1. Nuclear Medicine Physics & Instrumentation I
Lecture 2: Factors Relating to Radiation Detection
Unit IV: Miscellaneous Aspects of Nuclear Medicine Detections
CLRS 321
Nuclear Medicine Physics & Instrumentation I

2. Objectives
Discuss the sources and handling of background in counting instruments
Describe the random nature of nuclear decay and the application of statistical principles its measurement
Calculate standard deviation and coefficient of variation from a counting sample
Describe a Levy-Jennings plot and how it is used in monitoring instrument quality.
Calculate a chi-square test and describe its role in quality control of scintillation detectors

3. Background
Background responses are those detected but not originating with the intended source
Sources
Cosmic Radiation
Radiation from other decaying materials
Misrepresented electrical signals
All radiation measurements should note background and deduct this from the reading of the intended source (net)
Background measurements <1% of measured activity or counts can be safely disregarded (but still should be documented)

4. Noise Definition from book… Sources:
“any undesired fluctuation that appears superimposed on a signal source”
Sources:
Randomness of decay
Energy transfer variations
Electrical partial frequencies that develop
Background radiation

5. Random Decay
A gram of I-123 contains probably over a septillion atoms (1024).
With trillions upon quadrillions of I-123 atoms, we find that on average, half of the atoms decay in 13 hours
And based on the average time of decay equation (1.44 X T1/2), on average, I-123 atoms decay in about 19 hours.
This means that some may decay in less time, some in more—there’s no exact time.
Therefore, radioactive decay is a random process.

6. Random Decay Average (M): Standard deviation (s or σ)
Describes the spread of the values obtained
Ni = individual measurements
n = number of measurements made

7. Poisson Distribution
It is useful to describe variances in measuring radioactive decay by using a Poisson statistical distribution model
We are able to approximate the width of the frequency distribution with one measurement
If we have at least a value of 20 for each measurement, then the frequency distribution should follow a normal (or Gaussian Curve)

8. Poisson vs. Gaussian Distribution
From Prekeges:
Gaussian Distribution:
Poisson Distribution:

9. Poisson Distribution
Instead of giving a range of probabilities for a measurement based on standard deviations from the mean, Poisson is based on a range of probabilities for the mean based on standard deviations from the measurement.
From Sorenson (comparison of Poisson & Gaussian):

10. Variance
For random decay we use Poisson distribution to compare measured values to the probable true value.
The true value should be close to the average of measurements ( )
The mean has a 68.3% probability of falling within 1 Standard Deviation (σ) of our single measurement (N)
Or a 95.45% chance of falling within 2σ of N
Or a 99.7% chance of falling within 3σ of N
For a Poisson Distribution variance is given by

11. Percent Uncertainty Therefore, with variance being
The standard deviation can be approximated using our measurement:
The percent uncertainty ( or Coefficient of Variation [CV]) is given by
Which is also or

12. Poisson Distribution
Your textbook refers to % uncertainty as the coefficient of variation
Other texts refer to it at % error or % uncertainty
Still others will refer to it as standard deviation (though it really is not)
Note that the distribution spread is around N and not m (that would be a Gaussian Distribution)
Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 186.

13. So what does % uncertainty ( ) have to do with us?
We collect counts from our randomly decaying radioactive source over time.
We are trying to discriminate count variations from our source to…
Compare radionuclide uptake from background/noise
Form an image from uptake variations
If we have a lot of error in our counts due to the random process of decay, then…
Can’t accurately compare uptake from background/noise
Can’t accurately pinpoint concentrations of radionuclide
Can’t form a decent image from uptake variations

14. So consider this…
N = 100
N = 1000
N = 10,000
N = 100,000

15. Standard Deviations in quatrature
Key point—this means that your standard deviation compounds with multiple measurements
The book cites examples of figuring in backgrounds to low counts, but this will also come into play for SPECT imaging which you’ll study next semester

16. Conclusions about CV
More counts means increased uptake is truly increased uptake and not error caused by the random variation of the decay process.
Magic number in NM: 10,000 cts
(This means that our percent uptake compared to surrounding areas is only about 1% off due to random variation of decay)
Research magic number: 100,000 cts

17. Levi-Jennings Plot
For a Gaussian distribution, 95% of measurements should fall within ± 2 standard deviations
Used to track frequent quality measurements over time
By Dr. F.C. Turner - [USERPAGE|USERTALK] - 13:03, 15 February 2010 (UTC) - Transferred from en.wikipedia to Commons., Public Domain,

18. Chi-Square
A test to see if your system is compliant with the laws of nuclear radiation statistics.
A nuclear counting system should detect radiation events within an expected range of variance consistent with a Poisson Distribution
Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pp. 185&186.

19. Next Week: Dead time, spectra, and efficiency!