A Quadratic Nonlinear Prediction-Based Heart Motion Model following Control Algorithm in Robotic-Assisted Beating Heart Surgery

Abstract

Off-pump coronary artery bypass graft surgery outperforms the traditional on-pump surgery because the assisted robotic tools can cancel the relative motion between the beating heart and the robotic tools, which reduces post-surgery complications for patients. The challenge for the robot assisted tool when tracking the beating heart is the abrupt change caused by the nonlinear nature of heart motion and high precision surgery requirements. A characteristic analysis of 3D heart motion data through bi-spectral analysis demonstrates the quadratic nonlinearity in heart motion. Therefore, it is necessary to introduce nonlinear heart motion prediction into the motion tracking control procedures. In this paper, the heart motion tracking problem is transformed into a heart motion model following problem by including the adaptive heart motion model into the controller. Moreover, the model following algorithm with the nonlinear heart motion model embedded inside provides more accurate future reference by the quadratic term of sinusoid series, which could enhance the tracking accuracy of sharp change point and approximate the motion with sufficient detail. The experiment results indicate that the proposed algorithm outperforms the linear prediction-based model following controller in terms of tracking accuracy (root mean square).

A comprehensive multimodality heart motion prediction algorithm for robotic‐assisted beating heart surgery

“…Several heart motion prediction schemes have been proposed in the literature which can be categorized into two main families of model‐free (MF) and model‐based techniques (Table ). While the first approach has been rarely utilized in previous investigations, the model‐based technique has been employed in a large number of heart motion estimation studies using a wide range of prediction algorithms, eg, autoregressive (AR), Volterra series (VS), multivariate autoregressive (MVAR), last cycle (LC), linear parameter varying (LPV), geometric motion estimation (GME), Fourier series (FS), amplitude modulation (AM), and quadratic nonlinear (QN) . The model parameters have been often identified in these studies using Kalman filter (KF), extended Kalman filter (EKF), or recursive least square (RLS) method (Table ).…”

“…The performance of a prediction algorithm in satisfying these requirements depends largely on the data modalities it incorporates (Table ). The algorithms that relied purely on the past heart trajectory have not been able to provide a prediction performance even close to the desired one (Table ). The biological signals, such as electrocardiogram (ECG), respiratory volume (RV) and blood pressure (BP), however, contain valuable information concerning the heart motion, which can improve the prediction accuracy and horizon.…”

Physiological motion modeling for organ‐mounted robots

“…Approaches which attempt to fit predictive models to the periodic motion of the heart include the use of splines, but the vast majority involve frequency‐based models. Frequency‐based models used have included single Fourier series, dual Fourier series, discrete Fourier transforms, amplitude‐modulated Fourier series, and dual Fourier series with a quadratic coupling term . Transformations were used to model the point motion of the heart in simulation in .…”

“…Measurement modalities used in the previous works include sonomicrometry, stereo vision, monocular vision, fiber optic laser, and ultrasound . Each of these measurement modalities, excluding ultrasound, requires direct access to the heart through a sternotomy or thoracotomy, either to place sonomicrometry crystals or for direct line of sight for visual methods.…”

Beating Heart Motion Accurate Prediction Method Based on Interactive Multiple Model: An Information Fusion Approach

“…However, these controllers are inadequate in the performance due to their phase lag caused by the feedback measurement [ 2 ]. In the literature [ 8 , 12 – 18 ], researchers proposed higher effective model predictive control approaches by importing the prediction of the future heart motion in the feed-forward loop as in [ 2 , 12 , 16 , 19 ].…”