Needle-based procedures such as biopsies or radio-frequency ablation (RFA) of tumors are often considered to diagnose and treat liver cancer for their low invasiveness but raise difficulties for practitioners related to needle placement and visibility of internal anatomical structures. Efforts are being conducted to build real-time needle insertion simulators with both visual and haptic rendering, facing challenges related to model accuracy and real-time computational performance. This work focuses on the contact model involved in needle-tissue interactions in order to improve the realism of the resulting haptic rendering. We present a novel method to update the compliant coupling at high rates of a complete contact system involving the mechanics of a large object and the complete model of a flexible needle. These updates allow to adapt the contact directions to the needle deformations in the haptic thread, with the aim of improving the resulting haptic feedback. Updates of contact directions and the related mechanical system according to high-rate deformations decrease force feedback artifacts associated with low-rate mechanics while maintaining high-rate performances for the haptic loop.