and Cunha-Vaz JG: Outward transport of fluorescein from the vitreous in normal human subjects. Arch Ophthalmol 101:1117, Zeimer RC, Cunha-Vaz JG, and Johnson ME: Studies on the technique of vitreous fluorophotometry. Invest Ophthalmol Vis Sci 22:668, Zeimer RC, Blair NP, and Cunha-Vaz JG: Vitreous fluorophotometry for clinical research. I. Description and evaluation of a new fluorophotometer. Arch Ophthalmol, in press. 20. Zeimer RC, Blair NP, and Cunha-Vaz JG: Vitreous fluoropho-

8 No. 10 PHARMACOKINETIC INTERPRETATION OF VITREOUS FLUOROPHOTOMETRY / Zeimer er ol tometry for clinical research. II. Methodology of data acquisition and processing. Arch Ophthalmol, in press. 21. Araie M, Sawa M, Nagataki S, and Mishima S: Aqueous humor dynamics in man as studied by oral fluorescein. Jpn J Ophthalmol 24:346, Crank J: The Mathematics of Diffusion, 2nd ed. Oxford, Oxford University Press, 1975, pp Zeimer RC, Cunha-Vaz JG, Blair NP, and Rusin MM: Vitreous fluorophotometry made reliable and accessible to clinical investigators. ARVO Abstracts. Invest Ophthalmol Vis Sci 22(Suppl):58, Zeimer RC, Blair NP, Rusin MM, and Cunha-Vaz JG: The performance of a new commercial ocular fluorophotometer in the clinical environment. In Proceedings of the First International Symposium on Ocular Fluorophotometry, Coscas G, editor. In press. 25. Kaiser RJ and Maurice DM: The diffusion of fluorescein in the lens. Exp Eye Res 3:156, Neame KD and Richards TG: Elementary Kinetics of Membrane Carrier Transport. New York, John Wiley and Sons, Davson H, Welch K: The permeation of several materials into the fluids of the rabbit's brain. J Physiol (Lond) 218:337, Appendix Mathematical Basis of the Computer Simulation The main formulas are: FPF = 0.17*plasma fluorescein concentration (App. 1) where FPF is the free plasma fluorescein concentration. The plasma concentration is computed from the equation in Figure 1. The transport at the retina interface (x = R) is governed by: Cvit(R, t) = Cvit(R, t - dt) + (P in *FPF - P out *Cvit(R, t - dt))*dt/v(r) - (Cvit(R, t - dt) - Cvit(R - dr, t - dt))*d*dt*a(r)/dr*v(r) (App. 2) where Cvit(x, t) is the fluorescein concentration at distance x from the center and at time t. V(x) and A(x) are the volume and the surface, respectively, of a shell of radius x and thickness dr. D is the diffusion coefficient. The other symbols are identical to those in the text. An identical equation is written for the anterior interface next to the blood aqueous barrier. At locations away from the interface and in the posterior hemisphere the equation is: Cvit(r, t) = Cvit(r, t) + [(Cvit(r + dr, t - dt) - Cvit(r, t - dt)]*a(r) - (Cvit(r, t - dt) - Cvit(r - dr, t - dt)]*a(r - dr)*d*dt/dr*v(r) (App. 3) An identical equation is written for the anterior hemisphere. At the center 4 mm the posterior and anterior values are equalized. These calculations are performed for time intervals dt of one minute and increments dr of one millimeter.