3.1 X-rays
The X-rays section is very similar to that in PH2, so I’m not going to repeat anything, here are some quick diagrams with the key elements:
Key de nition:
X-rays High energy electromagnetic radiation, with photon energies between ∼ 100eV and ∼ 100keV .
3.1.1 Computerised axial tomography (CAT or CT) scans
In addition to simply using an x-ray tube and a Geiger detector to nd a 1-dimensional image, we can create 3D images from CAT scans. A CAT scan is produced by using rotating beams which move around the body to get images from all direction (slices as it were) from which a 3D image can be constructed. This is only used in emergencies since the X-ray does received is high.
3.2 Ultrasound
Ultrasound is a type of electromagnetic wave. In medical physics we use a piezoelectric crystal to generate ultrasound EM waves. A piezoelectric crystal is one that (deforms and as a result) emits EM radiation when a current is put through it and generates a current when an EM wave passes through it. We use this crystal in conjunction with ultrasound EM radiation because EM radiation it is re ected more from some tissues than others and as a result is great for imaging body tissues. When we use our detector, we must use a gel between the piezoelectric sensor and the body to prevent the ultrasound entering air since it will re ect from the air and never even enter the body.
3.2.1 Acoustical impedance
Acoustical impedance (Z) is a constant that de nes what fraction of ultrasound a body will re ect. We de ned it using:
Z = cρ
where c is the speed of sound (in the medium) and ρ is the density of that medium. We can then use this to nd the fraction of ultrasound re ected using:
where Z1 is the rst medium’s impedance and Z2 is the second medium’s impedance. The gel we apply when using ultrasound is called a coupling medium, this is a medium that almost the same acoustical impedance as skin to reduce re ections from the entry of the ultrasound to the skin. However, because ultrasound is used to measure re ections, this makes it not suitable for medium’s with high acoustical impedance, e.g. it can’t be used with the lungs since it will be re ected by the air inside them.
This allows us to determine the speed of the blood ow, and combined with the strength of the re ected pulse (which reveals the volume of blood) we can nd the ow rate.
3.4 Magnetic resonance imaging (MRI)
MRI is based on the principles of resonance and precession. Resonance is when a system oscillates with a high amplitude due to an input frequency (in this case magnets are used to vibrate ions). This resonance causes the nucleons which are being targets to change spin . Nucleons change from spin-up to spin-down and vice versa. In the case of MRI, we target hydrogen nuclei since we know there are many of these in the body. In both cases the spin precesses which means that it rotates around the magnetic eld direction (much like a spinning toy, e.g. a dreidel). The frequency of it’s precession depends on the strength of the magnetic eld and this is called the Larmor frequency (i.e. it’s our resonant frequency for nucleon precession). When the (electro)magnetic eld is turned o , the nucleons ip back releasing a radio wave which can be detected allowing us to nd the location of the atoms. The time taken for them to ip back is called the relaxation time and this will di ers depending on the surrounding so we can create an image of the tissues and because of this, it is extremely good for all tissues containing water (H2O). We use the di erent concentrations of hydrogen to build up a detailed image of the tissues. It doesn’t work as well with bones since they don’t tend to contain hydrogen. The only major disadvantages of MRI are the high cost of the machines, the claustrophobic aspect of the machine and the fact that it cannot be used with magnetic metals anywhere in the body since the magnet will pull these out. This makes it better than X-rays for imaging most of the body since X-rays can cause cancer.
3.6 Electrocardiograms (ECG)
Electrocardiograms can be used to look at the operation of the heart and blood ow. Normally the sequence of our double circulatory blood is ow is:
1. De-oxygenated blood enters the top right-hand chamber, the right atrium of the heart.
2. The right atrium pumps the blood past a valve which prevents back- ow and into the bottom right chamber, the right ventricle, which pumps it to the lungs to oxygenate.
3. The oxygenated blood returns to the top left-hand chamber, the left atrium of the heart.
4. The left atrium pumps the blood past another valve into the bottom left chamber, the left ventricle, where it is pumped to the rest of the body before returning to the heart (at step 1. again)
The four muscles of the heart are triggered to contract by a signal from the sinoatrial node. This is the node at the top-right of the heart that is controlled by the central-nervous and hormonal systems and it is what controls the heartbeat. The nervous impulses associated with our heartbeat can be detected outside the body using electrocardiography. Electrocardiography simply uses 12 electrodes applied to shaved skin with gel (to improve contact). Most of those electrodes are placed near the heart but some on the arms and legs, but none near the right leg since this is too far from the heart. The pd can then be monitored to see the heartbeat. Normally the surface potential-time graph should look this:
where QRS is the contraction of the ventricles, and P is contraction of the atria and T is the relaxation of the ventricles.
Surface potential The voltage measured on the skin due to the nerve signal within the body.
Contraction The shortening of muscles in response to a nerve stimulus.
For a normal pulse rate of 75 beats per minute, the shape above would be repeat every 0.8s (800ms).
3.7 Nuclear radiation in medicine
We looked at radiation earlier and as mentioned, α, β and γ particles have di erent potential to damage the body. In medical physics we must note how radiation a ect the body. The radiation can damage biological molecules because it interacts with the atoms which make it up. It can knock out electrons
or otherwise a ect the atom. This can change the make up of DNA causing mutations, but the body usually repairs this damage and many genetic changes are not damaging. This can lead to two things:
1. If it changes DNA which a ects the cell’s control mechanisms, this can lead to uncontrolled cell division (i.e. cause cancer/it’s carcinogenic). This kind of damage is caused by long-term exposure to low levels of radiation.
2. If it changes cells which are highly susceptible to radiation damage, that is those which are dividing, then these cells can su er constant damage. Examples of dividing cells include hair follicles and epithelial cells (which include the lining of the alimentary canal and the lungs). Low levels of radiation can be tolerated here, but large doses over a short period of tie can cause such damage that these cells are killed, which is why patients undergoing radiation therapy often lose their hair.
3.7.1 Measuring radiation
We measure radiation in many di erent ways in medical physics. As a physicist you may use activity in becquerels (Bq) which is the number of decays per second, but medics use other measurements. The rst is absorbed dose:
3.7.2 Radionuclides (Radioactive tracers)
Radioactive tracers Chemical compounds with an atom replaced by a radioactive isotope. They are used to track the uptake of a compound into the body.
We are expected to know about iodine-123 and iodine-131. I-123 is used to investigate the function of the thyroid and it decays by electron capture to an excited state of tellurium-123:
The iodine is injected in the form NaI which is biologically safe and the I-123’s half-life 13.3 hours is ideal for use as a tracer as it is long enough for production and administration but is short enough that the body is rid of it within a few days. The Tellurium produced is mildly toxic, but safe in the quantities used. The emitted γ rays are investigated with a gamma camera (see below). This kind of decay occurs in proton-rich nuclei and their electrons actually spend some time inside the nucleus. An electron combines with a proton to produce a neutron (and an electron neutrino):
This only occurs if there is a lower energy level available for the newly created neutron to occupy because neutrons are more massive than protons. The nucleus is formed in an excited state and the neutron drops down to a lower energy level emitting a photon. Iodine-131 is used in radioactive therapy to treat thyroid cancers, again using the fact that the thyroid absorbs iodine. I-131 decays by β− decay to an excited state of xenon-131, which rapidly decays by γ emission:
The β particles kill surrounding tissues, including the cancerous tissue. The γ is also useful because we can use it to monitor the e ectiveness of the uptake with a gamma camera (again see below). I-131 is not usually used as a tracer because of the dangerous β emission.
3.7.3 Gamma camera
A gamma camera consists of:
Collimator A piece of lead with narrow parallel channel. The lead absorbs all γ apart from those which travel along the channels (about 99% of the incoming γ photons, hence a strong source must be used with a long exposure time).
Scintillation crystal This crystal emits a ash of (visible) light when it absorbs a photon.
Photomultipliers Electronic devices in contact with the scintillation crystal which amplify the light and turn it into an electric signal.
Scintillation counter A counter to register the arrival of photons.
Output display A screen (typically an LCD) which builds up the image.
Each photon has 0.511MeV of energy because of the electron’s mass energy equivalence. The patient lies inside the scanner after a suitable tracer has been administered by injection, inhalation or ingestion. The γ scanner is lined with γ detectors which register coincidental and opposite events, i.e. they look for γ detected on opposite sides of the patient, they look for events nanoseconds apart and hence this is very unlikely to occur by chance. The positron typically moves less than 1mm before detection, so we can pinpoint the site of it’s emission pretty accurately. Using a long time, a large number of detectors and several slices, much like a CAT scan we can create a 3D image of the area. Most common uses of a PET scan are in search for metastases (secondary cancers). Fluorodeoxyglucose (FDG) is usually the tracer used (with F-18 being the radioactive isotope). F-18s half-life is only 110 minutes, but this is long enough for it to be prepared on site, administered and used for scanning. It is made from bombarding water enriched with O-18 with high-speed photons:
The oversight of this production routine is one of the primary jobs of a medical physicist.
Annihilation When a particle meets it’s antiparticle at low speeds annihilation occurs. Their mass’ turned into photons of the associated energies.