Pharmacokinetics and Pharmacodynamics of Systemically Administered Glucocorticoids

Abstract

Glucocorticoids have pleiotropic effects that are used to treat diverse diseases such as asthma, rheumatoid arthritis, systemic lupus erythematosus and acute kidney transplant rejection. The most commonly used systemic glucocorticoids are hydrocortisone, prednisolone, methylprednisolone and dexamethasone. These glucocorticoids have good oral bioavailability and are eliminated mainly by hepatic metabolism and renal excretion of the metabolites. Plasma concentrations follow a biexponential pattern. Two-compartment models are used after intravenous administration, but one-compartment models are sufficient after oral administration.

The effects of glucocorticoids are mediated by genomic and possibly nongenomic mechanisms. Genomic mechanisms include activation of the cytosolic glucocorticoid receptor that leads to activation or repression of protein synthesis, including cytokines, chemokines, inflammatory enzymes and adhesion molecules. Thus, inflammation and immune response mechanisms may be modified. Nongenomic mechanisms might play an additional role in glucocorticoid pulse therapy.

Clinical efficacy depends on glucocorticoid pharmacokinetics and pharmacodynamics. Pharmacokinetic parameters such as the elimination half-life, and pharmacodynamic parameters such as the concentration producing the half-maximal effect, determine the duration and intensity of glucocorticoid effects. The special contribution of either of these can be distinguished with pharmacokinetic/pharmacodynamic analysis. We performed simulations with a pharmacokinetic/pharmacodynamic model using T helper cell counts and endogenous Cortisol as biomarkers for the effects of methylprednisolone. These simulations suggest that the clinical efficacy of low-dose glucocorticoid regimens might be increased with twice-daily glucocorticoid administration.

Appendix

Statistical Data Synthesis

Published pharmacokinetic parameters are heterogeneous and their values vary between studies. Therefore, a statistical data synthesis is necessary to combine such values and estimate the population mean.[322] In the current paper we summarised the published values from different publications as the pooled mean $\overline{\overline x}$ where ${\bar x}_1, {\bar x}_2,\;...\;{\bar x}_{k}$ are the published mean values and the total number of subjects n was calculated as n = n₁ + n₂ + … + n_k (equation 3).

$$\overline{\overline x} = {{{n_1} \bullet {{\overline x}_1} + {n_2} \bullet {{\overline x}_2} + ... + {n_k} \bullet {{\overline x}_k}} \over n}$$

((Eq. 3))

The pooled standard deviation was calculated using the published standard deviations s₁, s₂, … s_k (equation 4).

$$\overline s = {\left[ {{{s_1^2({n_1} - 1) + s_2^2({n_2} - 1) + ... + s_k^2({n_k} - 1)} \over {n - k}}} \right]^{1/2}}$$

((Eq. 4))

Model for Simulation

We used an indirect response model for simulation of twice-daily dose fractions of methylprednisolone (figure 3 and figure 4). The pharmacokinetic model was a one-compartment model with a first-order formation rate and a first-order elimination rate where MPs is methylprednisolone succinate, MP is methylprednisolone, k _f is the formation rate constant, and k _e is the elimination rate constant (equation 5 and equation 6).

$${{dMPs} \over {dt}} = - {k_f} \bullet MPs$$

((Eq. 5))

$${{dMP} \over {dt}} = {k_f} \bullet MPs - {k_e} \bullet MP$$

((Eq. 6))

The pharmacodynamic model for T helper cell suppression was a precursor-dependent indirect response model as developed by Sharma et al.[273] and Booker et al.[30] ThE are extravascular T helper cells and Th are blood T helper cells. The rate constant k _in describes formation of new T helper cells, the time-varying rate constant k _p(t) describes the migration of T helper cells from the extravascular to the blood compartment, the rate constant k _out describes the removal of T helper cells, and I(t) describes the inhibitory effect of glucocorticoids on cell migration (equation 7 and equation 8).

$${{dThE} \over {dt}} = {k_{in}} - {k_p}(t) \bullet I(t) \bullet ThE$$

((Eq. 7))

$${{dTh} \over {dt}} = {k_p}(t) \bullet I(t) \bullet ThE - {k_{out}} \bullet Th$$

((Eq. 8))

The inhibitory function I(t) for the effect of methylprednisolone was an E _max model where parameter E _max is the maximum achievable effect and parameter CE₅₀ is the concentration producing the half-maximal effect (equation 9).

$$I(t) = 1 - {{{E_{\max}} \bullet MP(t)} \over {C{E_{50}} + MP(t)}}$$

((Eq. 9))

For the migration of T helper cells from the extravascular to the blood compartment a periodic function was applied where R _m is the mean input rate, R _b is the amplitude and t _z is the peak time in relation to time zero (equation 10).

$${k_p}(t) = {R_m} + {R_b} \bullet \cos \left[ {(t - {t_z}) \bullet {{2\pi} \over {24}}} \right]$$

((Eq. 10))

The pharmacodynamic model for cortisol suppression used the same inhibitory function I(t). The time-varying secretion of cortisol was described by k _in(t) and the elimination of cortisol by the rate constant k _out (equation 11).

$${{dCort} \over {dt}} = {k_{in}}(t) \bullet I(t) - {k_{out}} \bullet Cort$$

((Eq. 11))

The input function k _in(t) for secretion of cortisol was a dual cosine model that also allows for asymmetric inputs where T _max and T _min are the timepoints where the secretion is maximal and minimal, respectively (equations 12, 13 and 14).

$$\matrix{{{\rm{t}} = 0\;{\rm{to}}\;{{\rm{T}}_{\min}}} \hfill \cr {{k_{in}}(t) = {R_m} + {R_b} \bullet \cos \left[ {{{2\pi \bullet (t + 24 - {T_{\max}})} \over {2 \bullet ({T_{\min}} - {T_{\max}} + 24)}}} \right]} \hfill \cr}$$

((Eq. 12))

$$\matrix{{{\rm{t}} = {{\rm{T}}_{\min}}\;{\rm{to}}\;{{\rm{T}}_{\max}}} \hfill \cr {{k_{in}}(t) = {R_m} + {R_b} \bullet \cos \left[ {{{2\pi \bullet (t - 2 \bullet {T_{\min}} - {T_{\max}})} \over {2 \bullet ({T_{\max}} - {T_{\min}})}}} \right]} \hfill \cr}$$

((Eq. 13))

$$\matrix{{{\rm{t}} = {{\rm{T}}_{\max}}{\rm{to}}24{\rm{hours}}} \hfill \cr {{k_{in}}(t) = {R_m} + {R_b} \bullet \cos \left[ {{{2\pi \bullet (t - {T_{\max}})} \over {2 \bullet ({T_{\min}} - {T_{\max}} + 24)}}} \right]} \hfill \cr}$$

((Eq. 14))

Parameter values used for the simulation were: pharmacokinetic parameters: k_f = 5.73 h^–1, k_e = 0.31 h^–1, Vd = 80.96L; pharmacodynamic parameters for T helper cell suppression: CE₅₀ = 9.2 µg · L^–1, E_max = 1; system parameters of T helper cell variation: k_in = 383 cells · mm^–3 · h^–1, k_out = 0.335 h^–1, R_m = 0.088 h^–1, R_b = 0.022 h^–1, t_z = 13.2 (24-hour clock); pharmacodynamic parameters for cortisol suppression: CE₅₀ = 0.446 µg · L^–1, E_max = 1; system parameters of cortisol variation: k_out = 0.338 h^–1, t_min = 12.2 hours (24-hour clock), t_max = 21.4 hours (24-hour clock), R_m = 23.5 µg · L^–1 · h^–1, R_b = 22.5 µg · L^–1 · h^–1.