Robust and Optimal Control of Magnetic Microparticles inside Fluidic Channels with Time-Varying Flow Rates

Abstract

Targeted therapy using magnetic microparticles and nanoparticles has the potential to mitigate the negative side-effects associated with conventional medical treatment. Major technological challenges still need to be addressed in order to translate these particles into in vivo applications. For example, magnetic particles need to be navigated controllably in vessels against flowing streams of body fluid. This paper describes the motion control of paramagnetic microparticles in the flowing streams of fluidic channels with time-varying flow rates (maximum flow is 35 ml.hr −1 ). This control is designed using a magnetic-based proportional-derivative (PD) control system to compensate for the time-varying flow inside the channels (with width and depth of 2 mm and 1.5 mm, respectively). First, we achieve point-to-point motion control against and along flow rates of 4 ml.hr −1 , 6 ml.hr −1 , 17 ml.hr −1 , and 35 ml.hr −1 . The average speeds of single microparticle (with average diameter of 100 μm) against flow rates of 6 ml.hr −1 and 30 ml.hr −1 are calculated to be 45 μm.s −1 and 15 μm.s −1 , respectively. Second, we implement PD control with disturbance estimation and compensation. This control decreases the steady-state error by 50%, 70%, 73%, and 78% at flow rates of 4 ml.hr −1 , 6 ml.hr −1 , 17 ml.hr −1 , and 35 ml.hr −1 , respectively. Finally, we consider the problem of finding the optimal path (minimal kinetic energy) between two points using calculus of variation, against the mentioned flow rates. Not only do we find that an optimal path between two collinear points with the direction of maximum flow (middle of the fluidic channel) decreases the rise time of the microparticles, but we also decrease the input current that is supplied to the electromagnetic coils by minimizing the kinetic energy of the microparticles, compared to a PD control with disturbance compensation.