Introduction to Equivalent Dose
In radiobiology, it is well established that not all types of radiation cause the same degree of harm to living tissues. Densely ionizing radiation, such as alpha particles and neutrons, can cause more damage than the less ionizing gamma rays and electrons. This difference in biological effect occurs because densely ionizing radiation results in a higher density of ionization events, leading to a greater chance of irreversible damage to tissues and a lower chance of repair.
To account for this variation in biological effect, we use a quantity called the equivalent dose, which is defined as:
\[ H_{T,r} = D_{T,R} \cdot w_R \]
Where:
- Hₜᵣ is the equivalent dose in sieverts (Sv) for the tissue or organ.
- Dₜᵣ is the mean absorbed dose (in gray, Gy) for a specific tissue or organ from radiation type R.
- wᵣ is the radiation weighting factor for radiation type R, which accounts for the relative biological effectiveness (RBE) of different radiation types.
The equivalent dose is measured in sieverts (Sv), which is the SI unit used to describe the biological effect of ionizing radiation.
Radiation Weighting Factors
The radiation weighting factor wᵣ varies depending on the type of radiation. For example:
- For X-rays, gamma rays, and electrons, the radiation weighting factor is \( w_R = 1 \), indicating that these radiation types are less biologically damaging compared to others.
- For alpha particles, the radiation weighting factor is \( w_R = 20 \), which reflects their higher biological effectiveness.
- For neutrons, the radiation weighting factor varies depending on the neutron energy, but typically ranges between \( w_R = 5 \) to \( w_R = 20 \), indicating a significant potential for biological damage.
This weighting factor helps translate the absorbed dose into a measure that reflects the biological damage to tissues. Thus, by multiplying the absorbed dose by the radiation weighting factor, we get the equivalent dose.
Example Calculation
Suppose a person receives an absorbed dose of 2 gray (Gy) of alpha radiation to the liver. Using the appropriate radiation weighting factor for alpha particles, which is 20, we can calculate the equivalent dose:
\[ H_{T} = D_{T} \cdot w_R = 2 \, \text{Gy} \times 20 = 40 \, \text{Sv} \]
This result means the biological effect of the radiation on the liver is equivalent to a dose of 40 sieverts, which is much more harmful than the same absorbed dose from X-rays or gamma rays.
Summing Equivalent Doses from Different Types of Radiation
In real-world situations, individuals are often exposed to multiple types of radiation. The total equivalent dose is the sum of the equivalent doses from each type of radiation. For example, if a person is exposed to 3 Gy of gamma radiation (with \( w_R = 1 \)) and 1 Gy of alpha radiation (with \( w_R = 20 \)), the total equivalent dose would be calculated as follows:
\[
H_{\text{total}}=
3 \, \text{Sv} + 20 \, \text{Sv} =
23 \, \text{Sv}
\]
This total equivalent dose of 23 sieverts reflects the combined biological effects of the two radiation types on the tissues.
Summary of Equivalent Dose
| Radiation Type | Radiation Weighting Factor (wᵣ) | Examples |
|---|---|---|
| X-rays, Gamma rays, Electrons | 1 | Medical imaging (X-ray), Radiation therapy (gamma rays) |
| Alpha particles | 20 | Radon gas, Radioactive decay (e.g., uranium) |
| Neutrons | 5 - 20 (depending on energy) | Neutron sources, nuclear reactors |