Characterization of the Shells in Layer-By-Layer Nanofunctionalized Particles: A Computational Study

Abstract

Drug delivery carriers are considered an encouraging approach for the localized treatment of disease with minimum effect on the surrounding tissue. Particularly, layer-by-layer releasing particles have gained increasing interest for their ability to develop multifunctional systems able to control the release of one or more therapeutical drugs and biomolecules. Although experimental methods can offer the opportunity to establish cause and effect relationships, the data collection can be excessively expensive or/and time-consuming. For a better understanding of the impact of different design conditions on the drug-kinetics and release profile, properly designed mathematical models can be greatly beneficial. In this work, we develop a continuum-scale mathematical model to evaluate the transport and release of a drug from a microparticle based on an inner core covered by a polymeric shell. The present mathematical model includes the dissolution and diffusion of the drug and accounts for a mechanism that takes into consideration the drug biomolecules entrapped into the polymeric shell. We test a sensitivity analysis to evaluate the influence of changing the model conditions on the total system behavior. To prove the effectiveness of this proposed model, we consider the specific application of antibacterial treatment and calibrate the model against the data of the release profile for an antibiotic drug, metronidazole. The results of the numerical simulation show that ∼85% of the drug is released in 230 h, and its release is characterized by two regimes where the drug dissolves, diffuses, and travels the external shell layer at a shorter time, while the drug is released from the shell to the surrounding medium at a longer time. Within the sensitivity analysis, the outer layer diffusivity is more significant than the value of diffusivity in the core, and the increase of the dissolution parameters causes an initial burst release of the drug. Finally, changing the shape of the particle to an ellipse produces an increased percentage of drugs released with an unchanged release time.

Keywords: drug diffusion; drug dissolution; drug release; layer-by-layer; mathematical modeling.

FIGURE 1

Diagram of the cross section of a spherical two-layer system based on an internal core and concentric LbL coating (left, (A)). With reference to their releasing properties, the enveloping layers can be assimilated to a unique equivalent shell having averaged characteristics (right, (B)) (figures not to scale).

FIGURE 2

Schematic of the 2D cross-section of a multilayer system comprising an internal core Ω₀ and LbL-equivalent external shell Ω₁ (figure not to scale).

FIGURE 3

SEM Images of the MP as prepared (A), after eight layers (B) and after 14 layers (C). In vitro release data from the LbL-functionalized MPs (D). Each data point represents the mean ± standard deviation over a set of six tested samples.

FIGURE 4

FEM mesh in the two-layer spherical particle.

FIGURE 5

Best fit curve of simulation (red line) over experimental data (black line with error bars).

FIGURE 6

Top: concentration field at six different times labelled from A (after 3 s) to F (after 61000 s). Bottom: plot of the maximum concentration at the MP center vs. time at the 6 selected times.

FIGURE 7

Sensitivity of the release curves to the six model parameters varied with respect to their reference values in Table 1. The black curve refers to the reference values, the red curve to a smaller value, and the blue to a greater value (cfr. tables 1.2).

FIGURE 8

Sensitivity of the release curves to ellipse eccentricity λ.