Learning Objectives
- Describe the fundamental interactions of sound with tissues
- Explain the difference between reflection and scattering
- Calculate the amplitude and power, reflection and transmission coefficients, when supplied with appropriate acoustic impedance values
- Explain the origin of speckle in ultrasound images
- Describe the basic modes of operation of an ultrasound scanner and the information they provide
- Have a basic understanding of the key factors affecting spatial and temporal resolution
- Calculate the Doppler shift associated with scattering from a moving target and calculate the speed of a target given a measured Doppler shift
- Describe and explain a range of common artefacts that affect ultrasound imaging and be able to provide techniques for avoidance.
- Explain the potential biohazards of ultrasound imaging and describe the indices that are used to guard against these.
Ultrasound imaging is transmission of high frequency sound into the body. It involves the detection of echoes and signal processing, leading to the parametric display of returning echoes.
Ultrasound has widespread medical applications as it is safe (non-ionising radiation), relatively cheap and portable and versatile. It is particularly useful for imaging soft tissues especially in the context of preclinical studies, to see the anatomy and/or function.
Resolution is proportional to frequency, as the higher the frequency, the higher the resolution. Also penetration into the body is proportional to the frequency, lower frequencies penetrate deeper into the body.
Note: There are also many industrial (non-medical) applications
The standard ultrasound is same size as a filing cabinet but it is on wheels. They have lots of controls as they lots of parameters that can be tweaked for the particular area than is to be scanned. The ultrasound scanner clinical transducer is the instrument that is used to produce and receive the ultrasound signal. The thickness of the active element is 0.4mm and produces a frequency of around 5.4 MHz.
There are many different modes of Ultrasound Imaging:
Sound waves are a form of mechanical energy (vibration) that propagates due to the motion of particles in the medium. The density and elasticity are the fundamental physical properties that determine how sound waves propagate.
Robert Hooke discovered that stress is proportional to strain (Hooke’s Law). Using this is relation to ultrasound:
$ \beta $ is the bulk elastic modulus, $ \frac{\Delta V}{V_0} $ is the fractional volume change
$ \frac{\rho - \rho_0}{\rho_0} $ is the relative change in density
As as sound wave propagates, energy is lost and At boundaries between different materials, it can be reflected, refracted, or scattered. Remember that sound rarely travels through completely homogeneous media.
Acoustic impedance is the ratio of push (local pressure) variable to flow (how fast particles are moving) variable.
$ Z_{sp} = \frac{p}{v} $
where Zsp is the Acoustic Impedance, p is the press and v is the particle velocity. Note how similar this equation is to $ R = \frac{V}{I} $
$ Z_{sp} = \frac{p}{v} = Z_{ch} = \rho_0 c_0 $
Special case of infinite plane wave. Where c0 is the speed of sound
Pulse waves are required for range finding. The length of the pulse affects the resolution, sensitivity and total energy derived.
At a boundary between two media, the pulse wave splits into transmitted and reflected components with power being conversed across the boundary.
$ r = \bigg( \frac{Z_2 - Z_1}{Z_2 + Z_1} \bigg)^2 \quad t = \frac{Z_1}{Z_2} \bigg( \frac{2Z_2}{Z_2 + Z_1} \bigg)^2 $
$ R = \frac{Z_2 - Z_1}{Z_2 + Z_1} \quad T = \frac{2Z_2}{Z_2 + Z_1} $
Scattering occurs when there are small inhomogeneities in wavelength as well as a possible local variation in density, elasticity and speed. This ends up causing the ‘speckle’ artefact in an ultrasound image. It is highly dependent on size and frequency.
There are many objects or particles per resolution cell. The random arrangement gives rise to incoherent scattering or specie noise. Speckle is a random, deterministic, interference pattern that is an inherent characteristic of coherent imaging. Its texture does not correspond to underlying structure, and the interference effect is superimposed on average scattering magnitude.
When sound passes through tissue some of the energy it possess’ is lost due to scattering and absorption. Absorption is the conversion of wave energy to heat, and is dependent on frequency.
The lost of energy is characterised using an Attenuation coefficient, in a logarithm scale with units in dB.cm-1.MHz-1. Note that it is frequency dependent, the higher the frequency the more energy you lose.
Sound is attenuated as it propagates (depth), the ultrasound machine automatically calculates the attenuation coefficient and adjusts the brightness on the display so it is an even image (i.e. not darker with the increase in depth).
Echo location is the timing of echoes providing depth information.
The Piezoelectric effect is how we generate the sound pulses in the machine. In some materials, when a potential difference is varied across them, the material will vary in thickness. This can be used to generate a high frequency vibration. Mechanical distortion leads to the imbalance of distribution of electric charge (the reverse effect is also true). As a result, the electric field is proportional to the strain.
Inside an ultrasound probe, there are hundreds of wires connected up to hundreds of independent transmitters and receivers in a linear array. Thos is desirable, as you want to make it possible for the operator to ‘steer’ the sound. A circular wavefront can then be formed to focus the beam, by firing of small ultrasound pulses from the different transmitters at different times. This manipulation of the beam is known as beamforming.
The transducer has a natural resonant frequency, however at this frequency the pulse is long. This is undesirable in ultrasound, so they are dampened to create shorter pulses. This dampening however is inefficient and energy is wasted. Ideally, pulse length (Tp) would be equal to the wavelength, however due to physical limitations it is always longer than a single wavelength. A larger frequency and a larger bandwidth improves resolution.
The range resolution ($ \Delta r $), which is the ability to distinguish two scatterers at different depths behind each other, is inversely proportional to the frequency.
$ \Delta r = \frac{cT_p}{2} $
Tp is the length of pulse in time, c is the speed of sound, $ \Delta r is the range resolution $
In the horizontal (lateral) direction a higher frequency, larger aperture and tighter focus all contribute to an improvement in resolution.
Is the precision of ultrasound with respect to time, and is represented by the following equation:
$ T = N.\frac{2d}{c} $
T = time per frame, N = liens per frame, d = depth, c = $ \sqrt{ \frac{\beta}{\rho_0}} $ = speed of sound
In ultrasound, the doppler effect occurs twice, the moving target receives and transmits the sound wave. The change in frequency is negative as the velocity towards the original source reduces separation and increases frequency:
c = speed of sound, V = target velocity, f = frequency
There is no Doppler effect when a target is moving perpendicular to the sound direction. Only the component of the target velocity along the axis of the wave direction contributes to the Doppler Shift.
If Ultrasound f = 5 MHz, Blood velocity = 0.5 m/s, Angle = 45°, Sound speed = 1540 m/s.
Note: We will be able to hear this sound, and sometimes doctors use this in their diagnosis.
Unfortunately there are many common artefacts in Ultrasound, however fortunately most of these can be avoided by moving the transducer:
Ultrasound contrast agents are designed so more scattering occurs, so more pulses are reflected and received. The problem is that Blood on an Ultrasound is dark/black. Microbubble contrast agent, a few micrometers in diameter, can provide a non-linear response to ultrasound. For example this can be helpful to visualise tumours in a liver.
The intensity of a plane travelling wave:
Energy lost per unit area, per unit distance and time:
Assume all energy is absorbed as heat. The heat energy, assuming no heat is lost via conduction, convention or radiation is represent by:
$ \rho $ is the density, C is the specific heat capacity, and $ \Delta T $ is the change in temperature. Remember that I is the energy per unit time: $ \frac{dQ}{dt} = \mu I $
However heat is transported away via tissue perfusion.
Acoustic cavitation is the formation, motion and effects of acoustically driven cavities in fluids. It involves the tearing apart of the medium due to low pressure (i.e boiling).
Inertial cavitation refers to the sudden collapse of a cavity in the compression phase. It is governed by the inertia of the surrounding medium. Acoustic shock wave, High temperatures ~1kK, production of light. It is a very localised effect and free radicals are created.
Non-Inertial cavitation refers to stable oscillation of a cavity during isolation. This includes effects associated with motion of the surface and gas diffusion.
These are two guidelines which a clinician uses which air on the side of caution:
The thermal index is intended as a measure of an ultrasound beam’s thermal bioeffects.
$ TI = \frac{W}{W_{deg}} $
$ W_{deg} $ is the acoustic power required to raised temperature by 1°C (steady state), $ W $ is the current power output. Note TI is not an indication of actual temperature rise. Different models are used to calculate TI for soft tissue, bone (at focus), and cranial bone
The MI indicates the possibility of mechanical damage to the tissues as a result of cavitation. It is based on the analysis of pressure required to initiate inertial cavitation. It is a most basic level this index gives an idea of changes in acoustic pressure level with output power. Above 0.7 there is a theoretical risk of cavitation.
$ MI = \frac{P_{-ve}}{\sqrt{f}} $
$ P_{-ve} $ is the peak negative acoustic pressure. $ f $ is the ultrasound frequency. MI is not a probability. Pressure is derated by assumed attenuation in tissue.