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ENTC 4390 MEDICAL IMAGING

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					   ENTC 4390
MEDICAL IMAGING


 RADIOACTIVE DECAY
Nuclear Particles & Radiation
   Only a few of the many different nuclear
    emanations are used in medicine.
   In order of importance, the entities are:
    •   x-rays
        •   Electromagnetic waves of very short wavelength that
            behave in many ways like particles.
    •   Gamma (g) rays
        •   Electromagnetic waves similar to x-rays, but of even
            shorter wavelength.
    •   Neutrons
        •   Actual particles that are produced during the decay of
            certain radioacitve materials.
Radioactivity

                Don’t be confused by
                this picture!


                A single radioactive
                source does not emit
                all three types a, b
                and g.
3 Types of Radioactivity
 B field
 into
 screen




           Radioactive    detector
           sources
 a particles: helium nuclei          Easily Stopped
  b particles: electrons           Stopped by metal
 g : photons (more energetic than x-rays) penetrate!
   The nucleus of an atom consists of
    neutrons and protons, referred to
    collectively as nucleons.
   In a popular model of the nucleus (the
    “shell model”), the neutrons and protons
    reside in specific levels with different
    binding energies.
Materials Science Fundamentals

1.   The structure of an atom:
Materials Science Fundamentals

2. Elements/Atomic Number (Z) & Atomic
  Masses

Key: Chemical Behavior Determined by Z
 and Ionization
Materials Science Fundamentals

   Atomic Number:   # of Protons

   Mass Number: # of Protons and
           Neutrons

   Atomic Weight:   Total Mass of Atom
   If a vacancy exists at a lower energy level, a
    neutron or proton in a higher level may fall to fill
    the vacancy
    •   This transition releases energy and yields a more
        stable nucleus.
         • The amount of energy released is related to the
             difference in binding energy between the higher and
             lower levels.
         •   The binding energy is much greater for neutrons and
             protons inside the nucleus than for electrons outside the
             nucleus.
               •   Hence, energy released during nuclear transitions is much
                   greater than that released during electron transitions.
   If a nucleus gains stability by transition of a neutron
    between neutron energy levels, or a proton between
    proton energy levels, the process is termed an isometric
    transition.
    •   In an isomeric transition, the nucleus releases energy
        without a change in its number of protons (Z) or neutrons
        (N).
         •   The initial and final energy states of the nucleus are said to be
             isomers.
         •   A common form of isomeric transition is gamma decay (g) in
             which the energy is released as a packet of energy (a quantum
             or photon) termed a gamma (g) ray
         •   An isomeric transition that competes with gamma decay is
             internal conversion, in which an electron from an extranuclear
             shell carries the energy out of the atom.
   It is also possible for a neutron to fall to a lower
    energy level reserved for protons, in which
    case the neutron becomes a proton.
   It is also possible for a proton to fall to a lower
    energy level reserved for neurons, in which
    case the proton becomes a neuron.
    •    In these situations, referred to collectively as beta (b)
        decay, the Z and N of the nucleus change, and the
        nucleus transmutes from one element to another.
    •   In beta (b) decay, the nucleus loses energy and gains
        stability.
   In any radioactive process the mass
    number of the decaying (parent) nucleus
    equals the sum of the mass numbers of
    the product (progeny) nucleus and the
    ejected particle.
    • That is, mass number A is conserved in
      radioactive decay
   In alpha (a) decay, an alpha particle (two
    protons and two neutrons tightly bound
                           4
    as a nucleus of helium 2 He ) is ejected
    from the unstable nucleus.
    • The alpha particle is a relatively massive,
      poorly penetrating type of radiation that can
      be stopped by a sheet of paper.
   An example of alpha decay is:
          226
           88   Ra222Rn 2 He
                    86
                          4


          Radium     Radon   alpha particle
   ENTC 4390
MEDICAL IMAGING


  DECAY SCHEMES
   A decay scheme depicts the decay
    processes specific for a nuclide (nuclide
    is a generic term for any nuclear form).
    • Energy on the y axis, plotted against the
    • Atomic number of the nuclide on the x axis.
                              A
    Given a generic nuclide, Z X there are four
     possible routes of radioactive decay.
                                        A-4
    1. a decay to the progeny nuclide Z -2 P by emission of
          4
       a 2 He nucleus.
    2. (a) b (positron) decay to progeny nuclide Z -AQ by
                                                     1
       emission of positive electron from the nucleus.
    3. (b) b- (negatron) decay to progeny nuclide by Z 1 R
                                                         A

       emission of negative electron from the nucleus.
    4. g decay reshuffles the nucleons releasing a packet of
       energy with no change in Z (or N or A).
                          A
                          Z X
         A-4
                  
         Z -2 P                 
                                        A
                                      Z 1 R
Energy




                     A
                  Z -1Q               
                                         A
                                      Z 1 S




         Z-2       Z-1    Z     Z+1   Z+2

                    Atomic Number
ENTC 4390



BETA DECAY
   Nuclei tend to be most stable if they
    contain even numbers of protons and
    neutrons and least stable if they contain
    an odd number of both.
    • Nuclei are extraordinarily stable if they contain
      2, 8 ,14, 20, 28, 50, 82, or 126 protons.
       • These are termed nuclear magic numbers and
       • Reflect full occupancy of nuclear shells.
   The number of neutrons is about equal
    to the number of protons in low-Z stable
    nuclei.
    • As Z increases, the number of neutrons
      increases more rapidly than the number of
      protons in stable nuclei.
•Can get 4 nucleons in each
energy level-
   •lowest energy will favor N=Z,
•But protons repel one another
(Coulomb Force) and when Z is
large it becomes harder to put
more protons into a nucleus
without adding even more
neutrons to provide more of the
Strong Force.
   •For this reason, in heavier
   nuclei N>Z.
    ENTC 4390



ISOMERIC TRANSITIONS
   Isomeric transitions are always preceded
    by either electron capture or emission of
    an a or b (+ or -) particle.
   Sometimes one or more of the excited
    states of a progeny nuclide may exist for
    a finite lifetime.
    • An excited state is termed a metastable state
      if its half-life exceeds 10-6 seconds.
   An isometric transition can also occur by
    interaction of the nucleus with an electron in
    one of the electron shells.
    •   This process is called internal conversion.
         • The electron is ejected with kinetic energy Ek equal to
           the energy Eg released by the nucleus, reduced by the
           binding energy Eb of the electron



         • The ejected electron is accompanied by x rays and
           Auger electrons as the extranuclear structure of the
           atom resumes a stable configuration.
   The rate of decay of a radioactive
    sample depends on the number N of
    radioactive atoms in the sample.
    • This concept can be stated as
                      DN
                          -lN
                      Dt

       • where DN/Dt is the rate of decay, and the constant
        l is called the decay constant.
   The decay constant has units of time .
   It has a characteristic value for each nuclide.
   It also reflects the nuclides degree of
    instability;
    •   a larger decay constant connotes a more unstable
        nuclide
         • i.e., one that decays more rapidly.
    •   The rate of decay is a measure of a sample’s activity.
   The activity of a sample depends on the
    number of radioactive atoms in the
    sample and the decay constant of the
    atoms.
    • A sample may have a high activity because it
        contains a few highly unstable (large decay
        constant) atoms, or
    •    because it contains many atoms that are only
        moderately unstable (small decay constant).
   The SI unit of activity is the becquerel
    (Bq.) defined as
    • 1 Bq = 1 disintegration per second (dps)
   An older, less-preferred unit of activity is
    the curie (Ci), defined as
    • 1 Ci = 3.7 x 1010 dps
 Example
a. 201Tl has a decay constant of 9.49 x 10-3 hr -1. Find
    81
the activity in becquerels of a sample containing 1010
atoms.

                 DN          9.49  10-3                           atoms
Activity( A)  -      lN                1010 atoms  9.49  107
                 Dt              hr                                  hr
                         7 atoms      1 hr              4 atoms
            A  9.49  10                    2.64  10
                             hr     3600sec                sec
           A  2.64  104 Bq
Example
b. How many atoms of 11C with a decay constant of
                          6
   2.08 hr -1 would be required to obtain the same activity
   in the previous problem.
                        atoms            atoms          sec
             2.64 104         2.64 104          3600
        A                sec              sec          hr
    N 
        l        2.08 / hr               2.08 / hr
    N  4.57 107 atoms

• More atoms of 11C than of 201Tl are required to obtain
                  6            81
  the same activity because of the difference in decay
  constants.
   Note that the equation
                  DN
                      -lN
                  Dt

    • can be written as
                   dN
                       -lN
                   dt
    Rearranging and solving for N,
                        dN
                            -ldt
                        N


                                                 
natural log format              dN
                                    ln N  - ldt  -lt
                                N
                                            -lt
                            e   ln N
                                       e
                            N  Noe-lt
      •   where No is the number of atoms at time to .
   The physical half-life, T1/2, of a radioactive nuclide is
    the time required for decay of half of the atoms in a
    sample of the nuclide.
           N  Noe-lt
                    N  1
           T 1 / 2     e - lT1 / 2
                    No 2
             1
           ln 
              2  T  0.693
             -l           l
                     1/ 2
Example
   The half-life is 1.7 hours for 113mIn
    (Indium).
    a. A sample of 113mIn has a mass of 2mg.
   ENTC 4390
MEDICAL IMAGING


  DECAY SCHEMES
X-Rays
   Strong or high energy x-rays can
    penetrate deeply into the body.
   Weak or soft x-rays are used if only
    limited penetration is needed
   The energy of x-rays, as well as other
    nuclear particles is measured in
    •   electron-volts (ev)
    •   thousands of electron-volts (kev)
    •   millions of electron-volts (Mev)
   The diagnostic use of x-ray depends on
    the fact that various types of absorbs x-
    rays to a greater or lesser degree.
    •   Absorption by bone is quite high,
    •   Absorption by fatty tissue is low.
   This allows the use of the x-ray beam for
    delineating the details of body structure.
Gamma Rays
   X-rays are generally produced
    electrically.
   g_rays are the result of a radioactive
    transition in a substance that has been
    activated in a nuclear reactor.
   Once again, energy is measured in
    •   electron-volts (ev)
    •   thousands of electron-volts (kev)
    •   millions of electron-volts (Mev)
   The higher energy g-rays penetrate all
    human tissue quite easily.
     g-rays are used in conjunction with scanning
      systems to detect anomalies due to disease or
      neoplastic growth.
Neutrons
   Neutron applications in medicine are
    limited.
   Again, energy is measured in
    •   electron-volts (ev)
    •   thousands of electron-volts (kev)
    •   millions of electron-volts (Mev)
  Preflight - Gamma Ray Emission
Gamma rays are emitted due to electrons
 making transitions to nuclear energy levels.
  • true
  • false
            No, gamma rays are high energy photons
            emitted when nucleons make transitions
            between their allowed quantum states.
    Preflight - Nuclear Beta Decay
Beta rays are produced when the atom spontaneously
  repels all its electrons from its orbits.
   • true
   • false
Beta particles are electrons. However, the atom does not
emit its atomic electrons.
Beta electrons are emitted by a nucleus along with a
neutral weakly interacting particle called the neutrino
when one of the neutrons in the nucleus decays.
                Free neutrons are unstable - they decay.
                Sometimes in atoms with large numbers
 n  p e  of neutrons, one of its neutrons may be
        + -

                loosely bound - spontaneous decay!
Preflight - Positrons
Beta particles are:
    • Always negatively charged.
    • Always positively charged.
    • Some beta decays could produce positively
      charged particles with properties similar to
      those of electrons.
Some radioactive elements emit a positively
charged particle which is in all other respects
similar to an electron! Anti-matter!! Positrons!!!
 Preflight - Alpha Particles
 Alpha particles are:
   • Electrons
   • Protons.
   • Nuclei of Helium atoms
   • nuclei of Argon of protons and many more
Some Nuclei have lots atoms
protons. Lowest energy bound-states require about
equal numbers of protons and neutrons. Those
nuclei emit most tightly bound nuclear matter, i.e.,
Helium nuclei with two protons and two nuclei.

				
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posted:1/3/2013
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