Niklas Hartung, Wilhelm Huisinga
Institute of Mathematics, University of Potsdam, Germany
Objectives:
The a priori prediction of tissue partitioning constitutes a core element of physiologically-based pharmacokinetic modelling. There exist a number of different approaches to predict tissue-to-plasma water partition coefficients (Kpu), amongst them the Lukacova et al. (2008) model [1], used in the commercial PBPK software GastroPlus (Simulations Plus). Surprisingly, this model has only been introduced on a conference poster and without any theoretical derivation. It is motivated by an intriguing plot on the poster, showing the prediction of Kpu values as a function of a basic drug’s pKa value. For the well-established Rodgers et al. methods for moderate-to-strong bases [2] and for weak bases [3], there is a huge, seemingly undesirable jump in the predictions when switching models at pKa=7.0 (the threshold separating weak from moderate-to-strong bases), whereas the Lukacova et al. model desirably predicts a smooth dependence of Kpu on the pKa. The aim is to present a theoretical basis of a unified Rodgers et al. model—which was the motivation of the Lukacova et al. model—and to understand this phenomenon.
Methods:
A unified Rodgers et al. model was derived based on the assumption that a potentially ionisable drug is dissolved in extracellular and intracellular water, binds to interstitial binding proteins in its neutral & anionic form, and to cellular acidic phospholipids in its cationic form. The Lukacova et al. model was “extracted” from the poster. Experimental data on tissue constituents were extracted from Refs [2,3]. All Kpu models were implemented in MATLAB to reproduce the graphics on the Lukacova et al. poster [1] and understand the phenomenon.
Results:
All Kpu prediction models can calculate partitioning into red blood cells (Kpu_RBC) and therefore also blood-to-plasma ratios (B:P) based on fuP and haematocrit. In the Rodgers et al. model for weak bases, this calculation can be used to predict B:P a-priori (since it is not an input parameter), while in the Rodgers et al. model for moderate-to-strong bases, the predicted B:P simply coincides with the input parameter B:P (as expected). Surprisingly, we found that in the Lukacova et al. model, the predicted B:P differed from the input B:P since the affinity constant to acidic phospholipids (KA_AP) was not derived from Kpu_RBC by solving the Lukacova et al. model equation for KA_AP (as one would expect), but rather using that of the Rodgers et al. model for moderate-to-strong bases to solve for KA_AP. As a consequence, the simulation underlying the intriguing plot on the Lukacova et al. poster compared the two Rodgers et al. models and the Lukacova et al. model at considerably different B:P values! These differences explained much of the jump at pKa=7.0 between the two Rodgers et al. models, and question the validity of the Lukacova et al. model interpolation.
Moreover, the structure of the Lukacova et al. model differed from the formally derived unified Rodgers et al. model in several aspects concerning the interaction with interstitial binding proteins and acidic phospholipids. Without a theoretical derivation of the Lukacova et al. model, these differences can only be interpreted as model inconsistencies.
By construction, the B:P predicted with the unified Rodgers et al. model were consistent with the input B:P. The Kpu values predicted by the unified Rodgers et al. model showed a smooth dependence on the pKa, thus finally removing the remaining jump between the two Rodgers et al. models after correcting for B:P differences.
Conclusions:
Theoretical derivations and clearly stated assumptions are by no means “nice to have” model add-ons—rather, they constitute the basis of scientific progress and exchange. The presented study clearly shows the need of a theoretical derivation of the Lukacova et al. model, or its substitution by a theoretically sound model like the unified Rodgers et al. model.
References:
[1] Lukacova et al., AAPS conference poster (2008), https://www.simulations-plus.com/wp-content/uploads/Lukacova-General_Approach_Calc_Tissue_Plasma_Partition_Coefficients_PBPK_Modeling-AAPS-2008-1.pdf
[2] Rodgers et al., J Pharm Sci (2005) 94: 1259-1276
[3] Rodgers & Rowland, J Pharm Sci (2006) 95, 1238-1257
Reference: PAGE 32 (2024) Abstr 11096 [www.page-meeting.org/?abstract=11096]
Poster: Methodology - New Modelling Approaches