6.5.3 Using ultrasound

Humans can hear sound within the range of 20-20,000Hz. Ultrasound is longitudinal sound wave with a frequency greater than 20kHz (we can't hear this). It can be used to form images of the internal structures of the body and it is good because it is non-ionising (harmless) and non-invasive (no risk of infection) and quick. Medical imaging ultrasound has a frequency in the range of 1-15MHz. It can be refracted at a boundary between two substances and also diffracted. The wavelength of ultrasound in the human body is ,1mm so it can be used to identify features as small as a few mm. An ultrasound transducer is used to generate and to receive ultrasound. It can change electrical energy into sound and sound into electrical energy by means of the piezoelectric effect.

The piezoelectric effect
Crystals such as quartz produce an e.m.f (the energy transferred from chemical to electrical per unit charge) when compressed/stretched/twisted/distorted. This is a reversible process. When an external p.d. is applied across the opposite faces of the crystal the electric field can either compress/stretch the crystal.

To generate ultrasound a high-frequency (e.g. 5MHz) alternating p.d. is applied across the opposite faces of a crystal repeatedly compressing and expanding the crystal. The frequency chosen is the same as the natural frequency of oscillation of the crystal and the result is that the crystal resonates producing an intense ultrasound signal. As ultrasound transducer emits pulses of ultrasound (about 5,000 per second). The same transducer is used to detect ultrasound - any ultrasound incident on the crystal will make it vibrate so the crystal is compressed and expanded by tiny amounts. This generates an alternating e.m.f across the ends of the crystal which can be detected by electronic circuits. Modern ultrasound transducers use lead zirconate titanate or polyvinylidene fluorine rather than quartz.

A and B scans
A scans
This is the simplest type of ultrasound scan. A single transducer is sued to record along a straight line through the patient. Tis can be used to determine the thickness of bone/distance between the lens and retina of the eye (for example).

Each pulse sent by the transducer into the body of a patient will be partly reflected and partly transmitted at the boundary between two different tissues. The reflected pulse (known as the echo pulse) will be received at the transducer. It will have less energy than the original pulse due to energy losses within the body and because some of the energy of the original pulse is transmitted through the body. The pulsed voltage at the transducer is displayed on an oscilloscope screen/computer screen as a voltage-time graph. The amplitudes of the voltage signals are attenuated by absorption and reflection losses. The time interval is the time taken for the ultrasound pulse to travel from the (front of the) transducer to the retina and back to the transducer therefore the total distance travelled by the ultrasound pulse is 2L where L can be calculated provided the average speed of the ultrasound in the eye is known.

B scans
B scans produce a 2D image on a screen. The transducer is moved over the patients skin and the output of the transducer is connected to a high-speed computer. For each position of the transducer the computer produces a row of dots on the screen (each dot corresponds to the boundary between two tissues). The brightness of the dot is proportional to the intensity of the reflected ultrasound pulse.


Acoustic impedance
The fraction of ultrasound intensity reflected at the boundary depends on the acoustic impedance of both media. The acoustic impedance (Z) of a substance is defined as the produce of the density of the substance and the speed of the ultrasound in the substance. It has the SI unit kg m^-2 s^-1:

Z = ρc

The reflected intensity of ultrasound depends on the values of Z1 and Z2 (the acoustic impedances of two substances). For normal incidence, when the angle of incidence is 0°, the ratio of reflected intensity (Ir) to incident intensity (Io) is given by the following equation:

Ir/Io = (Z2-Z1)²/(Z2+Z1)²

Ir/Io = ((Z2-Z1)/(Z2+Z1))²

The ration fo Ir/Io is known as the intensity reflection coefficient. There is more reflection when the values of acoustic impedances are very different (e.g there will be a greater reflection at a one/muscle boundary than a blood-muscle boundary. The acoustic impedance of bone is much different to the rest of the body (the rest of the body is pretty similar) so bone is easily distinguishable in an ultrasound scan.

Coupling gel is very important. When an ultrasound transducer is placed on the skin of a patient air pockets will be trapped between the transducer and the skin. The air-skin boundary means that about 99.9% of the incident ultrasound will be reflected before it even enters the patient. To overcome this coupling gel is used. Coupling gel has a similar acoustic impedance to the skin and fills the air gaps between the transducer and the skin ensuring that almost all the ultrasound enters the patient's body. Here, we can use the term impedance/acoustic matching. This is when two substances have similar values of acoustic impedance and negligible reflection occurs at their boundary as a result.


Doppler imaging
The frequency of ultrasound changes when it is reflected off a moving object (this is known as the Doppler effect). Doppler ultrasound is a non-invasive technique that uses the reflection of ultrasound (from iron-rich blood cells) to help doctors evaluate blood flow through major arteries. It can be used to reveal blood clots/atheroma and evaluate the amount of blood flow to transplanted organs.

During Doppler ultrasound the transducer is pressed lightly over the skin above the blood vessel. It sends pulses of ultrasound and receives the reflected pulses from inside the patient.  Ultrasound reflected off tissues will return with the same frequency and wavelength but ultrasound reflected of moving objects (blood cells) will have a changed frequency. The frequency increases when blood is moving towards the transducer and decreases when blood is moving away from the transducer. The transducer is connected to a computer that produces a colour-coded image to show the direction and speed of the blood flow.

As we know ultrasound scans have a frequency of 5-15MHz. In blood flow analysis this can give a Doppler shift up to 3kHz. The frequency shift (Doppler shift in frequency) (Δf) is directly proportional to the speed (v) of approach/recession of the blood. 

The axis of the probe (ultrasound transducer) must be held at an angle θ to the blood vessel. This is because holding perpendicular would give no observed change in the frequency as cos90 = 0. The usual θ is 60°. The change in observed frequency (Δf) is given by the following equation:

Δf = (2 f v cosθ) / c

F: original ultrasound frequency
v: speed of moving blood cells
c: speed of ultrasound in the blood

6.5.2 Diagnostic methods in medicine

Radioactive isotopes have to be placed inside the patient and their radiation is detected from the outside. Gamma emitters are ideal sources as gamma photons are the least ionising and can also penetrate through the patient and be detected externally. Radioisotopes that are used for medical imaging must have a short half-life to ensure high enough activity from the source so only a small amount is needed for the image to form (this is also important as the patient is not subjected to a high dosage of radiation after the procedure). Radioisotopes such as fluorine-18 (used in PET scans) are produced artificially on-site (as they have a short half-life). Technetium-99m (produced by the natural radioactive decay of molybdenum-99) can be used to monitor the function of major organs such as the heart, liver, lungs, kidneys, and brain.

Radioisotopes are chemically combined with elements that will target the desired tissue to make a radiopharmaceutical (this is a medical tracer). E.g Tc-99m can be combined with sodium and oxygen to produce NaTcO4 (this will target the brain once injected). Its progress through the body can be traced using a gamma camera as the Tc-99m emits gamma photons. The concentration of Tc-99m can identify irregularities in the function of the body.


Fluorine-18 is a radiopharmaceutical used in PET scans (positron emission tomography). It has a half life of ~110 minutes and it will decay into a nucleus of oxygen-18, a positron, a neutrino, and a gamma photon. It has to be made in a laboratory near the hospital or with a particle accelerator (e.g high speed protons collide with oxygen-18 nuclei to produce fluorine-18 nuclei and neutrons.


The gamma camera
The gamma camera is a diagnostic tool that detects gamma photons emitted from radioactive nuclei injected into the patient, and an image is constructed which indicates the concentration of the tracer in the body. The gamma photons travel towards the collimator, any arriving at an angle are absorbed by the tubes so only those travelling along the axis of the tubes reach the scintillator. The scintillator is usually sodium iodide. A single photon striking the scintillator produces thousands of visible light photons (but not all the gamma photons produce these flashes as there is only a 1/10 chance a gamma photon will interact with the scintillation. The photons of visible light travel through the light guide into photomultiplier tubes. These are arranged in a hexagonal pattern and a single photon is converted into an electrical pulse. The outputs of each photomultiplier tube is connected to a computer and the electrical impulses are processed to locate the impacts of the photons on the scintillator. These impact positions construct a high quality image showing the concentrations of the tracer in the patient and the final image is displayed on a screen.

Gamma cameras produce an image that shows the function and processes of the body rather than the anatomy (like an x-ray).


Positron emission tomography
PET scans can be used to construct a detailed 3D image with gamma radiation (instead of X-rays). More often than not the radiopharmaceutical fluorodeoxyglucose (FDG) is used as it is similar to naturally occurring glucose but tagged with a radioactive fluorine-18 atom in place of an oxygen atom. Our bodies treat FDG as normal glucose and incorporate it into tissues with a high rate of respiration. Its activity can be monitored using gamma detectors. Carbon monoxide (with the carbon-11 isotope) can also be used as a radiopharmaceutical for PET scans. This emits a positron and has a half life of ~20 minutes. It attaches to haemoglobin in red blood cells (meaning it can be transported in the blood).

Pet scanners work as follows:

• the patient lies on a horizontal table surrounded by gamma detectors
• each detector consists of a photomultiplier tube and sodium iodide scintillator and produces a voltage pulse/signal for every gamma photon incident at its scintillator
• the detectors are connected to a computer
• the patient is injected with FDG
• the pet scanner detects the gamma photons emitted when positrons (from decaying Fl-18) annihilate with electrons inside the patient
• photons detected by the scanner come from the annihilation of these positrons, not from the gamma photons emitted by Fl-18 decaying. The annihilation of a positron and electron produces 2 gamma photons that are travelling in opposite directions (momentum is conserved)
• the computer determines the point of annihilation from the difference in arrival times of the photons at two diametrically opposite detectors and the speed of the photons (3x10^8)
• the voltage signals from the detectors are fed into the computer which analyses and manipulates the signals to form an image on a display screen
• different concentrations of the tracer show up as areas of different colours and brightnesses

Okay so we need to know the issues raised when equipping a hospital with an expensive scanner, such as a PET scanner. The advantages and disadvantages are as follows:

• Advantages
• non-invasive technique
• help diagnose different types of cancers/plan complex heart surgery/observe function of the brain
• help doctors to identify the onset of certain disorders of the brain (e.g. Alzheimer's)
• can be used to assess the effect of new medicines and drugs on organs
• Disadvantages
• very expensive due to the facilities required to produce the medical tracers
• only found at larger hospitals
• only patients with complex health problems are recommended for a PET scan.

6.5.1 Using X-rays

X-ray photons have 10-10,000 times more energy than a photon of visible light (depending on their wavelength). They are harmful to living cells and can kill them (useful for treating cancer).  X-ray photons are produced when fast-moving electrons are decelerated by interactions with atoms of a metal (e.g tungsten). The kinetic energy of the electrons is transformed into X-ray photons.

X-ray machines contain an X-ray tube that produces X-ray photons that pass through the patient to the detection plate (below the thing being X-rayed). An X-ray tube consists of an evacuated tube containing two electrodes (it is evacuated so electrons can pass through the tube without interacting with gas atoms). A large p.d. is created between the electrodes by an external power supply. The negative electrode (cathode) is a heater which produces electrons by thermionic emission. These electrons accelerate towards the positive electrode (anode). It is important to note that the anode is made from a metal known as the target metal (e.g tungsten). This must have a high melting point. This is because the X-ray photons are produced when the electrons are decelerated by hitting the anode, the energy output fo the X-rays is less than 1% of the kinetic energy of the incident electrons and the remainder of the energy is transformed into thermal energy of the anode (hence a high melting point). In many X-ray tubes oil is circulated to cool the anode/the anode is rotated to spread the heat over a larger surface area. The anode is shaped so the X-rays are emitted in a desired direction with lead to shield the radiographer from sporadic X-rays emitted in a different direction...

An electron accelerated through a p.d. 'V' gains the kinetic energy eV (from W = V Q). It is important to realise that one electron releases one X-ray photon. From the principle of conservation of energy we can determine that the maximum energy of a photon from an X-ray tube must equal the maximum kinetic energy of a single electron. The energy of a photon (eV) is equal to the Planck constant x the freqyency (maximum frequency is the speed divided by the minimum wavelength):

hf = eV

hc/λ = eV

λ = hc/eV

This means that the wavelength from an X-ray tube is inversely proportional to the accelerating p.d. (therefore increasing the current will increase the intensity of X-rays).


The term attenuation is used to describe the decrease in the intensity of electromagnetic radiation as it passes through matter (e.g bone attenuates X-rays more than tissue would). There are four attenuation mechanisms by which X-ray photons interact with atoms (each reduces the intensity of the collimated/parallel/ beam in the original direction of travel):

• Simple scatter
• the X-ray photon is scattered elastically (kinetic energy is conserved) by an electron
• This mechanism is important for X-ray photons with energy in the range of 1-20keV
• The X-ray photon interacts with an electron in the atom but has less energy than the energy required to remove the electron (work function) so the X-ray photon bounces off without a change to its energy
• Photoelectric effect
• the X-ray photon disappears and removes an electron from the atom
• This is significant for X-ray photons with energy less than 100keV
• the X-ray photon is absorbed by one of the electrons in the atom, the electron uses this energy to escape from the atom
• Attenuation of X-ray photons by this type of mechanism is dominant wen an X-ray image is taken as hospital X-ray machines use 30-100kV supplies
• Compton scattering
• the X-ray photon is scattered by an electron, it's energy is reduced, and the electron is ejected from the atom
• This is significant for X-ray photons with energy in the range of 0.5-5MeV
• The X-ray photon interacts with an electron in the atom and is ejected from the atom with reduced energy
• Pair production
• the X-ray photon disappears to produce an electron-positron pair
• This only occurs when X-ray photons have energy equal or greater than 1.02MeV
• An X-ray photon interacts with the nucleus of the atom, it disappears and the electromagnetic energy fo the photon is used to create an electron and a positron

The transmitted intensity of X-rays depends on the energy of the photons and on the thickness and type of the substance (e.g bones will attenuate X-rays more than soft tissue will). For a given substance and energy of photons the intensity falls with the thickness of the substance. Transmitted intensity can be calculated using the following equation:

I = I₀e^-xμ

(NOTE: the μ is meant to be like ^μ  (as in superscript) but for some reason it wouldn't format properly)

I₀: the initial intensity before absorption
x: the thickness of the substance
μ: the attenuation/absorption coefficient (the larger the μ the better absorber the substance is). SI unit: m^-1.


Soft tissues have a low absorption coefficient so a contrast medium is sue to improve the visibility of their internal structures in X-ray images. The most common are barium sulphate and iodine. They have relatively large atomic number (Z) which is good as μ ∝ Z³:

• iodine is used as a contrast medium in liquids (e.g to view blood flow). An organic compound of iodine is injected into blood vessels so that doctors can diagnose blockages in the blood vessels and structure of organs (e.g the hears) from X-ray images.
• Barium sulphate is used for digestive systems. It is given to the patient in the form of a white liquid mixture which is swallowed.

CAT scans

A CAT scanner records a large number of X-ray images from different angles and assembles them into a 3D image (with sophisticated software). In essence, a patient lies horizontally on their back and slide in/out of a gantry/large vertical ring. The gantry houses an X-ray tube on one side and an array of electronic X-ray detectors on the other side. These rotate within the gantry. The X-ray tube produces a fan-shaped beam of X-rays (~1-10mm thick). This thin beam irradiates a thin 'slice' of the patient, the X-rays are attenuated by different amounts by different tissues. The intensity of the transmitted X-rays is recorded by the detectors which send electrical signals to a computer. A 2D slice is acquired each time the X-ray tube and detectors complete one full rotation. The slices can be manipulated to produce a 3D image of the patient.

Advantages:

• CAT scans can be used to create 3D images - this can help doctors to assess the shape/size/position of disorders (e.g cancers)
• CAT scans can distinguish between soft tissues of similar attenuation coefficients

Okay so the spec doesn't say we need to know the disadvantages but they'll probably be useful to know:

• A traditional X-ray is quicker and cheaper
• The X-rays are harmful as they are ionising radiation - some CAT scans can be quite prolonged so expose the patients to a radiation dose equivalent to several years of background radiation
• Patients have to remain very still during the scanning process (any movement will blur the slice) - super tricky with young patients