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Parkinson's disease (PD) is a progressive neurological disorder often treated with Deep Brain Stimulation (DBS), a surgical procedure that involves implanting electrodes to improve motor function. Accurate electrode placement is critical for treatment efficacy but can be influenced by tissue deformation, insertion forces, and the mechanical properties of brain tissue. In this study, we investigated the role of layer interface angle as a controlled biomechanical factor affecting insertion forces and electrode deviation. A two-layer agar gel phantom was constructed to produce a prescribed stiffness transition between a lower-stiffness and a higher-stiffness gel layer, and its small-amplitude dynamic shear-stiffness contrast was characterized using magnetic resonance elastography (MRE) at 100 Hz. A stage-wise analytical model was formulated to describe the Z-direction axial force-depth response Fzz during indentation, fracture, relaxation, and frictional sliding, and a hybrid physics-guided residual neural network (PGNN) was explored as a secondary residual-correction approach for the remaining axial-force model discrepancies. The lateral interface-force change Fiy was obtained directly from the measured Y-direction force signal, while electrode deviation was quantified in a separate series of phantom experiments. Insertion experiments at interface angles of 0°, 15°, 30°, 45°, 60°, and 75° demonstrated that the lateral (Y-direction) interface force increased from 0.886 mN at 0° to 7.72 mN at 75°. For the deviation analysis, the mean value of the 0° group was defined as the zero reference; relative to this baseline, the largest group mean deviation was 0.0529 mm at 75°. These findings highlight the role of interface geometry in probe trajectory stability and provide a mechanistic baseline for future studies of probe insertion in two-layer media.
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