The form and interpretation of clearance curves for injected radioisotopes based on negative power laws, especially for 47Ca and estimating bone accretion rate.

Many hundreds of clearance curves for plasma and urine after a single injection of tracer are well fitted by y = sigmari = Ai exp(-Bit), r = 2 or 3, based on models with homogeneous compartments. Reanalyzing such sums as in a plot of log y versus log t shows that many of the original curves would fit y = At-alpha or At-alpha exp(-betat) over wide ranges of time and specific acitivity. Results of such reanalyses for a complete published series for serum albumin 131I are given, and an outline of those for various compounds in the human body labeled by 3H. For radiocalcium two such power laws can be fitted in one curve, with a transition between about 1 and 3 days, so that much of the log y versus log t plot consists of two straight lines. These lines are used for starting a numerical analysis that splits the curve into 2 non-linear components, plus a third one that is neglibible after 5 min from injection. An outline of the iteration method is given. The components are interpreted physiologically and used to predict total bone activities by (de)convolution, and these are compared with observed ankle activities and with excretion rates. The bone accretion rate is obtained mainly from the middle component and comes to 2 to 3 g Ca/day, while return of 47Ca from bone to plasma begins at about 1/2 day. These results seem imcompatible with any based on compartments. The concept of biological half-life then needs to be reconsidered.