Adaptive 2D-Path Optimization of Steerable Bevel-Tip Needles in Uncertain Model of Brain Tissue

Although there are many works in which path planning of robots is studied, but path planning of the bevel-tip needles with highly flexible body is different and difficult due to unique properties of soft tissues. Real soft tissues are nonhomogeneously elastic and uncertainly deformable and hence, during needle motions the planned path changes unknowingly. In this paper, a novel adaptive path planning of bevel-tip needles inside the uncertain brain tissue is presented. The proposed approach is based on minimization of a Lyapanov energy function used as the cost function which consists of 6 partial costs: path length, number of changes in bevel direction, tissue deformation, horizontal and vertical distances of the needle from target and the inverse distance from obstacles. Uncertainty is also modeled using three techniques; random distribution of elasticity, contamination of the brain image with imaging noise and the fuzzfication of obstacles. Uncertainty modeling helps the optimizer generate more reliable paths. The proposed needle path planning is simulated on a 2D modeled tissue on the basis that the needle's tip does not leave the 2D plane, meaning that (although the needle is rotationally flexible), the angle of needle's base and of needle's tip are always equal. Manipulation of needle's base has three possible states: stop in 0 degree (bevel-right), stop in +180 degree (bevel-left) and always spinning the needle's base (bevel-off). The proposed algorithm is designed so that the needle path does not get trapped into local minima and attractors. The main contribution of this work is in defining a novel and effective cost, namely bevel-change cost, in addition to application of a Lyapanov energy function of Hopfield neural network in needle path optimization.