Modelling and real-time dynamic simulation of flexible needles for prostate biopsy and brachytherapy

Percutaneous needle insertion constitutes a widely adopted technique for performing minimally invasive operations. Robot-assisted needle placement and virtual surgical training platforms have the potential to significantly improve the accuracy of these operations. For this, the development of mathematical models that provide a complete characterization of the underlying dynamics of medical needles is considered of paramount importance. In this paper, we develop two three-dimensional nonlinear rigid/flexible dynamic models of brachytherapy and local anaesthetic transperineal biopsy (LATP) needles. The proposed models relax the assumptions of previous investigations, quantify the vibrational behaviour and the rigid-body dynamics of medical needles and allow for real-time haptic and visual feedback information. Their accuracy and computational efficiency are assessed and validated using commercial software. The results show that, among the examined methods, the Rigid Finite Element Method provides the most accurate and numerically efficient solution for capturing the dynamics of flexible medical needles.