Modelling, Simulation and Planning of Needle Motion in Soft Tissues

Precise needle placement is required for the success of a wide variety of percutaneous interventions in medicine. Insertions into soft tissues can be difficult to learn and to perform, due to tissue deformation, needle deflection and limited visual feedback. Little quantitative information is known about the interaction between needles and soft tissues during puncture, and no effective physicallybased training, planning and guidance systems exist for such procedures. This work aims to characterise needle-tissue interaction by measuring contact forces and deformations that are applied during insertions into soft tissue phantoms. A new methodology for estimating the forces that occur along the needle shaft during insertion is described. The approach is based on physical experiments, as well as on linear elastic phantom models that are discretised by traditional Finite Element Methods. Shaft force distributions are derived from insertions into homogeneous and simple layered inhomogeneous tissue phantoms at several driving velocities, and are applied as boundary conditions to tissue models for physically-based simulations of needle insertion trajectories. A large-strain elastic needle model is coupled to the tissue models to account for needle deflection and bending during simulated insertion. Since the force-displacement relationship is only of interest along the needle shaft, a condensation technique is shown to reduce the computational complexity of linear simulation models significantly. The boundary conditions that determine the tissue and needle motion change as the needle penetrates, or is withdrawn from the tissue model. Boundary condition and local material coordinate changes are facilitated by fast low-rank matrix updates. Such numerical schemes have been seen in prior work involving point and surface interaction; however, in this work the condensation state, boundary conditions and material coordinates evolve as the needle penetrates the tissue volume, and as internal contact states change. These novel interactive simulation techniques allow users to manipulate a three-degree-of-freedom virtual needle as it penetrates virtual tissue models, while experiencing steering torques and forces through a planar haptic interface. Models and simulations are also used to formulate needle insertion as a trajectory planning and control problem. The concept of needle steering is developed, and a Needle Manipulation Jacobian is defined to express the relationship between the needle base and tip velocities. This concept is used in conjunction with a potential-field-based path planning technique to demonstrate needle tip placement and obstacle avoidance. Results from open loop insertion experiments are also provided.