An equilibrium model of TMDD is developed that recapitulates the essential features of the full general model and eliminates the need for estimating drug-binding microconstants that are often difficult or impossible to identify from typical in vivo pharmacokinetic data.

A new class of basic indirect pharmacodynamic models for agents that alter the loss of natural cells based on a lifespan concept are presented. The lifespan indirect response (LIDR) models assume that cells (R) are produced at a constant rate (k(in)), survive during a certain duration T(R), and finally are lost. The rate of cell loss is equal to the production rate but is delayed by T(R). A therapeutic agent can increase or decrease the baseline cell lifespan to a new cell lifespan, T(D), by temporally changing the proportion of cells belonging to the two modes of the lifespan distribution. Therefore, the change of lifespan at time t is described according to the Hill function, H(C(t)), with capacity (E(max)) and sensitivity (EC(50)), and the pharmacokinetic function C(t). A one-compartment cell model was examined through simulations to describe the role of pharmacokinetics, pharmacodynamics and cell properties for the cases where the drug increases (T(D) > T(R)) or decreases (T(D) < T(R)) the cell lifespan. The area under the effect curve (AUCE) and explicit solutions of LIDR models for large doses were derived. The applicability of the model was further illustrated using the effects of recombinant human erythropoietin (rHuEPO) on reticulocytes. The cases of both stimulation of the proliferation of bone marrow progenitor cells and the increase of reticulocyte lifespans were used to describe mean data from healthy subjects who received single subcutaneous doses of rHuEPO ranging from 20 to 160 kIU. rHuEPO is about 4.5-fold less potent in increasing reticulocyte survival than in stimulating the precursor production. A maximum increase of 4.1 days in the mean reticulocyte lifespan was estimated and the effect duration on the lifespan distribution was dose dependent. LIDR models share similar properties with basic indirect response models describing drug stimulation or inhibition of the response loss rate with the exception of the presence of a lag time and a dose independent peak time. The current concept can be applied to describe the pharmacodynamic effects of agents affecting survival of hematopoietic cell populations yielding realistic physiological parameters.

Target-mediated drug disposition (TMDD) models have been applied to describe the pharmacokinetics of drugs whose distribution and/or clearance are affected by its target due to high binding affinity and limited capacity. The Michaelis–Menten (M–M) model has also been frequently used to describe the pharmacokinetics of such drugs. The purpose of this study is to investigate conditions for equivalence between M–M and TMDD pharmacokinetic models and provide guidelines for selection between these two approaches. Theoretical derivations were used to determine conditions under which M–M and TMDD pharmacokinetic models are equivalent. Computer simulations and model fitting were conducted to demonstrate these conditions. Typical M–M and TMDD profiles were simulated based on literature data for an anti-CD4 monoclonal antibody (TRX1) and phenytoin administered intravenously. Both models were fitted to data and goodness of fit criteria were evaluated for model selection. A case study of recombinant human erythropoietin was conducted to qualify results. A rapid binding TMDD model is equivalent to the M–M model if total target density Rtot is constant, and RtotKD/(KD + C)2 ≪ 1 where KD represents the dissociation constant and C is the free drug concentration. Under these conditions, M–M parameters are defined as: Vmax = kintRtotVc and Km = KD where kint represents an internalization rate constant, and Vc is the volume of the central compartment. Rtot is constant if and only if kint = kdeg, where kdeg is a degradation rate constant. If the TMDD model predictions are not sensitive to kint or kdeg parameters, the condition of RtotKD/(KD + C)2 ≪ 1 alone can preserve the equivalence between rapid binding TMDD and M–M models. The model selection process for drugs that exhibit TMDD should involve a full mechanistic model as well as reduced models. The best model should adequately describe the data and have a minimal set of parameters estimated with acceptable precision.

The pharmacokinetics (PK) and pharmacodynamics (PD) of recombinant human erythropoietin (rHuEPO) were studied in rats after single i.v. and s.c. administration at three dose levels (450, 1350, and 4050 IU/kg). The plasma concentrations of rHuEPO and its erythropoietic effects including reticulocyte (RET), red blood cell (RBC), and hemoglobin (Hb) levels were determined. A two-compartment model with dual input rate and nonlinear disposition was used to characterize the PK of rHuEPO. The catenary indirect response model with several compartments reflecting the bone marrow and circulating erythropoietic cells was applied. The s.c. doses exhibited slow absorption (T max ϭ 12 h) and incomplete bioavailability (F ϭ 0.59). In placebo groups, RBC and Hb values gradually increased over time with growth of the rats, and the changes in the baselines monitored from 8 to 32 weeks of age were described by a nonlinear growth function. All doses resulted in dose-dependent increases in RET counts followed by an immediate decline below the baseline at around 6 days and returned to the predose level in 21-24 days after dosing. A subsequent steady increase of RBC and Hb levels followed and reached peaks at 6 days. A tolerance phenomenon observed at all dose levels was modeled by a negative feedback inhibition with the relative change in Hb level. The PK/PD model well described the erythropoietic effects of rHuEPO as well as tolerance, thereby yielding important PD parameters (S max ϭ 1.87 and SC 50 ϭ 65.37 mIU/ml) and mean lifespans of major erythropoietic cell populations in rats.Erythropoietin (EPO) is a glycoprotein hormone (30.5 kDa) produced in adult kidneys, and it is the major regulator of red cell production. Tissue hypoxia is the primary stimulus of the production of endogenous EPO. EPO binds to its receptors on the surface of erythroid progenitors in bone marrow, leading to their survival, proliferation, and differentiation, which in turn produces an increase in RBC and hemoglobin (Hb) concentrations (Fisher, 2003). Conversely, an excessive increase in RBC mass suppresses erythropoiesis to prevent blood from becoming more viscous, leading to the possibility of thrombosis and stroke. One study showed that transfusion polycythemia depressed bone marrow activity and reduced production of RBC in normal subjects (Birkhill et al., 1951). The negative feedback control in erythropoiesis has also been observed in humans after the subsequent rises of RBC and Hb following rHuEPO administration (Ramakrishnan et al., 2004). The exact mechanism and the primary regulators responsible for the counter-regulation are, however, not clearly elucidated.Comprehensive PK/PD models have been developed to quantitatively account for the pharmacokinetics and erythropoietic effects of rHuEPO (Ramakrishnan et al., 2003(Ramakrishnan et al., , 2004. The models depict nonlinear disposition kinetics and absorption kinetics mainly characterized by prolonged absorption and variable, incomplete bioavailability upon s.c. administration. Because eryth...

Hepcidin is a key regulator responsible for systemic iron homeostasis. A semi-mechanistic PK model for hepcidin and a fully human anti-hepcidin monoclonal antibody (Ab 12B9m) was developed to describe their total (free + bound) serum concentration-time data after single and multiple weekly intravenous or subcutaneous doses of Ab 12B9m. The model was based on target mediated drug disposition and the IgG-FcRn interaction concepts published previously. Both total Ab 12B9m and total hepcidin exhibited nonlinear kinetics due to saturable Fc-FcRn interaction. Ab 12B9m showed a limited volume of distribution and negligible linear elimination from serum. The nonlinear elimination of Ab 12B9m was attributed to the endosomal degradation of Ab 12B9m that was not bound to the FcRn receptor. The terminal half-life, assumed to be the same for free and total serum Ab 12B9m, was estimated to be 16.5 days. The subcutaneous absorption of Ab 12B9m was described with a first-order absorption rate constant k(a) of 0.0278 h⁻¹, with 86% bioavailability. The model suggested a rapid hepcidin clearance of approximately 800 mL h⁻¹ kg⁻¹. Only the highest-tested Ab 12B9m dose of 300 mg kg⁻¹ week⁻¹ was able to maintain free hepcidin level below the baseline during the dosing intervals. Free Ab 12B9m and free hepcidin concentrations were simulated, and their PK profiles were nonlinear as affected by their binding to each other. Additionally, the total amount of FcRn receptor involved in Ab 12B9m recycling at a given time was calculated empirically, and the temporal changes in the free FcRn levels upon Ab 12B9m administration were inferred.

Abstract. The objective of this study was to characterize the pharmacokinetics and pharmacodynamics (PK-PD) of romiplostim after single-dose administration in healthy subjects. The mean serum romiplostim concentrations (PK data) and mean platelet counts (PD data) collected from 32 subjects receiving a single intravenous (0.3, 1 and 10 μg/kg) or subcutaneous (0.1, 0.3, 1, and 2 μg/kg) dose were fitted simultaneously to a mechanistic PK-PD model based on pharmacodynamics-mediated drug disposition (PDMDD) and a precursor pool lifespan concept. The two-compartment PK model incorporated receptor-mediated endocytosis and linear mechanisms as parallel elimination pathways. The maximal concentration of receptors (assumed to be proportional to the platelet count), the equilibrium dissociation constant, and the first-order internalization rate constant for endocytosis of the drug-receptor complex were 0.022 fg/platelet, 0.131 ng/mL, and 0.173 h −1 , respectively. Romiplostim concentration stimulates the production of platelet precursors via the Hill function, where the SC 50 was 0.052 ng/mL and S max was 11.2. The estimated precursor cell and platelet lifespans were 5.9 and 10.5 days, respectively. Model-based simulations revealed that the romiplostim exposure and the platelet response are both dependent on the dose administered and the baseline platelet counts. Also, weekly dosing produced a sustained PD response while dosing intervals ≥2 weeks resulted in fluctuating platelet counts. Thus, the mechanistic PK-PD model was suitable for describing the romiplostim PK-PD interplay (PDMDD), the dose-dependent platelet stimulation, and the lifespans of thrombopoietic cell populations.

Filgrastim is a recombinant human granulocyte colony stimulating factor (G-CSF) that stimulates production of neutrophils. The objective of this analysis was to develop a pharmacokinetic (PK) and pharmacodynamic (PD) model to account for an increase in G-CSF clearance on multiple dosing because of an increase of the G-CSF receptor-mediated endocytosis. Data from 4 randomized studies involving healthy volunteers were used for analysis. Subjects received filgrastim (Neupogen) via subcutaneous (SC) and intravenous (IV) routes. Filgrastim was administered SC daily for 1 week at 2.5, 5, and 10 µg/kg doses and as single IV infusions (5 µg/kg over 0.5 hours) and SC (1 µg/kg) doses. PK data comprised serum concentration-time measurements and the blood absolute neutrophil count (ANC) was used for PD evaluations. Population nonlinear mixed-effect modeling was done using NONMEM VI (Version 6.1.0, Icon Development Solutions, Ellicott City, Maryland). The model depicted the decaying trend in C(max) values with repeated doses and an increase in ANC(max) values consistently with an increase in the G-CSF receptor pool. Simulated time courses of the total clearance exhibited an increasing pattern. The increase in filgrastim clearance on multiple dosing was attributed to the increased neutrophil count in the bone marrow and blood paralleled by an increase in the total G-CSF receptor density.

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