13.2 - Methods Of Dose Estimation

Fortunately, the only method we need to know is the MIRD method, and only in general terms.

The Medical Internal Radiation Dose (MIRD) Method

The Nuclear Medicine Society (NMS) has a committee known as the Medical Internal Radiation Dose (MIRD) Committee. They have developed a method of estimating the dose delivered to a target organ. This method relies on determining the radioactive decay occurring in a target organ (and related organs), calculating how much energy is deposited in the target organ from the organ itself and neighbouring structures, and determining the final dose within the target organ.

A warning: This is very hard to comprehend initially (well at least I found it tricky) but once I worked through it the sense behind it all came out….


Target Organ (T)

The target organ is the organ in which the dose is to be determined.

Source Organ (S)

The source organ is the point of origin of the ionising radiation. The source organ may also be the target organ.

Mean Energy Per Transition

The mean energy per transition ($\triangle$) released in the source organ is equal to the mean particle energy (E) multiplied by the average number of particles per transition (n), together with a conversion factor K. This gives the first equation:

\begin{align} \triangle = K E n \end{align}

I'm not sure what the K factor actually does.

Cumulated Activity

The cumulated activity $\tilde{A}$ is the total number of transitions that occur in a target organ from time = 0 to time = T.

\begin{align} \tilde{A} = \int_0^T A(t).dt \end{align}

The function $A(t)$ is:

\begin{align} A(t) = A(0).\exp(-\lambda_e.t) \end{align}

This all gets very complicated unless you take the time T to be $\infty$, in which case it all simplifies down to:

\begin{align} \tilde{A} = 1.44T_eA(0) \end{align}

Where $T_e$ is the effective half life and A(0) is the initial activity in the organ in question (see below).

Initial Activity in the Organ $A(0)$

A(0) means something different in the MIRD calculation. Instead of initial activity, A(0) stands for the initial activity in the organ in question. It is equal to:

\begin{equation} A(0) = f_2.q(0) \end{equation}

Where q(0) is the total activity within the body, and $f_2$ is the fraction of the activity present in the source organ.

Total energy emitted by source organ

The total energy emitted by the source organ is the product of the mean energy per transition $\triangle$ multiplied by the cumulated activity $\tilde{A}$. Furthermore, only a fraction f of the energy emitted by the source organ will be deposited in the target organ. The mass m of the target organ is also used to determine the mean dose $\bar{D}$.

\begin{align} \bar{D} = \frac{\tilde{A}.\triangle.f}{m} \end{align}

Mean dose to target organ per cumulated activity of the source organ

Almost there! This is where MIRD becomes simple!
The mean dose to target organ per cumulated activity of the source organ is written as [[$ S (T \leftarrow S)]] and is equal to:

\begin{align} S (T \leftarrow S) = \frac{\triangle.f}{m} \end{align}

Final equation

Substituting equation 7 into equation 6, we end up with:

\begin{align} \bar{D} = \tilde{A} \times S (T \leftarrow S) \end{align}

The $\tilde{A}$ value is specific for the fraction of dose within the source organ, and the effective half life of the radiopharmaceutical.
The $S(T \leftarrow S)$ value is specific for the energy and range of the released particles and the relationship of the source and target organs. MIRD have tabulated a list of $S(T \leftarrow S)$ values for different radionuclides and different organs.

Use of MIRD

MIRD allows the dose to a target organ to be determined for the nearby source organs. It splits the calculation of dose into two factors:

  • The pharmacokinetics of the radiopharmaceutical
  • The physical properties of the radiation and the organ structure

Therefore, despite being quite difficult to work through initially, the MIRD formula simplifies the calculation of dose to target organs.