A Mathematical Model of Dental Caries Used to Evaluate the Benefits of Alternative Frequencies of Bitewing Radiographs

Abstract

This paper describes the development of a mathematical model that can provide the basis for a decision support system to aid dentists (or patients) in making decisions about how often to perform (or receive) bitewing radiographs. The model, which describes the initiation and progression of approximal dental caries, is developed from an analysis of 4 to 13 sets of serial bitewing radiograph exams taken on over 700 individuals. Caries incidence is modeled as follows: (1) there is an underlying gamma distribution representing variation in an individual's expected annual number of new lesions; (2) an individual's distribution of new lesions in a year follows a Poisson process with expected value that can be thought of as having been randomly selected from the gamma distribution. Progression is modeled by assuming duration of carious lesions in each half of the dental enamel can be approximated by a piecewise exponential distribution. Using this model, we determine the relationship between when the next set of bitewing radiographs is performed and the probability carious lesions are detected before any lesions reach the inner half of the dentin. For high risk individuals with no unrestored enamel lesions from their last set of radiographs, bitewings should be scheduled yearly; for low risk individuals with no unrestored enamel lesions, bitewings could be scheduled every 2.5 to 3 years, though both of these conclusions depend on the patient's and/or dentist's attitude toward risk.