A geometrical approach to the PKPD modelling of inhaled bronchodilators

The present work introduces a new method to model the pharmacokinetics (PK) and pharmacodynamics (PD) of an inhaled dose of bronchodilator, alternative to classic compartmental representations or computational fluid dynamics. A five compartment PK model comprising alimentary tract absorption (gut), bronchial tree mucosa, bronchial muscles, plasma, and elimination/excretion pathways has been developed. Many anatomical and physiological features of the bronchial tree depend on bronchial generation or on mean distance from the larynx. Among these are diameters, resistances, and receptor density, which determine together the local response to the inhaled drug; integrating these local responses over the whole bronchial tree allows an approximation of total bronchodilator response and airflow resistance. While the PK part of the model reflects classical compartmental assumptions, the PD part adds a simplified geometrical and functional description of the bronchial tree to a typical empirical model of local effect on bronchial muscle, leading to the direct computation of the approximate forced expiratory volume in 1 s (FEV1). In the present work the construction of the model is detailed, with reference to literature data. Simulation of a hypothetical asthmatic subject is employed to illustrate the behaviour of the model in representing the evolution over time of the distribution and pharmacological effect of an inhaled dose of a bronchodilator. The relevance of particle size and drug formulation diffusivity on therapeutic efficacy is discussed.