Time dependent dispersion of nanoparticles in blood vessels

ABSTRACT

The dispersion of intravasculary injected nanoparticles can be efficiently described by introducing an effective diffusion coefficient Deff which quantifies the longitudinal mass transport in blood vessels. Here, the original work of Gill and Sankarasubramanian was modified and extended to include 1) the variati- on over time of Deff; 2) the permeability of the blood vessels and 3) non-Newtonian rheology of blood. A general solution was provided for Deff depending on space (?), time (?), plug radius (?c) and a subset of permeability parameters. It was shown that increasing the vessel plug radius (thus hematocrit) or permeability leads to a reduction in Deff, limiting the transport of nanoparticles across those vessels. It was also shown that the asymptotic time beyond which the solution attains the steady state behaviour is always independent of the plug radius and wall permeability. The analysis presented can more accurately predict the transport of nanoparticles in blood vessels, compared to previously developed models.

The dispersion of intravasculary injected nanoparticles can be efficiently described by introducing an effective diffusion coefficient Deff which quantifies the longitudinal mass transport in blood vessels. Here, the original work of Gill and Sankarasubramanian was modified and extended to include 1) the variati- on over time of Deff; 2) the permeability of the blood vessels and 3) non-Newtonian rheology of blood. A general solution was provided for Deff depending on space (?), time (?), plug radius (?c) and a subset of permeability parameters. It was shown that increasing the vessel plug radius (thus hematocrit) or permeability leads to a reduction in Deff, limiting the transport of nanoparticles across those vessels. It was also shown that the asymptotic time beyond which the solution attains the steady state behaviour is always independent of the plug radius and wall permeability. The analysis presented can more accurately predict the transport of nanoparticles in blood vessels, compared to previously developed models.

Cite this paper

nullGentile, F. and Decuzzi, P. (2010) Time dependent dispersion of nanoparticles in blood vessels.*Journal of Biomedical Science and Engineering*, **3**, 517-524. doi: 10.4236/jbise.2010.35072.

nullGentile, F. and Decuzzi, P. (2010) Time dependent dispersion of nanoparticles in blood vessels.

References

[1] Taylor, G. (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proceedings of the Royal Society of London, A, 219(1137), 186-203.

[2] Aris, R. (1956) On the dispersion of a solute in a fluid fl- owing through a tube. Proceedings of the Royal Society of London, A, 235(1200), 67-77.

[3] Gill, W.N. (1967) A note on the solution of transient dis- persion problems. Proceedings of the Royal Society of London, A, 298(1967), 335-339.

[4] Sankarasubramanian, R. and Gill, W.N. (1973) Taylor diffusion in laminar flow in an eccentric annulus. Proceedings of the Royal Society of London, A, 333, 115-132.

[5] Sharp, M.K. (1993) Shear-augmented dispersion in non- Newtonian fluids. Annals of Biomedical Engineering, 21(4), 407-415.

[6] Dash, R.K., Jayaraman, G. and Mehta, K.N. (2000) Shear augmented dispersion of a solute in a casson fluid flowing in a conduit. Annals of Biomedical Engineering, 28(4), 373-385.

[7] Nagarani, P., Sarojamma, G. and Jayaraman, G. (2004) Effect of boundary absorption in dispersion in casson fluid flow in a tube. Annals of Biomedical Engineering, 32(5), 706-719.

[8] Decuzzi, P., Causa, F., Ferrari, M. and Netti, P.A. (2006) The effective dispersion of nanovectors within the tumor microvasculature. Annals of Biomedical Engineering, 34(4), 633-641.

[9] Gentile, F., Ferrari, M. and Decuzzi, P. (2008) The transport of nanoparticles in blood vessels: The effect of vessel permeability and blood rheology. Annals of Biomedical Engineering, 2(36), 254-261.

[10] Gill, W.N. and Sankarasubramanian, R. (1970) Exact analysis of unsteady convective diffusion. Proceedings of the Royal Society of London, A, 316, 341-350.

[11] Decuzzi, P., Gentile, F., Granaldi, A., Curcio, A. and Indolfi, C. (2007) Flow chamber analysis of size effects in the adhesion of spherical particles. International Journal of NanoMedicine, 2(4), 1-8.

[12] Gentile, F., Chiappini, C., Fine, D., Bhavane, R.C., Pelu- ccio, M.S., Cheng, M., Liu, X., Ferrari, M. and Decuzzi, P. (2008) The margination dynamics of non spherical inertial particles in a microchannel. Journal of BioMechanics, 41(10), 2312-2318.

[13] Gentile, F., Curcio, A., Indolfi, C., Decuzzi, P. and Ferrari, M. (2008) The margination propensity of spherical particles for vascular targeting in the microcirculation. Journal of Nanobiotechnology, 6(9), 1-9.

[14] Lee, S.Y., Ferrari, M. and Decuzzi, P. (2009) Design of bio-mimetic particles with enhanced vascular interaction. Journal of Biomechanics, 42(12), 1885-1890.

[1] Taylor, G. (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proceedings of the Royal Society of London, A, 219(1137), 186-203.

[2] Aris, R. (1956) On the dispersion of a solute in a fluid fl- owing through a tube. Proceedings of the Royal Society of London, A, 235(1200), 67-77.

[3] Gill, W.N. (1967) A note on the solution of transient dis- persion problems. Proceedings of the Royal Society of London, A, 298(1967), 335-339.

[4] Sankarasubramanian, R. and Gill, W.N. (1973) Taylor diffusion in laminar flow in an eccentric annulus. Proceedings of the Royal Society of London, A, 333, 115-132.

[5] Sharp, M.K. (1993) Shear-augmented dispersion in non- Newtonian fluids. Annals of Biomedical Engineering, 21(4), 407-415.

[6] Dash, R.K., Jayaraman, G. and Mehta, K.N. (2000) Shear augmented dispersion of a solute in a casson fluid flowing in a conduit. Annals of Biomedical Engineering, 28(4), 373-385.

[7] Nagarani, P., Sarojamma, G. and Jayaraman, G. (2004) Effect of boundary absorption in dispersion in casson fluid flow in a tube. Annals of Biomedical Engineering, 32(5), 706-719.

[8] Decuzzi, P., Causa, F., Ferrari, M. and Netti, P.A. (2006) The effective dispersion of nanovectors within the tumor microvasculature. Annals of Biomedical Engineering, 34(4), 633-641.

[9] Gentile, F., Ferrari, M. and Decuzzi, P. (2008) The transport of nanoparticles in blood vessels: The effect of vessel permeability and blood rheology. Annals of Biomedical Engineering, 2(36), 254-261.

[10] Gill, W.N. and Sankarasubramanian, R. (1970) Exact analysis of unsteady convective diffusion. Proceedings of the Royal Society of London, A, 316, 341-350.

[11] Decuzzi, P., Gentile, F., Granaldi, A., Curcio, A. and Indolfi, C. (2007) Flow chamber analysis of size effects in the adhesion of spherical particles. International Journal of NanoMedicine, 2(4), 1-8.

[12] Gentile, F., Chiappini, C., Fine, D., Bhavane, R.C., Pelu- ccio, M.S., Cheng, M., Liu, X., Ferrari, M. and Decuzzi, P. (2008) The margination dynamics of non spherical inertial particles in a microchannel. Journal of BioMechanics, 41(10), 2312-2318.

[13] Gentile, F., Curcio, A., Indolfi, C., Decuzzi, P. and Ferrari, M. (2008) The margination propensity of spherical particles for vascular targeting in the microcirculation. Journal of Nanobiotechnology, 6(9), 1-9.

[14] Lee, S.Y., Ferrari, M. and Decuzzi, P. (2009) Design of bio-mimetic particles with enhanced vascular interaction. Journal of Biomechanics, 42(12), 1885-1890.