analysis of particle trajectories for magnetic drug targeting€¦ · analysis of particle...
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Analysis of particle trajectories for magnetic drugtargeting
Alexandra Heidsieck, Bernhard Gleich
Presented at the COMSOL Conference 2010 Paris
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Overview
1 Introduction
2 SimulationComsolMatlab
3 Results
4 Conclusion and Outlook
Introduction Simulation Results Conclusion and Outlook The End
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Nanoguide
Goals• Magnetic labeling of cells and viral
vectors with magnetic nanoparticles
• Targeted transfer of genetic materialin the cardiovascular system
• Accumulation of the labeled materialin blood vessels and the heart
Introduction Simulation Results Conclusion and Outlook The End
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Nanoguide
Optimized field sources
• Homogeneous distribution of particles inartery
• Accumulation of particles in a certain region
.
Prediction and manipulation of particletrajectories
Introduction Simulation Results Conclusion and Outlook The End
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Theory
Forces on the particles
• Magnetic force (∝ ∇|B|)• Hydrodynamic force (Stokes Law)
• Minor forces (e.g. gravitation,avalanche effect, . . . )
.
Major forces can be calculated withComsol
.
Algorithm for the equation of motion
Introduction Simulation Results Conclusion and Outlook The End
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Homogeneous distribution of particles
Geometry
• Mouse aorta
• Surrounded by four groups of threemagnets
• Laminar inflow, constant outletpressure
• Non-newtonian fluid (CarreauModel)
Introduction Simulation Results Conclusion and Outlook The End
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Magnetostatics
Introduction Simulation Results Conclusion and Outlook The End
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Fluiddynamics
Introduction Simulation Results Conclusion and Outlook The End
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Particle Trajectories
Problems with Comsol• Gradient on the mesh
• Stiff differential equation
• No “random“ parameters
Introduction Simulation Results Conclusion and Outlook The End
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Processing in Matlab
Matlab• Export into Matlab
• Spline interpolation of the magneticand fluidic fields
• Gradient on the Spline
• Generating particle properties
• Solving the differential equation
Introduction Simulation Results Conclusion and Outlook The End
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Particle Trajectories
Exemplary trajectories of ten particles
Introduction Simulation Results Conclusion and Outlook The End
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Particle Distribution
Introduction Simulation Results Conclusion and Outlook The End
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Particle Distribution (weighted by diameter)
Introduction Simulation Results Conclusion and Outlook The End
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Size Distribution
Introduction Simulation Results Conclusion and Outlook The End
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Experimental Results
Experimental data by D. Wenzel, Universitat Bonn
Introduction Simulation Results Conclusion and Outlook The End
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Conclusion
Conclusion• Successful simulation of particle
trajectories
• Possible to find the optimal particle types
• Design of adequate field sources
Introduction Simulation Results Conclusion and Outlook The End
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Outlook
Outlook• Minor forces
• Magnetisation of particles
• Fluid-structure interaction
• More complicated geometries
Introduction Simulation Results Conclusion and Outlook The End
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The End
Thank You for Your Attention!.
Introduction Simulation Results Conclusion and Outlook The End
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Properties
• vin = 0.2 m/s
• dnp = 100 nm
• mnp = 2 · 10−19 kg
• µnp = 5 · 10−13 Am2
• m~v = µ∇B + 6πη(γ)rnp(~u − ~v)−m~g
• η(γ) = η∞ + (η0 − η∞) ·(1 + (λγ)2
)n−1/2
Introduction Simulation Results Conclusion and Outlook The End
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References
Christoph Alexiou, Wolfgang Arnold, Roswitha J Klein, Fritz G Parak, Peter Hulin, Christian Bergemann,
Wolf Erhardt, S Wagenpfeil, and Andreas S Luebbe.Locoregional cancer treatment with magnetic drug targeting.Cancer Research, 60:6641–6648, 2000.
Christoph Alexiou, R Jurgons, R Schmid, A Hilpert, Christian Bergemann, Fritz G Parak, and H Iro.
In vitro and in vivo investigations of targeted chemotherapy with magnetic nanoparticles.J. Magn. Mater., 293:389–393, 2005.
Petra Dames, Bernhard Gleich, Andreas Flemmer, Kerstin Hajek, Nicole Seidl, Frank Wiekhorst, Dietmar
Eberbeck, Iris Bittmann, Christian Bergemann, Thomas Weyh, Lutz Trahms, Joseph Rosenecker, andCarsten Rudolph.Targeted delivery of magnetic aerosol droplets to the lung.Nature Nanotechnology, 2:495–499, 2007.
Bernhard Gleich, Thomas Weyh, and Bernhard Wolf.
Magnetic Drug Targeting: An Analytical Model for the Influence of Blood Properties on ParticleTrajectories.Applied Rheology, 18(5):1–7, 2008.
S. S. Shibeshi and W. E. Collins.
The Rheology of Blood Flow in a Branched Arterial System.Applied Rheology, 6:398–405, 2005.
Introduction Simulation Results Conclusion and Outlook The End