Dosimetry, Radiation Biology, and Protection

The biological effect of ionizing radiation depends on how much energy it deposits in tissue and on how that energy is distributed along the tracks. Two equal deposits of energy can do very different damage if one is spread thinly along a long electron track and the other is dumped densely along a short alpha track. Dosimetry separates these factors into a hierarchy of quantities: the physical energy deposit (absorbed dose), the same weighted by the type of radiation (equivalent dose), and finally weighted by the sensitivity of the irradiated tissue (effective dose). The health effects split into two classes with sharply different dose dependence.¹

Absorbed dose and linear energy transfer

The absorbed dose is the energy imparted to matter per unit mass,

measured in gray, $1\mathrm{Gy}=1J/kg$. The older unit, the rad, is $1\mathrm{rad}=10^{-2}\mathrm{Gy}$. Absorbed dose is defined for any radiation and any material, and it is what the stopping powers and attenuation coefficients of the previous lessons determine: a fluence of particles delivers a dose $D=\Phi ({\mu }_{\mathrm{en}}/\rho )E$ for photons of energy $E$, or $D=\Phi (1/\rho )(-\mathbf{d}E/\mathbf{d}x)$ for charged particles, where $\Phi$ is the fluence (particles per unit area).

The microscopic density of energy deposition is the linear energy transfer,

the energy a charged particle deposits locally per unit track length, measured in $keV/\mu \mathrm{m}$. It is the restricted stopping power, counting only energy deposited near the track. A fast electron set in motion by a gamma ray has a low LET, a few $keV/\mu \mathrm{m}$, and ionizes sparsely; an alpha particle has a high LET, of order $100keV/\mu \mathrm{m}$, and leaves a dense column of ionization. The same absorbed dose from these two radiations produces very different amounts of irreparable damage to the DNA in a cell, because dense ionization produces clustered double-strand breaks that the cell cannot repair reliably.

Equivalent and effective dose

To account for the greater damage per gray of high-LET radiation, the absorbed dose is multiplied by a dimensionless radiation weighting factor $w_R$ that reflects the relative biological effectiveness of the radiation type. The result is the equivalent dose to a tissue,

measured in sievert ($\mathrm{Sv}$); the older unit is the rem, $1\mathrm{rem}=10^{-2}\mathrm{Sv}$. The weighting factors are $w_R=1$ for photons, electrons, and muons; $w_R=20$ for alpha particles, fission fragments, and heavy ions; and an energy-dependent value from about $2$ to $20$ for neutrons, peaking near $1\mathrm{MeV}$. A gray of alpha radiation therefore carries the same equivalent dose as twenty grays of gamma radiation.

Different tissues also differ in their sensitivity to radiation-induced cancer. The effective dose sums the equivalent doses over organs, each weighted by a tissue weighting factor $w_T$,

again in sieverts. The $w_T$ (largest for bone marrow, colon, lung, stomach, and breast) are normalized so that a uniform whole-body equivalent dose gives an equal effective dose. Effective dose expresses the total stochastic risk of a nonuniform exposure as the whole-body dose that would carry the same risk.

Deterministic and stochastic effects

Radiation health effects fall into two classes with different dose dependence.

• Deterministic effects (tissue reactions) result from the killing of many cells and appear only above a threshold dose, above which the severity grows with dose. Skin erythema, cataracts, and the acute radiation syndrome are examples; the whole-body threshold for acute syndrome is a few gray delivered in a short time. Below the threshold the effect does not occur.
• Stochastic effects are cancer and heritable mutations, arising from a single cell's damaged but surviving DNA. Here the probability, not the severity, is assumed to rise with dose, with no threshold. Radiation protection adopts the linear-no-threshold (LNT) model, in which the excess cancer risk is proportional to effective dose down to zero, as a conservative basis for setting limits.

Background radiation

Everyone receives a continuous dose from natural and artificial sources, averaging a few millisieverts per year. The natural background is dominated by inhaled radon and its decay products, with contributions from cosmic rays, terrestrial gamma rays from uranium, thorium, and potassium-40 in soil and rock, and internal potassium-40 in the body. The largest artificial contribution is medical imaging.

The natural total near $2.4\mathrm{mSv}$ per year varies widely with altitude and local geology, and the medical average conceals a large spread, since a single CT scan can deliver several millisieverts.

Protection principles

External exposure is reduced by three levers, applied together and captured by the principle of keeping doses as low as reasonably achievable (ALARA).

• Time. The accumulated dose is the dose rate times the exposure time, so minimizing the time spent near a source reduces the dose proportionally.
• Distance. A point source obeys the inverse-square law: the fluence, and so the dose rate, falls as $1/r^2$. Doubling the distance quarters the dose rate, making distance the most powerful and cheapest lever.
• Shielding. Absorbers between source and worker attenuate the radiation. Charged particles are stopped by their range; gamma rays are attenuated exponentially, so high-$Z$ shields such as lead are used; neutrons are moderated by hydrogenous material and then captured.