Determination of the Number of Tissue Groups of Kinetically Distinct Transit Time in Whole-Body Physiologically Based Pharmacokinetic (PBPK) Models I: Theoretical Consideration of Bottom-Up Approach of Lumping Tissues in Whole-Body PBPK

Minimal physiologically based pharmacokinetic (mPBPK) models, consisting of system-specific (e.g., tissue volume and blood flow) and drug-related (e.g., tissue-to-plasma partition coefficient) parameters, are practically useful for pharmacokinetic analyses. However, biopharmaceutical principles were not clear on how peripheral tissues, adopted in whole-body physiologically based pharmacokinetic (WB-PBPK) models, could be kinetically consolidated into one or two tissue groups in the mPBPK models. In this theoretical examination, we studied the relationship between the progressive tissue lumping in the direction from the longest mean transit time (MTT_max) to the shorter one(s) and the slopes of the terminal (λ_ter)/distributional phases, assuming tissues with comparable MTTs are kinetically combined. The appropriateness of lumping was ascertained by evaluating the impact of difference in tissue MTTs during the lumping on the analytical solution of WB-PBPK models. We found that the ratio of MTT_max to the mean residence time in the body, viz., K_det, is related to the change in λ_ter by the progressive lumping and can serve as an index for the robustness of λ_ter. Calculations with two extreme cases revealed that, for caffeine at K_det < 0.03, the change in λ_ter was minimal even when all peripheral tissues were collectively lumped, whereas for artesunic acid at K_det > 50, the tissue of MTT_max could not be kinetically combined even with the tissue having the second-longest MTT without significantly affecting λ_ter. Therefore, we proposed K_det as an index for the robustness of λ_ter during tissue lumping and for the number of tissue groups with distinct transit times in WB-PBPK.

Determination of the Number of Tissue Groups of Kinetically Distinct Transit Time in Whole-Body Physiologically Based Pharmacokinetic (PBPK) Models II: Practical Application of Tissue Lumping Theories for Pharmacokinetics of Various Compounds

In our companion paper, we described the theoretical basis for tissue lumping in whole-body physiologically based pharmacokinetic (WB-PBPK) models and found that K_det, a coefficient for determining the number of tissue groups of distinct transit time in WB-PBPK models, was related to the fractional change in the terminal slope (FCT) when tissues were progressively lumped from the longest transit time to shorter ones. This study was conducted to identify the practical threshold of K_det by applying the lumping theory to plasma/blood concentration-time relationships of 113 model compounds collected from the literature. We found that drugs having K_det < 0.3 were associated with FCT < 0.1 even when all peripheral tissues were lumped, resulting in comparable plasma concentration-time profiles between one-tissue minimal PBPK (mPBPK) and WB-PBPK models. For drugs with K_det ≥ 1, WB-PBPK profiles appeared similar with two-tissue mPBPK models by applying the rule of FCT < 0.1 for lumping slowly equilibrating tissues. The two-tissue mPBPK model also appeared appropriate in terms of concentration-time profiles for drugs with 0.3 ≤ K_det < 1, although, some compounds (15.9% of the total cases), but not all, in this range showed a slight (maximum of 18.9% of the total AUC) deviation from WB-PBPK models, indicating that the two-tissue model, with caution, could still be used for those cases. Comparison of kinetic parameters between traditional (model-fitting) and current (theoretical calculation) mPBPK analyses revealed their significant correlations. Collectively, these observations suggest that the number of tissue groups could be determined based on the K_det/FCT criteria, and plasma concentration-time profiles from WB-PBPK could be calculated using equations significantly less complex.