The Physics andTechnology ofDiagnostic Ultrasound:A Practitioner’s Guide

Second Edition

Robert Gill, PhD

ContentsIntroduction 11.1 Introductory comments 11.2 Physics and mathematics 21.3 Mathematics: a brief review 2Equations 2Addition, subtraction, multiplication and division 3Units 3Scienti!c notation 3Logarithms 5Decibels 5Reality checking answers 51.4 Exercises 6Ultrasound interaction with tissue 72.1 Ultrasound waves and propagation 7Frequency analysis 82.2 Attenuation 92.3 Re"ection and scattering 11Re"ection 11Scattering 122.4 Refraction 13Pulsed ultrasound and imaging 173.1 Pulsed ultrasound 17Pulse duration 17Pulse repetition frequency (PRF) 173.2 Pulse echo principle 18Pulse repetition frequency limitations 18Frame rate limitations 20Summary 213.3 Principles of image formation 21Probes 22Endocavity and laparoscopic probes 233D probes 23A, B and Mmode 24

Transducers and focussing 254.1 Transducer principles 254.2 Focussing 264.3 Array transducers 30Transmit focussing 30Beam steering 31Receive focussing 32

Scanning the beam 32Matrix arrays 334.4 The ultrasound beam and image quality 33Sidelobes 33Slice thickness 34

Ultrasound instrumentation 375.1 Introduction 375.2 Block diagram 375.3 Probe 38Controls 385.4 Transmitter and transmit beam-former 38Controls 395.5 Receive beam-former 39Controls 395.6 Ampli!er 39Controls 395.7 TGC 40Controls 405.8 Dynamic range compression 41Controls 425.9 Scan converter 42Controls 425.10 Image memory 43Controls 435.11 Pre-processing 44Controls 445.12 Post-processing 45Controls 455.13 Display 465.14 Image storage 46Image artifacts 476.1 Introductory comments 476.2 Imaging assumptions 476.3 Attenuation artifacts 48Shadowing 48Enhancement 49Edge shadowing 496.4 Depth artifacts 51Propagation speed artifact 51Reverberation artifact 52Ring-down artifact 52Comet-tail artifact 53

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Range ambiguity 536.5 Beam dimension artifacts 54Beam width artifact 54Sidelobe artifact 56Slice thickness artifact 576.6 Speckle 586.7 Beam path artifacts 58Refraction artifact 58Mirror image artifact 596.8 Equipment and electrical artifacts 606.9 Summary 61Doppler ultrasound 637.1 Introductory comments 637.2 The Doppler e#ect 637.3 Measurement accuracy 657.4 Scattering of ultrasound by blood 667.5 Continuous wave Doppler 68Concept 68Acquisition, signal processing 68Display 697.6 Pulsed Doppler 69Concept 69Acquisition 70Signal processing 70Display 71Controls 737.7 Colour Doppler 73Concept 73Acquisition 73Signal processing 75Display 75Controls 76Strengths and limitations 76Power mode colour Doppler 78Doppler Tissue Imaging 78

Doppler artifacts 818.1 Introductory comments 818.2 Frequency aliasing 818.3 Intrinsic spectral broadening 84Spectral mirror artifact 858.4 Other spectral Doppler artifacts 868.5 Colour Doppler artifacts 88Colour aliasing 88Colour drop-out 88

Colour bleed 89Angle e#ects 89Twinkling artifact 89

Haemodynamic concepts 919.1 Cardiovascular system 919.2 Blood "ow and blood pressure 919.3 Stenotic disease 939.4 Continuity equation 949.5 Velocity waveform 959.6 Velocity pro!le 969.7 Venous disease 979.8 Summary 98Imaging performance & limitations 9910.1 Introductory comments 9910.2 Spatial resolution 99Axial resolution 99Lateral resolution 100Slice thickness 101E#ect on the image 10110.3 Contrast resolution 10110.4 Temporal resolution 102Frame rate 102Frame averaging (persistence) 103Frame rate display 10310.5 Limitations 104Bioe!ects and Safety 10511.1 Is ultrasound safe? 10511.2 Characterising ultrasound exposure 106Temporal variation 106Spatial variation 10711.3 Ultrasound bioe#ects and biohazards 108Thermal bioe#ects 108Mechanical bioe#ects 11011.4 Government regulation 11111.5 Policies and statements 111Additional modes and capabilities 11512.1 Introduction 11512.2 Compound imaging 11512.3 Harmonic imaging 11712.4 Ultrasound contrast agents 12112.5 3D and 4D imaging 12312.6 Speckle tracking 12612.7 Strain imaging 12612.8 Elastography 127

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Strain-based elastography 127Shear wave elastography 12812.9 Synthetic aperture imaging 12812.10 Arti!cial intelligence (AI) 12912.11 Extended !eld of view 130Answers to Mathematical Exercises 132The author 133Acknowledgements 134Index 135

List of TablesTable 1.1 Units for fundamental quantities. 2

Table 1.2 Units for derived quantities. 2

Table 1.3 Common pre!xes. 3

Table 1.4 Integer logarithms. 5

Table 1.5 Non-integer logarithms. 5

Table 1.6 Power ratios in decibels. 5

Table 2.1 Typical frequencies used in diagnostic ultrasound and thecorresponding wavelengths in soft tissue. 8

Table 6.1 Typical attenuation coe$cient values. 48

Table 6.2 Typical propagation speed values. 51

Table 10.1 Practical actions that can be taken to improve variousperformance parameters. 104

Table 11.1 De!nitions of the parameters used to measure ultrasoundexposure. 106

Table 11.2 De!nitions of the various measures of intensity. 108

Table 11.3 Recommended maximum TI values and exposure times forobstetric scanning, and for neonatal transcranial and spinal scanning.112

Table 11.4 Recommended maximum TI values and exposure times foradult transcranial scanning. 112

Table 11.5 Recommended maximum TI values and exposure times forother areas (except the eye). 112

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This last observation means that

For example, if we double the frequency from 3MHz to 6MHz we mustexpect the depth of penetration to halve.More generally, this relationship means that relatively low frequencies(e.g. 3 to 5MHz) must be used to scan deep regions (e.g. in abdominaland obstetric ultrasound) to ensure adequate penetration.For super!cial regions (e.g. thyroid, breast, peripheral vascular) consid‐erably higher frequencies can be used (e.g. 6 to 10MHz) since less pene‐tration is required.Note also that the higher frequencies used for scanning super!cial areasyield better image resolution than can be obtained when deeper regionsare scanned using lower frequencies.Since we want the best possible image resolution, we always try to

2.3 Reflection and scattering

ReflectionRe"ection and scattering are the two mechanisms that produce echoes.The word re!ection is used to describe the interaction of ultrasound withrelatively large and smooth surfaces. (Think of light re"ecting fromglass.) Scattering refers to the interaction of ultrasound with small struc‐tures (red blood cells, capillaries, etc.) within the tissues. (Think of lightscattering from the tiny water droplets in a fog.)Before we can discuss re"ection, we must introduce the concept of theacoustic impedance (sometimes called the characteristic impedance) of atissue. It is de!ned as shown in Equation 2.10, where z is the acousticimpedance, ρ is the density of the tissue (i.e. the weight per unit volume)and c is the ultrasound propagation speed. The units for acoustic imped‐ance are Rayls.

(2.10)Figures 2.7, 2.8 and 2.9 show how acoustic impedance a#ects re"ection.Notice that the amount of energy re"ected at an interface is determinedby how di#erent the acoustic impedances in the two tissues are.Mathematically, the fraction of the incident energy re"ected is given bythe following equation, where z1 and z2 are the acoustic impedances inthe !rst and second tissue respectively

(2.11)

112.3 Reflection and scattering

Use the highest frequency compatible with the depth of penetrationrequired.

The depth of penetration is inversely related to the frequency. Suggested activities1. Observe which probes and fre‐

quencies are used for di#erenttypes of examination in yourworkplace. Notice whetherthere is a trend to use higher fre‐quencies for more super!cial ar‐eas.

2. Suppose an ultrasound machinehas a maximum depth of pene‐tration of 20 cmwhen operatingat 4MHz. Calculate the penetra‐tion you would expect at fre‐quencies of 2.5, 3, 5, 7.5, 10 and15MHz. Put the results into a ta‐ble and think about typical clini‐cal applications where you coulduse each of these frequencies.

Figure 2.7 Total re!ection of the ultrasoundenergy at an interface between two tissueswith a very large acoustic impedance di"er‐ence (e.g. a so$ tissue - air interface). All theenergy is re!ected and none is transmi%edinto the second tissue. &e interface is seen inthe image as a strong linear structure.

Figure 2.8 Total transmission of the ultra‐sound energy when the two tissues have iden‐tical acoustic impedance (z1 = z2). No energyis re!ected and so there is no echo – the inter‐face is not seen in the ultrasound image.

5.10 Image memoryThe image memory is a section of the machine’s digital memory wherethe ultrasound image is stored. The format is like that used to store pho‐tographs in computers and portable devices. As shown in Figure 5.14, itcan be thought of as a two-dimensional array of individual storage loca‐tions (called pixels). The digital number stored in each pixel determineswhat shade of grey (or colour) is displayed at the corresponding point inthe machine’s display. The number of pixels in the image is chosen toensure that the spatial resolution of the image is not compromised. Sim‐ilarly the number of bits used for each pixel value must be su$cient toensure the dynamic range of the display is not compromised.In practice, the machine stores many (typically a hundred or more) im‐ages stretching back several seconds from the most recent image. Whenthe user freezes the image (which stops the imaging process), they canthen scroll back through these previous images to !nd the optimum onefor their purpose. This cineloop function is often very useful.In 3D imaging (see Chapter 12 for more detail), things become morecomplicated. Images are acquired from many di#erent scan planes andthese are processed to create a three-dimensional view of the anatomy.

ControlsAsmentioned above, two controls associated with the imagememory arethe freeze button and the cineloop function.Another useful imaging function is the ability to zoom in on a region ofanatomy.The preferred way to do this is while scanning the patient. The region ofinterest is identi!ed then zoom is activated. The machine enlarges theregion so that it occupies the entire image memory. Since it is now scan‐ning a smaller region, the frame rate increases. This can be a signi!cantadvantage, for example when imaging a fetal heart. This zoom functionis known as write zoom or pre-processing zoom since it is applied to theecho data before it is stored in the image memory. An example of its useis shown in Figures 5.15 and 5.16.Most machines also provide a read zoom or post-processing zoom func‐tion, where part of a stored image can be magni!ed on the display. Thistype of zoom has two disadvantages relative to write zoom. First, the im‐age may become pixellated (jagged) as it is magni!ed. Second, the framerate is unchanged, since the image had been acquired and stored beforeit was zoomed.The depth control determines the depth of tissue displayed, that is, thenumber of centimetres displayed on the screen. Reducing the depth mayallow the machine to increase the PRF, which increases the frame rate.Generally, the depth is set so that all the tissues of interest are displayedin the image and they occupy as much of the image area as possible (seeFigures 5.17 and 5.18).

435.10 Image memory

Figure 5.15 Abdominal scan showing liver andkidney. &e frame rate is 31fps (frames persecond).

Figure 5.16&e user has zoomed in on the kid‐ney. Now the frame rate is 79fps.

Figure 5.17&e depth se%ing is too large in thisimage.&e frame rate is 23fps.

Figure 5.18 Here the depth has been set appro‐priately so that it is as small as possible con‐sistent with including all the liver in theimage. Reducing the depth has increased theframe rate to 28fps.

Power mode colour DopplerThe colour Doppler display can be complex and confusing at times dueto the colour variations caused by changes in Doppler shift and "ow di‐rection (see Figure 7.25).In some situations, displaying the Doppler shift does not add value, and asimpler form of colour Doppler, power mode colour Doppler, can be moree#ective. Figures 7.26 and 7.27 show two examples of this modality.Power mode colour Doppler di#ers from standard colour Doppler in justone way. The colour at each point indicates the Doppler power, ratherthan the mean Doppler shift. This means the display is not a#ected byblood velocity, "ow direction or frequency aliasing.Some machines can modify the power mode image to indicate whether"ow is towards or away from the probe, as shown in Figure 7.28.As well as producing a more easily interpreted image, power modecolour Doppler has other advantages.• It is signi!cantly more sensitive than standard colour Doppler, so it

is the preferred mode when weak signals need to be detected anddisplayed.

• Flow is detected and displayed even when the Doppler angle is 90°.At this angle there is no real Doppler shift, but the machine detectssignal caused by the spectral mirror artifact (see Chapter 8). This"ow is not detected by conventional colour Doppler, since themean Doppler shift is zero.

Thus power mode colour Doppler is a specialised form of colourDoppler. Its advantages are the simpler display, the lack of drop-outwhen the Doppler angle is 90° and its ability to detect weak signals morereliably.

Doppler Tissue ImagingDoppler Tissue Imaging (or DTI) is another specialised application ofcolour Doppler. It is identical to standard colour Doppler except the wall!ltering is reversed. Signals from moving tissue are retained and signalsfrommoving blood are suppressed. The result is a colour-coded image ofmoving tissues (see Figure 7.29).

Figure 7.29 An example of Doppler Tissue Imaging in a cardiac image. Tissue velocity isdisplayed (assuming θ = 0°).

78 7. Doppler ultrasound

Figure 7.25 A colour Doppler image showingthe distribution of blood !ow in a thyroid. Notehow the variations in colour make it di(cult toget an overall feel for the distribution and den‐sity of the vessels.

Figure 7.26 A power mode colour Doppler im‐age showing the vascularity in a testicle. Com‐pared to Figure 7.25 it is much easier to assessthe distribution of the vessels in this image.Note the colour bar now shows how the colourvaries with signal strength.

Figure 7.27 Power mode colour Doppler is moresensitive than standard colour Doppler, makingit ideal for detecting trickle !ow like that seenin this severely stenosed common carotidartery.

Figure 7.28 Directional power mode colourDoppler image of a neonatal brain.

Since the machine knows the depth of the tissue at every point in the 3Dimage, it adds arti!cial lighting to the rendered image so that curved sur‐faces aremore easily seen. Examples are shown in Figures 12.27 and 12.28.Volume rendering is simpler in conception. The machine collapses allthe echoes in the volume into a single 2D image as viewed from a speci!cdirection. On its own, this would produce a confused mass of echoes, soit must be modi!ed to be useful. One use of volume rendering is to cap‐ture a colour Doppler image and render the Doppler information. Tissueechoes may be completely suppressed, or they may be hidden where thecolour Doppler is displayed (see Figure 12.29). Another approach is tothreshold the grey scale image, discarding all but the strongest echoes.This can be used to produce 3D views of the fetal skeleton, for example,as shown in Figure 12.30.When a volume of tissue is rendered as a 2D image, it can be di$cult totell what is in front andwhat is behind. Themachine can therefore createa video clip where the anatomy is rotated back and forth to help the userbetter understand the depth dimension. Several images are generated,each viewing the anatomy from a di#erent angle, as shown in Figure12.31. These images are played in sequence to create a rotating display.A very simple way to view 3D echo data is known as ‘reslicing’. As in CT,the idea is that an image is generated in a plane chosen by the user (seeFigure 12.32). Generally, this is not one of the original imaging planes.Indeed, reslicing is useful precisely because it can generate images thatcould not be obtained by conventional 2D imaging.There are alternatives to rendering the volume of echo data as a single3D image. One is ‘multi-plane’ (or ‘multi-slice’) imaging, where theanatomy is displayed as a series of parallel 2D images, just as in CT andMRI (see Figure 12.33).Another is ‘orthogonal’ imaging. Images are created in three di#erentplanes, each at 90° to the other two, as shown in Figures 12.34 and 12.35.The user can move the planes around within the imaged volume to ex‐plore the patient’s anatomy. This view is widely used for imaging the fetalheart, and in transvaginal and transrectal imaging.3D imaging has become a signi!cant tool in ultrasound. It can be used toexplore complex anatomy, as mentioned above. It can also be used as acommunications tool when discussing images with people not accus‐tomed to viewing a series of 2D images and interpreting them (for exam‐ple, in discussions with patients).Another use of 3D imaging is in telemedicine. An operator in a remotelocation can acquire a volume of echo data and transmit it to a specialistfor viewing and interpretation. This approach has been used by astro‐nauts and Antarctic scientists.What are the limitations of 3D ultrasound? At present the main issue isspatial resolution (see Figure 12.36). While resolution is good withineach individual image captured by the machine, the poorer slice thick‐ness resolution becomes signi!cant whenever a 3D image is created frommultiple 2D images. Matrix probes reduce this problem since they pro‐vide better slice thickness focussing.

124 12. Additional modes and capabilities

Figure 12.24 (Top) Photograph of a mechanical3D probe. (Bo%om) Cross-section through theprobe showing a motor driving a curved arraytransducer in a rocking motion.

Figure 12.25 (Top) Photograph of a matrix 3Dprobe. (Bo%om) Matrix probes steer the beam inthe elevation plane (arrow); this causes the entirescan plane to sweep through a volume of tissue.

Figure 12.26 &e machine creates one or moreimages from a volume of echoes (shown here forsimplicity as a cube).