Dose quantities and limits

On the second morning Marcel writes four words across the whiteboard: gray, sievert, equivalent, effective. "Half the arguments I have heard in twenty years came from people using these words loosely," he says. A contractor once reported a dose in gray to a regulator; a manager once added a skin dose to a whole-body dose and called the total an effective dose. This lesson sets out the quantities carefully, then the limits that are written in them.

Absorbed dose

The starting point is physical. The absorbed dose \(D\) is the energy deposited by ionizing radiation per unit mass of material:

The unit is the gray (Gy). Absorbed dose applies to any material and any radiation, and it is what deterministic thresholds are written in. It says nothing about which radiation delivered the energy, which matters for stochastic risk.

Equivalent dose and radiation weighting

To account for the greater harm done by dense tracks, the absorbed dose averaged over an organ or tissue \(T\) is multiplied by a radiation weighting factor \(w_R\). The result is the equivalent dose:

The unit is the sievert (Sv), which has the same dimensions as the gray but a different meaning.

The Canadian Radiation Protection Regulations set out the weighting factors to be used in schedules attached to the regulations, so that every licensee calculates doses the same way.

Effective dose and tissue weighting

Organs differ in their sensitivity to cancer. To combine doses to different organs into a single number that reflects total stochastic risk, each equivalent dose is multiplied by a tissue weighting factor \(w_T\), and the products are added:

The effective dose \(E\), also in sieverts, is the quantity in which the main dose limits are written. A uniform whole-body dose of 1 mSv gives an effective dose of 1 mSv; a dose of 10 mSv to the thyroid alone gives an effective dose of only \(0.04 \times 10 = 0.4\) mSv. Effective dose is a protection quantity: it is meant for setting limits, comparing options and demonstrating compliance, not for estimating the risk to a particular person, for which organ doses and age and sex specific models are better.

Operational quantities: what dosimeters measure

Effective dose cannot be measured directly; it needs the dose to every organ inside the body. Instruments and dosimeters are therefore calibrated in operational quantities defined by the International Commission on Radiation Units and Measurements (ICRU), which are measurable and designed to give a reasonable, usually slightly conservative, estimate of effective dose.

For penetrating gamma radiation, the reading of a whole-body dosimeter in Hp(10) is taken as the effective dose from external exposure. For weakly penetrating radiation, such as beta particles, the shallow quantity Hp(0.07) is the one that matters, and it is compared with the skin limit. Because lens dose limits were lowered, lens dosimeters reading Hp(3) are now used in some high-beta work areas.

Committed dose

A radionuclide taken into the body keeps irradiating tissue until it decays or is excreted. The committed effective dose is the total effective dose that an intake will deliver over the following 50 years for an adult, assigned in full to the year of intake. Lesson 7 shows how it is calculated with dose coefficients. Assigning the whole committed dose at once makes internal and external doses directly comparable and means limits are not exceeded later by an old intake.

The dose limits

With the quantities defined, the limits can be stated. They are set so that deterministic effects are prevented completely and stochastic risk is kept at a level that society accepts for workers and for the public.

The five-year limit is the one that matters most in practice at Canadian stations: a worker could receive 50 mSv in one year only if the other four years together stayed under 50 mSv. Licensees also set their own action levels, well below the limits, which trigger investigation and reporting to the CNSC when exceeded.

# Equivalent and effective dose with ICRP 103 weighting factors, then a check against limits.
W_R = {'photon': 1.0, 'electron': 1.0, 'proton': 2.0, 'alpha': 20.0}
W_T = {'red marrow': 0.12, 'colon': 0.12, 'lung': 0.12, 'stomach': 0.12, 'breast': 0.12,
       'remainder': 0.12, 'gonads': 0.08, 'bladder': 0.04, 'gullet': 0.04, 'liver': 0.04,
       'thyroid': 0.04, 'bone surface': 0.01, 'brain': 0.01, 'salivary glands': 0.01, 'skin': 0.01}
print("sum of tissue weighting factors =", round(sum(W_T.values()), 2))

def equivalent(absorbed_mGy):
    """absorbed_mGy: dict radiation -> mGy averaged over the organ"""
    return sum(W_R[r] * d for r, d in absorbed_mGy.items())

# Steam generator example: uniform 0.8 mSv external gamma plus 2.0 mSv to the lung from an inhaled particle
H = {t: 0.8 for t in W_T}              # uniform gamma: every tissue 0.8 mSv
H['lung'] += equivalent({'alpha': 0.1})  # 0.1 mGy alpha to lung = 2.0 mSv
E = sum(W_T[t] * H[t] for t in W_T)
print(f"lung equivalent dose {H['lung']:.2f} mSv; effective dose {E:.2f} mSv")

# Thyroid-only dose
print(f"25 mSv to the thyroid only -> effective dose {0.04 * 25:.2f} mSv")

# Annual record check (mSv): limits for a worker; skin and extremity are separate
record = {'effective': 3.2 + 0.6, 'skin Hp(0.07)': 14.0, 'extremity': 40.0, 'lens (ICRP)': 3.5}
limits = {'effective': 50.0, 'skin Hp(0.07)': 500.0, 'extremity': 500.0, 'lens (ICRP)': 50.0}
for q in record:
    print(f"{q:13s} {record[q]:6.1f} mSv of {limits[q]:5.0f}  ({100*record[q]/limits[q]:4.1f} % of limit)")

sum of tissue weighting factors = 1.0
lung equivalent dose 2.80 mSv; effective dose 1.04 mSv
25 mSv to the thyroid only -> effective dose 1.00 mSv
effective        3.8 mSv of    50  ( 7.6 % of limit)
skin Hp(0.07)   14.0 mSv of   500  ( 2.8 % of limit)
extremity       40.0 mSv of   500  ( 8.0 % of limit)
lens (ICRP)      3.5 mSv of    50  ( 7.0 % of limit)

Common confusions

Marcel ends with the mistakes he sees most. Adding skin or extremity doses to effective dose double-counts risk and breaks the definition. Reporting a neutron dose in gray when the limit is in sieverts leaves out the radiation weighting factor of up to 20. Using effective dose to describe a medical patient's individual risk ignores age and sex. Treating the dose limit as the target forgets that the limit is the edge of the acceptable region, not its centre; under ALARA, doses should be far below it. And forgetting the committed dose from an intake can make a worker appear to have room left under a limit that has in fact already been used.

Dose rate, dose and the units on the meter

Instruments add their own source of confusion. A survey meter shows a dose rate, in µSv/h or mSv/h, while a dosimeter accumulates a dose. A worker who stands for 12 minutes beside a valve reading 0.5 mSv/h receives 0.1 mSv; the meter never shows that number. Older instruments may read in units of exposure, the roentgen, which measures ionization in air rather than dose in tissue. For gamma rays in the energy range of most reactor work, 1 R corresponds to about 8.7 mGy in air and close to 10 mSv in tissue, so the old rule of thumb that one roentgen is about one rem, or 10 mSv, is adequate for field estimates but not for records.

Canadian practice uses SI units throughout: becquerel, gray and sievert. Records and reports to the CNSC and the National Dose Registry are always in millisieverts, and any instrument still reading in older units is converted before results are recorded.

A further distinction is between dose to a person and the reading of a dosimeter on that person. A dosimeter worn on the chest measures Hp(10) at the chest. If the worker leans over a source, the head and hands may receive more than the chest, which is why extremity rings, head dosimeters and multiple whole-body dosimeters are used in non-uniform fields such as steam generator entries. Where several whole-body dosimeters are worn, the program specifies how they are combined into an effective dose, often with weighting schemes for front and back or for different body regions.