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

Abstract

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 (MTTmax) to the shorter one(s) and the slopes of the terminal (lambda(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 MTTmax to the mean residence time in the body, viz., K-det, is related to the change lambda(ter) by the progressive lumping and can serve as an index for the robustness lambda(ter). Calculations with two extreme cases revealed that, for caffeine at K-det < 0.03, the change lambda(ter) was minimal even when all peripheral tissues were collectively lumped, whereas for artesunic acid at K-det > 50, the tissue of MTTmax could not be kinetically combined even with the tissue having the second-longest MTT without significantly affecting lambda(ter). Therefore, we proposed K-det as an index for the robustness of lambda(ter) during tissue lumping and for the number of tissue groups with distinct transit times in WB-PBPK.