Efficient physics-based tracking of heart surface motion for beating heart surgery robotic systems

Abstract

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.

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

“…This is typically achieved with iterative strategies such as optical flow (Horn and Schunck, 1981;Lucas and Kanade, 1981), which are based on the knowledge of the location of a feature in the previous frame to constrain a search for the corresponding feature in the next frame, assuming a small degree of motion and intensity coherence. Iterative strategies have been combined with predictive models of feature localization based on prior knowledge of anatomical periodicity, machine learning approaches and predictive filtering (Ginhoux et al, 2005;Ortmaier et al, 2005;Bachta et al, 2009;Bogatyrenko et al, 2011;Richa et al, 2010;Giannarou et al, 2012;Mahadevan and Vasconcelos, 2009;Puerto Souza et al) and have been extensively used in laparoscopic images with varying degrees of success (Sauvee et al, 2007;Elhawary and Popovic, 2011;Ortmaier et al, 2005;Yip et al, 2012).…”

Visual stabilization of beating heart motion by model-based transformation of image sequences

“…Moreover, the model makes use of the fact that the force generated by the myocardium can be represented as force volume relation or pressure as stated in medical experimental studies [13]. Therefore, based on the linear constitutive law, the heart motion is approximately characterized by a dynamic distributed parameter system in form of partial differential equations, according to [14]. Applying the meshless collocation method [15] and using the implicit Euler method for temporal discretization, the heart surface model is converted to a discrete-time system equation in state-space form…”

“…It should be noted that the approximation incorporates N landmarks, whose threedimensional positions l 0 are averaged over the period of the heart motion. The positions of these landmarks are reconstructed according to [14]. The reconstruction is based on the corresponding image features f 0 extracted from all images of the camera system.…”

“…The reference positions of the L surface points s 0 are obtained by interpolating between the landmarks l 0 according to [17]. An important point to emphasize is that in [14] the heart excitation is assumed to be generated by a uniformly distributed pressure inside the cardiac chambers. However, the heart motion is initiated with internal forces generated in a distributed fashion within the muscles.…”

“…The approximation matrix Φ k is then computed according to equation (14) by substituting the vector l 0 into s 0 . Finally, the current positions of the measurement points are projected to the current camera view at every time step k…”