Radiation Detection

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Radiation Detection Measurement II

• Pulse height spectroscopy
• Nonimaging detector applications
• Counting statistics

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Pulse height analyzers

• Many radiation detectors produce electrical
  pulses whose amplitudes are proportional to the
  energies deposited in the detector by individual
  interactions
• PHAs are electronic systems that may be used with
  these detectors to perform pulse height
  spectroscopy and energy-selective counting
• In energy-selective counting, only interactions
  that deposit energies within a certain energy
  range are counted

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PHAs (cont.)

• Energy-selective counting can be used to
• Reduce the effects of background radiation
• Reduce the effects of scatter
• Separate events caused by different radionuclides
  in a mixed radionuclide sample
• Two types of PHAs single-channel analyzers
  (SCAs) and multichannel analyzers (MCAs)
• Pulse height discrimination circuits incorporated
  in scintillation cameras and other nuclear
  medicine imaging devices to reduce effects of
  scatter

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Single-channel analyzer systems

• High-voltage power supply typically provides 800
  to 1,200 volts to the PMT
• Raising voltage increases magnitude of voltage
  pulses from PMT
• Preamp connected to PMT using very short cable
• Amplifies voltage pulses to minimize distortion
  and attenuation of signal during transmission to
  remainder of system

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SCA systems (cont.)

• Amplifier further amplifies the pulses and
  modifies their shapes gain typically adjustable
• SCA allows user to set two voltage levels, a
  lower level and an upper level
• If input pulse has voltage within this range,
  output from SCA is a single logic pulse (fixed
  amplitude and duration)
• Counter counts the logic pulses from the SCA for
  a time interval set by the timer

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Energy discrimination occurs by rejection of
pulses above or below the energy window set by
the operator
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SCA energy modes

• LL/UL mode one knob directly sets the lower
  level and the other sets the upper level
• Window mode one knob (often labeled E) sets the
  midpoint of the range of acceptable pulse heights
  and the other knob (often labeled ?E or window)
  sets a range of voltages around this value.
• Lower-level voltage is E - ?E/2 and upper-level
  voltage is E ?E/2

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Example of a single-channel analyzer
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Plotting a spectrum using a SCA

• The SCA is placed in window mode, the E setting
  is set to zero, and a small window (?E) is
  selected
• A series of counts is taken for a fixed length of
  time per count, with the E setting increased
  before each count but without changing the window
  setting
• Each count is plotted on graph paper as a
  function of baseline (E) setting

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Energy calibration of SCA

• On most SCAs, each of the two knobs permits
  values from 0 to 1,000 to be selected
• By adjusting the amplification of the pulses
  reaching the SCA either by changing the voltage
  applied to the PMT or by changing the amplifier
  gain the system can be calibrated so that these
  knob settings directly indicate keV
• A Cs-137 source, which emits 662-keV gamma rays,
  is often used for calibration

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Multichannel analyzer systems

• An MCA system permits an energy spectrum to be
  automatically acquired much more quickly and
  easily than does a SCA system
• The detector, HV power supply, preamp, and
  amplifier are the same as for SCA systems
• The MCA consists of an analog-to-digital
  converter, a memory containing many storage
  locations called channels, control circuitry, a
  timer, and a display

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Modern, computer-based multichannel analyzer
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After the analog pulses are digitized by the ADC,
they are sorted into bins (channels) by height,
forming an energy spectrum.
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Interactions of photons with a spectrometer

• An incident photon can deposit its full energy
  by
• A photoelectric interaction (A)
• One or more Compton scatters followed by a
  photoelectric interaction (B)
• A photon will deposit only a fraction of its
  energy if it interacts by Compton scattering and
  the scattered photon escapes the detector (C)
• Energy deposited depends on scattering angle,
  with larger angle scatters depositing larger
  energies

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Interactions (cont.)

• Even if the incident photon interacts by the
  photoelectric effect, less than its total energy
  will be deposited if the inner-shell electron
  vacancy created by the interaction results in
  emission of a characteristic x-ray that escapes
  the detector (D)

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Interactions (cont.)

• Detectors normally shielded to reduce effects of
  natural background radiation and nearby radiation
  sources
• An x-ray or gamma-ray may interact in the shield
  of the detector and deposit energy in the
  detector
• Compton scatter in the shield, with the scattered
  photon striking the detector (E)
• A characteristic x-ray from the shield may
  interact with the detector (F)

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Spectrum of Cesium-137

• Cs-137 decays by beta particle emission to
  Ba-137m, leaving the Ba-137m nucleus in an
  excited state
• The Ba-137m nucleus attains its ground state by
  the emission of a 662-keV gamma ray 90 of the
  time
• In 10 of decays, a conversion electron is
  emitted instead, followed by a 32-keV K-shell
  characteristic x-ray

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Energy spectrum
Pulse height spectrum
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Reasons for differences in spectra

• First, there are a number of mechanisms by which
  an x-ray or gamma-ray can deposit energy in the
  detector, several of which deposit only a
  fraction of the incident photon energy
• Second, there are random variations in the
  processes by which the energy deposited in the
  detector is converted into an electrical signal

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NaI(Tl) crystal/PMT

• Random variations in
• The fraction of deposited energy converted into
  light
• The fraction of the light that reaches the
  photocathode of the PMT
• The number of electrons ejected from the back of
  the photocathode per unit energy deposited by the
  light
• Cause random variations in the size of the
  voltage pulses produced by the detector, even
  when the incident x-rays or gamma rays deposit
  exactly the same energy

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Pulse height spectrum of Cs-137

• Photopeak corresponding to interactions in which
  the energy of an incident 662-keV photon is
  entirely absorbed in the crystal
• Compton continuum caused by 662-keV photons that
  scatter in the crystal, with the scattered photon
  escaping the crystal
• The Compton edge is the upper limit of the
  Compton continuum

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Pulse height spectrum (cont.)

• Backscatter peak caused by 662-keV photons that
  scatter from the shielding around the detector
  into the detector
• Barium x-ray photopeak caused by absorption of
  barium K-shell x-rays (31 to 37 keV)
• Photopeak caused by lead K-shell x-rays (72 to 88
  keV) from the shield

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Spectrum of Technetium-99m

• Tc-99m is an isomer of Tc-99 that decays by
  isomeric transition to its ground state, with the
  emission of a 140.5-keV gamma ray
• In 11 of the transitions, a conversion electron
  is emitted instead of a gamma ray

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Decay scheme of Tc-99m and pulse height spectrum
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Tc-99m (cont.)

• Photopeak caused by total absorption of the
  140-keV gamma rays
• Escape peak caused by 140-keV gamma rays that
  interact with the crystal by photoelectric effect
  but with resultant iodine K-shell x-rays (28 to
  33 keV) escaping the crystal
• Photopeak caused by absorption of lead K-shell
  x-rays from the shield
• Compton continuum is quite small because the
  photoelectric effect predominates in iodine at
  140 keV

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Energy resolution

• Energy resolution of a spectrometer is a measure
  of its ability to differentiate between particles
  or photons of different energies
• Determined by irradiating detector with
  monoenergetic particles or photons and measuring
  width of resulting peak in the pulse height
  spectrum
• Statistical effects in the detection process
  cause the amplitudes of pulses from detector to
  randomly vary about the mean pulse height, giving
  the peak a Gaussian shape

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Energy resolution (cont.)

• Width is usually measured at half the maximal
  height of the peak called the full width at
  half-maximum (FWHM)

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Energy resolution of a pulse height spectrometer
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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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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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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