Sound and Ultrasound: Acoustic Parameters
All our lives we are surrounded by sounds. In fact, it is our ability to create and comprehend sounds in the form of speech that is integral to our human development. As physicians we assess heart sounds, breath sounds, and bowel sounds, but few will contemplate the nature of sound. Without understanding the physical properties of sound and their interactions with the surrounding medium, it is difficult to understand the images produced in clinical ultrasound. The critical care practitioner also often acts as a sonographer, whose responsibility is to operate the equipment, obtain images, distinguish between real structures and artifacts, and manipulate the transducer. Without a solid knowledge of basic sound principles, these tasks are virtually impossible.
A sound is a wave created by a moving (vibrating) object and comprises areas of increased (compressions) and decreased (rarefactions) densities. This wave moves through a medium with a fixed speed (propagation speed), transmitting its energy, while the vibrating matter of the medium returns to its original position with each cycle (see ch002 in enclosed DVD). When the sound wave reaches an object, it is unable to penetrate, such as a wall; it may go around it (diffraction). This allows one to hear music around a corner. If the object is larger, such as a mountain, sound will bounce off (reflection) and return back to the source, creating a familiar phenomenon known as an echo. Echo was first described and named by the ancient Greeks.
Depending on the movement of the sound-generating object, the sound wave will acquire different characteristics known as acoustic parameters (Table 2-1). Some of those are related, while others are independent of each other. Though a sound wave is longitudinal with energy traveling in the same direction as the propagating wave, for the ease of representation it will be pictured as a transverse wave with energy distributed perpendicular to the direction of propagation like a wave on the surface of a pond (Figure 2-1).
|Acoustic Parameter||Units||Determined by||Values in Diagnostic Ultrasound|
|Period||μs||Sound source||0.1–0.5 μs|
|Frequency||MHz||Sound source||2–10 MHz|
|Intensity||Watt/cm2||Sound source||0.001–100 W/cm2|
|Wavelengths||mm||Source and medium||0.1–0.6 mm|
|Propagation speed||m/s||Medium alone||1500–1600 m/s|
The time necessary for the sound wave to complete one cycle is known as its period. The cycle is complete when the sound source has produced one vibration and the matter in the medium has returned to its original resting position. The period is measured in units of time (Table 2-1). One can probably use the fractions of the year, but that would be rather inconvenient, so most of the time it is measured in milliseconds ([msec] 1 thousandth), microseconds ([μsec] 1 millionth of a second), or nanoseconds (1 billionth). For example, a guitar D string takes 2.5 msec to completely travel across the reference object, such as a guitar fret, from left to right and left again to where it started; the sound it has generated will have a period of 2.5 msec (Figure 2-2).
Guitar D string vibration is creating a longitudinal wave in fundamental (shades of gray) and first harmonic (shades of red) frequencies. The fundamental frequency longitudinal wave is represented below by a transverse wave of the same frequency. The red dotted wave is a first harmonic wave with half the period and twice the frequency of the fundamental wave. Fundamental period is 2.5 of a millisecond; fundamental frequency is 400 Hz (0.4 kilohertz [kHz]); first harmonic frequency is 0.8 kHz.
Related to the period is the frequency of the sound wave (Table 2-1). Frequency (f) is a number of cycles completed in 1 second. A standard measure of frequency is hertz (Hz), which was named for Heinrich Rudolf Hertz (1847–1894), the first person to transmit and receive radio waves. One Hz is one cycle per second. The same guitar string with the period lasting 2.5 msec will complete 400 periods in 1 second and therefore have a frequency of 400 Hz or 0.4 kilohertz (kHZ) (Figure 2-2). Frequency is the reciprocal of the period (Table 2-1). That is:
kHz: kilohertz, thousands of cycles per second with a period of milliseconds.
MHz: megahertz, millions of cycles per second with a period of microseconds.
Humans can hear sounds with frequencies ranging from 20 Hz to 20 kHz. Speech generates 100–220 Hz, and singing 50 Hz–1.5 kHz. The human ear is most sensitive to 3–4 kHz sounds. The sound in the range of human hearing is known as audible sound, or simply sound, with frequencies >20 kHz known as ultrasound and <20 Hz known as infrasound. Thus, a distinction between sound and ultrasound is really quite capricious if not entirely baseless. Many other animals have wider range of hearing. For example, the domestic cat can hear up to 50 kHz. Though an ultrasound wave is a sound wave in every respect, ultrasound waves (particularly in the MHz range) tend to travel in a straight line, and diffract less and reflect more off smaller objects than lower-frequency waves. Typical periods and frequencies for diagnostic ultrasound are 0.1–0.5 μsec and 2–10 MHz, respectively, and are determined by the ultrasound source known as a transducer, or a probe (Table 2-1). With frequencies, much greater than those of diagnostic ultrasound, ultrasound waves start to behave a lot like electromagnetic microwaves, but those frequencies are never reached in medical applications.
Most emitted and reflected sounds have a mixture of frequencies, with the lowest one being the so-called fundamental frequency, and its multiples are harmonic frequencies, or, simply, harmonics. These concepts are demonstrated by the movement of the guitar string (Figure 2-2).
Amplitude, Power, and Intensity
As a sound wave propagates, the particles in the medium will move from the resting position. This creates areas of increased density and increased pressure on the surrounding area (compression). These changes in motion, pressure, and density will reach their peak and then subside with each vibration. The difference between a resting value of the parameter, such as density or pressure, and the peak one, during the period of the sound wave, is referred to as amplitude. You can pluck the guitar string softly (with less amplitude), creating less motion (pressure, density), or vigorously (with more amplitude), but because the string has the same period and frequency, the sound would not change. Simply stated, amplitude is the loudness or volume of the sound whether one can hear the sound or not (Table 2-1). In ultrasound applications, it is often referred to as an output gain or acoustic power (Figure 2-3). Because amplitude is the difference or ratio between two values of the parameter with the same unit, it cannot be described in absolute units (Table 2-1). In other words, one can always produce a louder or softer sound. Therefore, a relative scale is used. The relative units of this scale are Bells. They are named for Graham Bell and are defined as 0.1 of the Bell or decibels (dB), which are the most commonly used units in acoustic measurements (Tables 2-1 and 2-2).
The scale is logarithmic, meaning that the number is described by how many multiples of 10 one needs to create it (Table 2-2). Thus, the logarithm of 100 is 2, of 1000 is 3, and of 1/100 is −2.
More important, there are only two numbers to remember: 3 dB and 10 dB. Three decibels means 2-fold and 10 means 10-fold increase in the measured parameter, therefore −3 dB is 2 times less (one half) and −10 is 10 times less (0.1) than the original value. So if the parameter is pressure, then 3 dB sound will create twice the pressure on your eardrum (or be twice as loud) and 20 dB will be 100 times louder than the original one, while −3 dB will be only half that loud (Table 2-2).
It follows that power, or the amount of energy per second, delivered by the sound wave, is related to the amplitude and is in fact the amplitude squared (Table 2-1). When amplitude doubles, power increases fourfold.
The unit of power is watt (joules/s), named for James Watt, the Scottish engineer. The power of the sound wave distributed over the unit of surface is known as intensity (Table 2-1). Intensity is defined as the amount of energy per second delivered to the surface area of the medium. Intensity (measured in watt/cm2) therefore will be directly proportional to power (amplitude) and inversely proportional to the area over which that power is applied. The same sound beam with the same power when applied to a smaller surface area will deliver more energy to that area and is said to be more intense. The typical intensity of the diagnostic ultrasound equipment is 0.001–100 watts/cm2 (Table 2-1). In the case of diagnostic ultrasound, the “medium” is human tissue and the intensity will predict the bioeffect of the ultrasound (Tables 2-1 and 2-3). Those effects can be rather dramatic. One important example is ultrasonic lithotripsy, where the intensity of the ultrasound is used to decimate renal stones.
The speed of sound (propagation speed) is a fixed number and is related solely to the medium (Tables 2-1 and 2-3). This is a far-reaching statement and a unique feature of the physics of wave propagation. The speed of moving objects is an algebraic sum of the speed of the object and the observer. A couple of examples can help to demonstrate this point:
If a man is walking with the speed of 4 miles per hour (mph) down an escalator, which is moving at 3 mph relative to a stationary observer, he is moving at 7 mph.
If a police officer is chasing a getaway car and his car is moving at 110 mph, and the getaway car is moving at a 100 mph relative to that of the police officer, the speed of the chased car is −10 mph (the police officer is gaining on the getaway car).
It does not matter if the source of the sound or the observer is moving; the sound propagation speed remains the same (Table 2-1). A jet plane can fly faster than sound, but the roar of its engines will propagate at the same speed as if it were stationary on the ground; however, the frequency of the sound waves will change. If the sound is moving toward the observer, the period of the sound wave decreases and therefore the frequency increases (sound wave is compressed). If the sound is moving away, the opposite occurs (the wave is stretched). This is the so-called Doppler effect, which will be further discussed below, but for now remember: nothing can change the speed of sound in a particular medium; it is an established and fixed phenomenon.
Wavelength is the length of a single cycle and is measured in the units of length (Table 2-1 and Figure 2-4A). A picture of the wavelength is easy to confuse with that of the frequency; in fact, they will look exactly the same, but remember that here the axis is space, not time. Wavelength is determined by the frequency of the sound and the speed of sound in the medium (Table 2-1).
(A) Speed of sound in the medium is an intrinsic quality of the medium. As the speed of sound increases in the water, the wavelength becomes longer, while the frequency of the sound wave generated by the sound source does not change. In the same medium, higher-frequency ultrasound will create shorter wavelength. Shorter wavelength ultrasound produces better images by reflecting off smaller objects. Wavelength (mm) = Speed of sound in the medium (mm/μsec)/frequency (megahertz, MHz). (B) Shorter wavelength and higher-frequency ultrasound produce better images by reflecting off smaller objects. Because the speed of sound in the medium is an intrinsic quality of the medium, the wavelength in that medium will be inversely related to the frequency of the sound wave generated by the sound source.
Because the speed of sound in the medium is an intrinsic quality of the medium (Table 2-3), the wavelength in that medium will be inversely related to the frequency of the sound wave generated by the sound source (Table 2-1). In the same medium, the higher-frequency ultrasound therefore will generate a shorter wavelength. The longer the wavelength, the larger the size of the object the wave will need to encounter to be reflected. High-frequency ultrasound allows for reflection off smaller objects, which improves image quality (axial resolution) in the same medium (Figure 2-4B). In “soft tissue,” sound with frequency of 1 MHz will have a wavelength of 1.54 mm, and 500 kHz a wavelength of 3.08 mm.
So in diagnostic ultrasound, the rule is: the higher the frequency, the shorter the wavelength, and the better the image. Useful values of wavelengths in diagnostic ultrasound are 0.1–0.08 mm.
Interactions of Ultrasound and Medium
As the ultrasound wave travels through the medium, it releases some of its energy and reflects back to the source as an echo (Figure 2-6). The result is a dampening of the wave or reduction in its amplitude. This process is known as attenuation. Attenuation is dependent on the ultrasound frequency and the distance the ultrasound travels in the medium. Attenuation only affects the amplitude and the wave frequency or wave length. The greater the distance the ultrasound has to travel, the more attenuation will occur. To illustrate the relationship between frequency and attenuation, one just needs to rub one’s hands together. The faster you do it (higher frequency), the hotter the hands will get, because more heat energy is released by friction. Attenuation is always measured in negative decibels, and in the soft tissues one MHz frequency signal will attenuate −0.5 dB per every centimeter it travels (Figure 2-5).
Normal incidence. If there is no difference in impedance between the two boundaries, no reflection will occur; the larger the difference, the greater the amount of ultrasound is reflected back to the source. Distance to the boundary can be calculated from the time it takes for the ultrasound to reach the boundary and return to the source (time of flight, elapsed time). In the soft tissues, distance to the boundary (mm) = elapsed time (μsec) × 0.77 mm/μsec.
Heat generation will be discussed in the biological effects of the ultrasound, but reflection is important to image formation. It will also be discussed later in more detail, but some basics need to be addressed now.
When the sound wave strikes a boundary between two different tissue layers, some of the energy will proceed further, while the rest will return to the source of sound in the form of an echo. The timing and the energy of the echo signal will be related to the depth and the physical nature (acoustic impedance) of the boundary and will provide all the necessary information to create an image (Table 2-4 and Figure 2-6). The sound wave that is not reflected will go on until the next tissue boundary is met. The same phenomenon will take place again until the signal is lost due to attenuation. Because energy is not created in the process, whatever is not reflected (or converted to heat and lost) will be transmitted. The amount of reflected ultrasound energy will depend on the physical properties of the boundary. Those properties can be summarized in a calculated number of acoustic impedance. Impedance is measured in units of Rayls (Z). The units are named for the physicist Robert John Strutt, 4th Baron Rayleigh.