The Adaptive Hermite Fractal Tree (AHFT): a novel surgical 3D path planning approach with curvature and heading constraints

PURPOSE: In the context of minimally invasive neurosurgery, steerable needles such as the one developed within the Horizon2020-funded EDEN2020 project (Frasson et al. in Proc Inst Mech Eng Part H J Eng Med 224(6):775–88, 2010. 10.1243/09544119JEIM663; Secoli and y Baena in IEEE international conference on robotics and automation, 2013) aspire to address the clinical challenge of better treatment for cancer patients. The direct, precise infusion of drugs in the proximity of a tumor has been shown to enhance its effectiveness and diffusion in the surrounding tissue (Vogelbaum and Aghi in Neuro-Oncology 17(suppl 2):ii3–ii8, 2015. 10.1093/neuonc/nou354). However, planning for an appropriate insertion trajectory for needles such as the one proposed by EDEN2020 is challenging due to factors like kinematic constraints, the presence of complex anatomical structures such as brain vessels, and constraints on the required start and target poses. METHODS: We propose a new parallelizable three-dimensional (3D) path planning approach called Adaptive Hermite Fractal Tree (AHFT), which is able to generate 3D obstacle-free trajectories that satisfy curvature constraints given a specified start and target pose. The AHFT combines the Adaptive Fractal Tree algorithm’s efficiency (Liu et al. in IEEE Robot Autom Lett 1(2):601–608, 2016. 10.1109/LRA.2016.2528292) with optimized geometric Hermite (Yong and Cheng in Comput Aided Geom Des 21(3):281–301, 2004. 10.1016/j.cagd.2003.08.003) curves, which are able to handle heading constraints. RESULTS: Simulated results demonstrate the robustness of the AHFT to perturbations of the target position and target heading. Additionally, a simulated preoperative environment, where the surgeon is able to select a desired entry pose on the patient’s skull, confirms the ability of the method to generate multiple feasible trajectories for a patient-specific case. CONCLUSIONS: The AHFT method can be adopted in any field of application where a 3D path planner with kinematic and heading constraints on both start and end poses is required.