Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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AN IMAGING APPARATUS
The present invention relates to an im~gin~ apparatus, and more particularly to a
im~ging apparatus which enables a dual-headed gamma camera to be used for routine
diagnostic im~ging of positron-emitting radionuclides, as well as single-photon-emitting
5 radionuclides. Such a device is hereinafter referred to as a modified dual-headed gamma
camera.
A modified dual-headed gamma camera is used to image positron-emitting
radiopharmaceuticals in routine clinical applications. The present invention describes a
modified dual-head gamma camera which is capable of retaining the ability to image
10 single-photon-emitting radioph~rm~euticals. The invention thus enables opposing gamma
camera detectors to operate in coincidence mode, thereby obviating the need for
collimators. The subsequent improvement in sensitivity over a collimated system is
exploited by use of fast digital processing techniques to handle efficiently the relatively
high rate of single events, and by the application of a fully three-dimensional image
15 reconstruction technique to ensure efficient use of acquired data. The invention may be
incorporated as a switchable unit in future gamma camera system designs, or it may be
retro-fitted as a modular add-on to existing designs.
An example of an existing gamma camera im~ging system is described in granted
United States Patent Number US-A-4057727 (Muehllehner et al). The arrangement
20 described comprises a positron im~ging system having two opposed Anger cameras~ each
camera having an approximately one inch (0.0254m) thick unity layer of scintillation
crystal. However, the arrangement suffered from the drawback that, because such a thick
layer of scintillation crystal was present, there was poor event separation which gave rise
to poor spatial resolution. Because of the poor event separation the system also had a
25 low count rate. Additionally it was not possible to use all events for image reconstruction.
Radionuclide im~gin,~ is a means by which the physiology of a patient can be
studied and is therefore used as a tool in patient diagnosis and treatment management. The
basis of the technique is to introduce a radioactive substance into the patient after attaching
it chemically to a physiologically important pharmaceutical, and to use gamma ray
3 0 emissions from this radiopharmaceutical to construct images of its distribution at
subsequent times under certain controlled conditions. The clinical information obtained
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from the test depends on the biochemistry of the radiopharmaceutical, and the types of
radiopharmaceutical available are often limited by the chemical properties of the
radioactive element to be attached.
The commonest form of radionuclide im~ging iS to study gamma ray emissions
5 from radionuclides that emit single gamma ray photons of energies in the range 50-400keV.
The tomographic study of such emitters is usually termed SPET or SPECT, though static
and non-tomographic whole body scans are common. The equipment used to image these
emissions is the gamma camera, which is a position sensitive gamma ray detector. A
gamma camera detects gamma rays using a scintillation material (usually a single crystal
lO of thallium-doped sodium iodide). Gamma rays incident on the scintillation material
convert some of their energy into optical light which is detected by a number ofphotosensitive detectors (usually photomultiplier tubes optically coupled to the scintillator
by a lightguide). The detector obtains the directional information of each gamma ray by
means of an absorbing collimator, which limits the solid angle of acceptance to a narrow
15 range around a particular set of directions.
It is possible to use several planar images obtained at different orientations around
the patient to reconstruct a 3-dimensional (tomographic) image of the radiopharmaceutical
distribution.
Another form of radionuclide imZlging is positron emission tomography (PET). In
20 this case, the radioactive element emits a positron when it decays, which then collides with
a nearby electron in the patient. The positron and electron undergo mutual annihilation
resulting in the emission of two 51 l keV gamma rays in near-opposite directions. The near-
collinear property of these photons is useful in determining the location of the emission
point in the patient and collimation is not necessary if both gamma rays are detected. In
25 fact, because the energy of the gamma rays is so much higher than those encountered in
SPET, gamma cameras are not well-suited to detecting them. PET radionuclides aretherefore usually imaged with a dedicated PET imager, which consists of several rings of
position-sensitive scintillator/photomultiplier detectors operating in coincidence mode (i.e.
~ithout a collimator). The detectors (usually bismuth germanate, BGO, scintillators backed
30 by position-sensitive photomultipliers) are optimised to detect 51 lkeV gamma radiation.
Gamma ray events arriving at the detector rings at the same time are assumed to originate
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from the same ~nnihil~ion event and the line between the two serves as the locus of
possible emission sites within the patient. If many events are recorded, a tomographic
image of the radiopharmaceutical distribution may be reconstructed.
SPET im~ging with gamma-cameras is well established as a routine diagnostic tooland has a wide range of clinical applications in areas such as cardiology, oncology and
neurology. However, the single photon emitters tend to be heavy elements (e.g. technetium
99mTc) and the range of pharmaceuticals to which these can be attached is limited. Positron
emitters, on the other hand, tend to be lighter elements (e.g. fluorine '8F) and are more
readily attached to biologically important chemicals. For this reason, PET has been
developed over the past two decades into a highly valuable research tool, providing
physiological and medical im~gin~; data not obtainable in any other way.
Recently it has become apparent that PET techniques can make a major contribution
to diagnosis and patient management in routine medical practice (Schwaiger and Hutchins
1992, Broich ef al. 1992 and Hawkins et al 1992). Whilst specialised centres derive great
benefit from brain perfusion and functional im~ging the most important areas for more
general clinical application are in cardiology, demonstrating regional perfusion and
myocardial viability more precisely than by any other technique, and in oncology where
1 8F-fluorodeoxyglucose (FDG) has been demonstrated to provide unique information on
tumour staging and assessment of residual tumour viability following therapy.
Despite this, PET radionuclides are not currently used as routine diagnostic im~ging
agents. The chief reason for this is cost. Because of their higher energy, PET gamma ray
emissions are most effectively imaged by a dedicated PET imager. However, a dedicated
PET imager is currently approximately six times as expensive as a state-of the art, large
field of view modified dual-headed gamma camera. This is largely because PET imagers
consist of several detection rings, each comprising many small, high-cost position sensitive
detectors, whereas the comparatively simple modified dual-headed gamma camera consists
of only two large position-sensitive detectors. In addition to this, for a dedicated PET
- imager to be viable, it requires its own source of short-lived radionuclides on-site; for
example a cyclotron. A complete dedicated PET facility. with imager, cyclotron, and
associated buildings costs can be very expensive and accordingly. dedicated PET im~ging
is restricted to research use in specialist centres. Routine diagnostic scans are simply too
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expensive.
There have been several ~LLelllpL~ to develop a low-cost alternative to the dedicated
PET scanner. However, none of these is suitable for routine diagnostic im~gin~, either
because the cost remains prohibitively high, or because the count rate performance or
5 sensitivity is too low for practical routine use. If the count rate performance is poor, scans
simply take too long. If the sensitivity is too low, a high amount of radioactivity is required
to complete an acquisition in a reasonable time, and the radiation dose to the patient may
be too high for routine or repeated use.
According to the present invention there is provided an im~ginp; apparatus having
10 first and second gamma cameras, arranged such that the gamma cameras are substantially
diametrically opposed, means for detecting an event, processing means for counting events
and for manipulating data obtained from events so as to construct an image of an object,
characterised in that the solid angle of the gamma cameras is not limited by collimation.
Preferably shielding vanes are provided to reduce the number of single events.
A thin layer of scintillation crystal material is provided, typically of the order of
thickness of 0.095 m, which is the industry standard thickness. Improved sensitivity may
be obtained by removing the collimators which were present on prior art systems. This
permits the modif1ed dual-headed gamma camera to be used in coincidence mode without
collimators and increases the sensitivity of the apparatus over existing collim~te~:l systems.
20 Furthermore, the count rate is improved by using digital event detectors and pulse
separation techniques.
In a pl~r~lled embodiment the invention is a unit that is used to enhance the
performance coincidence detection and image reconstruction to a modified dual-headed
gamma camera to enable it to be used effectively in routine imzlging of PET radionuclides.
25 It takes the position and energy signals from each detector and uses them to determine that
an event has occurred, to distinguish overlapping events. and to perform the image
reconstruction using an eff1cient technique. The unit may be added as a stand-alone device
onto existing gamma camera designs or it may be incorporated as a switch-in integral
module in future designs. In either case, the invention can be easily disabled to allow the
30 system to operate in single-photon mode.
Shielding vanes may be necessary to reduce the number of single events reaching
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the detectors. Detector tuning and calibration, and gantry operation may be controlled by
the host system.
In addition to these preferred features of the invention, Digital Signal Processing
(DSP) means may be provided for enhancing the speed of processing data. This allows the
5 high singles count rate, which is a direct consequence of the thinner crystal layer, to be
handled. Preferably Fast Fourier Transformation is applied to the data, using said DSP
means.
Sensitivity and count rate performance may be further improved by application ofa fully 3-dimensional reconstruction technique because this uses approximately all of the
10 time coincidence events; unlike previous systems, which have rejected many of these
counts.
The invention described in this Application describes a viable low-cost alternative
to the dedicated PET imager that addresses system performance and is therefore the first
device that will facilitate the use of PET radionuclides in routine medical practice. In a
15 preferred embodiment the im~ging apparatus allows single-photon, as well as positron-
emission tomographic, whole body and planar scans to be carried out on the same system.
The im~ging ~ Lus' performance carmot compete with a dedicated PET scanner, and it
can only image longer-lived radionuclides, such as l8F, but can produce clinically useful
results and with its low cost it is the only practical method for routine im~ging of PET
20 radiopharrnaceuticals.
The main low-cost alternatives to the dedicated PET imager are discussed below:
The first is a Multiple Wire Proportional Chamber (MWPC). The multiple wire
proportional chamber is a form of position sensitive ionisation chamber comprising a large
area gas filled chamber cont~ining an array of fine wires. In a PET system, two opposing
25 MWPC s are operated in coincidence. The chief advantage of a MWPC system is its low
cost. MWPCs require a solid photon-electron converter within the chamber to make them
suitable for detecting 51 lkeV gamma rays. Ott (1993) reports that most MWPC detectors
achieve a single-photon detection eff1ciency up to 20% at 51 lkeV. While this is better than
gamma-camera efficiency. the detectors are very susceptible to scattered radiation and have
30 no energy discrimination ability. They therefore suffer a great deal from single event count
rates, and accidental coincidences. As a result of this MWPC systems actually have low
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count rate capability: the MUPPET system has a maximum data rate under 3kcps. The
HIDAC system (Townsend et al. 1987) has a maximum count rate capability of around
4kcps. This low data-rate is the main reason why the MWPC systems have not become
commercial products.
Ott notes that the improved efficiency of a hybrid detector consisting of Barium-
Fluoride scintillator in conjunction with a MWPC filled with UV-photon sensitive gas
(TMAE) may provide an effective, low-cost alternative to BGO systems.
The second low cost alternative is a Cost-Reduced PET Imager. The low data rate
of MWPC detectors has discouraged some researchers from this approach. A group in
10 Geneva are working on a project to develop a rotating PET scanner using BGO block
detectors, with the help of Siemens, (Townsend et al. 1993). This system is a cut-down
version of a static dedicated PET imager, and comprises two rotating, opposing sections
of a PET detector operating in coincidence. This system has the advantage that it uses
detectors optimised for SllkeV. However, it cannot image single photon emitting
15 radionuclides, and, although it is doubtless less expensive than a full dedicated PET imager,
it is estimated to be more expensive than the present invention.
The relative low cost of gamma camera systems make them an aKractive possible
alternative for low-cost and hence routine PET im~ging. However, the gamma camera is
optimised to image at energies around 140keV and cannot operate at 51 lkeV without
20 modification. If the modification is such that the original system set-up can be reverted to
easily, these systems have the advantage that they have the dual capability of single-photon
(SPET) work and routine PET im~ging Several attempts have been made at modifying a
gamma camera to image PET radionuclides. Some are briefly described below.
The most obvious method of modifying a gamma camera to image PET
25 radionuclides is to use a special collimator optimised for 511 keV radiation, and to operate
the detectors under a different set of control parameters and with a simple software
modification to enable them to accept the corresponding signal sizes. This method has been
used successfully to image PET radionuclides by several groups (Van Lingen et al. 1992~
Kalff et al. 1994) and nuclear medicine (SPET) system rnanufacturers are now offering
30 these collimators as product or work in progress with varying amounts of success (Britten
et al. 1995, Clarke et al. 1995). The first problem with im~ging 51 lkeV radiation with a
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collim~ted gamma camera is that the probability of a photopeak interaction in the crystal
is much lower than at l~OkeV. Production gamma cameras usually have a crystal thickness
of 9.5mm, at which the photopeak interaction efficiency for 511keV radiation is only
11.8%, compared with 90% at 140keV (Anger 1964). This, cornbined with the inherently
S poor efficiency of the collim~t~ ~1 method of image formation, results in a poor system
~ sensitivity. A typical level of a~lministered activity needed to obtain an FDG scan in a
reasonable time with a collimated gamma camera system is around 370MBq, resulting in
a total radiation dose to the patient of approximately 1 OmSv. Such levels are too high to be
recommended for routine use in many clinical situations.
A second problem comes from the relatively low attenuation coefficient for 51 1 keV
gamma rays, compared with those for gamma rays at the energies for which the garnma
camera is designed as can be seen from the graph in Figure 3.
Consequently, the amount of high-atomic number m~t.?ri~l (usually lead) needed to
bring about the sarne level of absorption as at 140keV is greatly increased, and collimators
15 designed for 51 lkeV therefore tend to be heavy if they are to be effective. Gamrna camera
systems rotate and need to be balanced, and this imposes weight restrictions on the
collimators that can be attached. Such weight restrictions can lead to compromises in the
collimator design and subsequently their im~ging performance can suffer. The commonest
problem is a high level of penetrating radiation, which reduces contrast in the f1nal image.
20 Such problems have been seen in practice to preclude certain types of clinical study (Clarke
etal. 1995).
The present invention has a sensitivity which is many times that of the collimated
gamma camera and therefore can be used with lower activities and consequently lower
radiation doses to the patient. It is therefore suited to routine diagnostic im~ing. It does
25 not suffer from weight restriction problems, because it does not need heavy collimators.
and the spatial resolution is likely to be better than collimated systems because the present
invention does not rely on collimator hole geometry.
., An alternative to the collimated approach is to make use of the dual-gamma nature
of PET radionuclide emissions in a similar way to the dedicated PET scanner by operating
30 two opposing gamma cameras in coincidence detection mode. Several groups haveattempted this, with poor results (Paans, Vaalburg and Woldring 1985, Sandell et al. 1992).
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The system developed by Paans, Vaalburg and Woldring could also converted back for
SPET use by means of a switch. The overriding problem with the systems is their poor
count rate capability. The reason for failure is a~p~ ly two fold. The first is that the
systems used in these early trials had poor pulse separation electronics. The second is that
only a small fraction of recorded events were used in the final image reconstruction.
The count-rate limiting factor is that the system must handle a large proportion of
events where only one of the two gamma rays has been detected. With a photopeak
detection efficiency of 12%, and with typical source geometries a true coincidence count
rate of 1 Okc/s means that each detector is h~n~llinE a singles count rate of around 200kc/s.
10 At this singles rate, approximately 18% of events from a single detector overlap one
another to some extent and the processing electronics must be able to handle this without
loss of counts and with minim~l loss of resolution. The systems used in early experiments
were unable to achieve this.
The main advantage of the present invention over the collim~te~ system, is its
15 efficiency, because although the chances of seeing a twin gamma ray event is only 12% of
that of seeing one of the two gamma rays (as in the collimated case), there are no
collimators and thus the solid angle is increased by around a factor of 1000. However, this
solid angle must be exploited if the system is to be of practical use. Early experiments did
not exploit the increased solid angle available because of problems in the reconstruction
20 process. Only when an impracticably small reconstruction volume was adopted did the
early attempts yield clinically useful count rates.
The present invention adopts a novel approach to overcome the aforementioned
problems. It uses fast digital hardware to improve the pulse separation and a modified data-
efficient reconstruction technique to include 100% of recorded data in the image25 reconstruction. The resulting device has a count rate capability which is suitable for most
routine clinical applications with the longer lived PET radiopharmaceuticals.
An embodiment of the present invention will now be described, by way of example
only, and with reference to the Figures in which:
Figure 1 shows a cross-sectional schematic of a typical gamma camera;
Figure 2 shows a Schematic view of a dedicated PET imager in operation;
Figure 3 shows a graph of linear attenuation coefficient against energy;
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Figure 4 shows a schematic overview of the invention in use with a modified dual-
headed gamma camera;
Figure 5 shows a functional schematic view of PET unit;
Figure 6 illustrates the formation of a coincidence trigger, and pulse pileup
5 separation;
~ Figure 7 shows diagrarnmatically that the point source response function is not
spatially invariant for a detector pair working in coincidence, in which shaded areas
represent the point response functions for a point near the edge of the FOV (a) compared
with that near the centre of the FOV (b); and
Figure 8 shows an axial slice of shell phantom con1~ining two point sources: a)
shows a simulated back-projection b) shows a forward projection from initial estimate c)
shows a final deconvolved image d) shows an original simulated emitter distribution.
Reference will also be made to a TABLE of results which sllmm~n~es the count rate
capability study for 60 x 46 cm detectors in a worst case scenario.
Figure l shows diagrammatically a gamma camera comprising a plurality of
photomultiplier tubes 2, a lightguide 3, a scintillator 4 and a collimator 5. Figure 2 is a
diagrammatical view of a patient 6 in a position sensitive detector ring 7 in a PET imager.
Referring now to Figure 4 which shows how energy and position signals from
detectors 10 of a gamma camera 1 1 are fed into a processing unit 12. The signals represent
20 raw analogue energy and position signals (E, X+, X-, Y+, Y-) from an Anger position
matrix 14. The following description therefore relates to such signals. However, it is
understood that the application of the invention need not necessarily be restricted to them
as the general principles may well apply to alternative applications.
The signals have the pulse-shaping particular to the make of gamma camera 11, but
25 unless pole-zero cancellation has been implemented the signals will probably exhibit the
characteristic time constant of the scintillator. This is 230ns for NaI(Tl) .
Referring now to Figure 5, the event trigger is carried out using the energy sum- signal from each detector A and B (channel A and B respectively). Suitably conditioned
signals (i.e. with a suitable risetime) are fast-digitised using a flash con~ erter running at a
3 0 clock speed of 40MHz or more. The resolution of the flash converter needs to be such that
fmal integrated signal resolution is not unduly impaired by over-course digitisation.
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Adjacent sets of samples are tested on each clock cycle to see if there is a gradient greater
than a predetermined threshold until both channels show a positive result (e.g. trigger point
Q as shown in Figure 6), at which point a coincidence event is detected. The duration of the
coincidence time window determines the number of random coincidences recorded (i.e.
5 events which are causally unconnected). For a 100ns coincidence window, and with a
singles rate in each detector of 200kc/s, the fraction of all measured coincidences which are
random will be around 20% for typical detector and patient geometries. For this reason, the
coincidence window needs to be as small as possible but at the sarne time keeping a
suff1cient signal-to-noise ratio. Digitisation at the speeds suggested above facilitate the use
10 of coincidence windows of less than 1 00ns.
The event stream from each detector suffers from overlapping events. At a singles
count rate of 200kc/s, 18% of the events in each stream overlap one another at least once.
It is therefore necessary to take this into account when integrating under the position and
energy signals. This can be done by using the single channel trigger to determine when each
15 pulse starts. By integrating the signals into accumulators and storing the sums at the onset
of each trigger it is possible to separate the overlapping events by using knowledge of the
characteristic decay of the signals. Details of pulse integration are shown in Figure 5.
Figure 6 depicts one possible sequence of overlapping events on energy channels
A and B. Only two events are coincident. P, Q and R are the first three trigger events
20 detected by the gradient test. At trigger P (origin~ting from channel A), channels A and B
start being integrated into a separate accumulator, until trigger Q occurs. The integrated
sums for channel A and B are stored temporarily. Note that trigger Q is also a coincidence
trigger, because it is detected in both channels A and B. The accumulators for channels A
and B are then cleared and start integrating again, until the next trigger (or a suitable time
25 longer than the typical signal envelope). In this example a third trigger, R, occurs because
of a lone pulse on channel B. At this point~ the accumulator contents for the integral Q-R
are stored temporarily and this trigger/integration process continues.
At this point~ because there has been a coincident event, the system attempts toseparate the events on channels A and B. For channel A~ the coincident event is "sitting on
30 the back" of a preceding event. The stored integral P-Q for that channel may be used to
determine the residual tail of the preceding event upon which the event of interest rests.
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This can be done by multiplying the integral by a value stored in a lookup table Cont~ining
the characteristic decay of a signal. The residual tail is then subtracted from the integral
stored for Q-R, which is also used to determine the residual tail which was lost because of
the trigger from a following event on channel B. This residual tail is than added to the result
S to give the value of the coincident event energy signal for channel A. The energy value for
channel B is arrived at in exactly the same way. Applying the sarne algorithm has the same
effect.
The position signals for channels A and B are separated in a similar fashion, except
that they take their trigger points levels from the energy channels.
In this way it is possible to detect coincident events and handle pulse pileup without
loss of events or undue loss in resolution. Baseline shifts caused by the build up of the
delayed component of the scintillator output can also be corrected digitally during the
integration process.
The arithmetical processes used in this determination is possible in real-time using
15 digital signal processors (DSPs).
Signal norm~ tion and position determination are then be carried out for each
detector as shown in Figure 5. This can be carried out digitally in the generally accepted
fashion, whereby the X coordinate in the field of view is given by:
(scaling factor) x (X+ - X-) / (X+ + X-)
The denominator serves to remove energy dependence in the result. Some systems
may use the total position sum (X+ + Y+ + X- + Y-) here. The Y coordinate is achieved
in a similar fashion.
The spatial coordinates are then used to determine the energy and spatial corrections
which need to be applied to the energy and position of the events in each detector. This can
also be done digitally using lookup tables. Energy and spatial errors are an unavoidable
- feature of gamma camera design and there are many techniques to determine and correct
for them.
Obtaining spatial corrections at 51 lkeV is made difficult by the same problem that
besets the generation of spatial corrections at the higher energies in SPET work (e.g. at
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364keV for '3iI). A line or spot phantom does not absorb enough radiation to produce an
effective correction map. The most probable solution is to tune the system for 51 lkeV such
that the signal sizes (and hence spatial distortions) are similar to those for 99mTc in the
single-photon mode, where spatial corrections are possible, and adopt the spatial
corrections obtained with 99mTc in single-photon mode for use at 51 1 keV.
As a f1rst step towards scatter rejection, an energy discrimination level should be
adopted for each coincidence event. Both single events making up a coincidence must be
included in the window for the event to be accepted. The choice of the position and width
of the energy window will depend on the energy resolution of the system and on the
10 usefulness of Compton-scattered radiation. Some radiation will Compton-scatter within the
detector such that only part of the energy of a gamma ray is deposited in the scintillator 4,
others will have scattered in the patient and therefore lost useful spatial information, some
will have scattered in both patient 6 and detector 7. However, many of these events may
possess correct spatial information because they have not been scattered in the patient.
Once the two corrected positions have been determined for a coincidence event, and
if the corrected energy lies within the energy discrimination window, the orientation of the
line of response (LOR) between the two coordinates can be calculated. For this calculation
the detector orientation and separation must be known and these values therefore need to
be obtained from the host system at intervals during the acquisition.
Once the LOR has been calculated, the event is characterised by the energy of each
gamma ray and a direction through space and can be used in the image reconstruction
process. The reconstruction process is described in the next section. The event information
may either be stored in sequential 'list' mode for subsequent processing, or used in real-
time back-projection if the processing equipment has suff1cient capability.
25 Data Efficient Image Reconstruction Technique.
If the reconstruction cannot use all of the true coincidence data the effective
maximum count rate performance is likely to be reduced. A maximum count rate of 1-21;c/s
might be expected for typical reconstruction scenarios (e.g. Townsend et al. 1987) in which
80% of all coincident events are discarded. Early attempts at getting gamma cameras to
30 work in coincidence failed partly because of this reason. This section explains the reasons
why such a high proportion of events were rejected and explores some alternative, more
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data-efficient, reconstruction techniques that have been developcd. One of these methods
has been adapted for use with this device.
Fully three-dimensional (3D) image reconstruction uses gamma-ray events with
lines-of-flight having components in the axial direction as well as those travelling in the
5 transaxial plane. Single-photon (SPECT) systems employing parallel-hole collimators and
typical multi-ring PET scanners with inter-ring septa use only those gamma-rays travelling
at angles close to a transaxial plane and are inherently inefficient for this reason.
The problem of 3-D reconstruction has been considered for some years (see e.g.
Jeavons 1980, Colsher 1980, Daube-Witherspoon and Muehllehner 1987) and most
10 attempts at its solution comprise a process where each individual event, or a set of filtered
2D projections, is back-projected through a 3D volume, followed by the deconvolution of
the system point source response function from the backprojected image in Fourier space.
The 3D back-projected image g(x) can be thought of as the convolution of the
radionuclide distribution f(~) with the backprojected image of a point source measured with
15 the same system, h(x, x'), where h(~, _') denotes the contribution to the image at position
x due to a point source positioned at x':
g(x) = ~f(x)h(x,x')dx ( 1 )
If the point response function h(x, x') is known, and g(x) is the acquired, back-
projected image of the radionuclide distribution, the true radionuclide distribution, f(~), can
20 be isolated by deconvolution via use of the discrete Fast Fourier Transform. Analytic
expressions for the point response function (or the ~lulopliate filter for the deconvolution)
have been derived (Colsher 1980).
The overriding caveat of this approach is that the point-response function is
assumed to vary only with position relative to the point source, x', and not with the position
25 in the backprojected image, x. In other words, the backprojected image of a point source
- is assumed to be the same wherever the source is positioned in the system.
Clearly this is not the case for a system using coincidence detection, because lines
of response of detected events origin~ting from near the centre of the detector arrangement
can lie at steeper angles (~) to the planes of the detectors than those em~n~ting from the
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edge of the field of view as can be seen in Figure 7.
The reason why so many experimenters have rejected a large fraction of the
coincident data is because they consider only those events which fall inside the maximum
value of q which satisfies the condition of spatial invariance of the point response function~
5 thereby allowing its deconvolution from the backprojected image. Such an approach is
most suitable for small regions of interest placed closed to the centre of the imaged volume,
where the number of events meeting the angular constraint is least. However, for practical
im~gin~c~ applications, a more efficient reconstruction method is essential.
An iterative approach which begins by reconstructing a small region of the
10 backprojected image using an appropriate value of limiting q may be used. The region
chosen is small enough so that the point-response function changes little within it. A
surrounding region of the backprojected region is then chosen, and for which a smaller
value of q is ap~lo~liate. The original image is deliberately convolved with the point-
response function corresponding to the new angle, is then added to the new region and the
15 result is deconvolved with the new point response function. The process iterates until the
entire region of interest is reconstructed.
Another approach can be summarised as follows: first, a low-statistics image is
reconstructed using a limited angular acceptance which meets the spatial invariance
condition of the point response function. The point response function is the deconvolved
20 from this back-projection (usually by prefiltering the projections) giving a first estimate of
the radionuclide distribution. This distribution is then forward-projected to provide an
estimate of the projections not measured because of the limited geometry of the detectors.
Scaling and adding the estimated missing projections to those actually measured allows the
result, which incorporates about 90% of the detected data, to be successfully filtered with
25 an ~plol,liate spatially-invariant point response function. Rather than applying a filter in
3D Fourier space, it is possible to use the analytic expression derived by Colsher (1980) to
apply an appropriate filter to the 2D projections or sinograms prior to backprojection.
The method proposed by Kinahan and Rogers (1989) and used successfully b-
others has been investigated further to test its suitability to this invention. However~ there
30 are some differences in the approach adopted for this study and those of others. Whereas
others have organised data into 2D projections. the present method does not. In this case
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the forward-projection process is based on a Monte Carlo process. That is events are
generated and projected randomly and individually into the solid angles which would
otherwise go undetected. In this way, the sum of the 'measured' and forward-projected data
simulate the response of a 4~ detector, and 100% of the true coincident events can be used
5 in the reconstruction. Although a Monte Carlo approach appears time consuming, use of
sufficient processing power may make this an alternative in clinical practice. In this
application, all backprojections are deconvolved in 3D Fourier space.
Once an event has been detected, its line of response (LOR)is tracked within thereconstruction volume. The volume is split into a voxel matrix. Note that the reconstruction
10 volume can be any size. It can even exceed the physical limits of the system if necessary.
Sufficient memory is allocated dynamically by the software to accommodate the contents
of the matrix. Each point is represented by a floating point number (though long integers
could be used to improve speed). The LORis the straight line between the points of
intersection of the gamma ray trajectories with the detector planes. The point of emission
15 of the original positron is assumed to lie along this LOR.
In a real system it may not lie along the LOR. The positron may have moved some
way before ~nnihil~ting, or the two gamma rays may not be quite collinear due to the
motion of the centre of mass of the positron-electron pair. Or this may occur because the
two detected gamma rays forming the coincidence are causally unconnected. Nevertheless,
20 in a real system the point of origin is assumed to lie on the LOR, and the fact it may not is
a contributing factor to noise.
The first step in the backprojection process is the calculation of the points ofintersection of the LOR with the bounding box. This helps to define the range of voxels
through which the LOR has to be tracked. The point of intersection of the LOR with each
25 of the inter-voxel planes it crosses is calculated and the distance of this intersection from
the point that the LOR enters the bounding box is stored along with the index of the plane
it is crossing. If the LORis parallel to a voxel side~ it will have a length in that voxel of 1Ø
If it passes through diametrically opposite corners of a voxel it will have a length in that
voxel of 1.732. These distances are then sorted sequentially as follows. The shortest
30 distance stored is the length of the LOR lying within the first ~ oxel. This length is added
to the image memory at the address of that voxel. The next largest distance minus the
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previous distance is the length of the LOR passing through the adjacent voxel, and is added
to the image memory at that voxel's address. This cycle is repeated until the entire LOR has
been accounted for in the reconstruction volume. By adopting long integer rather than
floating point arithmetic, the process is optimised for speed.
The backprojected image represents the distribution of emission points smeared
with the backprojected image of a point source (the point response function). For a detector
with limited geometry, the point response function will vary with position, and the
distribution of emission points for an extended source cannot be retrieved simply by
deconvolving the backprojected image with some nominal point response without
10 generating artefacts in the result.
As discussed above, the backprojected image of events meeting the condition of
point response function invariance, can yield a low-statistics estimate of the distribution
of emission sites. This low-statistics image can then be used to forward project generated
events into those solid angles of the system where events are not normally detected. When
15 this forward-projected image is scaled and added to the true backprojected image, the result
can be deconvolved with the point response function obtained for a 4~ detector.
The forward projection process works in the prograrn as follows. First, a special
patient scan is carried out where the angle of acceptance is limited to the maximurn that can
be achieved for a particular im~ging volume and detector size. In practice, this could form
20 a subset of the events detected in normal acquisition, and a copy of these could be stored
separately during the acquisition: a separate acquisition may not be required. These ~-
limited events are backprojected as described above, and the resultant image is then
deconvolved with the corresponding point response function. This response function is
determined empirically by generating events under the same conditions from a point-source
25 placed at the centre of the imaged volume. A frequency filter, such as a Hanning window,
(see e.g. Colsher 1980) with the cut-off set to the Nyquist frequency, is used to minimice
the effect of noise in the deconvolution process~ as described in detail below. The
deconvolved low-statistics image is then used as the generator for artificial, forward-
projected events.
The low-statistics generating image is prepared for event generation by first setting
voxels with contents lower than a suitable threshold. The rem~ining voxels are then scaled
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so that their total equals the number of events to be generated. The forward-projection
process then steps through the non-zero voxels and uses their centres as emission points.
Event direction cosines are generated as before. This time, if the event does not meet the
criterion of detection, its LOR is tracked through a forward-projection volume in exactly
S the same way as in the backprojection case. In this case, no limit on ~ is applied. The
generating image voxel content corresponding to the emission point is then decremented.
The process repeats until that generating image voxel is empty, in which case the program
moves on to the next non-zero voxel. The program proceeds in this manner until the
generating image is depleted.
Once the forward-projection is complete, it is scaled and added to the original,unlimited-~ backprojected image of the phantom. The scaling factor used is determined
from the ratio of the forward-projected events that do not meet the 'not-detected' to the
number of events detected in the original back-projection.
Finally, the summed image is deconvolved with a point response function
l S empirically determined for a 4~ detector to give the final result.
The deconvolution of the empirically-determined point response functions from the
backprojected data is carried out in the Fourier domain. For this purpose, the discrete 3-
dimensional Fast Fourier Transform (FFT) is used. The Nyquist critical frequency is set by
the im~ginp; matrix. A filter such as the Hanning filter (as used by Colsher 1980), with the
20 cut-off frequency set to the Nyquist frequency is used prior to carrying out the final inverse
transform to reduce the effect of noise on the deconvolution.
Note that the convolution theorem assumes that the response function and main data
structure are periodic in each direction. This is clearly not really the case. The point
response function is wrapped around prior to deconvolution, but the data is left intact.
25 When convolving data in such cirC~lm~t~nCeS, it is usually sensible to zero-pad one end of
the data area in each dimension to avoid the effect of overlapping the convolution of one
side of the data area with data from the opposite side. Deconvolving data which is non-zero
at the image edges with a point response function, which is very broad compared with the
size of the image~ similarly gives erroneous results whether the data is "zero-padded" or
30 not. If the data is zero-padded, the backprojected image (which is really a convolution)
then effectively has a sharp edge which gives artefacts when deconvolved. If there is
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zero-padding of the data, it is necessary to deconvolve one edge of the data using
information from the opposite edge. The only way to alleviate this problem is to ensure that
the important region of the data is at least a point response function's width inside the
image boundary. This is an important factor in the implementation of this technique.
An important potential use of a gamma-camera PET system is oncological whole-
body sc~nning and static im~ging. In whole body or static planar im~ging, detectors do not
rotate about the patient and therefore there is further restriction to the directions of the lines
of response (LORs) available for use in image reconstruction. The static and whole body
im~ging capability of such a system are considered to be a particularly attractive features
10 and may be implemented in a ~l~r~ d system.
To m~imi~e the efficiency of the system, the reconstruction algorithm uses as
many of these LORs as possible. In addition, since the LORs pass through the im~ging
volume at different angles they carry information about the depth distribution of the
emitting radiopharmaceutical so as to extract this information.
In order to position a patient under the scanner, it is necessary to observe an image
of the radioph~rrn~ceutical distribution in real time. A solution is proposed where a subset
of coincident events, which have a limited range of acceptance angles, are used directly
to form a low-statistics, real-time image. This is really a form of electronic collimation. The
subset of gamma ray events might be that used to determine the first estimate for the
forward-projection process if the solid angle is small enough to form a suitable image.
There is now described results of an experimental trial of the invention, which is
based solely on calculation and Monte Carlo software simulation.
Software simulation was written to determine the likely sensitivity and count rate
performance ofthe system under different im~ging situations, and to test the reconstruction
~5 technique.
For 60 x 46 cm the system is seen to be at least 65 times as sensitive as a typical
modified dual-headed collimated system, with a count rate capability of over 10kcps.
These results were obtained using 9.5 mm thick crystals. The following key is used in the
TABLE.
Rect = rectangular, Circ = circular detector.
Detectors are separated by 50cm in all cases.
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Standard errors given are statistical.
Photopeak efficiency assumed is 0.1 18.
Table I:
DetectorHomogenous Positron True Coincidence Fraction of all Sensitivity
Type Spherical Activity Ratewith 200kc/s Coincidences
Phantom Giving Singles Rate which are Random
Diameter 200kc/s (18% pileup at 200kc/s Singles
(mm) Singles Rate fraction in single Rate (lOOns
per Detector channel) coincidence
(kc/s~ window) (%)
(MBq) (c/s/MBq)
Circ 40cm 2 7.73 23.0 14.7 2970+80
Circ 40cm 200 7.76 15.7 20.1 2030+80
Circ 40cm 400 7.72 8.4 32.0 1080+30
Circ 40cm 500 7.75 5.8 40.7 760+50
Circ 40cm 2 13.10 13.~ 22.7 1030i50
Circ 40cm 200 13.03 10.1 28.1 780+20
Rect 60*46 2 4.88 22.5 15.0 4590~140
Rect 60*46 200 4.83 17.9 18.1 3700+110
Rect 60*46 400 4.89 13.1 23.1 2680~110
Rect 60*46 2 8.23 14.2 21.9 1730+80
Rect 60*46 200 8.23 11.1 26.3 1350+80
Dual - 200 - - 40
Collimator
Activity used in the system sensitivity calculations is taken to be the annihilation
event rate in the phantom. The system spatial resolution is estimated at around 7.5 mm
throughout the im~gin~; volume.
The reconstruction technique described above has been tested successfully by means
5 of a computer sirrLulation. Figure 7 shows axial slices of the reconstruction of a simulated
emission phantom during stages in the reconstruction process.
The static im~p;ing process mentioned above has been tested by means of computersimulation and 2D images have been successfully obtained.
It will be appreciated that the present invention has been described by way of one
10 embodiment only and variation may be made without departing from the scope of the
invention.
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