Physics associated with US is a slightly painful but essential part of understanding images you see.

Allows understanding of the limitations of echo and the artefacts seen on screen.

Very much a summary of key things to learn.

Sound:

Sound travels as a longitudinal mechanical wave and can be thought of as a series of vibrating particles in a line. Unlike electromagnetic waves (e.g. light) it requires particles to be able to be transmitted – i.e. cannot travel within a vacuum.

When it travels through a medium, there are areas of compression (high pressure and density where particles are closer together) and rarefaction (low pressure and density where particles are further apart).

Sound can be represented as a sine wave.

Amplitude:

Indicates sound wave’s strength – measured as the difference between peak pressure and average pressure. Magnitude of change in oscillation variable. Measured in decibels (logarithmic – change of 6db represents doubling of amplitude).

Wavelength:

Distance between two successive waves – measured from peak to peak (or trough to trough). Measured in metres of millimetres – US is 0.3 – 0.8mm.

Frequency:

Number of wave cycles/oscillations per second. Measured in hertz.

100 oscillations per second is 100Hz.

Audible sound lies between 20Hz to 20,000Hz (20kHz).

<20Hz is infrasound.

20kHz is ultrasound.

Medical ultrasound uses frequency range between 1.5 and 7 MHz (1 megahertz = 1 million Hz).

Propagation velocity:

Speed at which sound propagates through a medium.

Variable depending on density of tissue.

Higher density = higher speed.

Average propagation velocity for the heart is 1540m/s.

Velocity = frequency x wavelength

Distance = speed x time

Propagation velocity for tissue is fixed but the frequency of ultrasound can be adjusted.

Lower frequency will result in a longer wavelength.

Shorter wavelengths, and therefore higher frequencies, will give better resolution but poor penetration.

Acoustic impedance:

Each tissue has a different acoustic impedance which is most relevant at the boundaries between different tissue types.

When ultrasound crosses the boundary between two tissues with very different acoustic impedance (i.e. air and soft tissue, or bone and soft tissue), much of the ultrasound will be reflected back towards the probe.

This would be most marked at the air-skin boundary hence the use of gel to limit the impact.

Two types of reflection occur:

  • Specular reflection (mirror-like) – at boundaries where reflector is relatively large (at least two wavelengths in diameter) and smooth. Highly dependent on angle of incidence (beam). In order to maximise the energy reflected, beam needs to be perpendicular (90 degrees) to the reflector. Angle of incidence = angle of reflection if mirror flat.
  • Backscatter – occurs with small and rough surfaces. Returning signal will be weaker than specular but is not dependent upon angle.

Attenuation:

Energy lost by reflection/backscatter and absorption of energy by tissues (heat). Greater at higher frequencies.

The half-intensity depth (HID) is the depth (in cm) in soft tissue in which the intensity of the ultrasound is reduced by 50 per cent, and depends upon the frequency (f) of the ultrasound emitted by the transducer, measured in MHz: HID (soft tissue) = 6.

Refraction:

Change in direction of ultrasound pulse as it passes across a medium boundary. The part of the wave that hits the medium slows down before the rest of it causing bending. Can be used to focus US beam with a lens but also causes artefact.

Transducers:

Piezoelectric effect:

Crystals change shape when voltage is applied and alternating voltage causes them to oscillate and create ultrasound. If the crystals receive returning ultrasound waves they generate an electrical voltage themselves which can be detected as a signal.

Phased array probes have an array of piezoelectric elements (2D 128 crystals, 3D have several thousand) that can be ‘steered’ and focused electronically by altering the timing of activation elements.

Piezoelectric elements are mounted on a backing layer which has high impedance to limit reverberation artefact.

In front of the elements is a matching layer which improves impedance matching between elements and the body.

Beam is cylindrical for short period after leaving the probe (near field, Fresnel zone) before diverging (far field, Fraunhofer zone).

Image is best in the near field. Length of near field greater with high frequencies and wide transducers.

Focusing the beam doesn’t affect the length of near field but produces a narrower beam with higher resolution (better lateral resolution) at the expense of a wider beam in the far field. Focus can be controlled electronically with phased array probes, aided by acoustic lens.

Transducer will transmit a burst of US (few microseconds) and then wait for reflected US (few hundred microseconds) before transmitting next burst. The time taken and the intensity of any reflected US from tissue interfaces is used to build up an image.

Imaging using 2nd harmonics improves resolution (automatic on modern machines). Probe listens for signals of the fundamental frequency (original frequency) and the 2nd harmonic (multiples of original frequency). Structures will often look thicker with 2nd harmonic imaging.

A mode:

Plots amplitude of reflected signal as spikes depending on distance from the probe.

B mode:

Amplitude plotted as brightness of dot rather than spike.

M mode:

Displays motion against time along a single slice/line of site. Single slice means very high pulse repetition frequency can be used with high sampling rate for imaging rapidly moving structures e.g. valves.

2D imaging:

Series of scan lines to build up image. Around 120 lines sweep across 20-30 times per second, each of which needs to be sent and received. Frame rate is determined by number of lines – therefore increased with narrow width and depth.

Power:

Amount of energy (amplitude) delivered.

Gain:

Amount of amplification of received signal. High gain reduces lateral resolution and increases noise.

TGC:

Adjusts gain of different depths. Can be used to compensate for attenuation or to balance image.

Grey scale compression:

Alters number of shades of grey to determine contrast. Also called dynamic range.

Resolution:

The ability to discriminate between two objects that are close together in space (spatial resolution) or two events that occur close together in time (temporal resolution).

Spatial resolution is made up of axial resolution and lateral resolution.

Axial resolution – objects that lie along axis of US beam. Determined by transducer frequency and pulse length – higher frequency & shorter pulse length = better axial resolution. Axial resolution typically around 3mm.

Lateral resolution – aka azimuthal resolution, objects that lie side by side perpendicular to US beam. Varies according to how far objects lie from transducer. Narrower beam = better lateral resolution (affected by focus). Lat resolution also affected by high gain settings. Lateral resolution typically around 1mm.

Temporal resolution – frame rate – important in distinguishing events close in time. Frame rate dependent on data processing requirement. 2D typically 20-30fps whereas M-mode around 1800fps.

Imaging artefacts:

Structures or distortions seen on image which are not actually present.

Acoustic shadowing:

Highly reflective structure blocks US from penetrating any further. Causes echo dropout in far field.

Reverberation artefact:

US rebounds several times between two strong reflectors before returning to the transducer. Increases time taken to be detected and therefore displayed further away from probe than it is. Causes ‘ghost’ images in far field which will move in tandem with the original structure.

Beam width artefact:

Beam has finite width and machine has difficult discriminating between returning signal has arisen from the centre or edge of the probe – particularly in far field. Strong reflectors from the edge of the beam are displayed by the machine as being from the centre, ‘smearing’ the displayed echo. Can be minimised by focusing.

Side lobe artefact:

Similar to beam width artefact. Additional, unavoidable beams surrounding the main beam are interpreted as originating from main beam and are displayed far from their true location. Only occur in modern phased array probes (not in mechanical).

Safety:

2D and M-mode have lowest intensity. PW has highest.

Thermal – more important with TOE. Mechanical energy is converted to heat as it passes through tissues. Influenced by frequency, power, focus width and depth.

Mechanical – Cavitation occurs when gas bubbles are created as US passes through it. Not relevant with standard TTE but can cause resonance and disruption of bubble contrast agents. Can be measured by ‘mechanical index’. MI of <1 is considered safe.

Electrical – shock.

Infection.

Doppler physics:

Doppler principle:

Change in observed wavelength or frequency of a sound (or light) wave if the source is moving relative to them.

When ultrasound is reflected from moving blood cells the frequency is increased if the red cells are moving towards the ultrasound transducer, or decrease if moving away.

This change in frequency between transmitted and returning signal is the doppler shift.

Velocity can be calculated from this doppler shift (doppler equation):

V = c x fd / 2 x ft x cos0

Where V = velocity of red cells, c is the speed of sound in blood, fd is the doppler shift in frequency between transmitted and returning signals, ft is frequency of transmitted signal and 0 is the angle between ultrasound beam and direction of flow.

The larger the angle between direction of blood flow and beam, the greater the flow is underestimated.

Important to optimise alignment and keep angle below a maximum of 20 degrees.

Spectral doppler (PW & CW):

When US returns to transducer, the difference in frequency between transmitted and returning beams is compared to calculate the Doppler shift. Complex process using mathematical technical called Fourier analysis. This produces spectral doppler display.

This displays conventionally plot frequency shifts (shown as velocities) on the vertical axis against time on the horizontal axis. Zero line is shown.

Grey pixels show velocity & shade of grey reflects density of signal (proportion of cells moving at that particular velocity. Frequency range is -10 to +10 kHz which is in the audible range for humans so possible to listen to blood flow.

Can adjust:

  • Transmit power – controls amount of US energy delivered to patient.
  • Gain amplifies brightness of received signal but increases noise.
  • Baseline shift – shifts the zero point.
  • Velocity range – alters vertical velocity scale to higher or lower range.

Continuous wave doppler:

One transmit and one receiving crystal continuously.

Obtains signals from entire length of the beam so unable to look at specific point.

Can measure higher velocities than PW without aliasing.

Pulsed wave doppler:

Sample volume can be placed at a specific point.Sample volume length can be adjusted in theory but typically a length of 3mm is used.

Cannot transmit and receive continuously – transmits an ultrasound pulse and then samples only reflected signal from the point of interest which the machine calculates by time. Remainder of signals ignored.

Because the machine must wait for the transmitted pulse to return it limits how rapidly it can send out consecutive pulses – the pulse repetition frequency (PRF).

The further away the sample volume is from the transducer the longer the ’round trip time’ of the pulse so lower the PRF. This leads to aliasing which is one of the main limitations of PW doppler.

Aliasing:

A wave must be sampled at least twice per wavelength to measure wavelength accurately (Nyquist’s theorem).

This puts and upper limit on the doppler shift that can be measured using PW doppler (Nyquist limit) which is equals half the PRF.

Once the blood velocity exceeds this limit the spectral trace will appear at the top of the waveform ‘missing’, or appear on the opposite side of the baseline.

This effective puts a limit on the maximum velocity of blood that can be sampled with PW doppler and thus if flows are higher than this it may be necessary to switch to CW.

Nyquist limit = 0.5 x PRF

Aliasing can be reduced by:

  • Adjusting the doppler velocity scale as far as possible.
  • Sampling at the lowest possible distance from transducer.
  • Decreasing the frequency (longer wavelength means longer sampling time).
  • Increasing the angle of incidence.
  • Using high PRF PWD which samples at 2 points.

Colour doppler:

Flow assessed in region of interest – box.

Blue away red towards (BART).

Turbulent flow is green.

Aliasing also occurs – if flow velocity exceeds upper limit it will be coded as opposite colour.

Numbers at the top and bottom of velocity show the Nyquist limit above which aliasing will occur.

Smaller boxes require less processing power and therefore higher frame rate – so should always try to limit size of box to optimise image.

Can use m-mode through colour to look for change over time – e.g. LVOT for AR and descending aorta for diastolic flow reversal.

Tissue doppler:

Myocardial motion has stronger but lower velocity doppler signal so can be selected by filtering. Filters used to remove doppler signals returning from myocardium in order to optimise the signals related to blood flow.

Useful for systolic and diastolic function.

Place PW at MV/TV annulus 1cm towards apex after turning on TDI.

Power doppler:

Not used in echo.

Unidirectional (one colour).

Able to detect lower flow rates than colour.

Speckle tracking:

Measurement of myocardial strain is becoming increasingly popular and is the % change in length (deformation).

Uses TDI to measure the velocity of different areas of myocardium or speckle tracking.

Main difference is that TDI will only assess longitudinal function whereas speckle tracking can look in all three myocardial planes of contraction – longitudinal, radial, corkscrew.

Strain rate is the time taken to perform this.

Fluid dynamics:

Normal intracardiac blood flow is described a laminar. Turbulent flow can occur at stenoses where the concentric streams break down. Point at which laminar becomes turbulent is described by Reynolds equations.

Turbulent flow more likely when blood is high density and low viscosity and flows at high velocity through a wide calibre vessel.

As blood flow is pulsatile, increasing then decreasing in velocity with time, a number of velocity measurements need to be made from spectral doppler display.

Outermost edge of spectral trace is the peak velocity at any particular time point.

Brightest portion represents velocity of majority of cells (modal velocity).

Average velocity of red blood cells is expressed as the mean velocity.

SD and SV:

Flow through tube is velocity x cross section area if flow is constant.

As blood flow is pulsatile – need to calculate volume per contraction.

Measuring VTI (all the velocities of RBCs for each contraction at a certain point) can be done by tracing the doppler envelope.

Measured in cm and represents how far a column of blood is ejected – stroke distance.

Vol = area x length ; OR vol = are x velocity x time (as distance is s x t)

Area under speed/time graph is distance.

So area of under doppler graph = distance = velocity x time = VTI.

Therefore stroke volume can be calculated by measuring VTI and diameter at the same point.

Continuity equation:

Law of conservation of mass, flow in one area must = flow in another area (assuming blood is incompressible, vessels are not elastic and no blood is lost – closed circuit).

Therefore:

Meaning an unknown CSA (e.g. AVA) can be calculated by measuring VTI of the AV and CSA + VTI of another area – LVOT:

In theory can use Vmax although is less accurate.

Bernoulli equation – pressure gradients:

Doppler measurement os blood flow velocity can be used to calculate pressure gradients between two regions – e.g. across a valve.

The relationship between pressure gradient and velocity is expressed by the Bernoulli equation:

Where pressure change is the gradient between two regions, V1 is the velocity proximal to stenosis and V2 is distal.

If V2 is significantly greater than V1 then V1 may be ignored. Therefore the simplified Bernoulli equation may be used:

If LVOT flow >1m/s or Vmax >3m/s then need to use full equation.