Physics and Knobology

A complete study of transesophageal echo or any type of ultrasound imaging would be incomplete without a brief discussion of the physics that underly the ability to image tissue using ultrasonic waves. "Ultrasound" itself literally refers to sound that is above the range of human hearing. For reference, the usually referenced audible range of frequencies exists from 20 hertz to 20,000 hertz (or kHz). Those old enough to remember buying albums as CDs (compact discs) may recall their standard sampling rate of 44.1 kHz, chosen to be roughly twice the perceptible frequency limit to allow for full representation of the sound contained on the disc. Medical ultrasonic frequencies typically fall between 2 and 15 MHz - hundreds of times faster than what we can either audibly perceive. The following will discuss the basic properties of these waves and their relevancy to image acquisition and interpretation. Is it a little dull? Maybe, but understanding the physics behind ultrasonography will help you to better optimize images, and will also help you answer a few questions you might get on any of the Basic PTE, Advanced PTE, or CCEeXAM.

Table of Contents

Properties of Sound Waves

What we hear as sound is, at its core, a set of longitudinal waves that move through matter (typically air but tissue is the preferred medium for the ultrasound probe). Longitudinal waves move in the same direction as the propagation of the wave. A given molecule part of a longitudinal wave experiences cyclical periods of compression and rarefaction. Since longitudinal waves are more complicated to depict and demonstrate the following principles with, we will make the same leap that every other ultrasound resource I have seen has made and from this point forth ultrasound waves will be depicted as transverse waves for ease of comprehension. The properties of waves hold true for either transverse or longitudinal so this is a fair jump, but for the test, know that sound waves are longitudinal in nature.

The frequency of sound waves refers to the amount of cycles contained in 1 second and is reported in units of hertz (Hz). A frequency of 1 Hz would mean a sound wave only goes through one complete cycle of compression and rarefaction in 1 second. Anyone who has heard a sound on the lower end of the audible spectrum (around 20Hz) may have experienced the transition between a sound being perceived as a "note" versus a rapidly cycling vibration (this can be easily appreciated with a bit of skill around either analog or digital synthesizers). Ulrasonic frequencies are in the range of 2-15 MHz, meaning they cycle between 2 and 15 million times per second.

The period simply refers to the amount of time it takes for one complete cycle of a wave. By definition, it is the reciprocal of frequency. If a sound wave has a frequency of 20 Hz, that means it would cycle 20 times in 1 second. This would give it a "period" of 1/20th of a second.

It thus follows that: Period x Frequency = 1

Whereas frequency and period define waves in terms of time, wavelength defines the distance that one cycle of a wave covers. It is reported in standard units of distance; ultrasonic waves typically have wavelengths of less than 1mm. This is not an intrinsic property of the wave, but rather depends on the propogation velocity of the wave through the medium through which the wave travels (more below).

Recall your high school physics or science class. If yours was anything like mine, you probably performed a brief experiment where your science teacher struck a long metal railing with a hammer while the class stood hundreds of feet away at the other end of the metal railing. If you were perceptive, you noticed that you heard the sound of the hammer strike first from the railing itself, followed quickly afterwards by the sound which had traveled through the air. This is because sound has different propogation speeds depending on the medium through which it is traveling.

You may have also been mistaught (or misremembered) that sound travels fastest through materials with more density.

This false, forget it now.

Increased density will slow the speed of sound.

So why did the sound from the metal railing reach your ear first? It was due to the stiffness of the metal, not the density. Metal is decidedly more stiff than air, thus it conducted the sound much faster than did the air molecules.

Increased stiffness will increase the speed of sound.

In general I am not a fan of memorizing numbers, but I have seen the following value come up on practice exams and the CCEeXAM:

The speed of sound in soft tissue is ~1540 m/s (or 1.54mm/µs).

Why is this useful? Mathematically you can use it to relate wavelength and frequency. Is this a valuable tool that will help you diagnose tamponade in your postop heart transplant? No, but it will help you get the accreditation to drop the TEE probe in the first place. It will also help to explain some of the artifacts encountered later in typical imaging.

wavelength (mm) = 1.54mm/µs / frequency (MHz)

Amplitude refers to the "height" of a transverse wave. For a longitudinal wave, this is typically expressed in relative terms in units of decibels. The louder a wave, the higher a decibel level. 

Power is a bit more esoteric, and refers to the rate of energy transfer by a wave. It is expressed in units of watts. Power is proportional to amplitude squared.

power ∝ amplitude^2

Intensity refers to how the power of a wave is distributed over a given space. It is expressed in units of watts/area or watts/cm^2. For the purposes of standard, ultrasonographic image acquisition, the intensity is not high enough to cause meaningful damage to the tissues exposed. This safety is not an intrinsic property of ultrasound however - it is in theory possible to generate an ultrasound beam with enough intensity to have detrimental bioeffects.

Intensity (W/cm^2) = power (W) / area (cm^2)

Artifacts

Artifacts are frequently generated during ultrasound imaging, and a knowledge of how and why they are generated helps to correctly identify them as such. Again, not the most exciting however ignoring them can lead to easy misdiagnoses and looking silly in front of your cardiac anesthesia colleagues (did you really think that PA catheter was in the aortic arch?).

The Ultrasound Transducer

Ultrasound Modes

Doppler Imaging