Radiation Biophysics Module 31 : Attenuation of X-Rays Content Writer

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Course : PGPathshala-Radiation Physics

Paper 06 : Radiation Biophysics

Module 31 : Attenuation of X-rays

Content Writer: Dr. Aruna Kaushik, Institute of Nuclear Medicine & Allied Sciences, Delhi

Introduction

Attenuation is the removal of photons from a beam of X- or gamma rays as it passes through matter. In radiography, an X-ray beam is passed through a portion of the body and the image is projected onto a receptor. The beam that emerges from the body varies in intensity. This variation in intensity is caused by attenuation of X-rays in the body. Attenuation of X-rays depends on the penetrating characteristics of the beam and the physical characteristics of the tissues. The present chapter discusses the (a) definition and concept of attenuation (b) the factors that affect attenuation, (c) exponential attenuation, (d) attenuation of monochromatic and polychromatic X-ray beams, and (e) half value thickness.

Figure 1: Diagram depicting the process of attenuation of X-ray photons (Source: http://www.sprawls.org/resources/)

Objectives:

1. Attenuation 2. Attenuation Coefficient 2.1 Linear Attenuation Coefficient 2.2 Mass Attenuation Coefficient 2.3 Electronic Attenuation Coefficient 2.4 Atomic Attenuation Coefficient 3. Relation between attenuation coefficients 4. Factors affecting attenuation 4.1 Effect of Atomic number on attenuation 4.2 Effect of energy on attenuation 5. Exponential Attenuation 6. Attenuation of monochromatic radiation 7. Attenuation of polychromatic radiation 8. Half Value Layer (Penetrability of Photons) 8.1 Narrow Beam Geometry 8.2 Broad Beam Geometry 8.3 Relation Between  and HVL 9. Tenth Value Layer

10. Beam Hardening 11. Summary

1. Attenuation When a photon (gamma or X-rays) traverses through matter, it may undergo interaction (photoelectric interaction, Compton scattering, pair production or any other) depending on its energy and the atomic number of the traversed material. However, in diagnostic radiology or other clinical applications of radiation, we are more interested in the collective interaction of the large number of photons. When a group of photons traverse through a certain material, some of the photons interact with the material and some just pass through it without interaction. The interactions predominantly photoelectric and Compton scattering in the diagnostic radiology energy range, remove the photons from the incident beam. This removal of photons from incident beam by both absorption and scattering is called attenuation.

Figure 2: Diagrams show an unattenuated X-ray beam (top) and an attenuated X-ray beam passing through a foil (bottom) into detectors (Radiographics 1998; 18: 151-163)

2. Attenuation Coefficient:

An attenuation Coefficient is a measure of the quantity of radiation attenuated by a given thickness of absorber. The thickness of a material can be expressed in different units of measure, for example, metres, kilograms per metre squared, and electrons per metre squared.

2.1 Linear Attenuation Coefficient ()

The fraction of photons removed from a mono-energetic beam of X- or gamma rays per unit thickness of material is called the linear attenuation coefficient (). Thus,  = ∆푁⁄푁∆푥 (1) where N is the number of photons removed from the X-ray beam, N is the number of photons incident on the material and x is the thickness. It is expressed in units of per unit length (i.e. inverse centimetres (cm-1) or millimetres (mm-1) most commonly expressed in terms of centimetres or millimetres. In equation (1), for any given , x must be chosen so that the number of photons removed from the beam is much smaller than the total number of photons. As the thickness of the attenuating material increases, the equation is no longer correct and the relationship becomes nonlinear. Linear attenuation coefficient values indicate the rate at which photons interact as they move through material and are inversely related to the average distance photons travel before interacting. The rate at which photons interact (attenuation coefficient value) is determined by the energy of the individual photons and the atomic number and density of the material. For example, for 100 KeV photons, traversing soft tissue, the linear attenuation coefficient of 0.1 cm-1 signifies that for every 100 photons incident upon a 1 cm thickness of tissue, approximately 10 will be removed from the beam, either by absorption or scattering.

Figure 3: Diagram to explain concept of linear attenuation coefficient (Source: http://www.sprawls.org/resources/)

However, it may be noted that attenuation produced by thickness, x, will depend upon the number of electrons and atoms present in the layer. If the layer were compressed to half the thickness, it would still have the same number of electrons and still attenuate the X-rays by the same fraction, but of course, its linear attenuation coefficient (attenuation per unit length) would be twice as great. Linear attenuation coefficients will, therefore, depend upon the density of the material.

2.2 Mass Attenuation Coefficient

Mass attenuation coefficient is a more fundamental attenuation coefficient and is obtained by dividing the linear attenuation coefficient by the density of the material through which the photons pass. It is represented by the symbol /. Mass attenuation coefficient is independent of density. In some situations it is more desirable to express the attenuation rate in terms of the mass of the material encountered by the photons rather than in terms of distance. The quantity that affects attenuation rate is not the total mass of an object but rather the area mass. Area mass is the amount of material behind a 1-unit surface area, as shown below. The area mass is the product of material thickness and density:

Area Mass (g/cm2) = Thickness (cm) x Density (g/cm3)

The mass attenuation coefficient is the rate of photon interactions per 1-unit (g/cm2) area mass. The typical unit of the mass attenuation coefficient is per gram per centimetre squared (cm2/g), since the unit in which thickness is measured is gram per centimetre squared (the mass of a 1-cm2 area of material). The coefficient is the inverse of the unit in which thickness is measured.

Figure 4: Diagram to explain concept of mass attenuation coefficient (Source: http://www.sprawls.org/resources/)

Figure 5: Mass attenuation Coefficients for selected materials as a function of photon energy. Graph shows the variation of / for sodium iodide, lead, water and air. (Radiographics 1998; 18: 151- 163)

Figure 6: Mass attenuation coefficients for photons in air. Graph displays the mass attenuation coefficient for air (with an effective atomic number of about 7.6) for specific interactions with X-rays and the total attenuation as a function of energy. (Radiographics 1998; 18: 151-163)

2.3 Electronic Attenuation Coefficient

In order to compute the electronic attenuation coefficient, the number of electrons in unit area of a foil is calculated and the thickness of the foil is expressed as electrons per cm2. The electronic attenuation coefficient is obtained by dividing the mass attenuation coefficient by the number of electrons per gram. It is represented by e. The number of electrons per gram, Ne, is obtained from Avogadro’s number, NA as follows:

Number of electrons per gram = NAZ/A = Ne where A is atomic weight and Z is atomic number.

Electronic attenuation coefficient has dimensions of cm2/electron or m2/electron. It is very small compared with the mass coefficient because there are an enormous number of electrons in a slab of thickness 1 g/cm2.

2.4 Atomic Attenuation Coefficient

The atomic attenuation coefficient, a, is the fraction of an incident X-ray or gamma ray beam that is attenuated by a single atom (i.e. the probability that an absorber atom will interact with one of the photons in the beam). The atomic coefficient is obtained by dividing the mass attenuation coefficient

2 2 by the number of atoms per gram (= NA/A). Its dimensions are cm per atom or m per atom. The atomic coefficient is Z times as large as the electronic one, since there are Z electrons in each atom.

3. Relationships between Attenuation Coefficients

The relationship between the attenuation coefficients is summarized in Table 1.

Table1: Relation between Attenuation Coefficients

Coefficient Symbol Relation between Units of coefficients Units in which thickness coefficients is measured Linear  … cm-1 or mm-1 cm or mm Mass / / cm2/gram gram/cm2 2 2 2 2 Electronic e /.(1/ Ne) cm /electron or m /electron electron/cm or electron/m 2 2 2 2 Atomic a /.(Z/ Ne) cm /atom or m /atom atom/cm or atom/m

4. Factors affecting attenuation

The factors that affect attenuation are related to the incident X-ray beam and the properties of the material through which the radiation traverses. These factors include the incident beam energy, the thickness, atomic number and density of the material.

4.1 X-ray Photon Energy

Higher X-ray photon energies (shorter wavelengths) have greater penetration and lower attenuation values. Lower energy X-ray photons have higher attenuation and lower penetration values.

Figure 7: Effect of radiation energy on X-ray attenuation. Graph shows the variation in intensity versus thickness for two beams. (Radiographics 1998; 18: 151-163)

. 4.2 Thickness of Attenuator

The greater the thickness of the attenuating material, the greater is the attenuation. X-rays are attenuated exponentially.

4.3 Atomic Number of Attenuator

Materials with higher atomic numbers (Z) have higher attenuation values for a given thickness (Table 2). The higher atomic number indicates there are more atomic particles for interaction with the X-ray photons.

Figure 8: Effect of atomic number on X-ray attenuation. . Graph shows the variation in intensity versus thickness for two beams. (Radiographics 1998; 18: 151-163)

4.4 Density of Attenuator

Similarly, density of the material increases, the attenuation produced by a given thickness increases. Thus, different materials such as water, fat, bone, and air have different linear attenuation coefficients, as do the different physical states or densities of a material, such as water vapour, ice, and water (Table 2).

Table 2: Effect of Atomic Number and Density on Linear Attenuation

Material Effective Atomic Density (g/cm3)  (cm-1) at 50 keV Number (Z) Water Vapour 7.4 0.000598 0.000128 Air 7.64 0.00129 0.00029 Fat 5.92 0.91 0.193 Ice 7.4 0.917 0.196 Water 7.4 1 0.214 Compact Bone 13.8 1.85 0.573

5. Exponential Attenuation Relationships For a monoenergetic beam of photons incident upon either thick or thin slabs of material, an exponential relationship exists between the number of incident photons (N0) and those that are transmitted (N) through a thickness x without interaction:

−휇푥 푁 = 푁0푒 (1)

where x = absorber thickness, e = base of the natural logarithm system,  = attenuation coefficient, N = number of transmitted photons, and N0 = number of incident photons.

Figure 9: Exponential attenuation relationships. (Radiographics 1998; 18: 151-163)

6. Attenuation of monochromatic radiation

Above equation may be used to calculate attenuation by any thickness of material when the incident and transmitted photon intensity or photon number is measured. In diagnostic radiology, photon intensity (i.e. the number of photons in a beam weighted by its energy) is the quantity that is most often measured. Exponential reduction in the number of photons is demonstrated in figure below. If N/N0 is plotted as a function of x on linear graph paper, an exponential curve will be obtained. The logarithm of the number of photons transmitted varies linearly with the thickness of the attenuating material; therefore, if the logarithm of N/N0 is plotted against x, a straight line graph will result. This plot is called semilogarithmic plot because one axis is logarithmic and the other linear.

Figure 10: Attenuation of monochromatic radiation plotted on a linear and logarithmic scale (Radiographics 1998; 18: 151-163)

7. Attenuation of polychromatic radiation Polychromatic beams contain a spectrum of photon energies. With an X-ray beam, the maximum photon energy is determined by the peak kilovoltage (kVp) used to generate the beam. Because of the spectrum of photon energies, the transmission of a polychromatic beam through an absorber does not strictly follow equation (1). When a polychromatic beam passes through an absorber, photons of low energy are attenuated more rapidly than the higher energy photons; therefore, both the number of transmitted photons and the quality of beam change with increasing amounts of an absorber. A semilogarithmic plot of the number of photons in a polychromatic beam as a function of the thickness of the attenuating materials will not be a straight line but a curve. The initial slope of the curve is steep because the low energy photons are attenuated, but, as the beam becomes more monochromatic, the slope decreases. A comparison of the curves for polychromatic radiation is shown in Figure below.

Figure 11: Attenuation of polychromatic radiation (Radiographics 1998; 18: 151-163)

Figure 12: Graph shows a comparison of the curves for polychromatic and monochromatic radiation (Radiographics 1998; 18: 151-163)

8. Half Value Layer (Penetrability of Photons)

The half value layer (HVL) is defined as the thickness of material required to reduce the intensity of an X- or gamma-ray beam to one-half of its initial value. The HVL of a beam is an indirect measure of the photon energies (also referred to as the quality) of a beam, when measured under conditions of “good” or “narrow beam geometry.

8.1 Narrow Beam Geometry

Narrow beam geometry refers to an experimental configuration that is designed to exclude scattered photons from being measured by a detector.

(a) (b)

Figure 13: (a) Diagram demonstrating ideal set up for measurement of HVL (b) Diagram illustrating the narrow beam geometry (Radiographics 1998; 18: 151-163)

8.2 Broad Beam Geometry

In broad-beam geometry, the beam is sufficiently wide that a substantial fraction of scattered photons remain in the beam. The scattered photons reaching the detector result in an underestimation of the attenuation (i.e., an overestimated HVL).

Figure 14: Diagram illustrating the broad beam geometry (Radiographics 1998; 18: 151-163)

8.3 Relationship between  and HVL

For monoenergetic photons under narrow-beam geometry conditions, the probability of attenuation remains the same for each additional HVL thickness placed in the beam. Reduction in beam intensity can be expressed as (1/2)n where n equals the number of half value layers. For example, the fraction of monoenergetic photons transmitted through 5 HVLs of material is

(1/2)5 = 1/32 =0.031 or 3.1%.

Therefore, 97 % of the photons are attenuated (removed from the beam). The HVL of a diagnostic X- ray beam, measured in millimetres of aluminium under narrow-beam conditions, is a surrogate measure of the average energy of the photons in the beam

In the exponential equation for attenuation, N is equal to N0/2 when the thickness of the absorber is 1 HVL. Thus, for a monoenergetic beam;

-(HVL) N0/2 = N0e

Or HVL = 0.693/

For a monoenergetic incident photon beam, the HVL can be easily calculated from the linear attenuation coefficient, and vice versa. For example: given

 = 0.35 cm-1

HVL = 0.693/0.35 cm-1 = 1.98 cm

9. Tenth Value Layer The Tenth Value Layer (TVL) is the thickness of material necessary to reduce the intensity of the beam to a tenth of its initial value.

10. Beam Hardening Beam hardening is the preferential loss of lower energy photons by any absorber. As low energy photons are absorbed, mean photon energy increases, and the resultant X-ray beam becomes more penetrating. For polychromatic X-ray beams, the second HVL is always greater than the first

HVL. Beam hardening does not occur with monochromatic X-ray beams because there is no differential energy filtration.

11. Summary  Beam attenuation occurs when the photons from the primary beam are removed either by absorption or by scattering  Beam attenuation is affected by tissue thickness, atomic number, tissue density, and incident beam energy.  The HVL is the amount of material required to reduce the intensity to one-half its original value.  HVL = 0.693/;  is linear attenuation coefficient.  For polychromatic X-ray beams, the second HVL will always be greater than the first HVL.  Beam hardening does not occur with monochromatic X-ray beams because there is no differential energy filtration.

End of Module