Transcript Types of Rad. Measurements

Part D: Factors Relating
to Radiation
Measurement
Unit II: Nuclear Medicine
Measuring Devices
CLRS 321
Nuclear Medicine Physics &
Instrumentation I
http://en.wikipedia.org/wiki/File:Aurora-SpaceShuttle-EO.jpg
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 nonparalyzable 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
Background
Background responses are those detected
but not originating with the intended
source
Background measurements <1%
of measured activity or counts
Sources
can be safely disregarded (but
still should be documented)
– 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)
Noise
Definition from book…
– “any undesired fluctuation that appears
superimposed on a signal source”
Sources:
– Randomness of decay
– Energy transfer variations
– Electrical partial frequencies that develop
– Background radiation
Nuclear Counting Statistics:
Random Decay
0 hr
5 hr
10 hr
15 hr
20 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-123 13 hours?
Random Decay
What if we had a gazillion I-123 atoms?
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)
Random Decay
Average (M):
M
N
i
i
n
Standard deviation (s or σ)
– Describes the spread of the values obtained
s
2
(
N

M
)
 i
i
n 1
Ni = individual measurements
n = number of measurements made
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
Poisson vs. Gaussian
Distribution
From Prekeges:
Gaussian Distribution:
 2  m  (N )2
Poisson Distribution:
2  m
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):
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 ( N  m)
– 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
 m
2
Percent Uncertainty
– Therefore, with variance being  2  m
– The standard deviation can be approximated using
our measurement:   N
– The percent uncertainty ( or Coefficient of Variation
[CV]) is given by

N
or
X 100%
N
X 100%
N
Which is also
100%
N
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.
So what does % uncertainty ( 100%
) have
N
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
So consider this…
100%
N
N = 100
N = 1000
N = 10,000
N = 100,000
100  10
1000  31.6
10, 000  100
100, 000  316.2
100%
 10%
10
100%
 3.2%
31.6
100%
 1%
100
100%
 0.3%
316.2
Standard Deviations in
quatrature
3   
2
1
2
2
•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
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
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.
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.
Chi Square Example
Use Probability Table
(From Sodee)
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
7.078 would pass.
p < 0.1 = too much variability
p > 0.9 = not enough variability
Probe Dead Time
4000000
3500000
3000000
CPM
2500000
2000000
1500000
1000000
500000
0
Decreasing Distance
(i.e. Getting source closer to detector-)
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.
% Losses = [(Rt – Ro)/ Rt] x 100%
Rt = True Count Rate
R0 = Observed Count Rate
Example: True Count Rate =
496,332 CPM
Observed Count Rate = 423,229 CPM
[(496,332 - 423,229)/496,332] X 100% = 14.7 % Loss
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.
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.
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
[(21,000 – 9000) / 42000] x 100
= 30.8 % uptake
= 28.6% uptake
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.
Determining Dead Time
R1 = Source 1
R2 = Source 2
R12 = Source 1 & 2 together
Sources 1 and 2 have nearly equal amounts of activity
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.
Baseline Shift & Pulse Pileup
From Prekeges:
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…
Counts
40
30
20
10
0
25
50
75
100
125
150 175 200
Volts
225
250
275
300
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
Characteristic
X-ray (such as
I.C.)
Eγ-E γmin
(Max E tranferred to electron,
electron deposits E on crystal)
Emax 
(0.140MeV )2
 0.049MeV
(0.140MeV  0.2555MeV )
Eγ-28keV
(From γ E lost to Iodine
electron scattered and the
Escape of the ch. X-ray)
Emin 
Characteristic X-rays from
lead interactions
0.140 MeV
 0.090 MeV
2(0.140 MeV )
1
0.511MeV
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)
{
CsSb
Photocathode
NaI (Tl)
Crystal
Thickness
Crystal Thickness
affects Efficiency
Optical Window
(transparent
material)
{
CsSb
Photocathode
The thinner the
crystal the less
likely a gamma
photon will deposit
energy
Optical Window
(transparent
material)
{
CsSb
Photocathode
NaI (Tl)
Crystal
Thickness
The thicker the
crystal the more
likely a gamma
photon will deposit
energy
Optical Window
(transparent
material)
{
CsSb
Photocathode
NaI (Tl)
Crystal
Thickness
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)
Calculating Efficiency
Efficiency =
Counts/unit time
Disintegrations/unit time x Mean number/disintegration X 100
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)
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.)
1.72116 x 105 cpm
X 100
(0.6 μCi)(2.22 x 106 dpm/µCi)(0.838)
= 15.4%
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
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.
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.
Flat Field Collimator
Example: Thyroid Uptake Probe
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.
Sensitivity
CsSb
Photocathode
NaI (Tl)
Crystal
Concerns the
effects of efficiency
and geometry
combined.
Gamma Photon
Optical Window
(transparent
material)
Attenuation
Photons can be attenuated before detection in
two ways:
– Within the source itself
– Within the medium between source & detector
Next Week:
Intro to Gamma Cameras
http://www.svalbard-images.com/photos/photo-aurora-borealis-004-e.php