A mathematical model of potassium ion diffusion in dentinal tubules

• Published in: Archives of oral biology 1996-07, Vol.41 (7), p.679-687
• Main Authors: Stead, W.J., Orchardson, R., Warren, P.B.
• Format: Article
• Language: English
• Subjects: Dentin - anatomy & histology; Dentin - innervation; Dentin - metabolism; Dentin Permeability; Dentin Sensitivity - drug therapy; Dentinal Fluid - chemistry; Dentinal Fluid - metabolism; Dentinal Fluid - physiology; Dentistry; desensitizing agents; Diffusion; Humans; Hydrostatic Pressure; hypersensitive dentine; Ions; Models, Biological; Osmolar Concentration; potassium; Potassium - pharmacokinetics; Rheology
• ISSN: 0003-9969; 1879-1506
• DOI: 10.1016/S0003-9969(96)00073-8

Desensitizing agents containing potassium ions (K +) are believed to inactivate intradental nerves by raising extracellular [K +]. A mathematical model was used to investigate factors affecting [K +] in dentinal tubules. The most important factors affecting the steady-state tubular [K +] were the tubular fluid-flow velocity, salivary [K +] and the permeability to potassium ( k) of the barrier between the tubule and the pulp. Tubular [K +] decreased with increasing outward flow velocity and increasing k, whereas the dimensions of the tubule and odontoblast process had little effect. Following a 1 min simulated application of 500 mmol/l K + to the dentine surface, [K +] at the inner end of the tubule increased above steady-state levels for 20–30 min. The maximum [K +] attained at the inner end of the tubule was around 30 mmol/l for an impermeable barrier ( k = 0) and flow velocity of 1.4 μm/s, but lower maximum tubular [K +] were achieved when either the outward flow velocity or k was increased. The model suggests that applying potassium-containing preparations to dentine may increase [K +] at the inner ends of dentinal tubules to levels sufficient to inactivate intradental nerves. However, the localized increase in [K +] is transient, and the concentration change will be lessened by conditions that increase the tubular fluid-flow velocity or the permeability of the barrier between the tubule and pulp.