Soft tissue deformation for surgical simulation: a position-based dynamics approach

To assist the rehearsal and planning of robot-assisted partial nephrectomy, a real-time simulation platform is presented that allows surgeons to visualise and interact with rapidly constructed patient-specific biomechanical models of the anatomical regions of interest. Coupled to a framework for volumetric deformation, the platform furthermore simulates intracorporeal 2D ultrasound image acquisition, using preoperative imaging as the data source. This not only facilitates the planning of optimal transducer trajectories and viewpoints, but can also act as a validation context for manually operated freehand 3D acquisitions and reconstructions. The simulation platform was implemented within the GPU-accelerated NVIDIA FleX position-based dynamics framework. In order to validate the model and determine material properties and other simulation parameter values, a porcine kidney with embedded fiducial beads was CT-scanned and segmented. Acquisitions for the rest position and three different levels of probe-induced deformation were collected. Optimal values of the cluster stiffness coefficients were determined for a range of different particle radii, where the objective function comprised the mean distance error between real and simulated fiducial positions over the sequence of deformations. The mean fiducial error at each deformation stage was found to be compatible with the level of ultrasound probe calibration error typically observed in clinical practice. Furthermore, the simulation exhibited unconditional stability on account of its use of clustered shape-matching constraints. A novel position-based dynamics implementation of soft tissue deformation has been shown to facilitate several desirable simulation characteristics: real-time performance, unconditional stability, rapid model construction enabling patient-specific behaviour and accuracy with respect to reference CT images.