The Physics of Diagnostic Ultrasound

The Physics of Diagnostic Ultrasound
FRCR Physics Lectures The Physics of Diagnostic Ultrasound Mark Wilson Radiotherapy Physicist, Queen’s Centre for Oncology

Session 1 Overview Session Aims:
Introduction to sound waves and their characteristics Define Ultrasound Basic principles of image formation Describe the four main types of ultrasound interactions with matter

Sound Waves and Their Characteristics

Wave Motion Waves transfer energy from one location to another
Waves can be broadly described as either “Transverse” or “Longitudinal”

Propagation of Sound Sound waves are mechanical pressure waves (longitudinal) which propagate through a medium by compression and rarefaction of the particles As a sound pressure wave propagates through the medium, particles in regions of high pressure will be pushed together (compression) and particles in regions of low pressure will be pulled apart (rarefaction)

Propagation of Sound Rarefaction follows compression as the compressed particles transfer their energy to adjacent particles The compression (and subsequent rarefaction) continues to travel forward through the medium as the energy is transferred between particles

Power, P  p Intensity, I  p2
Power and Intensity A sound wave transports Energy through a medium from a source. Energy is measured in joules (J) The Power, P, produce by a source of sound is the rate at which it produces energy. Power is measured in watts (W) where 1 W = 1 J/s The Intensity, I, associated with a sound wave is the power per unit area. Intensity is measured in W/m2 The power and intensity associated with a wave increase with the pressure amplitude, p Power, P  p Intensity, I  p2

Wavelength, Frequency and Speed
Waves are characterised by their wavelength, frequency and speed The Wavelength,  , is the distance between consecutive peaks or other similar points on the wave. The Frequency, f, is the number of oscillations per second Frequency is measured in Hertz (Hz) where 1 Hz is one oscillation per second.

The Speed of sound, c , is the distance travelled by the wave per unit time and is equal to the wavelength multiplied by the frequency The speed of sound is dependent on the medium through which it travels and varies greatly in different materials The speed of the wave is determined by the bulk modulus, B, (measure of stiffness) and the density, , (mass per unit volume) of the medium Highly compressible media (low B), such as air, has a low speed of sound – 330 m/s Less compressible media, such as bone, has a higher speed of sound – 4080 m/s c =  f c =  B / 

Material Density (Kg/m3) c (m/s) Air 1.2 330 Fat 924 1450 Water 1000 1480 Kidney 1041 1565 “Average Tissue” 1050 1540 Muscle 1068 1600 Bone 1912 4080

The frequency of a sound wave is unaffected by changes in the speed of the wave as it propagates through different media Therefore, the wavelength changes as the wave travels through different media Wavelength increases with an increase in wave speed Higher frequency sound waves have a shorter wavelength  = c / f

What is Ultrasound?

Ultrasound The term “Ultrasound” refers to sound waves of such a high frequency that they are inaudible to humans Ultrasound is defined as sound waves with a frequency above 20 kHz Ultrasound frequencies in the range 3-15 MHz are typically used for diagnostic imaging purposes Medical diagnostic ultrasound uses ultrasound waves and the acoustic properties of the tissues in the body to produce an image

Ultrasound The use of ultrasound in medicine began shortly after the 2nd World War Dr. Karl Theodore Dussik’s work on transmission ultrasound investigation of the brain in 1942 (Austria) was the first published work on medical ultrasound Ultrasound was first developed for clinical purposes in 1956 in Glasgow Obstetrician Ian Donald and engineer Tom Brown developed the first prototype systems based on an instrument used to detect industrial flaws in ships They perfected its clinical use, and by the end of the 1950s, ultrasound was routinely used in Glasgow hospitals Commercial systems became available in the mid-1960’s

Ultrasound

Basic Principals of Image Formation

Pulse Echo Principal A short ultrasound pulse is delivered to the tissues, and where there are changes in the acoustic properties of the tissue, a fraction of the pulse is reflected (an echo) an returns to the source (pulse-echo principal) Collection of the echoes and analysis of their amplitudes provides information about the tissues along the path of travel Tissue 1 Tissue 2 Tissue 3 US Pulse Transducer Reflected Echoes

Distance (D) = speed (c) x time (t)  2d = c t
Pulse Echo Principal The ultrasound pulse will travel at the speed of sound and the time between the pulse emission and echo return will be known. Therefore, the depth, d, at which the echo was generated can be determined and spatially encoded in the depth direction. Distance (D) = speed (c) x time (t)  d = c t Tissue 1 Tissue 2 Tissue 3 US Pulse Transducer Reflected Echoes

Tomographic Imaging Repeating this process many times with incremental changes in pulse direction allow a volume to be sampled and a tomographic image to be formed. i.e. A tomographic image is formed from a large number of image lines, where each line in the image is produced by a pulse echo sequence Transducer

B-Mode Image A B-mode image is a cross-sectional image representing tissues and organ boundaries within the body Constructed from echoes which are generated by reflection of US waves at tissue boundaries, and scattering from small irregularities within tissues Each echo is displayed at a point in the image which corresponds to the relative position of its origin within the body The brightness of the image at each point is related to the strength (amplitude) of the echo B-mode = Brightness mode

B-Mode Image – How Long Does it Take?
1. Minimum time for one line = (2 x depth) / speed of sound = 2D / c seconds 2. Each frame of image contains N lines 3. Time for one frame = 2ND / c seconds E.g. D = 12 cm, c = 1540 m/s, Frame rate = 20 frames per second Frame rate = c / 2ND N = c / (2D x Frame rate) = 320 lines (poor - approx half of standard TV) Additional interpolated lines are inserted between image lines to boost image quality to the human eye 4. Time is very important!!!

Time Gain Compensation (TGC)
The deeper the source of echo  Smaller signal intensity Due signal attenuation in tissue and reduction of the initial US beam intensity by reflections Operator can TGC use to artificially ‘boost’ the signals from deeper tissues to compensate for this (like a graphic equaliser)

M-Mode Image Can be used to observe the motion of tissues (e.g. Echocardiography) Image the same position (one image line) repeatly. One direction of display is used to represent time rather than space Time Transducer at fixed point Depth

Basic Principles of Image Formation
M-Mode Image of Mitral Valve

Interactions with Matter

Interactions with Matter
Ultrasound interactions with matter are determined by the acoustic properties of the media through which it propagates As Ultrasound energy propagates through a medium, interactions include: Reflection Refraction Scatter Attenuation / Absorption

Reflection Reflection (specular reflection) occurs at tissue boundaries where there is a difference in the acoustic impedance, Z, of the two tissues When the incident ultrasound wave is perpendicular to the boundary, a fraction of it’s energy is reflected (an echo) directly back towards the source The remaining energy is transmitted into the second tissue and continues in the initial direction Incident Reflection (echo) Z1 Z2 Transmission

Reflection – Acoustic Impedance
The acoustic impedance of a material is a measure of the response of the particles of the medium to a wave of given pressure (e.g. resistance) The acoustic impedance of a medium is again determined by the bulk modulus, B, (measure of stiffness) and the density, , (mass per unit volume) of the medium Consider a row of masses (molecules) linked by springs (bonds) A sound wave can be propagated along the row of masses by giving the first mass a momentary “push” to the right This movement is coupled to the second mass by the spring m B m B m B m Sound wave

Small masses (m) model a material of low density linked by weak springs of low stiffness (b) A given pressure is applied momentarily to the first small mass m The small mass is easily accelerated to the right and its movement encounters little resistance from the weak spring b This material has a low acoustic impedance, as particle movements are relatively large in response to a given applied pressure m b m b m b m Sound wave

Large masses (M) model a material of high density linked by springs of high stiffness (B) In this case, the larger masses M accelerate less in response to the applied pressure Their movements are further resisted by the stiff springs B This material has a high acoustic impedance, as particle movements are relatively small in response to a given applied pressure M B M B M B M Sound wave

The acoustic impedance, Z, of a material is given by Recall that the speed of sound, c =  B /  B =  c2 Therefore,  = density (kg/m3) z =   B B = bulk modulus (kg/m-s2)  = density (kg/m3) z =  c c = speed of sound (m/s)

Material Acoustic Impedance (Kg/m2s) Air x 106 Fat 1.34 x 106 Water 1.48 x 106 Kidney 1.63 x 106 Muscle 1.71 x 106 Bone 7.80 x 106 There are relatively small differences in acoustic impedance for “soft tissues”

( ) Ir Z2 – Z1 R = = Ii Z1 + Z2 Reflection
The fraction of ultrasound intensity reflected at an interface is given by the intensity reflection coefficient, R The fraction of ultrasound energy reflected depends on the difference between the Z values of the two materials R increases rapidly as the difference in Z increases Ii Z1 Ir R = Z2 – Z1 Z1 + Z2 Ii Ir = ( ) 2 Z2 It

Reflection The fraction of ultrasound intensity transmitted at an interface is given by the intensity transmission coefficient, T Ultrasound imaging is only possible when the wave propagates through materials with similar acoustic impedances – only a small fraction of energy is reflected and the rest is transmitted Ii Z1 Ir T = Ii It = 1 - R Z2 It

Reflection Tissue Interface R T Liver – Fat 0.01 0.99 Fat – Muscle
At soft tissue – soft tissue interfaces 1-2% of the ultrasound intensity is reflected Tissue Interface R T Liver – Fat 0.01 0.99 Fat – Muscle 0.02 0.98 Muscle - Bone 0.41 0.59 Muscle - Air At soft tissue – air interfaces 99% of the incident intensity is reflected At soft tissue – air or soft tissue – bone interfaces, a large proportion of the incident intensity is reflected, making anatomy beyond such interfaces unobservable Acoustic coupling gel is used between the face of the ultrasound transducer and skin to eliminate air pockets

Reflection When the wave is not incident perpendicular to the interface, non-normal incidence, the reflected angle is equal to the incident angle (i.e. θr = θi) Echoes are directed away from the source of ultrasound and may be undetected The transmitted wave does not continue in the incident direction (i.e. θt ≠ θi) The change in direction is described by Refraction Incident Reflection (echo) θi θr Z1 Z2 θt Transmission (refraction)

Refraction sin θt sin θi = c2 c1
Refraction describes the change in direction of the transmitted ultrasound wave at a tissue interface when the wave is not incident perpendicular to the interface The angle of refraction, θt , is determined by the speed of sound change that occurs as the wave crosses the boundary The angle of refraction is related to the angle of incidence by Snell’s law: Incident Reflection (echo) θi θr Z1 = 1 c1 Z2 = 2 c2 θt Transmission (refraction) sin θt sin θi = c2 c1

Refraction

Refraction c2 < c1 c2 > c1 c1 c1 c2 c2
When c2 < c1 the angle of transmission is less than the angle of incidence When c2 > c1 the angle of transmission is greater than the angle of incidence c2 < c1 c2 > c1 Incident Reflection (echo) Incident Reflection (echo) θi θr θi θr c1 c1 c2 c2 θt θt Transmission (refraction) Transmission (refraction)

Refraction c2 > c1 A condition known as total reflection occurs when c2 > c1 and the angle of incidence exceeds an angle called the critical angle , θc When θi = θc the sound wave does not continue into the second medium but travels along the boundary The critical angle is calculated by setting θt = 90o in Snell’s law, giving sinθc = c1/c2 Incident Reflection (echo) θi θr c1 c2 θt Transmission (refraction)

Refraction Refraction does not occur when the speed of sound is the same in the two media, or when a sound wave is incident perpendicular to the interface This “straight-line” propagation is assumed by the ultrasound system during signal processing When refraction does occur, this can result in image artefacts due to the misplacement of anatomy in the image Displayed in image here Anatomical feature here

Scattering Reflection occurs at large tissue interfaces, such as those between organs, where there is a change in acoustic impedance These large specular reflectors represent a “smooth” boundary where the size of the boundary is much larger than the wavelength of the incident ultrasound wave Within most tissues and organs there are many small-scale variations in acoustic properties which constitute small-scale reflecting particles that are similar in size or smaller than the wavelength of the ultrasound These small non-specular reflectors represent a “rough” surface and give rise to acoustic scattering within the insonated tissues

Scattering Scattering from non-specular reflectors reflects sound in all directions Scattering is a weak interaction in that the amplitude of the returning echoes are significantly weaker than those from tissue boundaries Intensities of the returning echoes from non-specular reflectors within the tissue are not greatly dependent on beam direction, unlike specular reflectors The scattering pattern is characteristic of the particle size and gives rise to tissue or organ signatures that lead to a specific speckle or textured appearance in the ultrasound image

Non-specular Reflection
Scattering Tissue boundary interactions can also give rise to scatter Specular reflection assumes a “smooth” interface, where the wavelength of the ultrasound is much greater than the structural variations of the interface With higher frequency ultrasound waves, the wavelength becomes smaller and the interface no longer appears “smooth” Returning echoes are diffusely scattered (non-specular reflection) and only a fraction of the reflected intensity returns to the transducer Scattering from non-specular reflectors increases with ultrasound frequency, but specular reflection is relatively independent Non-specular Reflection Incident Z1 Z2 Transmission (refraction)

Attenuation As an ultrasound wave propagates through a tissue, the energy of the wave reduces with the distance travelled Attenuation describes the reduction in beam intensity with distance travelled and is primarily caused by scattering and tissue absorption of the incident beam The attenuation coefficient, , (in units dB/cm) is the relative intensity loss per cm of travel for a given tissue The attenuation coefficient varies widely between different tissues and media The attenuation coefficient for a given tissue varies with ultrasound frequency; Attenuation increases linearly with increasing frequency For “soft tissue”, the attenuation coefficient can be approximated as 0.5 (dB/cm)/MHz

Attenuation Coefficient
Tissue Attenuation Coefficient (1 MHz Beam, dB/cm) Water 0.0002 Blood 0.18 Brain 0.3 – 0.5 Liver 0.4 – 0.7 Fat 0.5 – 1.8 Muscle 0.2 – 0.6 Bone Lung 40

Attenuation Ultrasound beam intensity reduces exponentially due to attenuation, according to: 1 I = Ioe- d Io = Initial intensity Relative Intensity, I Low frequency 0.5 High frequency Distance travelled, d

Attenuation The ultrasound half-value thickness (HVT) is the thickness of tissue necessary to attenuate the incident intensity by 50% (or 3 dB) The HVT decreases as the frequency increases When penetration to deeper structures is important, lower frequency ultrasound transducers are required 1 Relative Intensity, I Low frequency 0.5 High frequency Distance travelled, d

Relative Intensity (dB) = 10 log10 (I2 / I1)
Attenuation In soft tissues a significant proportion of energy loss (attenuation) is due to tissue absorption Absorption is the process by which ultrasound energy is converted into heat energy in tissue Energy lost through absorption does not contribute to image formation Ultrasound attenuation is usually expressed in terms of decibels (dB) Decibel Notation Relative Intensity (dB) = 10 log10 (I2 / I1) Where I1 = initial intensity, I2 = final intensity

Thank you Any Questions?

Session 2 Overview Session Aims: Construction and operation of the ultrasound transducer Ultrasound instrumentation Ultrasound safety

Construction and Operation of the Ultrasound Transducer

Ultrasound Transducer
The transducer is the device that converts electrical transmission pulses into ultrasonic pulses, and ultrasonic echo pulses into electrical signals A transducer produces ultrasound pulses and detects echo signals using the piezoelectric effect The piezoelectric effect describes the interconversion of electrical and mechanical energy in certain materials If a voltage pulse is applied to a piezoelectric material, the material will expand or contract (depending on the polarity of the voltage) If a force is applied to a piezoelectric material which causes it to expand or contract (e.g. pressure wave), a voltage will be induced in the material

A piezoelectric material called PZT is commonly used in transducers A transducer only generates a useful ultrasound beam at one given frequency This frequency corresponds to a wavelength in the transducer equal to twice the thickness of the piezoelectric disk – This is due to a process known as Resonance! Choice of frequency is important – remember that attenuation increases with increasing frequency Image resolution increases with frequency Therefore, there is a trade-off between scan depth and resolution for any particular application

Linear Array Curvilinear/Convex Array Phased Array Rectangular FOV Useful in applications where there is a need to image superficial areas at the same time as organs at a deeper level Trapezoidal FOV Wide FOV near transducer and even wider FOV at deeper levels Sector FOV Useful for imaging heart where access in normally through a narrow acoustic window between ribs

Beam Shape - Diffraction
Diffraction is the process by which the ultrasound wave diverges (spreads out) as it moves away from the source Divergence is determined by the relationship between the width of the source (aperture) and the wavelength of the wave High Divergence Aperture small compared to  Low Divergence Aperture large compared to 

NEAR FIELD FAR FIELD NFL Near Field Length, NFL = a2 /  a = radius of transducer  = Wavelength

In the near field region the beam energy is largely confined to the dimensions of the transducer Need to select a long near field length to achieve good resolution over the depth you wish to scan too Near field length increases with increasing transducer radius, a, and decreasing wavelength,  Short wavelength means high frequency – not very penetrating Large transducer radius – Wide beam (poor lateral resolution) Trade-off between useful penetration depth and resolution!!

Beam width at focus, W = F / a
Beam Focusing An improvement to the overall beam width can be obtained by focusing Here the source is designed so that the waves converge towards a point in the beam, the focus, where the beam achieves its minimum width Beyond the focus, the beam diverges again but more rapidly that for an unfocused beam with the same aperture and frequency F a Beam width at focus, W = F / a W At focal point: Maximum ultrasound intensity Maximum resolution

Beam Focusing For a single element source, focusing can be achieved in one of two ways: A curved source A curved source is manufactured with a radius of curvature of F and hence produces curved wave fronts which converge at a focus F cm from the source F Source Focus

Beam Focusing For a single element source, focusing can be achieved in one of two ways: 2) An acoustic lens An acoustic lens is attached to the face of a flat source and produces curved wave fronts by refraction at its outer surface (like an optical lens). A convex lens is made from a material with the lower speed of sound than tissue. Lens Source Focus

Beam Shape Single transducer element is very small.
Beam of one element has very short near field length followed by significant divergence.

Beam Shape – Overlapping Groups of Elements
Image element line 3 Image element line 4 Fire elements 1-5 together Fire elements 2-6 together And then… And so on… Near field length increases as (N)2

Array Focusing Waves from outer elements 1 and 5 have greater path lengths than those from other elements Therefore signals do not arrive simultaneously at the target and reflections do not arrive at all elements at the same time

Array Focusing Time delays
Introduce time delays to compensate for extra path length on both transit and receive A large-summed signal is obtained for echoes from the focal zone Only a weak-summed signal (noise) results from echoes elsewhere

Multiple Zone Focusing
Fire transducer several times with different focus to compile better image However, more focus points decreases frame rate

Resolution in three planes
Image Resolution Resolution in three planes Axial Slice Thickness Lateral

Resolution Depends on Typical Value (mm)
Image Resolution Resolution Depends on Typical Value (mm) Axial Pulse length Lateral Beam width 2 – 5 Slice Thickness Beam height 3 - 8 Higher frequency improves resolution in all three planes Slice thickness is a hot topic for improvement – 2D arrays

Ultrasound Instrumentation

Instrumentation Transmitter Clock TGC Generator Transducer
Beam Controller x, y AD Converter z Signal Processor Image Store Archive Display

Command and control centre
Instrumentation Clock Command and control centre Sends synchronising pulses around the system Each pulse corresponds to a command to send a new pulse from the transducer Determines the pulse repetition frequency (PRF) PRF = 1 / time per line = c / 2D Where c is speed of sound and D is maximum scan depth If there are N lines, then Frame Rate = c / 2ND

Instrumentation Transmitter Responds to clock commands by generating high voltage pulses to excite transducer Transducer Sends out short ultrasound pulses when excited Detects returning echoes and presents them as small electrical signals

Instrumentation AD Converter Converts analogue echo signals into digital signals for further processing Needs to: Be fast enough to cope with highest frequencies Have sufficient levels to create adequate grey scales (e.g. 256 or 512)

Demodulation – removal of the carrier (ultrasound) frequency
Instrumentation Grey level Signal Processor Carries out: TGC application Overall gain Signal compression – fits very large dynamic range ultrasound signal on to limited greyscale display dynamic range Demodulation – removal of the carrier (ultrasound) frequency Liver Heart Linear Input Amp

Instrumentation Image Store Takes z (brightness) signal from processor Positions it in image memory using x (depth) and y (element position) information from beam controller Assembles image for each frame Presents assembled image to display Typically have capacity to store frames to allow cine-loop

Ultrasound Safety

Hazard and Risk Hazard describes the nature of the danger or threat (e.g. burning, falling, etc) Risk takes into account the severity of the potential consequences (e.g. death, injury) and the probability of occurrence There are two main hazards associated with ultrasound: - Tissue heating - Cavitation But is there any risk???

Tissue Heating During a scan some of the ultrasound energy is absorbed by the exposed tissue and converted to heat causing temperature elevation Elevated temperature affects normal cell function The risk associated with this hazard depends on the: - Degree of temperature elevation - Duration of the elevation - Nature of the exposed tissue Rate of energy absorption per unit volume q = 2I Where  = absorption coefficient,  = frequency, I = intensity

Tissue Heating Thermal effects in patient are complex
Temperature increase will be fastest at the focus resulting in a temperature gradient Heat will be lost from focus by thermal conduction The transducer itself will heat up and this heat will conduct into tissue enhancing the temperature rise near the transducer The presence of bone in the field will increase the temperature rise Blood flow will carry heat away from the exposed tissues It is impossible to accurately predict the temperature increase occurring in the body and a simple approach to estimate the temperature increase is used to provide some guidance - Thermal Index (TI)

Thermal Index (TI) TI = W / Wdeg
W = Transducer power exposing the tissue Wdeg = The power required to cause a maximum temperature rise of 1oC anywhere in the beam TI is a rough estimate of the increase in temperature that occurs in the region of the ultrasound scan A TI of 2.0 means that you can expect at temperature rise of about 2oC The difficulty with calculating the TI lies mostly in the estimation of Wdeg To simplify this problem there are three TIs

Soft-Tissue Thermal Index (TIS)
Maximum temperature Soft tissue Bone-at-Focus Thermal Index (TIB) Maximum temperature Bone Soft tissue

Ultrasound Safety Cranial (or Bone-at-Surface) Thermal Index (TIC)
Maximum temperature Bone Soft tissue All three TI values depend linearly on the acoustic power emitted by the transducer

Does Temperature Rise Matter?
Tissue Heating Does Temperature Rise Matter? Normal core temperature is 36-38oC and a temperature of 42oC is “largely incompatible with life” During an ultrasound examination only a small volume of tissue is exposed and the human body is quite capable of recovering from such an event Some regions are more sensitive such as reproductive cells, unborn fetus, and the CNS Temperature rises of between 3 and 8oC are considered possible under certain conditions There has been no confirmed evidence of damage from diagnostic ultrasound exposure

Cavitation Refers to the response of gas bubbles in a liquid under the influence of an ultrasonic wave Process of considerable complexity High peak pressure changes can cause micro-bubbles in a liquid or near liquid medium to expand – resonance effect A bubble may undergo very large size variations and violently collapse Very high localised pressures and temperature are predicted that have potential to cause cellular damage and free radical generation

frR  3 Hz m Cavitation Micro-bubbles grow by resonance processes
Bubbles have a resonant frequency, fr, depending on their radius, R. frR  3 Hz m This suggests that typical diagnostic frequencies (3 MHz and above) cause resonance in bubbles with radii of the order of 1 micrometer

MI = pr / f Mechanical Index (MI)
The onset of cavitation only occurs above a threshold for acoustic pressure This has resulted in the formulation of a mechanical index (MI) Mechanical index is intended to quantify the likelihood of onset of cavitation MI = pr / f where pr is the peak rarefaction pressure and f is the ultrasound frequency For MI  0.7 the physical conditions probably cannot exist to support bubble growth and collapse Exceeding this threshold does not mean there will be automatically be cavitation Cavitation is more likely in the presence of contrast agents and in the presence of gas bodies such as in the lung and intestine

British Medical Ultrasound Society (BMUS)
Ultrasound Safety British Medical Ultrasound Society (BMUS) Produce guidelines for safe use of diagnostic ultrasound These are agreed guidelines but there is no legal requirement to follow them See:

Thank you Any Questions?

The Physics of Diagnostic Ultrasound

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