Interaction of Radiation with Matter II

1. Interaction of Radiation with Matter II

3. Attenuation in Soft Tissue (Z = 7)

4. Linear Attenuation Coefficient Fraction of photons removed from a monoenergetic beam of x- or gamma rays per unit thickness of material is called linear attenuation coefficient (?), typically expressed in cm-1 Number of photons removed from the beam traversing a very small thickness ?x: where n = number removed from beam, and N = number of photons incident on the material

5. Linear Attenuation Coeff. (cont.) For monoenergetic beam of photons incident on either thick or thin slabs of material, an exponential relationship exists between number of incident photons (N0) and those transmitted (N) through thickness x without interaction:

6. Linear Attenuation Coeff. (cont.) Linear attenuation coefficient is the sum of individual linear attenuation coefficients for each type of interaction: In diagnostic energy range, ? decreases with increasing energy except at absorption edges (e.g., K-edge)

7. Attenuation in Soft Tissue (Z = 7)

8. Linear Attenuation Coeff. (cont.) For given thickness of material, probability of interaction depends on number of atoms the x- or gamma rays encounter per unit distance Density (?) of material affects this number Linear attenuation coefficient is proportional to the density of the material:

9. Linear Attenuation Data

10. Mass Attenuation Coefficient For given thickness, probability of interaction is dependent on number of atoms per volume Dependency can be overcome by normalizing linear attenuation coefficient for density of material: Mass attenuation coefficient usually expressed in units of cm2/g

11. Mass Attenuation Coeff. (cont.) Mass attenuation coefficient is independent of density For a given photon energy: In radiology, we usually compare regions of an image that correspond to irradiation of adjacent volumes of tissue Density, the mass contained within a given volume, plays an important role

12. Radiograph of Ice Cubes in Water

13. Mass Attenuation Coeff. (cont.) Using the mass attenuation coefficient to compute attenuation:

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

15. Narrow- and Broad-Beam Geometries

16. Half Value Layer (cont.) For monoenergetic photons under narrow-beam geometry conditions, the probability of attenuation remains the same for each additional HVL thickness placed in the beam Relationship between ? and HVL: HVL = 0.693/ ?

17. Effective Energy X-ray beams in radiology typically composed of a spectrum of energies (a polyenergetic beam) Determination of HVL in diagnostic radiology is a way of characterizing the hardness of the x-ray beam HVL, usually measured in mm of Al, can be converted to an effective energy Estimate of the penetration power of the x-ray beam, as if it were a monoenergetic beam

18. Mean Free Path Range of a single photon in matter cannot be predicted Average distance traveled before interaction can be calculated from linear attenuation coefficient or the HVL of the beam Mean free path (MFP) of photon beam is:

19. Beam Hardening Lower energy photons of polyenergetic x-ray beam will preferentially be removed from beam while passing through matter Shift of x-ray spectrum to higher effective energies as beam traverses matter is called beam hardening Low-energy (soft) x-rays will not penetrate most tissues in the body; their removal reduces patient exposure without affecting diagnostic quality of the exam

21. Fluence Number of photons (or particles) passing through unit cross-sectional area is called fluence (expressed in units of cm-2)

22. Flux Fluence rate (e.g., rate at which photons or particles pass through a unit area per unit time) is called flux (units of cm-2 sec-1) Useful in areas where photon beam is on for extended periods of time, such as fluoroscopy

23. Energy Fluence Amount of energy passing through a unit cross-sectional area is called the energy fluence. For monoenergetic beam of photons Units of ? are energy per unit area (e.g., keV per cm2)

24. Kerma A beam of indirectly ionizing radiation (e.g., x- or gamma rays or neutrons) deposits energy in a medium in a two-stage process: Energy carried by photons (or particles) is transformed into kinetic energy of charged particles (such as electrons) Directly ionizing charged particles deposit their energy in the medium by excitation and ionization

25. Kerma (cont.) Kerma (K) is an acronym for kinetic energy released in matter Defined as the kinetic energy transferred to charged particles by indirectly ionizing radiation For x- and gamma rays, kerma can be calculated from the mass energy transfer coefficient of the material and the energy fluence

26. Mass Energy Transfer Coefficient Mass energy transfer coefficient is the mass attenuation coefficient multiplied by the fraction of energy of the interacting photons that is transferred to charged particles as kinetic energy Symbol: Will always be less than the mass attenuation coefficient (ratio for 20-keV photons in tissue is 0.68; reduces to 0.18 for 50-keV photons)

27. Calculation of Kerma For monoenergetic photon beams with energy fluence ? and energy E, the kerma K is given by SI units of energy fluence are J/m2, of mass energy transfer coefficient are m2/kg, and of kerma are J/kg

28. Absorbed Dose Absorbed dose (D) is defined as the energy (?E) deposited by ionizing radiation per unit mass of material (?m): Absorbed dose is defined for all types of ionizing radiation SI unit of absorbed dose is the gray (Gy), equal to 1 J/kg. US units: 1 rad = 10 mGy

29. Mass Energy Absorption Coefficient Mass energy transfer coefficient describes the fraction of the mass attenuation coefficient that gives rise to initial kinetic energy of electrons in a small volume of absorber These electrons may subsequently produce bremsstrahlung radiation, which can escape the small volume of interest The mass energy absorption coefficient is slightly smaller than the mass energy transfer coefficient

30. Calculation of Dose Dose in any material is given by where

31. Exposure The amount of electrical charge (?Q) produced by ionizing EM radiation per mass (?m) of air is called exposure (X): Units of charge per mass (e.g., C/kg). Historical unit of exposure is the roentgen (1 R = 2.58 x 10-4 C/kg exactly)

32. Exposure (cont.) Exposure is a useful quantity because ionization can be directly measured with standard air-filled radiation detectors, and the effective atomic numbers of air and soft tissue are approximately the same Only applies to interaction of ionizing photons in air Relationship exists between amount of ionization in air and absorbed dose in rads for a given photon energy and absorber

33. Roentgen-to-Rad Conversion Factors

34. Exposure (cont.) Exposure can be calculated from the dose to air W is the average energy deposited per ion pair in air, approximately constant as a function of energy (W = 33.97 J/C)

35. Exposure (cont.) W is the conversion factor between exposure in air and dose in air In terms of the traditional unit of exposure, the roentgen, the dose to air is: