Purpose Tracking of beating heart motion in a robotic surgery system is required for complex cardiovascular interventions. Methods A heart surface motion tracking method is developed, including a stochastic physics-based heart surface model and an efficient reconstruction algorithm. The algorithm uses the constraints provided by the model that exploits the physical characteristics of the heart. The main advantage of the model is that it is more realistic than most standard heart models. Additionally, no explicit matching between the measurements and the model is required. The application of meshless methods significantly reduces the complexity of physics-based tracking. Results Based on the stochastic physical model of the heart surface, this approach considers the motion of the intervention area and is robust to occlusions and reflections. The tracking algorithm is evaluated in simulations and experiments on an artificial heart. Providing higher accuracy than the standard model-based methods, it copes successfully with occlusions and provides high performance when all measurements are not available. Conclusions Combining the physical and stochastic description of the heart surface motion ensures physically correct and accurate prediction. Automatic initialization of the physics-based cardiac motion tracking enables system evaluation in a clinical environment.

Abstract-A novel heart surface motion estimation framework for a robotic surgery on a stabilized beating heart is proposed. It includes an approach for the reconstruction and prediction of heart surface motion based on a novel physical model of the intervention area described by a distributedparameter system. Instead of conventional element methods, a meshless method is used for a spatial and temporal decomposition of this system. This leads to a finite-dimensional state-space form. Furthermore, the state of the resulting lumped-parameter system, which provides an approximation of the deflection and velocity of the heart surface, is dynamically estimated under consideration of uncertainties both occurring in the system and arising from noisy camera measurements. By using the estimation results, an accurate reconstruction of heart surface motion for the synchronisation of the surgical instruments is also achieved at occluded or non-measurement points.

Abstract-Most existing approaches for tracking of the beating heart motion assume known cardiac kinematics and material parameters. However, these assumptions are not realistic for application in beating heart surgery. In this paper, a novel probabilistic tracking approach based on a physical model of the heart surface is presented. In contrast to existing approaches, the physical information about heart kinematics and material properties is incorporated and considered in an estimation of the heart behavior. An additional advantage is that the time-dependencies and uncertainties of the heart parameters are efficiently handled by exploiting simultaneous state and parameter estimation. Furthermore, by decomposing the state into linear and nonlinear substructures, the computational complexity of the estimation problem is reduced. The experimental results demonstrate the high performance of the method proposed in this paper. The solution of the parameter identification problem allows a personalized physical model and opens up possibilities to apply the physics-based tracking of the heart surface motion in a clinical environment.

Abstract-In order to assist a surgeon while operating on a beating heart, visual stabilization makes the beating heart appear still by providing the current heart view as stationary and non-moving. In this way, the surgeon is not disturbed during an operation by the motion of the heart and has the impression of performing conventional surgery. In contrast to existing methods for visual stabilization, the proposed approach involves a model-based transformation of image sequences provided by a camera system. This transformation incorporates the knowledge of physical characteristics of the heart in form of a mathematical model of the heart surface. The main advantage of this transformation is that the uncertainties of the model and measurements are considered. This occurs by estimating the parameters of the transformation. Furthermore, the quality of the visual stabilization is additionally improved by adapting the parameters of the underlying physical model. The performance of the proposed approach is evaluated in an experiment with a pressure-regulated artificial heart. In comparison to standard approaches, it provides superior results illustrating the high quality of the visual stabilization.

Abstract-A reliable estimation of heart surface motion is an important prerequisite for the synchronization of surgical instruments in robotic beating heart surgery. In general, only an imprecise description of the heart dynamics and measurement systems is available. This means that the estimation of heart motion is corrupted by stochastic and systematic uncertainties. Without consideration of these uncertainties, the obtained results will be inaccurate and a safe robotic operation cannot be guaranteed. Until now, existing approaches for estimating the motion of the heart surface are either deterministic or treat only stochastic uncertainties. The proposed method extends the heart motion estimation to the simultaneous consideration of stochastic and unknown but bounded systematic uncertainties. It computes dynamic bounds in order to provide the surgeon with a guidance by constraining the motion of the surgical instruments and thereby protecting sensitive tissue.