Radiation Biophysics
Third Lecture: Energy Transfer

• Compton Processes in Tissue
  We'll of course cover interactions between radiation and tissue in excruciating detail in subsequent class periods. But a fwe remarks are in order now. An important factor in studies of soft biological tissue is that it is for the most part composed of low-Z elements: H, C, N, O, and smaller amounts of S (mostly in proteins) and P (mostly in nucleic acids). Other elements make a modest contribution to the absorbing material in bone and other harder tissues--Ca and (again) P. But the interaction of radiation with tissue primarily involves light elements, which have relatively low cross-sections for interaction with photons.

  Compton processes are the most important sources of interactions between tissue and photons in the 10 KeV to 10 MeV range. Other interactions do occur--mostly coherent interactions at very low energies, photoelectric effects at intermediate energies, and pair production at high energies. But the Compton effects predominate otherwise.

• Charged Particles and Matter
  The most important mechanism by which energy is deposited in biological systems is the interactions of high-energy electrons with tissue. A 200 KeV electron traveling through tissue will ionize or excite roughly 15000 water molecules. These ionizations and excitations (whether in water or in other (H,C,N,O)-containing biomolecules) are the principal source of radiation damage in tissue.
• Final Steps in Energy Absorption
  Energy is transferred in the following ways:
  1. Multiple collisions:
     Here, a fast electron bounces off of several bound electrons in the medium. The amount of momentum transferred in each event is small, so the input electron does not deviate very much from its original path. Sometimes the amount of energy imparted to the bound electron is enough that it itself is scattered off and starts the process again, but at a lower energy. These secondary traveling electrons are known as delta rays.
  2. Photoelectric processes:
     Here the primary electron is absorbed and a K or L-shell electron is ejected by the now-familiar (I hope!) photoelectric effect. The empty shell is then filled by an outer-shell electron with the resulting emission of a photon. This process has little relevance in low-Z media.
  3. Bremsstrahlung radiation:
     As we have mentioned, any decelerated electron radiates energy in the form of braking or bremsstrahlung photons, typically in the X-ray range. This is important for very high-energy input electrons, for which the kinetic energy is much larger than the rest mass energy.
  4. Direct collisions:
     This is a special case of the previous category, in which the electron stops altogether and all of its kinetic energy gets re-expressed as photons.

  If an electron enters a medium at high energy, it experiences the following fates:

  1. Bremsstrahlung emission;
  2. ionizations that leave the secondary electron more or less in place;
  3. ionizations in which the secondary electron travels and transfers energy to the medium in various ways.

  This last case is the "delta ray" case and is responsible for much of the effect of a high-energy electron. Every time one of these delta rays is produced, the original electron becomes less energetic and moves slower. This actually increases the amount of energy transferred per interaction, since slower electrons transfer more of their energy. Overall the energy brought in by the electron will be present in the medium through ionization and excitation, and through deposition of thermal energy (warming).

• Dose and Kerma: a Review
  This is a reminder: dose is defined as energy deposited per unit mass. We reiterate that the biological effects of radiation don't depend on the amount of energy transferred (Ein - Eout); they depend on the portion of that energy that actually stays behind as absorbed energy. Therefore biological effects depend on dose, which is energy absorbed per unit mass, not on kerma, which is energy transferred per unit mass. The biological effect of dose is dependent on the way that energy is partitioned among ionization, excitation, and thermal deposition. So even when we measure dose rather than kerma, we need to ask how the dose is partitioned before we can sort out the kinds of biological effects it will have.

  Kerma (energy transfer) tends to happen in the first few microns of depth into a medium, but the actual absorptions are often deeper. Thus the dose perhaps peaks at a moderate depth into the medium, while the kerma peaks at the surface. Some depositions of energy have relatively little impact on the tissue, whereas others affect tissue substantially. So we attempt to fudge this phenomenon by discussing "relative biological effectiveness" (RBE) of various kinds of radiation, so that the kinds of radiation that cause more extreme tissue effects are up-weighted relative to others.

• Neutron Interactions with Tissue
  Neutrons are heavy (m_n ~ 938 MeV/c²) and uncharged, so they behave differently from electrons. The fact that they are uncharged means that they do not interact Coulombically with tissue, although some of the products of their interactions with tissue are charged and can interact Coulombically.

  Neutrons can interact with matter in the following five ways:

  1. Elastic scatter:
     This is important for thermal (low-energy) neutrons and intermediate- energy neutrons. Here neutrons interact with nuclei and impart some of their kinetic energy to the nucleus. This produces a moving charged particle, and that can interact with a medium just as any moving charged particle can--with secondary ionizations, excitations, and thermal transfers. The energy transferred to the target nucleus is given by
     E_t = E_n * (4M_aM_N) cos²θ / (M_a + M_n)²
     which can be integrated over all angles theta to get an average energy transferred of
     E_t,ave = E_n * (2M_aM_N) / (M_a + M_n)²
     
  2. Inelastic scatter:
     This is significant for high-energy neutrons in which the nucleus, in effect, captures the neutron and re-emits it along with a gamma ray. The resulting gamma is usually energetic enough that it does not interact with the medium very much, and the nucleus does not get much energy imparted to it, so not much happens.
  3. Non-elastic scatter:
     
  4. Neutron capture:
     
  5. Spallation:
     
• Track Structure and Microdosimetry
  We'll cover this next week.