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    Diagnostic methods in medicine

    Chapter 16

    As we saw in the last chapter, X-rays are used to

    diagnose problems in a patient because they can

    be generated outsidethe body and then directed

    through the patients body to produce an image. An

    alternative approach is to place a source of radiation

    insidethe patient and use the radiation that emerges

    from inside the body to produce an image.

    An example of this approach is where a patient

    undergoes a bone scan (to see whether there iscancerous tissue in their bones). The patient is

    given an injection containing the radioactive

    substance. They then have a few hours in which

    to relax while the material circulates around their

    body. Next, they are placed in a machine called

    a gamma camera (Figure 16.1) which detects

    -rays coming from inside their body. The result

    is an image showing points in the body where the

    radioisotope has accumulated (Figure 16.2). After

    the scan, the patient must take care to ush the

    toilet twice after use and to avoid kissing otherpeople this is because the radioisotope is still

    Using radioisotopes

    active for several hours and it is present in their

    saliva and urine.

    In this chapter, we will look in detail at some

    ways in which radioisotopes (also known as

    radionuclides) are used for diagnosis. Radioisotopes

    are also used in treatment, where the radiation

    they produce is used to destroy harmful tissue,

    particularly cancerous tumours.

    Figure 16.1 A female patient undergoing a bone

    scan in a gamma camera. There are two detectors,

    one above the patient and one below.

    Figure 16.2 Bone scan images of a healthy patient.

    The radionuclide has been taken up by the patients

    bones; there is a lot of it in the bladder also.

    e-Learning

    Objectives

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    Chapter 16: Diagnostic methods in medicine

    Figure 16.3shows the system used for the

    extraction (elution) of Tc-99m from the container

    of Mo-99. A saline solution is passed through the

    container, and this dissolves out the Tc-99m.

    Radiopharmaceuticals

    To ensure that the radioisotope reaches the

    correct organ, it must be converted into aradiopharmaceutical. This means that it is

    chemically combined with other elements to produce

    a substance which will be taken up by the tissue of

    interest. For example, for a bone scan, Tc-99 m is

    combined with a phosphorus-containing compound

    and the patient injected with a dose of activity about

    600 MBq. This is taken up by bone tissue, particularly

    cancerous tissue where there is a high rate of

    metabolism as new cells are being formed.

    Because radiopharmaceuticals are designed to

    target particular organs or tissues in the body, they are

    often described as tracers.

    A summary of a few radioisotopes used by

    hospitals and their diagnostic use is given in

    Table 16.1.

    Choosing a radionuclideAll radioactive substances decay, some more quickly

    than others. There are several hundred different

    radionuclides which are found in Nature or which

    can be created in a nuclear reactor or a small linear

    particle accelerator (linac). So which ones are

    suitable for medical purposes?

    The radionuclide is put into the patients body and

    its radiation detected. This requires that the substance

    chosen should be a gamma emitter. (An alpha or beta

    source is not suitable because the body will absorb

    the - or -particles. These types of radiation are

    also extremely lethal inside the body because of their

    strong ionising properties.)

    The radionuclide should also have a short half-life.

    There are two reasons for this.

    It will give out its radiation quickly, so that only1 a small amount is needed to form an image in the

    gamma camera.

    Any radionuclide that remains in the patient2

    will soon decay away, ensuring that they are not

    exposed to hazardous levels of radiation.

    The problem then is that, if a hospital buys a batch of

    a short-lived radioisotope, it has bought something

    that is rapidly decaying away. What can be done to

    stop it decaying before the hospital has time to make

    use of it?

    One solution is illustrated by a radioisotope calledtechnetium-99m. This is an isotope of the element

    technetium (Tc) with nucleon number 99. Tc-99m is

    produced when molybdenum-99 undergoes decay.

    This happens in two stages:

    9942 Mo

    9943 Tc

    m+ 01 e + half-life 67 h

    9943 Tc

    m 9943 Tc + half-life 6 h

    9943 Tc decays by emission half-life 2.110

    5years

    The m indicates that 9943 Tcmis metastable, that is,

    it remains in an energetic state for some time before

    decaying by emission. Each -ray photon has an

    energy of 140 keV. How does this solve the hospitals

    problem? The nuclear medicine department of the

    hospital buys a supply of Mo-99, which is produced

    in a nuclear reactor. The Mo-99 then produces

    Tc-99m at a predictable rate, and this can then be

    extracted for use with patients.

    reduced

    pressure

    elution vial

    sodiumpertechnetate

    solution

    terminalfilter

    lead shielding

    salinereservoir

    one wayair filter

    Mo adsorbed on toalumina column

    99

    Figure 16.3 A simplied diagram of a technetium-

    99m generator. It is designed to minimise the risk

    that the technician will be exposed to radiation. An

    evacuated collection vial on the output side draws

    saline from the reservoir through the column. Here

    the saline dissolves the technetium to form a solution

    of sodium pertechnetate.

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    Chapter 16: Diagnostic methods in medicine

    240

    SAQ

    1 Mo-99 is used to produce Tc-99m. The half-life of

    molybdenum-99 is 67 h.

    a Explain why a hospital will require supplies of

    this substance to be delivered each week.b Explain why it would be inconvenient if the

    half-life of Mo-99 was much longer than

    67 h, and if it was much shorter

    than 67 h.

    The gamma cameraIt is over 50 years since the gamma camera

    (Figure 16.1) was rst invented, and it is now the

    major imaging device used in diagnostic nuclear

    medicine. It detects -ray photons coming fromsources such as technetium-99m inside the patient.

    Inside the camera is a single, very large crystal of

    sodium iodide with about 0.5% of thallium iodide,

    typically between 400 and 500 mm in diameter and

    912 mm thick. This crystal is a scintillator; that is, a

    gamma photon incident on this material may produce

    a ash of visible light in the crystal.

    Figure 16.4shows how the gamma camera

    constructs an image of the patients insides from these

    ashes of light.

    The gamma photons pass upwards through the collimator. The collimator consists of ahoneycomb of cylindrical tubes in a lead plate.

    The scintillator detects only photons travelling

    along the axis of these tubes. It therefore cuts

    out any -rays travelling at an angle to the

    scintillator.

    Radioisotope Uses

    uorine-18 (189 F) bone imaging

    technetium-99m (9943 Tcm) bone growth

    blood circulation in lung, brain and liver

    function of heart and liver

    iodine-123 (12353 I) function of thyroid

    function of kidney

    xenon-133 (13354 Xe) function of lung

    Table 16.1 Some radioisotopes used in hospitals and their uses.

    computer

    hexagonal array

    photomultipliertubes

    lightguide

    scintillator

    collimator

    display

    y

    a

    b

    x

    Figure 16.4 aThe structure of a gamma camera.

    bThe arrangement of photomultipliers.

    Answer

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    Chapter 16: Diagnostic methods in medicine

    avalanche of electrons. These eventually give rise

    to an electrical pulse at the last electrode. Thus

    a single electrical pulse is produced by a single

    photon of light incident on the photocathode.

    The electrical signals from the photomultipliersare processed electronically by a computer to

    produce a high-quality image on a screen. The

    output from each photomultiplier corresponds to a

    single point or pixel on the screen.

    Uses of the gamma camera

    A gamma camera is used in a bone scan. This is an

    example of a static study, in which a single image is

    produced a suitable time after the injection of

    the tracer.

    Another use is in situations where it is desired

    to see the progress of the tracer through the body.An example is a kidney scan (a renogram

    see Figure 16.6). The patient is given a

    radiopharmaceutical which will pass through their

    system and be excreted by the kidneys. A series of

    images of the kidneys are made over a period of time

    to see the process of excretion as it happens. This is

    an example of a dynamic study.

    The beam of gamma photons then strikes thescintillator crystal, where each photon produces

    a ash of light. About 10% of the incident -ray

    photon energy is converted into visible light.

    The light is detected by one or more of thephotomultiplier tubeswhich produce an

    electrical pulse for each photon of light they

    receive. The photomultipliers are arranged in a

    hexagonal array over the surface of the crystal.

    Figure 16.5shows a single photomultiplier tube.

    The incident gamma photon strikes the scintillatorcrystal to produce photons of visible light. A

    single light photon releases a single electron from

    the photocathode by the process of photoelectric

    effect. This electron is accelerated to the +100 V

    electrode (dynode) and on impact releases two

    or three secondary electrons. This process isrepeated at each electrode and soon there is an

    scintillation crystal

    +600 V

    +800 V

    +400 V

    +200 V

    0 V

    incident gamma-ray photon

    +500 V

    +700 V

    +300 V

    +100 V

    single electron

    dynode

    photocathode

    Figure 16.5 Details of a photomultiplier tube.

    Figure 16.6 A gamma camera image of a patients

    kidneys. The image, called a scintigram, has been

    coloured to show how the intensity of the -rays

    varies. The kidney on the left is functioning normally

    while the one on the right has very limited blood ow

    through it.

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    Chapter 16: Diagnostic methods in medicine

    242

    However, it is not the gamma photon emitted in

    this decay that we are interested in. Rather, it is the

    positron 0+1 e that is useful. Once emitted, it soon

    collides with an electron and the two are annihilated.

    Their mass is released as energy in the form of two

    gamma photons. These are emitted at 180 to each

    other (see Figure 16.7). In PET scanning, it is these

    two gamma photons that are detected.

    PET scanner

    A PET scanner looks similar to a CAT scanner but,

    of course, it is detecting -rays, not X-rays. The

    principle is illustrated in Figure 16.8.

    The patient is injected with a positron-emitting

    radiopharmaceutical, in this case a form of glucose

    (sugar) tagged with uorine-18. This tends to

    accumulate in tissues with a high rate of respiration.

    In this case, we imagine that the doctors are looking

    at brain function, so the tracer will be taken up most

    by active cells in the brain.

    The patient is surrounded by a ring of gamma

    detectors (similar to those in a gamma camera). These

    detect pairs of -rays coming from inside the patient

    and travelling in oppositedirections. The times at

    which they arrive at the detectors are compared and

    SAQ

    2 A gamma camera can be adjusted by changing

    the collimator.

    a The collimator is changed to one with lead

    tubes of larger diameter. Explain why this will

    allow a shorter exposure time, but will give a

    less well-dened image.

    b If the collimator is changed to one with lead

    tubes of longer length, more -rays will be

    cut out as they cannot pass through to the

    scintillator crystal. How will this affect the

    exposure time and the

    denition of the image?

    Positron emission tomography

    PET scanning is another technique which uses thefact that gamma rays can emerge from a source inside

    the body. The name is an abbreviation of positron

    emission tomography. As with CAT scanning,

    the word tomographyimplies that images of slices

    through the body can be obtained (using computer

    manipulation of the image data).

    The radiopharmaceuticals used in a PET scan

    contain radioisotopes that emit positrons; that is, they

    are +emitters. An example is uorine-18, which

    decays like this:

    189 F

    188 O +

    0+1 e + +

    gamma

    detectors

    e+

    e

    Figure 16.8 A patient undergoing a PET scan. In

    this case, -rays emitted by the tracer in the brain

    are being detected.

    Figure 16.7 Positronelectron annihilation. The

    masses of the positron e+and electron eappear as

    the energy of the two gamma photons.

    Answer

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    Chapter 16: Diagnostic methods in medicine

    SAQ

    3 Fluorine-18 is a +-emitting radioisotope

    commonly used in PET scanning. Its half-life

    is 110 minutes. Suggest why this

    makes it a good choice for

    this purpose.

    4 Tomography is a type of imaging.

    a Describe how tomography differs from

    conventional imaging.

    b Describe how a PET scan

    forms a tomographic image.

    Magnetic resonance imagingMagnetic resonance imaging, or MRI, is another

    technique from nuclear medicine. However, it does

    not rely on nuclides that are radioactive; rather, it

    relies on the fact that some atomic nuclei behave like

    tiny magnets in an external magnetic eld.

    (MRI was originally known as nuclear magnetic

    resonance imaging, but the word nuclear was

    dropped because it was associated in patients minds

    with bombs and power stations. To emphasise: MRI

    does not involve radioactive decay, ssion or fusion.)As in CAT scanning, PET scanning and the gamma

    camera, MRI scanning involves electromagnetic

    radiation, in this case radio frequency (RF)

    electromagnetic waves. The patient lies on a bed in

    a strong magnetic eld (Figure 16.10), RF waves are

    sent into their body, and the RF waves that emerge are

    detected. From this, a picture of the patients insides

    can be built up by computer. As we will see, MRI gives

    rather different information from that obtained by the

    other non-invasive techniques we have been looking at.

    from this the position at which they were emitted

    can be determined. Because gamma photons travel

    at the speed of light, the time interval that must be

    measured is very small.

    Gradually, a three-dimensional image of the

    distribution of radioactive tracer in the patient is built

    up and, from this, any abnormal functioning can be

    deduced. An image of a slice through the patient can

    be viewed on a computer screen.

    Uses of PET scanning

    PET scanning is an important diagnostic tool, in

    particular for showing up cancerous tissue. However,

    it has also proved very useful in showing up aspects

    of normal bodily functions, such as brain activity.

    Figure 16.9shows scans of a persons brain when

    they were reading aloud and then silently. Differentareas of the brain are active in these apparently

    similar situations.

    Figure 16.9 Articially coloured PET scans of a

    human brain when the subject was reading aloud

    (top) and silently (bottom). Reading aloud requires

    extra areas of the brain to be active in order to

    control the mouth and tongue and to listen to the

    sounds produced.

    Answer

    Answer

    Extension

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    Chapter 16: Diagnostic methods in medicine

    244

    of hydrogen atoms that are studied, since hydrogen

    atoms are present in all tissues. A hydrogen nucleus is

    a proton, so we will consider protons from now on.

    A proton has positive charge. Because it spins, it

    behaves like a tiny magnet with N and S poles. Figure

    16.11ashows a number of protons aligned randomly.

    When a very strong external magnetic eld is

    applied, the protons respond by lining up in the eld

    (just as plotting compasses line up to show the direction

    of a magnetic eld). Most line up with their N poles

    facing the S pole of the external eld, a low energy

    state; a few line up the other way round, which is an

    unstable, higher energy state (Figure 16.11b).

    A proton does not align itself directly along the

    external eld. In practice, its magnetic axis rotates

    around the direction of the external eld (Figure

    16.12), just like the axis of a spinning top. Thisrotation or gyration action is known as precession.Principles of nuclear magnetic resonanceThe nuclei of certain atoms have a property called

    spin, and this causes them to behave as tiny magnets

    in a magnetic eld. In MRI, it is usually the nuclei

    N

    SN

    S

    N

    S

    NS

    NS

    S

    N

    N

    S

    S

    N

    N

    S

    S

    N

    N

    S N

    SS

    N

    S

    N

    S

    N

    S

    N

    S

    N

    S

    N

    S

    N

    S

    N

    S

    N

    N

    S

    S

    N

    N

    SN

    S

    NS

    NS

    NS

    NS

    NS

    NS

    NS N

    S

    N S

    N S

    N

    S

    b

    a

    electromagnet

    external

    field

    N

    S

    Figure 16.11 How protons behave in a strong

    magnetic eld. aProtons are randomly directed when

    there is no external magnetic eld. bBecause protons

    are magnetic, a strong external magnetic eld causes

    most of them to align themselves with the eld.

    gravitational field

    spin

    spin

    axis of

    spin

    path of

    precession

    path of

    precession

    magnetic field

    axis of spin

    Figure 16.12 A spinning top (left) rotates about its

    axis; at the same time, its axis precesses about the

    vertical, which is the direction of the gravitational

    eld. In a similar way, a proton (right) spins and its

    axis of rotation precesses about the direction of the

    external magnetic eld.

    Figure 16.10 A patient undergoing an MRI scan of

    the brain. This is a form of tomography; the display

    shows different slices through the patients brain.

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    Chapter 16: Diagnostic methods in medicine

    In Figure 16.13, you can see that the relaxation

    of the protons follows an exponential decay pattern.

    Curves like this are characterised by two relaxation

    times:

    T 1,the spinlattice relaxation time, where the

    energy of the spinning nuclei is transferred to thesurrounding lattice of nearby atoms;

    T 2,the spinspin relaxation time, where the energy

    is transferred to other spinning nuclei.

    These relaxation times depend on the environment

    of the nuclei. For biological materials, it depends on

    their water content:

    Water and watery tissues (e.g. cerebrospinal uid)have relaxation times of several seconds.

    Fatty tissues (e.g. white matter in the brain)have shorter relaxation times, several hundred

    milliseconds.

    Cancerous tissues have intermediate relaxationtimes.

    This means that different tissues can be distinguished

    by the different rates at which they release energy

    after they have been forced to resonate. That is the

    basis of medical applications of nuclear magnetic

    resonance.

    The angular frequency of precession is called

    the Larmor frequency0, and depends on the

    individual nucleus and the magnetic ux densityB0

    of the magnetic eld:

    0= B0

    So, the stronger the external eld, the faster the

    protons precess about it. The quantity is called the

    gyromagnetic ratio for the nucleus in question and is

    a measure of its magnetism. (Note that the Larmor

    frequency is measured in radians per second. This

    means that, strictly speaking, it is not a frequency.)

    For protons, has the approximate value

    2.68108rad s1T1. To determine the frequencyf0

    of the precessing nuclei, we can use the equation

    0= 2f0

    Therefore:

    f0=B0

    2

    In an MRI scanner, the external magnetic eld is

    very strong, of the order of 1.5 T (thousands of times

    the strength of the Earths eld). The precession

    frequencyf0is

    f0=2.68 1081.5

    2= 6.4 107Hz = 64 MHz

    This frequency lies in the radio frequency (RF) region

    of the electromagnetic spectrum.

    You should recall that resonancerequires a

    system with a natural frequency of vibration; when

    it is stimulated with energy of the same frequency, it

    absorbs energy. In MRI, protons precessing about the

    strong external eld are exposed to a burst or pulse

    of RF waves whose frequency equals the frequency

    of precession. Each proton absorbs a photon of RF

    energy and ips up into the higher energy state; this is

    nuclear magnetic resonance (Figure 16.13).

    Now we come to the useful bit. The RF waves are

    switched off and the protons gradually relax into their

    lower energy state. As they do so, they release their

    excess energy in the form of RF waves. These can be

    detected, and the rate of relaxationtells us something

    about the environment of the protons.

    absorption

    Time00

    Energy

    ofprotons

    relaxation

    Figure 16.13 In nuclear magnetic resonance, a

    spinning nucleus is ipped into a higher energy state

    when it absorbs a photon of RF energy; then it relaxes

    back to its lower energy state.

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    Chapter 16: Diagnostic methods in medicine

    246

    produce an additional external magnetic eld that

    varies across the patients body. These coils are

    arranged such that they alter the magnitude of the

    magnetic ux density across the length, depth and

    width of the patient. This ensures that the Larmor

    frequency of the nuclei within the patient will be

    slightly different for each part of the body. This

    means that only a small volume of the body is at

    exactly the right eld value for resonance and so

    the computer can precisely locate the source of theRF signal within the patients body and construct

    an image.

    A computer that controls the gradient coils and RFpulses, and which stores and analyses the received

    data, producing and displaying images.

    Procedure

    The patient lies on a bed which is moved into the bore

    of the electromagnet. The central imaging section is

    about 0.9 m long and 0.6 m in diameter. The magnetic

    eld is very uniform, with variations smaller than 50

    parts per million in its strength. The gradient eld

    is superimposed on this xed eld. An RF pulse is

    then transmitted into the body, causing protons to

    ip (resonate). Then the receiving coils pick up the

    relaxation signal and pass it to the computer.

    SAQ

    5 Protons precess at a frequency of 42.6 MHz in an

    external eld of magnetic ux density 1.0 T.

    a Determine the frequency at

    which will they precess in a

    eld of magnetic ux density 2.5 T.

    b State the frequency of RF radiation that will

    cause the protons to resonate

    in this stronger magnetic eld.

    6 Figure 16.14shows how the amplitude of RF

    waves coming from watery tissue varies after

    resonance. Copy the graph and add lines and

    labels to show the graphs you would expect

    to see for cancerous and

    fatty tissues.

    Figure 16.14 See SAQ 6.

    MRI scanner

    Figure 16.15shows the main components of MRI

    scanner. The main features are:

    A large superconducting magnet which producesthe external magnetic eld (up to 2.0 T) needed to

    align the protons. Superconducting magnets are

    cooled to 4.2 K (269 C) using liquid helium.

    An RF coil that transmits RF pulses into the body.An RF coil that detects the signal emitted by therelaxing protons.

    A set of gradient coils. (For clarity, only one pairof gradient coils in shown in Figure 16.14.) These

    Time

    watery tissue

    00

    Amplitude

    large

    external

    magnet

    RF receiving coil

    RF transmitting coil

    computer

    longitudinal

    gradient coil

    Figure 16.15 The main components of an MRI

    scanner.

    Hint

    Answer

    Answer

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    Chapter 16: Diagnostic methods in medicine

    One disadvantage of MRI is that any metallic objects

    in the patient, such as surgical pins, can become

    heated. Also, heart pacemakers can be affected, so

    patients with such items cannot undergo MRI scans.

    Loose steel objects must not be left in the room as

    these will be attracted to the magnet, and the room

    must be shielded from external radio elds.

    Figure 16.17shows how an MRI scan can becombined with a CAT scan to show detail of both

    bone and soft tissue, allowing medical staff to see

    how the two are related. Compare this with

    Figure 16.16.

    SAQ

    7 An MRI scan might be considered a safer

    procedure than a CAT scan.

    a Explain why it might be considered to be safer.

    b Why might a CAT scan be chosen in preference

    to an MRI scan?

    c Explain why MRI is described

    as non-invasive.

    The result is an image like the one shown in

    Figure 16.16. This image has been coloured to show

    up the different tissues, which are identied by their

    different relaxation times.

    Advantages and disadvantages of MRI

    MRI has several advantages compared to other

    scanning techniques:It does not use ionising radiation which causes ahazard to patients and staff.

    There are no moving mechanisms, just changingcurrents and magnetic elds.

    The patient feels nothing during a scan (althoughthe gradient coils are noisy as they are switched),

    and there are no after-effects.

    MRI gives better soft-tissue contrast than a CATscan, although it does not show bone as clearly.

    Computer images can be generated showing any

    section through the volume scanned, or as a three-dimensional image.

    Figure 16.16 MRI scan through a healthy human

    head. Different tissues, identied by their differentrelaxation times, are coloured differently.

    Figure 16.17 A combined CAT scan and MRI scan,

    showing how the tissues revealed by MRI relate tothe bone structure shown by X-rays.

    Answer

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    Chapter 16: Diagnostic methods in medicine

    248

    Summary

    Medical tracers such as technetium-99m are used to diagnose the function of organs.A gamma camera detects gamma radiation coming from the medical tracer in the body and deducesits position.

    The main components of a gamma camera are: collimator, scintillator crystal, photomultiplier tubesand computer.

    In PET scanning, a +emitter is used as a tracer; -rays produced as the positrons annihilate with electronsare used to determine the position of the tracer.

    In MRI scanning, spinning, precessing protons are forced to resonate using radio frequency pulses. RFradiation from relaxing protons is used to obtain diagnostic information about internal organs, particularly

    soft tissues.

    The main components of an MRI scanner are: superconducting magnet, RF transmitter coil, RF receivercoil, set of gradient coils and computer.

    Questions

    a1 State one application of technetium-99m as a tracer. [1]

    Technetium-99m nuclei are produced when radioactive nuclei of molybdenum-99b

    emit -particles.

    Complete the nuclear reactions below:i

    9942 Mo99

    ? Tcm+ 01e + ?

    9943 Tcm 9943 Tc + ? [2]

    Suggest why technetium-99m is suitable as a tracer. [2]ii

    Molybdenum-99 has a half-life of 67 h. The initial activity of a sample ofiii

    molybdenum is 600 MBq. For this sample of molybdenum, calculate:

    the decay constant in s1 1 [1]

    the initial mass in grams of the sample [3]2

    the activity of the sample after 30 h. [2]3

    [Total 11]

    2 This question is about magnetic resonance imaging (MRI).

    Explain what is meant by:a

    the Larmor frequencyi

    0 of nuclei [2] relaxation time of nuclei. [3]ii

    Describeb two advantages of MRI compared with a CAT scan. [2]

    Outline some of the main components of an MRI scanner. [5]c

    [Total 12]

    continued

    Glossary

    Hint

    Hint

    Answer

    Answer

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    Chapter 16: Diagnostic methods in medicine

    a3 The diagram below shows the key components of a gamma camera.

    A-ray

    photonsB C

    photomultiplier

    tubes

    Name each component A, B and C and state its function. [6]

    A photomultiplier tube has 10 electrodes known as dynodes. An electron emittedb

    from the photocathode is accelerated towards the rst dynode. On impact, it

    produces, on average, three secondary electrons. These are accelerated towards

    the second dynode and the whole process is repeated. An electrical pulse lasting

    for 2.0 ns at the tenth dynode is produced. Calculate:

    the total number of electrons at the tenth dynode as a result of a singlei

    electron impacting the rst dynode [2]

    the average current from the last dynode. [3]ii [Total 11]

    Hint

    Hint

    Answer