A Comprehensive Approach to Characterize Navigation Instruments for Magnetic Guidance in Biological Systems

The non-invasive spatiotemporal control of cellular functions, organization of tissues, and even the behavior of small animals has become paramount for advanced therapies. As magnetic fields do not interact with biological matter, their application is not only suitable for in vitro experiments but also for in vivo applications, even in deep tissues. Particularly, the remote manipulation of paramagnetic entities through magnetic instruments has emerged as a promising approach across various biological contexts. Despite similarities in basic experimental concepts, variations in the properties and descriptions of those magnetic instruments among the authors and studies resulted in a lack of reproducibility and comparability. Therefore, this article addresses the question of how to standardize the characterization of magnetic instruments. Our emphasis lies on the ability of magnetic systems to control the movement of paramagnetic objects such as ferro- or superparamagnetic particles, within organisms. This movement is achieved by exerting a force on magnetic particles by exposing them to a locally varying magnetic field. While it is well-known that the exerted force depends on the spatial variation (i.e. the gradient) of the magnetic field, the magnitude of the field is equally important. However, this second factor is often neglected in the literature. Therefore, we conduct a comprehensive analysis and discussion of both factors. Furthermore, we propose a novel descriptor, termed "effective gradient", which combines both dependencies. To illustrate, we characterize different magnet systems by calculating and comparing the different quantities and relating them to two experiments with different superparamagnetic nanoparticles.