3.10.5.2
X-ray attenuation and contrast
Medical Physics | AQA A-Level Physics
Key Definition
X-ray attenuation: The reduction in X-ray intensity as the beam passes through a material. Governed by the equation $I = I_0 e^{-\mu x}$, where $\mu$ is the linear attenuation coefficientA measure of how strongly a material absorbs or scatters X-rays per unit thickness. Measured in m⁻¹. Higher $\mu$ means more attenuation. (m$^{-1}$) and $x$ is the thickness (m).
- The half-value thicknessThe thickness of material needed to reduce the X-ray intensity to half its original value. $x_{1/2} = \frac{\ln 2}{\mu}$. is the thickness that halves the intensity: $x_{1/2} = \frac{\ln 2}{\mu}$.
- The mass attenuation coefficientThe linear attenuation coefficient divided by the density of the material. $\mu_m = \mu / \rho$. Measured in m² kg⁻¹. Useful for comparing materials of different densities. is $\mu_m = \frac{\mu}{\rho}$, measured in m$^2$ kg$^{-1}$. It allows comparison between materials of different densities.
- ContrastThe difference in blackening between adjacent regions on an X-ray image. High contrast means clear distinction between different tissues. is the difference in blackening between regions. SharpnessThe clarity of edges and fine detail in an X-ray image. is the clarity of edges.
- Contrast enhancement: bariumA contrast agent with high atomic number (Z = 56) used for imaging the digestive system. Given as a barium meal (swallowed) or barium enema. Its high Z gives strong X-ray attenuation. (swallowed or as an enema) is used to image the digestive system. IodineA contrast agent with high atomic number (Z = 53) injected into the bloodstream. Used for imaging blood vessels. Its high Z increases X-ray attenuation in blood. (injected) is used for imaging blood vessels. Both have high atomic numbers, giving strong attenuation.
- The optimum X-ray energy for distinguishing different soft tissues is 30-100 keV. Below 30 keV, too much is absorbed; above 100 keV, too much passes through without interaction.
- Reducing patient dose: use beam definers (lead diaphragms) to limit the beam, aluminium filters to remove low-energy X-rays (which are absorbed by the patient without reaching the detector), and sensitive detectors to reduce exposure time.
Worked Example
An X-ray beam of intensity $I_0$ passes through 4.0 cm of tissue with $\mu = 0.20$ cm$^{-1}$. Calculate the fraction of intensity transmitted.
Show Solution
1
Use the attenuation equation
$$\frac{I}{I_0} = e^{-\mu x} = e^{-0.20 \times 4.0} = e^{-0.80}$$
2
Evaluate
$$\frac{I}{I_0} = 0.449 \approx 0.45$$
Answer
45% of the X-ray intensity is transmitted through the tissue.