Understanding the dynamics of superparamagnetic particles under the influence of high field gradient arrays

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.

A Combined Magnetic‐Acoustic Device for Simultaneous, Coaligned Application of Magnetic and Ultrasonic Fields

“…Our previous work has indicated that the accumulation of magnetic particles in vitro and in vivo strongly depends on the force profile of the magnet and this is further supported by the results of the present study. For the MAD design described here, the total magnetic force from the magnet was optimized at the target depth, but no subsequent attempt was made to tailor the force profile.…”

“…This type of force profile typically results in more particles accumulating closer to the edge of the magnet, rather than above the center, resulting in an inefficient accumulation distribution if the target is aligned coaxially with the MAD. Our previous simulation results suggest that force profiles that rapidly vary and peak in a confined spatial region lead to more efficient accumulation of carriers to a coaxially aligned target . The MAD emits this type of force profile beyond z = 15 mm, but at this range, the full‐width half‐maximum (FWHM) of the profile is ≈40 mm.…”

“…The lines show predicted values for the capture efficiency using the model from ref. . The “no magnet” case (black line) is taken as the proportion of particles yet to reach the outlet after a simulation time of 2 min.…”

“…Figure shows the change in image intensity produced by microbubble accumulation along the bottom of the channel. These data were compared with predictions for the accumulation of captured particles made using the model described in section 5 after normalization to the peak accumulation distribution (as the normalized accumulation distribution is mostly independent of the fluid velocity). The model predicted that the greatest accumulation of particles would be observed in a region ≈8 mm upstream from the center of the magnet, and qualitatively comparable behavior was seen for the intensity profiles, except at the highest flow velocity.…”

Remote manipulation of magnetic nanoparticles using magnetic field gradient to promote cancer cell death

“…Two different types of magnet array were compared with the magnet array used in this study via numerical modelling. A magnet array made up of pyramidal magnets, and a custom shaped Halbach magnet array based on [Barnsley 2016, Barnsley 2017 were taken into consideration (Fig. 9).…”