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.

^{ 1 }choroidal neovascularization combined with age-related macular degeneration,

^{ 2 }and macular edema, which may be associated with ocular disorders such as uveitis

^{ 3 }or with vascular diseases. Diabetic macular edema seems to be one of the most promising indications for TA

^{ 4 }

^{ 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 }

^{ 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.

^{ 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.

^{ 5 }will not be given in this report, as these parameters were not the focus of the present investigation.

^{ 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 }

^{ 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 (α) 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 (β) corresponds to the rate of TA dissolution in the vitreous body.

*D*is the dose of TA,

*V*is the volume of the vitreous body (fixed at 4 mL or 0.004 L), and

*F*

_{1}and

*F*

_{2}are parameters without dimensions. At time 0, the TA concentration is expressed as

^{ 8 }

*C*(0) is equal to 10 mg/L, when the dose of TA is 4 mg. Therefore,

*F*

_{1}.

*R*(CMT) may change with time. This change is described by an indirect pharmacodynamic model

^{ 11 }in which we assume that the change is rendered by

*R*

_{in}(

*t*) is the rate of production, and

*K*

_{out}·

*R*(

*t*) is the rate of elimination. In a normal subject, the CMT does not change, so that

*dR*(

*t*)/

*dt*= 0. Consequently,

*R*is interpreted as resulting from a value

*R*

_{in0 }, greater than the normal

*R*

_{inbas }value. At the beginning of treatment (time 0), R

_{in}is equal to

*R*

_{in0 }(>

*R*

_{inbas }).

*E*

_{max}= (

*R*

_{in0 }−

*R*

_{inbas }) and is the maximum effect of TA, obtained with an infinite TA concentration.

*C*

_{50}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

*R*

_{in0 }is equal to the

*R*measured at the time of injection.

^{ 12 }to evaluate typical parameters and interindividual and residual variability. In this type of model, two levels of variability can be distinguished.

*j*, characterized by a particular value

*P*

_{j}for the parameters α, β,

*F*

_{1},

*R*

_{inbas },

*E*

_{max},

*C*

_{50},

*s*, and

*K*

_{out}, the difference between the observed value of the response (

*R*

_{obs}) and the predicted value of

*R*, according to the following

^{2}(σ

^{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.

*P̅*is the median of the parameter in the population, and η is a random, normally distributed variable with a zero mean and variance ω. The parameters to be estimated are the medians

*P̅*and the variances ω and σ

^{2}. They are estimated by nonlinear mixed-effect modeling (NONMEM, ver. 5.0; GloboMax, Hanover, MD).

^{ 13 }The individual parameters

*P*

_{j}(post hoc estimates) are then estimated by the Bayesian method. For the sake of simplicity, the respective variabilities of the random effects ε and η 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.

*F*

_{1}and

*C*

_{50}, the confidence interval of the estimated parameters was narrow. A model in which

*C*

_{50}or

*F*

_{1}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) .

*R*

_{inbas }(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).

^{ 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 }

^{ 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.

^{ 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).

^{ 8 }although our population and theirs are not entirely comparable.

^{ 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.

^{ 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.

*C*

_{50}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).

Variable | |
---|---|

Age (y)^{*} | |

Mean± SD | 61.5 ± 11.2 |

Range | 37–79 |

Duration of diabetes (y)^{*} | |

Mean± SD | 14.5 ± 9.1 |

Range | 2–31 |

Treatment for diabetes (n, %)^{*} | |

Insulin | 15 (45%) |

No insulin | 18 (55%) |

Macular edema duration (mo)^{, †} | |

Mean± SD | 24.7 ± 15.4 |

Range | 12–60 |

Number of grid sessions^{, †} | |

Mean± SD | 1.9 ± 1.0 |

Range | 1–4 |

Panretinal photocoagulation (n, %)^{, †} | |

Performed | 27 (73%) |

Not Performed | 10 (27%) |

Stage of diabetic retinopathy (n, %)^{, †} | |

Severe NPDR | 10 (27%) |

Moderate NPDR | 7 (19%) |

Mild NPDR | 3 (8%) |

DR inactivated by PRP | 17 (46%) |

Lens (n, %)^{, †} | |

Phakia | 30 (81%) |

Pseudophakia | 7 (19%) |

High blood pressure (n, %)^{*} | |

Present and treated | 15 (45%) |

None | 18 (55%) |

Systolic blood pressure (mmHg)^{, ‡} | |

Mean± SD | 140.5 ± 14.9 |

Range | 111–170 |

Diastolic blood pressure (mmHg)^{, ‡} | |

Mean± SD | 76.5 ± 9.6 |

Range | 48–90 |

HbA1c (%)^{, ‡} | |

Mean± SD | 7.3 ± 1.1 |

Range | 4.5–9.6 |

Variable | |
---|---|

Total follow-up duration after the first injection, until the second injection, if any (d) | |

Mean ± SD | 171.9 ± 77.5 |

Range | 8–363 |

Total follow-up duration after the second injection (d) | |

Mean± SD | 100.4 ± 52.7 |

Range | 7–160 |

Total follow-up duration after the first injection, until after the second injection, if any (d) | |

Mean± SD | 209.9 ± 116.4 |

Range | 8–404 |

Interval between the first injection and the second, if any (d) | |

Mean± SD | 220.8 ± 53.7 |

Range | 120–363 |

CMT measurements after an injection, before reinjection, if any (n) | |

Mean± SD | 10.4 ± 4.0 |

Range | 2–17 |

CMT measurements after the first injection, before the second injection, if any (n) | |

Mean± SD | 11.5 ± 3.7 |

Range | 2–17 |

CMT measurements after the second injection (n) | |

Mean± SD | 7.6 ± 3.3 |

Range | 2–13 |

Variable | |
---|---|

First injection | |

CMT before injection (n = 37) | |

Mean± SD | 531.7 ± 147.0 |

Range | 319–958 |

CMT 4 weeks after injection (n = 36) | |

Mean± SD | 233.9 ± 55.5 |

Range | 157–376 |

CMT 12 weeks after injection (n = 31) | |

Mean± SD | 225.1 ± 81.3 |

Range | 137–486 |

CMT 24 weeks after injection (n = 25) | |

Mean± SD | 369.4 ± 143.1 |

Range | 162–634 |

Second injection | |

CMT before injection (n = 14) | |

Mean± SD | 524.6 ± 116.8 |

Range | 323–756 |

CMT 4 weeks after injection (n = 12) | |

Mean± SD | 217.3 ± 62.2 |

Range | 160–387 |

CMT 12 weeks after injection (n = 9) | |

Mean± SD | 204.7 ± 60.4 |

Range | 147–345 |

CMT 24 weeks after injection (n = 1) | 579 |

Median | Variance (η) | CV (%) | |||||
---|---|---|---|---|---|---|---|

Value | SE | Value | SE | ||||

α (d^{−1}) | 0.097 | 0.019 | 0.693 | 0.322 | 100 | ||

β (d^{−1}) | 0.043 | 0.017 | 0.058 | 0.044 | 24 | ||

F _{1} | 0.0036 | 0.0040 | 0 (fixed) | — | — | ||

K _{out} (d^{−1}) | 0.432 | 0.020 | 0.055 | 0.026 | 24 | ||

C_{50} (mg · L^{−1}) | 0.011 | 0.030 | 0 (fixed) | — | — | ||

R _{inbas } (μm · d^{−1}) | 109 | 7.8 | 0.048 | 0.031 | 22 | ||

E _{max} (μm · d^{−1}) | 249 | 50 | 0.616 | 0.374 | 92 | ||

s | 0.94 | 0.36 | 0.490 | 0.210 | 80 | ||

σ | 0.0635 | 0.0047 | 6.3 |

*F*

_{1}, parameter without dimensions (equation 1) ,

*K*

_{out},

*K*

_{out}· R(t), rate of elimination of the effect (equation 3 , R(t), response); C

_{50}, TA concentration producing a half-maximum effect;

*R*

_{inbas }, normal rate of production of the effect; E

_{max}, maximum effect of TA;

*s*, coefficient of sigmoidicity (equation 5) ; σ, standard deviation of the variable ε (equation 6) .

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**

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