1. Nuclear Medicine Physics & Instrumentation I
Part D: Factors Relating to Radiation Measurement
Unit II: Nuclear Medicine Measuring Devices
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
Calculate a chi-square test and describe its role in quality control of scintillation detectors
Define dead time and its effect in both paralyzable and non-paralyzable counting systems
Define baseline shift and pulse pileup
Describe the make up of an energy spectrum and identify its key characteristics
Identify factors that can impact detector efficiency
Calculate the efficiency of a scintillation detector and its efficiency factor

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. Nuclear Counting Statistics: Random Decay
0 hr hr hr hr hr
Mmmm…
It took about 17 hours for four of these eight I-123 atoms to decay.
How come?
Isn’t the half-life of I hours?

6. Random Decay
What if we had a gazillion I-123 atoms?

7. Random Decay
With trillions upon quadrillions of I-123 atoms, we find that on average, half of the atoms decay in 13 hours
Radioactive decay fits a Poisson Distribution Curve
A Poisson Distribution is derived from a normal frequency distribution (or Gaussian distribution)

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

9. Poisson Distribution
Radioactive decay follows the 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)
Poisson distribution is derived from a Gaussian curve and is slightly different

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

11. 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):

12. 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

13. 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 or
Which is also

14. Poisson Distribution
Your textbook refers to % uncertainty as the coefficient of variation
Other texts refer to it at % error
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.

15. 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 form a decent image from uptake variations

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

17. 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

18. Conclusions
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

19. 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.

20. Chi Square Example
X2 results are then compared to a probability chart based on the degrees of freedom
(Which is N-1)
We will do this in the last instrumentation lab.

21. Chi Square Example Use Probability Table (From Sodee)
p < 0.1 = too much variability
p > 0.9 = not enough variability
Our degrees of Freedom are 10-1 or 9.
Our results need to fall between the probabilities of 0.90 and 0.10 (remember, our result cannot be significant [0.05] on either end).
Our Chi-square of would pass.

22. (i.e. Getting source closer to detector-)

23. Dead Time A.K.A. Pulse Resolving Time (τ)
Time required to process individual detection events
Is a characteristic for each system
Dead time losses (also called coincidence losses) occur when an event is detected before the previous pulse duration has passed—usually happens in the pulse amplifier.

24. % Losses = [(Rt – Ro)/ Rt] x 100%
Rt = True Count Rate
R0 = Observed Count Rate
Example: True Count Rate = ,332 CPM
Observed Count Rate = 423,229 CPM
[(496, ,229)/496,332] X 100% = 14.7 % Loss

25. Non-paralyzable --- Pulses acquired during dead time ignored until maximum possible rate is reached
Paralyzable --- Each event introduces its own dead time until it jams things up
Simon Cherry, James Sorenson, & Michael Phelps, Physics in Nuclear Medicine, 3d Ed., (Philadelphia: Saunders (Elsevier) 2003), pg. 179.

26. Maximum Observed Count Rate
Paul Christian, Donald Bernier, James Langan, Nuclear Medicine and Pet: Technology and Techniques, 5th Ed. (St. Louis: Mosby 2004) pg 64.
Simon Cherry, James Sorenson, & Michael Phelps, Physics in Nuclear Medicine, 3d Ed., (Philadelphia: Saunders (Elsevier) 2003), pg. 179.

27. Practical Application – Thyroid Uptake
400 μCi I-123 Capsule counted at 39,000 CPM (observed)
[But True count rate = at 42,000 CPM (7.1% Dead Time Losses)]
% Uptake = [(Neck Counts – Thigh Counts) / Capsule] x 100
(Assume decay already calculated)
Observed
True
[(21,000 – 9000) / 39000] x 100
= 30.8 % uptake
[(21,000 – 9000) / 42000] x 100
= 28.6% uptake

28. Dead Time Correction
Paul Christian, Donald Bernier, James Langan, Nuclear Medicine and Pet: Technology and Techniques, 5th Ed. (St. Louis: Mosby 2004) pg 64.
Simon Cherry, James Sorenson, & Michael Phelps, Physics in Nuclear Medicine, 3d Ed., (Philadelphia: Saunders (Elsevier) 2003), pg. 179.

29. Determining Dead Time
R1 = Source R2 = Source R12 = Source 1 & 2 together
Sources 1 and 2 have nearly equal amounts of activity

30. Dead Time Calculations
Paul Christian, Donald Bernier, James Langan, Nuclear Medicine and Pet: Technology and Techniques, 5th Ed. (St. Louis: Mosby 2004) pg 64.
Simon Cherry, James Sorenson, & Michael Phelps, Physics in Nuclear Medicine, 3d Ed., (Philadelphia: Saunders (Elsevier) 2003), pg. 182.

31. Baseline Shift & Pulse Pileup
From Prekeges:

32. Energy Spectra
If we lived in a perfect world with no scatter and perfect detectors, we would get a gamma “pulse-height” spectrum that looked like… 40 30 20 10
Counts
Volts

33. The photopeak represents gamma interactions in which the entire energy of the photon has been deposited on the crystal
Figure 03: Peak broadening as seen with scintillation detectors

34. Characteristic X-ray (such as I.C.)
Eγ-E γmin
(Max E tranferred to electron, electron deposits E on crystal)
Eγ-28keV
(From γ E lost to Iodine
electron scattered and the
Escape of the ch. X-ray)
Characteristic X-rays from lead interactions

36. Optical Window (transparent material)
CsSb Photocathode
NaI (Tl) Crystal
Detector Efficiency
Concerns the degree to which ionizing radiation actually deposits energy on the NaI(Tl) crystal.
Gamma Photon
Optical Window (transparent material)

37. { Crystal Thickness affects Efficiency NaI (Tl) Crystal Thickness
CsSb Photocathode {
Crystal Thickness affects Efficiency
Optical Window (transparent material)

38. Optical Window (transparent material)
CsSb Photocathode {
The thinner the crystal the less likely a gamma photon will deposit energy
Optical Window (transparent material)

39. NaI (Tl) Crystal Thickness{
CsSb Photocathode
The thicker the crystal the more likely a gamma photon will deposit energy
Optical Window (transparent material)

40. NaI (Tl) Crystal Thickness{
CsSb Photocathode
Therefore, many thyroid probe crystals are about 5 cm thick, which is best suited for I-123’s 159 keV gamma photon energy
Optical Window (transparent material)

41. Calculating Efficiency
Counts/unit time
X 100
Disintegrations/unit time x Mean number/disintegration
Things to consider…
The raw definition of activity is disintegrations per unit of time, so usually you need to convert your activity to disintegrations
Often, your source has decayed, so you will need to calculate the activity when you conduct your efficiency calculation
The mean number/disintegration is derived from the percent abundance, which usually can be found in tables with information about the radionuclide
This is the percent of the disintegrations that are giving off the gamma photons you are measuring (and therefore, you are not measuring ALL of the disintegrations going on)
The percent is converted to decimal amount (e.g. 75% = 0.75)

42. Defininition: 1 μCi = 2.22 x 106 dpm
Efficiency Example
1.2 μCi I-131 Assayed 8 days ago
Counted at 172,116 cpm (1.72 X 105)
364 keV abundance in I-131 = 83.8 %
Defininition: 1 μCi = 2.22 x 106 dpm
(1st you’d have to decay calculate the 1.1 µCi. Conveniently the time elapsed is 1 half-life, so in this case, you have half the dose, or 0.6 µCi.)
x 105 cpm
X 100
= 15.4%
(0.6 μCi)(2.22 x 106 dpm/µCi)(0.838)

43. Finding Actual Counts using Efficiency as a Factor
From the previous efficiency example:
Efficiency = 15.4%
(Efficiency factor would be 0.154)
Measured amount was 172,116 cpm
What was the actual count rate considering the counting efficiency of our detector?
dpm = net cpm / efficiency factor
dpm = 172,116 cpm / 0.154
dpm = 1,117,636 cpm

44. Geometry Can affect count rate for well and probe
Higher volumes mean some gamma energy is being attenuated by the source
Higher volumes mean less of the activity interacts with the crystal
Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 178.

45. Geometry is an important consideration when performing thyroid uptakes.
Not only must we carefully center the detector on the thyroid gland, but we must also be consistent with distance for each measurement.

46. Flat Field Collimator Example: Thyroid Uptake Probe Isocount lines
Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 181.
Isocount lines
Fig 3-12 from “Imaging Systems,” Nuclear Medicine Technology and Techniques, 2nd Ed., Donald R. Bernier et al, Eds, [St. Louis: C.V. Mosby Co., 1989], p. 89.

47. Optical Window (transparent material)
CsSb Photocathode
Sensitivity
NaI (Tl) Crystal
Concerns the effects of efficiency and geometry combined.
Gamma Photon
Optical Window (transparent material)

48. Attenuation Photons can be attenuated before detection in two ways:
Within the source itself
Within the medium between source & detector

49. Next Week: Intro to Gamma Cameras