understand how the reflection of pulses of ultrasound at boundaries between tissues can be used to obtain diagnostic information about internal structures

Production and Use of Ultrasound – Cambridge A‑Level Physics (9702)

Learning Objective

Explain how the reflection of short ultrasound pulses at boundaries between tissues is used to obtain diagnostic information about internal structures.

1. What Is Ultrasound?

• Sound waves with frequencies above the upper limit of human hearing (> 20 kHz).
• Medical diagnostic scanners normally operate at 2 – 15 MHz.

  • Higher frequency → better spatial (axial and lateral) resolution but reduced penetration depth.
  • Lower frequency → deeper penetration but poorer resolution.

2. Piezo‑electric Transducer – Generation and Detection

2.1 Direct and Reverse Piezo‑electric Effects

• Direct effect: an alternating voltage applied to a piezo‑electric crystal (e.g., quartz, PZT) makes it expand and contract, producing a short burst of sound.
• Reverse effect: when an incoming acoustic wave compresses the crystal, it generates a voltage.
• Because the two effects are reversible, the same crystal can act as both transmitter and receiver.

2.2 Pulse‑Echo Mode

• The transducer first emits a brief pulse (using the direct effect).
• It then switches to receive mode and records the voltage produced by the reverse effect from any reflected echoes.

2.3 Key Pulse Parameters

• Frequency f – determines resolution and penetration.
• Pulse duration – shorter pulses give finer axial resolution.
• Peak‑to‑peak voltage – controls acoustic intensity (and therefore signal‑to‑noise ratio).

2.4 Schematic (reference)

3. Propagation of Ultrasound in Tissue

In a homogeneous medium the speed of sound c is

\$c=\sqrt{\dfrac{K}{\rho}}\$

where K is the bulk modulus and ρ the density of the tissue.

4. Specific Acoustic Impedance and Reflection at Boundaries

4.1 Definition

The specific acoustic impedance of a medium is

\$Z=\rho\,c\qquad\text{(units: Rayl; 1 MRayl = 10⁶ Rayl)}\$

4.2 Reflection and Transmission Coefficients

When a pulse meets a boundary between two tissues with impedances Z₁ and Z₂:

• Intensity reflection coefficient:
  

  \$R=\left(\frac{Z2-Z1}{Z2+Z1}\right)^2\$

• Intensity transmission coefficient (ignoring absorption):
  

  \$T=1-R\$

4.3 Typical Acoustic Impedances of Human Tissues

5. From Echoes to Diagnostic Information

1. Time‑of‑flight (range) measurement

   The interval Δt between pulse emission and echo reception gives the depth d of the reflecting interface:

   \$d=\frac{c\,\Delta t}{2}\$

   The factor ½ accounts for the round‑trip travel of the pulse.

2. Echo amplitude (strength)

   Amplitude is proportional to the reflection coefficient R. Large impedance mismatches (e.g., soft tissue ↔ bone) produce bright (strong) echoes; small mismatches give weak echoes.

3. Image formation – Ultrasound modes

   • A‑mode (Amplitude mode): 1‑D plot of echo amplitude versus depth.
   • B‑mode (Brightness mode): Transducer is scanned laterally; echo amplitudes are displayed as pixel brightness, producing a 2‑D cross‑section.
   • M‑mode (Motion mode): Records echo position versus time, useful for moving structures such as heart valves.

4. Interpretation of echo patterns

   • Hyperechoic (bright) – strong reflectors: organ capsules, tendons, calcifications, bone.
   • Anechoic (dark) – little or no reflection: fluid‑filled spaces (cysts, bladder, blood vessels).
   • Isoechoic (medium brightness) – relatively homogeneous soft tissue.

6. Clinical Applications of Pulse‑Echo Ultrasound

• Abdominal imaging – liver, gallbladder, kidneys; detection of lesions, stones, or cysts.
• Echocardiography – chamber dimensions, wall motion, valve function; colour Doppler added for flow assessment.
• Obstetrics – fetal growth, placental position, amniotic fluid volume, fetal heart activity.
• Musculoskeletal – tendon tears, muscle injuries, joint effusions, surface of bone.
• Vascular studies – vessel diameter, plaque character, blood‑flow velocity (Doppler).

7. Limitations and Sources of Error

• Attenuation increases with frequency; high‑frequency probes have limited penetration.
• Acoustic shadowing behind highly reflective structures (bone, calcifications) hides deeper tissue.
• Angle dependence – Doppler velocity measurements are accurate only when the beam is within ≈ 60° of the flow direction.
• Operator dependence – image quality and measurements rely on correct probe placement, pressure, and machine settings.
• Assumption of constant speed – using the average speed of 1540 m s⁻¹ introduces small depth errors when actual tissue speeds differ.

8. Example Calculations (Exam‑style)

1. Reflection coefficient for muscle ↔ bone

   Given Z_muscle = 1.66 MRayl and Z_bone = 7.75 MRayl:

   \$\$R=\left(\frac{7.75-1.66}{7.75+1.66}\right)^2

   =\left(\frac{6.09}{9.41}\right)^2\approx0.42\$\$

   ≈ 42 % of the incident intensity is reflected – a very bright echo.

2. Depth from time‑of‑flight

   Echo received after Δt = 130 µs. Using the average soft‑tissue speed c = 1540 m s⁻¹:

   \$d=\frac{1540\times130\times10^{-6}}{2}\approx0.10\ \text{m}=10\ \text{cm}\$

9. Summary Checklist (Exam‑style)

1. State the two piezo‑electric effects (direct and reverse) and explain why a single crystal can act as both transmitter and receiver.
2. Write the definition of specific acoustic impedance: Z = ρc.
3. Calculate the intensity reflection coefficient R for a given pair of tissues (e.g., muscle ↔ bone).
4. Use the time‑of‑flight formula d = cΔt/2 to determine the depth of an interface.
5. Interpret echo brightness (hyperechoic, anechoic, isoechoic) in terms of tissue composition.
6. Identify which ultrasound mode (A, B, M) is most appropriate for a particular clinical question.