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Optimization and Engineering
Published in: Optimization and Engineering 3/2018

21-06-2018 | Research Article

Controlling the Kelvin force: basic strategies and applications to magnetic drug targeting

Authors: Harbir Antil, Ricardo H. Nochetto, Pablo Venegas

Published in: Optimization and Engineering | Issue 3/2018

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Abstract

Motivated by problems arising in magnetic drug targeting, we propose to generate an almost constant Kelvin (magnetic) force in a target subdomain, moving along a prescribed trajectory. This is carried out by solving a minimization problem with a tracking type cost functional. The magnetic sources are assumed to be dipoles and the control variables are the magnetic field intensity, the source location and the magnetic field direction. The resulting magnetic field is shown to effectively steer the drug concentration, governed by a drift-diffusion PDE, from an initial to a desired location with limited spreading.
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Appendix
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Literature
Antil H, Hintermüller M, Nochetto R, Surowiec T, Wegner D (2017) Finite horizon model predictive control of electrowetting on dielectric with pinning. Interfaces Free Bound 19(1):1–30MathSciNetCrossRefMATH
Antil H, Nochetto RH, Venegas P (2018) Optimal control of kelvin force in a bounded domain. Math Models Methods Appl Sci 28:95–130MathSciNetCrossRefMATH
Braides A (2014) Local minimization, variational evolution and \(\varGamma\)-convergence, vol 2094. Lecture notes in mathematics. Springer, ChamCrossRefMATH
Brezis H (2011) Functional analysis, Sobolev spaces and partial differential equations. Springer, BerlinMATH
Brezzi F, Marini LD, Pietra P (1989) Two-dimensional exponential fitting and applications to drift-diffusion models. SIAM J Numer Anal 26(6):1342–1355MathSciNetCrossRefMATH
Choi H, Temam R, Moin P, Kim J (1993) Feedback control for unsteady flow and its application to the stochastic Burgers equation. J Fluid Mech 253:509–543MathSciNetCrossRefMATH
Dal Maso G (1993) An introduction to \(\varGamma\)-convergence, vol 8. Progress in nonlinear differential equations and their applications. Birkhäuser Boston Inc, BostonCrossRef
Dobson J (2006) Gene therapy progress and prospects: magnetic nanoparticle-based gene delivery. Gene Ther 13:283–287CrossRef
Ern A, Guermond J-L (2004) Theory and practice of finite elements, vol 159. Applied mathematical sciences. Springer, New YorkMATH
Fountain TWR, Kailat PV, Abbott JJ (2010) Wireless control of magnetic helical microrobots using a rotating-permanent-magnet manipulator. In: 2010 IEEE international conference on robotics and automation (ICRA), pp 576–581
Gijs MAM, Lacharme F, Lehmann U (2010) Microfluidic applications of magnetic particles for biological analysis and catalysis. Chem Rev 110(3):1518–1563CrossRef
Grief AD, Richardson G (2005) Mathematical modelling of magnetically targeted drug delivery. J Magn Magn Mater 293:455–463CrossRef
Guermond J-L, Pasquetti R (2013) A correction technique for the dispersive effects of mass lumping for transport problems. Comput Methods Appl Mech Eng 253:186–198MathSciNetCrossRefMATH
Hintermüller M, Ito K, Kunisch K (2002) The primal-dual active set strategy as a semismooth newton method. SIAM J Optim 13(3):865–888MathSciNetCrossRefMATH
Hinze M, Kauffmann A (1999) On a distributed control law with an application to the control of unsteady flow around a cylinder. In: Hoffmann KH, Leugering G, Tröltzsch F, Caesar S (eds) optimal control of partial differential equations. ISNM international series of numerical mathematics, vol 133. Birkhäuser, Basel, pp 177–190CrossRef
Hosu BG, Jakab K, Bánki P, Tóth FI, Forgacs G (2003) Magnetic tweezers for intracellular applications. Rev Sci Instrum 74(9):4158–4163CrossRef
Johnson C (1987) Numerical solution of partial differential equations by the finite element method. Applied mathematical sciences. Springer, New YorkMATH
Kelley CT (1999) Iterative methods for optimization. Number 18 in frontiers in applied mathematics. SIAM, PhiladelphiaCrossRefMATH
Komaee A, Shapiro B (2011) Magnetic steering of a distributed ferrofluid spot towards a deep target with minimal spreading. In: 2011 50th IEEE conference on decision and control and European control conference (CDC-ECC), pp 7950–7955
Lim JK, Yeap SP, Low SC (2014) Challenges associated to magnetic separation of nanomaterials at low field gradient. Sep Purif Technol 123:171–174CrossRef
Lübbe AS, Bergemann C, Riess H, Schriever F, Reichardt P, Possinger K, Matthias M, Dörken B, Herrmann F, Gürtler R (1996) Clinical experiences with magnetic drug targeting: a phase I study with 4’-Epidoxorubicin in 14 patients with advanced solid tumors. Cancer Res 56(20):4686–4693
Mahoney AW, Abbott JJ (2011) Managing magnetic force applied to a magnetic device by a rotating dipole field. Appl Phys Lett 99:134103CrossRef
Markowich PA, Zlámal MA (1988) Inverse-average-type finite element discretizations of selfadjoint second-order elliptic problems. Math Comput 51(184):431–449MathSciNetCrossRefMATH
Nacev A, Beni C, Bruno O, Shapiro B (2011) The behaviors of ferro-magnetic nano-particles in and around blood vessels under applied magnetic fields. J Magn Magn Mater 323(6):651–668CrossRef
Nelson BJ, Kaliakatsos IK, Abbott JJ (2010) Microrobots for minimally invasive medicine. Annu Rev Biomed Eng 12:55–85CrossRef
Petruska AJ, Abbott JJ (2013) Optimal permanent-magnet geometries for dipole field approximation. IEEE Trans Magn 49:811–819CrossRef
Rosensweig RE (1997) Ferrohydrodynamics. Dover Publications, Mineola
Shapiro A, Dentcheva D, Ruszczyński A (2014) Lectures on stochastic programming: modeling and theory, volume 9 of MOS-SIAM series on optimization. Society for industrial and applied mathematics (SIAM). Mathematical Optimization Society, PhiladelphiaMATH
Solanki A, Kim JD, Lee K-B (2008) Nanotechnology for regenerative medicine: nanomaterials for stem cell imaging. Nanomedicine 3(4):567–578CrossRef
Tröltzsch F (2010) Optimal control of partial differential equations: theory, methods and applications, vol 112. Graduate Studies in Mathematics
Metadata
Title
Controlling the Kelvin force: basic strategies and applications to magnetic drug targeting
Authors
Harbir Antil
Ricardo H. Nochetto
Pablo Venegas
Publication date
21-06-2018
Publisher
Springer US
Published in
Optimization and Engineering / Issue 3/2018
Print ISSN: 1389-4420
Electronic ISSN: 1573-2924
DOI
https://doi.org/10.1007/s11081-018-9392-7

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