Conversion – Absorbed to Equivalent Dose

Radiation weighting factors - current - ICRPEquivalent dose (symbol HT) is a dose quantity calculated for individual organs (index T – tissue). Equivalent dose is based on the absorbed dose to an organ, adjusted to account for the effectiveness of the type of radiation. Equivalent dose is given the symbol HT. The SI unit of HT is the sievert (Sv) or but rem (roentgen equivalent man) is still commonly used (1 Sv = 100 rem). Unit of sievert was named after the Swedish scientist Rolf Sievert, who did a lot of the early work on dosimetry in radiation therapy.

As was written, for radiation protection purposes, the absorbed dose is averaged over an organ or tissue, T, and this absorbed dose average is weighted for the radiation quality in terms of the radiation weighting factor, wR, for the type and energy of radiation incident on the body. The radiation weighting factor is a dimensionless factor used to determine the equivalent dose from the absorbed dose averaged over a tissue or organ and is based on the type of radiation absorbed. The resulting weighted dose was designated as the organ- or tissue equivalent dose:

equivalent dose - equation - definition

equivalent dose - definitionAn equivalent dose of one Sievert represents that quantity of radiation dose that is equivalent, in terms of specified biological damage, to one gray of X-rays or gamma rays. Equivalent dose is a non-physical quantity (wR is derived from biological consequences of ionizing radiation) widely used in dosimetry measured by dosimeters. Equivalent dose is designated by the ICRP as a “limiting quantity”; to specify exposure limits to ensure that “the occurrence of stochastic health effects is kept below unacceptable levels and that tissue reactions are avoided”.

Conversion of Absorbed Dose to Equivalent Dose

Note that the sievert is not a physical dose unit. For example, an absorbed dose of 1 Gy by alpha particles will lead to an equivalent dose of 20 Sv. This may seem to be a paradox. It implies that the energy of the incident radiation field in joules has increased by a factor of 20, thereby violating the laws of Conservation of energy. However, this is not the case. Sievert is derived from the physical quantity absorbed dose, but also takes into account the biological effectiveness of the radiation, which is dependent on the radiation type and energy. The radiation weighting factor causes that the sievert cannot be a physical unit.

Radiation weighting factors - current - ICRP
Source: ICRP Publ. 103: The 2007 Recommendations of the International Commission on Radiological Protection

As was written, each type of radiation interacts with matter in a different way and causes different biological damages. For example charged particles with high energies can directly ionize atoms. On the other hand electrically neutral particles interacts only indirectly, but can also transfer some or all of their energies to the matter. It would certainly simplify matters if biological effects of radiation were directly proportional to the absorbed dose. Unfortunately, biological effects depend also on the way in which the absorbed dose is distributed along the path of the radiation. Studies have shown that alpha and neutron radiation cause greater biological damage for a given energy deposition per kg of tissue than gamma radiation does. It was discovered, biological effects of any radiation increases with the linear energy transfer (LET). In short, the biological damage from high-LET radiation (alpha particles, protons or neutrons) is much greater than that from low-LET radiation (gamma rays). This is because the living tissue can more easily repair damage from radiation that is spread over a large area than that which is concentrated in a small area. Because more biological damage is caused for the same physical dose (i.e., the same energy deposited per unit mass of tissue), one gray of alpha or neutron radiation is more harmful than one gray of gamma radiation. This fact that radiations of different types (and energies) give different biological effects for the same absorbed dose is described in terms of factors known as the relative biological effectiveness (RBE) and the radiation weighting factor (wR).

References:

Radiation Protection:

  1. Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8/2010. ISBN-13: 978-0470131480.
  2. Stabin, Michael G., Radiation Protection and Dosimetry: An Introduction to Health Physics, Springer, 10/2010. ISBN-13: 978-1441923912.
  3. Martin, James E., Physics for Radiation Protection 3rd Edition, Wiley-VCH, 4/2013. ISBN-13: 978-3527411764.
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Nuclear and Reactor Physics:

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  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

See above:

Equivalent Dose