Controlled Helical Propulsion Against the Flow of a Physiological Fluid

Untethered helical magnetic devices (UHMDs) have the potential to navigate bodily fluids using permanent-magnet robotic systems for minimally invasive diagnostic and surgical procedures. These devices can be actuated by robotically moving rotating permanent magnets (RPMs) to achieve controllable steering and propulsion simultaneously in a wireless manner. To date, the vast majority of motion control systems using UHMDs are constrained to operate in the absence of a dynamic flow field and prior work did not rigorously address the fundamental roles of rheological, magnetic, and geometric characteristics of the UHMD and its surroundings on the resulting stability. In this work, we show how to construct the region of attraction of a UHMD driven by two synchronized RPMs inside fluid-filled lumen around an equilibrium point. We first present the governing hydrodynamic model of a magnetically-driven UHMD to describe its behavior against the flow of blood serum. Then we validate the model using 1-D frequency response characterization and show that it captures the measured linear relationship between the actuation frequency and propulsive thrust at various flow fields. We find that a region of asymptotic stability can be achieved around an equilibrium point allowing a 6-mm-long UHMD to overcome maximum volumetric flow field of 1.2 l/hr (i.e., 2.65 cm/s).