Introduction to Diagnostic Imaging Techniques
Welcome to Diagnostic Imaging Techniques! This chapter is a core part of CCEA A2 Unit 3: Medical Physics. In modern medicine, diagnosing an illness or injury often requires doctors to "look inside" the human body without performing surgery. Physics provides the tools to make this happen.
In this guide, we will break down the four main diagnostic imaging techniques covered in your specification: Ultrasound, Planar X-Rays, Computed Tomography (CT), and Magnetic Resonance Imaging (MRI). Don't worry if the physics equations or medical terms seem daunting at first — we will break down every process step-by-step with clear examples, memory aids, and key calculation guides.
1. Ultrasound Imaging
What is Ultrasound?
Ultrasound is defined as sound waves with frequencies higher than the upper limit of human hearing, which is greater than \(20\text{ kHz}\) (\(20,000\text{ Hz}\)). In diagnostic medicine, much higher frequencies are used, typically in the range of \(1\text{ MHz}\) to \(15\text{ MHz}\).
How is Ultrasound Generated and Detected?
Ultrasound waves are produced and detected using a handheld device called a transducer containing a piezoelectric crystal (such as Lead Zirconate Titanate, or PZT).
1. Emitting Ultrasound (The Piezoelectric Effect): When an alternating potential difference (voltage) is applied across the PZT crystal, the crystal rapidly expands and contracts (vibrates) at the same frequency. These high-frequency mechanical vibrations create ultrasound pressure waves that travel into the patient's body.
2. Receiving Echoes (The Reverse Piezoelectric Effect): When reflected ultrasound waves (echoes) return from tissue boundaries inside the body, they hit the PZT crystal. The mechanical pressure compresses the crystal, inducing an alternating potential difference across it. This electrical signal is processed by a computer to produce an image.
Acoustic Impedance (\(Z\))
Every tissue in the body resists the passage of sound waves differently. This property is called acoustic impedance, denoted by the symbol \(Z\).
The equation for acoustic impedance is:
\(Z = \rho c\)
Where:
• \(Z\) = Acoustic impedance in \(\text{kg}\cdot\text{m}^{-2}\cdot\text{s}^{-1}\) (also known as Rayls)
• \(\rho\) = Density of the medium in \(\text{kg}\cdot\text{m}^{-3}\)
• \(c\) = Speed of ultrasound in that medium in \(\text{m}\cdot\text{s}^{-1}\)
Intensity Reflection Coefficient (\(\alpha\) or \(I_r / I_0\))
When an ultrasound wave travels through the body and reaches a boundary between two different tissues (with acoustic impedances \(Z_1\) and \(Z_2\)), some of the wave is reflected back as an echo, while the rest is transmitted deeper into the body.
The fraction of the incident intensity that is reflected is given by the intensity reflection coefficient formula:
\(\frac{I_r}{I_0} = \frac{(Z_2 - Z_1)^2}{(Z_2 + Z_1)^2}\)
Where:
• \(I_0\) = Incident intensity of the ultrasound wave
• \(I_r\) = Reflected intensity of the ultrasound wave
• \(Z_1\) = Acoustic impedance of the first medium
• \(Z_2\) = Acoustic impedance of the second medium
Why Acoustic Coupling Gel is Essential:
Air has a very low acoustic impedance compared to human skin. If an ultrasound probe touches dry skin, the huge difference between \(Z_{\text{air}}\) and \(Z_{\text{skin}}\) causes roughly \(99.9\%\) of the ultrasound energy to reflect off the skin surface before entering the body. An acoustic coupling gel has an impedance very close to that of skin. Applying it eliminates the trapped air layer, allowing the sound waves to transmit efficiently into the tissue.
Ultrasound Scan Modes
• A-scan (Amplitude scan): A one-dimensional (1D) scan. The transducer sends out a pulse, and returning echoes are displayed on an oscilloscope screen as vertical voltage spikes (amplitudes) against time. By measuring the time delay between pulses and knowing the speed of sound in tissue, doctors can calculate distances and depths (e.g., measuring the diameter of an eye or the thickness of the skull).
• B-scan (Brightness scan): A two-dimensional (2D) real-time cross-sectional image. An array of transducers sweeps across the body. Returning echoes are displayed as 2D dots, where the brightness of each dot corresponds to the amplitude/strength of the returning echo (e.g., fetal scans during pregnancy).
• M-mode (Motion mode): Used to record rapid movements of internal structures over time, such as opening and closing heart valves.
• Doppler Ultrasound: Utilises the Doppler effect. When ultrasound reflects off moving red blood cells, the frequency of the returning wave shifts by \(\Delta f\). By measuring this frequency shift, the velocity and direction of blood flow in arteries and veins can be evaluated in real time.
Key Takeaway for Ultrasound: Ultrasound is completely non-ionising and safe for obstetric imaging. Coupling gel is used for impedance matching, not merely lubrication!
2. X-Ray Imaging and Computed Tomography (CT)
How X-Rays are Produced
X-rays are high-energy, high-frequency electromagnetic waves produced inside an evacuated X-ray tube:
1. Thermionic Emission: A low-voltage electric current heats a tungsten filament at the cathode (negative electrode), "boiling off" electrons.
2. High Voltage Acceleration: A large potential difference (\(30\text{ kV}\) to \(150\text{ kV}\)) across the tube accelerates these free electrons toward the rotating anode (positive target, usually made of tungsten or molybdenum).
3. Target Impact: The high-speed electrons strike the anode target, decelerating rapidly and releasing energy. Roughly \(99\%\) of this kinetic energy is converted into heat (requiring cooling mechanisms), while roughly \(1\%\) is emitted as X-ray photons.
The X-Ray Energy Spectrum
An X-ray emission spectrum consists of two distinct components:
• Bremsstrahlung ("Braking Radiation"): A broad, continuous spectrum. When fast electrons pass close to the positive nuclei of target atoms, they are deflected and decelerated by the electric field, losing kinetic energy which is emitted as a continuous range of X-ray photon energies.
• Characteristic Radiation: Sharp, discrete intensity peaks (e.g., \(K_\alpha, K_\beta\)). These occur when an incoming high-energy electron knocks out an inner-shell electron of a target atom. An outer-shell electron drops down to fill the vacancy, emitting an X-ray photon with an energy exactly equal to the difference between those two atomic energy levels.
X-Ray Attenuation and the Beer-Lambert Law
As an X-ray beam passes through matter, its intensity decreases due to absorption and scattering. This process is called attenuation.
The transmission of X-rays through tissue follows the exponential Beer-Lambert Law:
\(I = I_0 e^{-\mu x}\)
Where:
• \(I_0\) = Initial (incident) intensity of the X-ray beam
• \(I\) = Transmitted intensity after passing through the material
• \(\mu\) = Linear attenuation coefficient of the tissue (\(\text{m}^{-1}\) or \(\text{cm}^{-1}\))
• \(x\) = Thickness of the tissue (\(\text{m}\) or \(\text{cm}\))
Attenuation Mechanisms at Diagnostic Energies:
• Photoelectric Absorption: The dominant mechanism in diagnostic X-ray imaging. An incoming X-ray photon is completely absorbed by an inner-shell electron, ejecting it as a photoelectron. The probability of photoelectric absorption depends strongly on the atomic number of the material, proportional to \(Z^3\). This explains why dense bone (containing high-\(Z\) calcium and phosphorus) absorbs far more X-rays and appears bright white on radiographs compared to soft tissues.
• Compton Scattering: An X-ray photon collides with an outer-shell electron, ejecting the electron while the photon scatters with reduced energy in a different direction.
Note: Pair production occurs only at photon energies above \(1.02\text{ MeV}\), which is outside the range of diagnostic medical imaging.
Contrast Media
Soft tissues (e.g., stomach, intestines, blood vessels) have very similar linear attenuation coefficients and low atomic numbers, making them hard to distinguish on standard radiographs. To overcome this, patients are given contrast media containing elements with high atomic numbers (\(Z\)):
• Barium (\(Z = 56\)): Ingested as a "barium meal" or "barium swallow" to coat and clearly outline the gastrointestinal tract.
• Iodine (\(Z = 53\)): Injected into the bloodstream to highlight blood vessels (angiography) and assess kidney or cardiac function.
Computed Tomography (CT / CAT Scans)
While a standard planar X-ray produces a flat 2D shadow of overlapping structures, a CT scanner produces detailed 2D cross-sectional "slices" that can be reconstructed computationally into full 3D images.
• How CT Works: An X-ray tube and an array of sensitive detectors rotate synchronously around the patient lying inside a circular gantry. The tube sends narrow X-ray beams through the patient from hundreds of angles. A computer records the attenuation data at each angle and uses algorithms to calculate the attenuation value (Hounsfield units) for every tiny volume element (voxel), assembling a precise cross-sectional image free from 2D organ overlap.
Key Takeaway for X-Rays and CT: Both modalities use ionising radiation. CT scans provide exceptional 3D anatomical detail and soft-tissue discrimination compared to planar X-rays, but expose the patient to a significantly higher radiation dose.
3. Magnetic Resonance Imaging (MRI)
Physical Principle: Nuclear Magnetic Resonance (NMR)
MRI is based on the behaviour of hydrogen nuclei (\(^1\text{H}\) protons) in magnetic fields. Because the human body is mostly made of water (\(\text{H}_2\text{O}\)) and fat, it contains abundant hydrogen protons. Each proton possesses an intrinsic spin and behaves like a tiny microscopic bar magnet (magnetic dipole moment).
The 5 Steps of MRI Image Formation
Step 1: Alignment in the Main Magnetic Field (\(B_0\))
Normally, hydrogen protons in the body spin with random orientations. When the patient enters the scanner's powerful superconducting magnet (typically \(1.5\text{ T}\) to \(3.0\text{ T}\)), the protons align either parallel (low energy) or anti-parallel (high energy) to the external magnetic field \(B_0\). A slight excess aligns parallel, creating a net longitudinal magnetisation along the direction of \(B_0\).
Step 2: Precession & The Larmor Frequency
Under the influence of \(B_0\), the spinning protons do not simply stay still; their axes wobble around the direction of the magnetic field, like a spinning top. This wobbling motion is called precession. The frequency of precession is called the Larmor frequency (\(f_0\) or \(\omega_0\)), calculated using the Larmor Equation:
\(\omega_0 = \gamma B_0 \quad \text{or} \quad f_0 = \frac{\gamma}{2\pi} B_0\)
Where:
• \(f_0\) = Larmor precession frequency (\(\text{Hz}\) or \(\text{MHz}\))
• \(\gamma\) = Gyromagnetic ratio (a constant specific to the hydrogen nucleus)
• \(B_0\) = Magnetic field strength (\(\text{T}\))
Step 3: Resonance and RF Excitation
An RF transmitter coil emits a pulse of radiofrequency (RF) radiation precisely tuned to the Larmor frequency of the protons. Through resonance, the protons absorb this RF energy. This tips the net magnetisation vector away from the longitudinal axis into the transverse plane (at \(90^\circ\) to \(B_0\)), causing the protons to precess in phase with one another.
Step 4: Relaxation and Signal Detection
When the RF pulse is turned off, the protons relax back to their original equilibrium alignment along \(B_0\). As they do, they emit RF signals, which are detected by RF receiver coils:
• \(T_1\) Relaxation (Spin-Lattice Relaxation): The time taken for the net longitudinal magnetisation to recover back along \(B_0\) as protons transfer energy to their surrounding environment (lattice).
• \(T_2\) Relaxation (Spin-Spin Relaxation): The time taken for the transverse magnetisation to decay as precessing protons interact with each other and lose phase coherence.
Because different tissues (e.g., watery cerebrospinal fluid vs. fatty tissue vs. grey matter) have distinctly different \(T_1\) and \(T_2\) relaxation rates, the computer can generate images with outstanding soft-tissue contrast.
Step 5: Spatial Localisation using Gradient Coils
To pinpoint where each signal originates inside the patient's body, three sets of gradient magnetic coils (\(G_x, G_y, G_z\)) superimpose small, linearly varying magnetic fields over \(B_0\). Because the Larmor frequency depends directly on magnetic field strength (\(f_0 \propto B\)), each specific slice and coordinate in the body precesses at a uniquely identifiable frequency and phase.
Key Takeaway for MRI: MRI is completely non-ionising and provides superior contrast for soft tissues, the brain, and spinal cord. However, it cannot be used on patients with ferromagnetic implants or certain pacemakers due to the strong static magnetic field.
4. Comparison of Diagnostic Imaging Modalities
Here is a summary comparing the four techniques:
1. Ultrasound
• Radiation Type: Non-ionising (high-frequency sound waves).
• Key Advantages: Safe in pregnancy, portable, low cost, real-time dynamic imaging.
• Key Limitations: Cannot penetrate bone or gas/air pockets; lower resolution at depth.
2. Planar X-Ray
• Radiation Type: Ionising (electromagnetic radiation).
• Key Advantages: Fast, inexpensive, excellent resolution for assessing bone fractures and dental structures.
• Key Limitations: Ionising radiation dose; 2D projection causes superposition (overlapping) of organs.
3. Computed Tomography (CT)
• Radiation Type: Ionising (multiple X-ray beams from a rotating gantry).
• Key Advantages: High-resolution 3D reconstructions, excellent discrimination between bone and soft tissues, fast emergency diagnosis (e.g., trauma, acute stroke).
• Key Limitations: Substantially higher ionising radiation dose than planar X-ray; expensive equipment.
4. Magnetic Resonance Imaging (MRI)
• Radiation Type: Non-ionising (static magnetic fields and radiofrequency waves).
• Key Advantages: Outstanding soft-tissue contrast (brain, spinal cord, ligaments, tumours), multi-planar imaging without moving the patient.
• Key Limitations: Very expensive, lengthy scan times (up to \(45\text{ minutes}\)), sensitive to patient movement, loud acoustic noise, claustrophobic environment, strictly contraindicated for ferromagnetic implants/foreign bodies.
5. Calculation Examples & Exam Tips
Worked Example 1: Acoustic Impedance & Reflection
Question: Ultrasound travels from muscle (\(Z_1 = 1.70 \times 10^6\text{ kg}\cdot\text{m}^{-2}\cdot\text{s}^{-1}\)) into bone (\(Z_2 = 7.78 \times 10^6\text{ kg}\cdot\text{m}^{-2}\cdot\text{s}^{-1}\)). Calculate the percentage of ultrasound intensity reflected at the boundary.
Solution:
1. Use the intensity reflection formula:
\(\frac{I_r}{I_0} = \frac{(Z_2 - Z_1)^2}{(Z_2 + Z_1)^2}\)
2. Substitute the values:
\(\frac{I_r}{I_0} = \frac{(7.78 \times 10^6 - 1.70 \times 10^6)^2}{(7.78 \times 10^6 + 1.70 \times 10^6)^2} = \frac{(6.08 \times 10^6)^2}{(9.48 \times 10^6)^2}\)
3. Calculate the ratio:
\(\frac{I_r}{I_0} = \left(\frac{6.08}{9.48}\right)^2 = (0.6414)^2 \approx 0.411\)
4. Convert to percentage: \(0.411 \times 100\% = \mathbf{41.1\%}\) reflected.
Worked Example 2: X-Ray Attenuation Calculation
Question: A beam of X-rays with an initial intensity of \(I_0 = 120\text{ W}\cdot\text{m}^{-2}\) passes through a \(0.040\text{ m}\) thick layer of soft tissue with a linear attenuation coefficient \(\mu = 25.0\text{ m}^{-1}\). Calculate the transmitted intensity \(I\).
Solution:
1. State the Beer-Lambert equation:
\(I = I_0 e^{-\mu x}\)
2. Substitute the given values:
\(I = 120 \times e^{-(25.0 \times 0.040)} = 120 \times e^{-1.0}\)
3. Evaluate \(e^{-1.0}\):
\(e^{-1.0} \approx 0.3679\)
4. Multiply by \(I_0\):
\(I = 120 \times 0.3679 = \mathbf{44.1\text{ W}\cdot\text{m}^{-2}}\)
Top 5 Pitfalls to Avoid in the Exam
• Trap 1: Confusing ionising and non-ionising techniques. Always remember: Ultrasound and MRI are strictly non-ionising. Planar X-rays and CT scans are ionising.
• Trap 2: Misunderstanding coupling gel. Never write that ultrasound gel is used "as a lubricant" or "to make the probe slide smoothly". You must state that it provides acoustic impedance matching to eliminate the air-skin boundary and minimise unwanted reflection.
• Trap 3: Origin of the Larmor frequency. The external magnetic field (\(B_0\)) sets the Larmor precession frequency. The RF pulse does not create the precession; it resonates with the pre-existing Larmor frequency to tip the protons.
• Trap 4: Reason for high X-ray absorption in bone. Bone absorbs more X-rays primarily because of the high atomic number (\(Z\)) of calcium and phosphorus, as photoelectric absorption depends on \(Z^3\), not merely the physical density.
• Trap 5: Unit errors in exponential calculations. Ensure that thickness \(x\) and linear attenuation coefficient \(\mu\) are in compatible units (e.g., both in \(\text{m}\) and \(\text{m}^{-1}\), or both in \(\text{cm}\) and \(\text{cm}^{-1}\)) before evaluating \(e^{-\mu x}\).