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Tutorial 1 - Basic physics of ultrasound and the Doppler phenomenon

BASIC PHYSICS OF ULTRASOUND AND THE DOPPLER PHENOMENON

 

Medical ultrasound imaging consists of using high pitched sound bouncing off tissues to generate images of internal body structures.

 

Frequency

Frequency refers to the number of cycles of compressions and rarefactions in a sound wave per second, with one cycle per second being 1 hertz. While the term ultrasound generally refers to sound waves with frequencies above 20,000 Hz (the frequency range of audible sound is 20 to 20,000 Hz), diagnostic ultrasound uses frequencies in the range of 1-10 million (mega) hertz.

 

Wavelength

The wavelength is the distance traveled by sound in one cycle, or the distance between two identical points in the wave cycle i.e. the distance from a point of peak compression to the next point of peak compression. It is inversely proportional to the frequency. Wavelength is one of the main factors affecting axial resolution of an ultrasound image. The smaller the wavelength (and therefore higher the frequency), the higher the resolution, but lesser penetration. Therefore, higher frequency probes (5 to 10 MHz) provide better resolution but can be applied only for superficial structures and in children. Lower frequency probes (2 to 5MHz) provide better penetration albeit lower resolution and can be used to image deeper structures.

 

Propagation velocity

The propagation velocity is the velocity at which sound travels through a particular medium and is dependant on the compressibility and density of the medium. Usually, the harder the tissue, the faster the propagation velocity. The average velocity of sound in soft tissues such as the chest wall and heart is 1540 metres/second.

 

 

ULTRASOUND TISSUE INTERACTIONS

Figure 1: Interactions of Ultrasound with tissue: Echocardiography, Bonita Anderson, Dutoit, Wiley-BlackwellFigure 1: Interactions of Ultrasound with tissue: Echocardiography, Bonita Anderson, Dutoit, Wiley-Blackwell

The interaction of ultrasound waves with organs and tissues encountered along the ultrasound beam can be described in terms of attenuation, absorption, reflection, scattering, refraction and diffraction.

 

Attenuation

Sound energy is attenuated or weakened as it passes through tissue because parts of it are reflected, scattered, absorbed, refracted or diffracted.

 

Reflection

A reflection of the beam is called an echo and the production and detection of echoes forms the basis of ultrasound. A reflection occurs at the boundary between two materials provided that a certain property of the materials is different. This property is known as the acoustic impedance and is the product of the density and propagation speed. If two materials have the same acoustic impedance, their boundary will not produce an echo. If the difference in acoustic impedance is small, a weak echo will be produced, and most of the ultrasound will carry on through the second medium. If the difference in acoustic impedance is large, a strong echo will be produced. If the difference in acoustic impedance is very large, all the ultrasound will be totally reflected. Typically in soft tissues, the amplitude of an echo produced at a boundary is only a small percentage of the incident amplitudes, whereas areas containing bone or air can produce such large echoes that not enough ultrasound remains to image beyond the tissue interface.

Figure 2: Production of an echo depending on relative acoustic impedances of the two media: From: Aldrich: Crit Care Med, Volume 35(5) Suppl.May 2007.S131-S137Figure 2: Production of an echo depending on relative acoustic impedances of the two media: From: Aldrich: Crit Care Med, Volume 35(5) Suppl.May 2007.S131-S137




 Table 1: Percentage reflection of ultrasound at boundaries: From: Aldrich: Crit Care Med, Volume 35(5) Suppl.May 2007.S131-S137Table 1: Percentage reflection of ultrasound at boundaries: From: Aldrich: Crit Care Med, Volume 35(5) Suppl.May 2007.S131-S137

At a tissue–air interface, 99% of the beam is reflected, so none is available for further imaging. Transducers, therefore, must be directly coupled to the patient’s skin without an air gap. Coupling is accomplished by use of gel between the transducer and the patient.

 

Scattering

Not all echoes are reflected back to the probe. Some of it is scattered in all directions in a non-uniform manner. This is especially true for very small objects or rough surfaces. The part of the scattering that goes back to reach the transducer and generate images is called backscatter.

 

Absorption

Tissue absorption of sound energy contributes most to the attenuation of an ultrasound wave in tissues.

 

Refraction

The change in the direction of a sound wave on being incident upon a tissue interface at an oblique angle is refraction and is determined by Snell’s law. Follow this link for an explanation of this law: http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Ph...

 

 

TRANSDUCERS

Inside the core of the transducer are a number of peizo-electric crystals that have the ability to vibrate and produce sound of a particular frequency when electricity is passed through them. This is how ultrasound waves are formed. These transducers also act as receivers for the reflected echoes as they generate a small electric signal when a sound wave is incident upon it.

 

Duty factor

In most modes of ultrasound operation, only 1% of the time is spent in generating a pulse of ultrasound waves and 99% of the time is then spent listening for the echoes. This is called the duty factor…1% in such a case.

 

Pulse repetition frequency (PRF)

The PRF is the number of pulses (send and listen cycles) of ultrasound sent out by the transducer per second. It is dependent on the velocity of sound and on the depth of tissue being interrogated. The deeper the tissue being examined, the longer the transducer has to wait for echoes to come back, hence a lower PRF.

 

Beam

The ultrasound beam is focused by the transducer so as to be as close to a flat plane as possible. The beam is made up of tens to hundreds of scan lines.

 

Orientation

There is usually a dot, groove or light on one ends of the transducer to assist orientation. A corresponding marking is also displayed on the screen to help give an orientation to the images.

 

Resolution

Axial resolution:The ability to resolve objects in the line of the ultrasound beam. Factors affecting axial resolution include Spatial Pulse Length (SPL) and frequency.

Lateral resolution: Resolution at 90° to the direction of the beam. Factors affecting lateral resolution are width of the beam, distance from the transducer, frequency, side and grating lobe levels.

Temporal resolution: Refers to the ability to detect moving objects in the field of view in their true sequence. The number of frames generated per second (frame rate) determines temporal resolution.

 

 

DOPPLER EFFECT

Doppler shift is given by the following formula:

FD = (V X FO ) / C

where

FD is the Doppler shift

FO is the original frequency

V is the velocity of blood

C is the speed of sound in tissues

Therefore V = (FD X C) / FO

A further refinement of this formula is: V = (FD X C) / (2FO X Cosθ)

The original frequency is multiplied by 2 because the Doppler shift occurs twice – when the original wave is incident on the moving RBC and when the moving RBC reflects it back. Cosine theta (Cosθ) is applied as a correction for the angle between the ultrasound beam and the direction of blood flow. Cosθ = 1 if the beam is parallel to the direction of blood flow and maximum velocity is measured. Cosθ = 0 if the beam is perpendicular to the direction of blood flow and zero velocity is measured

It is noteworthy that for Doppler, maximum velocity information is obtained with the ultrasound beam aligned parallel to the direction of the blood flow being studied. Otherwise the peak velocity and consequently the pressure gradient (see below) will be underestimated. This is in sharp contrast to conventional echo where the best image quality is obtained with the ultrasound beam aligned perpendicular to the structure being studied.

Since the original frequency value (2FO) is in the denominator in the equation, it is important to remember that maximum velocity information is obtained using low frequencies (usually 2 MHz). This is in contrast to conventional 2-D echo where higher frequencies deliver higher resolutions.

There is a direct relationship between the peak flow velocity through a narrow valve and the pressure gradient across it. Understandably, when the valve orifice is small, blood flow has to accelerate in order to eject the same stroke volume. The smaller the orifice, the higher the acceleration and velocity. This increase in velocity can be measured using Doppler echo. The pressure gradient across the valve can be calculated using the simplified Bernoulli equation:

Pressure gradient = 4 v2

Where ‘v’ is the peak flow velocity of the jet through the orifice.

This equation is frequently used during Doppler evaluation of stenotic valves, regurgitant lesions and intra-cardiac shunts. The velocity information provided by Doppler complements the anatomical information provided by M-mode and 2-D echocardiography.

Analysis of the returning Doppler signal not only provides velocity information but also information about flow direction. By convention, velocities towards the transducer are displayed above the baseline and velocities away from the transducer are displayed below the baseline.

The returning Doppler signal is a spectral trace of velocity against a time axis. The area under the curve (AUC) of this spectral trace is known as the Velocity Time integral (VTI)….also known variably as TVI or FVI (flow velocity integral). The value of the VTI is determined by peak flow velocity and ejection time and can be calculated by the processor of most echo machines.

 

 

ARTIFACTS

The following section on artifacts has been taken in toto from: Basic physics of ultrasound imaging; Critical Care Medicine - Volume 35, Issue 5 Suppl (May 2007)

Artifacts are errors in images. They are normally caused by physical processes that affect the ultrasound beam and that in some way alter the basic assumptions the operator makes about the beam. To understand artifacts, one needs to consider the basic assumptions made in producing an ultrasound image:

  • Sound waves travel in straight lines.
  • Reflections occur from structures along the central axis of the beam.
  • Intensity of reflection corresponds to the reflector scattering strength
  • Sound travels at exactly 1540 m/sec. 
  • Sound travels directly to the reflector and back.

These assumptions do not always hold true. There are numerous cases of exceptions to these assumptions. Although some of these artifacts may actually provide useful information or allow for novel interpretations, the majority are potential pitfalls that may confuse the examiner if not considered. The major artifacts encountered in critical care ultrasound are outlined below.

 

Reverberation

Reverberation artifacts appear as multiple equally spaced lines along a ray line. Reverberation is caused by the sound bouncing back and forth between tissue boundaries and then returning to the receiver. Figure 3: Example of a reverberation artifact.Figure 3: Example of a reverberation artifact.

 

 

Ring Down

Ring-down artifacts are produced when small crystals such as cholesterol or air bubbles resonate at the ultrasound frequency and emit sound. Because the sound is emitted after the transducer receives the initial reflection, the system thinks the emitted sound is coming from structures deeper in the body. Air bubbles in the abdomen are shown. Figure 4: Example of a ring-down artifact.Figure 4: Example of a ring-down artifact.

 

 

Mirror Images

Sound can bounce off a strong, smooth reflector such as the diaphragm. The surface acts as mirror and reflects the pulse to another tissue interface. The ultrasound system believes the second interface is beyond the first surface, and this is where it appears on the scan. In Figure 5, the arrow shows the real object, which appears as if reflected in a mirror. Figure 5: Example of a mirror-image artifact.Figure 5: Example of a mirror-image artifact.

 

 

Reflections

Reflection is somewhat similar to the mirror image described above but has a very different appearance and is caused by multiple reflections. Sound can bounce off a strong, smooth reflector, such as the posterior bladder wall, and be reflected back to the transducer, giving the appearance of the structure deep to the bladder wall as would be seen with fluid collection. Figure 6: Example of a reflection artifact.Figure 6: Example of a reflection artifact.

 

 

Enhancement

Enhancement is seen as an abnormally high brightness. This occurs when sound travels through a medium with an attenuation rate lower than surrounding tissue. Reflectors at depths greater than the weak attenuation are abnormally bright in comparison with neighboring tissues. Enhancement of tissues (See arrow in Fig. 7 below) deeper than cysts or ducts is common. The attenuation of the sound through the fluid in these tissues is less than that of the surrounding tissues and results in this abnormal brightness. The tissues deeper than the gallbladder show abnormal brightness. Figure 7: Example of an enhancement artifact.Figure 7: Example of an enhancement artifact.

 

 

Attenuation

Tissues deeper than strongly attenuating objects, such as calcification, appear darker because the intensity of the transmitted beam is lower. In the scan of the gallbladder in Figure 8 below, the left side shows enhancement as described above; the right side shows decreased beam intensity because of attenuation in calcified gallstones (arrow). Figure 8: In this scan of the gallbladder, the left side shows enhancement described above; the right side shows a hypoechoic shadow distal to a brightly echogenic stoneFigure 8: In this scan of the gallbladder, the left side shows enhancement described above; the right side shows a hypoechoic shadow distal to a brightly echogenic stone

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