Magnetically-targeted drug and gene delivery

A problem presented at the UK MMSG Nottingham 2000.

Presented by:
Dr Jon Dobson (Department of Biomedical Engineering and Medical Physics, University of Keele)
SJ Chapman, LJ Cummings, J Dobson, E Gaffney, L Hazelwood, JR King, G Richardson

Problem Description

Novel applications for biocompatible, magnetic micro- and nanoparticles are being developed which include magnetically targeted drug and gene delivery. In these systems, therapeutic drugs or genes are attached to functionalized magnetic particles and injected near the target site. External magnetic fields of varying characteristics (usually produced by rare earth magnets) are applied to the site externally in order to concentrate the particles at the target. In the case of gene delivery, it is envisaged that this method will achieve higher transfection and hence expression rates. In the case of drug delivery, therapeutic drugs are concentrated at the site in the body where they are needed.

At present, there are several types of particles commercially available. These particles vary in size, magnetic properties and chemical composition (though the primary magnetic component of the particles is generally magnetite - Fe3O4). For the vast majority of these particles, the magnetic component exists in a superparamagnetic state. In this case, the force exerted on the particle is a translational force directed along the applied field vector and is dependent on the magnetic properties of the particle and the surrounding medium, the size and shape of the particles and the product of the magnetic flux density and the field gradient.

As different sites and applications have different requirements for these systems (for example, the distance to the magnet or the velocity of the flowing particles will vary) we would like to generate either a family of curves, a chart or a computer program which will enable us to choose the appropriate field strength and geometry for a particular application based on the known flow, physical properties of the particles and distance from the magnetic field source to the target.

We are also developing magnetically "blocked" particles to be used in these applications. These particles will experience a torque when the particle's magnetization vector is at an angle to the applied field. We propose to vibrate these particles by oscillating the magnetic field and would like to determine optimum vibrational frequencies based on a theoretical examination of viscous damping under physiologically relevant conditions. Applications and problems in magnetic hyperthermia will also be discussed.

Study Group Report

A general three-dimensional model was formulated, involving external magnetic forces and strokes drag, but neglecting inter-particle interactions and Brownian motion. To solve for particular situations the magnet geometry must be simple enough to allow explicit calculation of the magnetic field, hence we then considered a simple two-dimensional scenario in which the magnet was a finite one-dimensional plate, generating a two-dimensional field, and was placed parallel to the blood vessel, which was represented by a two-dimensional channel.

For this set-up, trajectories of the magnetic particles may be computed quite easily, and particle `capture' investigated. Roughly speaking, the crucial factor is (not surprisingly) found to be the separation between the channel and the magnet. For sufficiently large separations no particles can be captured and held by the magnetic field. For moderate separations a certain proportion of particles are captured, and accumulate in a single equilibrium spot on the vessel wall. For yet smaller separations, a greater proportion of particles are captured; and there are two possible equilibrium capture positions where particles accumulate on the vessel wall. These results are in qualitative agreement with simple in vitro experiments of the process, with similar geometry.

Many points of practical importance remain to be addressed, including particle–particle interactions (both magnetic and hydrodynamic); Brownian motion, and geometrical effects (both of the vessel and its walls, and the particles). In addition, although the particles have been shown to accumulate on the vessel wall in our simple model, what is important in practice is whether they become embedded, so that they remain in situ when the magnetic field has been removed. Further work is required to address all these issues satisfactorily.

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Follow-Up Activities

The following publications have been written as a result of this problem:

Mathematical modelling of magnetically targeted drug delivery
AD Grief & G Richardson (2005)
Journal of Magnetism and Magnetic Materials 293 (1), 455–463.

The following funding for further work has been obtained to investigate aspects of this problem:

Mathematical Modelling of magnetically targeted drug delivery
GW Richardson
Engineering and Physical Sciences Research Council, Postdoc funding, £61k, February 2003 to August 2004.