1. science
2. mathematics
3. algebra

Name _______________________________________________
Medical Imaging
BMEN 420-501 Spring 2015
Homework #4 and Nuclear Medicine Notes
All questions are from the introductory Powerpoint (based on Chapter 7) and text Medical Imaging Signals
and Systems, Chapters 8-9. Due Tuesday, April 13, 2015.
1. If nuclear medicine modalities use radioactive materials and don’t have very good resolution, what is their
great value to medical imaging as compared to most other modalities?
2
a. What does PET stand for?
b. SPECT?
2b. Explain the similar relationship between {projection radiography and CT} and {planar scintigraphy
and SPECT}
3. Is PET a tomographic or a projection technique? What mechanism (emission/detection) determines this?
Explain.
Planar scintigraphy instrumentation:
4. Unlike projection radiography and CT, in nuclear medicine we are not interested in detecting total intensity, but
in the detected decay rate of the source, expressed as counts/disintegrations per time. Nuclear medicine images
are thus built event-by-event. To detect these events, what instrument is used? Give both names.
Note: the GOAL of this instrument is to create an image that portrays the distribution of radioactivity (sites and
numbers of radioactive atoms) within the patient. That is, NUCLEAR MEDICINE MODALITIES MAP THE
DISTRIBUTION OF RADIOACTIVITY IN THE BODY.
5. There are seven components to the detector named in #4. See diagram 8.1. Fill in the blank with the
appropriate component following the description:
a. Thick slab of lead the same dimensions as the scintillation crystal with array of holes in it. Provides
an interface between the patient and the scintillation crystal by allowing only those photons traveling
in an appropriate direction to interact with the crystal. ____________________________________
b. Most commonly used detector in NM. Based on the property of certain crystals to emit light photons
(to scintillate) after deposition of energy in the crystal by ionizing radiation. Most commonly used is
sodium iodide with thallium doping ( NaI[T] ). __________________________________________
c. A vacuum tube that “receives” the thousands of light photons from the scintillation crystal (that were
produced by the incident ionizing gamma photon). This converts the light signal into an electrical
signal and amplifies the electrical signal. ______________________________________________
Additional important notes (think ‘There was an old lady who swallowed a fly…’): The response
(output) of the photomultiplier tube to the light photons that were produced by the scintillation crystal
with the arrival of a gamma photon is…
electrons that form a current pulse that has a pulse height that ranges from few millivolts to few volts.
There is an array of tubes that cover the entire scintillation crystal (to detect all events). More tubes
means more resolution, uniformity, but higher costs, more maintenance, difficult calibration. 37-91
tubes are used on current cameras.
d. Circuitry that determines 1) where on the face of the crystal the event occurred and 2) the combined
output of all the tubes (which represents the light output from the crystal which in turn represents the
energy deposited by the gamma photon). _____________________________________________
Additional important notes: the location (X,Y) of the event on the crystal can be determined to
within a fraction of the tube diameter by analyzing the spatial distribution of pulse heights. The rate of
(X,Y,Z) pulses coming from the camera is proportional to total radioactivity and size or height of (Z)
pulses is proportional to the energy deposited in the crystal by the gamma photon.
e. An analyzer that uses a scintillation counting system to obtain an energy spectrum from a radioactive
source in order to sort out desired events from Compton scattered events and reject photons that
have been Compton scattered ___________________________________________
Note: example 8.2 gives some more insight into this process if you are interested.
Circuitry used to “accept” or “reject” an event based on the output from the device in (e)
__________________________________________
g. Modern interface to the camera for image capture purposes _________________________________
f.
Planar scintigraphy Image Formation:
6. THE PRIMARY MECHANISM FOR CREATING IMAGES IN PLANAR SCINTIGRAPHY IS TO DETECT AND
ESTIMATE THE POSITION OF INDIVIDUAL SCINTILLATION EVENTS ON THE FACE OF AN ANGER
CAMERA.
Event position estimation is based on _________________________________________________
Hint: see “summary and key points” at the end of the chapter
7. If ak, k=1,…K represents amplitudes of tube responses, where there are K tubes located at (xk,yk), then
K
Z   ak represents the ____________________ of the light distribution, also denoted Z. The components of
k 1
the center of mass (X,Y) are calculated as:
X=____________________
Y=____________________
THE THREE VALUES (X,Y,Z) REPRESENT THE “HEART” OF AN ANGER CAMERA.
Example 8.3 gives excellent insight into this process.
8. Image acquisition modes. Fill in the blank:
a.
A “recording” of the imaging session without images being produced immediately. Instead, (X,Y)
signals and Z-pulse value are transmitted directly to computer memory, other physiological responses
can be recorded, time marks are included. Allows flexibility with future data manipulation.
_________________________________
b. The face of the Anger camera is represented as a matrix. An image is created during scan time by
starting with a zero image at the beginning of scan time and incrementing the pixel values as events
are accepted until a certain total count for the scan. ___________________________________
c.
A temporal succession of frame mode images. Allows the study of transient physiological processes
such as uptake, washout, redistribution. _______________________________________
d. A trigger signal (usually ECG-based) controls the distribution of data among multiple image matrices.
_____________________________________________
e. A variation of static frame mode acquisition where the body is divided into a matrix and a series of
static frames are acquired to cover the body. ______________________________________
9. Our imaging equation for planar scintigraphy can be developed (see section 8.3.3) as
0
 ( x, y ) 
0


A( x, y, z ) z
e
4 z 2
  ( x , y , z '; E ) dz '
dz
where Φ(x,y) is ____________________________________________________________
A(x,y,z) is ________________________________________________________________
μ(x,y,z’;E) is _______________________________________________________________
The distance from (x,y,z) to a detector position is just considered a function of z . Why do we use this
simplification?
10. The imaging equation as a whole is a type of projection, just like projection radiography. There are two
sources of depth-dependent attenuation between the radiation source inside the body and the detector:
1)
2)
Because of these effects, we expect that
1. Activity close to the camera will contribute a larger photon fluence rate than equivalent activity farther
from the camera.
2. Viewing the identical activity from one side of the body or the other will result in dramatically different
observed fluence rates (** SEE EXAMPLE FROM INTRODUCTORY PPT **).
Radiologists are trained to “correct” for this, just as they do for depth-dependent magnification in projection
radiography.
11. Rewrite equation 8.11 and explain it as a simplification of the imaging equation in #9.
12. The basic imaging equation includes terms for both _______________________ (the desired parameter) and
________________________________ (an undesired, but extremely important, additional factor). These two
terms are not separable. Hint: see “summary and key concepts”
Planar scintigraphy Image Quality:
13. Image quality in planar scintigraphy depends on three factors: (see “summary and key concepts”)
a.
b.
c.
14. The two factors that primarily affect image resolution are:
a.
b.
THESE TWO FACTORS COMBINE TO YIELD THE SYSTEM RESOLUTION OF THE ANGER CAMERA. THE
RESOLUTION OF THE CAMERA CAN BE CONSIDERED TO BE ITS ABILITY TO LOCALIZE A PHOTON
INTERACTION AND IS DEFINED BY A FWHM VALUE THAT DEPENDS ON THE PSFs OF THE
COLLIMATOR AND THE CAMERA.
15. It is common to assume that the PSF of the collimator, hC(x,y;|z0|), is Gaussian with FWHM equal to RC,
defined as collimator resolution. (Equation for RC is eqn. 8.12, but it is not necessary to know these details right
now). The collimator resolution is dependent on the depth of the source activity being detected, z0, and the
energy of the radiotracer used. *As always, our blurring can be expressed as a convolution with our
developed imaging equation.* Rewrite Equation 8.14 to reinforce this.
16. Blurring that takes place in the scintillator is characterized by the intrinsic resolution of the Anger camera.
There are two sources of the blurring [inaccuracy in estimation of (X,Y) ] in the scintillator:
1. Compton scatter events
2. Noise (statistical fluctuation)
We express the blurring due to intrinsic camera effects with a PSF, hI(x,y), a Gaussian with FWHM equal to RI.
Factor intrinsic resolution into our imaging equation by rewriting equation 8.18:
17. As we have discussed, a collimator experiences trade-off in sensitivity vs. resolution. A collimator with longer
“slits” will yield better resolution (stop more scatter events) but will also be less sensitive. While it is not
necessary to know the exact sensitivity equations, the example of 8.6 shows us that if we double the collimator
hole length, we reduce the sensitivity by ______________%.
18. Define field uniformity:
19. The intrinsic SNR of the planar scintigraphy image reflects a situation exactly like we discussed in
radiography: The SNR is made larger by increasing the number of detected photons. The count rate, however, is
affected by several factors. One of these factors is the resolving time of the camera. The inverse of the resolving
time is the __________________________________________. Exceeding the maximum counting rate will
cause ______________________________________________, where the photons are absorbed too close
together in the crystal to be counted as an event.
Emission Computed Tomography (PET and SPECT):
PLANAR SCINTIGRAPHY IS THE ONLY DIRECT NUCLEAR MEDICINE IMAGING METHOD, JUST AS
PROJECTION RADIOGRAPHY IS A DIRECT RADIOGRAPHIC IMAGING METHOD. SPECT AND PET, LIKE
CT, REQUIRE COMPUTED TOMOGRAPHIC IMAGE RECONSTRUCTIONS.
SPECT instrumentation:
SPECT image formation refers to true transaxial tomography with standard nuclear medicine pharmaceuticals
(the same as those used in planar scintigraphy that emit a single gamma photon upon decay). The options for
image detection in SPECT consist of a ring of detectors (expensive, never used) or a single detector (in this case,
the Anger camera), rotating around the patient. A single Anger camera rotating around the patient is the most
popular method. (See instrumentation photos in the introductory ppt)
**unlike CT acquisition, where we collimated our x-ray beam source into a slice in order to detect information
from a slice of the patient, the Anger camera detects from an area (think planar scintigraphy). After the series of
projections are acquired then, (lots of scintigraphy images from different angles), cross sections are extracted,
yielding a reconstructed volume. (See intro ppt for illustration)
PET instrumentation:
19. In PET, positron (antielectron: +1 charge, same rest mass as electron) emitting radionuclides are used. The
positron travels up to several mm in the tissue, meets a free electron, and mutual annihilation occurs. From
conservation of _______________, two gamma photons appear and from conservation of _________________,
they are emitted back-to-back.
20. It is possible to use an Anger camera to detect just one of the emitted photons. Images could then be
reconstructed using planar scintigraphy or SPECT reconstruction (if the camera rotates). HOWEVER, what
sharply distinguishes PET from SPECT is the use of rings of detectors and circuitry for Annihilation Coincidence
Detection. With this detection, only simultaneous gamma rays are declared events, and all others are rejected. If
two opposing detectors simultaneously detect the gamma rays, the annihilation event must have occurred
somewhere along that line.
That line is called the ________________________________.
*This concept makes detector collimation not only unnecessary, but undesirable.*
Note: Because PET and CT both require detector rotation and PET does not need collimation, it is state-of-theart to fuse anatomic and functional imaging with PET/CT systems, where detectors are rotated on the same
gantry, which leads to effective image registration between the two modalities. In addition, the CT maps
attenuation, which is a confounding factor in nuclear medicine. The CT image can be used then for image
“correction” on the nuclear medicine image.
SPECT Image Formation :
Notes on frame of reference (see Figure9.6):
In developing the imaging equation for planar scintigraphy, the x-y plane represented the detector surface
coordinates above the patient and z the depth into the patient. To study SPECT and PET, we will return to
notation we used when developing CT reconstruction. X-Y space is in the axial slice of the patient and z runs
l
head-to-toe on the patient. As with CT, represents the lateral position of the line integral and
the angle of detector rotation.
θ corresponds to
21. Our imaging equation with appropriate spatial variable changes from above, can be written as eqn 9.5
R
 ( ,  ) 
R


A( x( s ), y ( s )) s
e
2
4 ( s  R)
  ( x ( s '), y ( s '); E ) ds '
ds
keeping in mind that the parallel reconstructions along z are a separate computing issue after data acquisition.
What are the difficulties with reconstructing an image from the above equation?
22. What simplifications are commonly used to get us to equation 9.6? Rewrite Equation 9.6.
23. Use the line impulse function to rewrite the imaging equation exactly in the form of the CT imaging equation.
(see eqn 9.7)…
24. …. where we have the following relationships:
Desired object to reconstruct:
________in CT (attenuation map) ↔ ______ in SPECT (activity and location)
Data acquired (projection filled space from many angles):
_______ in CT↔ ________ in SPECT
One important difference:
SPECT uses actual data recorded by detectors (number of photons) in reconstruction. CT requires first a
logarithmic translation of intensities. (see equation 6.3 and 6.4).
25. Therefore, the reconstruction technique of choice is the convolution backprojection (the typically
“implemented” form of filtered backprojection). Rewrite Equation 9.10, the reconstructed activity map, A(x,y):
PET Image Formation :
Notes on frame of reference:
In developing the imaging equations for PET, we will be considering only 2D PET, since that is the natural form it
takes. We therefore assume a fixed ring of detectors receiving data from a given z plane. The cross-sectional
geometry then remains the same as CT and SPECT.
As with planar scintigraphy and SPECT, PET counts the number of detected photons, BUT these counts are now
based on ACDs rather than single gamma ray detections. Note that it is impossible to tell where the event
occurred on the line of response between two detectors 180 degrees apart. Therefore, like SPECT and CT, PET
measures over line integrals.
26. The imaging equation for PET can be written as 9.16
R
 ( ,  )  K
R
 A( x(s), y(s)) e

  ( x ( s '), y ( s '); E ) ds '
R
ds
R
Explain briefly the source of the difference in the integration limits between this equation and equation 9.5 that
was developed (and unsolvable) for SPECT.
27. Ignoring attenuation, as we did for SPECT, the activity map reconstruction equation can be written, just as
with SPECT as the inverse radon transform using the convolution backprojection method:
 
A( x, y )     (, )c ( x cos   y sin   )d d
0 
…where we have the following relationships:
Desired object to reconstruct:
________in CT (attenuation map) ↔ ______ in PET (activity and location)
Data acquired (projection filled space from many angles):
_______ in CT↔ ________ in PET
28. Unlike SPECT, PET has a straightforward approach for handling attenuation due to the fact that the
integration limits are different (see your answer to 26), giving a closed-form solution for attenuation correction. i.e.
In the case of PET (unlike SPECT) the attenuation term and the activity term can be separated. “Corrected
coincidence” allows for a more accurate reconstruction of the integral of activity along the line of response,
unaffected by attenuation in the body. See equation 9.22 for clarification.
How is this correction data acquired for PET?
29. ______________________________________ is a newer, more computer intensive approach to
reconstruction in PET and SPECT that implicitly takes the random nature of decay into account and can
incorporate models of attenuation, scatter, and blur.
Image Quality in PET and SPECT :
30. Image quality in SPECT and PET is limited by (see “summary and key points”)
a.
b.
c.
31. Rewrite the final expression for the reconstructed (blurred) image as related to the object (eqn. 9.26):
where h(r) represents the cascaded blurring sources.
32. This blurring in PET and SPECT also affects the axial resolution (note that this is mistakenly referred to as
“slice thickness”, which we will discuss in MRI). This effect is sometimes referred to as ___________________
_________________________________ (we will use this same term later in MRI).
33. The deterministic effects (attenuation, scatter, random coincidences) influence the “signal” component of
SNR; in other words, they affect an image’s _____________________________. Noise arises from random
statistical nature of radioactive decay and (somewhat) the hardware, influencing the “noise” component of SNR;
in other words, affecting the ________________________ of the technique.