A mathematical model of potassium ion diffusion in dentinal tubules

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.