# What is Dose?: Quantifying Ionizing Radiation Energy Deposition

Radiation dose, or absorbed dose, is the amount of ionizing radiation energy that is absorbed by a specific mass of matter. Mathematically, consider a small (infinitesimal) volume of matter dV with mass dm. If this volume is exposed to ionizing radiation, the energy absorbed (also called energy imparted) E_{abs} is defined as:

E_{abs} = E_{in} - E_{out} + \sum Q

Where E_{in} and E_{out} are the ionizing radiation energy entering and leaving the volume, respectively. The \sum Q term accounts for any mass-energy conversion that occurs within the volume; \sum Q is positive if mass is converted to energy and negative if energy is converted to mass. Sometimes, it will be helpful to divide ionizing radiation into its charged and uncharged components, in which case the absorbed energy would be equal to:

E_{abs} = \big[ (E_{in})_c + (E_{in})_u \big] - \big[ (E_{out})_c + (E_{out})_u \big] + \sum Q

The absorbed dose D would then be equal to the energy absorbed divided by the mass:

D = \frac{E_{abs}}{dm}

The unit for radiation dose is called the Gray (Gy), and is represented by 1 joule per kilogram in SI units. Dose is the most important quantity for radiation energy in medicine, as it is directly related to biological effects. Historically, the rad (radiation absorbed dose) has also been used as a dose unit, with 1 rad = 1 cGy.

## Kerma (K)

For uncharged particles such as photons, we are also interested in the amout of radiation energy that is transferred to matter as kinetic energy, a quantity called the kerma (Kinetic Energy Released to MAss). Mathematically, the energy transferred to matter E_{tr} is defined as follows:

E_{tr} = (E_{in})_u - (E_{out})_{u,nr} + \sum Q

Where a new term (E_{out})_{u,nr} has been introduced which quantifies uncharged radiation energy that leaves the volume, excluding radiative losses from charged particles; the most common radiative loss being bremmstrahlung radiation from electrons. So the only radiation energy leaving the volume for kerma calculation is from uncharged particles. The kerma K would then be equal to the energy transferred divided by the mass:

K = \frac{E_{tr}}{dm}

As with absorbed dose, the unit for kerma is the Gray.

## Collision Kerma (K_C) & Radiative Kerma (K_R)

The explanation of kerma in the previous section led to the distinction between radiative and non-radiative losses, where radiative losses occured as charged particles emit uncharged particles (e.g. bremmstrahlung radiation). The kerma can be divided into two components, the collision and radiative kerma, based on this distinction. The collision kerma can be calculated from the net energy transferred E_{net}, which quantifies the transferred energy from photons that is absorbed locally in our previously defined volume dV:

E_{net} = E_{tr} - (E_{out})_{u,r}

E_{net} = (E_{in})_u - (E_{out})_{u,nr} - (E_{out})_{u,r} + \sum Q

So the collision kerma also excludes the uncharged radiation energy leaving the volume from radiative losses. The collision kerma K_C would then be equal to the energy transferred divided by the mass:

K_C = \frac{E_{net}}{dm}

The remaining component of transferred energy, the radiative kerma K_R, is simply the energy transferred to radiative losses:

E_{r} = (E_{out})_{u,r}

K_R = \frac{E_{r}}{dm}

The total kerma is then equal to the sum of collision and radiative kerma:

K = K_C + K_R

## Summary

We have defined the concepts of dose and kerma, which are essential for quantifying how radiation deposits energy to matter. In particular, quantifying dose as a physical entity enables us to measure and then predict biological responses to ionizing radiation, providing informed decisions for radiation safety annd radiation therapy.