# MIRD: Medical Internal Radiation Dosimetry

Assessing the dose of radiopharmaceuticals to internal organs for un-encapsulated radiopharmaceutical sources is a challenging task because the radiopharmaceuticals move dynamically through the body over time. Two methodologies to assess internal dose have been put forth by the Society of Nuclear Medicine; the Medical Internal Radiation Dosimetry (MIRD) formalism and the Radiation Dose Assessment Resource (RADAR) formalism. Additionally, the International Commission on Radiological Protection (ICRP) report 53 and report 80 contain tabulated absorbed dose values for many radiopharmaceuticals.

#### Medical Internal Radiation Dosimetry (MIRD) Method

The MIRD method uses a simple model of the human body and considers organs to be source organs, which contain the radiopharmaceutical, and target organs, for which the absorbed dose is calculated. An organ can be both a source and a target.

##### MIRD - Step 1. Compute accumulated activity

Accumulated activity (As) depends on both administered activity (A) and on the fraction of that activity that is taken into the source organ (F). Accumulated activity at a given time is determined as: • As is the accumulated source activity at time (t)
• A0 is the administered activity
• Fs is the fraction of pharmaceutical which is the fraction of radiation accumulated in the organ
• λe is the effective decay constant

Note that effective half-life and decay constant are defined as below where physical half-life is the half-life of the radionuclide and biological half-life is the time required for half of the radionuclide to be expelled from the body.  ##### Step 2. Determine the S-factor

The S-factor is the mean dose per unit of activity and has units of Gy/Bq×s. Although the S-factor can be calculated, it is most often found in tables as a function of the radionuclide, source organ, and target organ. The MIRD phantom used in these computations are based on a greatly simplified model of a 70kg adult male.

Key Point: Tabulated S-factors are determined by Monte Carlo simulation for an assumed 70kg mean man phantom.

##### Step 3. Compute dose to the target organ

Dose to the target organ is determined by: ##### Step 4. Compute effective dose to the whole body

Effective dose may then be computed as: • Wt is the tissue weighting factor.