13.1 - Unsealed Source Concepts

The three important concepts are uptake, distribution and elimination. It is almost impossible to find information on these topics in radiation oncology textbooks, but I'll provide what I can.

## Uptake

I can't find a good definition of uptake. I presume it refers to the uptake of the radionuclide into the target organ.

## Distribution

Distribution refers to the organs of the body in which the radionuclide is deposited. It is ideal for the radionuclide to be deposited preferentially in the tumour.

## Elimination

Eliminaton refers to the loss of the radionuclide through either radioactive decay or biological excretion.

## Physical Half Life

The physical half life is the time it takes for half of the radionuclide to decay. The physical half life is related to the physical decay constant

(1)
\begin{align} t_\frac{1}{2} = \frac{ln(2)}{\lambda_p} \end{align}

## Biological Half Life

The biological half life is the time it takes for half of the radionuclide to be excreted from the body.

(2)
\begin{align} t_\frac{1}{2} = \frac{ln(2)}{\lambda_b} \end{align}

## Effective Half Life

The effective half life takes into account the physical half life and biological half life, which both reduce the activity of the radionuclide within the body. The effective decay constant is equal to the sum of the biological decay constant and the physical decay constant, ie:

(3)
\begin{align} \lambda_e = \lambda_b + \lambda_p \end{align}

The effective half life is therefore:

(4)
\begin{align} t_\frac{1}{2} = \frac{ln(2)}{\lambda_e} \end{align}