Abstract—Like any living species, Human kind has been exposed to nanoparticles during its entire existence. But the question of their toxicity has only been recently raised as a consequence of rapid growth of industrial activity. Nowadays, the impact of nanoparticles is not clearly known. For this reason Mathematics in Medicine Study Groups (M.M.S.G.) developed a mathematical model based on the different possible entries of nanoparticles into cells. To allow further studies on their toxicity, M.M.S.G. model has been here completed by introducing adapted equations of diffusion to represent its effects on nanoparticles penetrationand accumulation inside cells. It is mainly shown that due to their size (100nm), nanoparticles diffusion time is extremely short comparedtocharacteristic system evolution time. As a consequence, living cells are not shielded against high nanoparticle bursts which enter almost instantaneously inside and equalizeover all cell domain. More favourable situationcould only be expected with much larger nanoparticle size.

Index Terms—Diffusion, mathematical model, nanoparticles, penetration.

The authors are with ECE Paris, France (e-mail: lmartin@ece.fr, collin@ece.fr).

Cite: L. Martin, S. Collin, E. Jeandupeux, A. Deutsch, and A. Zeitoun, "A Diffusive Model for Nanoparticle Penetration into Living Cells," International Journal of Bioscience, Biochemistry and Bioinformatics vol. 4, no. 5, pp. 312-317, 2014.