---
title: Dosimetry, Radiation Biology, and Protection
module: Radiation and Applications
moduleNumber: 11
lessonNumber: 4
order: 1104
summary: >
  Absorbed dose is the energy deposited per unit mass, measured in gray. Equal
  absorbed doses do unequal biological damage because densely ionizing radiation
  deposits its energy along short tracks: weighting the dose by a radiation factor
  gives the equivalent dose, and weighting by tissue sensitivity gives the
  effective dose, both in sieverts. Deterministic effects have a threshold and a
  severity that grows with dose; stochastic effects are assumed to follow a
  linear-no-threshold probability. Natural background dominates the dose to the
  population, and protection rests on time, distance, and shielding.
topics: [Radiation and Applications]
sources:
  - book: Krane
    ref: "Ch. 7 — Detecting Nuclear Radiations; §7.5 Radiation Dose and Its Measurement"
  - book: Tipler & Llewellyn
    ref: "Ch. 11 — Nuclear Physics; §11-9 Radiation Dosage"
draft: false
---

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.[^krane-dose]

## Absorbed dose and linear energy transfer

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

$$
D = \frac{\d\bar\varepsilon}{\d m},
$$

measured in **gray**, $1\ \mathrm{Gy} = 1\ \mathrm{J/kg}$. 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
$D = \Phi\,(1/\rho)(-\d E/\d x)$ for charged particles, where $\Phi$ is the fluence
(particles per unit area).

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

$$
L = \frac{\d E}{\d l},
$$

the energy a charged particle deposits locally per unit track length, measured in
$\mathrm{keV/\mu m}$. 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 $\mathrm{keV/\mu m}$, and ionizes sparsely; an alpha particle has a high
LET, of order $100\ \mathrm{keV/\mu m}$, 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.

$$
% caption: Equal energy deposited by a low-LET electron and a high-LET alpha: the
% electron ionizes sparsely along a long, wandering track, while the alpha lays
% down a short, dense column of ionization that does more biological damage per
% unit dose.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  % electron track: long, sparse dots, wandering
  \draw[black, thick] (0.4,3.4) .. controls (2.0,3.7) and (3.5,2.9) .. (5.4,3.3);
  \foreach \x/\y in {0.7/3.45, 1.5/3.55, 2.3/3.35, 3.1/3.15, 3.9/3.1, 4.7/3.25} \fill[black] (\x,\y) circle (1.1pt);
  \node[black, font=\scriptsize, anchor=west] at (5.5,3.3) {low-LET electron};
  % alpha track: short, dense column
  \draw[acc, very thick] (0.4,1.2) -- (2.4,1.2);
  \foreach \x in {0.5,0.7,0.9,1.1,1.3,1.5,1.7,1.9,2.1,2.3} {\fill[acc] (\x,1.35) circle (1.3pt); \fill[acc] (\x,1.05) circle (1.3pt);}
  \node[acc, font=\scriptsize, anchor=west] at (2.6,1.2) {high-LET alpha};
\end{tikzpicture}
$$

## 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,

$$
H_T = \sum_R w_R\, D_{T,R},
$$

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** $w_T$,

$$
E = \sum_T w_T\, H_T, \qquad \sum_T w_T = 1,
$$

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.

$$
% caption: The dosimetry hierarchy: a radiation fluence deposits an absorbed dose
% in gray, weighting by radiation type gives the equivalent dose in sievert, and
% weighting by tissue sensitivity gives the effective dose in sievert.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  \node[draw=black, thick, fill=black!5, align=center, minimum height=1.0cm, minimum width=2.1cm] (flu) at (0,0) {f\/luence\\(per area)};
  \node[draw=black, thick, fill=black!5, align=center, minimum height=1.0cm, minimum width=2.1cm] (abs) at (3.3,0) {absorbed\\dose (Gy)};
  \node[draw=black, thick, fill=black!5, align=center, minimum height=1.0cm, minimum width=2.1cm] (equ) at (6.6,0) {equivalent\\dose (Sv)};
  \node[draw=black, thick, fill=black!5, align=center, minimum height=1.0cm, minimum width=2.1cm] (eff) at (6.6,-2.0) {ef\/fective\\dose (Sv)};
  \draw[->, black, thick] (flu) -- (abs);
  \draw[->, black, thick] (abs) -- (equ);
  \draw[->, black, thick] (equ) -- (eff);
  \node[black, font=\scriptsize, anchor=south] at (4.95,0.05) {times $w_R$};
  \node[black, font=\scriptsize, anchor=west] at (6.75,-1.0) {times $w_T$};
  \node[black, font=\scriptsize, anchor=south] at (1.65,0.05) {energy};
\end{tikzpicture}
$$

## 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.

$$
% caption: Deterministic effects have a threshold below which they do not occur and
% a severity that rises above it; stochastic effects are modeled as a probability
% rising linearly from zero dose with no threshold.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  \draw[->, black] (0,0) -- (8.2,0) node[right, black!70] {dose};
  \draw[->, black] (0,0) -- (0,4.4) node[above, black!70] {ef\/fect};
  % stochastic: straight line from origin (dashed neutral)
  \draw[black, very thick, densely dashed] (0,0.15) -- (7.6,3.9);
  \node[black, font=\scriptsize, anchor=south east] at (7.4,3.6) {stochastic (LNT)};
  % deterministic: flat zero then threshold rise (accent)
  \draw[acc, very thick] (0,0.1) -- (3.4,0.1)
    .. controls (4.2,0.2) and (4.8,1.6) .. (5.4,2.6)
    .. controls (5.9,3.4) and (6.4,3.9) .. (7.0,4.1);
  \draw[black, dashed] (3.4,0) -- (3.4,0.9);
  \node[anchor=north, black!70, font=\scriptsize] at (3.4,0) {threshold};
  \node[acc, font=\scriptsize, anchor=east] at (6.6,3.5) {deterministic};
\end{tikzpicture}
$$

## 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.

| Source | Typical annual effective dose |
| --- | --- |
| Radon and decay products (inhaled) | $\sim 1.2\ \mathrm{mSv}$ |
| Terrestrial gamma (soil, rock) | $\sim 0.5\ \mathrm{mSv}$ |
| Cosmic rays (at sea level) | $\sim 0.4\ \mathrm{mSv}$ |
| Internal ($^{40}\mathrm{K}$, $^{14}\mathrm{C}$) | $\sim 0.3\ \mathrm{mSv}$ |
| Medical (imaging, average) | $\sim 0.6\ \mathrm{mSv}$ |

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.

$$
% caption: The average annual effective dose is dominated by natural sources,
% radon foremost, with cosmic and terrestrial gamma and internal emitters, plus a
% substantial and growing medical contribution.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  \draw[->, black] (0,0) -- (0,4.4) node[above, black!70] {annual dose (mSv)};
  \draw[black] (0,0) -- (7.8,0);
  % bars
  \draw[acc, thick, fill=acc!25] (0.5,0) rectangle (1.5,3.0);
  \draw[black, thick, fill=black!10] (2.0,0) rectangle (3.0,1.25);
  \draw[black, thick, fill=black!10] (3.5,0) rectangle (4.5,1.0);
  \draw[black, thick, fill=black!10] (5.0,0) rectangle (6.0,0.75);
  \draw[black, thick, fill=black!10] (6.5,0) rectangle (7.5,1.5);
  \node[black, font=\scriptsize, anchor=north, align=center] at (1.0,-0.05) {radon};
  \node[black, font=\scriptsize, anchor=north, align=center] at (2.5,-0.05) {terr.};
  \node[black, font=\scriptsize, anchor=north, align=center] at (4.0,-0.05) {cosmic};
  \node[black, font=\scriptsize, anchor=north, align=center] at (5.5,-0.05) {internal};
  \node[black, font=\scriptsize, anchor=north, align=center] at (7.0,-0.05) {medical};
  \node[black, font=\scriptsize, anchor=south] at (1.0,3.0) {natural};
\end{tikzpicture}
$$

## 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.

> **Result.** The dose hierarchy converts a physical energy deposit into a risk
> estimate: absorbed dose in gray, weighted by $w_R$ to the equivalent dose and by
> $w_T$ to the effective dose, both in sieverts. Deterministic effects have a
> threshold; stochastic effects are managed under the linear-no-threshold model.
> Natural background, radon foremost, dominates the population dose, and external
> exposure is controlled by time, distance, and shielding. These same interactions
> and quantities underlie the beneficial uses of radiation, taken up
> [in the applications lesson](/nuclear-physics/radiation-matter-applications/nuclear-applications-dating-medicine).

[^krane-dose]: **Krane**, _Introductory Nuclear Physics_, §7.5 (Radiation Dose), and
**Tipler & Llewellyn**, _Modern Physics_, §11-9 (Radiation Dosage). The gray and
absorbed dose, linear energy transfer, the radiation and tissue weighting factors
giving equivalent and effective dose in sieverts, the deterministic/stochastic
distinction and the linear-no-threshold model, background sources, and the
time-distance-shielding protection principles. The weighting factors and dose
quantities follow the recommendations of the International Commission on
Radiological Protection (ICRP).