Interactive finite element simulation of the beating heart for image-guided robotic cardiac surgery

An interactive finite element simulation of the beating heart is described in which the intrinsic motion is implied from preoperative 4D tomographic scan data. The equations of motion are reversed such that, given changes in node displacements over time, the node forces that produce those changes are recovered. Subsequently, these forces are resolved from the global coordinate system into systems local to each mesh element such that, at each simulation time step, the collection of node forces can be expressed as simple weighted sums of current node positions. This facilitates the combination of extrinsic forces like those due to tool-tissue interactions, gravity, insufflation of the thoracic cavity and left lung deflation. The method has been applied initially to volumetric images of a pneumatically-operated beating heart phantom.