Prosthesis‐Implant Arch Area Ratio (PIAAR) – A New Geometric Paradigm, Replacing the Current 'A‐P Spread' of a Cantilever in Full‐Arch Implant Prosthesis: A Proof‐of‐Concept Experiment.

Purpose: The anterior‐posterior spread concept is relied upon to understand the bioengineering aspects of cantilevers in fixed complete denture prostheses. This concept is not evidence‐based. With no other category existing in contemporary implant dentistry, this conventional anterior‐posterior spread concept may have limited more precise and accurate biomechanical analysis. This paper aims to validate a scientific rationale for utilizing this new prosthesis‐implant arch area ratio instead of the preexisting anterior‐posterior spread concept. Materials and methods: Utilizing the preexisting mathematical principle of "Heron's formula," enabling the calculation of the area of a triangle with three known lengths and no angular information, a new prosthesis‐implant arch area ratio is introduced through algebraic derivation. Geometrically, three different sections of prosthetic cantilevers are defined as: (1) anterior cantilever; (2) lateral cantilever; (3) posterior cantilever. The prosthesis‐implant arch area ratio is defined as the prosthesis arch area (anterior, lateral, or posterior cantilever) divided by the sum of the platform arch area and the selected prosthesis arch area. As a proof‐of‐concept experiment, fifteen different laboratory cast arches (n = 15) were chosen; theorized four implant platforms were referenced from the conventional anterior‐posterior spread ration of 1:1.5, followed by calculating platform arch area and prosthesis arch area using Heron's formula. Then, three different horizontal arch width ratios (1:1, 1.25:1, and 1.5:1) under the constant linear height ratio of anterior‐posterior spread (1:1.5) were drawn to assign different experimental groups of prosthesis arch area on each patient scenario, followed by cantilever comparison combining all ratio values (n = 45). One‐way ANOVA and Tukey's post hoc multiple comparison tests were used for statistical analysis. Results: One‐way ANOVA revealed statistical differences of all prosthesis‐implant arch area ratios on each cantilever group; anterior cantilever, F(2, 42) = 8.326, p = 0.0009; lateral cantilever F(2, 42) = 43.92, p < 0.0001; posterior cantilever, F(2, 42) = 26.66, p < 0.0001, as well as cantilever's comparison, F(2, 132) = 240.8, p < 0.0001. Tukey's post hoc test showed a statistically significant ascending trend of prosthesis‐implant arch area ratio as the horizontal width ratio increases. Interestingly, the posterior cantilever had the greatest prosthesis‐implant arch area ratio. Conclusions: Compared to the preexisting anterior‐posterior spread concept, a new prosthesis‐implant arch area ratio seemed to be a more categorized, geometric, and perceptive modality of assessing the prosthetic cantilever in a full‐arch implant‐supported prosthesis, allowing a more systematic indexing of different full‐arch implant clinical scenarios with greater specificity and consistency. [ABSTRACT FROM AUTHOR]