Uncertainty of the iodine-131 ingestion dose conversion factor

Sample calculations of the roots and integration constants where performed using thefollowing values for the rate constants:ln( 2)ln( 2)ln( 2) ln( 2)λ = k = k = k =802 . d 025 . d 120 d 12 dbl t b(23)with f 1= 1.0, f blt= 0.3, f bbl= 0.9, and S = 1 Bq of 131 I ingested. With these inputs, the roots andintegration constants were determined. A high degree of precision was necessary during thenumerical calculation of these values due to the large difference in the magnitudes of the three rootsas well as taking powers of the roots in eqn (22). The final solutions for the time-dependent iodineactivity in the three compartments can be presented at a lower precision. For the base case givenhere, the iodine activity in each compartment as a function of time, t, can be expressed as,−2. 86t −0. 146t −0.tXt () = 1. 00e − 0. 000613e + 0.000588e0905 Bq , (24)−2. 86t −0. 146t −0.tYt () =−0. 301e − 0. 00949e + 0.291e0905 Bq , and (25)−2. 86t −0. 146t −0.tZt () = 0. 000640e − 0. 0320e + 0.0313e0905 Bq. (26)The activity of other isotopes of radioiodine in the various compartments as a function of time canbe calculated rather easily by multiplying eqns (24) - (26) by the factor,−( i − . ) teλ 0 0862 , (27)where λ iis the decay constant (in units of d -1 ) of the radioiodine in question. The integrated activityin each compartment after ingestion to a time T, in units of d, is determined using,10