Several models incorporate needle shape prediction, however prediction in multi-layer tissue for complex needle shape remains an issue. In this work, we present a method for trajectory generation of flexible needles that allows for complex curvatures, extending upon a previous sensor-based model. This model combines curvature measurements from fiber Bragg grating (FBG) sensors and the mechanics of an inextensible elastic rod for shape-sensing. We evaluate the method's effectiveness in single- and double-layer isotropic tissue prediction. The results illustrate a valid trajectory generation method accounting for complex curvatures in flexible needles.
Keywords: FBG; flexible needle; mathematical model; needle motion planning; tissue inhomogeneity.