Correctly computing targeting efficiency in magnetically targeted delivery from particle tracking models

Abstract

Magnetic targeted therapies have been shown to be very effective at treating tumours in animal models (e.g. Muthana et al.. (2015)), but have yet to be widely adopted in a clinical setting. The aim of this work is to correct a widely occurring, but subtle, error in the interpretation of models of magnetically targeted delivery. This can result in inaccuracies in the predicted targeting efficiency of up to an order of magnitude. In order to correct this error a model for magnetic targeting that is based upon a particle conservation law is developed. The close relationship between this model and the standard approach is demonstrated. Interpretation of magnetic particle dynamics in terms of a conservation law leads to an improved understanding of the overall process and results in an alternative, and correct, definition of the targeting efficiency. The particle conservation law approach is illustrated by considering targeting in a flow through a simple network, consisting of a vessel that branches into two daughter vessels, and compared to the standard procedure for computing targeting efficiency, which is based solely on a count of representative particle trajectories. It is shown that the analysis based on the conservation law yields a prediction that compares much more favourably to the results of simple in-vitro experiments performed in this set-up (Riegler et al., 2010) than the standard, but erroneous, approach based on counting particle trajectories. The method of computing targeting efficiency that is developed here, has wider applicability and can, for example, be applied to targeting in complex mammalian vasculatures.