Answer to Question #14246 Submitted to "Ask the Experts"

To calculate the committed effective dose for internal exposure, we have to multiply total radioactivity by the committed effective dose coefficient. What number should I take as total radioactivity? Is it the total number of radioactive nuclei or just initial activity at the first second?

For example, suppose someone ingested 120 mg of sodium-24 (²⁴Na). The number of nuclei (N0) of ²⁴Na is 3.1438 × 10²¹. Initial activity (A0) is 4.0462 × 10¹⁶ Bq. Committed effective dose coefficient for ²⁴Na is 4.3 × 10^-10 Sv Bq^-1 for an adult member of public.

If I take the total number of nuclei as the total radioactivity, the committed dose is 1.3518 × 10¹². If I take initial radioactivity (A0) as the total radioactivity, the committed dose is 1.74 × 10⁷ Sieverts (Sv). Which number is the correct one? How does fractional absorption in the gastrointestinal tract (f₁) factor affect this calculation (if f₁=1, f₁=0.5)?

The dose coefficients are calculated on the basis of unit activity intake—i.e., 1 becquerel. For ingestion this represents the amount of radioactivity taken in by mouth and assumed to be swallowed. The dose coefficients are calculated for acute intakes. If you are concerned about doses to adults, these coefficients may generally also be applied to chronic intakes by summing the activity intake for each year and applying the coefficients to these annual intakes.

In your example, the calculation using the activity that yields 1.74 × 10⁷ Sv is logically and mathematically correct. The calculation using the number of atoms is incorrect since the dose coefficients are based on activity intake. Of course, the choice of 120 mg of ²⁴Na is an unrealistic assumption since the extremely large quantity of activity represented by this mass makes the internal committed dose inconsequential since the affected individual would die a rather rapid death from the extremely high radiation dose that would ensue simply from the activity being in contact with the individual; a lethal dose would likely accrue within less than a second following intake.

Assuming the activity was sufficiently low that committed dose was a concern, the f₁ factor that represents fractional transfer out of the small intestine to systemic circulation does impact ultimate committed dose since the f₁ value affects how much of the activity gets distributed to other systemic tissues outside of the gastrointestinal (GI) tract. The f₁ value assumed for sodium compounds is 1.0 so there is typically no reason to use a different value. If, however, a different f₁ value did apply, 0.5 in the case you cite, one-half of the ingested activity would be subject to transport out of the GI tract. This means that the systemic tissue part of the calculated dose would be reduced by a factor of two compared to when the f₁ value is 1.0. At the same time, however, the dose to the GI tract would increase because now one-half of the activity would also be subject to transfer through the entire GI tract. Committed doses to both the entire GI tract and to the systemic tissues would have to be calculated and considered together to obtain effective dose per unit intake, which would be different from the current International Commission on Radiological Protection dose conversion coefficient for ²⁴Na.

I hope this is helpful.

George Chabot, PhD, CHP