Ultrasounds

Objectives

Lesson outcomes

Explain how piezoelectric crystals generate and detect ultrasound pulses.
Describe how reflected ultrasound pulses give diagnostic information about tissue boundaries.
Define and use specific acoustic impedance, including Z = rho c.
Use reflection coefficient and attenuation equations in ultrasound calculations.

Syllabus

CIE 9702 syllabus points

6 linked

24.1.1 understand that a piezo-electric crystal changes shape when a p.d. is applied across it and that the crystal generates an e.m.f. when its shape changes
24.1.2 understand how ultrasound waves are generated and detected by a piezoelectric transducer
24.1.3 understand how the reflection of pulses of ultrasound at boundaries between tissues can be used to obtain diagnostic information about internal structures
24.1.4 define the specific acoustic impedance of a medium as Z = ρc, where c is the speed of sound in the medium
24.1.5 use IR / I0 = (Z1 – Z2)2 / (Z1 + Z2)2 for the intensity reflection coefficient of a boundary between two media
24.1.6 recall and use I = I0e –µx for the attenuation of ultrasound in matter

Definitions

Required definitions

Specific acoustic impedance
the product of density and speed of sound in a medium, Z = rho c.

Lesson Notes

Student guidance and lesson notes

Overview

This lesson applies wave physics to medical ultrasound imaging. You will connect the piezoelectric effect to ultrasound generation and detection, then use acoustic impedance, pulse reflection, and attenuation to explain how images of internal structures are produced.

What You Need to Know

A piezoelectric crystal changes shape when a p.d. is applied and generates an e.m.f. when its shape changes.
An ultrasound transducer can act as both a transmitter and receiver because of this piezoelectric behaviour.
Short ultrasound pulses reflect at boundaries between tissues, and the time delay of the echo can be used to locate the boundary.
Specific acoustic impedance is Z = rho c, where rho is density and c is the speed of sound in the medium.
A larger difference in acoustic impedance at a boundary gives a larger reflected intensity.
Ultrasound intensity decreases with distance in matter according to an exponential attenuation model.

How to Work Through It

Start by recalling reflection, transmission, speed, time, and intensity from wave physics.
Link the piezoelectric effect to the two jobs of the transducer.
Use pulse travel time to calculate the depth of a reflecting boundary.
Practise calculations involving acoustic impedance, reflection coefficient, and attenuation.

Check Your Understanding

Why can the same ultrasound transducer send and receive pulses?
Why do tissue boundaries produce echoes?
How does a large impedance change affect the reflected intensity?
Why must the pulse travel distance be treated carefully when calculating tissue depth?

Common Mistakes

Forgetting that an echo travels to the boundary and back, so the depth is half the total travel distance.
Treating acoustic impedance as the same thing as density.
Assuming all ultrasound is reflected at a boundary rather than a fraction depending on the two impedances.
Using the attenuation equation without checking the units of the attenuation coefficient and distance.

Next Steps

Keep the reflection and attenuation models secure for comparison with X-ray imaging.
Be ready to explain why different imaging methods suit different tissues.