Measuring Radiation Dosage — Question 3

Question 3

Tissue weighting forms an effective-dose estimate from organ quantities

In a supplied protection model, tissue 1 has equivalent dose $H_1=2.00\,\mathrm{mSv}$ and weight $w_1=.120$; tissue 2 has $H_2=5.00\,\mathrm{mSv}$ and weight $w_2=.0400$. All other tissues receive zero dose; all tissue weights together sum to 1. Define $E=\sum_Tw_TH_T$.

1. Calculate effective dose.

2. If every tissue instead receives the same equivalent dose $H_0=3.00\,\mathrm{mSv}$, derive E and compare it with the unweighted sum over tissues.

Question 3 - Solution

Tissue weighting forms an effective-dose estimate from organ quantities

(a) Method and calculation

$$E=w_1H_1+w_2H_2+0.$$$$\boxed{E=.120(2.00)+.0400(5.00)=.440\,\mathrm{mSv}}.$$

(b) Interpretation and further calculation

$$H_T=H_0\Rightarrow E=H_0\sum_Tw_T\Rightarrow\boxed{E=H_0=3.00\,\mathrm{mSv}}.$$$$\boxed{E\ne\sum_TH_T}\quad\text{in general; the tissue weights must be included}.$$

Physical check

Effective dose is a weighted protection quantity, not a direct measurement of energy in one organ or a prediction of an individual clinical outcome.