# Lesson 15 - Dose equivalence

In this lesson we translate the physical dosimetric concepts learned in the previous lesson into the biological effects that we are usually called upon to quantify.  (I say "usually" with an eye toward our previous widely-defined concept of "detector" -- some of our "detectors" are NOT biological, e.g., detector response, total flux, TLD readings, etc.)

## Relative Biological Effectiveness

The direct translation of absorbed dose into biological effect can be obtained using a "reverse method" of measuring the ratio of the type and severity of a given biological effect (e.g., genetic damage, onset of leukemia, etc.) due to a given dose of some given particle at some given energy to the effect of the same dose of a reference particle.  The reference particle is usually 250 keV photons (or, more precisely, an x-ray source with this peak energy spectrum)..

Example:  If a dose of 10 rad of 5 MeV neutrons produces a 10 times greater incidence of leukemia in a controlled population than 10 rads of the reference 0.25 MeV photons, the "leukemia RBE" for 5 MeV neutrons would be 10.

Note that:

1. RBE differs for (a) different types of particle, (b) different energies for the same type of particle, and (c) different biological effects being examined.
2. Despite this detail of dependence, it DOES NOT depend on the dose level itself.  In our above example, we would take the results and ASSUME that 20 rad of 5 MeV neutrons would produce 10 times the leukemia incidence of 20 rads of the reference photons.   This might not be true.

## Quality Factor, Q

For regular health physics work, the idea of RBE is simplified to a so-called quality factor, Q, that is used the same way as RBE (i.e., a relative measure of biological effect for different types and energies of particles) with the following characteristics:

1. The biological effects of interest by which quality factors are defined are set to be the long-term health effects of cancer incidence and/or genetic effects of radiation.   This concentrates our concern on the most commonly measured (and worried about) health effects of occupational exposure and accidental public exposure.
2. Rather than depend on direct "rad vs. rad" biological effect measurements, the quality factor is defined for a given charged particle as depending on the linear energy transfer (LET) in water, which we learned earlier was a measure of how quickly a particle loses energy as it slows down.  The common unit for LET is keV/micrometer.
3. There are two "flavors" of LET (finite and infinite) based on whether all of the energy loss of a charged particle is considered imparted to the material in its path () or whether a lesser amount is considered imparted to the material in its path because of fact that delta rays (i.e., high energy secondary electrons) carry away some of the energy to be imparted some distance from the path (, where the is a distance).  In this notation, the subscript concerns the distance from the path that is considered to be "on" the path.  The Q value is defined using , imparting all of the energy lost by the particle to the particles path.

Note: Tables 5.1 and 5.2 give two translations from to Q that have been proposed.  Most of the response functions that you will encounter (at least for the next few years) are based on Table 5.1

1. For primary (i.e., uncharged) particles, we go with an average quality factor, , which is based on a dose-averaging of the quality factors of the secondary charged particles and scattered primary particles.   For example, if a neutron interaction produces 5 secondary particles (including the recoil nucleus), each one of which has an associated absorbed dose, , and quality factor, , the equation for the average quality factor would be:

where D is the total dose, given by:

Example: The text makes an interesting statement when it says that "The ICRP has suggested that for electrons a quality factor of unity may be used for all energies, regardless of what the table might seem to require."  Let's use our Chapter 3 charged particle slowing-down experience to see what the table might "seem to require" for electron energies of 1, 10 and 100 MeV in water of density 1 g/cc.

Answer:  Using the quadratic fits from Table 3.6, we would get ranges for electrons of:

1 MeV ==>

10 MeV ==>

100 MeV ==>

These would translate into values of 0.24, 0.19, and 0.33, well within the Q=1 range from both Table 5.1 and Table 5.2.

## Dose Equivalence

The unit for dose equivalence is the Sievert (Sv); the common symbol is H.  The equation for dose equivalence is::

H will be in units of Sievert if D is in units of Gray (Gy).  is, of course, dimensionless, but don't be fooled by this fact into thinking that the Sievert is somehow "equal" to the Gray; the two units measure different things (i.e., relative biological effect vs. deposited energy), so should not be confused.

In the "other" units, H will be in rem ("Roentgen equivalent man" is how I learned it) if D is in rad.