Dynamics of Magnetic Nanoparticles in Newly Formed Microvascular Networks Surrounding Solid Tumours: A Parallel Programming Approach
Cancer Research Journal
Volume 4, Issue 1, January 2016, Pages: 9-23
Received: Dec. 14, 2015; Accepted: Dec. 31, 2015; Published: Jan. 21, 2016
Views 2790      Downloads 62
Author
Paul M. Darbyshire, Computational Biophysics Group, Algenet Cancer Research, Nottingham, UK
Article Tools
Follow on us
Abstract
In this paper we extend a previous 2D parallel implementation of a continuous-discrete model of tumour-induced angiogenesis. In particular, we examine the transport and capture of magnetic nanoparticles through a newly formed vascular network of blood vessels. We demonstrate how our models can be used to describe the dynamics of magnetic nanoparticles in a microvasculature and observe that the orientation of the blood vessels with respect to the magnetic force crucially affects particle capture rates leading to heterogeneous particle distributions. In addition, efficiency of magnetic particle capture depends on the ratio between the magnetic velocity and blood vessel aspect ratio. Such simulations allow a more detailed understanding of the use of magnetic nanoparticles as a mechanism for targeted anti-cancer drug delivery.
Keywords
Nanotechnology, Microvascular Network, High Performance Computing (HPC), Compute Unified Device Architecture (CUDA), Graphical Processing Unit (GPU), Parallel Processing
To cite this article
Paul M. Darbyshire, Dynamics of Magnetic Nanoparticles in Newly Formed Microvascular Networks Surrounding Solid Tumours: A Parallel Programming Approach, Cancer Research Journal. Vol. 4, No. 1, 2016, pp. 9-23. doi: 10.11648/j.crj.20160401.12
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
Albini, A., Tosetti, A. F., Li, W. V., Noonan, D. M. and Li, W. W. Cancer prevention by targeting angiogenesis Nature Reviews Clinical Oncology 9, 498-509. 2012.
[2]
Ferrara, N. and Kerbel, R. S. Angiogenesis as a therapeutic target. Nature, 438 967–974. 2005.
[3]
Carmeliet, P. Angiogenesis in life, disease and medicine. Nature, 438: 932–936. 2005.
[4]
Bouard S. de, Herlin, P. and Christensen, J. G. Antiangiogenic and anti-invasive effects of sunitinib on experimental human glioblastoma. Neuro-Oncology, Vol. 9, No. 4, 412–423. 2007.
[5]
Norden, A. D, Drappatz, J. and Wen P. Y. Novel antiangiogenic therapies for malignant gliomas. The Lancet Neurology, Vol. 7, No. 12, 1152–1160. 2008.
[6]
Peirce, S. M. Computational and mathematical modeling of angiogenesis. Microcirculation, 15 (8), 739–751. 2008.
[7]
M. Scianna, M., Bell. C. and Preziosi L. A review of mathematical models for the formation of vascular networks. Oxford Centre for Collaborative Applied Mathematics. 2012.
[8]
Rejniak A. K. and Anderson A. R. A. Hybrid models of tumor growth. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 3 (1), 115–125. 2011.
[9]
Darbyshire, P. M. Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup. Computational Biology and Bioinformatics. Vol. 3, No. 5, 65-73. 2015.
[10]
Darbyshire, P. M. The Numerical Solution of a Hybrid Continuous-Discrete Model of Tumour-Induced Angiogenesis is Implemented in Parallel and Performance Improvements Analysed. European Journal of Biophysics. Vol. 7, No. 4, 167-182. 2015.
[11]
Darbyshire, P. M. Performance Optimisations for a Numerical Solution to a 3D Model of Tumour-Induced Angiogenesis on a Parallel Programming Platform. Cell Biology. Vol. 5, No. 3, 38-49. 2015.
[12]
Darbyshire, P. M. 3D Visualisation of Tumour-Induced Angiogenesis Using the CUDA Programming Model and OpenGL Interoperability. Journal of Cancer Treatment and Research. Vol. 3, No. 5, 53-65. 2015.
[13]
Paweletz, N. and M. Knierim M. Tumor-related angiogenesis. Critical Reviews in Oncology and Hematology, 9, 197–242. 1989.
[14]
Paku, S. and N. Paweletz. First steps of tumor-related angiogenesis. Laboratory Investigation, 65, 334–346. 1991.
[15]
Schor S. L., Schor A. M., Brazill G. W. The effects of fibronectin on the migration of human foreskin fibroblasts and Syrian hamster melanoma cells into three-dimensional gels of lattice collagen fibres. Journal of Cell Science, 48, 301–314, 1981.
[16]
Bowersox J. C. and Sorgente N. Chemotaxis of aortic endothelial cells in response to fibronectin. Cancer Research 42, 2547–2551. 1982.
[17]
Quigley J. P., Lacovara J., and Cramer E. B. The directed migration of B-16 melanoma-cells in response to a haptotactic chemotactic gradient of fibronectin. Journal of Cell Biology 97, A450–451. 1983.
[18]
Stokes C. L., Lauffenburger D. A., and Williams S. K. Migration of individual microvessel endothelial cells: stochastic model and parameter measurement. Journal of Cell Science, 99: 419–430. 1991.
[19]
Stokes C. L., Rupnick M. A., Williams S. K., and Lauffenburger D. A. Chemotaxis of human microvessel endothelial cells in response to acidic fibroblast growth factor. Laboratory Investigation, 63, 657–668, 1991.
[20]
Stokes C. L., and Lauffenburger D. A. Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. Journal of Theoretical Biology, 152, 377–403. 1991.
[21]
Anderson, A. R. A. and Chaplain, M. Continuous and discrete mathematical models of tumour-induced angiogenesis, Bulletin of Mathematical Biology, 60, 857-900. 1998.
[22]
Anderson, A. R. A., Sleeman, B. D. S., Young, I. M. and Griffiths, B. S. Nematode movement along a chemical gradient in a structurally heterogeneous environment: II. Theory. Fundamental and Applied Nematology, 20, 165–172. 1997.
[23]
Muthukkaruppan, V. R., Kubai, L., and Auerbach, R. Tumor-induced neovascularization in the mouse eye. Journal of the National Cancer Institute, 69, 699–705. 1982.
[24]
Paweletz, N. and Knierim M. Tumor-related angiogenesis. Critical Reviews in Oncology and Hematology, 9, 197–242. 1989.
[25]
Williams, S. K. Isolation and culture of microvessel and large-vessel endothelial cells; their use in transport and clinical studies. Microvascular Perfusion and Transport in Health and Disease, 204–245. 1987.
[26]
Cho, K. J., Wang, X., Nie, S. M., Chen, Z., and Shin, D. M. Therapeutic nanoparticles for drug delivery in cancer. Clinical Cancer Research, 14, 1310-1316. 2008.
[27]
Lammers, T., Hennink, W. E., and Storm, G. Tumour-targeted nanomedicines: principles and practice. British Journal of Cancer, 99(3), 392-397. 2008.
[28]
Lammers, T., Kiessling, F., Hennink, W. E., and Storm, G. Drug targeting to tumors: principles, pitfalls and (pre-) clinical progress. Journal of Controlled Release, 161(2), 175-87. 2012.
[29]
Farrell, D., Ptak, K., Panaro, N. J., and Grodzinski, P. Nanotechnology-based cancer therapeutics--promise and challenge--lessons learned through the NCI Alliance for Nanotechnology in Cancer. Pharmaceutical Research. 8 (2), 273-278. 2011.
[30]
Markovsky, E., Baabur-Cohen, H., Eldar-Boock, A., Omer, L., Tiram, G., Ferber, S., Ofek, P., Polyak, D., Scomparin, A., and Satchi-Fainaro, R. Administration, distribution, metabolism and elimination of polymer therapeutics. Journal of Controlled Release, 161 (2), 446-460. 2012.
[31]
Holgado, M. A., Martin-Banderas, L., Alvarez-Fuentes, J., Fernandez-Arevalo, M., and Arias, J. L. Drug targeting to cancer by nanoparticles surface functionalized with special biomolecules. Current Medicinal Chemistry, 19, 3188-3195. 2012.
[32]
Basile, L., Pignatello, R., and Passirani, C. Active targeting strategies for anticancer drug nanocarriers. Current Drug Delivery, 9, 255-268. 2012.
[33]
Daniels, T. R., Bernabeu, E., Rodríguez, J. A., Patel, S., Kozman, M., Chiappetta, D. A., Holler, E., Ljubimova, J. Y., Helguera, G., and Penichet, M. L. The transferrin receptor and the targeted delivery of therapeutic agents against cancer. Biochimica et Biophysica Acta, 820(3), 291-317. 2012.
[34]
Li, C., Li, L., and Keates, A. C. Targeting Cancer Gene Therapy with Magnetic Nanoparticles. Oncotarget, 3, 365-370. 2012.
[35]
Thakor, A. S., and Gambhir, S. S. Nanooncology: The Future of Cancer Diagnosis and Therapy. A Cancer Journal for Clinicians, 63, 395–418. 2013.
[36]
Gobbo, O. L., Sjaastad, K., Radomski, M. W., Volkov, Y., and Prina-Mello, A. Magnetic Nanoparticles in Cancer Theranostics. Theranostics, 5(11), 1249-1263. 2015.
[37]
Grief, A. D, and Richardson, G. Mathematical modelling of magnetically targeted drug delivery. Journal of Magnetism and Magnetic Materials, 293, 455–463. 2005.
[38]
Furlani, E. P., and Ng, K. C. Analytical model of magnetic nanoparticle transport and capture in the microvasculature. Physical Review E, 73, 061919. 2006.
[39]
Babincova, M., and Babinec, P. Magnetic Drug Delivery and Targeting: Principles and Applications. Biomedical papers of the Medical Faculty of the University Palacky, Olomouc, Czechoslovakia, 53(4), 243–250. 2009.
[40]
Furlani, E. P. Magnetic Biotransport: Analysis and Applications. Materials, 3, 2412-2446. 2010.
[41]
Valova, L., Jadlovsky, J., Streltsova, O. I., Kopcansky, P, Hnatic, M., Timko, M., Kubovcikova, M., Koneracka, M., and Zavisova, V. Numerical Modeling of Nanoparticles Tracking in the Blood Stream. Mathematical Modeling and Computational Science, 7125, 284-289. 2012.
[42]
Cherry, E. M., and Eaton, J. K. A comprehensive model of magnetic particle motion during magnetic drug targeting. International Journal of Multiphase Flow, 59, 173–185. 2014.
[43]
Sharma, S., Katiar, V. K., and Uaday, S. Mathematical Modelling of Magnetic Nanoparticles in a Blood Vessel in a Magnetic Field. Journal of Magnetism and Magnetic Materials, 379, 102-107. 2015.
[44]
Uthra, C. R., and Vasanthakumari, R. A Mathematical Model for the Movement of Magnetic Nanoparticles in the Field of Small Magnets Described by Poiseuille Flow. Applied Mathematics, 5 (3): 68-72. 2015.
[45]
Nvidia Corporation. CUDA C programming guide. Version 6.0. 2014.
[46]
Cheng, J., Grossman, M and McKercher, Ty. Professional CUDA C Programming. Wrox. 2014.
ADDRESS
Science Publishing Group
548 FASHION AVENUE
NEW YORK, NY 10018
U.S.A.
Tel: (001)347-688-8931