Equations for tracer experiments.

The use of isotopes makes possible quantitative measurements of many biochemical and physiological processes, hitherto secure from such detailed observation. Perhaps the most frequent use of this tool is in the observations of physiology that are concerned with the transfer of fluid from one portion of the body to another, and in the biochemical observations of the formation of one compound from another. It is the purpose of this paper to present in detail some of the mathematical equations that govern such flow and synthesis, and to show incidentally that many of these equations are common to the fields of physics, and chemistry, as well as to the biological disciplines to which they will be applied here. A series of case studies will be presented, including, as examples, the formation of cholesterol from deuterium-marked body water, the uptake of phosphorus by the red blood cell and the flow of sodium out of the plasma into cerebrospinal fluid. Mathematical analysis of this kind is certainly not novel; indeed, Burton (1) reports that Harcourt and Esson (2) concerned themselves with similar studies in 1866 when chemical kinetics was just beginning. In another connection, Rutherford, Chadwick and Ellis (3) have expressed some equations governing the familial relationship between radioactive parent elements and their daughters; they report that Bateman (4) as early as 1910 developed a theory which covers the general case of radioactive decay and recovery. The mathematics apply so generally that any survey of the literature must necessarily be incomplete.