title: A mathematical model of potassium ion diffusion in dentinal tubules.
abstract: 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/1 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 microns/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.
authors.affiliation: Unilever Dental Research, Port Sunlight Laboratory, Bebington, Wirral, U.K.
authors.forename: W J
authors.initials: WJ
authors.lastname: Stead
authors.forename: R
authors.initials: R
authors.lastname: Orchardson
authors.forename: P B
authors.initials: PB
authors.lastname: Warren
mesh_terms: D003804:Dentin / Q000033:anatomy & histology / Q000294:innervation / Q000378:metabolism*; D003806:Dentin Permeability; D003807:Dentin Sensitivity / Q000188:drug therapy; D019234:Dentinal Fluid / Q000737:chemistry / Q000378:metabolism / Q000502:physiology*; D004058:Diffusion; D006801:Humans; D006874:Hydrostatic Pressure; D007477:Ions; D008954:Models, Biological; D009994:Osmolar Concentration; D011188:Potassium / Q000493:pharmacokinetics*; D012212:Rheology
chemical_list: D007477:Ions; D011188:Potassium