Adaptive Quasi-Static Modelling of Needle Deflection During Steering in Soft Tissue

In this letter, we present a model for needle deflection estimation in soft tissue. The needle is modelled as a vibrating compliant cantilever beam that experiences forces applied by the tissue as it is inserted. Each of the assumed vibration modes are associated with a weighting coefficient whose magnitude is calculated using the minimum potential energy method. The model only requires as input the tissue stiffness and needle-tissue cutting force. Contributions of this letter include the estimation of needle-tissue contact forces as a function of the tissue displacement along the needle shaft, while allowing for multiple bends of the needle. The model is combined with partial ultrasound image feedback in order to adaptively calculate the needle-tissue cutting force as the needle is inserted. The image feedback is obtained by an ultrasound probe that follows the needle tip and stops at an appropriate position to avoid further tissue displacement. Images obtained during early stages of the insertion are used to predict the deflection of the needle further along the insertion process. Experimental results in biological and phantom tissue show an average error in predicting needle deflection of 0.36 mm.