Physics of ultrasound

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Definition

Ultrasound is a high frequency sound, exceeding the upper limit of human hearing – 20.000 cycles per second (20 KHz). Knowledge of basic ultrasound physics is essential for understanding image formation, echo machine settings optimization, advantages and limitations of the technique.

General principles

Sound is a longitudinal mechanical wave transmitted through the medium by local displacement of particles within the medium. The displacement of the particle from their equilibrium position produces changes in the medium density (areas of compression/rarefaction). Ultrasound is defined as sound with frequencies above the human audible range between 20 Hz and 20.000 Hz [1]. Diagnostic medical ultrasound uses frequencies from 1.000.000 to 40.000.000 Hz = 1 to 40 megahertz (MHz). The ultrasound wave is often graphically displayed as a sine wave in which the peaks and nadirs represent the areas of compression and rarefaction, respectively (Figure 1) [2]. Ph1.png
Figure 1. Ultrasound wave

Properties of sound waves

Sound waves are characterized by the following parameters:
Frequency - The frequency of the sound wave is the number of oscillations per unit of time.
Amplitude - The magnitude of the pressure changes, i.e. the difference between the pressure peaks and pressure nadirs (The strength of the wave, loudness of the sound). Amplitude is measured in decibels, a logarithmic unit that relates acoustic pressure to some reference value. The primary advantage of using a logarithmic scale to display amplitude is that a very wide range of values can be accommodated and weak signals can be displayed along side much stronger signals. There are some other logarithmic variables used in clinical practice (e.g. pH).
Since sound waves are mechanical waves, they are further characterized by the following additional parameters which depend on the medium in which the wave propagates: Wavelength - The length of one period of the wave; e.g. from one pressure peak to the next. The wavelength depends on the frequency and the medium in which the sound wave propagates.
Velocity - The speed at which sound propagates through a given medium. Velocity through a given medium is inversely related to the density and directly related to stiffness of that medium. Ultrasound waves travel faster through a stiff medium, such as bone. In echocardiography, the velocity of sound is assumed to be approximately 1,540 m/sec (or 1.54 m/msec). Sound waves travel through the air with speed of 330 m/s. The typical velocities for different tissues are provided in table 1.

Medium Velocity (m/sec)
Fat 1450
Water 1480
Soft tissue 1540
Kidney 1560
Blood 1570
Muscle 1580
Bone 4080

The wave equation: product of wavelength (λ) and frequency (f) represents the velocity (c) of the sound wave.
c = λ f

Velocity through soft tissue is assumed to be constant (1540 m/s) hence there is an inverse relationship between frequency and wavelength:

Interaction between ultrasound and tissue

Attenuation

Attenuation is a measure of the rate at which the intensity of the ultrasound beam diminishes as it penetrates the tissue. Attenuation always increases with depth and the higher the frequency of ultrasound is, the more rapidly it will attenuate.

Reflection, refraction and scattering

When the ultrasound beam crosses a boundary between two media some of the ultrasound energy is reflected at the interface and some is transmitted through the interface (Figure 2).
Ph2.png
Figure 2. Reflection and refraction of ultrasound waves


The transmitted portion of the energy is refracted, depending on the angle of incidence and differences in acoustic impedance (resistance at the interface) between the tissues. The acoustic impedance of a medium is the product of speed of sound in the medium and the density of the medium.
Ultrasound images are created by reflection of the ultrasound beam. The amount of ultrasound reflected depends upon the relative changes in the acoustic impedance between the two media or tissues. Depending on size targets can reflect directly back to the transmitter in an angle dependant fashion (specular echoes) or scatter the ultrasound in more directions (scattered echoes). Targets that are small relative to the wavelength of the transmitted ultrasound produce scattering and such objects that reflect energy concentrically are called Rayleigh scatterers (for example scatters from moving red blood cells forms the basis for Doppler echocardiography). Scattered echoes contribute to the visualization of surfaces that are parallel to the ultrasonic beam and also provide the substrate for visualizing the texture of gray-scale images (basis for speck tracking imaging).

References

  1. Feigenbaum's Echocardiography, 6th Edition, 2005, Lippincott Williams & Wilkins
  2. Echocardiography essentials: Physics and instrumentation. http://www.escardio.org/congresses/euroecho2010/Documents/teaching-course-slides/euroecho2010-beladan-99.pdf

Further reading and external links

EAE basic echocardiography course. Physics of echocardiographic imaging

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