LET distributions and the influence of various physical factors in modifying radiation damage

Ionizing radiations produce observable effects in living organisms by a series of events, many of which are little understood. For all these radiations the essential step in the process is the passage of rapidly moving charged particles through, or in the immediate vicinity of, a cell. As it passes, the charged particle leaves a track of ionized and excited atoms and molecules which in turn initiate biochemical and biological events which probably form a very complex series and which eventually result in an observable effect such as mutation or the failure of the cell to divide. In an attempt to gain a clearer understanding of the early physico-chemical steps in the process, the dependence of the degree of radiation effect on the characteristics of the radiation and on various physical and chemical factors has been widely studied. It is generally agreed that the most satisfactory physical specification of the quantity of radiation which a cell receives is the absorbed dose. As pointed out by Rossi, absorbed dose is a macroscopic concept and gives no information about the local deposition of energy at the sub-cellular and molecular level. A relatively simple, and therefore crude, way of describing the spatial distribution of energy deposition along a short portion of a charged particle track is to give the linear energy transfer (LET), which has been defined as the of dEL/dl where dEL is the average energy locally imparted to the medium by a charged particle of specified energy in traversing a distance dl. The concept of LET takes no account of the statistical fluctuations in the quantity of energy locally imparted in the track segment dl nor of the combined effect of more than one track. In spite of these limitations the LET concept has been widely used in comparing radiations of various kinds. The LET as defined above applies to a particular kind of particle with a particular energy. A specific value of the LET can be assigned only to a monoenergetic beam of particles which traverse a sample so thin that their energy does not change appreciably in passing through it. In general one has to deal with a distribution of LET values corresponding to a distribution of the kinetic energies which the particles may possess as they traverse some part of a cell. The particle fluence as a function of energy is dependent on the initial distribution of energies with which the charged particles are generated, and on the nature and extent of the medium in which these particles dissipate their energy in slowing down. Calculation of the fluence distribution is greatly simplified if it can be assumed that particles are generated essentially uniformly in a region whose dimensions are large compared to the range of the particles. Such an equilibrium distribution will be assumed for the calculations reported here. According to the definition, the linear energy transfer includes only energy 'locally imparted' to the medium and therefore excludes energy carried away from the primary track by high-energy secondary electrons or δ -rays. The fraction of the total energy lost by a charged particle per unit length of track (the stopping power) which is to be considered locally absorbed will depend upon the volume of the region in which the local energy absorption is considered important, e. g. a DNA molecule or a chromosome. As a first approximation to the calculation of the locally absorbed fraction, a two-group model has been proposed (Burch, Spencer and Attix) in which collisions of the primary particle are classified into two groups: (a) dissipative collisions in which the energy transferred in a collision with another electron is less than a cut-off value, Δ, and (b) major collisions in which the energy transferred is greater than Δ and in which the resulting δ-ray is considered as a separate particle independent of the primary particle track. The particle fluence distribution or LET distribution may be presented in a number of forms and various investigators have used different basic LET data in calculating the distributions. For purposes of comparison, the LET distributions presented here for a number of radiations are all based on the same assumptions. The steps in the calculations of the distributions are as follows: (1) Determination of the initial energy distribution of the electrons set in motion in the medium; (2) Determination of the particle fluence of these electrons by the slowing-down data of McGinnies calculated from the theory of Spencer and Fano; (3) Multiplication of the particle fluence by the LET to obtain the energy dissipation distribution with energy, Q(E), being the energy dissipated per unit energy interval by electrons with energy, E, and closely related to Burch's QT; (4) Conversion of the distribution, Q(E), to a distribution with respect to LET, Q(L), and then for convenience of presentation to a distribution with respect to A = log10 LET. Each of the graphs gives the fraction of the dose which is dissipated per unit internal of A by electrons which have a given value of A