Fig. 3.1
Energy loss by ionization. Multiple Coulomb scattering (MCS) with multiple events. Reproduced from Nunes [1]
As mentioned, regarding the energy loss by ionization, −dE/dx corresponds to 1/β 2 and equals 1/E (continuous drop: formulas, tables, or approximations). With MCS, formulas and approximations are used. Nuclear fragmentation consists of simple events, and many secondary particles of several species are produced at large angles (this process is difficult to describe using a formula; see Fig. 3.2). A diagrammatic representation of a nucleus–nucleus collision is shown in Fig. 3.3.
3.1.1.2 Linear Energy Transfer
The term linear energy transfer (LET) is often used in dosimetry and describes the effect of radiation on the matter. It represents the retarding force acting on ionizing charged particles traveling through matter—that is, how much energy ionizing particle material passed through the transfer unit of distance. LET depends on the nature of the radiation and the material traversed [3]. Thus, a high LET radiation will attenuate the radiation more rapidly, preventing deeper penetration. The high concentration of deposited energy can cause more severe injury to any microscopic structure near the particle track. LET is expressed as keV/μm or MeV/cm.
Despite the similarity between LET and stopping power, it must be remembered that they are different because stopping power has a nuclear component, and this component does not cause electron excitation. The carbon ions have sufficiently high LET components to provide biological efficiency as well as superior depth-dose distribution. The LET of carbon ion beams strongly increases in the incidence point on the body with increasing depth, reaching a maximum in the peak area (Fig. 3.4); in contrast, the LET beams of neutrons remains uniform at any depth in the body. This property is extremely advantageous from the therapeutic point of view in terms of its biological effect in the tumor. Thus, carbon ion beams form a large peak in the physical body due to an increase of dose and its biological efficacy to proceed at greater depths in the body. This fact is very important because of its potential use in the treatment of intractable cancers that are resistant to photon beams.
Fig. 3.4
Comparison of linear energy transfer (LET) and relative biological effectiveness (RBE) for carbon ions at 290 MeV. Spread-out Bragg peak = 60 mm. Courtesy National Institute of Radiological Sciences (NIRS)
The linear energy transfer of charged particles in a medium is L = dE/dl, where dE is the average energy lost due to collisions and dl is the distance traversed by the particle. The behavior of increasing values of LET and relative biological effectiveness (RBE) are shown in Fig. 3.4.
3.1.2 Radiation Dose
3.1.2.1 Absorbed Dose
The absorbed dose is the energy deposited per unit mass in the medium (target) during exposure to ionizing radiation. It is measured in Gray (Gy), with 1 Gy = 1 J/kg. Thus, 1 Gray represents the absorption of 1 J of radiation per 1 kg of matter using the International System of Units. Because 1 J = 107 ergs and 1 kg = 1,000 g, 1 Gy = 107 × 10−3 erg/g = 104 erg/g = 100 cGy.
3.1.2.2 Equivalent Dose
The equivalent dose takes into account the biological effectiveness of different types of radiation. It is calculated by multiplying the absorbed dose by a radiation weighting factor appropriate to the type and energy of the radiation and can be calculated using the following equation:
For high doses, the International Commission on Radiological Protections recommends a different definition of the equivalent dose:
where H e is the equivalent dose and the weighting factors are replaced by the RBE value for a given radiation type (R) using a specific end point (e). The unit used here for dose is the Gray equivalent (GyE).
3.1.2.3 Effective Dose
The effective dose takes into consideration the dose due to ionizing radiation delivered nonuniformly. It takes into account both the type of radiation and the nature of each organ being irradiated. For a nonuniform radiation exposure, a different tissue weight factor (W T ) is used to reflect the different radiogenic sensitivity from different organs. The effective dose is given in Sv and is calculated as follows:
where H E is the effective dose, W T is the tissue weight factor defined by regulation, and H T is the equivalent dose absorbed by tissue T.
3.1.2.4 Relative Biological Effectiveness
When high doses are employed in particle therapy, the GyE unit has been used for heavy ions, whereas researchers working with protontherapy still use the cobalt Gray equivalent (CGE). The International Commission on Radiation Units and Measurements proposed replacing this unit with RBE-weighted absorbed dose, defined as D RBE,V = RBE × D V . The unit is given in Gy (RBE). The volume (v) must be specified and may correspond to the tumor volume or the planned target volume.
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