Nuclear medicine

By Mikael Jensen

Risø National laboratory(Ver. 1 6/9/05) © 2003 by M. Jensen)

1 IntroductionNuclear Medicine comprises the medical use of radioactive isotopes for in vivo and in vitro diagnosis

and therapy. The most important field is the use of radioactive tracers (radiopharmaceuticals) for im-aging of organs, distribution of metabolism or patophysiological processes by the use of position sen-sitive detectors for detection of penetrating ionising radiation, most often gamma rays. These imaging techniques are the topic of the present text. It should, however, be remembered that nuclear medicine has a wider area of application and contains other important diagnostic and therapeutic techniques such as RadioImmuno Assay (RIA), Whole body counting (WBC), isotope dilution analysis, clear-ance techniques and radionuclide therapy.

The workhorses of nuclear medicine are the radioactive isotopes. The known nuclides are commonly shown in a diagram giving the number of neutrons, N, in the nuclide along the horizontal axis and the number of protons, Z, along the vertical axis, as depicted in Figure 1. This diagram is known as the “The Chart of Nuclides”.

Stable nuclides or stable isotopes are located along the “line of stability”. For lighter elements, N is more or less equal to Z. For heavier elements, an increasing overweight of neutrons are necessary for stability. Above Z = 92 (Uranium) the nuclides become increasingly unstable towards a special kind

N

Z

Figure 1 The chart of nuclides. Z = number of protons. N = number of neu-trons. Example: 153Gd has Z = 64 and N = 89.

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of instability called fission. This puts an upper level to the number of protons in any nuclide, stable or unstable, at about Z=108. This is sketched graphically in Figure 2.

Each point in the nuclides chart corresponds to a definitive isotope. An isotope is given by the N, Znumbers or more commonly by giving the symbol of the element in question (of course given by Z) and the total number of particles (the mass number, A = N+Z) in the upper left hand corner of the el-ements symbol, as for example:

14C, 31P, 238U

2 RadionuclidesMost known nuclides are unstable, implying that they disintegrate over time, yielding decay prod-

ucts. The unstable or radioactive nuclides lie in a halo around the line of stable isotopes in the chart of nuclides. The further you get from stability the shorter becomes the expected lifetime. Beyond this

N

Z

Sn=0”neutron drip line”

Sp=0”proton dripline”

Fission barrier

Figure 2 Limits to existence.

14C

Z=6, Carbon

A=14=6+8

8 neutrons

Figure 3 Composition of radioactive atom, Carbon 14. In the neutral at-om, the number of electrons is equal to the number of protons in the nu-cleus (Z).

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halo of radionuclides, no bound system exists, not even for the shortest period of time. A theoretical nuclide containing for example 3 protons (Lithium) and 12 neutrons simply does not exist and cannot stay together.

An example of the composition of a radioactive atom from the unstable halo in shown in Figure 3.

3 Modes of disintegrationA given radionuclide has a characteristic way of stabilisation, which can be described by the disin-

tegration rate k [time-1] and the type of emissions caused by the disintegration.

The emissions are normally one or more of the following nuclear radiations (particles):

•Alpha radiation (helium nuclide)

•Beta radiation (electrons or anti-electrons, also called positrons)

•Gamma radiation (energetic electromagnetic radiation)

Some nuclides can exist in excited states for extended periods of time, before releasing the excess energy in the form of gamma radiation, but without altering the composition of the nuclide. These so-called isomeric states are very important for nuclear medicine as they represent nuclides capable of delivering only gamma rays without any contribution from particle emission. (It should, however, be remembered that the so-called internal conversion always can transform part of the gamma rays into electrons).

Isomeric states are denoted by the letter m next to the mass number, as for example in:99m Tc, 81m Kr

The information in the chart of nuclides can be found on the internet at many sites, but one of the more authoritative sources is:

http://www2.bnl.gov/ton/

4 Rutherford’s law of decay and the definition of isotopeA given chemical element is characterised by the proton number (Z). The number of neutrons inside

the nucleus only contribute to the atomic mass, but not to the chemical characteristics of the substance. Carbon (Z=6) can exist as one of the several isotopes (Number of neutrons = 3, 4, 5, 6, 7, 8, 9…):

9C, 10C, 11C, 12C, 13C, 14C, 15C

Only the carbon isotopes 12C and 13C are stable.

A given number of atoms, n, of a specific nuclide (or “isotope”) has a well defined rate of disinte-gration k. This is actually the probability per unit time for the individual nucleus to disintegrate. In differential terms:

dn = -k·n·dt

This differential equation can easily be integrated to the solution:

n(t) = n0 · exp(-k·t)

The activity A is defined as the number of disintegrations per unit time:

A= k·n

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The activity is measured in a special unit called Becquerel (Bq) (most often used are the prefixed units: kiloBecquerel kBq, MegaBecquerel MBq and GigaBecquerel GBq).

The activity also follows the exponential law of decay given above (Rutherford’s law):

A(t)=A0 · exp(-k·t)

Finally, the following relation exist between disintegration rate and the so-called half life:

T½ = ln(2) / k

It is normally the half-life we use to characterize an isotope (the half-life is given in the chart of nu-clides). Of course the half-life can be used to compute activity as function of time:

A(t=T½) =0.5 · A0

A(t=2T½) =0.25 · A0

A(t=10T½) = A0/1024 ≅ 0.001· A0

A(t) = A0· 2-(t / T½)

5 Isotopes and RadiopharmaceuticalsAs mentioned, we normally prefer the use of pure gamma ray emitters for imaging. The half-life

should more or less match the imaging situation in question. A short half-life reduces the total radia-tion dose to the patient, but cannot be used for the imaging of a process which only slowly homes the isotope to the organ in question. A long half-life, however nice to work with, will lead to higher radi-ation dose to the patient and also potential radioactive waste problems.

The isotope should be linked to a definite chemical compound in a specific position before use. Such a radioactively labelled chemical compound designed for medical diagnosis or treatment is called a radiopharmaceutical and is normally administered to the patient in form of an intravenous injection. The radioactive compound is distributed throughout the body by the blood circulation. Over time the compound should bind to the organ or process under study. Subsequently, the emitted gamma radia-tion should be measured in order to give an image.

6 Penetration of gamma rays through matterGamma rays or γ−photons have a definite probability of passing unchanged through a given thick-

ness of matter. The intensity I (photons per unit area per unit time) decreases as function of the matter thickness x by the well-known attenuation formula:

I(x) = I0· exp(-µ·x)

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where µ is called the linear attenuation coefficient. µ is a function of photon energy and also the com-position (mainly density) of the matter in question. The dimension of µ is m-1. This is shown graphi-cally in Figure 4.

Occasionally, it is better to state the thickness of the attenuating matter by its “weight per area”, that is, the product of thickness and density: x·ρ. Here the unit can then be, for example mg/cm2. The at-tenuation law can be rephrased to give:

I(x) = I0exp((-µ/ρ)·(xρ))

When thus used, µ ⁄ρ is called the mass attenuation coefficient. In general, the mass attenuation coef-ficient is less sensitive to the actual physical state of the attenuator, such as pressure and temperature, etc.

The half-value layer thickness is the thickness of a layer that causes are 50% reduction in intensity:

x1/2 = ln(2) / µ or x1/2ρ = ln(2) / (µ/ρ)

Good tables of attenuation coefficients for all elements and many composite materials can be found on the National Institute of Standards’ web page at the address:

http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html

6.1 Microscopic description of attenuationThe attenuation of gamma rays takes place through one of the following 3 microscopic interactions,

graphically illustrated in Figures 5 and 6.

Photoelectric effect: A gamma ray of energy E can interact with a bound electron, with total transfer of energy to the electron. Thus, the gamma ray vanishes and the atom in question emits an electron having an energy equal to the difference between the original photon energy, E, and the binding en-ergy of the electron. This is the most dominant process at low photon energy (E<50 keV) and for high Z materials. When the energy of the photon is just below or just above the binding energy of an inner, closely bound electron, the probability of attenuation changes abruptly. The photon cannot cause emission of a hard bound electron by photoelectric effect when its own energy is less than the binding

I0

x

I

Figure 4 Left: Graphical illustration of attenuation. Right: attenuation for water.

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energy. Such discontinuities in the attenuation curve are called K-edges, L-edges, etc. referring to the electron orbital in question, see for example the curve for lead in Figure 9.

Compton effect: Instead of being absorbed completely, a photon can be scattered by an atomic elec-tron changing the direction and energy of the original photon and transferring part of the energy into kinetic energy of the electron. Both the scattered gamma ray and the electron are emitted from the atom. This process is called “Compton Scattering” and dominates gamma ray attenuation at interme-diate energies for most materials. The energy of E‘γ of the scattered photon is a function of the scat-tering angle θ:

An object irradiated by a mono-energetic beam of photons becomes a source of scattered radiation with many energies and directions.

Pair effect: The third important interaction between gamma rays and matter is called the pair effect. It only takes place when the energy of the gamma ray is above the energy equivalent of 2 electron rest masses. Above this energies threshold E = 2mec2 = 2·511 keV = 1022 keV, the gamma ray can form an electron + positron pair in the close vicinity of an atomic nucleus.

By this effect the gamma ray disappears and part of its energy goes to the creation of the electron positron pair (see Figure 6). The rest of the energy is imparted to the electron positron pair as kinetic energy. Normally the positron will annihilate close to the point of creation and thus by itself becoming

Figure 5 Left: Photoelectric effect. Right: Compton effect.

Figure 6 Pair effect. A gamma ray of 1.02 MeV hits the nucleus of an atom sending out a beta particle and a positron which in turn interacts with a resting electron, causing emission of two gamma rays of 0.51 MeV. (Note: the electron itself has no energy, even though the drawing suggest that. “mev” Should be MeV.)

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a source of 511 keV gamma radiation. The pair effect is only important for the attenuation of gamma rays of very high energy.

The total attenuation effect is the sum of the 3 individual effects.

µtotal = µphoto + µCompton + µpair

Photon attenuation can be seen from the graphs of total attenuation in Figure 9.

Lead is about 200 times more effective for stopping gamma radiation per distance unit below 100 keV, but only a factor of 10 better at energies above 1 MeV (and this mainly due to the difference in density).

6.2 Other effectsFor very small deflections of the primary gamma ray scattering can take place where the momentum

is taken up by the entire atom. In this case, there is practically no energy transfer from the gamma ray and we talk about coherent scattering. The coherent scatter only introduces very small angles of de-viation on the photons, and is normally of less importance than the compton scattering proces.

Also other interactions (due to the nucleons) can take place, but these processes have much lower probabilities than the above mentioned three important interactions.

7 Imaging of gamma ray sourcesAny gamma ray source will send out gamma rays isotropically (in all directions), as illustrated in

Figure 7. A radiation source in general can normally only be imaged by a system with an optical ele-ment, a “lens”. However, no lenses for gamma ray are available (except black holes, but these are sel-dom available at the surface of the earth).

Normal imaging and localisation thus requires a discrimination of gamma rays as function of their direction. This is what we call collimation.

Collimation is done by a “collimator” made out of an absorbing material, normally lead. Small holes in the collimator select one or few directions for the incoming gamma rays before they are allowed to

Figure 7 A gamma ray source will send out gamma rays iso-tropically.

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hit a detector, as illustrated in Figure 8. While directional discrimination of a collimator can be made quite well, it is always at the price of a large drop in sensitivity. The collimator only works by throw-ing away most of the gamma ray information. Collimators can most effectively be made for gamma radiation of low energy (E<350 keV), where lead is still a good absorbing material.

While collimators for gamma radiation above 500 keV are still possible, these devices become thick and heavy. The spatial discrimination (resolution) of such systems become bad (several cm).

Figure 8 Collimator only allowing rays parallel with the hole to go through. The loss of sensitivity this way will be more than a factor of 100.

Figure 9 Example of linear attenuation coefficients for water (more or less like soft tissue) and lead.[1]

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8 Gamma ray imaging by scanningOriginally, imaging in nuclear medicine was done by probing the patient for radioactivity with a sin-

gle, point-collimated detector. While this process can give good geometrical resolution, it is very wasteful in terms of sensitivity (very few photons are measured at a time) and is thus very time con-suming. Of course such a scanning system is not useful for capturing dynamic processes where the radioisotope distribution evolves during the scanning.

9 Gamma camera (Anger camera)For imaging of distribution of radiopharmaceuticals, the scanners have almost completely been re-

placed by the so called gamma camera (also called the Anger camera after the inventor Hal Anger), as illustrated in Figure 10.

This device still uses a collimator, normally a parallel hole collimator made out of a 5 - 10 mm thick slap of lead with many thousands of parallel small holes (<2 mm diameter). Behind the collimator, the camera is equipped with a large detector crystal (so called scintillator, normally sodium iodide) at least 10 mm thick and 500 mm in diameter. Gamma rays hitting the camera face parallel to the direc-tion of the collimator holes will pass the collimator and hit the crystal, here giving rise to absorption.

In scintillators the absorption will be followed by light emission called scintillation. Normally, scin-tillation is the result of either photo process or compton effect in the scintillator material. In both cas-es, the energy lost by the gamma ray results in a flash of light photons from the point of interaction in the crystal. The light flash can be detected by an array of light sensitive devices (photomultiplier tubes, PMT’s) mounted on the back of the sodium iodide crystal. The total energy imparted to the crystal can be judged by sum of all PMT outputs, and the relative position inside the crystal can be decoded by looking at the proportion of output signal between individual photo multipliers.

The energy and position information can be digitised and each scintillation event can be stored at the associated location in an image matrix, thus giving rise to the digital gamma camera image.

10 Energy discrimination and photopeakThe gamma camera works most effectively for gamma radiation energies above 80 keV and below

250 keV. At lower energies, the attenuation and scattering of the gamma rays inside the patient is large, thus attenuating the image before it is collected. The high energy limit is mainly due to the lim-

Figure 10 Gamma camera.

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itations in collimator construction and the required thickness of the scintillation crystal necessary to stop high energy photons.

Typical modern cameras have circular or rectangular detectors with dimensions of the order of 30 to 100 cm. The intrinsic geometrical resolution of light localisation in the crystal is in the order of 2-3 mm. The image size is of course limited by detector size, but multi-headed cameras or scanning camera heads moving up and down the patient can make whole body examinations from composite images in the order of 20-40 minutes total acquisition time.

The gamma camera head is of course heavy (collimator, sodium iodide, crystal and shielding). A special gantry with counter weight is often necessary to hold the detector head.

The single event detected from the crystal is analysed in terms of the energy before being accepted. Low energy events (below the photo-effect peak, so called photopeak) will normally be the result of a Compton process, either in the patient, in the crystal or in the collimator. Such events will not cor-respond to the correct position and are discarded.

Practical limits to energy resolution are about 15% FWHM.

Count rate limitations are given by the confluence of the light output of many simultaneous scintil-lation events in the crystal. Current generation cameras normally can maintain resolution and energy discrimination up to above 50,000 counts per second.

11 Gamma cameras only give the projection imageThe gamma cameras can detect and discriminate the point of entry of the gamma ray into the camera

head, but can normally not discriminate from what depths in the patient the radiation is coming. Thus, the gamma cameras image is a projecting of all activity throughout the patient. Images are taken either from the front of the patient (anterior projection) or from the back of the patient (posterior projection), as illustrated with the two whole-body skeletons in Figure 11.

Figure 11 Gamma camera images (scintigraphy) of a bone seeking 99mTc-labelled ra-diopharmaceutical.

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While these two projections should be identical for non-attenuated gamma rays, they will be quite different and yield independent information in real world imaging because of the attenuation of the gamma rays inside the patient. The anterior image will normally reflect activity lying close to the front surface of the patient while the posterior image will reflect information from the back part of the pa-tient. The best total quantitative representation of activity is given by the geometric mean of the inte-rior and exterior image, but it is clear that the image is limited to a 2-dimensional representation of the activity distribution. The interpretation of a gamma camera image can thus be quite difficult unless other projections are available. This limitation is overcome when multiple projections are obtained from many directions and total information reconstructed.

This is the subject of SPECT (single proton emission computed tomography) and PET (positron emission tomography) covered in later chapters. These methods can yield 3D information on the ac-tivity distribution: in the case of PET even without the use of lead collimators.

Modern gamma cameras are stable, relatively cheap (2 - 4 million DKK). All bigger hospitals have departments of nuclear medicine mainly concerned with gamma camera imaging. (In Denmark nucle-ar medicine is operating together with clinical physiology). Each department normally have several cameras.

12 Isotopes and radiopharmaceuticalsThe most commonly used radiopharmaceuticals are labelled with the 6-hour half-life isomer 99mTc

(Technetium) which emits 140 keV gamma rays (and very little other radiation). This isotope can be obtained from an isotope generator brought into the hospitals once a week. The generator contains 99Mo which decays with 66 hours half-life into 99mTc.

The radioactive Technetium can be chemically coupled to many different compounds. This is done in the hospital departments. The radioactive products are made available as radiopharmaceuticals for a variety of diagnostic situations. The most common gamma camera examinations are:

•bone (skeleton)

•kidneys and bladder

•thyroid

•lungs (ventilation and perfusion)

•tumours

With modern cameras and 99mTc-labelled radiopharmaceuticals, a geometrical resolution at 10 mm depth in the patient close to the surface of the collimator is about 6 mm FWHM, but deteriorates with depth and distance from the collimator to more than 20 mm at 15 cm distance. Clearly, this resolution is much lower than obtainable by X-ray techniques, but the information often reflects the function more than the stationary anatomy. This information is normally not available from the standard X-ray techniques.

Each point in a gamma camera image matrix reflects the result of the collection of individual gamma rays at this exact location. Thus each image cell can be regarded as a counter and the contents of the image cell is subject to normal Poisson statistics. Having collected a total of N counts in a matrix cell, the standard deviation of this image cell will be:

σ=√N

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In order to obtain good images without too much statistical noise, many counts have to be collected in the entire image matrix of several million events.

Even with this many counts, the limit of geometrical resolution is very often given more by the sta-tistical noise than by the ultimate geometrical resolution of the camera.

13 References[1]Harshaw Booklet on Scintillation Detectors" Harshaw Chemical Company, 1972

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