ULTRASOUND M Theory Any sound with a frequency above 20,000 Hz (or 20 kHz) - that is, above the highest audible frequency - is defined to be ultrasound. In practice, it is possible to create ultrasound frequencies up to more than a gigahertz. (Higher frequencies are difficult to create; furthermore, they propagate poorly because they are very strongly absorbed.) Ultrasound has a tremendous number of applications in medicine, in which it is used extensively both for diagnosis and for therapy. 176dB/C 4 Persist Of 20 OPEHSCT Fr RateSurv SonoCT XRes Skull Tumor THUMB SUCKER Frequency f (Hz) of ultrasound: f = =, here T is period of ultrasound wave 1. 2n = 2nf, here T 2. Relationship between circular frequency, period and frequency: wo = is period (sec), wo is circular frequency (rad/sec), f is frequency (Hz). 3. Wavelength of ultrasound 1 (m): 1 = Tv = , here T is period (sec); vis speed of ultrasound (m/sec), f is frequency of ultrasound (Hz). 4. Intensity of ultrasound wave I (W/m²): I = Paoºv, here wo is circular frequency (rad/sec), p is density of the medium in which ultrasound propagates (kg/m³); A is the amplitude of particles vibration in ultrasound wave (m), v is speed of ultrasound (m/sec), wo is circular frequency (rad/sec). 5. Ultrasound pressure P (Pa): P = =, here F is force (N) and A is area (m²). %3D p2 here I is intensity of 2ρν' 6. Relationship between ultrasound intensity and pressure: I = ultrasound (W/m?), P is ultrasound pressure (P), p is density of the medium in which ultrasound propagates (kg/m'); v is speed of ultrasound (m/sec). 7. Acoustic impedance Z. Reflections at boundaries between two different media occur because of differences in a characteristic known as the acoustic impedance of each substance. Impedance is defined as Z = pv, here p is density of the medium in which ultrasound propagates (kg/m³); v is speed of ultrasound (m/sec). 8. The intensity reflection coefficient r is defined as the ratio of the intensity of the reflected wave relative to the incident (transmitted) wave. This statement can be written mathematically as (Z,-Z2)? (Z,+Zz)²' boundary. where Zi and Z2 are the acoustic impedances of the two media making up the 4Z, Z2 9. The intensity transmission coefficient ß is: ß = (Z, +Z,)? 10. Relationship between a and ß: r + ß = 1 11. Attenuation of ultrasound wave in tissue. As the ultrasound beam travels through tissue layers, the intensity of the original signal becomes attenuated as the depth of penetration increases. the intensity attenuates according to the law: I = I̟e¯2ah, here Io is initial intensity of ultrasound (W/m?), a is attenuation coefficient (m'), h is penetration depth (m). 12. Sound level L (dB): L = 10lg (-), here I is intensity of sound (W/m?); Io = 10-12W/m? is threshold of hearing. vtv. 13. Doppler effect f' = vFvs The observer moves with a speed vo; the source moves with speed vs; the observer hears a frequency f", the source frequency is f, speed of sound is Speaker- microphone V. 14. Doppler-shifted ultrasound Another major use of ultrasound in medical diagnostics is to detect motion and determine velocity through the Doppler-shifted ultrasound. This technique is used to monitor fetal heartbeat, measure blood velocity, and detect occlusions in blood vessels, for example. The magnitude of the Doppler shift in an echo is directly proportional to the velocity of whatever reflects the sound. Af = f, here Af is Doppler shift in an echo or beat frequency pler shift of an echo, known registered by the detector, v is speed of ultrasound in corresponding medium, f is frequency of ultrasound emitted by the detector, v, is velocity of object that reflects ultrasound wave. 3. In physiotherapy ultrasound with frequency f = 800 kHz and intensity I = 1 W/cm is used. Find amplitude of tissue molecules vibration under the action of this ultrasound wave. The density of tissue is p = 1050 kg/m³ and speed of ultrasound propagation in the tissue v = 1500 m/sec.