Inferring pulmonary exposure based on clinical PK data: accuracy and precision of model-based deconvolution methods

Determining and understanding the target-site exposure in clinical studies remains challenging. This is especially true for oral drug inhalation for local treatment, where the target-site is identical to the site of drug absorption, i.e., the lungs. Modeling and simulation based on clinical pharmacokinetic (PK) data may be a valid approach to infer the pulmonary fate of orally inhaled drugs, even without local measurements. In this work, a simulation-estimation study was systematically applied to investigate five published model structures for pulmonary drug absorption. First, these models were compared for structural identifiability and how choosing an inadequate model impacts the inference on pulmonary exposure. Second, in the context of the population approach both sequential and simultaneous parameter estimation methods after intravenous administration and oral inhalation were evaluated with typically applied models. With an adequate model structure and a well-characterized systemic PK after intravenous dosing, the error in inferring pulmonary exposure and retention times was less than twofold in the majority of evaluations. Whether a sequential or simultaneous parameter estimation was applied did not affect the inferred pulmonary PK to a relevant degree. One scenario in the population PK analysis demonstrated biased pulmonary exposure metrics caused by inadequate estimation of systemic PK parameters. Overall, it was demonstrated that empirical modeling of intravenous and inhalation PK datasets provided robust estimates regarding accuracy and bias for the pulmonary exposure and pulmonary retention, even in presence of the high variability after drug inhalation. Supplementary Information The online version contains supplementary material available at 10.1007/s10928-021-09780-x.

With nDose being the nominal dose, FPul being the pulmonary bioavailability, and PF1 and 2 as the proportionality factors (Parameterization from Borghardt et al. (1)).

S2.1. Ordinary differential equations
Model_IIIa (Olodaterol, Borghardt et al. (1)) Model_Transit (PF-00610355, Diderichsen et al. (5)) For 'Model Transit', dosing was performed into the 'Abs.fast' compartment, with transition from 'Abs.fast' to 'Abs.med' representing the transit process rather than parallel absorption. . The naïvepooled analysis did not distinguish between these clearances; however, as interindividual variability (IIV) was put on the nonrenal part, both clearances were implemented as separate processes in the population PK analysis. The respective values for CLR and CLNR were 10.5 and 63.7 L/h, respectively. # For models with less than four systemic PK compartments originally (Models I, NaL, and Transit), Q values for the missing compartments (3 and 4) were set to 0 to remove drug transfer to these compartments while still allowing for automation of the simulation/re-estimation process. The corresponding Volumes of distribution were set to 1 to avoid division by 0. Initial parameters for parallel retries were varied randomly using the rnorm function in R (random sampling from a specified normal distribution) as follows, resulting in a lognormal distribution of parameters:

S2.2. Parameter values used for simulation
FPul, PF1 and PF2 were logit transformed beforehand to constrain the values between 0 and 1. The semi-mechanistic model was adapted to oral inhalation. The assumed pulmonary availability was 50%, with 80% of the lung dose depositing in the peripheral lung (alveolar parenchyma). The remaining 20% were equally distributed between the trachea and bronchi.

S4. Non-compartmental analysis
The AUC0-last in plasma, as well as the area under the first moment curve (AUMC0-last), were calculated via the log-linear trapezoidal method after both intravenous administration and oral inhalation. Extrapolation of the AUC to infinity was performed by addition of the last observed concentration divided by the terminal slope of log-transformed concentration data (Clast/λz). λz was determined by linear regression over the last three observations. The AUMC0-last was extrapolated to infinity by addition of the term ((Clast • tlast)/λz + Clast/ λz 2 ), tlast denoting the time of the last observed concentration. Pulmonary bioavailability (FPul) was calculated as shown in Eq. S5: Inferring on pulmonary AUC (AUC0-inf,Lung) was performed as follows: The AUC0-inf,plasma and AUMC0-inf,plasma were used to determine the mean residence time (MRT) for both administration routes: Tinf denotes the duration of the intravenous infusion.
The mean absorption time (MAT) was calculated by subtracting the mean residence time (MRT) after inhalation from the MRT after intravenous administration: The MAT was then used to infer on the pulmonary absorption rate constant ka: To infer on the pulmonary AUC0-inf, the equation for AUC calculation in plasma (Eq. S11) was adjusted to the lung, inserting FPul as the bioavailability (F) and the pulmonary absorption rate ka as the elimination rate from the lung: VLung was set to 0.840 L based on literature values for lung weight (7).
These analyses, performed in parallel to the population PK analyses, yielded ambivalent results for both scenarios. While the NCA performed on the dataset simulated with 'Model IIIa' resulted in plausible, yet biased values, the simulation with 'Model II' could not be analyzed with an NCA, as for some individuals the MRT after inhalation was shorter than after i.v. administration. In depth evaluation of the data indicated that this was due to biased AUMCtz-Inf values, i.e., the extrapolated area of the AUMC was underestimated compared to the true area. In agreement, analysis of inhalation PK data from individuals with negative MAT values showed that the terminal slope λz was overestimated (i.e. a steeper terminal profile was assumed, Figure S4) compared to the true value. For this reason, and as this specific terminal part of the AUMC often constitutes a substantial part of the AUMC0-Inf (33), these individuals were characterized by an underestimated AUMCinhaled. Combined with sometimes overestimated AUMC0-inf,i.v. values, this can explain the finding of negative MAT values. Thus, NCA for drugs with long terminal half-lives may necessitate even longer observation times or more accurate bioanalysis to adequately capture the terminal phase of the concentration-time profiles. This however might not always be feasible. Even for individuals with a positive MAT, the mean predicted AUC0-inf,lung was over tenfold higher than the true value. Furthermore, an NCA is only applicable if the same assumptions hold true as for the parallel absorption models, i.e. MCC and pulmonary metabolism being negligible (26). This leads to the conclusion that, the PK modeling approaches are more robust towards non-optimally designed sampling schemes, as well as providing more reliable estimates for the duration of pulmonary retention. S6. Comparison of parameter estimates between PPP, IPP, and ALL