Taoming Liu1, Dominique Franson2, Nate Lombard Poirot3, Russell Jackson1, Nicole Seiberlich1,2, Mark A. Griswold1,2,4, and Murat Cenk Cavusoglu1,2
1Electrical Engineering and Computer Science, Case Western Reserve University, Cleveland, OH, United States, 2Biomedical Engineering, Case Western Reserve University, Cleveland, OH, United States, 3Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH, United States, 4Radiology, University of Hospitals of Cleveland, Cleveland, United States
Synopsis
This paper presents a Jacobian-based inverse kinematics and open-loop
control method for an MRI-guided magnetically-actuated steerable intravascular
catheter system. The catheter is directly actuated by magnetic torques
generated on a set of current-carrying micro-coils embedded on the catheter tip
by the magnetic field of MRI scanner. The Jacobian matrix is derived from a
three dimensional kinematic continuum model of the catheter deflection. The
inverse kinematics are numerically computed by iteratively applying the inverse
of the Jacobian matrix. Experimental evaluation compares a catheter prototype’s
desired trajectory to the actual trajectory.
Purpose
The proposed MRI-guided magnetically-actuated steerable intravascular
catheter will assist cardiac ablation to treat atrial fibrillation1-3
(Fig. 1a). The catheter body is directly actuated by magnetic torques.
Current-carrying micro-coils embedded on the catheter body interact with the
magnetic field of MRI scanner to generate the magnetic torques (Fig. 1b). The
catheter system is not subject to the mechanical transmission problems that
exist in other actuation methods (such as tendon-driven4 and
hydraulic5 actuation). Consequently, this magnetic actuation method
increases the bandwidth of the system by reducing backlash and friction. Currently,
accurate control of the catheter tip position poses a challenge. Here, an open-loop
control method using Jacobian-based inverse kinematics is presented. This
method will help the physicians by facilitating intuitive control of the
catheter while precisely moving the catheter to the desired ablation targets on
the atrial wall6-7.Methods
The deflection of the catheter is controlled by the amount of the
current going through these electromagnetic coils. Liu et al.3 developed
a method where a finite differences approach is combined with beam theory and
rotation groups to model the three dimensional deflection of the proposed catheter.
The deflection includes bending and torsional motions. In the present study, the
Jacobian matrix (J) relating changes of the currents through the coils (i) to
changes of the tip position (P) is derived. As a closed form expression that
directly relates the tip position to the actuation currents is not available, the
Jacobian is computed indirectly as $$$J = \frac{dP}{dX}\frac{dX}{di}$$$, from the kinematic model of the catheter tip position as a function
of deflection angles (X), and the three dimensional deflection model of the catheter3 relating
the actuation currents and the deflection angles. The inverse kinematics is
then numerically computed by iteratively applying the inverse of the Jacobian
matrix. During the iteration, a damped least square method is used to avoid numerical
instability during computation of the Jacobian matrix’s inverse. Given a
desired trajectory for the tip of the catheter, the current corresponding to
each point on the trajectory is calculated using the proposed Jacobian-based inverse
kinematics method. The estimated trajectory currents are subsequently used to
actuate the catheter.Results
The experiments to validate the proposed method are conducted in a 3T
clinical scanner (Skyra, Siemens Medical Solutions, Erlangen, Germany). The
experimental setup is shown in Fig. 2. The catheter prototype is mounted vertically
inside an aquarium tank and immersed in a phantom filled with distilled water doped
with a gadolinium-based contrast agent. One current-carrying coil set, consisting
of one 100-turn axial coil and two 30-turn orthogonal side coils, is embedded
on the catheter. The catheter is tracked by a catadioptric digital camera
system (Fig. 3).
Four distinct trajectories (butterfly, circle, lemniscate, and square)
are used for evaluating the performance of the control. These trajectories,
consisting of 200 set currents each, are chosen because of their similarity to
the circumferential and linear ablation lesions employed in atrial fibrillation
ablation6. Each trajectory
shape is recorded 7 times during the experiments. As the presented control
scheme is open-loop (which does not use any feedback from measurement of
catheter position), offset and drift type errors between the desired and
observed trajectories are expected. Therefore, shape repeatability of the
trajectories (allowing the trajectories to be translated and rotated, but not
scaled) is used as the error metric.
Fig. 4a shows the shape comparisons between the given desired
trajectory of the tip (red) and the observed trajectories which are transformed
without scaling (blue). Additionally, the repeatability (Method 2) is also
computed by comparing one of the measured trajectories randomly selected as a
reference trajectory, and shapes of the other measured trajectories (Fig. 4b).
The root-mean-square (RMS) of the errors between desired and observed catheter
tip trajectories are reported in Table I.
Discussion
The low mean and variance values for the RMS errors indicate very good
repeatability of the trajectory shapes. In other words, the overall shape of
the observed trajectory is similar to the corresponding trajectory pattern
provided, even for complicated patterns, such as the butterfly pattern. The
resulting repeatability error is not sensitive to offset (and some drift) types
of errors that are inherent to open-loop control schemes, and can easily be
eliminated by either physician-in-the-loop or closed-loop control of the
catheter.Conclusion
The repeatability results demonstrate that the proposed open-loop
control can actuate the catheter to successfully perform complex ablation
trajectories required for atrial fibrillation ablation. This study paves the
way for effective and accurate closed-loop control of the robotic catheter with
real-time feedback from MRI guidance in subsequent research.Acknowledgements
NSF IIS 1524363, NSF IIS 1563805, and NIH R01 EB018108.References
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