A Theory of the Kinetics of Alkaline Earth and Tracer Metabolism

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Abstract
The fractional retention, R, of a single injection of an alkaline earth tracer in man and animals may be described by a relatively simple power function with 2 adjustable constants, namely R=(t+GK)-bGKb where t is the time after injection, and b and GK are constants. The principles of reaction kinetics appear to provide a theoretical basis for this equation and also a quantitative method for correlating Ca metabolism with that of its tracers. The function results from a n-th order kinetic equation, if it is assumed that the tracer is deposited in a purely inorganic system of bone crystals of constant mass. The concentration of the Ca in the surrounding soln. is assumed to be constant. This function applies to gross Ca metabolism, but it also applies to tracers if the specific activity of the gross Ca deposited with the tracer at t = O remains constant; that is, the tracer cannot mix with the other Ca in the system. Theb b= l/n and GK = co -1/b(b/k), where (n + 1) is the order of the reaction, k is a rate constant, and co is the ratio (at t = O) of the Ca deposited with the tracer to that already present in the system. The proposed mechanism corresponds to that of recrystallization. A modification of this method to described the case of continuous uptake of the tracer at a constant rate predicts only a limited accumulation of tracer at long times. The theory is shown to be consistent with some relevent experimental data.