Multi-bevel steerable needles: A mechanics-driven framework for simultaneous optimization of deflection, insertion...

Accurate needle placement in minimally invasive procedures is strongly influenced by the coupled mechanical effects of needle flexibility, tissue resistance, and bevel-tip geometry. This study presents a mechanics-based framework for analyzing multi-bevel steerable needles by integrating experimentally characterized phantom properties, analytical force estimation, and cantilever-beam deflection modeling. A 2% agar phantom was mechanically characterized through compression testing, and its nonlinear response was represented using a two-parameter Mooney-Rivlin constitutive model. The identified material parameters were subsequently combined with the measured needle geometry and bevel angles to calculate the transverse force generated during needle-phantom interaction. This calculated transverse force was then used as the loading input for an Euler-Bernoulli cantilever-beam model to predict the lateral deflection of the inserted needle. The analytical predictions were compared with independently measured needle deflections obtained from controlled insertion experiments at a maximum insertion depth of 130 mm. Fourteen single- and dual-bevel configurations were investigated. The (30 + 15)^o dual-bevel configuration produced the largest maximum deflection, reaching approximately 16.0 mm, compared with 14.3 mm and 13.3 mm for the 15° and 30° single-bevel reference configurations, respectively. The results demonstrate that appropriate combinations of primary and secondary bevel angles can increase lateral steering capability while maintaining moderate insertion and penetration forces. The proposed framework provides a quantitative approach for relating phantom mechanical properties and needle-tip geometry to transverse force generation and needle deflection, thereby supporting the mechanics-based design of steerable needles for minimally invasive applications.