A Differential Hypothesis on Mucosal Resilience Compensation in Complete Dentures: A Conceptual Framework for Load Distribution Analysis

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Abstract
Background/Objectives: The stability of complete dentures is strongly influenced by the biomechanical properties of the oral mucosa, whose heterogeneity results in non-uniform load distribution, while its clinical evaluation remains predominantly qualitative. This article proposes a theoretical differential hypothesis aimed at providing a conceptual mathematical framework for interpreting the relationship between mucosal resilience and load distribution in complete dentures. Methods: The denture-mucosa system was represented along a one-dimensional coordinate, defining resilience R(x) and pressure P(x) as continuous functions related by a first-order differential equation, interpreted through elementary principles of differential calculus. Results: A theoretical simulation based on physiological parameters (F = 50 N, Young’s modulus 19.75 MPa, R = 2 mm) highlights that areas of thinner mucosa tend to behave as stress concentration points, while spatial variability of resilience generates deformation gradients potentially associated with prosthetic instability. Conclusions: The model, although simplified and non-predictive, provides a coherent interpretative framework and can support the integration of biomechanical parameters into clinical reasoning and prosthetic planning. No clinical recommendations should be derived from this model until experimental validation has been performed.

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