Abstract
The aim of this study was to characterize the behaviour of superparamagnetic particles in magnetic drug targeting (MDT) schemes. A 3-dimensional mathematical model was developed, based on the analytical derivation of the trajectory of a magnetized particle suspended inside a fluid channel carrying laminar flow and in the vicinity of an external source of magnetic force. Semi-analytical expressions to quantify the proportion of captured particles, and their relative accumulation (concentration) as a function of distance along the wall of the channel were also derived. These were expressed in terms of a non-dimensional ratio of the relevant physical and physiological parameters corresponding to a given MDT protocol.The ability of the analytical model to assess magnetic targeting schemes was tested against numerical simulations of particle trajectories. The semi-analytical expressions were found to provide good first-order approximations for the performance of MDT systems in which the magnetic force is relatively constant over a large spatial range.The numerical model was then used to test the suitability of a range of different designs of permanent magnet assemblies for MDT. The results indicated that magnetic arrays that emit a strong magnetic force that varies rapidly over a confined spatial range are the most suitable for concentrating magnetic particles in a localized region. By comparison, commonly used magnet geometries such as button magnets and linear Halbach arrays result in distributions of accumulated particles that are less efficient for delivery.The trajectories predicted by the numerical model were verified experimentally by acoustically focusing magnetic microbeads flowing in a glass capillary channel, and optically tracking their path past a high field gradient Halbach array.
Highlights
Targeted delivery of therapeutic agents has, in recent years, been an active area of research, with magnetic drug targeting (MDT) being proposed as a promising technique for localizing therapy efficiently
Numerical simulations were performed to ascertain the trajectories of magnetic microbeads in a steady, laminar flow, under the influence of the magnet array shown in figure 1, to investigate how the capture efficiency and accumulation distributions varied with the flow velocity, Figure 3
The numerically predicted trajectories of particles under the influence of laminar flow and magnetic force were verified experimentally by flowing magnetic microbeads in a glass square capillary channel with an internal width of 0.3 mm and focusing them using acoustic radiation forces generated by a ultrasonic standing wave (USW) field, upstream from a linear Halbach array
Summary
Targeted delivery of therapeutic agents has, in recent years, been an active area of research, with magnetic drug targeting (MDT) being proposed as a promising technique for localizing therapy efficiently. In order to optimize MDT as a minimally-invasive drug delivery strategy, external magnets should be designed to minimize off-target side effects, and maximize the efficiency of drug delivered to the target tissue. For this reason, it is important to understand the performance of magnetic systems by considering the dynamics of superparamagnetic particles in flow as they experience the force applied by a spatially-varying magnetic field. Magnet optimization is usually assessed in terms of the total magnetic force generated over a spatial range of interest (Alexiou et al 2006, Hayden and Häfeli 2006, Häfeli et al 2007, Takeda et al 2007, Sarwar et al 2012, Barnsley et al 2015, 2016), and simulation studies often do not consider whether this leads to optimal delivery to the target volume
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