A novel method for planning liver resections using deformable Bézier surfaces and distance maps

Background and Objective: For more than a decade, computer-assisted surgical systems have been helping surgeons to plan liver resections. The most widespread strategies to plan liver resections are: drawing traces in individual 2D slices, and using a 3D deformable plane. In this work, we propose a novel method which requires low level of user interaction while keeping high flexibility to specify resections. Methods: Our method is based on the use of Bézier surfaces, which can be deformed using a grid of control points, and distance maps as a base to compute and visualize resection margins (indicators of safety) in real-time. Projection of resections in 2D slices, as well as computation of resection volume statistics are also detailed. Results: The method was evaluated and compared with state-of-the-art methods by a group of surgeons (n=5, 5-31 years of experience). Our results show that theproposed method presents planning times as low as state-of-the-art methods (174 s median time) with high reproducibility of results in terms of resected volume. In addition, our method not only leads to smooth virtual resections easier to perform surgically compared to other state-of-the-art methods, but also shows superior preservation of resection margins. Conclusions: Our method provides clinicians with a robust and easy-to-use method for planning liver resections with high reproducibility, smoothness of resection and preservation of resection margin. Our results indicate the ability of the method to represent any type of resection and being integrated in real clinical work-flows.