title: Semi-analytical solution for the in-vitro sedimentation, diffusion and dosimetry model: surveying the impact of the Peclet number.
abstract: 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 of the 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 of the 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 τ. The Pe number shows the ratio of the convective to the diffusive mass transport rates and τ is a dimensionless time parameter. The quality of the results for an extensive range of Pe and τ 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 τ 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.
authors: Hydraulic Machinery Research Inst., School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.
authors: Ali
authors: A
authors: Mahnama
authors: Department of Mechanical Engineering, Vrije Universiteit Brussel, Brussels, Belgium; Hydraulic Machinery Research Inst., School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.
authors: Ghader
authors: G
authors: Ghorbaniasl
authors: Department of Physics, University of Tehran, Tehran, Iran.
authors: S Mehdi Vaez
authors: SMV
authors: Allaei
authors: Hydraulic Machinery Research Inst., School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran. Electronic address: anour@ut.ac.ir.
authors: Ahmad
authors: A
authors: Nourbakhsh
mesh_terms: D004058:Diffusion; D004305:Dose-Response Relationship, Drug; D066298:In Vitro Techniques; D008962:Models, Theoretical; D053758:Nanoparticles
keywords: Advection diffusion equation; Cell culture; ISDD; Nanaoparticle; Semi-analytical solution