A geometrical approach to the PKPD modelling of inhaled bronchodilators

Modeling

Modeling is coming to the fore as it is now widely accepted and indeed expected during drug discovery and development. Modeling integrates knowledge, increases understanding and provides the ability to predict an outcome either before it occurs or when it is not possible to measure. This makes modeling an attractive option for inhaled drugs as it is not possible to routinely measure what is occurring to the drug (pharmacokinetics) and what effect the drug is having (pharmacodynamics) at local microscopic sites of such a diverse and complex organ as the lung. Many pieces of information (data and knowledge) exist like the pieces of a jigsaw puzzle and modeling brings the pieces together in a scientific and mechanistically coherent manner to increase understanding of both the efficacy and safety of inhaled drugs.

The Pharmacokinetics of Inhaled Drugs

The pharmacokinetic (PK) profile of a drug after inhalation may differ quite markedly from that seen after dosing by other routes of administration. Drugs may be administered to the lung to elicit a local action or as a portal for systemic delivery of the drug to its site of action elsewhere in the body. Some knowledge of PK is important for both locally- and systemically-acting drugs. For a systemically-acting drug, the plasma concentration-time profile shares some similarities with drug given by the oral or intravenous routes, since the plasma concentrations (after the distribution phase) will be in equilibrium with concentrations at the site of action. For a locally-acting drug, however, the plasma concentrations reflect its fate after it has been absorbed and removed from the airways, and not what is available to its site of action in the lung. Consequently, those typical PK parameters which are determined from plasma concentration measurements, e.g., area under the curve (AUC), Cmax, tmax and post-peak t1/2 may provide information on the deposition and absorption of drugs from the lung; however, the information from these parameters becomes more complicated to decipher for those drugs which are locally-acting in the lung. Additionally, the plasma concentration profile for both locally- and systemically-acting drugs will not only reflect drug absorbed from the lung but also that absorbed from the gastrointestinal (GI) tract from the portion of the dose which is swallowed. This absorption from the GI tract adds a further complication to the interpretation of plasma concentrations, particularly for locally-acting drugs. The influence of physiological and pathological factors needs to be considered in the absorption of some inhaled drugs. The absorption of some hydrophilic drugs is influenced by the inspiratory maneuver used during initial inhalation of the drug, and at later times after deposition. Similarly, the effects of smoking have been shown to increase lung permeability and increase the absorption of certain hydrophilic drugs. The effects of different disease states of the lung have less defined influences on absorption into the systemic circulation.

Validation of a simplified-geometry model of inhaled formoterol pharmacodynamics in asthmatic patients

PharmacoKinetics (PK) and PharmacoDynamics (PD) mathematical models of inhaled bronchodilators represent useful tools for understanding the mechanisms of drug action and for the individuation of therapy regimens. A PK/PD model for inhaled bronchoactive compounds was previously proposed, incorporating a simplified-geometry approach: the key feature of that model is a mixed compartmental and spatially distributed representation of the kinetics, with the direct computation of representative flow rates from Ohm's law and bronchial diameter profiles. The aim of the present work is the enrichment and validation of this simplified geometry modeling approach against clinical efficacy data. The improved model is used to compute airflow response to treatment for each single virtual patient from a simulated population and it is found to produce very good fits to observed FEV₁ profiles. The model provides a faithful quantitative description of the increasing degree of improvement with respect to basal conditions with continuing administration and with increasing drug dosages, as clinically expected.

Exposure-Response and Clinical Outcome Modeling of Inhaled Budesonide/Formoterol Combination in Asthma Patients

Exposure-response and clinical outcome (CO) model for inhaled budesonide/formoterol was developed to quantify the relationship among pharmacokinetics (PK), pharmacodynamics (PD) and CO of the drugs and evaluate the covariate effect on model parameters. Sputum eosinophils cationic proteins (ECP) and forced expiratory volume (FEV1) were selected as PD markers and asthma control score was used as a clinical outcome. One- and two-compartment models were used to describe the PK of budesonide and formoterol, respectively. The indirect response model (IDR) was used to describe the PD effect for ECP and FEV1. In addition, the symptomatic effect on the disease progression model for CO was connected with IDR on each PD response. The slope for the effect of ECP and FEV1 to disease progression were estimated as 0.00008 and 0.644, respectively. Total five covariates (ex. ADRB2 genotype etc.) were searched using a stepwise covariate modeling method, however, there was no significant covariate effect. The results from the simulation study were showed that a 1 puff b.i.d. had a comparable effect of asthma control with a 2 puff b.i.d. As a result, the 1 puff b.i.d. of combination drug could be suggested as a standardized dose to minimize the side effects and obtain desired control of disease compared to the 2 puff b.i.d.

Translational model to predict pulmonary pharmacokinetics and efficacy in man for inhaled bronchodilators

Translational pharmacokinetic (PK) models are needed to describe and predict drug concentration‐time profiles in lung tissue at the site of action to enable animal‐to‐man translation and prediction of efficacy in humans for inhaled medicines. Current pulmonary PK models are generally descriptive rather than predictive, drug/compound specific, and fail to show successful cross‐species translation. The objective of this work was to develop a robust compartmental modeling approach that captures key features of lung and systemic PK after pulmonary administration of a set of 12 soluble drugs containing single basic, dibasic, or cationic functional groups. The model is shown to allow translation between animal species and predicts drug concentrations in human lungs that correlate with the forced expiratory volume for different classes of bronchodilators. Thus, the pulmonary modeling approach has potential to be a key component in the prediction of human PK, efficacy, and safety for future inhaled medicines.

Pharmacokinetics and Bioavailability of Inhaled Esketamine in Healthy Volunteers

BACKGROUND

Esketamine is traditionally administered via intravenous or intramuscular routes. In this study we developed a pharmacokinetic model of inhalation of nebulized esketamine with special emphasis on pulmonary absorption and bioavailability.

METHODS

Three increasing doses of inhaled esketamine (dose escalation from 25 to 100 mg) were applied followed by a single intravenous dose (20 mg) in 19 healthy volunteers using a nebulizer system and arterial concentrations of esketamine and esnorketamine were obtained. A multicompartmental pharmacokinetic model was developed using population nonlinear mixed-effects analyses.

RESULTS

The pharmacokinetic model consisted of three esketamine, two esnorketamine disposition and three metabolism compartments. The inhalation data were best described by adding two absorption pathways, an immediate and a slower pathway, with rate constant 0.05 ± 0.01 min (median ± SE of the estimate). The amount of esketamine inhaled was reduced due to dose-independent and dose-dependent reduced bioavailability. The former was 70% ± 5%, and the latter was described by a sigmoid EMAX model characterized by the plasma concentration at which absorption was impaired by 50% (406 ± 46 ng/ml). Over the concentration range tested, up to 50% of inhaled esketamine is lost due to the reduced dose-independent and dose-dependent bioavailability.

CONCLUSIONS

We successfully modeled the inhalation of nebulized esketamine in healthy volunteers. Nebulized esketamine is inhaled with a substantial reduction in bioavailability. Although the reduction in dose-independent bioavailability is best explained by retention of drug and particle exhalation, the reduction in dose-dependent bioavailability is probably due to sedation-related loss of drug into the air.

Pharmacometric Models for Characterizing the Pharmacokinetics of Orally Inhaled Drugs

During the last decades, the importance of modeling and simulation in clinical drug development, with the goal to qualitatively and quantitatively assess and understand mechanisms of pharmacokinetic processes, has strongly increased. However, this increase could not equally be observed for orally inhaled drugs. The objectives of this review are to understand the reasons for this gap and to demonstrate the opportunities that mathematical modeling of pharmacokinetics of orally inhaled drugs offers. To achieve these objectives, this review (i) discusses pulmonary physiological processes and their impact on the pharmacokinetics after drug inhalation, (ii) provides a comprehensive overview of published pharmacokinetic models, (iii) categorizes these models into physiologically based pharmacokinetic (PBPK) and (clinical data-derived) empirical models, (iv) explores both their (mechanistic) plausibility, and (v) addresses critical aspects of different pharmacometric approaches pertinent for drug inhalation. In summary, pulmonary deposition, dissolution, and absorption are highly complex processes and may represent the major challenge for modeling and simulation of PK after oral drug inhalation. Challenges in relating systemic pharmacokinetics with pulmonary efficacy may be another factor contributing to the limited number of existing pharmacokinetic models for orally inhaled drugs. Investigations comprising in vitro experiments, clinical studies, and more sophisticated mathematical approaches are considered to be necessary for elucidating these highly complex pulmonary processes. With this additional knowledge, the PBPK approach might gain additional attractiveness. Currently, (semi-)mechanistic modeling offers an alternative to generate and investigate hypotheses and to more mechanistically understand the pulmonary and systemic pharmacokinetics after oral drug inhalation including the impact of pulmonary diseases.

Determination of the pharmacokinetics of glycopyrronium in the lung using a population pharmacokinetic modelling approach

AIMS

Glycopyrronium bromide (NVA237) is a once-daily long-acting muscarinic antagonist recently approved for the treatment of chronic obstructive pulmonary disease. In this study, we used population pharmacokinetic (PK) modelling to provide insights into the impact of the lung PK of glycopyrronium on its systemic PK profile and, in turn, to understand the impact of lung bioavailability and residence time on the choice of dosage regimen.

METHODS

We developed and validated a population PK model to characterize the lung absorption of glycopyrronium using plasma PK data derived from studies in which this drug was administered by different routes to healthy volunteers. The model was also used to carry out simulations of once-daily and twice-daily regimens and to characterize amounts of glycopyrronium in systemic compartments and lungs.

RESULTS

The model-derived PK parameters were comparable to those obtained with noncompartmental analysis, confirming the usefulness of our model. The model suggested that the lung absorption of glycopyrronium was dominated by slow-phase absorption with a half-life of about 3.5 days, which accounted for 79% of drug absorbed through the lungs into the bloodstream, from where glycopyrronium was quickly eliminated. Simulations of once-daily and twice-daily administration generated similar PK profiles in the lung compartments.

CONCLUSIONS

The slow absorption from the lungs, together with the rapid elimination from the systemic circulation, could explain how once-daily glycopyrronium provides sustained bronchodilatation with a low incidence of adverse effects in patients with chronic obstructive pulmonary disease. Its extended intrapulmonary residence time also provides pharmacokinetic evidence that glycopyrronium has the profile of a once-daily drug.