Annals of Biomedical Engineering

, Volume 41, Issue 1, pp 68–77 | Cite as

Cationic Nanoparticles Have Superior Transvascular Flux into Solid Tumors: Insights from a Mathematical Model

  • Triantafyllos StylianopoulosEmail author
  • Konstantinos Soteriou
  • Dai Fukumura
  • Rakesh K. JainEmail author


Despite their great promise, only a few nanoparticle formulations have been approved for clinical use in oncology. The failure of nano-scale drugs to enhance cancer therapy is in large part due to inefficient delivery. To overcome this outstanding problem, a better understanding of how the physical properties (i.e., size, surface chemistry, and shape) of nanoparticles affect their transvascular transport in tumors is required. In this study, we developed a mathematical model for nanoparticle delivery to solid tumors taking into account electrostatic interactions between the particles and the negatively-charged pores of the vessel wall. The model predictions suggest that electrostatic repulsion has a minor effect on the transvascular transport of nanoparticles. On the contrary, electrostatic attraction, caused even by small cationic charges (surface charge density less than 3 × 10−3 C/m2) can lead to a twofold or more increase in the transvascular flux of nanoparticles into the tumor interstitial space. Importantly, for every nanoparticle size, there is a value of charge density above which a steep increase in transvascular transport is predicted. Our model provides important guidelines for the optimal design of nanoparticle formulation for delivery to solid tumors.


Vascular permeability Electrostatic and hydrodynamic interactions Surface charge density Nanomedicine Cancer therapy 



The authors thank Dr. Vikash Chauhan for his insightful comments on the manuscript. This work was supported by a Marie-Curie International Reintegration Grant (No. PIRG08-GA-2010-276894), the National Cancer Institute (P01-CA080124, R01-CA126642, R01-CA115767, R01-CA096915, R01-CA085140, R01-CA098706, T32-CA073479, Federal Share Proton Beam Program Income Grant), and a DoD Breast Cancer Research Innovator award (W81XWH-10-1-0016).

Conflict of Interest

R.K.J. received research grants from Dyax, MedImmune and Roche; consultant fees from Dyax, Enlight, Noxxon and SynDevRx; owns equity in Enlight, SynDevRx and XTuit, serves on the Board of Directors of XTuit and Board of Trustees of H&Q Capital Management. No reagents or funding from these companies was used in these studies. Therefore, there is no significant financial or other competing interest in the work. The other authors declare no competing financial interests.

Supplementary material

10439_2012_630_MOESM1_ESM.pdf (287 kb)
Supplementary material 1 (PDF 287 kb)


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Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  1. 1.Department of Mechanical and Manufacturing EngineeringUniversity of CyprusNicosiaCyprus
  2. 2.Edwin L. Steele Laboratory for Tumor BiologyMassachusetts General Hospital, Harvard Medical SchoolBostonUSA

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