Sound
Sound is a wave, i.e. traveling variations of some quantity (pressure). It involves mechanical motion in the medium through which it travels. Pressure variations cause particles of the medium to vibrate due to increase and decrease of density.
Sound : Frequency and Period
Sound is described by terms that describe waves:
Frequency: How many cycles occur in one second, measured in Hertz. (1 Hz = 1/s). Human hearing: 20 Hz to 20 000 Hz, or 20 KHz. Ultrasound: beyond 20 KHz. Frequency is important in ultrasound because of its impact on resolution and penetration of sonographic images.
Period: Time that takes for one cycle to occur. Inverse of frequency ? if frequency increases period decreases. For example, the period for 5 MHz (5 million Hertz) ultrasound is 1 / 5, 000, 000 = 0.0000002 = 0.2 µs. 1 µs is 1 millionth of a second (0.000001 s). Period is an important concept for pulsed ultrasound, as we'll see later.
Sound : Wavelength and Speed of Propagation
Wavelength: Length of space over which one cycle occurs. It is usually expressed in millimeters. One millimeter, 1 mm, is one thousandth of a meter (0.001 m). Wavelength is important when considering resolution of images.
Propagation Speed: Speed at which a wave moves through a medium. Measured in meters per second, or millimeters / microsecond.
Wavelength depends on the frequency and propagation speed:
Wavelength (mm) = Propagation Speed (mm/microsecond) / Frequency(MHz)
Previous relationship says that if frequency increases wavelength decreases.
Propagation speed depends on the medium. In soft tissue it averages 1540 m/s, or 1.54 mm/µs.
Density and stiffness determine propagation speed. Density is the concentration of matter (mass per unit volume: kg/m³ ). Hardness is the resistance of a material to compression (inverse of compressibility). Hardness is usually dominant factor on propagation speed:
Gas --> low propagation speed
Liquid -->higher propagation speed
Solid -->highest propagation speed.
Propagation speed is what imaging instruments use to correctly locate echoes on the display.
A-line
Positional information is determined by knowing the direction of the pulse entering the patient and measuring the time it takes the echo to return to the transducer. Range equation:
V = 2d / t
Sound : Harmonics
These are sinusoidal waves. Each curve is characterized by a single frequency (number of cycles per second).
Original frequency (black line) is the fundamental frequency, the even (red) and odd (green) multiples are the harmonics.
Strong pressure waves suffer deformation --> generation of harmonics --> non-linear propagation .
Harmonic frequency echoes improve the quality of sonographic images.
Pulsed Ultrasound
Frequency, period, wavelength and propagation speed are sufficient to describe continuous-wave (cw) ultrasound. Cycles repeat indefinitely.
Sonography uses pulsed ultrasound, i.e. a few cycles of ultrasound separated in time with gaps of no signal.
We need to define new parameters: pulse-repetition frequency, pulse-repetition period, pulse duration, duty factor, spatial pulse length.
Pulse repetition frequency (PRF): Number of pulses occurring in 1 s. Usually expressed in kHz.
Pulse repetition period (PRP): Time from the beginning of one pulse to the beginning of the next. Usually expressed in microseconds (µs).
PRP decreases as PRF increases. More pulses occur in a second, less time from one to the next.
PRF is controlled automatically in sonographic instruments, but operator may control it in Doppler instruments (more on this later).
Pulse duration: Time it takes for one pulse to occur = period times the number of cycles in the pulse. Expressed in ms.
Sonographic pulses ~ 2-3 cycles long, Doppler pulses ~ 5-20 cycles long. Pulse duration decreases if number of cycles in a pulse is decreased or if frequency is increased.
Operator chooses frequency.
Note: Frequency increases, period decreases, reducing pulse duration increases
Number of cycles in pulse decreases, pulse duration decreases.
Shorter pulses improve quality of images.
Duty factor: Fraction of time that pulsed US is on. Longer pulses increase the duty factor because the sound is on more of the time.
Higher PRF increase duty factor because there is less "dead" time between pulses.
Duty Factor = Pulse Duration (microseconds) / PRP (microseconds)
Dimensionless because it's a fraction. It is expressed as a decimal or as a percentage if multiplied by 100.
Example: Pulse duration is 4 µs, PRP is 160 µs:
Duty Factor = 4 / 160 = 0.025 = 2.5 %
Typical duty factors for sonography are ~0.1 to 1.0 %. For Doppler ~ 0.5 to 5.0 %.
Note: PRF increases, PRP decreases, duty factor increases
Spatial pulse length: Length of a pulse from front to back = length of each cycle times the number of cycles in the pulse. Shorter pulse length improves resolution.
Amplitude, intensity
Indicators of how strong or intense the ultrasound is.
Amplitude is the maximum variation occurring in an acoustic variable, i.e. how far the variable gets away from its normal, undisturbed value.
Amplitude is measured in units of pressure: MPa (Mega Pascals)
Intensity is the rate at which energy passes through unit area.
Average intensity of a sound beam is the total power in the beam divided by the cross-sectional area of the beam.
Note: Beam power increases, intensity increases. Beam area decreases (focusing), intensity increases
Power is the rate at which energy is transferred. Measured in watts.
Beam area is expressed in cm²
Therefore Intensity is measured in mW/cm²
Intensity is important when discussing bioeffects and safety. Intensity is proportional to the square of the amplitude. So if amplitude is squared, intensity is quadrupled.
Intensity varies in diagnostic ultrasound because it's highest at the center of the beam and falls off near the periphery.
It also varies along direction of travel due to focusing and attenuation.
In pulsed ultrasound, intensity varies with time: It's zero between pulses and not equal to 0 during each pulse.
Temporal peak (TP) is the greatest intensity found in a pulse.
Temporal average (TA) includes the "dead" time between pulses. It is the lowest value.
Pulse average (PA) is in between for a given pulse beam.
PA and TA are related by the duty factor:
TA intensity = PA intensity x Duty Factor.
Note: If duty factor increases, TA intensity increases.
If sound is continuous, duty factor is = 1 and PA and TA intensities are equal to each other.
In real-life equipment intensity is not constant within pulses.
Starts out high and decreases towards the end of the pulse. Damped pulses.
TA averaged over the pulse repetition period.
PA averaged over the pulse duration
TP no averaging.
Putting together spatial and temporal considerations we end up with 6 intensities:
Since SATA averages both in space and time it's the lowest value. SPTP does not average --> highest value.
Attenuation
Weakening of sound as it propagates. It limits imaging depth and the instrument must compensate for it.
Attenuation includes absorption (conversion to heat), and reflection and scattering of the sound as it encounters tissue interfaces.
Absorption is the main factor that contributes to attenuation.
Echoes from reflection and scattering are essential to create an image but contribute little to attenuation.
Attenuation is quantified in decibels (dB).
Attenuation coefficient (alpha) is the attenuation that occurs with each cm the sound wave travels. The farther the sound travels the greater the attenuation.
Decibels result from taking 10 times the logarithm of the ratio of two intensities.
Assume intensity1 = 10mW/cm² and intensity2 = 0.01mW/cm²
Note: If attenuation coefficient increases, attenuation increases. If path length increases, attenuation increases
Attenuation increase with increasing frequency:
Attenuation (dB) = « x frequency (MHz) x path length (cm)
Attenuation limits the depth of images (penetration). Note: If frequency increases penetration decreases
Frequencies used in diagnostic ultrasound range from 2 to 15 MHz. Lower frequencies are used for deeper penetration.
Impedance
Intensity of reflected echoes and the transmitted pulse depends on the incident intensity at a boundary and the impedances of the media on either side.
Impedance is the relationship between acoustic pressure and the speed of particle vibration.
Equal to density of a medium multiplied by propagation speed. Impedance units are rayls.
Note: Density increases, impedance increases
Propagation speed increases, impedance increases
Perpendicular incidence. The strengths of the reflected and transmitted pulses are determined by the impedances of the two media at the boundary.
Intensity reflection coefficient:
Note: Difference between impedances increases, IRC decreases.
Intensity transmission coefficient:
Note: IRC increases, ITC decreases
If impedances are equal, there is no echo, transmitted intensity is equal to the incident intensity.
If there is large difference between impedances, there will be nearly total reflection, for example in air-soft tissue interface. This is why a gel is used to provide a coupling medium for sound to travel into the body.
Oblique Incidence
Refraction
A change in the direction of sound when crossing a boundary. Refraction induces lateral position errors on an image.
Rule of thumb: If speed increases 1% as sound enters medium 2, the transmission angle will be ~1% greater that incident angle.
If perpendicular incidence, no refraction. If boundary is smooth, reflections are specular.
If reflecting object is the size of the wavelength or smaller, or if boundary is rough then incident sound will be scattered.
Bakcscatter intensities vary with frequency and scatterer size. frequency increases, intensity increases.
Speckle