Physics of Ultrasound!

Sound

Longitudinal mechanical wave. Unlike electromagnetic waves (light, radio) needs particles to be transmitted – cannot travel through a vacuum.
When sound travels through a medium areas of compression (high pressure and density) and rarefaction occur. This represented by a sine wave of amplitude by velocity.

Amplitude

Magnitude of change in an oscillating variable. It indicates power. It is the difference between the peak and trough pressures. Measured in decibels (logarithmic).

Wavelength

Distance between the same points (eg the peaks) of 2 successive waves. Measured in m. US 0.3-0.8mm.

Frequency 

Number of cycles (oscillations) per second. Measured in hertz. 
Audible sound 20-20,000 Hz (20kHz)
<20Hz is infrasound. >20kHz is ultrasound.
Medical US devices use frequencies of 3-15 megaHz. ECHO 3-5.

Propagation velocity

Speed which a wave propagates though a medium. Depends on the density of the medium. Faster the denser the molecules.

Air 330 m/s
Fat, soft tissue and muscle all around 1500
Bone 3500

Velocity = frequency x wavelength

Distance = speed x time

Propagation velocity of mediums cannot be changed but the frequency of the ultrasound can. A lower frequency will result in a longer wavelength.
Shorter wavelengths, and therefore higher frequencies, give better resolution but less penetration.

Acoustic impedance

Different for each tissue.
When US crosses a boundary between tissues of different impedances, much of the sound will be reflected back to the transducer. Air has a propagation velocity very different from soft tissues meaning most US reflected back. Same with bone.

Specular (mirror-like) reflection occurs at medium boundary where the reflector is large and smooth. Dependent on angle of beam. Needs to be 90 for maximum. Angle of incidence = angle of reflection if mirror flat.
Backscatter occurs with small and rough surfaced structures. Weaker than specular but not dependent on angle.

Attenuation

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

Refraction

Change in direction of US as it passes medium boundary (some reflected and some refracted – goes on but has been bent to a different angle). The part of the wave that hits the medium 1st slows down before the rest of it which is why it bends. Can be used to focus US beam with a lens but also causes artefact.

Transducers

Piezoelectric effect – piezoelectric crystals change shape when a voltage applied and so oscillate with an alternating current and generate ultrasound. Returning US causes them to oscillate and generate a voltage which can be detected and processed.
Phased array transducers contain >100 PE elements and the beam can be steered and focused by altering the timing of activation of the elements.
PE elements mounted on a backing layer with high impedance. Matching layer behind the lens over PE layer.

Beam is cylindrical for a short distance after leaving transducer (near field) and then diverges (far field). Imaging best in near field. Length of near field greater with high frequencies and wide transducers.
Focusing the beam has no effect on the length of the near field but makes it narrower and increases resolution at the expense of a wider far field (improves lateral resolution). Can choose the focusing point. 

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 and the 2nd harmonic. Structures will often look thicker with 2nd harmonic imaging.

A-mode

Plots amplitude of reflected signal as a spike against distance from probe.

B-mode

Amplitude represented by brightness of a dot rather than a spike.

M-mode

Displays motion against time along a single line of sight. Single scan line means very high pulse repetition frequency can be used with a high sampling rate which helps visualise rapid motion (eg valves)

2-D

Series of scan lines side by side build up an image. With ECHO around 120 scan lines sweep across 20-30 times per second. For each scan line a pulse has to be emitted and received. Number of frames generated each second determined by no of scan lines and depth. Reducing width and depth will increase the frame rate and improve resolution.

Power

Amount of energy (amplitude) delivered

Gain

Amount of amplification

TGC

Adjusts the gain from different depths (boosts gain from far fields) for even image. Compensates for attenuation. Can be independently altered.

Grey scale compression

Alters no.s of shades of grey to determine contrast. Also termed dynamic range.

Resolution

Ability to discriminate between objects close together in space (spatial) or time (temporal). Lateral spatial resolution improved with narrower beam (focussed on area of interest) and low gain. Deeper means worse lateral resolution as the beam diverges.
Temporal resolution improved with increasing frame rate.
Pulse length determines axial resolution – shorter the better. Crystal has to accelerate and decelerate to and from the transmitted frequency which puts limitations on pulse length. The band width is the number of frequencies in the beam. Band width and pulse length cannot be changed independently.

Artefacts

Acoustic shadowing – highly reflective structures block the beam and cause echo dropout behind them.

Reverberation – US rebounds several times between strong reflectors before returning to transducer. This increases the time to return which is interpreted as the structure being further away than it is causing ghost images beyond the structure. These will move in tandem with the structure.

Beam width artefact – machine has difficulty distinguishing whether returning signal has originated from centre of beam or edge. Strong reflectors at the edge of the far field cause smearing of the image.

Side lobe artefact – additional beams surrounding the main beam give signals 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

M-mode and 2D have lowest intensity; PW the highest

Thermal

Mechanical energy of US converted into heat energy as it passes through tissues. Frequency, power, focus and depth all influence it. Most relevant with TOE probes.

Mechanical

Cavitation can occur where gas bubbles created as US passes through tissues. Not an issue with standard TTE but can cause resonance and disruption of bubble contrast agents.

Electrical

Shock

Infection

Doppler Physics

Doppler principle

A change in the observed frequency of sound depending on whether the observer is moving towards or away from the source.
Velocity can be calculated from this doppler shift (doppler equation).
The larger the angle between the direction of blood flow and the beam, the greater flow is underestimated. Should be aligned with flow as much as possible and kept below max of 20 degrees.

Spectral doppler

CW and PW

US beam returns to transducer and difference in frequency between transmitted and returning waves compared to calculate doppler shift using Fourier analysis. A spectral doppler display is produced. Plots velocities against time. Grey pixels show velocity and the shade of grey reflects the density of the signal (the proportion of cells moving at that particular velocity).
Can adjust

  • Power
  • Gain
  • Baseline
  • Velocity range

CW

Uses one transmit and one receiving crystal continuously.
Obtains signals from the entire length of the beam so unable to look at specific point.
Can measure higher velocities than PW without aliasing.

PW

Sample volume can be placed at specific point.
Cannot transmit and receive continuously. Pulse transmitted and the reflected signal only sampled from point of interest (calculated by time) – other signals ignored. As pulse transmitted and then ‘listened for’, the frequency of how often pulses can be transmitted is limited (PRF). The further away the sample volume, the longer the round trip takes and the lower the PRF. This causes aliasing.

Aliasing

A wave must be sampled at least twice per wavelength to measure wavelength accurately.

Nyquist limit = 0.5 x PRF


Aliasing can be reduced by:

  • Shifting the baseline
  • Adjusting the doppler velocity scale
  • Decreasing the frequency (longer wavelength means longer sampling time)
  • Increasing the angle of incidence
  • High PRF PWD which samples at 2 points

Colour doppler

Flow assessed at multiple points in a region of interest (box).
Colour codes flow according to mean velocity and direction.
Towards red; away blue (BART).
Turbulent flow green.
Suffers from aliasing – if flow velocity exceeds upper limit then will be coded as opposite colour. Numbers at top and bottom of velocity show the Nyquist limit above which aliasing will occur.
The smaller the colour box the higher the frame rate (making it narrower and shallower improves it but cutting off near bit makes no difference).
Colour M-mode used at level through LVOT to measure jet width of AR compared to LVOT.

Tissue doppler

Myocardial motion has a stronger but lower velocity doppler signal so can be selected by filtering (whereas it is filtered out for colour flow).
PW 1cm below (towards apex) MV annulus used to assess diastolic function.

Power doppler (not used in ECHO)

Unidirectional (1 colour).
Able to detect lower flow rates than colour.


Fluid dynamics

Outermost edge of spectral display is the peak velocity (Vmax).
Brightest portion is the velocity of most of the RBCs (modal velocity).
Average velocity (mean velocity).

SD and SV

Flow through a tube is velocity x cross sectional area if flow is constant.
Blood flow is pulsatile rather than constant so need to calculate volume per contraction.
Measuring the VTI (measurement of all the velocities of RBCs for each contraction at a certain point) can be done by tracing the spectral doppler envelope.
Measured in cm and represents how far the column of blood is ejected (stroke distance). 

Vol = area x length
or
Vol = area x velocity x time (as distance = s x t)

Area under speed / time graph is distance
So area of under doppler graph = distance = velocity x time = VTI

Flow volume (SV) = SD (VTI) x CSA

CSA = π r
2
orCSA = 0.785 x (diameter)

Thus SV can be calculated by measuring VTI and diameter at the same point.

Continuity equation


By the law of conservation of mass, flow in one area must = flow in another area (assuming blood incompressible, vessels not elastic and no blood lost). Therefore:

CSAA x VTIA = CSAB x VTIB

This means that an unknown CSA (such as the AV) can be calculated by measuring the VTI of the AV and the CSA and VTI of another area (e.g. LVOT)

Less mathematically correct can use 
CSAA x VmaxA = CSAB x VmaxB


Pressure gradients (Bernoulli equation)

pressure gradient = 4 x (V22 – V12)

V1 = velocity proximal to stenosis and V2 = distal velocity

If V2 is significantly greater than V1 then V1 can be ignored meaning

gradient = 4 x V2 

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

TDI and Speckle tracking

Strain = % change in length (deformation).
Measured with TDI (velocity of different areas of myocardium) or speckle tracking.
TDI is only longitudinal (towards or away from probe). Speckle tracking can look in all 3 ways the myocardium moves (longitudinal, radial, corkscrew).
Strain rate is the time it takes to do this.

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