unit i: physics associated with nuclear medicine instrumentation part a: atomic structure and...

Unit I: Physics Associated with Nuclear Medicine InstrumentationPart A: Atomic Structure and Radiation’s

Interaction with Matter

Lecture 2

CLRS 321

Nuclear Medicine Physics and Instrumentation 1

Lecture 2 Objectives(From your Textbook)

• Name and describe the primary forms of radioactive decay.

• Diagram the schematics of the various radioactive decay processes.

• Define Decay Constant.• Use the General form of the radioactive decay equation

to calculate precalibration and post calibration quantities of radioactivity.

• List the radioactive units and define curie and becquerel.• Write the equations for average half-life and effective

half-life and calculate effective and biological half-lives.

Decay Schematics

Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-11, p 49.

• Recently has become relevant to nuclear medicine http://www.xofigo-us.com/index.php

– Helium nucleus (2 protons, 2 neutrons) with no electrons.

– + 2 charge (it immediately wants two negative charges, i.e. electrons)

– An electron stripper. Excites and steals electrons from surrounding atoms, thus creating ion pairs (a positive ion and a negative ion).

– One Alpha can produce hundreds of thousands of ion pairs—very, very bad for biochemistry.

Decay Processes:Alpha Decay

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Decay Processes:Alpha Decay

Radium 223

Radon 219

Polonium 215

α

α

T1/2 = 11.4 hrs

T1/2 = 4 sec

T1/2 = 1.8 msec

Decay Processes:Beta Decay

• Used in nuclear medicine for therapies• High Velocity, negatively charged electron emitted from

a neutron-heavy nucleus• Neutron proton + beta + antineutrino + energy

– Energy=kinetic energy to beta + instantaneous gamma emission

• 1 MeV beta specific ionization: 45 ion pairs/cm– (1 MeV Alpha specific ionization: 60,000 ion pairs/cm)

• But beta more penetrating than alpha

n = p + β- + v + energy

Decay Processes:Beta Decay

Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-12, 2-13, p 49.

Decay Processes:Gamma Decay

• Result of a nucleus in a higher energy state

• Energy needs to be released for the nucleus to return to a more stable lower energy state

• May result as part of alpha and beta decay, or from a metastable nucleus

Like the electron shells, an atomic nucleus can have different energy states of specific energies. A nucleus of a certain type of atom will have specific “quantum”-like levels of energized states. It dissipates the energy by emitting electromagnetic radiation (gamma rays) at energies equivalent to the energized state.

Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 15.

Decay Processes:Gamma Decay

Energy States of the Nucleus

Decay Processes

• Isomeric Tranisition– Energized state of a nucleus: metastable– Transitions by releasing energy in the form of a gamma

photon– Parent & daughter have same atomic mass and number– Unlike I-131 and some beta emitters, the gamma

emission is not instantaneous– Not really a disintegration but a change in energy state

of the nucleus.– Prime example: Tc-99m Tc-99

Decay Processes:Beta Decay to Isomeric Transition Decay


Decay Processes:Positron Emission

P + N + + + + 2

2 X 511 keV 180

M. Crosthwaite “Nuclear Medicine not Unclear Medicine”

Happens with proton-rich nuclei, or either decay will occur by electron capture (explanation to follow).

Decay Processes:Positron Emission

Decay Processes:Electron Capture


http://commons.wikimedia.org/wiki/File:Electron_capture_NT.PNG

Decay Processes:Internal Conversion

• Often accompanies isomeric transition

Complex Decay Schemes


Multiple Gamma Emissions

Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Table 2-1, p 50.

• Decay Constant (λ):– Average proportion of atoms present

that will decay over a selected period of time.

• ex: 0.33/hour, means that 1/3 of atoms will decay in an hour

Mathematics of Decay

Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 50.

• Using calculus, we can derive the following:

• We can figure out the number of atoms remaining after the passage of a given amount of time (t).

What is e????Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 50.


• Change of atoms is directly related to decay and therefore atomic disintegration

• Disintegration is directly related to radioactivity (or Activity), Therefore…



• Easier to use half-life (T1/2) than decay constant (λ).


1/2

1/2

1/2

1/2

1/2

1

2

2

ln(2) ln( )

0.693

0.693

T

T

T

e

e

e

T

T

0T

tA A e

1/2

0.693

0

t

TtA A e

We know that we’ll have half of the activity after one half life (T1/2)

The natural log (ln) of the natural log base (e) to a given power is equal to that exponent.

The natural log (ln) of 2 = 0.693 (try it in your calculator)

Using substitution…

• Decay Factor

The “Decay Factor” (DF) can be multiplied against an original amount of activity to determine the amount of activity present after a period of time.



• Decay example (from book)



Radioactivity Units:Units, in General


Radioactivity Units

• Anytime a nuclide changes form it “disintegrates” to take on the new form.

• Radioactivity is measured according to the number of these disintegrations per unit time.


Radioactivity Units

• Becquerel (Bq)– SI unit– Based on a radioactive sample that decays at

1 disintegration per second (dps)– Because NM doses are much larger (mCi—

3.7 X 107 dps), we usually convert to mega Becquerels (Mbq—a million [106] Becquerels)

1 mCi = 37 MBq

Example: 3720 740

MBqmCi MBq

mCi

Radioactivity Units

• Average decay time:

Other Decay Calculations



Effective Half-life


• Effective half-life– Besides decaying the radionuclide is also

being metabolized by biological process, so effective half-life tells us about the activity remaining in the body after time.

– The decay constants for biological process and decay are cumulative.



• λ = 0.693/T1/2 for both bio and radioactive (or physical) half-lives

• Dividing each side of the decay constant equation by 0.693, we get…



• That equation can also be expressed as…



• Effective Half-life Example (from book)– Tc-99m MAA in the lungs

• Physical half-life of Tc-99m is 6 hrs• Biological half-life of MAA is 3 hrs

1 1 1 3 1

3 6 6 2efft hrs hrs hrs hrs

OR

(The answer is 2 hrs)

(3 6 ) /(3 6 ) 2efft hrsX hrs hrs hrs hrs


Next time:Next time:

Interactions of ionizing Interactions of ionizing radiation with matterradiation with matter

http://exclamationmark.wordpress.com/2006/08/30/the-amazing-colossal-man-

1957/

unit i: physics associated with nuclear medicine instrumentation part a: atomic structure and...

Documents

energy slide

alpha decay slide

gamma decay energy states

decay constant

gamma decay result

metastable nucleus slide

higher energy state

radioactive decay equation