understand the use of X-rays in imaging internal body structures, including an understanding of the term contrast in X-ray imaging

Production and Use of X‑rays

Learning objectives

By the end of this lesson you should be able to:

• Explain that X‑rays are produced by electron bombardment of a metal target (bremsstrahlung and characteristic radiation).
• Use the equations Emax=eV and λmin=hc/E to relate tube voltage to photon energy and minimum wavelength.
• Identify the main components of an X‑ray tube and describe their functions.
• Apply the exponential attenuation law I = I₀ e‑μx and discuss how the linear attenuation coefficient μ depends on material atomic number, density and photon energy.
• Define “contrast” in X‑ray imaging, calculate it, and list the factors that affect it.
• Explain why contrast agents are used and give examples of common agents.
• Recognise the trade‑off between contrast, resolution, noise and patient dose (ALARA).

1. How X‑rays are produced

1.1 Electron bombardment of a metal target

In an X‑ray tube a high‑voltage supply accelerates electrons from the heated cathode toward a metal anode (usually tungsten). The rapid deceleration of these electrons on striking the target – electron bombardment of a metal target – generates X‑rays by two mechanisms:

1. Bremsstrahlung (braking radiation) – the electric field of the nuclei in the target slows the electrons, producing a continuous spectrum of photons. The maximum photon energy equals the kinetic energy of the incident electron:

   Emax = eV

2. Characteristic radiation – an incident electron ejects an inner‑shell electron from an atom of the target. An outer‑shell electron then fills the vacancy, emitting a photon whose energy equals the difference between the two atomic energy levels. This gives sharp spectral lines (e.g. Kα, Kβ) that are specific to the target material.

1.2 Derivation of the minimum wavelength

The energy of a photon is related to its wavelength by E = hc/λ. Substituting E = eV (the maximum photon energy) gives:

λmin = \dfrac{hc}{eV}

Using h = 6.626 × 10⁻³⁴ J·s, c = 3.00 × 10⁸ m s⁻¹ and e = 1.60 × 10⁻¹⁹ C, the constant simplifies to:

1.3 Example calculation (V = 100 kV)

• Maximum photon energy:
  

  Emax = eV = (1.60 × 10⁻¹⁹ C)(100 × 10³ V) = 1.60 × 10⁻¹⁴ J ≈ 100 keV

• Minimum wavelength (using the quick‑calc):
  

  λmin = 1240 nm·kV / 100 kV = 0.0124 nm

2. Components of an X‑ray tube

3. Attenuation of X‑rays in the body

3.1 Exponential attenuation law

The intensity of an X‑ray beam after passing through a material of thickness x is:

I = I₀ e‑μx

• I₀ – incident intensity
• I – transmitted intensity
• μ – linear attenuation coefficient (m⁻¹)
• x – thickness of the material (m)

3.2 Worked‑out attenuation example

Calculate the transmitted intensity through 5 cm of soft tissue (μ = 0.20 cm⁻¹) followed by 2 cm of cortical bone (μ = 0.50 cm⁻¹).

1. Soft tissue:
   

   I₁/I₀ = e‑0.20 × 5 = e‑1.0 ≈ 0.37

2. Bone (applied to the beam that has already passed through tissue):
   

   I₂/I₁ = e‑0.50 × 2 = e‑1.0 ≈ 0.37

3. Total transmission:
   

   I₂/I₀ = (I₁/I₀) × (I₂/I₁) = 0.37 × 0.37 ≈ 0.14

Thus only about 14 % of the original photons emerge, illustrating how combined layers of different tissues attenuate the beam.

3.3 Dependence of μ on material and photon energy

• Atomic number (Z) – photoelectric absorption varies roughly as μ ∝ Z³ / E³. High‑Z tissues (bone) attenuate far more than low‑Z tissues (soft tissue, air).
• Photon energy (E) – at low energies the photoelectric effect dominates, giving high contrast; at higher energies Compton scattering dominates, reducing contrast but allowing deeper penetration.
• Density (ρ) – a denser material contains more atoms per unit volume, increasing μ.

4. Contrast in X‑ray imaging

4.1 Definition

Contrast is the difference in image density (or pixel value) between two adjacent structures. It enables the visual discrimination of one tissue from another on a radiograph.

4.2 Clinical relevance

Adequate contrast is essential for common diagnostic tasks such as:

• Detecting fractures (bone vs. surrounding soft tissue)
• Identifying pulmonary infiltrates or pleural effusions (lung tissue vs. air)
• Assessing the position of medical devices (e.g., catheters, implants) against soft‑tissue background

4.3 Quantitative measure

For two regions with recorded intensities I₁ and I₂ the contrast percentage is

C = \frac{|I₁ - I₂|}{I₁ + I₂} \times 100 %

4.4 Factors that affect contrast

4.5 Example – chest radiograph

For a 10 cm path:

• Air (lung): μ ≈ 0.02 cm⁻¹ → I/I₀ = e⁻⁰·² ≈ 0.82
• Rib bone: μ ≈ 0.5 cm⁻¹ → I/I₀ = e⁻⁵ ≈ 0.007

The large difference in transmitted intensity produces the high contrast that makes ribs clearly visible against the dark lung fields.

5. Use of contrast agents

When natural differences in μ are insufficient (e.g., soft‑tissue imaging), high‑Z substances are introduced to locally increase attenuation.

6. Optimising image quality

• Resolution – ability to distinguish fine detail; limited by focal‑spot size, detector pixel size and geometric unsharpness.
• Noise – statistical variation in photon counts; reduced by increasing exposure (more photons) but this raises dose.
• Patient dose – must be kept as low as reasonably achievable (ALARA). Dose ∝ (tube current × exposure time) × V².
• Contrast‑dose trade‑off – lowering tube voltage improves contrast but also increases dose; the optimal setting balances diagnostic need against safety.

7. Summary checklist

• Two X‑ray production mechanisms: bremsstrahlung (continuous) and characteristic radiation (line spectra) – both arise from electron bombardment of a metal target.
• Maximum photon energy: Emax = eV; minimum wavelength: λmin = hc/eV ≈ 1240 nm·kV / V.
• Key tube components and their functions (cathode, focusing cup, anode, glass envelope, high‑voltage supply).
• Exponential attenuation law I = I₀ e⁻ᵐᵘˣ with a worked‑out example; μ depends on atomic number, density and photon energy.
• Contrast definition, quantitative formula, clinical relevance, and the four main influencing factors (ρ, Z, thickness, photon energy).
• Purpose of contrast agents and examples of iodine‑based and barium preparations.
• Balancing contrast, resolution, noise and patient dose (ALARA principle).