Characterizing the Magnetic Gradient Force of Untethered Magnetic Devices Using Two Synchronized Rotating Magnetic Dipoles

Great care is required when employing two-dipole magnetic actuation systems to navigate untethered magnetic devices (UMDs) in in vivo medical applications, as uncontrolled gradient forces may lead to tissue trauma or damage. Therefore, it is critical to evaluate the full range of forces that may act on UMDs during operation. This article introduces a novel method for estimating the upper and lower bounds of the maximal magnetic gradient force acting on UMDs under the influence of two synchronized rotating magnetic dipoles. This study investigates the characteristics of the magnetic gradient force generated by a single rotating dipole and by two synchronized rotating dipoles. The results demonstrate that two synchronized dipoles are more likely to produce an approximately gradient-free region than a single dipole. Within this gradient-free region, the synchronized dipoles were robotically controlled to navigate a UMD inside an agar gel phantom. Closed-loop motion control experiments revealed that the maximum tracking error of a helical UMD actuated by two robotically controlled synchronized rotating dipoles was 3.89 mm.