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ORIGINAL PAPER

An adaptive finite element model for steerable needles Michele Terzano1 · Daniele Dini2   · Ferdinando Rodriguez y Baena2 · Andrea Spagnoli1 · Matthew Oldfield3 Received: 31 May 2019 / Accepted: 17 February 2020 © The Author(s) 2020

Abstract Penetration of a flexible and steerable needle into a soft target material is a complex problem to be modelled, involving several mechanical challenges. In the present paper, an adaptive finite element algorithm is developed to simulate the penetration of a steerable needle in brain-like gelatine material, where the penetration path is not predetermined. The geometry of the needle tip induces asymmetric tractions along the tool–substrate frictional interfaces, generating a bending action on the needle in addition to combined normal and shear loading in the region where fracture takes place during penetration. The fracture process is described by a cohesive zone model, and the direction of crack propagation is determined by the distribution of strain energy density in the tissue surrounding the tip. Simulation results of deep needle penetration for a programmable bevel-tip needle design, where steering can be controlled by changing the offset between interlocked needle segments, are mainly discussed in terms of penetration force versus displacement along with a detailed description of the needle tip trajectories. It is shown that such results are strongly dependent on the relative stiffness of needle and tissue and on the tip offset. The simulated relationship between programmable bevel offset and needle curvature is found to be approximately linear, confirming empirical results derived experimentally in a previous work. The proposed model enables a detailed analysis of the tool–tissue interactions during needle penetration, providing a reliable means to optimise the design of surgical catheters and aid pre-operative planning. Keywords  Needle insertion · Needle steering · Cohesive elements · Finite element method · Crack propagation · Programmable bevel-tip needle

1 Introduction Indentation and penetration of soft tissues is a common process in biology and medicine. Minimally invasive surgery by means of needle insertions is successfully applied for tumour biopsy, brachytherapy, deep brain stimulation and localised drug delivery (Elsayes et al. 2011; Lobo et al. 2012). This Electronic supplementary material  The online version of this article (https​://doi.org/10.1007/s1023​7-020-01310​-x) contains supplementary material, which is available to authorised users. * Daniele Dini [email protected] 1



Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy

2



Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK

3

Department of Mechanical Engineering Sciences, University of Surrey, Guildford, Surrey GU2 7XH, UK



has significant benefits for the patient and overall cost of treatment and care; however, percutaneous needle insertions can be difficul