Abstract
It has been demonstrated from recent research that modern uses of multiscale analysis, uncertainty quantification techniques, and validation experiments is essential for the design of nanodevices in biotechnology and medicine. The 3D immersed molecular electrokinetic finite element method (IMEFEM) will be presented for the modeling of micro fluidic electrokinetic assembly of nanowires, filaments and bio-molecules. This transformative bio-nanotechnology is being developed to enable gene delivery systems to achieve desired therapeutic effects and for the design and optimization of an electric field enabled nanotip DNA sensor. For the nanodiamond-based drug delivery device we will discuss the multiscale analysis, quantum and molecular mechanics, immersed molecular finite element and meshfree methods, uncertainty quantification, and validation experiments. In addition, we will describe the mathematical formulation of pH control interactions among chemically functionalized nanodiamonds, and their interactions with polymers. For the nanotip sensor, we will discuss the underlying mechanics and physical parameters influencing the bio-sensing efficiency, such as the threshold of applied electric field, biomolecule deformation, and nanoscale Brownian motion. Through multiscale analysis, we provide guidelines for nanodevice design, including fundamental mechanisms driving the system performance and optimization of distinct parameters.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
A. Adnan, R. Lam, H. Chen, J. Lee, D. Schaffer, A. Barnard, G. Schatz, D. Ho, W.K. Liu, Atomistic simulation and measurement of ph dependent cancer therapeutic interactions with nanodiamond carrier. Mol. Pharm. 8, 368–374 (2011)
M. Gay, L. Zhang, W.K. Liu, Stent modeling using immersed finite element method. Comput. Methods Appl. Mech. Eng. 195, 4358–4370 (2006)
A.M. Kopacz, W.K. Liu, S.Q. Liu, Simulation and prediction of endothelial cell adhesion modulated by molecular engineering. Comput. Methods Appl. Mech. Eng. 197(25–28), 2340–2352 (2008)
A.M. Kopacz, N. Patankar, W.K. Liu, The immersed molecular finite element method. Comput. Methods Appl. Mech. Eng. 233–236, 28–39 (2012)
J. Kotz, P. Treichel, J. Townsend, Chemistry and Chemical Reactivity (Brooks Cole, Belmont, 2009)
T.R. Lee, Y.S. Chang, J.B. Choi, D.W. Kim, W.K. Liu, Y.J. Kim, Immersed finite element method for rigid body motions in the incompressible navier-stokes flow. Comput. Methods Appl. Mech. Eng. 197(25–28), 2305–2316 (2008)
Y. Liu, W.K. Liu, Rheology of red blood cell aggregation by computer simulation. J. Comput. Phys. 220(1), 139–154 (2006)
Y. Liu, L. Zhang, X. Wang, W.K. Liu, Coupling of navier-stokes equations with protein molecular dynamics and its application to hemodynamics. Int. J. Numer. Methods Fluids 46, 1237–1252 (2004)
Y. Liu, J.H. Chung, W.K. Liu, R. Ruoff, Dielectrophoretic assembly of nanowires. J. Phys. Chem. B 110(29), 14098–14106 (2006)
W.K. Liu, D.W. Kim, S. Tang, Mathematical foundations of the immersed finite element method. Comput. Mech. 39, 211–222 (2006)
W.K. Liu, Y. Liu, D. Farrell, L. Zhang, X.S. Wang, Y. Fukui, N. Patankar, Y. Zhang, C. Bajaj, J. Lee, J. Hong, X. Chen, H. Hsua, Immersed finite element method and its applications to biological systems. Comput. Methods Appl. Mech. Eng. 195, 1722–1749 (2006)
Y. Liu, W.K. Liu, T. Belytschko, N. Patankar, A.C. To, A.M. Kopacz, J.H. Chung, Immersed electrokinetic finite element method. Int. J. Numer. Methods Eng. 71, 379–405 (2007)
P. Uthe, The development of polycationic materiala for gene delivery applications, Ph.D. dissertation, University of North Carolina, Chapel Hill (2010)
X. Wang, W.K. Liu, Extended immersed boundary method using fem and rkpm. Comput. Methods Appl. Mech. Eng. 193(12–14), 1305–1321 (2004)
L. Zhang, A. Gerstenberger, X. Wang, W.K. Liu, Immersed finite element method. Comput. Methods Appl. Mech. Eng. 193(21–22), 2051–2067 (2004)
X.Q. Zhang, M. Chen, R. Lam, X. Xu, E. Osawa, D. Ho, Polymer-functionalized nanodiamond platforms as vehicles for gene delivery. ACS Nano 3, 2609–2616 (2009)
Acknowledgements
This work was supported by NSF CMMI 0856333 and NSF CMMI 0856492. WKL is supported by World Class University Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (R33-10079).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, W.K., Kopacz, A.M., Lee, TR., Kim, H., Decuzzi, P. (2013). Immersed Molecular Electrokinetic Finite Element Method for Nano-devices in Biotechnology and Gene Delivery. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations VI. Lecture Notes in Computational Science and Engineering, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32979-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-32979-1_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32978-4
Online ISBN: 978-3-642-32979-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)