Inverse real-time Finite Element simulation for robotic control of flexible needle insertion in deformable tissues

Abstract

This paper introduces a new method for automatic robotic needle steering in deformable tissues. The main contribution relies on the use of an inverse Finite Element (FE) simulation to control an articulated robot interacting with deformable structures. In this work we consider a flexible needle, embedded in the end effector of a 6 arm Mitsubishi RV1A robot, and its insertion into a silicone phantom. Given a trajectory on the rest configuration of the silicone phantom, our method provides in real-time the displacements of the articulated robot which guarantee the permanence of the needle within the predefined path, taking into account any undergoing deformation on both the needle and the trajectory itself. A forward simulation combines i) a kinematic model of the robot, ii) FE models of the needle and phantom gel iii) an interaction model allowing the simulation of friction and puncture force. A Newton-type method is then used to provide the displacement of the robot to minimize the distance between the needle's tip and the desired trajectory. We validate our approach with a simulation in which a virtual robot can successfully perform the insertion while both the needle and the trajectory undergo significant deformations.

Real-time Teleoperation of Flexible Beveled-tip Needle Insertion using Haptic Force Feedback and 3D Ultrasound Guidance

“…A finite difference method is then used with the model to compute the Jacobian matrix J tip linking the motion of the needle base to the tip velocity as defined in (7).…”

“…We use the Jacobian matrix J tip,t linking the base velocity to the tip velocity to identify the manipulability ellipsoid at the tip [25]. J tip,t is directly extracted from the left half of the Jacobian matrix J tip computed in (7). The manipulability ellipsoid can be characterized by three unitary orthogonal axis u i ∈ R 3 each associated to one of the singular values σ i of J tip,t .…”

“…Many research work have focused on the modeling of the needle/tissue interaction to predict the deformation of the needle during the insertion [2], [3], [4]. Such models have then been used in robotic control frameworks to assist the surgeon and to improve the targeting accuracy [5], [6], [7]. Robots can indeed be of great help to perform repetitive gestures with consistency and accuracy.…”

Simulation of Balloon-Expandable Coronary Stent Apposition with Plastic Beam Elements

“…We decide to use beam elements in a similar way, in order to model the more complex (nonlinear) deformation undergone by a balloon-expandable stent. The use of connected beam elements has already been proved efficient in medical simulation to model slender structures, such as endovascular coils for brain aneurysm in [4] or flexible needles in [1]. The use of beam elements in these studies allows to achieve low computational times (up to interactive simulations), but once again is limited to elastic deformations.…”

Fast simulation of stent deployment with plastic beam elements

“…We decide to use beam elements in a similar way, in order to model the more complex (nonlinear) deformation undergone by a balloon-expandable stent. The use of connected beam elements has already been proved efficient in medical simulation to model slender structures, such as catheters for navigation in [8], endovascular coils for brain aneurysm in [9], flexible needles in [10] and [11], or vascular networks [12]. The use of beam elements in these studies allows to achieve low computational times (up to interactive simulations), but once again is limited to elastic deformations.…”