Radiation Detection & Measurement II

Pulse height spectroscopy

Nonimaging detector applications

Counting statistics

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

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

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

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

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

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

Example of a single-channel analyzer

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

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

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

Modern, computer-based multichannel analyzer

After the analog pulses are digitized by the ADC, they are sorted into bins (channels) by height, forming an energy spectrum.

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

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)

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)

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

Pulse height spectrumEnergy spectrum

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

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

Pulse height spectrum of Cs-137

A. Photopeak corresponding to interactions in which the energy of an incident 662-keV photon is entirely absorbed in the crystal

B. Compton continuum caused by 662-keV photons that scatter in the crystal, with the scattered photon escaping the crystal

C. The Compton edge is the upper limit of the Compton continuum

Pulse height spectrum (cont.)

D. Backscatter peak caused by 662-keV photons that scatter from the shielding around the detector into the detector

E. Barium x-ray photopeak caused by absorption of barium K-shell x-rays (31 to 37 keV)

F. Photopeak caused by lead K-shell x-rays (72 to 88 keV) from the shield

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

Decay scheme of Tc-99m and pulse height spectrum

Tc-99m (cont.)

A. Photopeak caused by total absorption of the 140-keV gamma rays

B. 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

C. 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

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

Energy resolution (cont.)

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

100% peak ofcenter at height Pulse

FWHM resolutionEnergy

Energy resolution of a pulse height spectrometer

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

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”

Thyroid uptake (cont.)

• Emissions from the patient’s neck are counted, typically at 4 to 6 hours after administration, and again at 24 hours after administration

• Each time the patient’s thyroid is counted, the patient’s 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

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

phantomin capsulepatient ofcount Initial

phantomin standard ofcount Initial

count Background - phantomin standard ofCount

countThigh -count Thyroid Uptake

1/2t/T693.0

count Background - phantomin capsule ofCount

countThigh -count Thyroid Uptake e

Counting statistics

• Sources of error

• Characterization of data

• Probability distribution functions for binary processes

• Estimating the uncertainty of a single measurement

• Propagation of error

Sources of error

Three types of errors in measurements:1. Systematic error – measurements differ from

the correct values in a systematic fashion

2. Random error – caused by random fluctuations in whatever is being measured or in the measurement process itself

3. Blunder

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

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

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

N

xxxx N

21

Measures of variability

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

x

N

xxxxxx N

deviation standard fractional

deviation standard

1 variance

2

222

212

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

x

Confidence intervals

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

Propagation of error equations