Radiation Detection

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Radiation Detection Measurement III

• Nonimaging detector applications
• Counting statistics

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Thyroid probe

• Used for measuring
• Uptake of I-123 or I-131 by the thyroid gland of
  patients
• Monitoring activities of I-131 in the thyroids of
  staff members who handle large activities of
  I-131
• Usually consists of a 5.1-cm diameter and 5.1-cm
  thick cylindrical NaI(Tl) crystal coupled to a
  PMT and preamp
• Shielded on sides and back with lead and equipped
  with a collimator to detect photons from a
  limited portion of the patient

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Thyroid uptake measurements

• May be performed using one or two capsules of
  I-123 or I-131 sodium iodide
• A neck phantom, consisting of a Lucite cylinder
  of diameter similar to the neck and containing a
  hole parallel to its axis for a radioiodine
  capsule, is required
• Each capsule is placed in the neck phantom and
  counted
• One capsule is swallowed by the patient
• The other capsule is called the standard

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Thyroid uptake (cont.)

• Emissions from the patients neck are counted,
  typically at 4 to 6 hours after administration,
  and again at 24 hours after administration
• Each time the patients thyroid is counted, the
  patients distal thigh is also counted for the
  same length of time, to approximate nonthyroidal
  activity in the neck, and a background count is
  obtained
• All counts performed with NaI(Tl) crystal same
  distance (20 to 25 cm) from phantom, neck, or
  thigh

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Thyroid uptake (cont.)

• Single capsule technique
• Avoids cost of second capsule and requires fewer
  measurements
• More susceptible to instability of equipment,
  technologist error, and dead-time effects

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Sodium iodide well counter

• Used for clinical tests such as Schilling tests
  (test of vitamin B12 absorption), plasma or red
  blood cell volume determinations, and
  radioimmunoassays
• Consists of a cylindrical NaI(Tl) crystal with a
  hole in the crystal for insertion of samples
• Extremely high efficiency, permitting it to assay
  samples containing activities of less than 1 nCi

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NaI well counter (cont.)

• Crystal coupled to a PMT and preamp
• Should have a thick lead shield
• Used to count samples containing nanocurie
  activities in the vicinity of millicurie
  activities of high-energy gamma-ray emitters
• Departments that perform large numbers of
  radioimmunoassays often use automatic well
  counters

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Sample volume effects

• Position of the sample in a sodium iodide well
  counter has dramatic effect on detection
  efficiency
• When liquid samples in vials of a particular
  shape and size are counted, detection efficiency
  falls as volume increases
• In tests comparing a liquid sample from the
  patient with a reference sample, it is crucial
  that both samples be in identical containers and
  have identical volumes

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Dead-time effects

• High efficiency of NaI well counter can cause
  unacceptable dead-time count losses, even with
  sample activities in the microcurie range
• In general, well counters should not be used at
  apparent count rates exceeding about 5,000 cps

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Dose calibrator

• Most dose calibrators are well-type ionization
  chambers filled with argon (Z 18) and
  pressurized to maximize sensitivity
• Cannot directly measure activity measures
  intensity of radiation emitted by a dose of a
  radiopharmaceutical
• Manufacturer determines calibration factors
  relating the intensity of the detector signal to
  activity for specific radionuclides commonly used
  in nuclear medicine

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Counting statistics

• Sources of error
• Characterization of data
• Probability distribution functions for binary
  processes
• Estimating the uncertainty of a single
  measurement
• Propagation of error

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Sources of error

• Three types of errors in measurements
• Systematic error measurements differ from the
  correct values in a systematic fashion
• Random error caused by random fluctuations in
  whatever is being measured or in the measurement
  process itself
• Blunder

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Random error in radiation detection

• Processes by which radiation is emitted and
  interacts with matter are random in nature
• Whether a particular radioactive nucleus decays
  within a specified time interval
• The direction of an x-ray emitted by an electron
  striking the target of an x-ray tube
• Whether a particular x-ray passes through a
  patient to reach the film cassette of an x-ray
  machine
• Whether a gamma ray incident upon a scintillation
  camera crystal is detected
• Counting statistics enable judgments on the
  validity of measurements subject to random error

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Accuracy and precision

• If a measurement is close to the correct value,
  it is said to be accurate
• If measurements are reproducible, they are said
  to be precise
• Precision does not imply accuracy
• If a set of measurements differs from the correct
  value in a systematic fashion, the data are said
  to be biased

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Measures of central tendency

• The mean (average) of a set of measurements is
  defined as follows
• To obtain the median of a set of measurements,
  they must first be sorted by size
• The median is the middlemost measurement if the
  number of measurements is odd
• The median is the average of the two middlemost
  measurements in the number of measurements is even

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Measures of variability

• Variance and standard deviation are measures of
  the variability (spread) of a set of measurements

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Binary processes

• A trial is an event which may have more than one
  outcome
• A binary process is a process in which a trial
  can only have two outcomes, one of which is
  arbitrarily called a success
• A measurement consists of counting the number of
  successes from a specified number of trials

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Binary processes (cont.)
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Probability distribution functions

• A probability distribution function (PDF) (also
  known as a probability density function)
  describes the probability of obtaining each
  outcome from a measurement
• There are three PDFs relevant to binary
  processes
• Binomial
• Poisson
• Gaussian

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Binomial PDF

• The binomial PDF exactly describes the
  probability of each outcome from a measurement of
  a binary process

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Binomial PDF (cont.)

• The sum of the probabilities for all outcomes for
  the binomial PDF is 1.0
• Mean and standard deviation are
• If probability of a success in a trial is much
  less than 1,

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Poisson and Gaussian PDFs

• Because of the factorials in the expression for
  the binomial PDF, it is difficult to use if
  either x or N is large
• The Poisson and Gaussian PDFs are approximations
  to the binomial PDF that are often used when x or
  N is large

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Estimated standard deviation

• The standard deviation can be estimated, as
  previously described, by making several
  measurements
• If the process being measured is a binary
  process, the standard deviation can be estimated
  from a single measurement
• The single measurement is probably close to the
  mean the standard deviation is approximately the
  square-root of the mean also approximately the
  square-root of the single measurement

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Confidence intervals
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Propagation of error

• In nuclear medicine, calculations are frequently
  performed using numbers that incorporate random
  error
• It is often necessary to estimate the uncertainty
  in the results of these calculations
• Propagation of error equations are used to obtain
  the standard deviation of the result

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Propagation of error equations