The bulletin of mathematical biophysics

, Volume 28, Issue 3, pp 433–441 | Cite as

A mathematical theory of enamel solubility and the onset of dental caries: II. Some solubility equilibrium considerations of hydroxyapatite

  • Stuart O. Zimmerman


Equilibrium solubility considerations are presented based on the assumption that equating the kinetic expressionq, developed in part I, to zero can describe the equilibrium or steady state between hydroxyapatite and salt solutions. From this expression is derived Hodge's empirical equilibrium equation,C=KH. Further, a lograithmic transformation of this equation results in an expression that accounts for the equilibrium calcium, phosphorus andpH relation found by Levinskas and Neuman. Finally, it also shows the relation between log (C·P) andpH necessary for typical artificial carious lesions as found by Coolidge, Besic and Jacobs. A discussion of a recent theory of hydroxyapatite solubility of LaMer reveals calculation errors that vitiate his results. It is shown that logK1 (K1 is the ratio of the rate constants inq and can serve as a solubility equilibrium constant for hydroxyapatite) varies by only 1.2 units when calculated from three diverse sets of data. This variation is less than that reported by LaMer (when the errors of calculation in that work are corrected) and considerably less than the range of 11 among attempts to calculate a conventionalpK sp , as summarized by Hodge.


Apatite Hydroxyapatite Dental Caries Solubility Product Hydroxylapatite 
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Copyright information

© N. Rashevsky 1966

Authors and Affiliations

  • Stuart O. Zimmerman
    • 1
  1. 1.W. G. Zoller Memorial Dental ClinicUniversity of ChicagoChicagoUSA

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