24.1a Ultrasound: production and pulse-echo imaging
Definitions
Ultrasound longitudinal (sound) waves with frequency above the upper limit of human hearing, about 20 kHz.
Piezoelectric effect a p.d. applied across certain crystals (e.g. quartz) makes them change shape; conversely, deforming the crystal produces a p.d.
Transducer a device that converts energy from one form to another; here it both emits and receives ultrasound. Key points Production : an alternating p.d. makes the piezoelectric crystal vibrate; at its resonant frequency the amplitude is largest.Detection : a returning echo makes the crystal vibrate, generating a small alternating p.d.The same transducer sends a short pulse , then listens for echoes before the next pulse. Echoes come from boundaries between tissues; the time delay gives the depth of each boundary. Medical ultrasound uses about 1 to 10 MHz : short wavelength gives fine detail. Safe (non-ionising); good for soft tissue and a fetus, poor through bone or air.
transducer
gel
pulse
echo
boundary
d
Pulse-echo: the transducer emits a pulse, part reflects at each boundary, and the echo time gives the depth d = ½ct.
p.d. t
pulse
echo 1
echo 2
t
Echo display (A-scan): time between the transmitted pulse and each echo gives the depth of each boundary.
Watch out! The echo goes there and back : d = ½ct, not ct. The crystal emits at its resonant frequency; the pulse must end before the echo returns.
24.1b Acoustic impedance, reflection and attenuation
Definitions
Specific acoustic impedance (Z) the product of the density of a medium and the speed of sound in it: Z = ρc.
Intensity reflection coefficient the ratio of the reflected intensity to the incident intensity at a boundary.
Attenuation the gradual decrease in intensity of a beam as it passes through a medium (by absorption and scattering).
Linear attenuation coefficient (μ) the constant in I = I0 e-μx : the fractional decrease in intensity per unit thickness. Key points Reflection at a boundary depends on the difference in Z : big difference, strong reflection. Soft tissue to soft tissue: small difference, weak echo, most passes on to deeper boundaries. Air-skin: huge difference, nearly total reflection , so coupling gel (Z close to skin) removes the air gap. Intensity falls exponentially with depth; higher frequency attenuates more, so trade detail against depth. Echoes from deep boundaries are weaker: they suffer attenuation both ways and partial reflection at each boundary. Equations Z = ρc
specific acoustic impedance
kg m-2 s-1
IR /I0 = (Z2 - Z1 )2 / (Z2 + Z1 )2
intensity reflection coefficient
no unit
I = I0 e-μx
attenuation through thickness x
W m-2
Z₁ = ρ₁c₁
Z₂ = ρ₂c₂
incident I₀
reflected IR
transmitted
At a boundary the incident intensity splits into reflected and transmitted parts; IR depends on (Z2 - Z1 )2 .
I x
I₀
small μ
large μ
Attenuation: intensity falls exponentially with thickness x; larger μ gives a steeper fall.
Watch out! Use Z values, not densities alone, in the reflection coefficient; the difference is squared . Gel is needed because air-skin reflects almost everything, not because gel "conducts" sound better.
24.2a Production of X-rays
Definitions
X-rays high-energy (short-wavelength) electromagnetic radiation produced when high-speed electrons are decelerated by a metal target.
Braking radiation (bremsstrahlung) the continuous spectrum of X-rays emitted as electrons decelerate in the target. Key points Electrons from a heated cathode (thermionic emission) are accelerated through a large p.d. (tens of kV) to a metal anode target (e.g. tungsten). Only about 1% of the electron energy becomes X-rays; the rest heats the target, so it is cooled (rotating anode, oil, high melting point metal). The spectrum is continuous up to a maximum photon energy, with characteristic lines from inner-shell electron transitions in the target. Maximum photon energy = eV, when an electron loses all its KE in one interaction: this sets λmin . Higher tube p.d.: smaller λmin , more penetrating (harder ) X-rays. Higher tube current: more X-rays (greater intensity). An aluminium filter removes low-energy X-rays that would only be absorbed by the skin.
heated cathode
tungsten target
electrons
X-rays
vacuum
+ (kV)
X-ray tube: electrons from the heated cathode hit the tungsten target and X-rays leave through a window.
intensity λ
λmin
characteristic lines
continuous
X-ray spectrum: continuous braking radiation from λmin = hc/eV, with sharp characteristic lines of the target metal.
Watch out! Tube p.d. sets the shortest wavelength (maximum energy); tube current sets intensity, not λmin . Characteristic line positions depend on the target metal , not on the p.d.
24.2b X-ray imaging, contrast and CT scanning
Definitions
Contrast the difference in degree of blackening between neighbouring regions of an image (between structures).
CT scan (computed tomography) X-ray images of many thin slices, taken from many different directions, combined by computer to build a three-dimensional image. Key points Image = X-ray shadow : bone attenuates strongly (large μ), soft tissue weakly. Good contrast needs very different μ values; soft tissues give poor contrast. Contrast media (barium meal, iodine) have large μ to show soft organs such as the gut or blood vessels. Sharpness improves with a small source (focal spot) and a collimated beam. CT : tube and detectors rotate round the patient; each slice is built from many 1-D projections, then slices stack into a 3-D image.CT gives 3-D detail and better soft-tissue contrast, but a much larger radiation dose . X-rays are ionising : keep doses as low as possible.
I / I₀ x
1
soft tissue
bone
contrast
Bone has a much larger μ than soft tissue, so far less X-ray gets through: the difference gives contrast.
patient
X-ray tube
detectors
rotates
CT: the X-ray tube and opposite detector array rotate around the patient, recording one slice from many angles.
Watch out! Contrast depends on the difference in μ, not on μ itself. CT is not one X-ray photo: it reconstructs slices from many angles, giving 3-D information.
24.3 PET scanning
Definitions
Tracer a substance containing a radioactive nuclide that is introduced into the body and absorbed by the tissue being studied.
Annihilation the process in which a particle and its antiparticle (e.g. an electron and a positron) meet and their total mass-energy is converted into photons.
PET scanning positron emission tomography: imaging the distribution of a β+ -emitting tracer by detecting pairs of gamma photons from annihilation. Key points Tracer (e.g. fluorine-18 in a glucose analogue) collects where metabolic activity is high (e.g. tumours, active brain regions). The nuclide decays by β+ emission ; the positron travels ~1 mm, then annihilates with an electron. Two gamma photons leave in opposite directions (momentum conserved, initial momentum ~0). Each photon has energy = rest energy of an electron = 0.511 MeV (kinetic energies negligible). A ring of detectors records photons arriving at the same time ; the annihilation lies on the line joining the two detectors. Arrival-time difference fixes the point on that line; many events build a 3-D image of tracer concentration. PET shows function (metabolism), not just structure; often combined with CT.
γ γ
annihilation
detector ring
PET: an annihilation sends two 0.511 MeV gamma photons back-to-back to detectors on the ring; the line between them passes through the source.
e⁺
e⁻
γ 0.511 MeV
γ 0.511 MeV
momentum before ≈ 0
Positron-electron annihilation: mass converts to two photons of equal energy moving in opposite directions.
Watch out! The two photons go in opposite directions (180° apart); that is what places the source on a line. Photon energy is 0.511 MeV each (not 1.02 MeV each): the pair shares 2me c2 . The patient receives β+ -emitting tracer; the gamma photons are what is detected, not the positrons.