Chapter 12:Physics of Ultrasound - Human Health Campus

1 IAEAI nternational Atomic Energy AgencySlide set of 54 slides based on the Chapter authored Lacefieldof the IAEA publication (ISBN 978-92-0-131010-1):Diagnostic Radiology Physics: A Handbook for Teachers and StudentsObjective:To familiarize students with Physics or Ultrasound , commonly used in diagnostic imaging 12:Physics of UltrasoundSlide set preparedby (S. Paulo, Brazil, Institute of Physics of S. Paulo University) . Introduction . Ultrasonic Plane . Ultrasonic Properties of Biological . Ultrasonic . Doppler . Biological Effects of UltrasoundChapter OF CONTENTSD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12, INTRODUCTIOND iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12,3 Ultrasoundis an acoustic wave with frequencies greater than the maximum frequency audible to humans, which is 20 kHz Ultrasoundis the most commonly used diagnostic imaging modality, accounting for approximately 25% of all imaging examinations performed worldwide nowadaysIAEAD iagnostic Radiology Physics.

2 A Handbook for Teachers and Students Chapter 12, INTRODUCTION Diagnostic imagingis generally performed using Ultrasound in the frequency range from2 to 15 MHz The choice of frequencyis dictated by a trade-off between spatial resolutionand penetration depth, since higher frequency waves can be focused more tightly but are attenuated more rapidly by tissueThe information in an ultrasonic imageis influenced by the physical processesunderlying propagation, reflection and attenuation of Ultrasound waves in INTRODUCTIOND iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12,5 Attractive characteristics: relatively low cost portability of an Ultrasound scanner the non-ionizing nature of Ultrasound waves the ability to produce real-time images of blood flowand moving structures such as the beating heart the intrinsic contrast among soft tissue structures thatis achieved without the need for an injected INTRODUCTIOND iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12,6 Ultrasoundhas a wide range of medical applications: cardiac and vascular imaging imaging of the abdominal organs in uteroimaging of the developing fetus Ongoing technological improvements continue to expand the use of Ultrasound for many applications: cancer imaging musculoskeletal imaging ophthalmology ULTRASONIC PLANE WAVESD iagnostic Radiology Physics.

3 A Handbook for Teachers and Students Chapter 12,7 Anacoustic waveis atravelingpressure disturbancethat produces alternating compressions rarefactions(expansions) of the propagationmediumThe compressionsand rarefactionsdisplace incremental volumes of the medium and the wave propagates via transfer of momentum among incremental volumes Each incremental volume of the medium undergoes small oscillations about its original position but does not travelwith the pressure disturbanceIAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12, ULTRASONIC PLANE One-Dimensional Ultrasonic WavesA pressure plane wave, p (x,t), propagating along one spatial dimension, x, through a homogeneous, non-attenuating fluid medium can be formulated starting from Euler s equation and the equation of continuity:( )( )0,,= + txuttxpxo ( )( )0,1,= + txuxtxpt ois the undisturbed mass density of the medium is the compressibility of the medium ( , the fractional change in volume perunit pressure in units of Pa 1)u(x,t) is the particle velocity produced by the waveIAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12,9( )( )0,,= + txuttxpxo ( )( )0,1,= + txuxtxpt ULTRASONIC PLANE One-Dimensional Ultrasonic WavesEuler s equation, which can be derived starting from Newton s second law of motion:Equation of continuity, which can be derived by writing a mass balance for an inc remental volume of the medium:( )( )0,1,22222= txptctxpxAcoustic wave equation is obtained, combining both equations : oc1=is the speed of soundA monochromatic plane wave solution is.

4 ()()kxtPtxp = cos,Pis the amplitude of the wave = 2 fis the radian frequencyk= 2 / is the wave numberIAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12, ULTRASONIC PLANE Acoustic Pressure and IntensityThe strength of an Ultrasound wave can also be characterizedby itsintensity,I,which is theaverage power per unit cross-sectional areacPI0222)m/W( =Pis the pressure amplitude of the wave; ois the undisturbed mass density of the medium; cis the speed of soundDiagnostic imaging is typically performed using peak pressures in the range MPaWhen the acoustic intensity IdBis expressed indecibels, dB:()refdBIIIlog10)dB(=Irefis the reference intensitytSEI =evaluated over a surface perpendicular to the propagation direction. For acoustic plane waves, the intensity is related to the pressure amplitude by:IAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12, ULTRASONIC PLANE Reflection and TransmissionAn Ultrasound imagedisplays the magnitude (absolute value of amplitude) of Ultrasound echoes, so a physical understanding of acoustic wave reflectionis valuable for interpreting the images angle of incidence r angle of reflection tangle of transmissionat a planar interface between a material with sound speed c1and a second material with a higher sound speed c2Z is the acoustic impedanceFor plane wave: oocZ== ois the undisturbed mass density ofthe medium cis the speed of soundis the compressibility of the medium IAEAD iagnostic Radiology Physics.

5 A Handbook for Teachers and Students Chapter 12, ULTRASONIC PLANE Reflection and TransmissionAcoustic version of Snell s lawir =itcc sinsin12=A plane wave traveling in a semi-infinite half-space that is incident upon a planar interface with a second semi-infinite half-spaceThewave transmittedinto thesecondmediumisbent toward the normalifc1>c2andaway fromthe normalifc1<c2 This change in direction is termed refractionand can be an important source of artifacts in some clinical imaging applicationsThe limiting case of refractionoccurs when c2> c1and i> arcsin(c1/c2), in which case tis imaginaryand the wave istotally reflectedIAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12, ULTRASONIC PLANE Reflection and TransmissionTheamplitudesof theincidentandreflectedwaves (PiandPr,respectively) are related by thereflection coefficient,R.

6 For planewaves in fluid media, thereflection coefficientis given by:titiirZZZZPPR coscoscoscos1212+ ==A reflectionis produced when an acoustic wave encounters a difference in acoustic impedance, so an Ultrasound imagemay be thought of as a map of the relative variations in acoustic impedance in the tissues 1 R 1 Anegative valueofRimplies that thereflected wave is inverted with respect tothe incident waveZ is the acoustic impedanceFor plane wave: oocZ==IAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12,14()() > < +== 2112121121122sin and 0 sinor coscoscos2cc cccc ccZZZPPT iitiiit ULTRASONIC PLANE Reflection and TransmissionThe amplitudesof the incidentand transmittedwaves (PiandPt, respectively) are related by the transmission coefficient,T.

7 For plane waves in fluid media, the transmission coefficientis given by:In case ofnormal incidence: i= t= 012121212coscoscoscosZZZZZZZZPPR titiir+ =+ == ()() > <= +=+== 2112121121122122sin and 0 0 sinor Z2 Zcoscoscos2cc cccc ccZZZZPPT iitiiit IAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12, ULTRASONIC PLANE AttenuationAttenuation of ultrasonic waves in a medium is due to: specular reflections divergence scattering from inhomogeneities thermal absorption:is the most significant source of attenuationin diagnostic Ultrasound ()()kxtPtxp = cos,Monochromatic plane wave equation()()kxtPetxpx = cos,with attenuationPis the amplitude of the wave = 2 fis the radian frequencyk= 2 / is the wave number (Np/m ) is the frequency-dependent amplitude attenuation coefficientIAEAD iagnostic Radiology Physics.

8 A Handbook for Teachers and Students Chapter 12, ULTRASONIC PLANE Attenuation()()kxtPtxp = cos,Monochromatic plane wave equation (Np/m ) is the frequency-dependent amplitude attenuation coefficient Np=Neper (1Np dB)In soft tissues is proportional to fm, where 1 <m< 2 For most applications of diagnostic ultrasoundm 1()()kxtPetxpx = cos,with attenuationThe primary consequence of frequency-dependent attenuation is that higher frequency wavesare attenuated more rapidlythan lower frequency waves and thus yield shallower penetration depths for imagingIAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12, ULTRASONIC PROPERTIES OF BIOLOGICAL sound speed, acoustic impedance, and attenuation coefficientAcoustic properties from Zagzebski (1996) and Shung (2006)Material sound speed (m/s)Air330 Water1480 Fat1450-1460 Liver1555-1570 Blood1550-1560 Muscle1550-1600 Skull bone 3360-4080 sound speeds highest : in solids lowest : in gasesSound speed in soft tissuesis similarto the sound speed in waterat body temperatureThis similarity between water and soft tissue holds for most acoustic properties and justifies the use of equationsfor fluid media to analyze wave propagation in biomedical ultrasoundAcoustic Properties of Selected MaterialsIAEAD iagnostic Radiology Physics.

9 A Handbook for Teachers and Students Chapter 12,18 Acoustic properties from Zagzebski (1996) and Shung (2006).MaterialAcoustic Impedance(MRayl) Properties of Selected MaterialsUnit of acoustic impedance ZMRayl1 M = 1061 Rayl = 1 Pa s ULTRASONIC PROPERTIES OF BIOLOGICAL sound speed, acoustic impedance, and attenuation coefficientAcoustic impedances high values : of solids intermediate values: ofliquids and soft tissues low values: of gasesIAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12,19 MaterialAttenuation Coefficient(dB/cm at 1 MHz) coefficientsof biological tissues are usually reported in dB/(cm MHz)The conversion between Np and dB is: 1 Np dBAcoustic properties from Zagzebski (1996) and Shung (2006).Acoustic Properties of Selected ULTRASONIC PROPERTIES OF BIOLOGICAL sound speed, acoustic impedance, and attenuation coefficientIAEAD iagnostic Radiology Physics.

10 A Handbook for Teachers and Students Chapter 12, ULTRASONIC PROPERTIES OF BIOLOGICAL ScatteringSimilar to the mechanism of specular(mirror-like) reflection, scatteringoccurs when an ultrasonic wave encounters a variation in the acoustic impedanceof the medium Scatteringoccurs when the wave encounters features with dimensions similar to or smallerthan the wavelength Scattered echoesare omnidirectional and are significantly weaker than specular reflections Constructive and destructiveinterference of echoes scattered backward from cellular-scale tissue features to the transducer are the source of the speckletexture that dominates the internal appearance of organs in Ultrasound images IAEAD iagnostic Radiology Physics: a Handbook for Teachers and Students Chapter 12, ULTRASONIC PROPERTIES OF BIOLOGICAL Nonlinear Propagation This effect is negligible at lowacoustic intensities However,near the focusof beams used fordiagnosticimagingthedensity variationsproduced by the wavebecomesignificantsuch that thecompressive phaseofthe wave propagates at ahigher velocitythan therarefactional phaseof the waveNonlinearityarises inacoustic propagationbecause thepressure wave alters the density ofthe mediumand thesoundspeeddepends ondensityaccordingto 1=cIAEAD iagnostic Radiology Physics.