Semi-analytical solution for the in-vitro sedimentation, diffusion and dosimetry model: Surveying the impact of the Peclet number

Reducing size of the particles to the nanoscale range gives them new physicochemical properties. Several
experiments have shown cytotoxic effects for different kinds of engineered nanoparticles (ENP). In-vitro
cell culture assays are widely utilized by researchers to evaluate cytotoxic effects ofthe ENPs. The present paper deals with the "In vitro Sedimentation, Diffusion and Dosimetry (ISDD)" model. This mathematical model uses an advection-diffusion equation with specific assumptions and coefficients to estimate the dose ofthe particles delivered to the cells monolayer in the culture medium. In the present work, utilizing the generalized integral transform technique (GITT), a semi-analytical solution is developed for the ISDD model. The parameters affecting the ISDD predictions are integrated into two dimensionless numbers, Pe and taw. The Pe number shows the ratio of the convective to the diffusive mass transport rates and is a dimensionless time parameter. The quality of the results for an extensive range of Pe and taw numbers is surveyed through application of the developed formula to two series of test cases. A comparison of the results with those obtained from numerical methods shows deviations in the numerical results at high Pe numbers. Applying the developed formula, ISDD predictions for a wide practical range of Pe and taw numbers are calculated and plotted in two- and three-dimensional plots. The curves and formula obtained in this study facilitate the achievement of ISDD predictions with higher accuracies and capabilities for verification of the results.

Jaar van publicatie:2014

Trefwoorden:Nanaoparticle, ISDD, Advection diffusion equation, Semi-analytical solution, Cell culture