A Constraint-Driven Automated Framework for Optimizing Multi-Tool Fiducial Configurations in Surgical Navigation

The accuracy of optical tracking tools is crucial for surgical navigation. While commercial tools are reliable, their proprietary design knowledge limits accessibility and adaptability for specialized clinical and research applications. This study introduces an open, reproducible optimization framework based on point-based rigid registration theory, defining a unified pose estimation deviation metric and deriving its analytical expression for both expectation and variance. The approach incorporates constraints for intra-group uniqueness and inter-group compatibility, using exhaustive configuration generation and geometric evaluation to rank designs by predicted accuracy. Numerical simulations confirmed the derived formula, with under 5% average prediction error for the expectation and strong agreement for the variance. Optimized four-fiducial tools were compared to commercial references via tip calibration, distance measurement, and registration tests. Most optimized tools (75%) achieved accuracy comparable to or modestly better than commercial tools (e.g., tip calibration 0.22 mm vs. 0.28 mm, distance measurement 0.18 mm vs. 0.20 mm, FRE 0.13 mm vs. 0.16 mm, TRE 0.48 mm vs. 0.51 mm). All four experiments showed a strong positive correlation between the theoretical metric and measured error (Pearson's r>0.98, all p<2.2×10-7; exact Spearman p≤2.8×10-6). Beyond these numerical results, the primary contribution is a systematic, open design methodology that formalizes knowledge historically proprietary to commercial vendors, enabling researchers and engineers to generate high-precision custom tracking tools for diverse surgical navigation scenarios.