Unsealed Source Dosimetry

The calculation of dose from unsealed radionuclides is the subject of internal radiation dosimetry.

The calculation can be performed by either:

The Classic Method

I haven't been able to find a description yet! Sorry.

The Absorbed Fraction Method

This is also called the "MIRD" [Medical Internal Radiation Dose] method. Confusingly, the group looking after this method is also called 'MIRD'. The method is said to be more complicated, more accurate and more versatile, although the results are approximately the same as those derived from the Classic method. It would be facetious to suggest that its higher level of complication has resulted in it being widely accepted as the standard, it is probably because it is more accurate.

The radionuclide will deliver a radiation dose (measured in Gray) commensurate with its initial activity (A₀) and physical half-life. In the case of unsealed sources however, there is the added complication of needing to factor in how long the radionuclide is in the patient to deliver dose. All of the unsealed sources are soluble and are excreted by the kidneys as a matter of preference (this is the fastest elimination method, the most efficient and involves not recycling as occurs with some substances in the bowel. The rate at which a body eliminates any chemical is called the biological half-life. So in a person with an acutely anuric patient (no kidney function), the biological half-life will be infinity.

These two measures combined, give the effective half-life. I won't go into the vague derivation of the equation (I'd have to look it up first!), but the equation to determine effective half-life from physical and biological half-life is as follows:

$\frac{1}{t_{1\over 2}{(Effective)}} = \frac{1}{t_{1\over 2}{(Physical)}} + \frac{1}{t_{1\over 2}{(Biological)}}$

The damage caused by the absorbed dose is a reflection of the absorbed dose and a weighting factor (Q) that reflects the nature of the particle and its energy. The damage from $\alpha -particles$ is much greater than photons so the weighting factor for $\alpha -particles$ is larger than that for photons. In fact photons have a weighting of 1 as the 'standard' particle, and $Q_{\alpha -particles} = 20$. This weighting factor is very relevant to unsealed sources as the 'penetration' of $\alpha -particles$ is much greater because they are distributed internally before decay.

The general procedure for calculating the radiation dose to a target organ from a source organ in the same body is a three step process:

1. the source organ is assessed to determine:
   1. the amount of activity it contains
   2. the time that the activity remains there
2. the total amount of dose emitted from the source organ, which depends on:
   1. the energy of the emissions and
   2. the frequency of emissions (activity)
3. the fraction of the source organ's emitted energy absorbed by the target organ, which depends on:
   1. emission type
   2. emission energy
   3. anatomical proximity of organs
   4. anatomical size and shape

Although No.2 is known fairly accurately, the anatomic aspects of No.3 will vary from one patient to the next. Even No.1 is difficult as the pharmacodynamics of the individual can be quite variable, and biodistribution might not be uniform as assumed within an organ. The situation is helped somewhat by using standard anatomic models of 'average' size and shape to represent the human. Thus the values gained for the absorbed fraction model from the variety of organs can at best be a mathematical estimate of reality.

Factor 1 above (the amount of activity contained and the time it is present) is called the cumulated activity (in Bq.sec)