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

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

What is ultrasound?

Ultrasound is sound with frequencies above the human hearing range (>20 kHz). Think of it as a super‑fast “ping” that can travel through the body and bounce back from different tissues.

How is it produced?

  • Piezoelectric crystals change shape when an electric voltage is applied.

  • When the crystal vibrates, it pushes on the surrounding fluid (usually water or gel) and creates a pressure wave.

  • Typical frequencies used in medical imaging: 2–15 MHz.

Propagation through tissue

The speed of sound in soft tissue is about 1540 m s⁻¹. The wave travels until it reaches a boundary where the acoustic impedance changes.

Acoustic impedance is defined as \$Z = \rho c\$, where \$\rho\$ is density and \$c\$ is sound speed.

Reflection at a boundary

The fraction of the wave that is reflected is given by the reflection coefficient:

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

A large difference in impedance (e.g., bone vs. muscle) gives a strong echo, while similar impedances give weak echoes.

Depth calculation

The time delay between transmission and reception tells us how far the boundary is:

\$d = \frac{v\,t}{2}\$

The factor ½ accounts for the wave travelling to the boundary and back again.

Common acoustic impedances

TissueDensity (kg m⁻³)Speed of sound (m s⁻¹)Impedance (Rayl)
Water100014801.48 × 10⁶
Muscle104015801.65 × 10⁶
Bone190040807.75 × 10⁶

Analogy: Echo in a canyon

Imagine shouting in a canyon. The sound travels, hits a cliff, and echoes back. The louder the echo, the steeper the cliff. In the body, a bone is like a steep cliff – it reflects a strong echo, while a soft organ is a gentle slope – it reflects a faint echo.

Exam tip box

Remember:

  • Reflection coefficient formula – key to quick calculation.

  • Typical ultrasound frequency range: 2–15 MHz.

  • Speed of sound in soft tissue ≈ 1540 m s⁻¹.

  • Depth formula: \$d = vt/2\$.

Tip: When given a time delay, first double the distance travelled (to the boundary and back) before dividing by the speed.

Sample exam question

  1. A 3 MHz ultrasound pulse travels through soft tissue (speed 1540 m s⁻¹). The echo from a bone surface returns after 2.0 ms. What is the depth of the bone?

  2. Calculate the reflection coefficient at the muscle–bone interface using the impedances above.

Answer guide:

  1. Depth: \$d = \frac{1540 \times 0.002}{2} = 1.54\$ m.

  2. Reflection coefficient: \$R = \left(\frac{7.75-1.65}{7.75+1.65}\right)^2 \approx 0.84\$ (84 % of the energy is reflected).

Key take‑away

Ultrasound imaging relies on the physics of sound waves: production, propagation, reflection, and time‑of‑flight. By mastering these concepts, you’ll be able to interpret ultrasound images and answer exam questions with confidence.