Page 18 
  Page 19 

Chapter 4 Acoustic impedance

CONTENTS

Acoustic impedance and reflection 20
Intensity reflection coefficient 21
The intensity reflection equation 21
Acoustic impedance and ultrasound imaging 21

LEARNING OBJECTIVES

1. Describe what is meant by the term acoustic impedance.
2. Explain the properties of a substance which determine its acoustic impedance.
3. List a set of body tissues in order of their acoustic impedance.
4. Describe how the amount of ultrasound energy reflected at the interface between two substances is determined by their acoustic impedances.
5. Give the meaning of the term intensity reflection coefficient.
6. Explain why ultrasound is good at imaging different soft tissues but poor at imaging soft tissue/bone and soft tissue/air.

Acoustic impedance (Z) is the property of a substance, which describes how the particles of that substance behave when subjected to a pressure wave, i.e. a sound wave. Acoustic impedance gives the relationship between excess pressure P and particle velocity U0 as shown in Figure 4.1.

image

Fig. 4.1 A particle subjected to excess pressure P traveling at velocity U0. This gives the acoustic impedance formula:

image

If the substance has densely packed particles, for example bone, then it will take a high excess pressure for them to move at a given velocity. Therefore this type of substance will have high acoustic impedance.

On the other hand if the substance has loosely packed particles, for example air, then it will take a much lower excess pressure for them to move at the same velocity. Therefore this type of substance will have low acoustic impedance.

Acoustic impedance gives a measure of the resistance a substance has to the propagation of a sound wave through it. It is normally calculated from density ρ and speed of sound c as follows:


image


density ρ kg/m3
speed of sound c m/s
acoustic impedance Z rayls (= kg/m2/s)
  Page 20 

In this book, speed and velocity have the same meaning. The acoustic impedance of various substances is given in Table 4.1.

Table 4.1 The acoustic impedance of various substances

Substance Acoustic Impedance in Megarayls (kg/m2/s) × 106 Speed (m/s)
Air 0.0004 330
Fat 1.38 1450
Water 1.48 1480
Blood 1.61 1570
Kidney 1.62 1560
Liver 1.65 1550
Muscle 1.70 1580
Soft tissue (average) 1.63 1540
Bone 7.80 3500
PZT (Crystal) 30 3870

Note: the acoustic impedances of air and bone are very different.

ACOUSTIC IMPEDANCE AND REFLECTION

When an ultrasound beam strikes an interface between substances it is the acoustic impedances of the two substances that determine whether reflection takes place and the amount of energy reflected. The examples below illustrate this.

In substances with the same acoustic impedance there is total transmission of energy and therefore no reflection, see Figure 4.2.

image

Fig. 4.2 Total transmission of ultrasound energy as it passes across an interface between two substances of the same acoustic impedance

In substances with a small difference in acoustic impedance a small amount of energy is reflected but the majority is transmitted, see Figure 4.3.

image

Fig. 4.3 A small amount of reflected energy and a large amount of transmitted energy as ultrasound passes across an interface between two substances with a small difference in acoustic impedance

In substances with a large difference in acoustic impedance there is a large amount of reflected energy and a small amount of transmitted energy, see Figure 4.4.

image

Fig. 4.4 A large amount of reflected energy and a small amount of transmitted energy as ultrasound passes across an interface between two substances with a large difference in acoustic impedance

  Page 21 

INTENSITY REFLECTION COEFFICIENT

This gives the proportion of energy reflected from an interface between two substances and has a value between 0 and 1, where 0 = total transmission and 1 = total reflection.

The intensity reflection coefficient for various interfaces is given in Table 4.2.

Table 4.2 The intensity reflection coefficient for various interfaces

Interface Intensity Reflection Coefficient R Percentage of Energy Reflected (%R)
Fat/Muscle 0.0108 1.08
Bone/Muscle 0.412 41.2
Air/Soft tissue 0.999 99.9

Note the high reflection coefficients for bone/muscle and air/soft tissue.

For most soft tissue/soft-tissue interfaces the percentage of energy reflected is 1% or less.

THE INTENSITY REFLECTION EQUATION

This equation allows you to calculate the intensity reflection coefficient (R) for an interface between two substances providing you know their acoustic impedances.


image


Ir = reflected intensity
Ii = transmitted intensity
Z1 and Z2 = acoustic impedances of the two substances

Example

What is the intensity reflection coefficient R for an interface between liver (Z1 = 1.65 Mrayls) and fat (Z2 = 1.35 Mrayls)?


image


ACOUSTIC IMPEDANCE AND ULTRASOUND IMAGING

The difference in acoustic impedance between two substances is known as the acoustic impedance mismatch. It is this acoustic impedance mismatch at an interface which is responsible for ultrasound energy being reflected back toward the probe and being used to produce an image.

If there is a large acoustic mismatch, e.g. between bone and muscle or air and soft tissue, then a large proportion of energy is reflected. This results in a strong echo, which produces a bright image on the display. However, very little energy is transmitted across the interface and any echoes produced beyond the interface do not have enough energy to produce an image, see Figure 4.5.

image

Fig. 4.5 Diagram showing an interface with strong reflection but poor transmission/penetration

If the acoustic impedance mismatch is small, e.g. between two soft tissues, then a small proportion of energy (1% or less) is reflected. The rest of the energy is transmitted across the interface to produce further echoes from other interfaces deeper within the subject, see Figure 4.6.

image

Fig. 4.6 Diagram showing echoes reflected from a series of soft tissue/soft-tissue interfaces

From the above it can be seen that where there is a large acoustic impedance mismatch across an interface, ultrasound will not produce a useful image beyond that interface. Therefore it is not practical to use ultrasound to produce images of soft-tissue subjects which contain gas or bone. However, ultrasound imaging is very good at discriminating between substances with small differences in acoustic impedance and is therefore excellent at differentiating between different types of soft tissues.

  Page 22 

SUMMARY

Acoustic impedance describes how the particles of a substance behave when subjected to a pressure wave
Acoustic impedance also gives a measure of the resistance a substance has to the propagation of a sound wave through it
A substance which has densely packed particles will have a high acoustic impedance
A substance which has loosely packed particles will have a low acoustic impedance
It is the acoustic impedance mismatch between two substances that determines the amount of energy reflected at an interface
Soft tissue/air and soft tissue/bone interfaces produce strong reflections because of the large acoustic impedance mismatch between these substances. However, there is not enough energy transmitted to produce a useful image beyond these interfaces
Ultrasound imaging is very good at discriminating between substances with small differences in acoustic impedance such as soft tissues