Mathematical pharmacokinetics modeling of parenteral depot formulations

Introduction. The development of parenteral depot formulations of drugs with modified release is a critical area in the treatment of chronic diseases such as cancer, schizophrenia, and diabetes. These formulations improve treatment adherence, maintain stable plasma concentrations, and reduce the frequency of injections. However, their development is fraught with technological and pharmacokinetic challenges, including nonlinear release of the active ingredient and high interindividual variability.

Aim. To systematically analyze and summarize current methodological approaches to mathematical modeling of the pharmacokinetics of parenteral long-acting drug formulations.

Materials and methods. A targeted literature search was conducted in PubMed, Google Scholar, and Scopus for the period 2015–2025 using Boolean operators and combinations of relevant keywords. The review includes data on clinically used long-acting parenteral formulations as well as on polymeric carriers (PLGA, hydrogels, in situ gels, and hybrid systems). To illustrate instrumental approaches, we consider compartmental PK models, PBPK models, and models based on machine learning methods.

Results and discussion. The characteristic features of pharmacokinetic profiles of parenteral depot formulations are summarized, including the phases of initial burst, lag phase, controlled release, and late decay, as well as their relationship with the physicochemical properties of the carrier and the drug substance. The variability of the profile is shown to be associated with a combination of technological parameters (particle size, polymer composition and architecture), injection site and route of administration, and individual patient characteristics. The capabilities of nonlinear mixed-effects models, PBPK approaches, and machine learning-based models are demonstrated for describing inter- and intraindividual variability, performing simulations of dosing regimens, and supporting in silico optimization of formulation development. A basic system of ordinary differential equations (ODEs) is proposed that reflects sequential release from different depot fractions followed by distribution and elimination of the drug.

Conclusion. Pharmacokinetic modeling of parenteral long-acting formulations is a key instrument within the MIDD (Model-Informed Drug Development) concept, enabling integration of mechanistic knowledge on release, absorption, and distribution with clinical data. The proposed basic ODE model structure can serve as a methodological framework for developing and adapting models for specific drug products, thereby supporting optimization of formulation composition and dosing regimens and reducing the extent of costly in vivo studies.

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