Kerma

In Section 15.15 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I define the kerma. It’s measured in the same units as absorbed dose: J/kg, or gray. What’s the difference between the two? Kerma indicates the energy transferred to charged particles, while dose indicates the energy imparted to (or absorbed by) the tissue. Kerma is more closely related to the number of photons in the tissue, but absorbed dose is more closely related to biological damage. In Radiation Therapy Physics, Hendee, Ibbott and Hendee distinguish between kerma and dose.

The kerma (an acronym for kinetic energy released in matter) is the sum of the initial kinetic energies of all IP [ion pairs] liberated in a volume element of matter, divided by the mass of the matter in the volume element. The absorbed dose is the energy actually absorbed per unit mass in the volume element. If ion pairs escape the volume element without depositing all of their energy, and if they are not compensated by ion pairs originating outside the volume element but depositing energy within it (electron equilibrium), the kerma exceeds the absorbed dose. The kerma also is greater than the absorbed dose when energy is radiated from the volume element as bremsstrahlung or characteristic radiation. Under conditions in which electron equilibrium is achieved and the radiative energy loss is negligible, the kerma and absorbed dose are identical. The output of x-ray tubes is sometimes described in terms of air kerma expressed as the energy released per unit mass of air.

Figure 15.32 of IPMB plots the energy transferred and the energy imparted in 2-cm-thick slices versus depth when a 10 MeV photon beam is incident on water, calculated using Russ’s program MacDose.

If we divide both energies by the mass of the slice and average over many simulations, we get plots of the absorbed dose (dashed curve) and the kerma (solid curve). Hendee et al. provide a similar plot in their Figure 5-7.

The difference between kerma and absorbed dose is useful in explaining the skin-sparing effect of high-energy photons such as multi-MV x rays used in radiation therapy. As shown in Figure 5-7, the kerma is greatest at the surface of irradiated tissue because the photon intensity is highest at the surface and causes the greatest number of interactions with the medium. The photon intensity diminishes gradually as the photons interact on their way through the medium. The electrons set into motion during the photon interactions at the surface travel several millimeters in depth before their energy is completely dissipated… These electrons add to the ionization produced by photon interactions occurring at greater depths. Hence, the absorbed dose increases over the first few millimeters below the surface to reach the greatest dose at the depth of maximum dose (d_max) several millimeters below the surface [d_max is about 0.05 m in Fig. 15.32 of IPMB]. This buildup of absorbed dose over the first few millimeters below the skin is responsible for the clinically important skin-sparing effect of high-energy x and γ rays. Beyond d_max, the absorbed dose also decreases gradually as the photons are attenuated. At depths greater than d_max, the kerma curve falls below that for absorbed dose because kerma reflects the photon intensity at each depth, whereas absorbed dose reflects in part the photon intensity at shallower depths that sets electrons into motion that penetrate to the depth.

William Hendee, the lead author of Radiation Therapy Physics, is a giant in medical physics. He was the editor of the journal Medical Physics from 2005 to 2013. In addition to Radiation Therapy Physics, he wrote another textbook, with E. Russell Ritenour, about Medical Imaging Physics. These two books are at a level similar to IPMB, but with less mathematics and a narrower focus, overlapping our Chapters 13-18. A fourth edition of Radiation Therapy Physics is out, with a new title: Hendee‘s Radiation Therapy Physics.

My connection to Hendee is that—according to an interview for the American Society for Radiation Oncology—he worked for a couple years as a graduate student at Vanderbilt University with Robert Lagemann. I knew Lagemann when I was a graduate student at Vanderbilt twenty years after Hendee was there, and I served as the Robert T. Lagemann Assistant Professor of Living State Physics at Vanderbilt from 1995 to 1998.

Listen to Hendee discuss medical physics in his own words.