# Absorbed dose

Common symbols
D
SI unitGray
Other units
In SI base unitsJkg−1

Absorbed dose is a measure of the energy deposited in a medium by ionizing radiation. The unit of measure derived from the SI system is the gray (Gy), which is defined as one Joule of energy absorbed per kilogram of matter.[1] Absorbed dose is used in the calculation of dose uptake in living tissue in both radiation protection (reduction of harmful effects), and radiology (potential beneficial effects for example in cancer treatment). It is also used to directly compare the effect of radiation on inanimate matter.

The non-SI CGS unit rad is sometimes also used, predominantly in the USA.

## Stochastic risk

External dose quantities used in radiation protection and dosimetry

The quantity absorbed dose is of importance in radiation protection for calculating radiation dose. However, absorbed dose is a physical quantity and used unmodified is not an adequate indicator of the likely health effects in humans. For stochastic radiation risk (defined as the probability of cancer induction and genetic effects) consideration must be given to the type of radiation and the sensitivity of the irradiated tissues which requires the use of modifying factors.

To represent stochastic risk the equivalent dose H T and effective dose E are used, and appropriate dose factors and coefficients are used to calculate these from the absorbed dose.[2] Equivalent and effective dose quantities are expressed in units of the sievert or rem which implies that biological effects have been taken into account. The derivation of stochastic risk is in accordance with the recommendations of the International Committee on Radiation Protection (ICRP) and International Commission on Radiation Units and Measurements (ICRU). The coherent system of radiological protection quantities developed by them is shown in the accompanying diagram.

## Deterministic effects

Conventionally, unmodified absorbed dose is not used for comparing stochastic risks but only for acute dose giving rise to tissue effects, such as in acute radiation syndrome.

### Effects of acute radiation exposure

Phase Symptom Whole-body absorbed dose (Gy)
1–2 Gy 2–6 Gy 6–8 Gy 8–30 Gy > 30 Gy
Immediate Nausea and vomiting 5–50% 50–100% 75–100% 90–100% 100%
Time of onset 2–6 h 1–2 h 10–60 min < 10 min Minutes
Duration < 24 h 24–48 h < 48 h < 48 h N/A (patients die in < 48 h)
Diarrhea None None to mild (< 10%) Heavy (> 10%) Heavy (> 95%) Heavy (100%)
Time of onset 3–8 h 1–3 h < 1 h < 1 h
Headache Slight Mild to moderate (50%) Moderate (80%) Severe (80–90%) Severe (100%)
Time of onset 4–24 h 3–4 h 1–2 h < 1 h
Fever None Moderate increase (10–100%) Moderate to severe (100%) Severe (100%) Severe (100%)
Time of onset 1–3 h < 1 h < 1 h < 1 h
CNS function No impairment Cognitive impairment 6–20 h Cognitive impairment > 24 h Rapid incapacitation Seizures, tremor, ataxia, lethargy
Latent period 28–31 days 7–28 days < 7 days None None
Symptom Mild to moderate Leukopenia
Fatigue
Weakness
Moderate to severe Leukopenia
Purpura
Hemorrhage
Infections
Alopecia after 3 Gy
Severe leukopenia
High fever
Diarrhea
Vomiting
Dizziness and disorientation
Hypotension
Electrolyte disturbance
Nausea
Vomiting
Severe diarrhea
High fever
Electrolyte disturbance
Shock
N/A (patients die in < 48h)
Mortality Without care 0–5% 5–95% 95–100% 100% 100%
With care 0–5% 5–50% 50–100% 99–100% 100%
Death 6–8 weeks 4–6 weeks 2–4 weeks 2 days – 2 weeks 1–2 days
Table Source[3]

The measurement of absorbed dose in tissue is of fundamental importance in radiobiology as it is the measure of the amount of energy the incident radiation is imparting to the target tissue.

### Dose Computation

The absorbed dose is equal to the radiation exposure (ions or C/kg) of the radiation beam multiplied by the ionization energy of the medium to be ionized.

For example, the ionization energy of dry air at 20 °C and 101.325 kPa of pressure is 33.97±0.06 J/C.[4]:305 (33.97 eV per ion pair) Therefore, an exposure of 2.58×10−4 C/kg (1 roentgen) would deposit an absorbed dose of 8.76×10−3 J/kg (0.00876 Gy or 0.876 rad) in dry air at those conditions.

When the absorbed dose is not uniform, or when it is only applied to a portion of a body or object, an absorbed dose representative of the entire item can be calculated by taking a mass-weighted average of the absorbed doses at each point.

More precisely,[5]

${\displaystyle {\bar {D_{T}}}={\frac {\int _{T}D(x,y,z)\rho (x,y,z)dV}{\int _{T}\rho (x,y,z)dV}}}$

Where

${\displaystyle {\bar {D_{T}}}}$ is the mass-averaged absorbed dose of the entire item T
${\displaystyle T}$ is the item of interest
${\displaystyle D(x,y,z)}$ is the absorbed dose as a function of location
${\displaystyle \rho (x,y,z)}$ is the density as a function of location
${\displaystyle V}$ is volume

### Medical considerations

Non-uniform absorbed dose is common for soft radiations such as low energy x-rays or beta radiation. Self-shielding means that the absorbed dose will be higher in the tissues facing the source than deeper in the body.

The mass average can be important in evaluating the risks of radiotherapy treatments, since they are designed to target very specific volumes in the body, typically a tumour. For example, if 10% of a patient's bone marrow mass is irradiated with 10 Gy of radiation locally, then the absorbed dose in bone marrow overall would be 1 Gy. Bone marrow makes up 4% of the body mass, so the whole-body absorbed dose would be 0.04 Gy. The first figure (10 Gy) is indicative of the local effects on the tumour, while the second and third figure (1 Gy and 0.04 Gy) are better indicators of the overall health effects on the whole organism. Additional dosimetry calculations would have to be performed on these figures to arrive at a meaningful effective dose, which is needed to estimate the risk of cancer or other stochastic effects.

When ionizing radiation is used to treat cancer, the doctor will usually prescribe the radiotherapy treatment in units of gray. Medical imaging doses may be described in units of coulomb per kilogram, but when radiopharmaceuticals are used, they will usually be administered in units of becquerel.

## Other uses

Absorbed dose is also used to manage the irradiation and measure the effects of ionising radiation on inanimate matter in a number of fields.

### Component survivability

Absorbed dose is used to rate the survivability of devices such as electronic components in ionizing radiation environments.

The measurement of absorbed dose absorbed by inanimate matter is vital in the process of radiation hardening which improves the resistance of electronic devices to radiation effects.

Absorbed dose is the physical dose quantity used to ensure irradiated food has received the correct dose to ensure effectiveness. Variable doses are used depending on the application and can be as high as 70 kGy.

The following table shows radiation quantities in SI and non-SI units:

Quantity Unit Symbol Derivation Year SI equivalence
Activity (A) curie Ci 3.7 × 1010 s−1 1953 3.7×1010 Bq
becquerel Bq s−1 1974 SI
rutherford Rd 106 s−1 1946 1,000,000 Bq
Exposure (X) röntgen R esu / 0.001293 g of air 1928 2.58 × 10−4 C/kg
Fluence (Φ) (reciprocal area) m−2 1962 SI
Absorbed dose (D) erg erg⋅g−1 1950 1.0 × 10−4 Gy
gray Gy J⋅kg−1 1974 SI
Dose equivalent (H) röntgen equivalent man rem 100 erg⋅g−1 1971 0.010 Sv
sievert Sv J⋅kg−1 × WR 1977 SI

Although the United States Nuclear Regulatory Commission permits the use of the units curie, rad, and rem alongside SI units,[6] the European Union European units of measurement directives required that their use for "public health ... purposes" be phased out by 31 December 1985.[7]