Summary — What This Chapter Covers
- Piezo-electric crystal: a p.d. changes its shape; a change of shape produces an e.m.f. It both makes and detects ultrasound.
- Acoustic impedance Z = ρc; reflection coefficient IR/I0 = (Z1 − Z2)2/(Z1 + Z2)2.
- Attenuation: I = I0e−μx for ultrasound and X-rays.
- X-rays: electrons hit a metal target; λmin = hc/(eV). CT combines many images into 2D slices and then a 3D image.
- PET: β+ tracer; positron–electron annihilation gives two gamma photons of 0.511 MeV in opposite directions.
1. Production and Use of Ultrasound
24.1
Echoes at boundaries
A piezo-electric crystal changes shape when a p.d. is applied across it, and generates an e.m.f. when its shape changes. An alternating p.d. at the crystal’s resonant frequency makes it vibrate, sending out ultrasound. Returning echoes make the crystal vibrate and generate an e.m.f., so the same transducer detects them. It transmits short pulses and listens between them.
At a boundary between tissues, part of the pulse is reflected. The time delay gives the depth (distance = speed × time ÷ 2), and the strength of the echo depends on the specific acoustic impedance Z = ρc of each medium. The bigger the difference in Z, the more is reflected. Air and skin are so different that almost everything reflects, so a coupling gel with Z close to skin is used. Ultrasound is also attenuated exponentially as it passes through tissue.
Ultrasound
Z = ρc IR/I0 = (Z1 − Z2)2/(Z1 + Z2)2 I = I0e−μx
Worked Example
Fat has Z = 1.38 × 106 kg m−2 s−1 and muscle 1.70 × 106 kg m−2 s−1. Find the fraction of intensity reflected at a fat–muscle boundary. An echo from it returns 65 μs after the pulse; the speed of sound is 1540 m s−1. How deep is it?
Practice Question
Ultrasound passes through 4.0 cm of tissue with attenuation coefficient 50 m−1. What fraction of the intensity remains?
2. Production and Use of X-rays
24.2
Bombardment, attenuation, CT
X-rays are produced when high-speed electrons, accelerated through a p.d. V, bombard a metal target (such as tungsten). Most of the energy becomes heat. The maximum photon energy occurs when one electron gives all its kinetic energy eV to one photon, so there is a minimum wavelength: eV = hc/λmin.
X-rays are attenuated exponentially in matter. Bone has a much larger attenuation coefficient than soft tissue, so fewer X-rays pass through it and it shows up clearly. Contrast is the difference in degree of blackening between regions; it is good when the attenuation coefficients of neighbouring tissues are very different. For soft tissues of similar μ, a contrast medium (such as barium) is used.
CT scanning: X-ray images of one section are taken from many different angles and combined by computer to give a 2D image of that section (slice). This is repeated along an axis, and the 2D images of many sections are combined into a 3D image.
X-rays
λmin = hc/(eV) I = I0e−μx
3. PET Scanning
24.3
Memorise