Model predictive control of a robotically actuated delivery sheath for beating heart compensation

Fig. 1.. Model predictive control (MPC) can be used to steer the robotically actuated delivery sheath (RADS) in order to assist the clinician during cardiovascular surgery. The potential of MPC in cardiovascular surgery can be demonstrated by compensating for the aortic heart valve (AHV) motion in a representative case of transapical transcatheter aortic valve implantation. The RADS ① is inserted through the apex ② into the left ventricle ③ and oriented towards to the aortic annulus ④. The articulating tip ⑤ of the RADS can be steered inside the left ventricle under ultrasound ⑥ image guidance in two degrees of freedom by two pairs of antagonistically configured tension wires. Pre-operative ultrasound data ⑦ can be used as an input to the MPC strategy to anticipate and compensate the AHV motion during surgery.

Fig. 2.. An overview of the robotically actuated delivery sheath (RADS). The articulating tip of the RADS is actuated in two degrees of freedom by two pairs (red and green) of antagonistic-configured tension wires driven by a two pulleys with radii (rp) and angles (ψx and ψy). Three coordinate systems are assigned to describe the tip pose of the RADS: Ψ0 is the reference frame fixed to the shaft, Ψi is the intermediate frame assigned to the arc section and frame (Ψt) is fixed to the articulating tip. Displacement of the tension wires (t1,…,t4) by δx and δy (inset centre) results in instrument bending along the x- and y-axes (frame (Ψ0)), respectively. The arc of the RADS with parameters, bend angle (θ), backbone length (ℓ), radius (r) and curvature (κ) lies in a plane described by the arc plane (inset right). The orientation of the arc plane about the z-axis of the reference frame (Ψ0) is denoted by angle (ϕ). Further, the tendon distance to the backbone arc (ℓ) is denoted db. A rigid link (not completely shown) of length (lt) is attached to the arc (frame (Ψi)) of the RADS.

Fig. 3.. Overview of the geometric relations used to estimate an initial value for the arc curvature (κ^) of the robotically actuated delivery sheath (RADS). The arc length (ℓ) and rigid link length (lt) combined with the RADS tip position (|rt0|) are used to estimate the bend angle (θ^). The estimated bend angle (θ^) and the approximated length (12(ℓ+lt)) are used to evaluate an initial estimate of the arc curvature (κ^) of the RADS.

Fig. 4.. Ultrasound image segmentation to evaluate the centroid location (px,py) of the robotically actuated delivery sheath (RADS). The RADS tip (frame (Ψt)) is positioned in the ultrasound image plane denoted by frame (Ψu) using axial positioning along the x-axis (frame (Ψ0)). (a) Radial cross-sectional view of the RADS in 2D ultrasound images. (b) Gaussian filtering using a 2D kernel. (c) Canny edge detection with hysteretic thresholding. (d) Random sample consensus (RANSAC) to localize the centroid (px,py) of the RADS (centre of the blue circle). The green and red points are considered inliers and outliers, respectively.

Fig. 5.. Experimental evaluation and validation of image segmentation using a sequence of 600 ultrasound images. (a) Compares the performance between varying random sample consensus (RANSAC) iterations using a ground truth obtained by manual segmentation. (b) Describes the relation between the number of iterations and the localization error using a ground truth obtained after 106 RANSAC iterations.

Fig. 6.. A pre-operative two-dimensional transoesophageal echocardiogram (TEE) of the aortic heart valve (AHV) annular plane. The centre location of the aortic heart valve annulus is manually segmented for multiple cardiac cycles. The human evaluated annulus centre positions are used for fitting a motion model. The blue line demonstrates the manually segmented annulus position during the cardiac cycle. The corresponding red line describes the position of the fitted model. Further, the velocities and accelerations of the AHV models are provided.

Fig. 7.. Model-predictive control (MPC) strategy is used to steer the robotically actuated delivery sheath (RADS). The referenced tip position by the clinician is denoted by rd, while rAHV describes the position of the aortic heart valve with a priori knowledge obtained from pre-operative ultrasound images. The tip position obtained by ultrasound image segmentation is denoted by y, with corresponding filtered position described by y^. The arc parameters denoted by a is provided as an input to the RADS and the Kalman filter. The resulting positioning error is given by err, which is used to adapt the Kalman filter.

Fig. 8.. The experimental setup used to control the robotically actuated delivery sheath (RADS) using a model-predictive control strategy. ① RADS. ② Container filled with water in which the RADS is inserted. ③ Ultrasound transducer. ④ Ultrasound image with a radial cross-sectional view of the RADS. ⑤ Motors and corresponding electronics used to control the articulating tip of the RADS. ⑥ Translation along the longitudinal axis of the RADS in order to position the tip in the two-dimensional ultrasound image plane. The top inset shows the flexible segment (articulating tip) of the RADS, which uses a hinged tube construction. The bottom inset depicts a longitudinal cross-section with dimensions of the RADS. An antagonistic configuration of a pair of tension wires (red) is actuated by a pulley-driven system. Each pair of tension wires (total of two pairs) is guided through the flexible shaft and through two incompressible brass tubes (yellow) to actuate a single degree of freedom of the articulating tip.

Fig. 9.. Representative experimental model-predictive control results of the articulating tip of the robotically actuated delivery sheath during tracking of (a) circular reference path (rd) and (rAHV= 0), (b) constrained circular reference path (rd) and (rAHV=0) and (c) and (d) aortic heart valve (AHV) motion trajectories according to rAHV=[fxfy0]T and rd=0. The red line trajectory represents the reference path ( r) described in (25), while the blue line represents the actual path ( y=[pxpy0]T) followed by the articulating tip.