A Proposed Mechanism for the Uptake of Radioactive Tracers by an in Vitro Hydroxyapatite System

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Abstract
Several mechanisms have been proposed to describe the uptake of radioactive tracers by hydroxyapatite (synthetic bone) in vitro, namely, ion exchange, diffusion, and recrystallization or aging. In this paper the case for recrystallization is considered. The rate equation for recrystallization was derived from the equations for crystal growth by assuming that the over-all change in the surface area of the crystal is small. On integration of the rate equation a power function is obtained where (1 - [alpha]) is the fraction of tracer remaining in solution at time t; gamma is a constant; b = 1/(n-1); and n in the order of the reaction. The uptake results for radioactive calcium, radium, phosphate and yttrium can be described, over the whole time range studied by a single power function, with n = 10 for calcium and radium, 7.3 for phosphate, and 3.4 for yttrium. The values of n are closely related to the number of ions of interest in the unit-cell; that is, for hydroxyapatite, Ca10(PO4)6(OH)2; n = 10 for Ca and 6 for PO3 4-.

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