# Equivalent dose

External dose quantities used in radiation protection and dosimetry
Relationships of SI external "protection" dose quantities

Equivalent dose is a radiation-weighted dose quantity which takes into account the type of ionizing radiation producing the dose. Equivalent dose is used in radiological protection to represent the stochastic (probability of cancer induction and genetic effects) but not deterministic effects (severity of acute tissue effects) of ionizing radiation.

## Uses

The equivalent dose is calculated by multiplying the absorbed dose by a radiation weighting factor appropriate to the type and energy of radiation. To obtain the equivalent dose for a mix of radiation types and energies, a sum is taken over all types of radiation energy doses.[1] This takes into account the varying biological effect of different radiation types.

### External dose

Equivalent dose HT is used for assessing stochastic health risk due to external radiation fields that penetrate uniformly through the whole body, or for assessing the individual equivalent dose to organs. However it needs further corrections when the field is applied only to part(s) of the body, or non-uniformly, to measure the overall risk. In that case a further quantity called effective dose must be used to take into account the varying sensitivity of different organs and tissues to radiation.

### Internal dose

The ICRP states "Radionuclides incorporated in the human body irradiate the tissues over time periods determined by their physical half-life and their biological retention within the body. Thus they may give rise to doses to body tissues for many months or years after the intake. The need to regulate exposures to radionuclides and the accumulation of radiation dose over extended periods of time has led to the definition of committed dose quantities".[2]

The ICRP defines an equivalent dose quantity for individual committed dose, which is used to measure the effect of inhaled or ingested radioactive materials.

Committed equivalent dose, H T(t) is the time integral of the equivalent dose rate in a particular tissue or organ that will be received by an individual following intake of radioactive material into the body by a Reference Person, where s is the integration time in years.[3] This refers specifically to the dose in a specific tissue or organ, in the similar way to external equivalent dose.

## Calculation

The radiation weighting factor represents the relative biological effectiveness of the radiation. It aims to correct the absorbed dose, for the different biological effect of different types of radiation. An equivalent dose of radiation is estimated to have the same biological effect as an equal amount of absorbed dose of gamma rays, which is given a weighting factor of 1.

Equivalent dose HT is calculated using the mean absorbed dose deposited in body tissue or organ T, multiplied by the radiation weighting factor WR which is dependent on the type and energy of the radiation R. The International Commission on Radiological Protection (ICRP) has assigned radiation weighting factors to specified radiation types dependent on their relative biological effectiveness. [4]

Radiation weighting factors WR (formerly termed Q factor)
used to represent relative biological effectiveness
according to ICRP report 103[1]
x-rays, gamma rays,
beta particles, muons
1
neutrons < 1 MeV 2.5 + 18.2·e-[ln(E)]²/6
1 MeV - 50 MeV 5.0 + 17.0·e-[ln(2·E)]²/6
> 50 MeV 2.5 + 3.25·e-[ln(0.04·E)]²/6
protons, charged pions   2
alpha particles,
Nuclear fission products,
heavy nuclei
20

Calculating from absorbed dose

$H_T = \sum_R W_R \cdot D_{T,R}\$

where

HT is the equivalent dose absorbed by tissue T
DT,R is the absorbed dose in tissue T by radiation type R
WR is the radiation weighting factor defined by regulation

Thus for example, an absorbed dose of 1 Gy by alpha particles will lead to an equivalent dose of 20 Sv.

The radiation weighting factor for neutrons has been revised over time and remains controversial.

## History

The concept of equivalent dose was developed in the 1950s.[5] In its 1990 recommendations, the ICRP revised the definitions of some radiation protection quantities, and provided new names for the revised quantities.[6] Some regulators, notably the International Committee for Weights and Measures (CIPM) and the US Nuclear Regulatory Commission continue to use the old terminology of quality factors and dose equivalent, even though the underlying calculations have changed.[7]

## Units

The SI unit of measure for equivalent dose is the sievert, defined as one Joule per kg.[8] In the United States the roentgen equivalent man (rem), equal to 0.01 sievert, is still in common use, although regulatory and advisory bodies are encouraging transition to sieverts.[9]

## Related quantities

### History and use of dose equivalent terminology

The similar-sounding term dose equivalent is now used for operational quantities, and the following dose quantities are defined as such by the ICRU and ICRP.

• ambient dose equivalent
• directional dose equivalent
• personal dose equivalent

Prior to 1990, the ICRP used the term "dose equivalent" to refer to the absorbed dose at a point multiplied by the quality factor at that point, where the quality factor was a function of linear energy transfer (LET). Currently, the ICRP's definition of "equivalent dose" represents an average dose over an organ or tissue, and radiation weighting factors independent of LET are used instead of quality factors. Starting with the publication of ICRP 60, the ICRP stopped using the exact words "dose equivalent" alone in that order, but four similar quantities were defined:[6]

### Use of old factors

The International Committee for Weights and Measures (CIPM) and the US Nuclear Regulatory Commission continue to use the old terminology of quality factors and dose equivalent. The NRC quality factors are independent of linear energy transfer, though not always equal to the ICRP radiation weighting factors.[7] The NRC's definition of dose equivalent is "the product of the absorbed dose in tissue, quality factor, and all other necessary modifying factors at the location of interest." However, it is apparent from their definition of effective dose equivalent that "all other necessary modifying factors" excludes the tissue weighting factor.[10]

### Dosimetry reports

Cumulative equivalent dose due to external whole-body exposure is normally reported to nuclear energy workers in regular dosimetry reports.

In the US, three different equivalent doses are typically reported: