Abstract: Dentin sensitivity and the success of dental restorations depend on microscopic parameters such as dentin tubule diameter. This study proposes an approach beyond traditional fixed averages in analyzing tubule diameter changes. A dynamic average model (Arithmetic, Geometric, Harmonic) that accounts for outgoing and incoming new tubule populations is adapted to dentin morphology. It is demonstrated how the effective diameter value from these dynamic averages creates an exponential effect (r4) on dentinal fluid flow rate (Q) according to Hagen-Poiseuille law. Mathematical analysis reveals that small increases in tubule diameter (Δr) cause a larger increase (∼ 16Δr) in flow rate than expected. A specific increase in tubule diameter leads to approximately a 3.16-fold increase in flow rate. This study provides a theoretical mathematical framework for predicting macroscopic outcomes of micro-morphological changes in dental practice, establishing a quantitative hypothesis requiring future experimental validation.

Keywords: Dentin tubule, variable average, dynamic average, Hagen-Poiseuille law, dentin sensitivity, mathematical modeling, geometric mean, harmonic mean

Pages: 223-232