Endovascular Magnetically Guided Robots: Navigation Modeling and Optimization

Abstract

Abstract-This paper deals with the benefits of using a nonlinear model-based approach for controlling magnetically guided therapeutic microrobots in the cardiovascular system. Such robots used for minimally invasive interventions consist of a polymer binded aggregate of nanosized ferromagnetic particles functionalized by drug-conjugated micelles. The proposed modeling addresses wall effects (blood velocity in minor and major vessels' bifurcations, pulsatile blood flow and vessel walls, and effect of robot-to-vessel diameter ratio), wall interactions (contact, van der Waals, electrostatic and steric forces), nonNewtonian behaviour of blood and different driving designs as well. Despite nonlinear and thorough, the resulting model can both be exploited to improve the targeting ability and be controlled in closed-loop using nonlinear control theory tools. In particular, we infer from the model an optimization of both the designs and the reference trajectory to minimize the control efforts. Efficiency and robustness to noise and model parameter's uncertainties are then illustrated through simulations results for a bead pulled robot of radius 250µm in a small artery.Index Terms-Endovascular navigation, magnetic steering, nonlinear modeling, optimal trajectory, nonlinear controller and observer.

Electromagnetic Steering of a Magnetic Cylindrical Microrobot Using Optical Feedback Closed-Loop Control

“…The term stiction refers to both adhesion due to van der Waals forces and friction forces. These forces are difficult to model, [26] but they introduce uncertainty in the dynamics of a microrobot with closed-loop control.…”

Observer-based controller for microrobot in pulsatile blood flow

“…This section is devoted to briefly introduce these forces and the magnetic motive force (see e.g. [10] for more details). For sake of simplicity, we here only consider a 1D model.…”

“…Whatever the proposed design, these systems face nonlinear forces: blood drag, electrostatic force, etc [10], [11]. Among these forces, the nonlinear drag force both prevails at a small scale and is the most disturbed by external time-varying perturbations because of the pulsatile blood flow.…”

“…Moreover, the devices resolution is not compatible with the precision required to discriminate the spatial parabolic blood flow profile (see Fig 1) the robot faces depending on its position in the vessel. Another solution relies on a priori knowledge of the blood velocity, either using computational solutions of the Navier Stokes equation [14], or analytical expressions of the blood velocity profiles [10]. However, the former is not well suited for real-time purposes, whilst the latter requires a precise a priori knowledge of the vessel geometry.…”

Simulation and Planning of a Magnetically Actuated Microrobot Navigating in the Arteries

“…Different external forces could be added to the model (1), such as the weight (f g ), electrostatic (f e ), van der Waals (f v ), contact or steric forces. The interested reader may refer to [20] for detailed formulation of microforces. Fig.2 illustrates the evolution of these microforces with varying microrobot radius r and wrt.…”