Essentials of Nuclear Medicine Physics, Instrumentation, and Radiation Biology. Rachel A. Powsner
the ratio of intensity at the point the beam exits the attenuator, Iout, to the intensity it had where it entered, Iin. Attenuation is an exponential function of the thickness, x, of the attenuator in centimeters. That the function is exponential can be understood to mean that if half of the beam is lost in traversing the first centimeter of material, half of the remainder will be lost traversing the next centimeter, and so on. This resembles the exponential manner in which radioactivity decays with time. Expressed symbolically,
where μ, the linear attenuation coefficient is a property of the attenuator. When, as is usually the case, thickness is given in centimeters, the linear attenuation coefficient is expressed as “per centimeter” or “cm–1”. As might be expected, the linear attenuation coefficient is greater for dense tissue such as bone than for soft tissue such as fat. In general, the linear attenuation coefficient depends on both the energy of the photons and on the average atomic number (Z) and thickness of the attenuator. The lower the energy of the photons or the greater the average atomic number or thickness of the attenuator, the greater the attenuation (Figure 2.6).
Figure 2.3 Angle of photon scattering.
Figure 2.4 Photoelectric effect.
A separate term, the mass attenuation coefficient (μ/ρ), is the linear attenuation coefficient divided by the density of the attenuator. When the density of a material is given in grams/cm3 the units of the mass attenuation coefficient are cm2/gram.
Absorption of radiation describes another aspect of the process of attenuation. Attenuation describes the weakening of the beam as it passes through matter. Absorption describes the transfer of energy from the beam to the matter.
Half‐value and tenth‐value layers
A material’s effectiveness as a photon attenuator is described by the attenuation coefficient. An alternative descriptor, one that is the more easily visualized, is the “half‐value layer” (HVL) which is simply the thickness of a slab of the attenuator that will remove exactly one half of the radiation of a beam. A second slab of the same thickness will remove half of the remainder (see comment below regarding monoenergetic beams), leaving one quarter of the original beam, and so forth. For a gamma photon of 100 keV, the HVL in soft tissue is about 4 cm [1].
Table 2.1 Predominant photon interactions in common materials at diagnostic energies
| Material | Atomic number (Z) | Density (gm/cm3) | Predominant interaction |
|---|---|---|---|
| H2O | 7.4 | 1.0 | Compton scatter |
| Soft tissue | 7.5 | 1.0 | Compton scatter |
| Glass (silicon) | 14 | 2.6 | Compton scatter |
| O2 (gas) | 16 | 0.0014 | Compton scatter |
| NaI (crystal) | 32 | 3.7 | Photoelectric effect |
| Lead | 82 | 11.4 | Photoelectric effect |
| Leaded glass | 14, 82 | 4.8–6.2 | Photoelectric effect |
For any attenuator the HVL can be determined experimentally using a photon source and a suitable detector. For calculations involving attenuation of high‐intensity radiation beams, an entirely similar concept, the tenth‐value layer (TVL), is useful. The TVL is the thickness of the attenuator that will transmit only one tenth of the photons in the beam. For a monoenergetic beam (containing photons of identical energies) directed at a material, two such thicknesses will transmit only one hundredth of the beam. If, however, the beam contains photons of different energies this rule is not applicable (see text box on beam hardening).
Figure 2.5 Attenuation.
Table 2.2 lists half and tenth value layer of lead for photons emitted by some common medical radionuclides.
For a monoenergetic beam of photons, the linear attenuation coefficient, μ, is related to the HVL as follows:
Beam hardening
When a beam contains photons of different energies such as an X‐ray beam, it is termed polychromatic. As a polychromatic beam penetrates a material, lower energy photons are extinguished or scattered preferentially over higher energy photons and the result is that, while the overall intensity is diminished, the average energy of the transmitted fraction of the beam is increased. This phenomenon is known as beam hardening. A hardened beam is more penetrating and so a second HVL or TVL will be slightly thicker than the first.
Figure 2.6 The amount of attenuation of a photon beam is dependent on the photon energy and the thickness (and/or atomic number) of the attenuator.
Table 2.2 HVL and TVL of lead for photons of common medical nuclides
| Nuclide | Gamma energy (keV) |
Half‐value layer (cm)
|
|---|