A stochastic model for turnover of radiocalcium based on the observed power laws

• Published in: Mathematical biosciences 1968-05, Vol.2 (3), p.199-224
• Main Authors: Wise, M.E., Osborn, S.B., Anderson, J., Tomlinson, R.W.S.
• Format: Article
• Language: English
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/0025-5564(68)90019-9

Following injection of a radionuclide such as 47 Ca, the specific activities in plasma are nearly proportional to a negative power of the time for several hours, and to the ordinates of a gamma probability curve for several days, while the theory of compartments predicts that these should be described by sums of negative exponentials. Here they are interpreted without compartments in the accepted sense, but in terms of cycle and sojourn times inside and outside the plasma of the injected atoms, each of which has to undergo many cycles. A distribution of cycle times is deduced that is consistent with the observed specific-activity time curves. This can arise from first passages in series of random walks with different parameters. The variation in these parameters is shown to provide a direct interpretation of the observed powers and of their complete distribution between −0.5 and ca. −0.17 in a large series of cases.