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(Investigative Ophthalmology and Visual Science. 2004;45:3435-3441.)
© 2004 by The Association for Research in Vision and Ophthalmology, Inc.
DOI:  10.1167/iovs.03-1110
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Pharmacokinetic–Pharmacodynamic Modeling of the Effect of Triamcinolone Acetonide on Central Macular Thickness in Patients with Diabetic Macular Edema

François Audren,1 Michel Tod,2 Pascale Massin,1 Rym Benosman,1 Belkacem Haouchine,1 Ali Erginay,1 Charles Caulin,3 Alain Gaudric,1 and Jean-François Bergmann3

1From the Ophthalmology Department and 3Unit of Therapeutic Research, Hôpital Lariboisière, Université Paris 7, Paris, France; and the 2Department of Pharmacy-Toxicology, Hôpital Cochin, Université Paris 5, Paris, France.


   Abstract
Top
 Abstract
Methods
 Results
 Discussion
 Conclusion
 References
 
PURPOSE. To develop a population model capable of describing the profile of the effect of intravitreal triamcinolone acetonide in the treatment of diabetic diffuse macular edema.

METHODS. The results of 51 injections in 37 eyes (33 patients) with diffuse diabetic macular edema were studied, by using population pharmacokinetic–pharmacodynamic modeling, without triamcinolone concentration measurements. This approach was supported by the pharmacokinetic hypothesis that the intravitreal triamcinolone concentration decreases in accordance with an exponential biphasic equation. Central macular thickness (CMT), measured by optical coherence tomography was chosen as the pharmacodynamic parameter.

RESULTS. The pharmacodynamic profile of the effect of triamcinolone on CMT was characterized by a curve in three phases: a fast decrease, a steady state, and a relapse. The confidence interval of most of the estimated parameters of the model was narrow. The mean estimated half-life of triamcinolone ± SD was 15.4 ± 1.9 days, and the mean maximum duration of its effect (±SD), 140 ± 17 days.

CONCLUSIONS. Pharmacokinetic–pharmacodynamic modeling using CMT constitutes a valid alternative to pharmacokinetic studies. This approach worked excellently in the present study, and the results are consistent with those published for the intraocular pharmacokinetics of triamcinolone acetonide in the human eye. The authors conclude that this type of investigation is of interest, as it avoids intraocular measurements as far as possible.

Intravitreal triamcinolone acetonide (TA) has been proposed recently as a treatment for various retinal diseases, such as proliferative vitreoretinopathy,1 choroidal neovascularization combined with age-related macular degeneration,2 and macular edema, which may be associated with ocular disorders such as uveitis3 or with vascular diseases. Diabetic macular edema seems to be one of the most promising indications for TA4 5 (Gillies MC, et al. IOVS 2003;44:ARVO E-Abstract 3219). Several studies have shown that intravitreal injection of TA is dramatically, although transiently, effective in reducing macular thickening caused by diffuse diabetic macular edema, which has been refractory to all other treatments.4 5

The commercially available preparation of TA appears to be safe, in toxicity studies of pigmented rabbits.6 7 Although recent data have raised doubts in this respect (Perlman E, et al. IOVS 2003;44:ARVO E-Abstract 4899), no toxic accident has been reported in humans. In any case, TA medication was not initially designed for intraocular administration, and the lack of elementary ocular pharmacologic information does not yet allow its rational use. To date, the only study dealing with the ocular pharmacokinetics of TA in humans is the recent publication by Beer et al.,8 who focused on the decrease in the intracameral concentration of TA after a single intravitreal injection of 4 mg, and found that the mean elimination half-life of TA was 18.6 days, with considerable intersubject variation. However, only five patients were included in the study.

The purpose of the present study was to propose a method of evaluating the pharmacologic effect of TA on diffuse macular edema, using population pharmacokinetic–pharmacodynamic modeling. The pharmacodynamic parameter we measured, by optical coherence tomography (OCT), was central macular thickness (CMT).


   Methods
Top
 Abstract
 Methods
Results
 Discussion
 Conclusion
 References
 
Study Design and Eye Characteristics
Data were obtained from two previous phase II studies conducted in our clinical unit. The first,5 which dealt with TA efficacy, included diabetic patients with bilateral diffuse macular edema refractory to laser treatment. In all cases, macular laser photocoagulation had been performed at least 6 months before TA injection. Diffuse macular edema was defined as macular thickening with no sign of vitreomacular traction on biomicroscopy or OCT. For inclusion, CMT, measured by OCT, had to be bilateral and greater than 380 µm in both eyes. Glycated hemoglobin (HBA1c) had to be less than 9.5% and systolic and diastolic blood pressure, less than 150 and 90 mm Hg, respectively. The second study (unpublished data) included patients with the same characteristics, but with unilateral macular edema and CMT greater than 300 µm.

Patients were excluded from these studies if they had a history of glaucoma or had experienced an increase in intraocular pressure exceeding 15 mm Hg after 1 month of treatment with topical 0.1% dexamethasone three times daily in both eyes. Also excluded were patients who had undergone panretinal photocoagulation or cataract or vitreous surgery during the previous 6 months. Each eligible patient received complete oral and written information concerning the study protocol, and patients who agreed to participate signed a consent form. Both studies were approved by the local ethics committee and were conducted according to the principles of the Declaration of Helsinki.

In the two studies, 4 mg TA (Kénacort Retard; Bristol-Myers Squibb, Paris, France) was injected into the vitreous body (total volume: 0.1 mL) with full asepsis under subconjunctival anesthesia with 0.5 mL 1% lidocaine. As additives, this preparation contained benzyl alcohol, sodium chloride, sodium carboxymethylcellulose, and polysorbate 80. TA was injected 4 mm posterior to the limbus, through the inferior pars plana, with a 30-gauge needle.

No intravitreal reinjection of TA was allowed until 6 months after the first injection. A second injection could then be performed, in the previously treated eye, in case of a relapse of macular edema, and/or in the fellow eye, in case of bilateral macular edema.

The results of this treatment as regards visual acuity and intraocular pressure, reported in detail elsewhere,5 will not be given in this report, as these parameters were not the focus of the present investigation.

The results reported concern 51 injections in 37 eyes of 33 patients, 17 included in the first study and 16 in the second. Twenty-three eyes had one injection, and 14 eyes, two injections. Patient and eye characteristics are given in Table 1 .


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  		TABLE 1. Baseline Characteristics

 
CMT Measurements
The main parameter measured in both studies was CMT. It was measured automatically, using the mapping software of the coherence tomography system (A5 software with the OCT2; Carl Zeiss Meditec, Dublin, CA), as reported elsewhere.9 The normal mean retinal thickness in the central macula area is 170 ± 18 µm.9 10 With OCT mapping, we demonstrated that the reproducibility of CMT measurement was good, with a reproducibility coefficient of 6%.9

CMT was measured as follows: After the first injection, it was measured twice a week during the first 2 weeks and once a week during the next 2 weeks. After a second injection, CMT was measured once a week for 4 weeks. Thereafter, it was measured 6, 8, 10, 12, 16, 20, and 24 weeks after injection, and then every 4 weeks if no reinjection was performed. However, this schedule was only approximate, except for the 4-, 12-, and 24-week measurements, which were performed in all cases. Other measurements were sometimes omitted, or the intervals between them varied among individuals. The dates of measurements were expressed in days after injection (measurements were performed at the same time of day during the month after injection, with a margin of error of 2 hours). Baseline characteristics of follow-up schedules after TA injection are given in Table 2 .


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  		TABLE 2. Baseline Characteristics of Follow-up Schedules after TA Injection

 
CMT values before TA injection and 4, 12, and 24 weeks thereafter are shown in Table 3 .


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  		TABLE 3. CMT before TA Injection and 4, 12, and 24 Weeks Thereafter

 
Pharmacokinetic–Pharmacodynamic Modeling
We used population pharmacokinetic–pharmacodynamic modeling; no intraocular concentrations were measured directly. The modeling was based on a pharmacokinetic hypothesis and a pharmacodynamic hypothesis.

The Pharmacokinetic Hypothesis.
When a solution of TA is injected into the vitreous body, TA is eliminated with first-order kinetics—that is, the elimination rate is proportional to the concentration. After such an injection, the intravitreal concentration of TA decreases according to an exponential biphasic equation.8 Because the TA deposits remain visible in the vitreous cavity for 1 to 3 months,8 this two-phase decrease can be interpreted as follows: Phase 1 (fast decrease) was clearance from the vitreous body of the water-soluble TA at the time of injection. The slope of this phase ({alpha}) corresponds to the rate of TA elimination from the vitreous. Phase 2 (slow decrease) was clearance from the vitreous body of TA, which becomes water-soluble after dissolution of the TA crystals. The slope of this phase (ß) corresponds to the rate of TA dissolution in the vitreous body.

The kinetic modeling equations are the following

(1)
where D is the dose of TA, V is the volume of the vitreous body (fixed at 4 mL or 0.004 L), and F1 and F2 are parameters without dimensions. At time 0, the TA concentration is expressed as

(2)
According to Beer et al.,8 C(0) is equal to 10 mg/L, when the dose of TA is 4 mg. Therefore,

The parameters to be estimated are {alpha}, ß, and F1.

The Pharmacodynamic Hypothesis.
The measured response R (CMT) may change with time. This change is described by an indirect pharmacodynamic model11 in which we assume that the change is rendered by

(3)
where Rin(t) is the rate of production, and Kout·R(t) is the rate of elimination. In a normal subject, the CMT does not change, so that dR(t)/dt = 0. Consequently,

(4)
In diabetic patients, the increase in R is interpreted as resulting from a value Rin0, greater than the normal Rinbas value. At the beginning of treatment (time 0), Rin is equal to Rin0 (>Rinbas).

TA inhibits this production increase, in a concentration-dependent manner, according to an empiric sigmoidal model (Hill’s equation):

(5)
where Emax = (Rin0 – Rinbas) and is the maximum effect of TA, obtained with an infinite TA concentration. C50 is the concentration that produces a half-maximum effect. The parameter s is the coefficient of sigmoidicity, without units. This model predicts that CMT increases when TA is removed from the eye (i.e., that TA does not have a curative effect). The response at time t is calculated by numerical integration of dR(t)/dt. The initial Rin0 is equal to the R measured at the time of injection.

Data Analysis
Data were analyzed by a population approach. All the measurements for each patient were modeled simultaneously, by nonlinear mixed-effect modeling,12 to evaluate typical parameters and interindividual and residual variability. In this type of model, two levels of variability can be distinguished.

(1) Residual variability, which describes, for a patient j, characterized by a particular value Pj for the parameters {alpha}, ß, F1, Rinbas, Emax, C50, s, and Kout, the difference between the observed value of the response (Robs) and the predicted value of R, according to the following

(6)
where {epsilon} is a normally distributed random variable, with a zero mean and variance sigma2 ({sigma}2) to be estimated. This formulation implies that the coefficient of variation of the CMT measurements is both constant and independent of the level of measurement.

(2) Interindividual variability, which assumes that the values of the parameters change from one patient to another—that is, have a particular distribution, assumed to be log-normal (a usual hypothesis is in this type of model). Thus,

(7)
where is the median of the parameter in the population, and {eta} is a random, normally distributed variable with a zero mean and variance {omega}. The parameters to be estimated are the medians and the variances {omega} and {sigma}2. They are estimated by nonlinear mixed-effect modeling (NONMEM, ver. 5.0; GloboMax, Hanover, MD).13 The individual parameters Pj (post hoc estimates) are then estimated by the Bayesian method. For the sake of simplicity, the respective variabilities of the random effects {epsilon} and {eta} are expressed as coefficients of variation (CV). In this type of model, the effect of the covariates is introduced assuming that they modify the values of the medians. Schematically, the method used herein includes three steps: (1) visual examination of the scatterplots of the residuals (post hoc estimates minus the median value) as a function of the potential covariates, to detect a potential relationship; (2) incorporation of an equation that describes this relationship in the population model and fits the model; and (3) determination of whether the decrease in the objective function (roughly, the weighted sum of the squared residuals) is statistically significant, using the likelihood ratio test, at a 0.01 threshold.14 15 In the current study, 11 covariates were tested: age, duration of diabetes, treatment with insulin, or no insulin treatment, duration of macular edema before the first TA injection, number of grid photocoagulation sessions, panretinal photocoagulation (performed or not performed), stage of diabetic retinopathy (severe, moderate, or mild nonproliferative or inactivated), high blood pressure (present and treated, or none), diastolic and systolic blood pressure measurement, and the Hb1Ac concentration.


   Results
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 Abstract
 Methods
 Results
Discussion
 Conclusion
 References
 
The values of the estimated parameters are shown in Table 4 . None of the potential covariates significantly affected the parameters of the model.


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  		TABLE 4. Results for Modeling of the Changes in CMT

 
Except for F1 and C50, the confidence interval of the estimated parameters was narrow. A model in which C50 or F1 are fixed at 0 and 0.01, respectively, was significantly less adequate than the complete model. Therefore, these parameters are necessary to describe the present data, and the imprecision of their values resulted from the lack of data for the phase of TA elimination from the vitreous body and the lack of TA concentration measurements. Figure 1 illustrates some examples of CMT measurements and the individual curves calculated using individual parameters. The fit is excellent, as shown in Figure 2 . The estimated half-life of TA (mean ± SD) was 15.4 ± 1.9 days (Fig. 3) .



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  		FIGURE 1. Examples of individual central macular thickness (CMT) curves calculated from individual CMT values (circles). (A, B) The measured and estimated CMTs, respectively, after the first injection of TA in the right and left eye of the same patient. (C, D) The measured and estimated CMTs, respectively, after the first and second injection in the same eye of another patient. Curves were calculated using the Bayesian individual estimates of the parameters of the population model for each patient.

 


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  		FIGURE 2. Measured CMT and CMT predicted by the model (straight line), equation y = x: predicted CMT = measured CMT.

 


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  		FIGURE 3. Histogram of the half-life of TA elimination from the vitreous body.

 
From these data, the maximum duration of the effect of TA can be estimated as the time until the concentration of TA reaches C50. If the first phase of elimination is disregarded,

As this maximum duration (mean ± SD) was 140 ± 17 days (Fig. 4) , another dose should be injected before this time to avoid a relapse. The maximum effect of TA (mean ± SD) on the decrease in CMT was 240 ± 75 µm/d (Fig. 5) .



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  		FIGURE 4. Histogram of the duration of the effect of 4 mg TA. The histogram shows that the distribution is non-Gaussian and that although the SDs are large, the duration of the effect ranged from 145 to 150 days in most patients.

 


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  		FIGURE 5. Histogram showing the interindividual variability of the maximum effect of a single injection of 4 mg TA. The histogram shows that the distribution is non-Gaussian and that although the SDs are large, the maximum rate of CMT decrease achievable at high concentrations of TA varied between 210 and 260 µm per day in most patients (this last range must be attributed to the relative homogeneity of the initial CMTs and to the lowest measured CMTs in our study, which are close to normal).

 
As the model allows the estimation of Rinbas (i.e., the normal value for the CMT growth rate), the minimum CMT that can be obtained with 4 mg TA can be estimated using equation 4 , to compare it with the physiologic CMT. The mean ± SD of the minimum CMT was 217 ± 51 µm, which is close to the normal physiologic thickness (170 ± 18 µm, the histogram showed a Gaussian-like symmetric distribution; data not shown).


   Discussion
Top
 Abstract
 Methods
 Results
 Discussion
Conclusion
 References
 
Intravitreal TA treatment was recently proposed for diabetic macular edema, and it has been strikingly effective for reducing macular thickness due to this condition, and for improving visual acuity.4 Intravitreal administration is especially advisable for diabetic patients, because it allows a high intraocular concentration of steroids while avoiding systemic side effects, especially blood glucose perturbation.3 16

Few data on the pharmacokinetics of TA in the eye are currently available.8 18 19 As stated in the introduction, the only publication dealing with the pharmacokinetics of TA in the human eye is the report by Beer et al.,8 who found that after intravitreal injection of 4 mg TA, aqueous humor concentrations followed a two-compartment model, with a mean elimination half-life of 18.6 days (448 ± 136 hours) in nonvitrectomized eyes. Although their study included only five patients, it was performed with rigorous methodology. The interindividual variability of its results suggests that a much larger number of patients should be studied to obtain enough data to calculate parameters reliably. The main obstacle to such a study is the difficulty of obtaining vitreous or aqueous humor samples, which necessitates invasive procedures that seem difficult to perform on a large scale. In the present study, we attempted to implement an alternative approach to this type of basic pharmacokinetic study, while avoiding invasive intraocular procedures.

We used all the data collected during our trials, without exception. We are aware that the collection of our data may seem haphazard because of the different number of CMT measurements per patient and the irregular interval of measurements. However, we do not consider this to be a real methodological flaw, as systematic measurements were performed exactly 4, 12, and 24 weeks after injection, thus allowing the comparisons planned in the protocols.5 The other measurements were performed at irregular intervals, because it was too difficult for patients to come for evaluation at precise dates, considering that they had to make an average of more than 10 visits in 24 weeks (mostly during the first 2 months). However, the measurements do not have to follow the same periodic pattern when the data are analyzed by a population approach. This approach is especially useful when the data are heterogeneous,12 because what is termed the mixed-effect model correctly accounts for the heterogeneity of the measurements, patients, and dosage history. In many respects, this method is akin to meta-analysis. Furthermore, when the measurements are sparse, it is better to collect data at randomized times, because this yields more information about the structure of the model.20 Because the pharmacodynamic part of the TA model was unknown, it was better to collect the data in randomized fashion, as we did in this study. Last, theoretical studies about optimal design in population approaches have shown that the design is more efficient when the number of data points per individual are equal to the number of parameters to be estimated in the structural model.21 This was the case in our study (10.5 points per patient vs. 11 parameters).

The use of pharmacokinetic–pharmacodynamic modeling without pharmacokinetic data may be disquieting. One of the main criticisms of this method is the need to use a pharmacokinetic hypothesis based on the results of another study. We chose to use the results of a study by Beer et al.,8 although our population and theirs are not entirely comparable.

The measured parameter we used was CMT, measured by OCT, which appears to be a very powerful tool, because CMT measurement is obtained by a fast, standard, noninvasive procedure, and allows reproducible sensitive monitoring of macular edema.9 In addition, CMT measurements can be repeated many times in a large number of subjects. In the present study, we used CMT as a pharmacodynamic parameter that replaced the pharmacokinetic parameter of the intravitreal concentration of TA.

The model we developed can be represented by a three-phase curve. In the first phase, a fast decrease of CMT was noted, which in the best cases may decline to normal thickness in a few days. In the second phase, CMT tended to decrease slowly or to remain stable. In the third phase, a relapse occurred, after various intervals. This last parameter was our least precise result, because of the relative lack of CMT measurements for the period between 3 and 6 months after TA treatment.

This model fits the CMT measurements performed with OCT very well, as shown in Figures 1 and 2 . It allowed us to measure the half-life of TA in the vitreous. We found a half-life of 15.4 ± 1.9 days, which is very similar to the one calculated by Beer et al.8 In addition, the maximum duration of the effect of TA that we calculated (140 ± 17 days) was longer than the time for which the TA concentration was measurable in Beer’s study (93 ± 28 days in the absence of vitrectomy). In our opinion, this discrepancy is due to the interval between the elimination of TA and end of its effect. This interval is the result of a remnant effect that is usual for corticosteroid agents. Therefore, the measurement of CMT, which reflects both the concentration and activity of TA, may be even more useful in the clinical field than measuring the TA concentration.

The pharmacokinetic–pharmacodynamic population approach also allows assessment of the influence of various covariates, which may partly explain the variability of the present results. We found in our study that none of the covariates tested affected the model, possibly because of the relatively small number of eyes in the series, the small range of variation of certain covariates, or the low frequency of some categorical events. We postulate that this absence of covariate effects was due to the amount of TA injected, which may have allowed a high concentration of TA to be maintained in the vitreous body and in the biophase (i.e., in the macular retina), thus producing an effect close to the maximum effect. This concentration may have neutralized the possible effects of all the conventional or other parameters that may modify CMT. This hypothesis is supported by the minimum CMT we obtained (217 ± 51 µm) which is close to the normal physiologic thickness and by our calculated C50 for TA (0.011 ± 0.030 mg/L), which is low compared with the TA concentrations measured by Beer et al.8 (for example, their measured aqueous concentration at day 31 ranged from 0.088 to 0.79 mg/L).

Clinicians should become acquainted with the three-phase response to TA, because of its consequences for the timing of the evaluation of the effectiveness of TA treatment. The rapidity of action of TA, which to our knowledge has never been described in detail in the literature, shows that the reactivity of the macular retina to a pharmacologic agent remains high, despite the long duration of macular edema. This rapidity and reactivity may have a profound effect on our strategy for the treatment of diffuse macular edema, by helping us to optimize the timing of TA treatment and to determine the best time for TA reinjection.


   Conclusion
Top
 Abstract
 Methods
 Results
 Discussion
 Conclusion
References
 
Population pharmacokinetic–pharmacodynamic modeling is not commonly used in clinical ophthalmology. The recent development of new pharmacologic treatments for retinal diseases will require investigations to determine reliable pharmacologic parameters and define the modalities of administration of these treatments. Intravitreal TA was recently proposed for the treatment of diabetic diffuse macular edema. Pharmacokinetic–pharmacodynamic modeling, using CMT as the pharmacodynamic measured parameter, constitutes an alternative approach to conventional pharmacokinetic studies. In the current study, this approach worked excellently, and our results are consistent with those of the only published study of the intraocular pharmacokinetics of TA in the human eye. We believe that this type of investigation is of interest, as it avoids, as far as possible, the need for intraocular measurements. Note, however, that the present results cannot be extrapolated to other retinal diseases or even to macular edema of etiology other than diabetes.


   Footnotes
 
Submitted for publication October 6, 2003; revised February 24 and June 10, 2004; accepted June 17, 2004.

Disclosure: F. Audren, None; M. Tod, None; P. Massin, None; R. Benosman, None; B. Haouchine, None; A. Erginay, None; C. Caulin, None; A. Gaudric, None; J.-F. Bergmann, None

The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

Corresponding author: François Audren, Department of Ophthalmology, Hôpital Lariboisière, 2 Rue Ambroise Paré, 75475 Paris Cedex 10, France; francoisaudren{at}hotmail.com.


   References
Top
 Abstract
 Methods
 Results
 Discussion
 Conclusion
 References
 

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