Bush__The_Essential_Physics_for_Medical_Imaging - Biomedical ...

TABLE 16-4. PRESSURE AND REFLECTION COEFFICIENTS FORVARIOUS INTERFACESLiver-kidneyLiver-fatFat-muscleMuscle-boneMuscle-lungMuscle-air-0.006-0.100.120.64-0.81-0.990.000030.0110.0150.410.650.99that allows ultrasound transmission through structures such as the lung is known asan "acoustic window."When the beam is perpendicular to the tissue boundary, the sound is returnedback to the transducer as an echo. As sound travels from a medium of lower acousticimpedance into a medium of higher acoustic impedance, the reflected wave experiencesa ISO-degree phase shift in pressure amplitude (note the negative sign onsome of the pressure amplitude values in Table 16-4).The above discussion assumes a "smooth" boundary between tissues, where thewavelength of the ultrasound beam is much greater than the structural variations ofthe boundary. With higher frequency ultrasound beams, the wavelength becomessmaller, and the boundary no longer appears smooth relative to the wavelength. Inthis case, returning echoes are diffusely scattered throughout the medium, and onlya small fraction of the incident intensity returns to the source (the ultrasound transducer,as described below).For nonperpendicular incidence at an angle 8 i (Fig. 16-5B,C), the ultrasoundenergy is reflected at an angle 8r equal to the incident angle, 8i = 8 r • Echoes aredirected away from the source of ultrasound, causing loss of the returning signalfrom the boundary.Refraction describes the change in direction of the transmitted ultrasound energy ata tissue boundary when the beam is not perpendicular to the boundary. Ultrasoundfrequency does not change when propagating into the next tissue, but a change inthe speed of sound may occur. Angles of incidence, reflection, and transmission aremeasured relative to the normal incidence on the boundary (Fig. 16-5B,C). Theangle of refraction (8r) is determined by the change in the speed of sound thatoccurs at the boundary, and is related to the angle of incidence (8D by Snell's law:sin8rsin8 i = ~where 8i and 8, are the incident and transmitted angles, C] and C2 are the speeds ofsound in medium 1 and 2, and medium 2 carries the transmitted ultrasound energy.For small angles of incidence and transmission, Snell's law can be approximated asC2~= C28iCl