An analytical model for deflection of flexible needles during needle insertion

This paper presents a new needle deflection model that is an extension of prior work in our group based on the principles of beam theory. The use of a long flexible needle in percutaneous interventions necessitates accurate modeling of the generated curved trajectory when the needle interacts with soft tissue. Finding a feasible model is important in simulators with applications in training novice clinicians or in path planners used for needle guidance. Using intra-operative force measurements at the needle base, our approach relates mechanical and geometric properties of needle-tissue interaction to the net amount of deflection and estimates the needle curvature. To this end, tissue resistance is modeled by introducing virtual springs along the needle shaft, and the impact of needle-tissue friction is considered by adding a moving distributed external force to the bending equations. Cutting force is also incorporated by finding its equivalent sub-boundary conditions. Subsequently, the closed-from solution of the partial differential equations governing the planar deflection is obtained using Green´s functions. To evaluate the performance of our model, experiments were carried out on artificial phantoms.