Nanoparticle uptake by a semi-permeable, spherical cell from an external planar diffusive field. III. Analysis of seeded plate experiments

• Published in: Journal of engineering mathematics Vol. 152; no. 1
• Main Author: Miklavcic, Stanley J.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.06.2025
• Subjects: Cell culture; Diffusion rate; Exposure; Mathematics; Nanoparticles; One dimensional models
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-025-10454-7

Whether its for expediting targeted drug delivery or more generally for the potential risk posed to health through exposure to contaminated environments, the internalization of nanoparticles by biological cells has been the subject of much experimental research. One particular experimental system involving a 2D cell culture exposed to a nanoparticle solution is here modeled mathematically with the goal of identifying both cell-specific and environment-specific properties that govern the rate of nanoparticle uptake and the capacity for internalization by cells. Three models are presented and compared with experimental data. The first model considered, previously used in the literature to analyze experimental measurements, is discounted for its unrealistic behavior and lack of adequate representation of the cells. The predictions of the second and third models, not previously considered, compare favorably with experimental measurements. We find generally that the experimentally measured rates of uptake are foremost dictated by the manner of exposure: unidirectional diffusion toward the 2D cell culture. This rate is then modulated by cell-specific properties. The latter are here represented physically by cell size and internal diffusion rate, and biologically by two phenomenological parameters. We find that for 2D cultures of close-packed cells, the second, finite domain (per unit area) 1D model presented here is appropriate. For cells free in solution or 2D cell cultures distributed at low surface density, or 3D cultures of cells grown on polymeric scaffolds, the third, 3D isolated cell model is more appropriate.