The purpose of this study was to develop a physiologically based pharmacokinetic (PBPK) model predicting the pharmacokinetics (PK) of different compounds in pregnant subjects. This model considers the differences in tissue sizes, blood flow rates, enzyme expression levels, glomerular filtration rates, plasma protein binding, and other factors affected during pregnancy in both the maternal and fetal models. The PBPKPlus™ module in GastroPlus® was used to model the PK of cefuroxime and cefazolin. For both compounds, the model was first validated against PK data in healthy non-pregnant volunteers and then applied to predict pregnant groups PK. The model accurately described the PK in both non-pregnant and pregnant groups and explained well differences in the plasma concentration due to pregnancy. The fetal plasma and amniotic fluid concentrations were also predicted reasonably well at different stages of pregnancy. This work describes the use of a PBPK approach for drug development and demonstrates the ability to predict differences in PK in pregnant subjects and fetal exposure for compounds excreted renally. The prediction for pregnant groups is also improved when the model is calibrated with postpartum or non-pregnant female group if such data are available.

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Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical branching lemma that proves local confluence from confluence of the critical branchings. The analysis of local confluence of rewriting systems on algebraic structures, such as groups or linear algebras, is complicated because of the underlying algebraic axioms. This article introduces the structure of algebraic polygraph modulo that formalizes the interaction between the rules of an algebraic rewriting system and the inherent algebraic axioms, and we show a critical branching lemma for algebraic polygraphs. We deduce a critical branching lemma for rewriting systems on algebraic models whose axioms are specified by convergent modulo rewriting systems. We illustrate our constructions for string, linear, and group rewriting systems.