Releasing capsules are widely employed in biomedical applications as smart carriers of therapeutic agents, including drugs and bioactive compounds. Such delivery vehicles typically consist of a loaded core, enclosed by one or multiple concentric coating strata. In this work, we extended existing mechanistic models to account for such multi-strata structures, including possible concurrent erosion of the capsule itself, and we characterized the release kinetics of the active substance into the surrounding medium. We presented a computational study of drug release from a spherical microcapsule, modeled through a non-linear diffusion equation incorporating radial asymmetric diffusion and space- and time-discontinuous coefficients, as suggested by the experimental data specifically collected for this study. The problem was solved numerically using a finite volume scheme on a grid with adaptive spatial and temporal resolution. Analytical expressions for concentration and cumulative release were derived for all strata, enabling the exploration of parameter sensitivity—such as coating permeability and internal diffusivity—on the overall release profile. The resulting release curves provide mechanistic insight into the transport processes and offer design criteria for achieving controlled release. Model predictions were benchmarked against in vitro experimental data obtained under physiologically relevant conditions, showing good agreement and validating the key features of the model. The proposed model thus serves as a practical tool for predicting the behavior of composite coated particles, supporting performance evaluation and the rational design of next-generation drug delivery systems with reduced experimental effort.
Citation: Elia Onofri, Emiliano Cristiani, Andrea Martelli, Piergiorgio Gentile, Joel Girón Hernández, Giuseppe Pontrelli. A general multi-stratum model for a nanofunctionalized releasing capsule: An experiment-driven computational study[J]. Mathematical Biosciences and Engineering, 2026, 23(1): 1-21. doi: 10.3934/mbe.2026001
Releasing capsules are widely employed in biomedical applications as smart carriers of therapeutic agents, including drugs and bioactive compounds. Such delivery vehicles typically consist of a loaded core, enclosed by one or multiple concentric coating strata. In this work, we extended existing mechanistic models to account for such multi-strata structures, including possible concurrent erosion of the capsule itself, and we characterized the release kinetics of the active substance into the surrounding medium. We presented a computational study of drug release from a spherical microcapsule, modeled through a non-linear diffusion equation incorporating radial asymmetric diffusion and space- and time-discontinuous coefficients, as suggested by the experimental data specifically collected for this study. The problem was solved numerically using a finite volume scheme on a grid with adaptive spatial and temporal resolution. Analytical expressions for concentration and cumulative release were derived for all strata, enabling the exploration of parameter sensitivity—such as coating permeability and internal diffusivity—on the overall release profile. The resulting release curves provide mechanistic insight into the transport processes and offer design criteria for achieving controlled release. Model predictions were benchmarked against in vitro experimental data obtained under physiologically relevant conditions, showing good agreement and validating the key features of the model. The proposed model thus serves as a practical tool for predicting the behavior of composite coated particles, supporting performance evaluation and the rational design of next-generation drug delivery systems with reduced experimental effort.
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Elia Onofri, Emiliano Cristiani, Andrea Martelli, Piergiorgio Gentile, Joel Girón Hernández, Giuseppe Pontrelli. A general multi-stratum model for a nanofunctionalized releasing capsule: An experiment-driven computational study[J]. Mathematical Biosciences and Engineering, 2026, 23(1): 1-21. doi: 10.3934/mbe.2026001
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