xrays

Introduction - Radiation and Dose

Overview

  • The effects of irradiating a body, including the human body, are described using dose quantities.

Absorbed Dose

  • Definition: The energy absorbed by a body per unit mass.
  • SI Unit: Gray (Gy).
  • Conversion: 1 Gy = 1 J/kg of body mass.

Exposure

  • Definition: Describes the ionizing ability of photons in air.
  • It is defined as the charge released in an air mass due to X-rays or gamma radiation per unit mass.
  • Unit: Coulombs per kilogram (C/kg).

Older Units

  • Rad: 100 rad = 1 Gy
  • Roentgen (R): 1 R = 2.58 C/kg.

Penetration Ability of Ionizing Radiation

  • Depends on:
    • Type of particles (charged or uncharged).
    • Energy of the particles.
    • Composition of the interacting matter.

Attenuation of Uncharged Particles

  • For a parallel beam of uncharged particles (photons or neutrons) with initial number $N_0$, passing through material of thickness $x$:
    • The proportion of the initial particles $N/N_0$ that pass through the material without interacting can be expressed mathematically.

Shell Interactions and Characteristic Radiation

  • Interactions occur in atomic shells:
    • K, L, M, N shells.
  • Emission of an electron leaves a vacancy in the shell.
  • The vacancy is filled by an electron from an outer shell.
    • This process is accompanied by the emission of characteristic radiation.

Compton Scattering

  • Definition: A photon interacts with a "free" electron rather than tightly bound electrons, leading to elastic scattering.
  • Energy Sharing:
    • The photon energy is shared between:
    • A secondary photon.
    • The ejected electron.
  • Energy Transfer:
    • At low energies (~keV):
    • A small portion of photon energy is transferred to the electron; for example, for a 50 keV photon, approximately 4 keV is transferred.
    • At high energies (>1 MeV): Energy is approximately equally distributed between the photon and electron.

Attenuation Coefficient in Compton Scattering

  • In first approximation:
    • $
      ewline \mu_x$ = electron density of the material
    • The probability of interaction per electron is independent of atomic number $Z$ (except for hydrogen).
    • Energy Dependence:
    • Below 100 keV: $
      ewline \mu$ changes minimally.
    • At higher energies: $
      ewline \mu$ decreases slowly.

Clinical Approach

  • Clinical significance of photon-matter interactions is mainly in Radiology.
  • The photoelectric effect is responsible for differences in penetrating ability of radiation in different tissues.
  • These differences depend strongly on the atomic number (Z).

Tissue Differentiation

  • At photon energies of a few dozen keV:

    • Penetration in bone is reduced compared to soft tissues due to density differences, mainly caused by high concentrations of:
    • Calcium ($Z = 20$)
    • Phosphorus ($Z = 15$)

  • At higher energies (>100 keV):

    • The Compton effect predominates, and differentiation is primarily based on density differences.

Principles of Radiology

Components of an X-ray Machine

  • Main components include:
    • High-voltage power supply
    • X-ray tube
    • Imaging system

X-ray Tube

  • A vacuum-sealed glass tube that contains:
    • Filament: A wire that gets heated.
    • Target: Where electrons strike.
  • When an electric current (several amperes) passes through the filament:
    • Filament heats to approximately 2000°C and releases electrons.
  • Acceleration: Electrons are accelerated toward the target by a strong electric field, where the target is usually tungsten ($W, Z = 74$).
  • Kinetic Energy: A potential difference produces electrons with approximately 100 keV kinetic energy.
  • The number of electrons striking the target depends on current x time (mAs).
  • Bremsstrahlung Radiation: Stopping electrons at the target produces Bremsstrahlung radiation, and the total number of emitted photons is proportional to mAs.

X-ray Film

Role of X-ray Film

  • X-ray film is a common medium for recording diagnostic images. Key component: Photographic emulsion.

Film Structure

  • Films may be:

    • Single-emulsion
    • Double-emulsion:
    • Has a base ~200 μm thick made of transparent polyester.
    • Emulsion is attached via an adhesive layer consisting of gelatin, grains of:
      • Silver bromide
      • Silver iodide
      • Sometimes silver chloride

  • The film surface is coated with a protective layer.

Image Formation and Processing

Photon Absorption

  • When a photon is absorbed by a grain, it reacts with the negative bromine ion causing a chemical change.
  • Radiation causes chemical changes in many grains, which creates a latent image (invisible).

Processing Stages

  • Film processing converts the latent image into a visible image trough different stages:

    1. Development
    2. Fixing
    3. Washing
    4. Drying

  • Processing can be:

    • Manual
    • Automatic

  • Different optical densities correspond to different concentrations of silver atoms.

H-D Curve (Characteristic Curve)

  • Definition: Optical density varies with exposure.
  • Horizontal Axis: Logarithm of relative exposure.
  • The curve is referred to as the H-D curve or characteristic curve.
  • Approximate Expression: d=dmax(1−e−kX)d = d_{max} (1 - e^{-kX})
    • Where:
    • $d_{max}$: maximum optical density of the film
    • $X$: exposure
    • $k$: constant
  • The linear portion represents the diagnostically useful region.

Film Contrast (Grade)

  • Slope of the Curve: At a point of the curve, defined as AdA(logX)\frac{Ad}{A (log X)}, is called the film grade $G$ or contrast.
  • Average Grade: Defined between:
    • $d = 0.25$ to $d = 2$.
  • The slope of the straight section is denoted as $y$ (gamma).

Linear Section Equation

  • The equation for the linear section of the film is:
    OD=logX+COD = log X + C

    • Where:
    • $OD1$, $OD2$: optical density values
    • $X1$, $X2$: corresponding exposures

  • $C$: constant.

Film Sensitivity (Speed)

  • Determined by the horizontal position of the H-D curve; a position further to the left indicates a more sensitive film.

Exposure and Optical Density

  • Note: Increasing the number of photons does not significantly affect contrast.
  • Optical density depends only on exposure $X$, measured in R or C/kg.
  • For fixed conditions of high voltage, distance, and X-ray tube, exposure depends on mAs (current x time).