Raman-based real-time dissolution prediction using a deterministic permeation model.

The purpose of this study was to develop a deterministic permeation model (DPM) that predicts the in vitro release profile of an active ingredient (API) embedded in hydroxypropyl-methylcellulose (HPMC) matrix tablets based on Raman spectra. So far in the literature, such mechanistic models were utilized only for formulation optimization (off-line dissolution prediction), while the real-time prediction of dissolution profiles based on Process Analytical Technology (PAT) data was performed by empirical methods such as Partial Least Squares (PLS) regression. Our work represents a novel conceptual approach that utilizes a mechanistic model to predict dissolution profiles based on data yielded by PAT tools. Tablets containing various API- and HPMC-amounts were produced using different compression pressures according to a 33 full factorial design, their Raman spectra were recorded before dissolution testing. The DPM was constructed using one-third of the measured dissolution profiles and is presented as a system of differential equations together with its analytical solution. The parameters of DPM were estimated by the training data set containing the spectroscopically determined API- and HPMC- amounts and the tableting pressures used, then the release profiles of the remaining two-thirds of the tablets were predicted. The Raman spectra-based predictions of DPM were compared with predictions of an Artificial Neural Network (ANN). It was found that the two methods yield similar results, however, the mechanistic approach has the benefit of requiring a lower amount of training samples. Although the model is based on a remarkable simplification of reality, it facilitates a deeper understanding of the behavior of the formulation. The DPM could improve our understanding of the effect of HPMC and tableting pressures on the release kinetics of the HPMC matrix tablets and participate in the development of PAT-based new surrogate dissolution methods for Real-Time Release testing (RTRt).

Asymptotics and bioavailability in a 17-compartment pharmacokinetic model with enterohepatic circulation and remetabolization.

A 17-compartment linear pharmacokinetic model is designed, describing the complex process of enterohepatic circulation as a superposition of the net (remetabolizationfree) enterohepatic circulation, and remetabolization with subsequent intestinal absorption of the parent drug. Basically, the model is built by doubling the model describing the circulation of the parent drug in the body, so that the remetabolizable metabolite circulates in a model of the same structure as does the parent compound. The two submodels are cross-connected with arrows denoting the transition of the particular substance into the complementary part of the complex model. Asymptotic properties of the model are investigated, in particular, explicit formulas for its pharmacokinetic endpoints are given using the elements of its transition probability matrix. Conversely, taking account of the effect of bile cannulation, intravenous, intraportal and oral administration of the drug, as well as of the intravenous and intraportal administration of the remetabolizable metabolite, the transition probabilities of the system are determined in terms of certain measurable pharmacokinetic endpoints and the flow rates through the kidneys, liver and the cardiac output. Finally, the influence of the enterohepatic circulation and remetabolization process on bioavailability is examined. In particular, the inclusion-exclusion formula is derived, expressing its joint efficiency (defined as the relative increase of bioavailability) by means of the efficiencies of the net enterohepatic circulation and of the remetabolization process.

Asymptotics and bioavailability in multicompartment pharmacokinetic models with enterohepatic circulation.

Analysing discrete as well as continuous linear autonomous pharmacokinetic models, it is shown that their asymptotic behaviour is independent of the rates of kinetic processes and timing of drug application. Consequently, for the description of pharmacokinetic endpoints, i.e. the total amounts of drug eliminated through different organs under various ways of administration, in such a model the knowledge of total amounts delivered to individual compartments and its transition probability matrix P=[p(ij)] is sufficient.A design and analysis of a 9-compartment pharmacokinetic model with enterohepatic circulation (EHC), avoiding several common simplifications, test the applicability of our method. The central compartment of the model is the liver acting as filter and linking the systemic and enterohepatic circulation. Explicit formulas are given for pharmacokinetic endpoints of the model using the elements of the transition probability matrix P. Conversely, the transition probabilities are determined in terms of certain measurable pharmacokinetic endpoints and the flow rates through the kidneys, liver and the cardiac output, contributing that way to the structural identifiability problem. As a further consequence, the bioavailability of the drug with and without EHC can be determined and the efficiency of EHC expressed as the 'probability' of the enterohepatic cycle.Finally, we apply our method to analyse and compare various pharmacokinetic models, describing the EHC of drugs, based on some previously published articles.