Bone age and remodeling: a mathematical treatise.

Remodeling of an element of mineralized bone is described by specifying the probability per unit time of being replaced as a function of age of the element. The functional dependence of this probability is called the "law of remodeling." The properties of this stochastic law of remodeling are discussed in terms of random, selective, and redundant remodeling. A relationship between the law of remodeling and the mean bone tissue age is derived. It is shown how the probability density of bone age for individual elements of bone depends on the law of remodeling. The mathematical formalism is exemplified by assuming a specific parametric form of the law. A procedure for experimentally determining the law is suggested based on tracing the resorption of single fluorescent labels. Finally, the extension of the model to a real skeleton with regional differences in turnover rates is discussed.