Abstract
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.
Similar content being viewed by others
References
Baish, J. W., P. A. Netti, and R. K. Jain. Transmural coupling of fluid flow in microcirculatory network and interstitium in tumors. Microvasc. Res. 53:128–141, 1997.
Baxter, L. T., and R. K. Jain. Transport of fluid and macromolecules in tumors. II. Role of heterogeneous perfusion and lymphatics. Microvasc. Res. 40:246–263, 1990.
Boucher, Y., and R. K. Jain. Microvascular pressure is the principal driving force for interstitial hypertension in solid tumors: implications for vascular collapse. Cancer Res. 52:5110–5114, 1992.
Bungay, P. M., and H. Brenner. The motion of a closely fitting sphere in a fluid-filled tube. Int. J. Multiph. Flow 1:25–56, 1973.
Campbell, R. B., D. Fukumura, E. B. Brown, L. M. Mazzola, Y. Izumi, R. K. Jain, V. P. Torchilin, and L. L. Munn. Cationic charge determines the distribution of liposomes between the vascular and extravascular compartments of tumors. Cancer Res. 62:6831–6836, 2002.
Chauhan, V. P., Z. Popovic, O. Chen, J. Cui, D. Fukumura, M. G. Bawendi, and R. K. Jain. Fluorescent nanorods and nanospheres for real-time in vivo probing of nanoparticle shape-dependent tumor penetration. Angew. Chem. Int. Ed. Engl. 50:11417–11420, 2011.
Chauhan, V. P., T. Stylianopoulos, Y. Boucher, and R. K. Jain. Delivery of molecular and nanomedicine to tumors: transport barriers and strategies. Annu. Rev. Chem. Biomol. Eng. 2:281–298, 2011.
Chauhan, V. P., T. Stylianopoulos, J. D. Martin, Z. Popovic, O. Chen, W. S. Kamoun, M. G. Bawendi, D. Fukumura, and R. K. Jain. Normalization of tumour blood vessels improves the delivery of nanomedicines in a size-dependent manner. Nat. Nanotechnol. 7:383–388, 2012.
Clauss, M. A., and R. K. Jain. Interstitial transport of rabbit and sheep antibodies in normal and neoplastic tissues. Cancer Res. 50:3487–3492, 1990.
Decuzzi, P., and M. Ferrari. Design maps for nanoparticles targeting the diseased microvasculature. Biomaterials 29:377–384, 2008.
Deen, W. M. Hindered transport of large molecules in liquid-filled pores. AIChE J. 33:1409–1425, 1987.
Dellian, M., F. Yuan, V. S. Trubetskoy, V. P. Torchilin, and R. K. Jain. Vascular permeability in a human tumour xenograft: molecular charge dependence. Br. J. Cancer 82:1513–1518, 2000.
Diop-Frimpong, B., V. P. Chauhan, S. Krane, Y. Boucher, and R. K. Jain. Losartan inhibits collagen I synthesis and improves the distribution and efficacy of nanotherapeutics in tumors. Proc. Natl. Acad. Sci. USA 108:2909–2914, 2011.
Gerlowski, L. E., and R. K. Jain. Microvascular permeability of normal and neoplastic tissues. Microvasc. Res. 31:288–305, 1986.
Hashizume, H., P. Baluk, S. Morikawa, J. W. McLean, G. Thurston, S. Roberge, R. K. Jain, and D. M. McDonald. Openings between defective endothelial cells explain tumor vessel leakiness. Am. J. Pathol. 156:1363–1380, 2000.
Hobbs, S. K., W. L. Monsky, F. Yuan, W. G. Roberts, L. Griffith, V. P. Torchilin, and R. K. Jain. Regulation of transport pathways in tumor vessels: role of tumor type and microenvironment. Proc. Natl. Acad. Sci. USA 95:4607–4612, 1998.
Hood, J. D., M. Bednarski, R. Frausto, S. Guccione, R. A. Reisfeld, R. Xiang, and D. A. Cheresh. Tumor regression by targeted gene delivery to the neovasculature. Science 296:2404–2407, 2002.
Jain, R. K. Transport of molecules across tumor vasculature. Cancer Metastasis Rev. 6:559–593, 1987.
Jain, R. K. Determinants of tumor blood flow: a review. Cancer Res. 48:2641–2658, 1988.
Jain, R. K. Normalizing tumor vasculature with anti-angiogenic therapy: a new paradigm for combination therapy. Nat. Med. 7:987–989, 2001.
Jain, R. K. Normalization of tumor vasculature: an emerging concept in antiangiogenic therapy. Science 307:58–62, 2005.
Jain, R. K., and T. Stylianopoulos. Delivering nanomedicine to solid tumors. Nat. Rev. Clin. Oncol. 7:653–664, 2010.
Longmire, M., P. L. Choyke, and H. Kobayashi. Clearance properties of nano-sized particles and molecules as imaging agents: considerations and caveats. Nanomedicine (Lond) 3:703–717, 2008.
McDougall, S. R., A. R. Anderson, and M. A. Chaplain. Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. J. Theor. Biol. 241:564–589, 2006.
Netti, P. A., D. A. Berk, M. A. Swartz, A. J. Grodzinsky, and R. K. Jain. Role of extracellular matrix assembly in interstitial transport in solid tumors. Cancer Res. 60:2497–2503, 2000.
Nugent, L. J., and R. K. Jain. Extravascular diffusion in normal and neoplastic tissues. Cancer Res. 44:238–244, 1984.
Park, S., and K. Hamad-Schifferli. Evaluation of hydrodynamic size and zeta-potential of surface-modified Au nanoparticle-DNA conjugates via Ferguson analysis. J. Phys. Chem. 112:7611–7676, 2008.
Pluen, A., Y. Boucher, S. Ramanujan, T. D. McKee, T. Gohongi, E. di Tomaso, E. B. Brown, Y. Izumi, R. B. Campbell, D. A. Berk, and R. K. Jain. Role of tumor-host interactions in interstitial diffusion of macromolecules: cranial vs. subcutaneous tumors. Proc. Natl. Acad. Sci. USA 98:4628–4633, 2001.
Popovic, Z., W. Liu, V. P. Chauhan, J. Lee, C. Wong, A. B. Greytak, N. Insin, D. G. Nocera, D. Fukumura, R. K. Jain, and M. G. Bawendi. A nanoparticle size series for in vivo fluorescence imaging. Angew. Chem. Int. Ed. Engl. 49:8649–8652, 2010.
Ruoslahti, E., S. N. Bhatia, and M. J. Sailor. Targeting of drugs and nanoparticles to tumors. J. Cell Biol. 188:759–768, 2010.
Sarin, H. Physiologic upper limits of pore size of different blood capillary types and another perspective on the dual pore theory of microvascular permeability. J. Angiogenes Res. 2:14, 2010.
Schmitt-Sody, M., S. Strieth, S. Krasnici, B. Sauer, B. Schulze, M. Teifel, U. Michaelis, K. Naujoks, and M. Dellian. Neovascular targeting therapy: paclitaxel encapsulated in cationic liposomes improves antitumoral efficacy. Clin. Cancer Res. 9:2335–2341, 2003.
Sevick, E. M., and R. K. Jain. Viscous resistance to blood flow in solid tumors: effect of hematocrit on intratumor blood viscosity. Cancer Res. 49:3513–3519, 1989.
Smith, F. G., and W. M. Deen. Electrostatic effects on the partitioning of spherical colloids between dilute bulk solution and cylindrical pores. J. Colloid Interface Sci. 91:571–590, 1983.
Stohrer, M., Y. Boucher, M. Stangassinger, and R. K. Jain. Oncotic pressure in solid tumors is elevated. Cancer Res. 60:4251–4255, 2000.
Stylianopoulos, T., M. Z. Poh, N. Insin, M. G. Bawendi, D. Fukumura, L. L. Munn, and R. K. Jain. Diffusion of particles in the extracellular matrix: the effect of repulsive electrostatic interactions. Biophys. J. 99:1342–1349, 2010.
Stylianopoulos, T., A. Yeckel, J. J. Derby, X. J. Luo, M. S. Shephard, E. A. Sander, and V. H. Barocas. Permeability calculations in three-dimensional isotropic and oriented fiber networks. Phys Fluids (1994) 20:123601, 2008.
Sugahara, K. N., T. Teesalu, P. P. Karmali, V. R. Kotamraju, L. Agemy, O. M. Girard, D. Hanahan, R. F. Mattrey, and E. Ruoslahti. Tissue-penetrating delivery of compounds and nanoparticles into tumors. Cancer Cell 16:510–520, 2009.
Tong, R. T., Y. Boucher, S. V. Kozin, F. Winkler, D. J. Hicklin, and R. K. Jain. Vascular normalization by vascular endothelial growth factor receptor 2 blockade induces a pressure gradient across the vasculature and improves drug penetration in tumors. Cancer Res. 64:3731–3736, 2004.
Torchilin, V. P. Targeted pharmaceutical nanocarriers for cancer therapy and imaging. AAPS J. 9:E128–E147, 2007.
Wong, C., T. Stylianopoulos, J. Cui, J. Martin, V. P. Chauhan, W. Jiang, Z. Popovic, R. K. Jain, M. G. Bawendi, and D. Fukumura. Multistage nanoparticle delivery system for deep penetration into tumor tissue. Proc. Natl. Acad. Sci. USA 108:2426–2431, 2011.
Wu, J., S. Xu, Q. Long, M. W. Collins, C. S. Konig, G. Zhao, Y. Jiang, and A. R. Padhani. Coupled modeling of blood perfusion in intravascular, interstitial spaces in tumor microvasculature. J. Biomech. 41:996–1004, 2008.
Yuan, F., M. Dellian, D. Fukumura, M. Leunig, D. A. Berk, V. P. Torchilin, and R. K. Jain. Vascular permeability in a human tumor xenograft: molecular size dependence and cutoff size. Cancer Res. 55:3752–3756, 1995.
Yuan, F., M. Leunig, S. K. Huang, D. A. Berk, D. Papahadjopoulos, and R. K. Jain. Microvascular permeability and interstitial penetration of sterically stabilized (stealth) liposomes in a human tumor xenograft. Cancer Res. 54:3352–3356, 1994.
Yuan, F., H. A. Salehi, Y. Boucher, U. S. Vasthare, R. F. Tuma, and R. K. Jain. Vascular permeability and microcirculation of gliomas and mammary carcinomas transplanted in rat and mouse cranial windows. Cancer Res. 54:4564–4568, 1994.
Acknowledgments
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.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Associate Editor Konstantinos Konstantopoulos oversaw the review of this article.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Stylianopoulos, T., Soteriou, K., Fukumura, D. et al. Cationic Nanoparticles Have Superior Transvascular Flux into Solid Tumors: Insights from a Mathematical Model. Ann Biomed Eng 41, 68–77 (2013). https://doi.org/10.1007/s10439-012-0630-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10439-012-0630-4