A study of photon interaction parameters in lung tissue substitutes.

The study of photon interaction with different composite materials has become a topic of prime importance for radiation physicists. Some parameters of dosimetric interest are the mass attenuation coefficient, effective atomic number, and electron density; these help in the basic understanding of photon interactions with composite materials. The photon interaction parameters such as mass attenuation coefficient (μ/ρ), effective atomic number (Zeff), and effective electron density (N el) must be identical for the phantom material and their tissue. In the present study, we have evaluated the photon interaction parameters such as (μ/ρ), Z eff and N el of 13 lung tissue substitutes. The variations of these parameters of lung tissue substitutes with photon energy are graphically represented. The photon interaction parameters of lung tissue substitutes are compared with that of lung tissue. The variation of photon interaction parameters of the studied lung tissue substitutes is similar that of the lung. Logically, it can be shown that Alderson lung is good substitute for lung than the other substitutes.

Introduction

The study of photon interaction with different composite materials has become a topic of prime importance for radiation physicists. Some parameters of dosimetric interest are the mass attenuation coefficient, effective atomic number, and electron density; these help in the basic understanding of photon interactions with composite materials. The mass attenuation coefficient (μ/ρ) is a measure of the number of photons interacting (scattered/absorbed) with the target material. It is the fundamental tool to derive many other parameters of dosimetric interest such as mass energy absorption coefficient, molecular, atomic and electronic cross sections, effective atomic number, and electron density. For about 100 elements, the mass attenuation coefficient data are compiled in the form of the software package WinXCom,[1] whereas work is still in progress to find the mass attenuation coefficients of composite materials. For a complex medium, the “effective atomic number” is in some cases a convenient parameter for representing X-ray and gamma ray interactions, for example, in designs of radiation shielding or in calculations of absorbed dose. This number is very useful in choosing a substitute composite material in place of an element for a given energy depending on the requirement. The effective atomic number of a multielement material is not a constant (Hine[2]). It is varying with photon energy, depending on the relative importance of the interaction processes involved. The effective atomic number is calculated from the atomic numbers of the constituent elements, weighted according to the different partial interaction process by which the photon interacts, and hence it is an energy dependent parameter. It signifies that, at a given energy, a composite material would interact with photons in the similar way as a single element of atomic number equivalent to that composite material. The effective electron number or electron density (N) is also very useful in choosing a substitute composite material in place of an element for that energy depending on the requirement. The energy absorption in the given medium can be calculated by means of well-established formulae if certain constants such as Z and n class="Chemical">N of the medium are known. In fact, these values can provide an initial estimation of the chemical composition of the material.

Hence in the present study, it has been evaluated the photon interaction parameters such as (μ/ρ), Z, and N of 13 lung tissue substitutes were evaluated. The reference lung material was the healthy adult lung tissue listed in ICRU-44[3] and ICRP-89,[4] referred here as ICRU-44 lung tissue. The lung tissue substitutes investigated included that developed by Griffith et al.,[5] designated Grif-G, a second lung tissue substitute developed at Lawrence Livermore n class="Chemical">National Laboratory, designated LLLL1,[6] ALT2,[7] the Alderson Lung material,[3] LN1,[8] LN10/75,[3] MS20/L,[8] LTES,[8] LN300,[9] and an unnamed material designated here as SK-LNG.[10] Two additional tissue substitutes, A150 and M3,[3] were included.

Subjects and Methods

When a beam of photons passes through and interacts within the absorber, the photons are either absorbed (photoelectric effect, pair and triplet production, photo nuclear) or scattered (coherent and incoherent scattering). The sum of the cross sections, per atom for all the above process factors, is determined from the intensity of the transmitted beam of photons. In the present work, the mass attenuation coefficients and photon interaction cross sections in the energy range from 1 keV to 100 GeV are generated using WinXCom.[1] The total molecular cross section [σm] is computed from the following equation using the values of mass attenuation coefficients [(µ/ρ)]:

where n is the number of atoms of ith element in a given molecule, (µ/ρ) is the mass attenuation coefficient of biomolecule, N is the Avogadro's number, and Ai is the atomic weight of element i. (µ/ρ) was estimated based on the chemical composition. The effective (average) atomic cross section for a particular atom in the compound (σa) is estimated using the equation

The effective electronic cross section (σe) is computed from mass attenuation coefficient (µ/ρ) of ith element in the given molecule

where, fi is the fractional abundance (a mass fraction of the ith element in the molecule) and Zi is the atomic number of the ith element in a molecule. Finally, the Z is estimated as following:

The effective electron density, N, expressed in the number of electrons per unit mass is closely related to the effective atomic number. For an element, the electron density is given by n class="Chemical">N = NZ/A. This expression can be generalized for a compound:

In the present work, N and Z for the tissue substitutes of Lung were evaluated using equation (4) and (5).

Results and Discussion

The computed mass attenuation coefficients, Z and N of lung tissue substitutes, are shown in Figures 1–3. The variation of Z and n class="Chemical">N is dominated by of different photon interactions. The variation of photon interaction parameters of the studied lung tissue substitutes is similar that of the lung. In the lower energy region, photo electric interaction dominates and Z varies similar to photo electric absorption. There is a slight increase in the Z up to few keV and becomes maximum then decreases sharply, showing that contribution of scattering processes increases which decreases Z. This is also confirmed by previous author,[11] who confirmed that Z of composite material for photoelectric interaction is greater than other processes. It remains constant from 0.2 to 2 MeV which shows that coherent and incoherent processes increases. From 2 to300 MeV, there is regular increase in the Z with photon energy. This is due to the increase in incoherent and pair production processes. From 300 MeV onward Z remains constant which is due to dominance in pair production processes.Z values vary due to different elemental composition. The variation of N with photon energy is also similar that of the Z. Various procedures can be applied to the simulation of body tissues. The “effective atomic number (Z) method” is applicable to simulte the tissue substitutes for photon interactions. In this method, the effective atomic number, mass attenuation coefficient, energy absorption coefficient, and kerma value of tissue substitutes are compared with their original tissues. The ratios of mass attenuation coefficient, effective atomic number, and effective electron density between the lung and their substitutes are given in the Tables 1–3. These ratios are almost equal to one for Alderson lung compared with other substitutes. So that logically it can be concluded that the Alderson lung seems to be a good substitute for lung than the other substitutes. Hence, the computed values are useful in the simulation of tissue substitutes.

Figure 1

Variation of mass attenuation coefficients of lung tissue substitutes with photon energy for total photon interaction

Figure 3

Variation of Nel of lung tissue substitutes with photon energy for total photon interaction

Table 1

Comparison of mass attenuation coefficient of lung with their substitutes

Table 3

Comparison of N of lung with their substitutes

Variation of Zeff of lung tissue substitutes with photon energy for total photon interaction

The mass attenuation coefficient, electron mass stopping power, mass angular scattering power, mass stopping power, and kerma factors must be identical for the tissue substitutes.[12] Also, if equal masses of two materials are to have the same volume, then the mass densities of the two must be the same. It is obvious that the above can only be achieved if the material is made to have the same elemental constituents and in the same proportion by weight as the real tissue; it is only for such materials that the term “tissue equivalent” should be used. The photon interaction parameters like (μ/ρ), Z, and N gives the information about the elemental constituents and their proportion in the material. Hence, the present work is useful in the simulation of tissue substitutes.

Table 2

Comparison of Z of lung with their substitutes