10.6.2 Half Life

Radionuclides

Radionuclides (radioactive substances) are used in various imaging and therapeutic applications. When radionuclides are administered to a patient, they are processed by the body, where their decay occurs over time.

Types of Half-Life in Biological Contexts

The rate of decay of radionuclides in the body is influenced by two primary factors:

1. Physical Decay Process

• This is the inherent radioactive decay of the radionuclide, measured as the physical half-life $( T_p)$.
• Physical Half-Life $( T_p)$: The time required for the number of radioactive nuclei in a sample to reduce to half of its original quantity due to radioactive decay.

2. Biological Process of Excretion

• Radionuclides are also eliminated from the body by biological processes such as excretion or metabolic activity.
• This process is measured by the biological half-life $( T_b)$.
• Biological Half-Life $( T_b)$: The time it takes for half of a substance to be removed from the body by biological means, independent of radioactive decay. Both these processes occur simultaneously, impacting how long the radionuclide remains active within the body.

Effective Half-Life

To understand the combined effect of physical and biological decay, we use the concept of effective half-life $( T_E)$. The effective half-life gives us a measure of the actual time it takes for the activity of the radionuclide in the body to halve, considering both decay and biological elimination.

The formula for calculating the effective half-life is:

$$\frac{1}{T_E} = \frac{1}{T_b} + \frac{1}{T_p}$$

Where:

• $T_E$ is the effective half-life,
• $T_b$ is the biological half-life,
• $T_p$ is the physical half-life.