Kinetic Model for Describing the Spring Effect and Incomplete Dissolution in Low-Solubility Drug Formulations Based on the Quality-by-Design (QbD) Approach

Background/Objectives: Enhancing the bioavailability of active pharmaceutical ingredients (APIs) with low solubility -classified under the Biopharmaceutics Classification System (BCS) as class II and class IV -is a major challenge in pharmaceuticals development. Stabilizing APIs in amorphous form significantly increases their apparent solubility but results in complex dissolution profiles characterized by the "spring effect," a temporal high concentration peak during dissolution. These dissolution profiles are very challenging to be quantitatively evaluated due to the lack of appropriate mathematical models compatible with a Quality-by-Design (QbD) approach. Methods: A kinetic model was developed by considering the mechanistic aspects of the process. The model postulates three stages of the dissolution: hydration and dissolution of the amorphous API within the carrier, diffusion of the dissolved API into the medium, and equilibrium-driven interactions between the dissolved API and its thermodynamically stable crystalline form. Results: This model provides insights into release acceleration, slow final dissolution, and the spring effect, and elucidates scenarios where complete dissolution cannot be achieved due to the absence of sink conditions. While microscopic molecular phenomena -such as liquid-liquid phase separation (LLPS) and polymeric crystallization inhibition -are extensively documented in the academic literature, their individual isolated parameters are inherently unobservable under routine pharmaceutical industrial and GMP testing conditions. To bridge this gap, the developed model establishes a robust, apparent kinetic framework that fits macroscopically observable dissolution profiles. Conclusions: This method provides a robust framework for interpreting drug release profiles and optimizing formulation development using a QbD approach, specifically supporting regulatory requirements and batch-to-batch consistency evaluations across similar polymer-matrix systems. The model enables the determination of kinetic parameters such as t_max and c_max, and explains their dependence on the actual pharmaceutical formulation.