A Partial Differential Equation Approach to Inhalation Physiologically Based Pharmacokinetic Modeling

Abstract

The heterogeneous nature of the lungs and the range of processes affecting pulmonary drug disposition make prediction of inhaled drugs challenging. These predictions are critical, as the local exposure cannot be measured and current inhalation physiologically based pharmacokinetic (PBPK) models do not capture all necessary features. Utilizing partial differential equations, we present an inhalation PBPK model to describe the heterogeneity in both lung physiology and particle size. The model mechanistically describes important processes, such as deposition, mucociliary clearance, and dissolution. In addition, simplifications are introduced to reduce computational cost without loss of accuracy. Three case studies exemplify how the model can enhance our understanding of pulmonary drug disposition. Specific findings include that most small airways can be targeted by inhalation, and overdosing may eradicate the advantage of inhalation. The presented model can guide the design of inhaled molecules, formulations, as well as clinical trials, providing opportunities to explore regional targeting.

A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs

“…To build sufficient trust into a pulmonary PK model to use it for identification of optimal drug characteristics, an adequate and systematic model evaluation is a prerequisite. However, previous mechanistic modeling attempts, most noticeably the ones by Caniga et al [56] and Boger et al [20], lack such a thorough evaluation. Indeed, the approach by Caniga et al, differentiating between airways and alveolar space albeit less mechanistically than in the here-presented model, was evaluated for inhaled mometasone [56] and more recently for additional fast dissolving drugs (formoterol, salbutamol, and budesonide) [57].…”

“…A PDE model published by Boger et al mechanistically included all pulmonary PK processes [20]. However, this model was based on a hypothetical drug, and while most of the characteristics of this hypothetical drug can be considered reasonable, such as a K p,lung of 4.9 or the oral bioavailability of 20%, no in vitro assays can be used to characterize drug characteristics such as permeability, dissolution kinetics, and solubility.…”

“…back flow of drug to the lungs from the systemic disposition is not considered [17][18][19]. One mechanistic partial differential equation (PDE)-based model is available, which included all relevant pulmonary PK processes [20]. This model, however, was not evaluated against clinical data.…”

Bridging inhaled aerosol dosimetry to physiologically based pharmacokinetic modeling for toxicological assessment: nicotine delivery systems and beyond

“…The methods/approaches described in this section are based on various modeling efforts and issues that need to be further developed and validated to be applicable for inhalation, in particular for evolving aerosols. A tremendous amount of work has been done by several groups to understand dosimetry for inhalation exposures, but most of it was focused on gas exposure or for non-evolving aerosols containing solid particles (Ramsey and Andersen 1984;Csanady et al 1994;U.S.EPA 1994;Anjilvel and Asgharian 1995;Kumagai and Matsunaga 1995;Sarangapani, Teeguarden, et al 2002;Phalen et al 2010;Boger and Wigstrom 2018).…”

“…Initial inhalation PBPK models developed for occupational or environmental exposures are comprised of either 1, 3, or 4 respiratory compartments (Figure 6). Lately, PBPK models are being developed that include all 24 generations of the RT (Backman et al 2018;Boger and Wigstrom 2018), but the necessity for inclusion of this level of detail remains to be validated and benchmarked with other models. Moreover, inhalation PBPK models coupled to computational dosimetry approaches (whole-lung or CFD-coupled) are recommended for development while simultaneously accounting for accuracy versus feasibility and practical use.…”