Basic Ultrasound Physics
Ultrasound uses sound waves.
Audible 20Hz and 20 000Hz.
Infra sound Below 20Hz
Ultrasound Above 20 000Hz
Ultrasound is high frequency mechanical vibrations or pressure waves above a frequency the human ear can hear.
Ultrasound uses a pulse-echo technique of imaging the body.
Pulses transmitted into patient and give rise to echoes when they encounter interfaces/reflectors.
These interfaces/reflectors are caused by variations in the "acousitc impedence" between different tissues.
Echo signals are amplified electronically and displayed on a monitor using shades of grey (from black to white), stronger reflectors = brighter shades of grey and appear white in an image. Those with no echoes will appear black, such as a full bladder.
Tissues with multiple interfaces are termed echogenic,
solid organs: spleen, liver and kidneys.
Structures with no internal interfaces are hypoechoic and return no echoes.
characteristic of liquid filled structures such as gall bladder and the urinary bladder.
Properties of an ultrasound wave
- Frequency higher than 20 000Hz (20kHz)
- Propagation of sound waves longitudinal, the mechanical displacement being in the same direction as propagation.
- A medium is needed for sound waves to go through, no medium = no soundwaves
- This propagation is whereby the particles of the medium which the sounds is going through oscillate (move) back and forth from their original rest positions, in the same line as the wave. This is also know as Simple Harmonic Motion
- The motion of the these particles is cause by 2 factors; the pressure of the wave (which forces them to move in the beginning) and the forces of the restoring molecules (also known as the elasticity of the medium)
- The soundwaves are transmitted as an alternation series of compressions (zones of high pressure) and rarefractions (zones of low pressure).
- The physical disturbance can be shown in a diagram (the dot diagram), and the individual movement of each particle in the diagram is/ can be described mathematically by the wave equation
- Also the amount of particle movement is dependent on the pressure change associated with the wave, therefore the increased pressure change equals the increased particle movement, and therefore louder sound
Interactions of ultrasound with soft tissues
When an ultrasound wave passes through tissues
- Attenuation: Reduction in amplitude and intensity of wave
- Refraction: Change in direction & velocity of wave
Attenuation is the rate at which intensity wave diminishes with the depth it covers or its penetration.
- Frequency of wave - Higher the frequency, higher the attenuation and less penetration of the wave
- Type of tissue the wave is traveling
- Depth the wave travels - more distance wave has to travel the more energy is lost.
When a sound wave is incident on a interface between two tissues, part of it is reflected back into the original medium. The amount of energy reflected back depends on impedance.
The greater the difference in impedance between the tissues forming the interface the greater the amount of energy that is reflected back.
Impedance is a property of a tissue defined as density of tissue and velocity of sound in that tissue.
Denoted as Z = d ( kg/m3) X c ( m/s2)
Reflection co-efficient ( R) is the ratio of the intensity of the reflected wave to the incident wave.
R = (Z2 –Z1) ²
( Z2+Z1) 2
The greater R, the greater the degree of reflection. i.e. R for a soft tissue interface such as liver and kidney is 0.01, i.e. only 1% of the sound is reflected. Muscle/bone interface 40% is reflected and for a soft tissue/air interface 99% is reflected.
This is the basis of ultrasound as different organs in the body have different densities and acoustic impedance and this creates different reflectors. In some cases the acoustic impedance can be so great that all the sound waves energy can be reflected, this happens when sound comes in contact with bone and air. This is the reason why ultrasound is not used as a primary imaging modality for bone, digestive tract and lungs.
Absorption is the main form of attenuation. Absorption happens as sound travels through soft tissue, the particles that transmit the waves vibrate and cause friction and a loss of sound energy occurs and heat is produced. In soft tissue sound intensity decreases exponentially with depth.
Diffuse scatter when an objects size relative to the wave length becomes smaller. Imagine placing a thin stick upright in large rippling puddle or lake shore. The waves striking the stick will barely change course. The same applies to sound when the wave length of the sound waves are much larger than the object they are striking little or no sound waves will be reflected back. Because of this no strong reflections are seen as the sound, if reflected at all does not go directly back to the transducer. An example of this can be seen as speculation of an ultrasound image.
Echo ranging is a technique used to determine the distance of an object from the transducer. This technique relies on reflection.
The echo ranging equation is z=ct.
z = distance c = speed of ultrasound in tissue t = time
A sound beam is transmitted into a medium and is reflected back from an object. The elapsed time between the transmitted pulse and the received echo is converted into the total distance traveled. (The z value is only half of the distance traveled away and back to the transducer. )
The equations for transmission and reflection of ultrasound intensity are independent of frequency for specular reflection. Therefore changing the transducer frequency does not alter the fraction of intensity tranmitted/reflected at an interface. Transmission coefficient - %T = 4 Z2 Z1 / (Z2 + Z1) sqaured.
Sound speed (c) is equal to one over the square root of the density times compressibility.OR c= square root compressibility / square root density.This indicates that if the density of a material is increased the speed of sound in that material will also be increased.Sound travels faster in media that are denser than air because of reduced compressibility.The velocity of ultrasound remains constant for a particular medium.Where c=frequency X wavelength.Indicating that for a constant velocity as the frequency is increased the wavelength is reduced.Ultrasonic waves are reflected at boundaries where there is a difference in acoustic impedance (Z) of the materials on each side of the boundary. This difference in Z is commonly referred to as the impedance mismatch. The greater the impedance mismatch, the greater the percentage of energy that will be reflected at the interface or boundary between one medium and another.The fraction of the incident wave intensity that is refracted can be derived because particle velocity and local particle pressures must be continuous across the boundary. When the acoustic impedances of the materials on both sides of the boundary are known, the fraction of the incident wave intensity that is reflected can be calculated with the equation below. The value produced is known as the reflection coefficient. Multiplying the reflection coefficient by 100 yields the amount of energy reflected as a percentage of the original energy.Reflection - sound is reflected at an interface regardless of the thickness of the material from which it is reflected.The reflection coefficient:
Nature of ultrasound
Ultrasound uses high frequency (above 20 kHz) mechanical vibrations or pressure waves that the human ear cannot detect. Typical diagnostic sonographic scanners operate in the frequency range of 2 to 18 megahertz, hundreds of times greater than the limit of human hearing. The choice of frequency is a trade-off between spatial resolution of the image and imaging depth: lower frequencies produce less resolution but image deeper into the body.
Superficial structures such as muscles, tendons, testes, breast and the neonatal brain are imaged at a higher frequency (7-18 MHz), which provides better axial and lateral resolution. Deeper structures such as liver and kidney are imaged at a lower frequency 1-6 MHz with lower axial and lateral resolution but greater penetration.
PERIOD: time taken for one particle in the medium through which the wave travel, to make one complete oscillation (cycle)about its rest position, in response to the wave
FREQUENCY: the number of oscillations per second of the particle in the medium responding to the wave passing through it
WAVELENGTH: the distance between 2 consecutive, identical positions in the pressure wave
VELOCITY: the speed of propagation of a sound wave, determined by a combination af the density and compressibility of the medium through which it is propagating
PHASE:the stage at which a wave is within a cycle
AMPLITUDE:a measure of the degree of change within a medium, caused by the passage of a sound wave and relates to the severity of the disturbance
POWER: rate of flow of energy through a given are
INTENSITY: the power per unit area
Properties of interfaces
An interface is the junction of two media with different acoustic properties.
It does not matter which impedance is the larger or smaller for two materials composing an interface; the difference between them sqaured is the same. This means that the same amount of reflection occurs at an interface going from high impedance to low impedance or vice versa
Acoustic impedanceinteractions of ultrasound with tissue
Acoustic Impedance (Z) is a measure of the resistance to sound passing through a medium. Z= density X speed of sound. It is similar to electrial resistance.
Unit - kg/m2/s called rayl
Materials with a higher density have increased c which therefore means the acoustic impedance is higher. eg bone.
Gases have low acoustic impedance.
Impedance mis-match - a difference in acoustic impedances cause some portion of the sound to be reflected at the interface. Therefore we want the acoustic impedance of two different materials to be as similar as possible to ensure that the beam is reflected at a specular reflector.
Whenever a sound wave encounters a material with a different density (acoustical impedance), part of the sound wave is reflected back to the probe and is detected as an echo. The greater the difference between acoustic impedance, the larger the echo is. If the pulse hits gases or solids, the density difference is so great that most of the acoustic energy is reflected and it becomes impossible to see deeper.
"a source of sound acts asif it is composed of an infinite number of point sources of sound. The waves from these pointsources combine with each other to form a wavefront wich then determinates the direction of wave travel. The intensity at any point within the beam is determined by the sum of the contributions from all the pointsources. Interferences occurs between the waves from the pointsources, leading to variation in intensity within the beam."
As an ultrasound beam passes through a medium, it loses energy and therefore undergoes a reduction in amplitude and intensity... this loss of energy is determined by the characteristics of the medium. Attenuation is frequency dependent thus dictating the limit of penetration of an ultrasound beam at a given frequency, resulting in the resolution/penetration trade-off in diagnostic sonography. Five processes responsible for attenuation of an ultrasound beam... reflection/scattering/absorption/refraction/beam divergence
Is a physical parameter that describes the amount of energy flowing through a unit cross-sectional area of a beam each second or the rate at which the wave transmits the energy over a small area
unit - watt per square cm or joule per second per sqaure cm.
- it can be used to describe the loudness of sound, in dB.
Indicates the strength of the detected echo or the voltage induced in a crystal by a pressure wave.
Is a measure of the degree of change within a medium, caused by the passage of a sound wave, relates to the severity of the disturbance
distance (z) is equal to the product of speed of sound times the time of travel.z=ct
Echo ranging is used to determine the distance travelled by the sound beam. If the velocity of the ultrasound in the medium and the elapsed time from the original transmitted pulse are known echo ranging prinicple states that the distance to an interface can be determined.