# Absorbed dose

Absorbed dose is a measure of the energy deposited in an irradiated medium by ionizing radiation per unit mass. 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.

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

The SI unit of measure is the gray (Gy), which is defined as one Joule of energy absorbed per kilogram of matter.[1] The older, 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 occurring over a long time scale, 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 quantities 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, in radiation protection, unmodified absorbed dose is only used for indicating the immediate health effects due to high levels of acute dose. These are tissue effects, such as in acute radiation syndrome, which are also known as deterministic effects. These are effects which are certain to happen in a short time.

### 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.

## Development of the absorbed dose concept and the gray

Using early Crookes tube X-Ray apparatus in 1896. One man is viewing his hand with a fluoroscope to optimise tube emissions, the other has his head close to the tube. No precautions are being taken.

The Radiology Martyrs monument, erected 1936 at St. Georg hospital in Hamburg, more names added in 1959.

Wilhelm Röntgen first discovered X-rays on November 8, 1895, and their use spread very quickly for medical diagnostics, particularly broken bones and embedded foreign objects where they were a revolutionary improvement over previous techniques.

Due to the wide use of X-rays and the growing realisation of the dangers of ionizing radiation, measurement standards became necessary for radiation intensity and various countries developed their own, but using differing definitions and methods. Eventually, in order to promote international standardisation, the first International Congress of Radiology (ICR) meeting in London in 1925, proposed a separate body to consider units of measure. This was called the International Commission on Radiation Units and Measurements, or ICRU,[a] and came into being at the Second ICR in Stockholm in 1928, under the chairmanship of Manne Siegbahn.[6][7][b]

One of the earliest techniques of measuring the intensity of X-rays was to measure their ionising effect in air by means of an air-filled ion chamber. At the first ICRU meeting it was proposed that one unit of X-ray dose should be defined as the quantity of X-rays that would produce one esu of charge in one cubic centimetre of dry air at 0 °C and 1 standard atmosphere of pressure. This unit of radiation exposure was named the roentgen in honour of Wilhelm Röntgen, who had died five years previously. At the 1937 meeting of the ICRU, this definition was extended to apply to gamma radiation.[8] This approach, although a great step forward in standardisation, had the disadvantage of not being a direct measure of the absorption of radiation, and thereby the ionisation effect, in various types of matter including human tissue, and was a measurement only of the effect of the X-rays in a specific circumstance; the ionisation effect in dry air.[9]

In the late 1950s, the CGPM invited the ICRU to join other scientific bodies to work on the development of the International System of Units, or SI.[11] It was decided to define the SI unit of absorbed radiation as energy deposited per unit mass which is how the rad had been defined, but in MKS units it would be J/kg. This was confirmed in 1975 by the 15th CGPM, and the unit was named the "gray" in honour of Louis Harold Gray, who had died in 1965. The gray was equal to 100 rad, the cgs unit.

## 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 s−1
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 m−2
Absorbed dose (D) erg erg⋅g−1 1950 1.0 × 10−4 Gy
gray Gy J⋅kg−1 1974 J⋅kg−1
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,[12] the European Union European units of measurement directives required that their use for "public health ... purposes" be phased out by 31 December 1985.[13]

## Notes

1. ^ Originally known as the International X-ray Unit Committee
2. ^ The host country nominated the chairman of the early ICRU meetings.

## References

1. ^ ICRP 2007, glossary.
2. ^ ICRP 2007, paragraphs 104 and 105.
3. ^ "Radiation Exposure and Contamination - Injuries; Poisoning - Merck Manuals Professional Edition". Merck Manuals Professional Edition. Retrieved 2017-09-06.
4. ^ Podgorsak, E. B., ed. (2005). Radiation Oncology Physics: A Handbook for Teachers and Students (PDF). Vienna: International Atomic Energy Agency. ISBN 92-0-107304-6. Retrieved 25 November 2012.
5. ^ ICRP 2007, p. 1.
6. ^ Siegbahn, Manne; et al. (October 1929). "Recommendations of the International X-ray Unit Committee" (PDF). Radiology. 13 (4): 372–3. doi:10.1148/13.4.372. Retrieved 2012-05-20.
7. ^ "About ICRU - History". International Commission on Radiation Units & Measures. Retrieved 2012-05-20.
8. ^ a b Guill, JH; Moteff, John (June 1960). "Dosimetry in Europe and the USSR". Third Pacific Area Meeting Papers — Materials in Nuclear Applications. Symposium on Radiation Effects and Dosimetry - Third Pacific Area Meeting American Society for Testing Materials, October 1959, San Francisco, 12–16 October 1959. American Society Technical Publication. 276. ASTM International. p. 64. LCCN 60014734. Retrieved 2012-05-15.
9. ^ Lovell, S (1979). "4: Dosimetric quantities and units". An introduction to Radiation Dosimetry. Cambridge University Press. pp. 52–64. ISBN 0 521 22436 5. Retrieved 2012-05-15.
10. ^ Gupta, S. V. (2009-11-19). "Louis Harold Gray". Units of Measurement: Past, Present and Future : International System of Units. Springer. p. 144. ISBN 978-3-642-00737-8. Retrieved 2012-05-14.
11. ^ "CCU: Consultative Committee for Units". International Bureau of Weights and Measures (BIPM). Retrieved 2012-05-18.
12. ^ 10 CFR 20.1004. US Nuclear Regulatory Commission. 2009.
13. ^ The Council of the European Communities (1979-12-21). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 19 May 2012.