Power Function Retention of Radionuclides in a Wound

NCRP Report 156 describes soluble radionuclide retention kinetics in a wound, segregated into four retention categories: weak (W), moderate (M), strong (S), and avid (A). An alternate single-parameter model, the negative power function, t, is presented in this paper to describe the time behavior of radionuclide retention. With this mathematical description, γ is a single parameter that can be used to assign the wound retention category rapidly. Using the power function description of wound retention, the various wound categories present as straight lines on log scales with different slopes corresponding to the various retention categories. Regression analysis of average retention values in NCRP 156 shows γ = 0.735 ± 0.132, 0.514 ± 0.015, 0.242 ± 0.016, and 0.053 ± 0.023 for the weak, moderate, strong, and avid categories, respectively. A case study is presented (REAC/TS Registry case 1284) where a power function is shown to fit retention data in a Pu/Am hand wound up to 2,000 d (5.4 y) post-accident.