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# POCUS Physics

An understanding of physics that the ultrasound machine uses to form the on screen image is helpful when it comes to interpreting the images we see.  These physics principles effects the depth in which objects are plotted, the grayscale that objects are represented, and come into play when we see ultrasound imaging artifacts.

# Sound

Sound is a mechanical compression wave that travels through a medium such as air or water.  Sound is produced when an object vibrates compressing the material around it, which in turn pushes on the other particles in the medium propagating the wave forward.  Sound cannot exist in a vacuum because there is no material to compress and propagate that energy forward. The denser a material is, the faster the sound wave will travel.

A sound wave is a longitudinal wave that moves in a direction parallel to source of disturbance composed of areas of compression where particles are pressed together and areas of rarefication where the particles are pulled apart.

# Ultrasound

The human ear can hear sounds in frequencies between 20 to 20,000Hz.  Ultrasound probes operate in frequency ranges above what the human ear can hear between 2-18Mhz.

# Wave Compentes

Sound waves are often represented as a sine wave, and we can use this to describe the components of a wave.

Peak: Is the point of wave to greatest positive deflection on the Y-axis and corresponds with the point of highest compression on a longitudinal wave.

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Trough: Is the point greatest negative deflection on the Y-axis and corresponds with the point of greatest rarefication on a longitudinal wave.

Amplitude: Represents the maximum displacement from a particles position of rest to the peak or trough of a wave.   A Low amplitude soundwave would be heard as a quite sound, where a High amplitude wave would a louder sound.

Wavelength: Is the length between two repeating points (Ex: peak to peak) on a wave and represents a complete single wave cycle.

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Frequency: represents the number of times a wave repeats over a given period of time.  Frequency is measured in Hertz(Hz) which is the number of wave cycles per second.  Low Frequency sounds would be heard as bass tones, and High Frequency sounds would be a high pitch sound.

# Frequency

In ultrasound frequency matters.  Ultrasound probes are generally broken down into high and low frequency probes with mid-frequency probes bridging in the gap in capability between the two.

There is an inverse relationship between image resolution and the penetration of the soundwaves into the body affecting the depth we are able to image based on the frequency we are using.  As Frequency increases, image resolution increases and penetration decreases.  Conversely, as frequency decreases, image resolution decreases, and penetration increases.  This phenomenon affects the type of probe we chose based on what application we are using that probe for.

One way to think about the difference between high and low frequency sound is to think about a neighbor throwing a wild house party.   We can hear the thumping bass beats of the dance music from within our house, but we are not able hear the high pitch treble sounds of the singing until we have gotten closer to the party, where we are able to make out the individual words of the music.

High Frequency probes like the Linear Probe (AKA: Vascular Probe) are optimized to provide high resolution images while sacrificing depth. These probes are ideal for evaluating shallow structures like the Carotid Artery or for Ultrasound Guided IV Placement.

Low Frequency probes like the Curvilinear Probe (AKA Abdominal Probe) are able image deeper structures within the body but not at the same resolution as a high frequency probe. This probe type is good in applications like the FAST scan, OB scans, or evaluating the Aorta or IVC.

Mid-Frequency probes like the Phased Array (AKA Cardiac Probe) provides a balance between the two other probe types.  In addition to the balance of image resolution and penetration, the phased array probe is tuned to have a rapid scan rate than the other probe types.  Meaning there is a high number of cycles per second generating additional images.  This would be similar to a camera having a high frame rate, smoothing the motion that we see on screen which is ideal for imaging rapidly moving organ like the heart.  Where a low frame rate would give a choppy appearance to the motion.

# Propagation Speed

The speed of sound through a medium is directly impacted by the density of the substance the sound wave is traveling through.  As density of the medium increases the speed of sound increases. Propagation speed matters in ultrasound because it is this speed that is used to determine the distance a structure or tissue is from the probe.

The Ultrasound machine uses the equation Distance = Rate x Time. In this equation Time is the amount of time it takes for a pulse of sound to be emitted from the probe, "bounce" off a target then return to the probe.  The time it took for a pulse of sound to make this round trip is halved, because we are only concerned about the time it took the soundwave to reach a tissue, not the time it took to return to the probe.

So how fast does a soundwave move through the body?  Blood, bone, and muscle all have different densities, therefore different propagation speeds.  Because of this the Ultrasound machine uses the average speed of sound through soft tissue which is 1540m/s.  There are circumstances where this assumption is violated, when a pulse of sound moves through a tissue that has either a faster or slower propagation speed than 1540m/s.  In these cases an Ultrasound Image artifact is created and that tissue we be falsely plotted at an incorrect depth.

# Echogenicity

Echogenicity refers to a tissue's ability to generate echos.  Some factors that contribute to a tissue's ability to generate an echo return is it's density, elasticity, and fluid content.  Echogenicity is plotted in the greyscale, where high amplitude echo returns are plotted and white, low amplitude returns are plotted as dark grey, and area in which no echo returns are detected, those areas are plotted as black.

An echo is created each time a soundwave encounters a change in density.  A real life example of this is when shout to create an echo within a canyon or hallway.  Air has a uniform density so as the soundwave travels through the air no echo is created, but once that soundwave hits the canyon wall there is a large change in density creating a strong echo.  The larger the change in density the between two mediums, or tissues the more amount of energy will be reflected back to its source.  An example of this would be to imagine how loud an echo would be if we shout at a flat concrete wall, vs yelling into a pillow.

# Acoustic Attenuation

Acoustic Attenuation refers to the loss of energy or amplitude of a soundwave over time and distance.  This should make sense, as each particle within the medium hits the next one in line, propagating the wave, a certain amount of energy is lost.  Repeat this process enough times, eventually all the initial energy that was used to create the wave will be lost.  This sound energy is absorbed by the tissue and is transformed from acoustic energy into thermal energy, heating the tissue.

# Acoustic Impedance

Acoustic Impedance (Z) is the resistance a soundwave encounters moving through a tissue and is a product of the density of the tissue and its propagation speed.

Z = D x C

Z = Acoustic Impedance

D = Tissue Density (Kg/m^3)

C = Velocity of the Soundwave through the tissue (m/s)

As a soundwave travels through the body each time there is a change in acoustic impedance a portion of the energy is reflected back (creating an echo), transmitted forward, and scattered

The amount of ultrasound energy that is reflected back to the probe vs being transmitted forward is determined by the differences in acoustic impedance between the two tissues.  The higher the difference of acoustic impedance between two tissues the greater the amount of ultrasound energy will be reflected back to the probe. If the difference in acoustic impedance between two tissues is small the majority of the ultrasound energy will be transmitted forward.

R = [(Z2 – Z1) / (Z2 + Z1)]^2

R = Reflection Fraction

Z1 = Acoustic Impedance of Tissue 1

Z2 = Acoustic Impedance of Tissue 2

Acoustic Impedance (Z):

Air = 0.0004 Kg/m^2s

Water = 1.48 Kg/m^2s

US Gel = 1.5 Kg/m^2s

Soft Tissue = 1.63 Kg/m^2s

We are going to run the numbers between Air vs Soft Tissue, and US gel vs Soft Tissue to help illustrate how differences in acoustic impedance impact how much ultrasound energy is reflected and scattered vs being transmitted forward into the body.  This should also help demonstrate why it is important that we use an acoustic coupling agent like ultrasound gel, or a water bath when using ultrasound.

Example of an Ultrasound Beam Travelling through Air into Soft Tissue

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Z1 = Air 0.004 Kg/m^2s

Z2 = Soft Tissue 1.63 Kg/m^2s

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R = [(1.63 - 0.0004)/(1.63 + 0.0004)]^2

R = (1.629/1.6304)^2

R = 99.82%

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Meaning 99.82% of the initial energy produced by the probe is going to be reflected or scattered, with less than 1% of that energy being transmitted deeper into the body.

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Example of an Ultrasound Beam Travelling through US Gel into Soft Tissue

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Z1 = US Gel 1.5 Kg/m^2s

Z2 = Soft Tissue 1.63 Kg/m^2s

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R = [(1.63 - 1.5)/(1.63 + 1.5)]^2

R = (0.13/3.13)^2

R =0.17%

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In this scenario there is a small difference in acoustic impedance between the US Gel and Soft tissue.  So here 0.17% of the initial ultrasound energy will be reflected back to the probe, with 99.82% of the Ultrasound energy will be transmitted into the body being able to be used for imaging purposes.

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