Path tracking control of a steerable catheter in transcatheter cardiology interventions

The tendon-driven steerable catheter is composed by a 310-mm-long catheter body and a 47-mm-long steerable segment at the distal tip side space(Fig. 2A). The steerable segment is able to generate a \(60^{\circ }\) steering angle from the straight position. Two antagonistic steering wires travel along the length of the catheter body up to the tip of the 25-Fr steerable catheter to actuate the steerable segment (Fig. 2B). Expect for the tendon-driven steering motion, based on our previous work [32], a catheter driver system with the sleeve-based grippers and the spur gear is used to generate decoupled 2 degrees of freedom (DOFs) (i.e., translation and rotation) (Fig. 2C).

The “bicycle” model is often used in autonomous driving by characterizing the system with two main wheels, capturing both lateral and longitudinal motion. Regarding the catheter, assuming that the translational motion and the rotational motion propagate ideally from the base through the catheter body to the tip, the distal steerable segment of the catheter can be modeled as a kinematic nonholonomic system, an extension of the “bicycle" model [33], including all the three actuated DOFs. As shown in Fig. 3, the front wheel (A) of the bicycle is attached to the tip of the catheter, and the rear wheel (B) is located on the proximal end of the steerable segment. Generally speaking, advancing the catheter can be approximated as “cycling” forward at a speed, \(\textbf{u}\), and bending the catheter with an angle, \(\theta \), is like steering the front wheel of the bicycle. The combination of these two motions will generate a circular trajectory with a constant curvature radius, r, and a rotation center at point C. Furthermore, by rotating the catheter about its longitudinal axis with a rotation angle, \(\varphi \), one can control the angle of the planar trajectory.

This work combines two control strategies: 1) path tracking control, a high-level controller, is used to correct the motion of the steerable catheter when it deviates from the path; 2) feedback control, a low-level controller, is used to drive the actuation system to reach a desired steering angle (Fig. 4).

The experiment was performed by actuating and controlling a tendon-driven steerable catheter using a sleeve-based robotic catheter driver. Moreover, a 6-DOFs EM sensor (NDI, Canada) was attached to the tip of the steerable catheter as the pose sensor, and an FBG stylet (FBGS, Technologies GmbH. Germany) with 1 cm spacing was placed in the channel of the catheter as the curvature sensor (Fig. 6). All the data communication was conducted and synchronized on the ROS (robot operating system).

The EM generator was placed below the catheter to generate the magnetic field for tracking the EM sensor, which acquires the pose at 40 Hz with a standard deviation of 1.4 mm, A calibration procedure was implemented to compute the registration matrix between the vessel phantom and the EM coordinate. The position of eight calibration pillars was measured, which were pre-set on the phantom with a 6-DOFs EM probe (NDI, Canada). Each position was acquired ten times to reduce the acquisition error and reject the noise from the EM sensor. Then the transformation matrix, \(\textbf{T}\), between the pillar’s positions in phantom space \(\{\textbf{PH}\}\) and the pillar position in the EM space \(\{\textbf{EM}\}\) was calculated based on the singular value decomposition approach [36].

The wavelengths from the FBG interrogator Were obtained (FBGS, Technologies GmbH. Germany) and converted to a point cloud depicting the shape of the catheter [37]. To measure the steering angle, two points were selected at the distal end of the FBG stylet to represent the orientation of the tip and two points behind to represent the orientation of the base. Those last two points were selected by calibrating the steering angle with a protractor.

As the ground truth to evaluate the accuracy of the proposed approach, a camera (Prosilica GT, Allied Vision Technologies GmbH. Germany) with a resolution of 31 megapixels and frame rates of 53 frames per second was mounted on a shelf above the phantom to record the trajectory of the catheter (Fig. 6). One piece of green tape was attached to the tip of the catheter as the tracking markers. Before each test, a checkboard with \(25\times 25\) mm squares was put below the camera for calibration. The camera data was processed by converting the unit from pixel to millimeter based on the calibration data.

The vessel phantom had the laser cutting boundary for the shape of the vessel and two acrylic planes for constraining motion in a plane (Fig. 6). The 3D anatomical model of the vessel was manually segmented and reconstructed using 3D slicer (Harvard University, National Institutes of Health), based on the CT scan images that we obtained from the hospital (Ospedale San Raffaele, Milan, Italy). Then, the 3D anatomy was projected in the coronal plane in Matlab (Mathworks, Massachusetts, USA), similar to the fluoroscopy image in the clinical procedure. The center line was extracted from the boundary of the vessel as the desired path (Fig. 7A). To reduce the friction resulting from the radial compression of the wooden boundary against the catheter body, a scaling factor of 1.5 to the vessel phantom was applied. The experiment was carried out in the first 60 mm section of the vessel phantom, which is the projection of the femoral vein and the iliac vein and the most tortuous part.

To evaluate the accuracy of the control framework at each measured point j, we calculated the tracking error, \(e_j\), which was the minimum Euclidean distance between the measured tip position of the catheter \(\textbf{p}_{j} \left( x_{j},y_{j} \right) \) from the camera data and the pre-defined desired path \(\textbf{p}_{i} \left( x_{i},y_{i} \right) \), which contains I points (Eq. 7).However, the distribution of errors along the entire path is not normal, because the level of challenge in navigating the catheter under various environmental constraints is different due to the insertion speed \(\textbf{u}\), and the path geometry. To comprehensively evaluate tracking accuracy throughout the entire path, all the measurement was divided into ten equal sections, which contain n measured points. The associated median value (MED) in each section was calculated, which allowed us to intuitively compare the performance of the controller under different settings. Matlab (Mathworks, USA) was also used to calculate the maximum value (Max), and interquartile range (IQR). We examined the data set distribution with the Shapiro-Wilk normality test and applied corresponding descriptive statistics to compare different groups. In total, eight tests were carried out, and the velocity dependency was analyzed by setting the insertion speed \(\textbf{u}\) at 1 mm/s, 2 mm/s, and 3 mm/s.

The proposed autonomous control framework was compared with a hybrid control system, which used a joystick controller (PS4, SONY Inc.) as the control element. In this system, the experiment participant was asked to maintain the tip of the catheter at the center of the vessel by controlling the steering DOF of the catheter with the joystick, while the catheter driver autonomously progressed the catheter at a constant insertion speed of 1 mm/s. After three tests, the most confident trajectory was selected as the hybrid control group to compare with the proposed autonomous control framework.

The controller was validated in both a free space and a constrained environment. In the first half of the path, there is no contact between the catheter and the boundary of the phantom (Fig. 7B). Then the catheter body collided with the upper boundary but navigation continues (Fig. 7C). The MED, Max, IQR was computed to evaluate the tracking accuracy in the region with and without environmental constraints.

With the proposed controller, the tip of the robotic catheter successfully follows the center line of the vessel phantom. Figure 8A–H presents the trajectories recorded by the camera corresponding with different insertion speed and control gains, in which the real trajectories of the catheter tip in blue follow the centerline in red, and away from the black vessel border. The results of the Shapiro–Wilk normality test on the tracking error (p-value \(< 0.05\)) show that the error distributes abnormally on the path. The Kruskal–Wallis test shows that the insertion speed is significantly affecting the tracking performance (p-value \(< 0.05\)). The tracking results in the box plots indicate that the increase in the insertion speed will raise the tracking error because the robot doesn’t have enough time to respond and converge to the desired path. When the catheter is inserted at 1 mm/s, the controller has the most accurate performance with a MED along the entire path of 1.43 mm, and a Max of 2.19 mm (Fig. 9A). Compared with the hybrid control system, which has a MED value of 2.65 mm and a Max of 5.51 mm, the result in group H with the optimal control gain has a median value below 2 mm and a maximum error below 3 mm (Fig. 9B). The Mann–Whitney U test indicates a highly significant difference between the performances of those two methods (p-value \(< 0.05\)).

The contact between the catheter body and the vessel wall was identified at approximately \(50\%\) of the trajectory where a salient drop was observed. To show the precision of the controller in both free space and the contact region, the MED, Max, and IQR in those regions were calculated and compared (Table 1). No significant difference was identified with the Mann–Whitney U test, indicating that the controller performed consistently in both free space and contact regions (p-value \(> 0.05\)), across different insertion speeds regarding groups H, G, and C.

We proposed a control framework to allow a safer and more autonomous insertion by avoiding contact between the catheter tip and the vessel wall. Our method achieves a convincing result and the insertion velocity has been considered in the control loop. In cardiovascular applications, the required precision that clinicians indicate as being acceptable is typically in the order of 1–3 mm [38, 39]. Our results from the in vitro studies showed that fidelity of the tracking could satisfy this requirement. Note that the test path does not cover the entire vessel which is 330 mm, because of the limited length of the catheter. A shortcoming of this work is the lack of adaptive methodology for regulating the insertion speed and the control gain factors. The insertion speed affects the performance of the controller and the final procedure time. The control gain factors are sensitive to the radius of the path and the contact region. Given these same wrenches, a Bayesian optimization approach may be used to choose those parameters for the patient-specific path.

In the future, the proposed controller can be extended in these two directions. 1) Path tracking with 3-D path: combing the rotation of the working plane could allow the catheter to achieve any points in the cartesian space. Furthermore, the working plane should be properly chosen to compensate for the gravity effect. 2) Adaptive control: The insertion velocity and the control gain factors could be regulated automatically based on the Bayesian optimization method to self-adapt different paths, which can reduce tracking errors and minimize the procedure time.