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The Transport of Nanoparticles in Blood Vessels: The Effect of Vessel Permeability and Blood Rheology

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Abstract

The longitudinal transport of nanoparticles in blood vessels has been analyzed with blood described as a Casson fluid. Starting from the celebrated Taylor and Aris theory, an explicit expression has been derived for the effective longitudinal diffusion (D eff) depending non-linearly on the rheological parameter ξc, the ratio between the plug and the vessel radii; and on the permeability parameters \(\Uppi\) and \(\Upomega ,\) related to the hydraulic conductivity and pressure drop across the vessel wall, respectively. An increase of ξc or \(\Uppi\) has the effect of reducing D eff, and thus both the rheology of blood and the permeability of the vessels may constitute a physiological barrier to the intravascular delivery of nanoparticles.

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Notes

  1. Notice that the expression \(G(\xi_{\rm c}) A^{2}(\xi_{\rm c})\) in Eq. (24) is slightly different from a similar function E(z c) introduced in Sharp.15

References

  1. Ananthakrishnan V., Gill W. N., Barduhn A. J. (1965) Laminar dispersion in capillaries: Part I. Mathematical analysis. AIChE J. 11:1063–1072

    Article  CAS  Google Scholar 

  2. Aris R. (1956) On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235(1200):67–77

    Google Scholar 

  3. Decuzzi P., et al. (2004) Adhesion of microfabricated particles on vascular endothelium: a parametric analysis. Ann. Biomed. Eng. 32(6):793–802

    Article  PubMed  Google Scholar 

  4. Decuzzi P., Causa F., Ferrari M., Netti P. A. (2006) The effective dispersion of Nanovectors within the tumor microvasculature. Ann. Biomed. Eng. 34:633–641

    Article  PubMed  CAS  Google Scholar 

  5. Fahraeus R. (1929) The suspension stability of the blood. Physiol. Rev. 9:241–274

    Google Scholar 

  6. Fung Y. C. (1990) Biomechanics. Springer, New York

    Google Scholar 

  7. Ganong W. F. (2003) Review of medical physiology, 21st ed. Lange Medical Books/McGraw-Hill, Medical Publishing Division, New York

    Google Scholar 

  8. Gentile, F., C. Chiappini, R. C. Bhavane, M. S. Peluccio, M. Ming-Cheng Cheng, X. Liu, M. Ferrari, and P. Decuzzi. Scaling laws in the margination dynamics of non-spherical inertial particles in a microchannel, submitted to J. Biomech

  9. Gill W. N. (1967) A note on the solution of transient dispersion problems. Proc. R. Soc. Lond. A 298:335–339

    CAS  Google Scholar 

  10. Gill W. N., Sankarasubramanian R. (1970) Exact analysis of unsteady convective diffusion. Proc. R. Soc. Lond. A 316:341–350

    Article  Google Scholar 

  11. Latini M., Bernoff A. J. (2001) Transient anomalous diffusion in Poiseuille flow. J. Fluid Mech. 441:399–411

    Article  CAS  Google Scholar 

  12. Lindquist T. (1931) The viscosity of the blood in narrow capillary tubes. Am. J. Physiol. 96:562–568

    Google Scholar 

  13. Phillips C. G., Kaye S. R. (1997) The initial transient of concentration during the development of Taylor dispersion. Proc. R. Soc. Lond. A 453:2669–2688

    Google Scholar 

  14. Sharan M., Popel, AS (2001) A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall. Biorheology 38:415–428

    PubMed  CAS  Google Scholar 

  15. Sharp M. K. (1993) Shear-augmented dispersion in non-Newtonian fluids. Ann. Biomed. Eng. 21:407–415

    Article  PubMed  CAS  Google Scholar 

  16. Siegel P., Mosè R., Ackerer P. H., Jaffre J. (1997) Solution of the advection–diffusion equation using a combination of discontinuous and mixed finite elements. Int. J. Numer. Methods Fluids 24:595–613

    Article  Google Scholar 

  17. Taylor G. (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219(1137):186–203

    CAS  Google Scholar 

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Authors and Affiliations

  1. Center of Bio-/Nanotechnology and -/Engineering for Medicine – BioNEM, University of Magna Graecia at Catanzaro, Viale Europa – Loc. Germaneto, 88100, Catanzaro, Italy

    Francesco Gentile & Paolo Decuzzi

  2. The Brown Foundation Institute of Molecular Medicine for the Prevention of Human Diseases, The University of Texas Health Science Center, Houston, TX, 77031, USA

    Mauro Ferrari & Paolo Decuzzi

  3. The University of Texas M.D. Anderson Cancer Center, Houston, TX, USA

    Mauro Ferrari

  4. Rice University, Houston, TX, USA

    Mauro Ferrari

  5. Alliance for NanoHealth, Houston, TX, USA

    Mauro Ferrari

  6. Center of Excellence in Computational Mechanics – CEMeC, Politecnico di Bari, Via Re David 200, Bari, Italy

    Paolo Decuzzi

Authors
  1. Francesco Gentile
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  2. Mauro Ferrari
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  3. Paolo Decuzzi
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Correspondence to Paolo Decuzzi.

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Gentile, F., Ferrari, M. & Decuzzi, P. The Transport of Nanoparticles in Blood Vessels: The Effect of Vessel Permeability and Blood Rheology. Ann Biomed Eng 36, 254–261 (2008). https://doi.org/10.1007/s10439-007-9423-6

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  • DOI: https://doi.org/10.1007/s10439-007-9423-6

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