Hinge-axis normalization and Hawley--Bonwill posterior-arch constraints for mandibular arch coordination in orthognathic surgery

Abstract

\begin{abstract} \textbf{Objective:} To present and formalize a hinge-axis-referenced optimization framework for mandibular arch coordination in orthognathic planning, incorporating Hawley--Bonwill posterior-arch constraints as explicit computational priors. \textbf{Materials and methods:} This manuscript is structured as a methods/formulation study with an illustrative retrospective application. The core contribution is a constrained optimization model that aligns the mandibular arch to the maxillary arch at final occlusion while penalizing deviation from the THA-referenced closure path and from Hawley--Bonwill posterior geometry. We detail model variables, objective terms, constraints, and implementation workflow. A retrospective consecutive series (42 preoperative, 38 postoperative scans) is used for two descriptive analyses: (i) technical validation and (ii) a comparative simulation benchmark between a baseline rigid-registration planner and the proposed THA--HB optimizer; no causal inference is attempted. \textbf{Results:} The formal model was implementable within the digital mounting/matching workflow and produced reproducible optimization outputs. In the comparative simulation benchmark, the proposed THA--HB method showed descriptively improved output metrics versus baseline rigid registration (lower $E_{\mathrm{trans}}$, $E_{\mathrm{yaw}}$, and $I_{\mathrm{close}}$ in paired summaries), without inferential claims. \textbf{Conclusion:} The principal contribution is a technically explicit optimization formulation for THA-consistent mandibular arch coordination with Hawley--Bonwill-constrained posterior geometry. The accompanying retrospective series is preliminary and illustrative, and it should not be interpreted causally; the framework is intended to support future prospective comparative studies and reproducible computational surgical planning.% \end{abstract} %%%%%%%%%

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