How Things Work: Ultrasound imaging

For decades, physicians have been able to visualize the underlying structures of a patient’s body using sound. It was in the late 1940s that Dr. George Ludwig first exploited the concept of ultrasound to characterize human tissue. Today, Dr. Ludwig might not even recognize the devices that his work has inspired; ultrasound imaging can now be viewed in 3-D or animated through time and called “4-D,” which is performed through an internal probe and can be colored according to Doppler shift. Although the common perception of ultrasound imaging is its use in obstetrics, it has found an array of medical applications in specialties ranging from urology to cardiology.

Ultrasound imaging relies on acoustics, the science of sound, to produce an image. A sound is a mechanical wave that propagates through some medium (air, human tissue, or other materials). These waves possess a number of characteristics, but imaging relies heavily on each wave’s frequency and amplitude. The frequency of a sound wave is the number of mechanical oscillations per second, and its unit is the Hertz. The average person can perceive sounds between 20Hz and 20,000Hz; ultrasound generally exists above the 20,000Hz upper limit.

The ultrasound probe is the hand-held probe that the clinician uses on a patient. The probe contains transducers which act as signal transmitters and receivers: a transducer fires off a sound wave in the ultrasound frequency range and waits for it to return as an echo. Along the way, the sound wave is altered by the acoustic impedance of each tissue and the reflectivity of different tissue interfaces. There are four styles of ultrasound imaging, known as “modes,” which vary based on their signal processing algorithms and the arrangement of transducers. In A-Mode, a transducer is used to create a 1-D image along the depth direction at a fixed point in time. In B-Mode, multiple transducers are used to create a 2-D image at a fixed point in time. Multiple 1-D A-Mode shots can be taken and animated in M-Mode to give the impression of motion. There is also Doppler mode in which the compression and rarefaction of sound waves can be interpreted to determine which direction a material is moving in. With the Doppler mode, the clinician can tell if blood is moving away or toward the probe, and even color the screen accordingly. The functioning of the A-mode, in which there is a single transducer that creates a plot of echoes as a function of depth, is the simplest to understand.

Explained here is an example from the A-mode, taken from a lecture taught by Dr. Lihong Wang of Washington University’s Optical Imaging Lab (http://oilab.seas.wustl.edu). In the lecture, Wang considered a sandwich of two tissue types: some muscle, some fat, and more muscle. For simplicity, it was assumed that the ultrasound probe was placed in normal incidence to the sample — at a right angle to the material interfaces.
As with light beams, a sound wave striking an interface creates reflection and refraction waves: some of the signal continues in its original direction (refraction), and some reverses in direction (reflection). If the signal is sent at an angle to the interface, the angles introduce geometry and trigonometry to the calculations — fortunately, these calculations do not need to be taken into consideration for normal incidence.

The speed of sound in a material depends on the material’s density and elastic modulus, or measurement of how stiff the material is. This follows the formula vs=sqrt(elastic modulus/density). The speed of sound is approximately 1580 m/s in muscle and 1480 m/s in fat. Extending this, the characteristic acoustic impedance is calculated as Z0=density x vs; in this example, these values are Zmuscle=1.6E6 kg/(m2s) (a unit known as a rayl) and Zfat=1.4 E6 rayls – the acoustic impedances of soft tissues tend to be on the same order of magnitude, but vary widely from other materials. As a comparison, Zair = 415 rayls and Zsteel = 4.7E7 rayls.

Each interface has a different reflectivity, a value ranging –1 to 1 which determines how much of the original signal travels in each direction away from the interface. The reflectivity at the muscle-fat interface is Rm–f=(Zfat–Zmuscle)/(Zfat+Zmuscle)=.067 and the reflectivity at the fat-muscle interface is Rf-m=(Zmuscle –Zfat)/(Zmuscle+Zfat)=-.067. This means that 6.7 percent of the signal is reflected back from the muscle-fat interface.

The depth or distance the signal must travel to reflect from an interface back to the transducer can be related to the time it takes from signal generation to the echo. The formula is simply T=2 x distance/Vs.
So, if we waited 7μs (or 7E–6 s) to hear the echo that returned from the first interface, this would imply that the depth of the first layer of muscle is distance=(Vs x T)/2=.55cm. The depth of the second interface is then calculated.
These calculations are only the beginning; Compiling this A-Mode data on reflection time and transmittance will allow a clinician to determine the depth of desired tissues like tumors. This has important implications in treatment. For more information, refer to chapter four of Introduction to Physics in Modern Medicine by Suzanne Amador Kane, available on Google Books.