Experimentally validated CEL finite element modeling of probe insertion and cavity formation in agar gel for DBS...

Accurate electrode placement is essential for effective deep brain stimulation (DBS). However, the mechanics governing probe insertion and withdrawal under controlled conditions remain insufficiently characterized. Experimentally validated computational frameworks capable of quantifying probe insertion mechanics and post-removal cavity formation in controlled surrogate materials are still limited.

A Coupled Eulerian-Lagrangian (CEL) finite element model was implemented to simulate probe insertion and removal in agar gel, used here as a controlled surrogate material. The computational domain consisted of a 50 × 50 × 70 mm Eulerian gel block and a 50 × 50 × 20 mm void region above the insertion site to allow material transport and minimize boundary effects. The gel was modeled using Eulerian elements to accommodate large deformation, while the Nitinol probe was treated as a rigid body. Mesh convergence analysis identified an optimal resolution of 0.6 million elements. Experiments at four clinically relevant insertion speeds (3.24-9.07 mm/s) were performed to validate simulated reaction forces and post-removal cavity deformation under controlled laboratory conditions.

The CEL model accurately reproduced the force-time response throughout insertion and withdrawal, achieving R² values up to 0.98 and peak force errors between 2% and 12%. The simulation also captured cavity formation and subsequent contraction, with the diameter stabilizing at roughly 60% of the probe diameter, consistent with experiments. Speed-dependent cavity closure observed experimentally was not fully captured by the current rate-independent elastic-plastic material model, highlighting the limitations of the simplified constitutive description.

This work presents the first experimentally validated application of a CEL-based modeling framework for DBS probe insertion and withdrawal in homogeneous agar gel. The model reproduces probe-gel interaction forces and cavity evolution, establishing a mechanically validated baseline that can support future extensions to multilayer tissue models and more physiologically representative simulations. The validated contact mechanics and CEL framework are structurally independent of the specific constitutive description, although the quantitative mechanical response remains dependent on the selected material model. While not intended as a direct clinical predictive tool, the framework provides a controlled foundation for systematic investigation of probe insertion mechanics in surrogate materials relevant to DBS research.