Niklas Hartung (1), Jens Markus Borghardt (2)
(1) University of Potsdam, Germany (2) Drug Discovery Sciences, Boehringer Ingelheim Pharma GmbH & Co. KG, Biberach, Germany
Objectives:
Pulmonary absorption of orally inhaled drugs depends on the deposition pattern, dissolution process, and mucociliary clearance. Especially for slowly dissolving drugs, the complex interplay of saturable dissolution and mucociliary clearance results in nonlinear absorption and particle size-dependency [1-2]. Several recently proposed pharmacokinetic models for pulmonary pharmacokinetics strive to describe these processes in mechanistic detail [3-5]. Mucociliary clearance has been resolved spatially by transit compartment models and dissolution by the Nernst-Brunner equation. However, all models simultaneously describing the impact of saturable dissolution and mucociliary clearance have considerably simplified one of these two processes. Indeed, it is difficult to formulate a compartmental model representing this interplay accurately. The present work aims to overcome this hurdle by describing pulmonary absorption in a partial differential equation framework in order to integrate these two mechanisms in full detail.
Methods:
We modelled the simultaneous effects of mucociliary clearance and saturable dissolution by a location- and size-structured population equation (a partial differential equation) [6]. The main quantity in this model is a location-and size-resolved density, from which amounts can be recovered via integration over the two structuring variables. Mucociliary clearance is resolved along a typical airway, parametrized from physiological airway data and a mucus velocity model [7]. Dissolution is described by the Nernst-Brunner equation, and saturation via an additional location-resolved dissolution compartment, from which systemic absorption takes place. Deposition patterns were simulated with the MPPD v2.11 software [8], assuming inhalation patterns and particle sizes as described in the respective publications.
Results:
The structured population model was solved numerically using the method of characteristics [9]. In this approach, we used a fixed location grid adapted to changes of mucus velocity along the airway, and a time-dependent size grid, depending on the saturable dissolution process. Model predictions were compared to two sets of clinical data on fluticasone propionate, a slowly dissolving inhaled glucocorticoid used for treatment of asthma bronchiale and chronic obstructive pulmonary disease: i) using the same dose, but different particle sizes [1] and ii) different doses, but the same particle sizes [2]. In both scenarios, the model was able to qualitatively reproduce the observed nonlinear absorption patterns.
Conclusions:
We demonstrated that a structured population model can be used to describe the complex interplay of mucociliary clearance and saturable dissolution, in particular particle size-dependent and dose-nonlinear absorption patterns. Representing the interplay of all major processes, this framework could be used to predict the pulmonary bioavailable fraction for arbitrary lung deposition patterns, to assess local uptake profiles to eventually evaluate inhaled formulations and treatment schedules. Future work aims at confronting the model to other substances, as well as to include a more detailed physiological airway representation.
References:
[1] Usmani OS. Respiratory Drug Delivery (2014) 1:155-162.
[2] Presentation by Hochhaus G. https://www.fda.gov/Drugs/NewsEvents/ucm576064.htm
[3] Borghardt JM et al. AAPS J (2015) 17:853-870.
[4] Boger E et al. CPT:PSP (2016) 5:201-210.
[5] Chaudhuri SR and Lukacova V. Orally Inhaled Nasal Drug Prod. (2010) Nov:26-30.
[6] Metz JAJ and Diekmann O. The dynamics of physiologically structured populations (1986), Springer.
[7] Hofmann W and Sturm R. J Aerosol Med (2004) 17:73-89.
[8] https://www.ara.com/products/multiple-path-particle-dosimetry-model-mppd-v-211
[9] McOwen R. Partial Differential Equations: Methods and Applications (1996), Prentice Hall.
Reference: PAGE 27 (2018) Abstr 8720 [www.page-meeting.org/?abstract=8720]
Poster: Drug/Disease Modelling - Absorption & PBPK