Analysis of Dynamic Response of an MRI-Guided Magnetically-Actuated Steerable Catheter System

Abstract

This paper presents a free-space open-loop dynamic response analysis for an MRI-guided magnetically-actuated steerable intra-vascular catheter system. The catheter tip is embedded with a set of current carrying micro-coils. The catheter is directly actuated via the magnetic torques generated on these coils by the magnetic field of the magnetic resonance imaging (MRI) scanner. The relationship between the input current commands and catheter tip deflection angle presents an inherent nonlinearity in the proposed catheter system. The system nonlinearity is analyzed by utilizing a pendulum model. The pendulum model is used to describe the system nonlinearity and to perform an approximate input-output linearization. Then, a black-box system identification approach is performed for frequency response analysis of the linearized dynamics. The optimal estimated model is reduced by observing the modes and considering the Nyquist frequency of the camera system that is used to track the catheter motion. The reduced model is experimentally validated with 3D open-loop Cartesian free-space trajectories. This study paves the way for effective and accurate free-space closed-loop control of the robotic catheter with real-time feedback from MRI guidance in subsequent research.

Fig. 1.

(a) Illustration of catheter ablation procedure [5]. (b) Illustration of a proof-of-concept catheter prototype in a magnetic field, including a set of embedded current-carrying coils [5].

Fig. 2.

(a) A proof-of-concept catheter prototype used in the validation experiments. The unit of the dimensions is in mm. (b) Diagram of the catheter prototype with one coil set. Each coil set is composed of two orthogonal side coils and one axial coil.

Fig. 3.

(a) Experimental configuration of catheter during system identification. $\overrightarrow{B_0}$ denotes the direction B₀ magnetization field vector of the MRI scanner, $\overrightarrow{g}$ denotes the gravity vector direction. S and C are respectively the catheter base and local coil coordinate frames. θ is the deflection angle of the catheter relative to its rest configuration. (b) 2D pendulum model of the catheter.

Fig. 4.

Input-Output model of the catheter dynamics. i is the input current of the coils and θ is the deflection angle of the catheter. H(s) is the linearized dynamics of the catheter.

Fig. 5.

Frequency response of the reduced 2^nd order transfer function superimposed on the the estimated 15^th order system. Also, shown are the experiment data and camera Nyquist frequency (drawn with a black line), which is used during the model reduction.

Fig. 6.

Shows the fit of the estimated and reduced order models to validation chirp signal with sweep from 1 Hz to 8 Hz. (a) Original scale. (b) Magnified scale.

Fig. 7.

(a) Experiment setup inside a clinical MRI scanner. (b) Front view of the experiment setup. The catheter prototype is immersed in a phantom filled with distilled water doped with a gadolinium-based contrast agent. It is clamped vertically by a mechanism made from LEGO® bricks. The mirror next to the tank displays the actuated catheter in side perspective.

Fig. 8.

One processed image using a color-based segmentation algorithm for the labeled markers located on the base, coil, and tip of the catheter. Green curves only simply connect the markers and are not intended to represent the whole body of the catheter.

Fig. 9.

Catheter trajectories tracked via camera-based vision system. Fig. 9a shows the tracked base, coil, and tip markers together with the desired marker trajectory. Fig. 9b shows the resulting tracked and desired trajectories after the rigid body transformation for alignment without scaling.

Fig. 10.

Visualization of the method utilized for estimating the magnitude response for the catheter system based on observed output and input desired trajectories.

Fig. 11.

Magnitude and phase response analysis of the circle trajectory

Fig. 12.

Tracking results for circle and lemniscate trajectories at different pause time between trajectory points. Figs. 12a, 12c show tip location together with the desired trajectory. Figs. 12b, 12d show coil tangent orientation.

Fig. 13.

Tracking errors for circle and lemniscate trajectories at different pause times.