Report

Title Elementary Principles • • • • • • • • What is sound and how is it produced? Audible sound vs. ultrasound Waves, “wavelength” Pressure, intensity, power Frequency and period Acoustic impedance Reflection Review metrics Production of sound “Clink” “Clink” “Clink” Particle vibrations Talking Air vibrations Voice box Ear drum Sound • A mechanical disturbance propagating through a medium – Mechanical: particle motion is involved – Particle vibrations – Energy is transmitted through the medium – Particles themselves do not propagate through the medium. Bell Jar Experiment Generation of ultrasound Piezoelectric ‘element’ Generation of ultrasound Piezoelectric ‘element’ (vibrates when driven with an electrical signal) Sound travels in “waves” • A wave is an oscillating disturbance that travels through a medium • Many forms of energy travel in waves • Sound travels as a wave Two Types of Waves Mechanical Electromagnetic ocean waves radio waves seismic waves x-rays sound waves light waves Mechanical Waves: • characterized by physical motion of particles in the medium • cannot travel through a vacuum • (Electromagnetic waves CAN travel through a vacuum.) Longitudinal Particle motion (vibration) parallel to direction of wave travel Particle motion (vibration) perpendicular to direction of wave trav Picture of slinky • “Compressional (or longitudinal) wave traveling along a slinky • Simply snap one end back and forth • Transverse wave obtained by jerking up and down Ultrasound waves in tissue • Sound waves used for medical diagnosis are LONGITUDINAL. • Transverse waves are not involved at all (at least not until recently … “supersonic imaging” and ARFI imaging involve transverse waves, though these are not produced by the transducer). Other types of elasticity imaging • Acoustic radiation force imaging (ARFI) – Tissue displacement created by energetic acoustic pulses from the transducer • SuperSonic Shear wave Imaging – Energetic pulse • =>shear wave • Create shock front – High speed imaging • Tracks shear wave – Reconstruct speed • Related to elasticity US Innovations, Advances RSNA 2008 (Supersonic Imagine white paper, Jeremy Bercoff www.supersonicimagine.fr) Compression and rarefaction Continuous Transmission Schlieren Photography Water Light beam This is a way to view sound waves. The compressions and rarefactions disturb light propagating through the beam. One can view these disturbances. Compression and rarefaction Compression: density is higher than normal Rarefaction: density is lower than normal Compression and rarefaction Pulsed Transmission Pressure amplitude Amplitude Amplitude: measure of the amount of change of a time varying quantity. Pressure amplitude • pascals (Pa) – 1 Pa = 1N/m2 • megapascals (MPa) (mega = 1,000,000) • Other units – Pounds/square inch (32 lb/in2 ~ 220 kPa) (kilo = 1,000) – mm of mercury (blood pressure) – cm of water PSI kPa 30 207 35 240 40 280 45 310 Pressure of the atmosphere • pascals (Pa) • megapascals (MPa) (mega = 1,000,000) • Other units – Pounds/square inch (32 lb/in2 ~ 250 kPa) (kilo = 1,000) – mm of mercury (blood pressure) – cm of water Ways we describe amplitude • High vs. low • Loud vs. soft • Strong echoes vs. weak echoes • Bright dots vs. dim dots Ways we describe amplitude • High vs. low • Loud vs. soft • Strong echoes vs. weak echoes • Bright dots vs. dim dots Frequency • Number of oscillations per second – By the source – By the particles • Called “pitch” for audible sounds • Expressed in hertz (Hz) – 1 Hz = 1 cycle/s – 1 kHz = 1,000 cycles/s – 1 MHz = 1,000,000 cycles/s Frequency • Number of oscillations per second – By the source – By the particles • Called “pitch” for audible sounds • Expressed in hertz (Hz) – 1 Hz = 1 cycle/s – 1 kHz = 1,000 cycles/s = 103 cycles/s – 1 MHz = 1,000,000 cycles/s = 106 cycles/s – 2.5 MHz = 2,500,000 cycles/s = 2.5 x 106 cycles/s – 7.5 MHz = 7,500,000 cycles/s = 7.5 x 106 cycles/s Frequency Supersonic vs. Ultrasonic • Supersonic = faster that sound • Ultrasonic = sound whose frequency is above the audible (greater than 20 kHz) Pressure amplitude Amplitude Amplitude: measure of the amount of change of a time varying quantity. WaveT Period Distance Pressure vs. distance at two different times. Wave motion at a specific point in space. The wave variable (pressure in this case) varies over time. Period = time for 1 cycle. Period vs. frequency period period Wave Period T • Amount of time for 1 cycle • Equal to the inverse of the frequency 1 T f • What is the period for a 10 Hz wave? Wave Period T • Amount of time for 1 cycle • Equal to the inverse of the frequency 1 1 1 T s f 10 / s 10 • What is the period for a 10 Hz wave? Wave Period T • Amount of time for 1 cycle • Equal to the inverse of the frequency 1 T f 1 1 1 f 100/ s 100Hz T 0.01s 1 / 100s • If the period is 0.01 s, what is the frequency? Dividing fractions • To divide 1 fraction (1/2) by another (1/4) – Invert the denominator – Multiply the numerator by the inverted denominator 1 2 1 4 4 2 2 1 2 1 4 Wave Period T • Amount of time for 1 cycle • Equal to the inverse of the frequency 1 T f Frequency Period 1,000 Hz 1 ms 1 MHz 1 ms 10 MHz 0.1 ms Metric System Unit Prefixes Prefix Meaning Symbol Example micro 10-6 m mm (micrograms) milli 10-3 m mm (millimeters) centi 10-2 c cm (centimeters) deci 10-1 d dB (decibel) kilo 103 k km (kilograms) Mega 106 M MHz Please note: the sound emitted from your 3.5 MHz transducer is 3.5 MHz, not 3.5 mHz or 3.5 mhz! Wave Period T • Amount of time for 1 cycle • Equal to the inverse of the frequency 1 T f Frequency Period 1,000 Hz 1 ms Period expressed as a fraction 1/1,000 s 1 MHz 1 ms 1/1,000,000 s 10 MHz 0.1 ms 1/10,000,000 s Wavelength Pressure fluctuations l • Wavelength is the distance between any two corresponding points on the waveform. Wavelength vs. frequency • As frequency increases, wavelength decreases. • Wavelength is inversely proportional to frequency. • If you double the frequency, the wavelength is halved. • If you triple the frequency, wavelength is cut to 1/3 of the original. Wavelength depends on speed of sound and Frequency c sound speed l f frequency Wavelength is “directly proportional” to sound speed. (For a given frequency, if 1 medium’s sound speed is 2 times that of another, the wavelength for any frequency will also be two times that of the other.) Suppose the speed of sound is 330 m/s. For a 1 kHz sound wave, what is the wavelength? c 330m/s 330m/s l s/c .33 m f 1,000c/s 1,000 Suppose the speed of sound is 330 m/s. For a 1 kHz sound wave, what is the wavelength? c 330m/s 330m/s l s .33 m f 1,000/s 1,000 Suppose the speed of sound is 330 m/s. For a 1 kHz sound wave, what is the wavelength? c 330m/s 330m/s l s .33 m f 1,000/s 1,000 The average speed of sound in soft tissue is 1,540 m/s. What is the wavelength for a 3 MHz sound beam? c 1540m/s l 0.000513m 0.513mm f 3,000,000/s The average speed of sound in soft tissue is 1,540 m/s. What is the wavelength for a 3 MHz sound beam? c 1540m/s l 0.000513m 0.513mm f 3,000,000/s 1 meter=1,000 millimeters; 1 mm = 0.001 m c 1540m/s 1,540,000m m/s l .513mm f 3,000,000/s 3,000,000/ s When the speed of sound is 1,540 m/s, and frequency is expressed in MHz: 1,540m/s 1,540,000mm/s The frequency is “F” MHz = F,000,000 /s where F may be 3, 5, 7.5, etc, then c 1,540,000mm/s 1.54mm l f F,000,000/s F (MHz) Wavelength vs. Frequency For soft tissue, c=1,540 m/s lsoft tissue 1.54mm F(MHz) 1 MHz has a 1.54 mm wavelength 2 MHz has a ? mm wavelength. Typical Wavelengths F 2 MHz 2.5 MHz 5 MHz 7.5 MHz 10 MHz Wavelength (l) 0.72 mm 0.62 mm 0.31 mm 0.21 mm 0.15 mm In medical ultrasound, wavelengths usually are less than a mm Power • Rate at which energy comes out of the transducer • Includes energy throughout the beam • Units are in watts (W) • Typical values – 10 mW – 80 mW Intensity Units are mW/cm2 W/m2 Relationship Between Intensity and Amplitude • Intensity, I is proportional to the amplitude squared I A2 – if A is “1” I is 1 – if A is “2” I is 4 – if A is “3” I is 9, etc Relationship Between Intensity and Acoustic Pressure Amplitude • Under “ideal” conditions (large distance from the source; no reflectors around) Intensity, I is given by: 2 P I 2 rc – P is the pressure amplitude (Pascals) – – – r is the density in the medium (kg/m3) c is the speed of sound (m/s) I is expressed in W/m2 Propagation Of Ultrasound Through Tissue Speed, attenuation, reflection, refraction, scatter Speed of Sound • Determined by properties of the medium – Stiffness – Density • Not determined by the source of sound c B r B=“Bulk modulus” (stiffness) r=“density” (grams/cm3) (kilograms/m3) c=speed of sound (m/s) Relative Speed of Sound • Solids • Liquids • Gases (ie, air) fast intermediate slow Speed of Sound Tissue Air Fat Water Liver Blood Muscle Skull bone Speed of sound (m/s) 330 1460 1480 1555 1560 1600 4080 Speed of Sound Tissue Air Fat Water Liver Blood Muscle Skull bone Speed of sound (m/s) 330 1460 1480 1555 1560 1600 4080 Note, the range of speeds at which sound travels in various soft tissues (that do not contain air) is narrow. Speed of Sound • The average speed of sound in soft tissue is taken to be 1540 m/s. • This value is assumed in the calibration of scanners. • Scanners now have controls that allow the sonographer to select alternative values Acoustic Impedance (Z) • Important in reflection • A property of the tissue • Given by the speed of sound (c) times the density r Z rc • Unit is the rayl, 1 rayl = 1 kg/m2s Suppose the density of liver is 1.061g/cm3. If the speed of sound is 1,555 m/s, what is the acoustical impedance of liver? z rc 1.061g / cm 1,555m/s 3 z 1,061kg/ m 1,555m/s 3 kg m z 1649 10 3 (or kg / m 2s) m s z 1649 106 kg / m 2s 6 Suppose the density of liver is 1.061g/cm3. If the speed of sound is 1,555 m/s, what is the acoustical impedance of liver? z rc 1.061g / cm 1,555m/s 3 z 1,061kg/ m 1,555m/s 3 kg m 2 z1 g/cm 1649 10 (or kg / m s) 3 = 1,000g/1,000cm 3 3 = 1,000kg/1,000,000cm3 = 1,000kg/m3 m s 6 2 z 1649 10 kg / m s 1cm 6 1m=100cm 1m x 1m x 1m = 100cm x 100cm x 100cm =1,000,000cm3 1m Suppose the density of liver is 1.061g/cm3. If the speed of sound is 1,555 m/s, what is the acoustical impedance of liver? z rc 1.061g / cm 1,555m/s 3 z 1,061kg/ m 1,555m/s 3 kg m z 1.64910 3 (or kg / m 2s) m s z 1.649106 kg / m 2s 6 John William Strutt “Lord Rayleigh” (1842-1919) • Unit is the rayl, 1 rayl = 1 kg/m2s • If the density doubles, the impedance doubles • If the Speed of sound doubles, the impedance doubles Acoustic Impedance Tissue Air Fat Water Liver Blood Muscle Skull bone Impedance (Rayls)) 0.004 x 106 1.34 x 106 1.48 x 106 1.65 x 106 1.65 x 106 1.71 x 106 7.8 x 106 Acoustic Impedance Tissue Air Fat Water Liver Blood Muscle Skull bone Impedance (Rayls)) 0.004 x 106 1.34 x 106 1.48 x 106 1.65 x 106 1.65 x 106 1.71 x 106 7.8 x 106 Note, the range of impedances of soft tissues (that do not contain air) is relatively narrow. Ways we describe amplitude • High vs. low • Loud vs. soft • Strong echoes vs. weak echoes • Bright dots vs. dim dots Reflection • Partial reflection of a sound beam occurs at tissue interfaces. • Interfaces are formed by tissues that have different impedances. • Examples: – Muscle-to-fat – Bone-to muscle – Red blood cell-to-plasma Reflection Types of Reflectors • Specular – Large – Smooth • Diffuse reflecting interface – Echoes travel in all directions • Scatter – Small interfaces – Scattered echoes travel in different directions. Reflection Coefficient, R R is the ratio of the amplitude reflected to the incident amplitude. The greater R is, the more sound gets reflected, and the higher is the amplitude. Also, the greater R is, the less gets transmitted to deeper tissues. Z 2 Z1 R Z 2 Z1 Impedance Mismatch Another way to express “Z2 – Z1” • Small mismatch – Weak echo – Most sound gets transmitted through • Large mismatch – Strong echo – Less sound gets transmitted through Compute the reflection coefficient for an interface formed by muscle and air. (Sound is traveling through muscle and encounters an air interface) Z 2 Z1 0.0004106 1.7 106 0.0004 1.7 R .99 6 6 Z 2 Z1 0.000410 1.7 10 0.0004 1.7 Amplitude Reflection Coefficients Muscle-liver Fat-muscle Muscle-bone Muscle-air .02 .1 .64 .99 Note, the reflection coefficient between soft tissues is relatively weak; reflection at interfaces between soft tissue and bone is much stronger. Reflection at interfaces between tissue and air approaches 100%. Tissue-to-air interface This is why we have to use coupling gel on the patient! Nonperpendicular beam incidence Reflected beam does not travel back to transducer For a perfectly smooth interface, qr = qi Nonperpendicular beam incidence Reflected beam does not travel back to transducer Echo amplitude depends strongly on the orientation of the beam with respect to the interface! Nonperpendicular beam incidence Reflected beam does not travel back to transducer Echo amplitude depends strongly on the oprientation of the beam with respect to the interface! Assignment: bring in examples of echo amplitudes that vary with angle of incidence. Signal Effects The transducer serves both as the transmitter and echo detector. Specular reflector Diffuse reflector Fetal skull only partially outlined because of unfavorable incident angle. “Specular Highlight” is a term being coined to describe this situation. Refraction in water Conditions for Refraction •Beam is incident obliquely •Sound speeds are different Snell’s Law Sine of an angle angle A Compute the refracted angle if the incident beam is propagating through muscle and the transmitted beam is through fat. The incident beam angle is 30 degrees. c2 1460m / s sin(q t ) sin(q i ) sin(30) c1 1600m / s1 1460m / s sin(q t ) 0.5 0.45625 1600m / s1 qi So, the angle whose sin is 0.45626 is found using qt arcsin(0.45625) 27.1degrees qt Change (2.9 degrees) Change in Beam Direction for 30o angle of incidence at a tissue interface • • • • Bone-soft tissue Muscle-fat Muscle-fluid Muscle-blood 19.1o 2.9o 1.2o 0.8o Refraction is strongest at interfaces where there are large changes in the speed of sound. Scatter can be called multi-directional reflection. Diffuse Reflector Scatterer Scattering of ultrasound Scatter can be called multi-directional reflection. Diffuse Reflector Scatterer Gray Scale Image Lung/liver easily differentiated because of differences in scattering levels “Echogenic” • Tendency of a tissue to produce echoes, usually from scattering • Terms – Echogenic – Hypoechoic – Hyperechoic – Anechoic – isoechoic Angle Effects Diffuse Reflector Image contrasting specular vs scattering Diffuse reflector? Likely, most interfaces have some degree of surface roughness. Presents a bit of a diffuse surface. Echoes from diaphragm highly dependent on orientation Echoes from liver are not. Rayleigh Scattering • Objects much smaller than the wavelength • Scattering varies with the fourth power of the frequency (I a f4) – Doubling the frequency increases the scattered signal intensity by 24 = 2 x 2 x 2 x 2 = 16! Rayleigh Scattering (blood) • Objects much smaller than the wavelength • RBC’s are about 8 micrometers in diameter • They are considered Rayleigh scatterers in medical ultrasound 10 mm 100 mm; wavelength for 15.4 MHz ultrasound Attenuation Causes of Attenuation • Reflection and scatter at interfaces – Very small contribution within organs – Can be significant at calcifications, stones • Absorption – Beam energy converted to heat – Diagnostic beams usually cause negligible heating Attenuation The Attenuation Coefficient (Amount of attenuation per unit distance) Units are dB/cm Decibels • Units that allow one to compare the intensity or amplitude of one signal relative to that of another. • (The loudness level of audible sounds often is given in decibels.) Decibels • To express the relationship between two intensities, I2 and I1, in dB, dB = 10 log(I2 /I1 ) – Take ratio – Take the log of the ratio – Multiply by 10 Decibels • Example, let I2 be 100 I1 • dB = 10 log(I2 / I1) • dB = 10 log(100/1) • dB = 10 log(100) = 10 x 2 = 20 • When the intensity is increased by 20 dB, it is increased by 100 times! Amplitude ratio A2/A1 1 1.414 2 4 10 100 1000 1/ 2 1/ 10 1/ 100 Log A2/A1 dB 0 0.15 0.3 0.6 1 2 3 0.3 1 2 0 3 6 12 20 40 60 6 20 40 Intensity ratio I2/I1 Log I2/I1 1 0 2 0.3 4 0.6 16 1.2 100 2 10,000 4 1,000,000 6 1/ 0.6 4 1/ 2 100 1/ 4 10,000 Attenuation The Attenuation Coefficient (Amount of attenuation per unit distance) Units are dB/cm Typical attenuation coefficients (dB/cm) • • • • • • Water Blood Liver Muscle Skull bone Lung 0.002 dB/cm 0.18 0.5 1.2 20 41 Values are at 1 MHz Adult Liver 4 MHz 7 MHz Dependence on Frequency Frequency Dependence (liver) •1 MHz •2 MHz •4 MHz 0.5 dB/cm 1.0 dB/cm 2.0 dB/cm To find the attenuation at a given frequency, use simple ratios. Calculate attenuation Calculate attenuation • • • • If a 3 MHz ultrasound beam travels through 5 cm of muscle, how much is the beam attenuated? (The AC of muscle at 1 MHz is 1.2 dB/cm) First, determine the attenuation coefficient at 3 MHz. It is 3/1 x 1.2 dB/cm, or 3.6 dB/cm. Then, the total attenuation is just the AC times the distance, or Attenuation = 3.6 dB/cm x 5 cm = 18 dB Attenuation terms: “attenuating” Attenuation terms: Enhancement Attenuation terms: Shadowing Units commonly used in ultrasound Quantity Unit Abbreviation Length Area meter, m, cm centimeter square meters m2 Volume cubic meters m3 Time seconds s period seconds s Units commonly used in ultrasound Quantity Unit Abbreviation mass gram g speed meter per second m/s frequency cycles per second s-1 (Hz) power watts intensity Watts per square W/cm2 centimeter W