The Geometric PATZi Method for Full-Arch Reconstruction of the Atrophic Maxilla: Complete Cone-Beam Computed Tomography Coordinate Protocol, Worked Implant-Length Calculations, and a Software Reference Specification

This is the authors' abstract. We don't add key points for this paper.

Full-arch reconstruction of the atrophic maxilla increasingly relies on remote cortical anchorage, yet freehand surgery is still commonly planned without a patient-specific calculation of implant length, and operating rooms are stocked with broad implant inventories to absorb the resulting uncertainty. The conceptual rationale for coordinate-based PATZi (posterior, anterior, tilted, zygomatic) planning was recently introduced in a brief perspective article; the present report is its methodological companion and provides the complete operational protocol. We define an eleven-trajectory classification (P1-P3, A1-A2, T1-T3, Z1-Z3) in which every implant is described by a planned post-reduction entry coordinate (E) and a cortical target coordinate (X) on cone-beam computed tomography (CBCT). The entry-to-target distance is computed exactly as the three-dimensional Euclidean distance S3D, and the clinical implant length is then selected from it through explicit, recorded adjustments for landmark selection, device geometry, and safety. The article presents the anatomic definition and multiplanar evaluation of each subtype, the geometric variables and calculation rules, a step-by-step clinical protocol, worked numerical examples on schematic coordinates, a subtype-specific safety matrix, and a reference software specification that separates deterministic geometry from proposed artificial intelligence (AI) modules for segmentation, landmark proposal, and inventory prioritization. The approximate 15-mm prosthetic envelope is used to position E and is never added to implant length. All anticipated benefits, including inventory reduction, are framed as hypotheses, and a staged validation pathway with defined primary outcomes is specified. The method is offered as a reproducible planning language and software reference for surgeons and developers, pending clinical validation.