Ph.D. Student Work Plan – ANR IDEAL Project General Objective: The Ph.D. student will participate in the development of advanced numerical methods aimed at ensuring the stability, performance, and realism of a real-time haptic simulator for learning inferior alveolar nerve block (IANB) anesthesia. The work will focus specifically on modeling needle–tissue interactions, the efficient solution of highly constrained systems, and multi-degree-of-freedom haptic feedback. Description: The work will consist primarily of numerical modeling, stability analysis, and software development. The Ph.D. student will contribute to the design and implementation of needle–tissue contact models that incorporate friction and stick-slip effects, as well as to the development of solution strategies adapted to overconstrained systems encountered during interaction with rigid and lightweight anatomical structures.

Particular attention will be paid to asynchronous and multi-frequency resolution methods to ensure stable and realistic haptic feedback in real time, including translational and rotational forces (5 DOFs). The developments will be integrated and validated within the open-source platform
SOFA, in conjunction with haptic devices designed for dental anesthesia training. Expected results: 
• Robust and stable numerical models for simulating needle–tissue interactions, including friction effects and stick-slip transitions.
• Efficient solution methods for highly constrained systems, compatible with asynchronous and real-time simulation architectures.
• A 5-DOF haptic simulation prototype integrated into a training environment at the IANB, validated using scenarios representative of clinical practice.