Asymptotic forms of tracer clearance curves: theory and applications of improved extrapolations

Tracer clearance curves are conventionally extrapolated beyond times of observation by using monoexponential asymptotic forms. The inadequacy of the resulting predictions, especially as to the mean transit time and quantities derived from it, has been previously demonstrated experimentally. Here improvements in extrapolations and in the resulting predictions are derived theoretically and tested on previously published data, venous as well as externally recorded. First, secure lower bounds on the mean transit times are constructed, and shown to be much higher than conventional outright estimates for venous data (twice as high in some cases). Next, new asymptotic forms of tracer clearance curves from kinetically heterogeneous systems are derived; they are not monoexponential, but they are as robust, contain as few parameters and are as easily connected to data. It is shown theorectically that for real organs these new asymptotic forms should extrapolate and predict better than monoexponentials, and this is demonstrated on previously published venous data from perfused muscle. In particular, the resulting outright predictions of mean transit times are substantially better than the best lower bounds. Furthermore, a correction is derived to the standard estimate of the rate of regional cerebral blood flow. In an application to previously published data recorded externally, that correction reduces the estimated flow rate by 4%.