Principal Investigator/Program Director (Last, First, Middle):
Kagan, Harris
Introduction
The reviewers made some good points as well as many that reflect our failure to clearly present the novelty in
the proposed work. In light of the fact that magnetic confinement of positrons has been investigated in the past
we re-state the innovation here: Whereas previous techniques of magnetically confining positron range
demonstrated resolution improvements in 2D, resolution in directions parallel to the field was essentially
unchanged. In our approach spatial resolution will improve in all three dimensions. Moreover, this will not be
accomplished using a simple resolution recovery method; instead, data will be acquired from the object (e.g., a
small animal) in two or more orientations relative to the direction of the magnetic field. In our proposed
investigation, the multiple PET projection datasets will be recombined using a post-smoothed, penalized
maximum likelihood reconstruction. While the method is most applicable to nuclides having higher positron
energies, which are becoming more important in preclinical and molecular imaging, we also predict a
significant positive effect for F-18—especially in lung tissue. This reconstruction technique was reported to
NIH as an invention conceived under funding from R01 EB430, which is now investigating design parameters
for scaling up dual-ring high-resolution PET systems.
Both reviewers also had questions regarding the qualifications of the investigators, which are addressed by
updated biosketches and the following comment (very brief due to space limits). Drs. Harris Kagan and Klaus
Honscheid are senior physics investigators with expertise in radiation detector physics and very large-scale
readout systems (rather larger than PET). Both have worked as part of the CIMA Collaboration (a medical
imaging collaboration involving CERN, OSU, University of Michigan, and numerous European institutions)
since 2001 developing imaging technology for Compton cameras and very high resolution PET. Because of
the departure from the mainstream technologies in the field, peer-reviewed publications are only now starting
to appear. Dr. Kagan now serves as Principal Investigator on a DoE funded project for developing diamond
detectors, has served as the Principal Investigator on DoE funded projects for developing silicon detectors, and
also has a strong background in imaging by way of holography and digital holography. These senior
investigators will be complemented by Neal Clinthorne, who while often viewed as having expertise mainly in
SPECT has in fact been PI on numerous NIH grants for PET as well as CT. In addition he has a strong
background in technology transfer and commercialization.
Responses to the specific comments of each reviewer follow.
Reviewer 1:
1. The investigators need to present data on more “realistic” positron energies than those for Tc-94m,
especially that for F-18 (635 keV max positron energy), because the improvement in resolution will obviously
be much less than that for Tc-94m (or even O-15 with a 1.7 MeV max positron energy).
Data are now presented for a variety of positron emitters including F-18. Alternatives to F-18 are becoming
increasingly realistic in biomedical research using small animals due to their longer half-lives, to their ability to
label existing SPECT agents (Tc-94m, I-124), to their suitability for labeling monoclonal antibodies, antibody
fragments and peptides, which take some time to localize (I-124, Br-76), and to the fact that some can be
generator-produced (Cu-62). In contrast to F-18, most of the alternative positron-emitting nuclides of interest
emit higher energy positrons amenable to improved resolution through magnetic confinement.
2. …the investigators need to fully consider the reconstruction and quantification challenges introduced by the
creation of an anisotropic PSF.
The key innovation noted above is a new data acquisition technique and image reconstruction that will result in
a significantly more uniform if not isotropic PSF (in isodense tissue) and better spatial resolution.
3. As the investigators themselves admit, the preliminary data in section C.4 make best-case assumptions
regarding orientation that eliminate these important issues.
There are two sets of images presented in Section C.4 (Figs. 9 and 10). The first presents anticipated
performance from the best-case orientation. As noted, this is not the practical situation except for maybe
Jaszczak-style phantoms. Objects having more realistic 3D structure will surely exhibit artifacts due to out-ofplane structures in addition to potential quantification issues due to the anisotropic PSF (note that a similar
situation exists without magnetic confinement near the borders of tissues having significantly different
densities). The images shown in Fig. 10 on the other hand show information taken in two orientations of the B7/11/2016PHS 398/2590 (Rev. 09/04, Reissued 4/2006)
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field—both worst-case orientations—and then combined. The overall result in this preliminary experiment is
not quite as good as the best-case orientation; however, it is better than either worst-case orientation alone.
4. …it is not clear that it is an advantage (to the overall goals of the study) to use an “unproven” [Compton]
PET technology…
The technology has been proven to achieve very high spatial resolution (Section C.1). “Compton PET” is
perhaps an unfortunate term in the sense that it connotes the same technical challenges as a Compton-scatter
camera. At its essence, Compton PET is absolutely no different than conventional PET. The most probable
interaction for 511 keV photons in any detector—semiconductor or scintillator—is Compton-scatter. Just as in
PET using more conventional detectors, lines-of-response are formed the same way: by interactions of
annihilation photons in opposed detectors in time-coincidence. The primary reason for using the proposed
device is that it has sharper, cleaner (free from tails), and more uniform spatial resolution than any existing
PET device due to the outstanding resolution of the detectors and lack of secondary photon interactions
(Section C.1). This will obviously be critical when investigating performance increases using magnetic
confinement especially for low-energy emitters like F-18. As far as the wirebond issue, the example was just to
point out that we found a problem with the existing system that prevented long-term operation in a magnetic
field and solved it. The detectors continue to work in high fields. The system still has to have the magnetic
components replaced but the technology risk is pretty minimal at this point.
5. There is a question about SA#4. While it is certainly true that acquisition and reconstruction in emission
tomography usually involves a resolution-noise tradeoff, it is not clear how the effect of a magnetic field on
positron range influences this tradeoff...
The rationale for this aim is discussed more fully in Section B under “Rationale for Specific Aims.”
6. As the investigators point out, others have already proposed (and measured) the effects of a magnetic field
on reduction of positron range, so the proposal is not innovative.
See discussion of innovation above. That said, this proposed work would be the first study using a PET device
with sub-millimeter resolution and the first to study the impact of the effect all the way to image reconstruction.
7. The PI, Dr. Harris, is a professor of physics at Ohio State. He has many “physics-type” publications, but no
imaging publications…
This issue is addressed in the preamble and with updated biosketches.
8. The investigators propose to study the effect of a magnetic field on reduction of positron range. Such a
study is not novel, but it may be significant. Unfortunately, the investigators have done a poor job of providing
evidence for significance. The approach also has at least two concerns (the use of Compton PET technology
and an unjustified aim).
Novelty is addressed in the preamble. Significance of higher energy positron emitters, high-resolution PET,
and Aim 4 is addressed above and in Section B.
Reviewer 2:
1. The authors propose to simulate and develop a PET scanner that can operate in a 7T magnetic field in order
to improve the resolution of the resulting PET images. While this is a significant goal, it is not particularly novel.
Thanks for the significance vote. We actually propose to use the high resolution PET scanner only as a
convenient tool to acquire data to test our proposed 3D range reduction method not as an innovative end in
itself. As for the novelty of 3D range reduction using a magnetic field, refer to the discussion in the preamble.
2. In addition, there are concerns whether the PIs can deliver the relevant technology before the ongoing
commercial efforts in the area of MRI-PET hybrid systems
We are not competing with manufacturers in a horse-race to build yet another1st generation PET/MRI device.
The proposed investigation is more appropriately described as the development of a technique that will
strongly influence the design of 2nd or 3rd generation PET/MRI devices and beyond by significantly reducing
positron-range effects. The PET system we have chosen to use is merely a tool to obtain the information.
3. The first [aim] is to develop simulation tools in order to predict system performance for the eventual system.
This appears to be based almost completely on previously developed simulation models.
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Wherever feasible we will continue to use existing models and simulation tools such as EGS-4 and GEANT4
both for design and for predicting the effects of positron range. It doesn’t make sense to develop new tools
where those existing are sufficient. However, it will be important to corroborate predictions of positron range
with experimental measurements and trace discrepancies to either simulations or measurements. The first
comparisons of our work with previous experiments using EGS-4 are listed in Section C.2
4. One significant limitation of using the magnetic field to increase the resolution of PET images is the effect of
non-colinearity of emitted photons. This effect seems to be missing from the analysis included here.
The impact of photon non-colinearity has been analyzed for this revision. Its effect is small (0.37mm FWHM
for the proposed PET instrument, which is added in quadrature with other resolution contributions).
5. The actual scanner to be constructed is proposed in aim 2. While the PIs describe a system that would be
capable of collecting PET images, is it not clear to me how well this scanner will be able to approximate a full
ring 3D scanner that would be needed in practice.
Unlike the effects of acolinearity and detector resolution, the effect of positron-range is independent of the PET
scanner geometry. The upshot is that we can use any geometry capable of recording the 3D object
distribution. With the proposed single-slice device, the acquisition method will be “step-and-scan.” The object
will be translated in small axial steps to record a 3D dataset. It will also be necessary to rotate the object (or
the scanner itself around the object). Reconstruction from these measurements is straightforward.
6. No time plan for this development is given…,
We have added a schedule. We expect the instrument development portion of the work to be complete for 3D
data acquisitions within the first year and capable of 2D (slice) acquisitions in the first six months.
7. …it’s not clear what benefits this system would have over previously constructed systems as well as the
state-of-the-art commercially available … systems, especially those based on MRI-PET hybrids
Refer to the new discussion in Section B. To summarize, the 1st generation systems under development now
are geared toward making simultaneous PET and MRI a reality. They are ideal for evaluating the research
relevance of PET/MRI but they are not particularly well suited to the measurements proposed here for two
reasons: (1) The spatial resolution of existing hybrids is generally not as high as state-of-the-art dedicated
small animal PET scanners due to hard constraints on the ring diameter and lack of sufficient depth-ofinteraction resolution. Even the resolution of present dedicated scanners is marginal for the measurements
proposed here. For example, on the MicroPET Focus 120 resolution has been measured as 1.65mm FWHM
on-axis degrading to 2.4mm in the radial direction at 2cm off-axis [91]—less than desirable for the studies
proposed here. (2) The small magnet bore on hybrid devices under development introduce additional issues
such as difficulties in accurately reorienting the object and more detected scatter (due to the small ring
diameter relative to the size of the FOV). These issues are not present in the proposed system.
8. An additional component of this aim is the development of maximum likelihood image reconstruction
methods. It appears that there will be significant overlap with RO1 EB430-34 …
Clarifying the separation, the basic post-smoothed, penalized ML reconstruction has already been developed
under EB430 and will also be used in this investigation. That work must be extended to include positron range
response in magnetic fields as described in Section C.4—work not covered by R01 EB430.
9. The PIs propose to map the field of the 7T system down to 2T. This seems highly speculative, since the field
decays away from the edge of the magnet with a very high rate.
This is a good point. Instead, we will make measurements at 0T, 3T, and 7T using big-bore 3T and 7T
magnets available at OSU.
10. The level of innovation seems to be small in the current proposal. It is not clear what advantage this
project would have over previous approaches and those ongoing in the corporate sphere.
Innovation was addressed above. As far as advantages: First, as noted in Section B, small animal PET or
hybrid systems that exist are not as suitable for the measurements as the high resolution device proposed.
Second, work on taming the positron is complementary to ongoing work in the corporate sphere to develop
hybrid systems and if successful will have an impact on the design of future PET/MRI hybrids.
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A. Specific Aims[Revised]
The long-term objective of this investigation is to develop PET instrumentation for molecular imaging of small
animals that has unprecedented spatial resolution. Recent results (Section C) demonstrate that it is possible
to achieve sub-millimeter spatial resolution in PET. Moreover, the biomedical community is placing strong
emphasis on molecular imaging techniques in small animals with PET with sub-millimeter resolution. This
emphasis has yielded other exciting work in this direction with the development of new scintillators and
photodetectors such as arrays of silicon photomultipliers. With the quest toward deep sub-millimeter resolution
two general questions remain: how far can one really go and how much resolution is enough. This initial study
will address many of the issues associated with these questions. Perhaps the major issue or limitation which
must be addressed upon entering the sub-millimeter regime is the range of the positron in tissue, the distance
between the decaying isotope and the positron annihilation point, as this is perhaps the largest contribution to
image blur. This becomes especially true for more novel radionuclides such as I-124 and Tc-94m, which are
gaining importance in molecular imaging studies with small animals.
Embedding the PET field-of-view (FOV) within a strong magnetic field can reduce positron range by generating
a Lorentz force on the components of the positron momentum transverse to the magnetic field vector. In a
vacuum, the positrons take a helical path leading to a significant reduction in range; in tissue, positrons also
scatter so their path is more complicated and not quite helical but nevertheless their range can often be
significantly reduced (Section C.2). For lower energy positrons, such as those emitted from F-18, only a small
range reduction appears likely in water until field strengths reach levels of 20T or more. This is undoubtedly
due to scattering in tissue. However even for lower energy positron emitters larger gains are possible in lung
tissue due to the very low density of this tissue (Section C.2). For higher energy positron emitters (I-124 or Tc94m), significant reductions are possible at field strengths much less than 10T (Section C).
The idea of using a magnetic field to constrict the range of positrons in PET is not new. It was explored late in
the last century by Raylman, Hammer and Christensen[1]. Although they demonstrated the predicted results
for Ga-68, the overall improvement they observed was dominated by the modest spatial resolution inherent to
instruments of the time (~5mm FWHM). Moreover, the relative frequency of PET studies that might have been
able to take advantage of this improvement—those using O-15 and Rb-82—has steadily decreased over time.
The landscape has changed somewhat in recent years. With strong emphasis on molecular imaging
techniques in small animals with PET from the biomedical research community, there has been renewed
interest in long half-life positron emitting radionuclides. An unfortunate side-effect is that many of the desirable
species emit positrons that can travel a considerable distance in tissue before annihilating. At the same time,
new detection methods have demonstrated the capability of intrinsic PET resolution better than the mean
range of even F-18 positrons.
With this as background, we feel it is worth revisiting the idea of limiting the positron range using a large
magnetic field. Our approach is somewhat different than that studied previously, for example, in Raylman,
Hammer and Christensen [1] or Levin and Hoffman [2] where they described improved resolution of the object
transverse to the magnetic field direction. Our approach is to construct a system that can take data in multiple
orientations relative to the magnetic field direction to attain improved spatial resolution in three dimensions. In
order to observe effects down to the sub-millimeter distance scale, we propose to use a PET system design
that has sharper, cleaner (free from tails), and more uniform spatial resolution than any other existing PET
device due to the outstanding resolution of the detectors and lack of secondary photon interactions.
The specific tasks we propose to evaluate the effects of any PET system in a large magnetic field are:
Aim 1: Quantify the performance limits of the system and the performance changes as a function of magnetic
field. Develop the Monte Carlo model to corroborate previous simulations (e.g. positron range of Levin and
Hoffman [2]) and simulation with measurements. Combine the positron-range simulations in various tissues
with a model for the scanner to be implemented in Aim 2 to predict the overall system performance. Use
Monte Carlo methods to estimate misclassification rates and compare with the observations in Aims 3 and 4.
Use Monte Carlo methods to simulate the electronic effects of dead-time and shaping time to understand the
electronic constraints of the system and compare them with the results of Aim 4. Simulate the effects of
magnetic fields on the various detector elements to understand the optimum system geometry.
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Aim 2: Construct a 7T magnetic-field compatible high resolution prototype PET device. This device will have a
single-slice geometry to eliminate rate effects, minimize cost and so that is can be easily rotated relative to field
direction. The device will be based on our demonstrated high resolution single-sided silicon pad detectors
which will be depth of interaction sensitive and will have better than 1mm spatial resolution in the field-of-view
in zero magnetic field.
Aim 3: Acquire data in the 3T and 7T MRI facilities at The Ohio State University and in 0T with the same
system. As part of this study we will acquire the necessary data and reconstruct images of point sources,
closely separated source pairs, phantoms, etc. to quantify the resolution as a function of magnetic field and
position in the field of view. We will perform this study using a variety of positron emitters with a range of
energies.
Aim 4: Quantify noise-resolution tradeoffs under various acquisition scenarios and compare with predictions
from simulations in Aim 1.
Establishing the feasibility and quantifying the performance gains of a high resolution PET system in a
magnetic field is one step towards developing a PET molecular imaging device of small animals with
unprecedented spatial resolution. The next stage in the development would require a demonstration that noise
reduction tradeoff curves are superior to existing PET devices as well as a demonstration that the detector
technologies and system components have the appropriate performance characteristics in the magnetic field.
This proposal is directed and answering these questions.
B. Background and Significance [Revised]
PET for molecular imaging in small animals
Positron emission tomography is a readily used diagnostic tool in neurology, cardiology and oncology. PET’s
major strength is the ability to visualize and quantify metabolic processes. Over the past decade numerous
instruments aimed at small animal PET have been developed [3-42]. Several have been commercialized and
are now in extensive use. The most well-known of the commercial instruments for small animal PET is the
series of MicroPET systems pioneered at UCLA [5-9, 31]. The MicroPET R4 is a rat sized system having a
resolution of 2.2mm across a 40mm field-of-view and an absolute efficiency of ~2.2% for a 250-650keV
window and an absolute efficiency of ~1.2% for a 350-650keV window [43]. This system has become a
workhorse for PET tumor imaging studies at many institutions. There have been a number of updates and
improvements to the basic technology and recently other instruments have become commercially available
[44]. Although such devices have pioneered the way for PET tumor imaging, spatial resolution across the fieldof-view remains in the 1-2mm range for a volume resolution of 8l. Biomedical scientists have a strong desire
for spatial resolutions less than 1mm FWHM in 3D so that tracer concentration in volumes as small as 1l can
be reliably quantified [7]. This is especially true for imaging mice.
Imaging with novel positron emitters [New]
F-18 has been the most widespread radionuclide in PET. Its 110 minute half-life is convenient for many
studies, it’s a pure positron emitter with low endpoint energy positrons (635 keV), and it is reasonably
straightforward to label a variety of compounds—FDG of course being the most common. Other “elements of
life” including C-11, N-13, and O-15 have also been widely used. Even though their short half-lives render
many radiochemical syntheses difficult and their positron energies are higher than desired, these nuclides
have found clinical use in C-11 acetate and C-11 methionene for cancer imaging, N-13 ammonia for heart
imaging, and O-15 water in brain activation studies (although it has largely been replaced by functional MRI).
For a long while, PET purists only seriously considered the above postiron-emitting nuclides for imaging (other
than Rb-82 as a curiosity for heart imaging). In the newer era of molecular imaging, however, where animal
models of human disease are used to study methods of detection, mechanisms of progression, and earlier
assessment of the efficacy of treatment (with emphasis on cancer), a large number of new imaging probes are
under development. Some are labeled using F-18 and C-11; however, an increasing number are not. The
short half-lives of F-18 and C-11 are inappropriate for labeling compounds such as polypeptides or monoclonal
antibodies that may take hours or even days to reach their maximum target-to-background ratios. Longer lived
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positron emitters are required. Fortunately, the nuclide chart is replete with possibilities; Tc-94m, I-124, Br-76,
Ga-68, Zr-89, and Y-86 in addition to many other non-conventional positron emitters are finding increasing use
in preclinical imaging using small animals. A small sample of these ongoing developments is provided in
references [bunch-o-refs] with PET chemistry group at Washington University a driving force in the
development.
While these “new” positron emitting nuclides allow radiochemists and biomedical investigators a new degree of
creative freedom, many come with additional baggage in the form of cascade gamma-rays and positrons
having relatively high endpoint energies.
For additional background on some of these alternative
radionuclides, Laforest, et al. gives an excellent overview of the challenges in small animal imaging [91]. In
particular, the large positron range of many emitters can seriously degrade resolution and noise properties of
PET images. As outlined in the previous section, the subject of this investigation focuses on the development
and evaluation of method that will significantly reduce the effect of positron range in 3D.
Spatial resolution in PET [Revised]
In order to put the performance degradations of positron-range in the right context, consider the following
common view of the components of spatial resolution in PET
2
2
2
2
rtot  rdet
 racol
 r2  rmot
 rrec
where rtot is the composite resolution in reconstructed images, rdet is the contribution from the PET detector, racol
is the contribution due the acolinearity of the annihilation radiation, and rβ the contribution due to positron
range. Degradations to spatial resolution due to animal movement from respiration, for example, are denoted
by rmot. Obviously, this is a complex issue that can either be small relative to the other contributions or not
depending on the location, the positron emitter, etc. It is a topic of active research and we shall not deal with it
further here. Finally, rrec is additonal blurring in the reconstruction (assuming no resolution recovery is
attempted) to tame noise. We assume that each resolution component represents the rms uncertainty of the
induced coincidence line response function (CLRF) of the specific effect converted to an “equivalent Gaussian
FWHM” by multiplying by sqrt(8ln(2)) (2.35). Regardless of the shape of the individual CRLF contributions, if
all uncertainties are of similar magnitude, the overall CRLF tends toward Gaussian and the overall FWHM
becomes an accurate depiction of reality. This is a simplified view of resolution since there is no accounting for
noise or the fact that blurring can be “undone” by the reconstruction; nevertheless, it serves as a convenient
point of departure for discussing the contribution of each effect.
The degradation from acolinearity is due to the non-zero momentum of the positron-electron pair at
annihilation. Since most positrons thermalize before annihilation, this momentum is most strongly related to
that of the electron—and in particular, the momentum of valence electrons (due to Coulombic repulsion of
positrons from the nucleus). As one might expect, the momentum distribution and resulting angular deviation
is material dependent and in fact angular correlation of annihilation radiation spectroscopy (ACAR) uses just
this effect to characterize various materials. One might also suspect that the residual momentum would cause
a corresponding Doppler shift in the annihilation radiation from mβc2 (511) keV. Indeed, this is the case and
the energy deviation has been used to verify that the angular uncertainty for water (δ = 8.8 mrad FWHM) is
close to that actually observed in human subjects (9.6 mrad) in PET with the shape of the response nearly
Gaussian [japanese]. A simple geometric argument relates this uncertainty to the FWHM blurring contribution
to each PET line-of-response (LOR) as δ x R1R2/(R1+R2), where R1 and R2 are the distances from the
annihilation to detection of each photon. This reduces to the commonly used 0.0022 x D (or 0.0024 x D) at the
center of the FOV where D is the PET ring diameter in millimeters. For the 17 cm detector separation of the
proposed measurement system, the acolinearity contribution is ~0.37 mm FWHM. Considering that detectors
with outstanding depth-of-interaction (DOI) resolution will allow ring diameters as small as 4–5 cm for mouse
imaging, the contribution of acolinearity will ultimately only be ~100 µm, which must be added in quadrature
with other resolution components. In comparison with positron range, the additional blurring due to acolinearity
will be negligible in well designed small animal PET systems of the future.
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The PET detector—especially in small animal imaging with F-18 labeled tracers—has traditionally been the
largest.factor in overall spatial resolution. Not surprisingly, it has been the subject of extensive investigations
over the years. While we give an overview of developments and the overall state of the field in regards to
small animal PET devices, because of the sheer number of investigations it is infeasible to cover all in detail.
Due to the short turnaround for resubmission that NIH has offered us, we rather inelegantly point out two things
in this section: (1) PET detector resolution will likely not remain the dominating component in the above
expression (but the field is not there yet), and (2) present instruments—including MRI/PET hybrid systems—
have limitations for performing our proposed measurements and our approach using a modified very high
resolution silicon PET device [92] is preferable.
Detector resolution is limited by several factors including detector element size, inter-element scatter, depth-ofinteraction uncertainty, and decoding errors also known as “block-effect” degradations in multiplexed
scintillator/photodetector systems [2]. There have been many efforts and much progress toward sub-millimeter
spatial resolution in PET. The bulk of these attempts have taken the approach of further subdividing the
detector elements (scintillation crystals) to 1mm x 1mm or less. Some notable efforts in this trend are the
MicroPET II, its commercial version, the microPET™ Focus 120 from CTI Molecular Imaging, the MMP II at
MGH, and the MiCES series of scanners at U. Washington [6, 10, 45, 46]. The resolution for MicroPET II
ranges from 0.83mm x 0.83mm x 1.2mm (0.83µl) on-axis to 1.5mm x 1.2mm x 1.2mm (2.2µl) at 2cm. For the
Focus, it is 1.3mm (2.5µl) on-axis. For the MMP-II, the resolution is 1.2mm on-axis, 1.6 at 2cm off. And for
QuickPET II, the reported resolutions range from 1.1mm on-axis to 2.0mm at 2.2cm. There are, of course,
numerous other efforts aimed at high resolution with scintillators [19, 47-49]. Recently, 0.6mm FWHM was
reported using small arrays of 0.5mm x 0.5mm x 10mm LSO scintillators [50]. While resolution at the center of
the FOV for these devices is good, it degrades off-axis due to unmeasured depths-of-interaction (DOI) in the
scintillation detectors. High resolution detector technologies other than scintillation detectors have been
proposed—and a few built—as well. Some have demonstrated sub-millimeter spatial resolution. The HIDAC
system [18], the NRL HPGe PET [24], RPC PET [51], PET using silicon strip detectors [52, 53], and PET using
CZT [54-57] are examples.
Spatial resolution in a practical system for small animal imaging must be accompanied by efficiency, which can
be increased by increasing the solid-angle subtended by the detector or by using thicker detectors. Greater
solid-angles can be obtained by stretching the axial extent of the ring or by shrinking its diameter. While
reducing ring size is an attractive option from the standpoint of cost, parallax effects due to unmeasured DOI in
thick crystals become severe at small diameters exacerbating the problem of non-uniform transverse
resolution. This will obviously be a big effect for the small-bore 1st generation hybrid PET/MRI devices.
Detectors demonstrating DOI capability remain a subject of active investigation—especially those based on
scintillators [16, 48, 49, 55, 61-78]. Many of these methods are based on multi-layer approaches using
individual photodetectors [79] or phoswichs [36, 62, 67, 68, 73, 80]. There have recently been several efforts
based on position-sensitive avalanche photodiodes (APDs) that have shown good position resolution in
reading out long, narrow scintillation crystals [61, 64] and 3–4mm depth resolution in 1mm x 20mm crystal [64].
Indeed, some instruments are even proposing stacked detectors of silicon photomultipliers (SiPMT) and
continuous LSO [81]. We note that SiPMTs are extremely promising devices for achieving high spatial
resolution (including DOI) but their practical application in high resolution scanners awaits the development of
dense, reliable arrays and readout electronics (no small feat given the length of time it took to develop even
low-gain APD arrays).
Another issue affecting high resolution PET detectors is the fact that the most prevalent interaction of 511 keV
photons in any detector is scatter (Compton and coherent): 59% for BGO, 67% for LSO, 82% for NaI(Tl). After
the initial scatter, the photon may be absorbed elsewhere in the detector resulting in mis-positioning (intercrystal scatter or ICS), or it may escape resulting in loss of efficiency. ICS only has a small effect on the width
of the central “spike” of the CLRF. The more insidious effects are tails several millimeters long on the
response. These compromise the noise performance of the scanner and may not be apparent from the
viewpoint of the FWHM of the reconstructed point or line response. And while our investigations of positron
range could likely deal with these response tails, it would be better if they were absent (assuming that suitable
high resolution block detectors with good DOI resolution were even available for the high magnetic field
environment).
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With the ongoing developments in detectors including the infusion of new technologies such as SiPMTs,
semiconductor detectors, and positioning methods having good ability to identify the site of the initial photon
interaction in 3D, it is highly likely that within a decade, PET detector resolution will not be an issue with
coincidence line responses of <1mm FWHM (including acolinearity) the norm across the entire FOV. We are
not there yet, however. Existing small animal PET instruments as well as those to emerge from research labs
in the short-term are not the best or even particularly good choices for our investigations aimed at controlling
the flight of the positron. What is required is sub-millimeter spatial resolution over the FOV, sufficient DOI
resolution, freedom from ICS effects, and of course magnetic field compatibility.
For the detectors we propose for the measurements, because of their outstanding DOI resolution, their clean
resolution offered by escape of the scattered photon from the detector, and their coincidence line response
resolution of 0.67mm FWHM (1.4mm pads / √24 x 2.35 for the equivalent Gaussian or FWHM, 0.7mm for the
triangular response), positron-range in many cases becomes the dominant influence on resolution. Moreover,
we have recently developed detectors having 1mm x 1mm x 1mm pads [Euromedim2006].
Why not use “existing” PET/MRI hybrids for these measurements? A number of devices have been proposed
over the years and several prototypes constructed. For example, Raylman et al. report on a device using
remote PSPMTs and two opposed arrays of 2mm x 2mm x 10mm crystals [Raylman1, Raylman2]. A similar
approach has been reported by the UC Davis group except that high-gain PSAPDs are coupled to an 8x8
element array of 1.43mm x 1.43mm x 6mm LSO crystals through optical fibers [Catana]. A proposed
instrument consisting of a split-solenoid MRI magnet and arrays of LSO scintillators coupled to outboard
PSPMTs is described in [CTI]. And Brookhaven is investigating placement of their RatCAP APD-based
scanner within a small-bore MRI magnet [BNL]. There are other examples as well.
These are important 1st generation devices aimed at further understanding the rationale for combining MRI and
PET as well as the requirements for such instruments. They are excellent for these purposes. But, virtually all
use small ring diameters and relatively thick crystals in coarse-grained arrays with no DOI resolution. One of
the requirements of our investigation is the measurement of range effects of the same order as—or smaller
than—the spatial resolution of these 1st generation instruments. Because of this, the instrument we propose
for the measurements as noted above and in Section C.1 is more suitable than existing PET/MRI devices.
Be that as it may, it is likely that in the near future there will be many usable methods of obtaining submillimeter
resolution in PET. The major source of resolution loss for all will then be the range of the positron in tissue. In
order to study this issue further, and to evaluate the effectiveness of strong magnetic fields in improving spatial
resolution, we chose to use a PET instrument, which is capable of easily achieving submillimeter resolution
due to its DOI sensitivity, small effect from acolinearity, and small detector elements as shown in Section C.1.
Positron range in water and tissue [Revised]
The range of a positron depends on its energy and the composition through which it travels. Several authors
have studied positron range in water and lung tissue using Monte Carlo simulation methods [2, 3]. Some of the
results for different positron-emitters are given in Table 1. As a measure of positron range we list both the
FWHM and FWTM of the x coordinate of the annihilation point distribution. In cases marked with an asterisk
we have used a linear approximation to scale the Levin and Hoffman data taking into account the maximum
positron energy. As expected, the range depends on the tissue the positrons travel through decreasing with
density and increases with increasing positron energy. The values in Table 1 were obtained without a magnetic
field. In order to study the effects of a magnetic field on the positron range we used EGS-4 to develop our own
simulation. Our EGS-4 simulation tracks the positrons in three dimensions and the resulting distribution of
annihilation points was projected on the image plane to assess their impact on the spatial resolution. Our
results for no magnetic field are presented in the last three columns of Table 1. There is generally good
agreement between the three studies. Sanchez, Andrea and Larsson [93] found that the full width at 10%
(FWTM) or 20% of the maximum of the annihilation point distributions yielded more appropriate values to
assess the effect of the positron range on the overall spatial distribution of the PET system.
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Isotope
F-18
Max. Positron
Energy [KeV]
Kagan, Harris
Sanchez, Andreo, Larsson
[93]
Levin and Hoffman [2]
Tissue
FWHM
[mm]
FWTM
[mm]
Tissue
FWHM
[mm]
FWTM
[mm]
Tissue
FWHM
[mm]
FWTM
[mm]
Water
0.10
1.03
Water
0.19
0.91
Water
0.16
0.96
Lung
0.37
2.70
Lung
0.28
2.64
Water
0.28
1.70
Water
0.24
1.70
Lung
0.52
4.90
Lung
0.40
4.88
Water
0.33
2.12
Water
0.32
2.32
Lung
0.62
6.50
Lung
0.48
6.36
Water
0.41
3.10
Water
0.44
4.00
Lung
0.83
10.10
Lung
0.80
10.47
Water
0.49
3.70
Water
0.64
4.28
Lung
0.98
11.50
Lung
1.28
12.06
Water
0.76
Water
0.83
6.90
Lung
1.43
Lung
1.44
28.0
635
Lung
Water
C-11
0.19
1.86
970
Lung
Water
N-13
0.28
2.53
1190
Lung
Water
O-15
0.50
4.14
1720
Lung
Water
Ga-68
0.6*
4.6*
1899
Lung
Water
Tc-94m
Our Results (EGS 4)
0.8*
8.2*
1428
Lung
Table 1 Simulated positron range in water and lung tissue for different positron-emitters.
It should be evident that as the spatial resolution in PET improves into the deep sub-millimeter region positron
range effects will first become visible first as tails and then in the core of the resolution function. Sanchez et al.
[93] studied the relative spatial resolution loss due to the positron distance of flight as function of the overall
spatial resolution of the PET system. Figure 1 (taken from [93]) clearly shows the increasing impact of the the
Figure 1 Relative loss in spatial resolution due to the positron distance of flight [93].
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positron range as the system resolution improves. As PET cameras approach sub-millimeter resolution the
effect of the positron range becomes important not only for high energy positron emitters such as Ga-68 but
also for F-18 in particular when imaging lung tissue.
Opportunities to improve spatial resolution [Revised]
We have outlined the case that positron range will become the limiting factor to good (deep sub-millimeter)
image quality in PET systems designed with the following characteristics: small size to reduce non-collinearity
effects, high detector spatial resolution for good image resolution, and segmentation for DOI sensitivity. One
clear way of reducing positron range is to embed the PET FOV in a strong magnetic field thereby generating a
Lorentz force on the positron causing it to spiral around the magnetic field direction. If multiple scattering of the
positron in tissue is not too large then the resulting helical motion should reduce the effective positron range in
directions perpendicular to the applied magnetic field. Such a scenario has been investigated by Hammer,
Raylman and Christensen [1]. They found that the simulation and experiment agreed and some improvement
(27% in FWHM transverse to the magnetic field) was possible with high field (10T) for Ga-68. However the
inherent spatial resolution of the detector system (~5mm) and small bore of the magnet produced results which
clearly need to be extended to the state-of-the-art of scanners today. In particular, their observed small range
reduction (2% in FWHM) with 10T for F-18 should be verified given that modern scanners have 4 times better
spatial resolution.
Based on the work of Hammer, Raylman and Christensen and others the embedding of the PET FOV presents
a method for high resolution scanners to achieve sub-millimeter image resolution. Although the sub-millimeter
regime has its own peculiarities our initial work (Section C.2) confirms this idea. The significant outstanding
issue is that the previous methods only resulted in an improved reconstructed resolution in two dimensions.
We propose a new data acquisition and reconstruction method (Section C.4) that will improve reconstructed
resolution in all three spatial dimensions.
Additional benefits – nearly simultaneous PET/MRI
Both PET and MRI are diagnostic imaging tools in common use today. PET’s major strength is the ability to
visualize and quantify metabolic processes. MRI’s main use is in anatomical imaging of soft tissue structures
such as the brain. Images from dual studies are difficult to correlate because data from two discrete scanners
are necessary and a separate procedure to co-register the image sets must be performed. As a result,
temporal co-registration is impossible. While not a goal of the present investigation, once a high resolution
PET system can operate within a large magnetic field nearly simultaneous PET and MRI scans can be
performed.
Rationale for the Specific Aims: The proposed work and how it moves toward the long-term objective [Revised]
The proposed work involves simulation of the PET performance in a magnetic field, modification of a small high
resolution PET scanner which can be operated in a large magnetic field, perform measurements to necessary
to demonstrate improved resolution in 3D and quantify the increase in performance achievable with magnetic
confinement. Each part of this investigation plays a direct role toward the long term objective of sub-millimeter
PET image resolution for small animals.
Work in Aim 1 is necessary for (1) predicting positron range and the effects of the magnetic field on range; (2)
performing design studies for the proposed PET measurement device (although these will be straightforward
given that a prototype scanner already exists (Section C.1); and (3) for generating Monte Carlo data to
compare with measurements conducted in Aim 3. Work here will also model the distribution of Comptonscattering in the object (which will be relatively small due to the slice-collimated geometry of the scanner) so
that it can be compensated in the reconstructions.
The high resolution PET measurement device will be constructed in Aim 2. As noted above, it will be based on
an existing prototype. The primary work will be repackaging the instrument to eliminate magnetic materials, to
allow the entire tomograph to be re-oriented in the large-bore 7T and 3T magnets, and to incorporate new
motion controls that will allow 3D data acquisition. Since the PSF induced by positron-range is not a function
of the PET device itself, there is great leeway in construction and 3D data acquisition will be performed by
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scanning a sequence of slices by axially translating the object. Scanner development will proceed in three
phases. The first will develop a single-slice 2D tomograph in which only the object is capable of computercontrolled rotation. The second will add axial translation to allow full 3D data acquisition. And in the final
phase, additional hardware will be constructed to allow the detectors to rotate around the stationary object.
Because of the incomplete detector ring, some rotation either the object or the detectors will be required to
obtain a full dataset for each slice. The ability for independent rotation of each allows maximum flexibility in
setting the orientation of the B-field relative to the object. In all three phases, manual re-orientation of the
tomograph relative to the field will be possible. Work in Aim 2 will also extend the reconstruction method
developed in R01 EB430 to reconstruct 3D data from the scanner. It will addtionally be extended to
incorporate various positron blurring functions—including those anticipated in 3T and 7T fields—and to
implement the reconstruction method presented in Section C.4
The bulk of the experimental measurements aimed at validating our approach will be performed in Aim 3. Both
F-18 and Ge-68 will be used and data will be collected at 0T and at various orientations at 3T and 7T. Various
acquisition protocols will be used and results compared with our predictions from Aim 1 as well as with
calculations from Aim 4.
There are several reasons for including the bias-variance tradeoff studies in Aim 4. First, they help tie all the
work together. If all the models used are accurate depictions of reality then the performance from (1)
reconstrudtions of the Monte Carlo data from Aim 1, (2) reconstructions from the measurements in Aim 3, and
(3) predictions from the calculations in Aim 4 should match. Assuming performance predictions match, the
second reason for including Aim 4 is that it allows performance of various data acquisition scenarios to be
predicted. For example, while we show a composite reconstructoin from simulated data in two orientations in
Section C.4, is it better to split the data acquisition time among more? Does it matter at all? This study allows
issues such as these to be examined in detail without incurring charges for unnecessary magnet time. Third,
as noted in an earlier section, resolution must often be scrubbed in the image reconstruction process to
sufficiently regulate noise. At what reconstructed resolution—if any—does the effect of magnetic confinement
offer only marginal gains over no confinement? Or is there nearly always a significant noise advantage?
Obviously, it will depend on the positron energy but these questions can be answered in a well-defined way.
There are numerous other benefits for including such machinery such as the ability to examine the covariance
and bias structures arising in the reconstructions.
Unique facilities
Our collaboration has two unique facilities and several strengths which puts us in a unique position to complete
the proposed studies. First we have access to large bore 3T and 7T magnets. The 7T magnet (Philips Altera)
is part of the new state-of-the-art MRI facility of the Wright Center for Innovation in Biomedical Imaging at The
Ohio State University. Second we have a detector assembly facility for design, layout, construction, testing
and repair of state-of-the-art detectors. Our collaboration posseses the unique feature of having the
demonstrated ability to construct and repair high resolution silicon detector modules and keep them operating
[84, 85]. Thus we should be able to solve any problems associated with hardware quickly during the study.
Finally our collaboration possesses the imaging knowledge and skills having performed simulation and
reconstruction on a variety of geometries and devices. This combination uniquely positions us to perform this
study.
C. Preliminary Work [Revised]
C.1 PET with submillimeter spatial resolution
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Figure 2 shows two views of the high resolution PET experimental setup used to acquire preliminary data [92].
The mechanics of the proposed system are similar to this system and constructed from non-magnetic
materials. Two 512-pad (32x16 array, 1.4mm x 1.4mm x 1mm thick) silicon detectors were oriented
horizontally to image a single slice. The detectors of the porposed system are the same detectors used here.
To cut down background radiation, sources were placed in a shielded cavity and collimated with tungsten to a
Figure 2: Experimental setup for high resolution PET data acquisitions. Left: disassembled showing silicon detectors,
tungsten slice collimation, shielded source cavity, and rotating table. Laser is used to align silicon detectors coplanar
with tungsten slit. Right: assembled device showing source shielding, protective plastic boxes for silicon detectors and
position-insensitive BGO detectors (“end-caps”) for improved timing and energy resolution.
1.5mm slice. The idea of this system is that photons from positron annihilation Compton scatter in the silicon
pad detectors and the resulting Compton electron will be measured in the silicon pad detector. To collect the
scattered photon for possible energy discrimination and additional timing information, the silicon detectors were
flanked by four BGO scintillation detector modules scavenged from a CTI 931 PET scanner. No position
information was available from these BGO detectors (although different scintillation detectors could provide
additional position information). For the results described in this section the BGO scintillation detector system
was not used. Because the detectors do not record the full sinogram, the object must be rotated using the
computer controlled rotation stage on the instrument (For the updated instrument proposed in Section D.2
both the object and eventually the detectors will be capable of rotating around the tomograph axis for
maximum flexibility in data acquisition relative to the orientation of the B-field.)
Using a laser, detectors were aligned in a plane parallel to that of the slit using pitch and roll adjustments. The
1mm thickness of each detector was then centered vertically on the open slit. Line sources were imaged at
several rotational positions in the field-of-view and a ML calibration method was used to estimate the unknown
geometric parameters of the instrument (detector positions, axis-of-rotation, etc.) Because of the large timewalk with our present version of the silicon detector readout electronics, which uses a 200 ns shaper in the
fast-channel, a 200 ns time-window was used. Detectors were biased slightly less than depletion (due to bias
supply limits) and were operated at a triggering threshold of ~20keV. Depending on the maximum distance of
source activity from the isocenter, increments of the rotation stage for data acquisition ranged from 1º to 30º.
For the initial studies we acquired an equal number of events at each view with each silicon detector read out
in serial mode with all pads being readout.
Figure 3 shows the initial results from the tomograph in Fig. 2 compared with those from the Concorde
MicroPET R4. Shown at the left is an image of two hematocrit tubes filled with F-18 FDG acquired using the
MicroPET. Each tube had an inside diameter of 1.1mm, a wall-thickness of 0.2mm. The tubes were taped so
that there was no space between them (separation between F-18 lines: 0.4mm). The measured resolution of
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the MicroPET R4 after accounting for the source size and using the MAP reconstruction algorithm that models
detector blurring is ~1.6mm FWHM (volume resolution 4µl). The center image shows four pairs of the same
sources at 5mm, 10mm, 15mm, and 20mm off-axis acquired using the high resolution PET setup and
reconstructed using plain-vanilla maximum likelihood with no modeling of detector response. The scales are
the same in the left and center images. The two line sources in each pair are clearly separated. Accounting
for the source size, the resolution is 800µm x 800µm x 650µm (axial) FWHM (0.42µl). In contrast to systems
without DOI resolution, performance is nearly constant across the FOV. To demonstrate that this is no
resolution-recovery “trick” of the reconstruction, each pair of sources is apparent in the corresponding
sinogram (Fig. 2, right). Recently, detectors having 1mm x 1mm x 1mm elements have been fabricated and
should allow intrinsic resolution of approximately 650 µm FWHM including the effect of acolinearity.
This result clearly demonstrates that prototype PET system is capable of achieving high (sub-millimeter) spatial
resolutions. The significant remaining question is whether it is feasible for the detectors to operate in a large
magnetic field. This is addressed in Section C.3.
Figure 3: F-18 sources in two adjacent hematocrit tubes on-axis for MicroPET R4 (left) and for four pairs at 5mm, 10mm,
15mm, and 20mm off-axis for the high resolution PET test system shown in Fig 1 (center). Tubes have an internal
diameter of 1.1mm and wall thickness of 0.2mm. MicroPET reconstructed using MAP algorithm; prototype high resolution
PET using maximum likelihood with a simple system matrix that does not account for finite detector size. Resolution
correcting for source size is approximately 1.6mm FWHM for MicroPET R4 and 800µm FWHM for the new instrument.
Image at right is efficiency-corrected sinogram demonstrating the intrinsically high spatial resolution. Each hematocrit
tube in each pair is evident at the appropriate projection angle.
In the upcoming period we propose to use the above PET technique within its realm of applicability as a high
resolution imaging tool to address the issue of positron range on image resolution. The results of this
investigation should be applicable to all high resolution PET systems capable of operation at high magnetic
field-strengths.
C.2 Reduction of positron range in magnetic fields
The importance of the positron distance of flight has been discussed in Section B. Here we discuss our
preliminary simulation work using EGS-4 of the effect of strong magnetic fields on positron range. While the
total distance traveled by a positron between emission and annihilation is not affected by an external magnetic
field, the positrons no longer move in straight lines between scatter interactions with the material they travel
through. The Lorentz force acts on the moving positrons forcing them onto a helical path thereby reducing the
range which is defined as the distance between emission and annihilation points. The size of this effect
depends on the direction of the positron relative to the magnetic field direction. It is largest for positrons
traveling perpendicular to the direction of the magnetic field. Figure 3 shows simulated positron range
distributions for different positron emitters in both water and lung tissue. Each configuration was simulated with
and without a 7-T magnetic field. The reduction in range is clearly visible in Figure 3. The size of the effect
depends both on the positron energy and the density of the material the positrons travel through. In order to
obtain quantitative results we project the range distribution onto an axis perpendicular to the magnetic field
direction. An example for positrons emitted by Ga-68 in water is shown in Figure 4. Cusp-like distributions are
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observed in these studies similar to studies without magnetic field but with significantly reduced tails.
Numerical results for different positron emitters are listed in Table 2. A substantial reduction in range can be
obtained for radionuclides with large positron energies such as Tc-94m or Ga-68 but even for F-18 the average
positron range can be reduced by strong magnetic fields in particular in less dense media such as lung tissue.
In Water
No Magnetic Field
In Lung Tissue
7 T Magnetic Field
No Magnetic Field
7 T Magnetic Field
F-18
Ga-68
Tc-94m
Figure 3: Simulated positron range distributions for F-18, Ga-68 and Tc-94m in water and lung tissue with
and without a magnetic field. The range distribution is projected onto a plane perpendicular to the direction
of the magnetic field.
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Figure 4 Positron distance of flight in water for Ga-68, (a) without magnetic field, (b) projected onto a plane
perpendicular to a 7-T magnetic field, (c) projected onto a plane parallel to a 7-T magnetic field, and (d) range
projection onto an axis parallel and perpendicular to an 7-T magnetic field.
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Isotope
Max. Positron
Energy [KeV]
F-18
635
C-11
N-13
O-15
Ga-68
Tc-94m
Tissue
FWHM
[mm]
FWTM
[mm]
Water
0.16
0.80
Lung
0.32
1.08
Water
0.32
1.20
Lung
0.48
1.52
Water
0.40
1.44
Lung
0.64
1.76
Water
0.60
1.96
Lung
0.88
2.24
Water
0.80
2.20
Lung
1.00
2.48
Water
1.12
2.80
Lung
1.20
2.84
970
1190
1720
1899
1428
Table 2 Simulated positron range in water and lung tissue for different positron-emitters in a 7T magnetic field
perpendicular to the image plane.
We conclude that embedding the PET FOV in a large magnetic field (7T) should reduce the positron range
distribution in water and this effect should be observable with a PET system with sub-millimeter resolution.
C.3 Magnetic field compatibility of proposed detectors
In order to identify the issues associated with high field operation of a Compton PET system, we tested a
silicon detector hybrid module similar to that which we propose to use for this investigation and similar to that
used for the results in Section C.1. This module is shown is Figure 6. The silicon detector had 512-pads
(32x16 array, 1.4mm x 1.4mm x 1mm thick) and was readout via four VaTaGP3 ASIC’s. We chose to measure
the pulse height spectrum of Am-241 to look for an effect due to the magnetic field. We initially setup to
acquire an Am-241 spectrum in the 8T magnetic of the Ohio State University MRI facility. Within one minute of
operation the hybrid failed. Upon further investigation we discovered that three wire bonds to the integrated
circuit had broken on the high current lines which power the digital readout. These are shown in the right
image of Figure 6. To understand this result we constructed a wire bond test system and operated it in the 8T
magnetic field. We put 133mA through the test wire bonds which is roughly twice the peak current the real
wires bonds have during readout operation.
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Figure 6: Left Image: Photograph of the silicon detector module tested in an 8T magnetic field. Right Image: Photograph
of the three broken wires (first, fourth, and sixth ones in) after the initial test in the 8T field.
In the real device the current in the bond wires changes in magnitude with frequency. We found that for DC
and high frequency operation we could not reproduce the breaking of bonds. However at roughly the readout
frequency of the ASIC we were able to break bonds. Our solution was to encapsulate the wire bonds of the
test setup. Upon testing this configuration we found that we did not break a wire bond after 18 hrs of
continuous testing at the same frequency which previously had broken bonds.
Figure 7: The Am-241 pulse height spectra obtained using a silicon pad detector and VaTaGP3 electronics operating in
0T (red curve) and 8T (black curve) magnetic fields.
We repaired the broken detector system, encapsulated the wire bonds and took Am-241 spectra at 0, 2, 4, 6,
and 8T. The total time in the 8T magnetic field was 8 hrs. No wire bonds were broken during the test nor were
any other problems observed. For these tests the detector was operated at 100V and at a trigger threshold of
approximately 20keV and each data run was a fixed number of events. Figure 7 shows the Am-241 results for
data runs taken at 0T (red curve) and 8T (black curve). We observe no difference in the spectra obtained at
0T and at 8T. That the raw spectra appear nearly identical indicates that the trigger efficiency and energy
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resolution did not change in the magnetic field. We conclude that the proposed silicon detector system will
operate and have the same performance in the 7T field as we measure on the bench at 0T.
C.4 Method for reducing effects of positron range in 3D
As evident from the information above, while the magnetic field improves spatial resolution by reducing range
in directions transverse to the field, it has little to no effect on the range of positrons emitted with significant
momentum parallel to the magnetic field vector. The point spread functions resulting from this static magnetic
confinement may actually exhibit worse imaging performance than using no confinement at all. To visualize
this, refer to the projections of Monte Carlo generated PSFs for I-124 shown in Figure 8. The leftmost image is
a planar projection of the PSF with no applied magnetic field. It has a sharp central peak and broad, diffuse
Distance (mm)
0 Tesla
9 Tesla XZ-Plane
9 Tesla XY-Plane
-4
-4
-4
-3
-3
-3
-2
-2
-2
-1
-1
-1
0
0
0
1
1
1
2
2
2
3
3
3
-4
-2
0
2
-4
-2
0
2
Distance (mm)
-4
-2
0
2
Figure 8. Projections of the PSF due to range of I-124 positrons in water. Left: No magnetic confinement; PSF is
isotropic. Center: Orientation of B-field vector is parallel to bottom of page. Note long tails extending in z-direction.
Right: Orientation of B-field is into the page.
tails that tend to average any out-of-plane structures resulting in an additional background “haze” in the slice
being viewed. At 9T, projections of the resulting PSFs in two orthogonal directions are shown at the center
and right. If one is viewing slices in the X-Y plane (rightmost image), resolution of in-plane structures will
obviously be much better than with no magnetic field. However, notice the sharpness of the tails of the
response function in the X-Z projection (center). Rather than a diffuse background, these sharp tails will
generate artifacts in the slice being viewed from structures in adjacent planes. In short, while positron range
will be reduced and images will exhibit improved spatial resolution, artifacts will be worse than with no
magnetic field.
The solution—one that will improve spatial resolution in 3D to essentially that shown in the X-Y projection of
Figure 8—is to acquire PET measurements in multiple orientations of the magnetic field vector relative to the
object. It is of course difficult to change the orientation of a 9T magnet but it is much easier to orient the object
in two or more directions relative to the magnetic field.
The next significant question is once such PET information is obtained, how should it be reconstructed? The
answer is particularly straightforward: a single estimate of the distribution of radiotracer is obtained by
considering all measurements simultaneously. Specifically, the sets of projection data from each B-field
orientation are combined using a maximum likelihood (or penalized likelihood or maximum a posteriori) image
reconstruction that accounts correctly for uncertainties in the measurements. Although resolution recovery—
assuming the system response is modeled correctly—is possible for all the above cases, the situation in which
at least two orientations (preferably orthogonal) of a strong magnetic are used will provide a noise-resolution
tradeoff superior to either the use of no field or a field oriented in only one direction.
For the reconstructed images shown below, we assume the probability mass function of the measurements
can be represented as a conditionally Poisson model where the conditioning is with respect to the unknown
object:
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 A 
y 
 b 
y   ~ PoissonA   λ  b   
 

 

(1)
where y = [y11,…,y1N]T and y = [y21,…,y2N]T represent the recorded events for two orientations, which may
be binned into histograms (or “sinograms”) or instead may be just a list of the endpoints of each recorded
coincidence (or other information-preserving transformation of the data). The matrices A and A represent the
aperture function or system response of the tomograph in the two orientations of the magnetic field. For
example, with the magnetic field vector parallel to the axis of the PET instrument, A would model a response
function that has low uncertainty due to positron range in the x-y plane and high uncertainty along the axis of
the tomograph. In contrast, A—if the magnetic field vector is perpendicular to the previous orientation—
would model low uncertainty along the tomograph axis and high uncertainty in some orthogonal direction. The
symbol λ=[λ1,…,λM]T is a discrete representation of the object—e.g., voxels. More orientations of the field
can be accommodated in the above model by augmenting the composite system matrix (in square brackets in
(1)) with an additional A accounting for the correct orientation of the magnetic field relative to the object. As in
similar models for PET the vectors b represent additive interference due to randoms and scatter.
Once the reconstruction problem has been set up in this fashion, numerous methods can be used to obtain the
estimate, the EM-algorithm being a particularly suitable choice for solving for the corresponding maximum
likelihood or penalized maximum likelihood estimate. The key things to note are that (1) both sets of
measurements arise from a single, unknown object λ that must be estimated, and (2) the system model must
account for the PSF induced by the positron range for each orientation of the magnetic field.
Calculations of image effect of range reduction
The PSF for I-124 positron annihilations in water shown in Figure 8 was used to blur data from the simulated
resolution phantom (rod diameters 4.8, 4.0, 3.2, 2.4, 1.6, and 1.2 mm) . One million detected annihilations
were recorded in a simulated single-slice PET scanner with resolution similar to the instrument that will be
used for the experiments described in Section D, and then reconstructed using a maximum likelihood method
(EM algorithm) that modeled the spatial resolution of the PET system but not the range of the positron. The
corresponding image is shown in Figure 9 left below.
Figure 9.
Left: Reconstructed PET images for
simulated data corresponding to resolution phantom
filled with I-124 resolution phantom with no magnetic
field. Right: Same phantom at 9T field strength with
magnetic field vector perpendicular to the page. Both
datasets have one million detected events. Intrinsic
resolution of the PET scanner implied in the simulations
is ~700µm FWHM—similar to the instrument that will be
used in the proposed investigation. This represents the
ideal situation: artifacts from out-of-plane activity are
non-existent
The PSF modeling I-124 positron range at 9T field was also calculated and used to blur the phantom assuming
the constant axis of the phantom (direction along rods) was oriented parallel to the B-field. This case will give
the best resolution for such a phantom but it is unrealistic in practice since real objects tend not to have a
constant activity distribution along one direction. Again, one million detected events were used to reconstruct
the image in Figure 9 on the right. Notice the significantly improved spatial resolution. As noted, in reality this
case is somewhat unrealistic (except for micro-Jaszczak phantoms!).
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Figure 10. Left: Orientation
of B-field parallel to bottom
of page. Center: orientation
of B-field perpendicular to
bottom of page. Right:
Reconstruction from both
orientations.
Using the proposed acquisition and reconstruction method, datasets were simulated in two orientations of the
B-field relative to the object; each orientation contains a mean of 500K events (1M total) and data were
reconstructed using the ML technique described above. The leftmost image of Figure 10 is a reconstruction
corresponding to a B-field to the right, the image in the center is a reconstruction from data acquired when the
B-field is pointing toward the bottom of the page, and finally, the reconstruction on the right is made using both
field orientations. These preliminary results are encouraging but the proposed work will quantify the actual
advantages in terms of better noise-resolution tradeoffs as well as freedom from artifacts due to structures in
adjacent planes using magnetic range confinement.
D. Methods and Experimental Design
Work will be a collaborative effort among OSU and Michigan. Although there will be exceptions, the division of
the work among the institutions is best visualized in the following way. Monte Carlo modeling of PET
performance in a magnetic field (Aim 1) will be performed at both OSU (simulation of positron range) and
Michigan (Monte Carlo model of the scanner). Construction of the high resolution PET scanner compatible with
the 7T magnetic field (Aim 2) including basic detector performance characterizations, construction of hybrids
and readout electronics, assembly into modular subsystems, testing and integration into the scanner platform
will be performed at OSU. Performance measurements with the scanner (Aim 3) will be performed at OSU by
both OSU and Michigan personnel. Quantifying the scanner performance (Aim 4) including image
reconstruction algorithms and data processing will be performed at Michigan.
D.1 Aim 1: Monte Carlo modeling of PET performance in a magnetic field
The overall goal here is to combine accurate simulations of positron range in various tissues with an accurate
Monte Carlo model of high resolution scanner to be inserted into the magnet bore. These models will be used
not only for predicting the resolution improvements at different field strengths but also to aid in the design of
the scanner and for generating data to compare with measurements (D.4).
D.1.1 Simulate the positron range in various materials in a 7Tmagnetic field
EGS4 and GEANT4 will be used to simulate the positron range in various materials and in various magnetic
fields. The input positron spectra will be calculated as in Levin and Hoffman [2]. The modernization of EGS
and GEANT have allowed their cutoff energies to be lowered to below 1keV. We will use a 1keV cutoff energy
which compares well with the 3keV used in Levin and Hoffman [2]. We will begin by reproducing F-18 and O15 results of Levin and Hoffman described in C.2. After establishing that the positron range tool we have
developed is sound we will apply it to I-124, Ga-68 and Tc-94m.
D.1.2 Design a Monte Carlo model of the high resolution scanner
EGS4 and GEANT4 will be used to enter the geometry and perform a Monte Carlo simulation of the scanner.
These models will be used to aid in the design of the scanner, to generate data to compare with the various
experiments planned (D.4) and to predict the resolution for various experiments at different field strengths (D.4)
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D.2 Aim 2: Construct a high resolution PET scanner compatible with an 7T magnetic field
In order to have the sensitivity to observe and quantify the results of the effect of the magnetic field on a PET
scanner a sub-millimeter scanner compatible with a 7T magnetic field is required. As shown earlier this is
difficult to accomplish with a scintillation detector based system. Our expertise and experience drives us to a
Compton-PET system with an inherent resolution across the FOV of roughly 800m.
D.2.1 Construct a sub-millimeter PET scanner compatible with a 7T magnetic field
To keep the cost of the instrument reasonable, we propose methods that will only require a single-slice
scanner. The scanner is designed so that it can be positioned in at least two orientations relative to the
magnetic field: one in which the axis of the PET device is aligned with the field and one in which it is orthogonal
to the field direction. The scanner will provide experimental evidence to validate the predictions of the Monte
Carlo calculations of D.1.
The scanner will be similar to that shown in Fig. 1 except it will not have the scintillation detectors and
photomultiplier tubes and it will be constructed with non-magnetic materials. Two 512-pad (32x16 array,
1.4mm x 1.4mm x 1mm thick) silicon detectors will be oriented horizontally to image a single slice. To cut
down background radiation, sources will be placed in a shielded cavity and collimated to a 1.5mm slice. This
will allow flexibility in the use of different shielding configurations to control the rate. This is important because
of limitations in the electronics discussed below. The original instrument used a machinable tungsten alloy,
which proved to be ferromagnetic. The new instrument will use lead but the material is not critical since its
primary purpose is to reduce the singles rate in each detector from out of plane activity rather than to provide
sharp collimation. The entire unit will be placed in a plastic cube so that the scanner may be easily oriented
parallel or perpendicular to the magnetic field direction. Because the partial detector ring will not cover the full
angular range, a computer controlled rotary table will be used to rotate the source to emulate a full ring. The
rotary mechanism will use a pneumatic drive so that it will operate in a magnetic field. Furthermore, in order to
accommodate 3D phantoms (for evaluation of out-of-plane artifacts, etc.), a pneumatic translator will be
incorporated to move the object along the axis-of-rotation so that a sequence of PET slices can be acquired.
The detector system will be interfaced, as before, through a combination of VME and NIM electronics. The
VME system and rotary table will be, in turn, interfaced to a PC. Data acquisition electronics for the test
scanner will be upgraded as new devices become available in the course of our investigations. Using a laser,
detectors will be aligned in a plane parallel to that of the slit using pitch and roll adjustments. The 1mm
thickness of each detector will then be centered vertically on the open slit. Point sources will be imaged at
several rotational positions in the field-of-view and the ML calibration method will be used to estimate the
detector positions relative to one another and to the axis of rotation. Because of the large time-walk with our
present version of the silicon detector readout electronics, which uses a 200 ns shaper in the fast-channel, a
250 ns time-window will be used. A schematic of the trigger and reset electronics is shown in Figure 11. The
present plan is to use a simple trigger consisting of a coincident hit (within 250 ns) in each silicon detector to
trigger the readout. A timing correction based on pulse-height will be performed post data taking by recording
both the energy and triggering time for each detector using a VME time-to-digital converter. We expect to
achieve a time coincidence spread of less than 25ns which should be good enough to reject background
events. This setup will allow us to produce images where the inherent resolution of the device is small
compared to the effect of positron range.
D.2.2 Implement 2D multi-resolution ML image reconstruction
Calibration and data correction algorithms already exist for the scanner shown in Fig. 1. These will be
extended as necessary to accommodate the new setup. Furthermore, a penalized, post-smoothed ML
reconstruction has already been developed for the multi-orientation PET measurements generated by the
Monte Carlo studies in Section C.4 [86]. The development of system response models is straightforward for
the silicon PET instrument above and will take advantage of similar work now being conducted under R01
EB430-34, which is exploring potential advantages of silicon-based PET instruments over those of more
conventional construction. The positron range component of the response will be implemented as a “preblurring” operation on the image space before projection with the intrinsic instrument response. Kernels for the
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smoothing operation will be obtained from Monte Carlo studies from Aim 1 at the appropriate magnetic field
strength. Obviously for backprojection, the order of the intrinsic response and range smearing operations are
reversed. A good test of the accuracy of the response models, which will not only be used for image
reconstruction but also for the performance predictions described in Section D.4 will be agreement between
predictions and sample statistics derived from reconstructions of experimental data.
Much of the work of this investigation will use single-slice PET data and therefore only a 2D reconstruction will
suffice; nevertheless, as resources (e.g., magnet time) permit, we will acquire multiple sequential slices using a
pneumatic translator to move the phantom. In this case, the 3D reconstruction is needed. Because of the
simple slice geometry, it is not difficult to extend the above reconstruction methods to 3D.
While 3D may not be very useful for “short” half-life tracers such as F-18, it will be usable for longer lived
tracers such as Ge/Ga-68 and will provide valuable information on how much PET performance can be
improved in the more realistic volume PET situation.
Figure 11: A schematic of the trigger and reset electronic circuitry. Signals from the silicon detectors arrive at
the intermediate board where a coincidence generates a trigger.
D.2.3 Conduct phantom imaging studies, compare performance with predictions at 0T
Studies of spatial resolution in air and water at 0T will be made throughout the FOV by using a Na-22 point
sources and capillary tubes filled with F-18. Images will be reconstructed using the appropriate PET
reconstruction algorithm developed in D2.2. Resulting images will be compared with those reconstructed from
Monte Carlo data generated using the corresponding geometry. The sample variance and PSF of images
reconstructed from repeated measurements will be compared to bound calculations. Efficiency will also be
measured at several locations in the FOV for the partial scanner ring. Both the partial scanner ring efficiency
will be compared to the corresponding Monte Carlo predictions.
One of the issues noted in Section C.4 was that imaging performance may actually be less satisfactory with
magnetic confinement due to a more structured crosstalk among planes in the object transverse to the
magnetic field vector. To evaluate this effect we will construct special two- or three-slice phantoms—each slice
being 1–1.5mm thick—having a different configuration of activity in each slice. An example might be slices of a
micro-Jaszczak hotspot phantom filled with Ge-68-loaded epoxy with each slice rotated to a different
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orientation. Another example would be a hotspot phantom adjacent to a slice of acrylic having no activity. It
will not be necessary to perform 3D imaging of these phantoms to see the effects of crosstalk, although, we will
have the slice-by-slice imaging capability noted above for long half-life nuclides.
D.3 Aim 3: Perform measurements necessary to demonstrate improved resolution in 3D
D.3.1 Map the magnetic field distribution
The fringes of the magnetic field will be mapped up to 2T. Using a simple model for the magnet the measurted
data up to 2T will be extrapolated to yield the magnet fringe field distribution. We should then be able to locate
the scanner in the fringe field of the magnet fairly precisely to explore effects from 0 to 7T.
D.3.2 Conduct imaging studies, compare performance with predictions at 7T
Studies of spatial resolution in air, water and plastic from 0T to 7T will be made throughout the FOV using a
Ge-68 point source and thin tubes containing F-18. In addition imaging of standard micro-Jaszczak hot- and
cold-spot phantoms with F-18 and F-18 in foam or tissue equivalent plastic will be performed as well as
imaging the 3D phantoms described in Section D.2.3. The goal of these experiments is to collect data for
qunatifying the real value of magnetic confinement under different scenarios. That will be done in Aim 4 where
the resolution-noise tradeoff under various imaging scenarios will be evaluated and compared with
experimental data and with predictions made using Monte Carlo data generated using methods in D.1.
D.4 Aim 4: Quantify the increase in performance achievable with magnetic confinement
All these methods will have a different tradeoff between resolution and variance of the reconstructed intensity
estimates. The fact that resolution can be traded against noise is only starting to be recognized in PET but in
principle it is possible to continue to improve the spatial resolution of the reconstruction almost without limit (as
long as enough events have been detected). The cost of this improvement is typically an exponential increase
in variance implicitly defining a resolution-noise tradeoff curve that will be different for each acquisition
protocol. Because each imaging system or acquisition protocol is capable of producing images having similar
spatial resolution but with very different noise characteristics, it is a more telling measure of performance to
compare the noise in reconstructed images over the range of spatial resolution. One PET measurement
technique that produces a resolution-noise curve lying entirely below another can be said to have uniformly
better performance, although it’s certainly possible for curves to cross one another.
There are a number of methods for quantifying noise-resolution tradeoff but our choice at this point because of
concordance of results with intuition in evaluating limiting SPECT system performance [87], because the
predicted limiting performance can be achieved using an appropriately regularized maximum likelihood
reconstruction [88], and because the methodology is being more fully developed to quantify volume PET
imaging performance under funding from a companion grant (NIH EB430-34), is the modified uniform CramèrRao bound [89]. Given a desired PSF f0 for the reconstructed images, the Fisher information matrix for the
particular PET system F (which includes the data acquisition protocol), and a tolerance δ quantifying the
maximum norm of the allowable difference between f0 and the PSF actually obtained in the reconstruction, the
bound gives the limiting variance achievable by any reconstruction method. As noted, under typical conditions,
the appropriately penalized maximum likelihood reconstruction that has been post-smoothed with the PSF
kernel f0 nearly achieves this limiting performance making the M-UCRB especially relevant for comparing
performance among systems.
The M-UCRB is described by the following equations:
  fo  f
 i2  foT I  F 1 FI  F 1 fo
   I  F 1 fo
f  I  F  Ff o
1
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where fo is the desired PSF at the j-th voxel in the parameterized object, f is the PSF actually achieved, δ is the
allowable tolerance of the difference between the desired and actual response, and α parametrically controls
both the variance and the tolerance. The Fisher information matrix is given by the usual form for these
problems
F  A T diag1 Aλ  b A ,
where—and λ is the radiotracer distribution in the object, b is the background due to random coincidences and
scatter, and A is the composite system response matrix—describing the blur due to positron range, the
intrinsic response of the PET instrument, attenuation, and multiple orientations of the magnetic field. Because
of the relatively small dimension of the imaging problems that will be used in this investigation (2D slices rather
than full volume PET); bound calculations are tractable using the full Fisher information matrix using a
conjugate-gradient methods we have employed previously. This will be true even for “3D” acquisitions
obtained by sequentially acquiring multiple slice data with the single-slice scanner. In many cases of interest it
may even be feasible to calculate the inverse matrix necessary for the bound directly.
Meaningful bound calculations require accurate models of the imaging process including positron range; as an
added benefit, these models will be used for image reconstruction as well. The system matrix will consist of a
component describing the intrinsic response of the PET scanner as well as a smoothing operator
characterizing the range of the positron in the object. The intrinsic response model for the silicon-based
instrument above is particularly straightforward because of its simple geometry, depth-of-interaction sensitivity,
and relative freedom from intra-detector Compton scatter. Smoothing operators characterizing positron range
will be estimated from Monte Carlo calculations. An incorrect positron range model will be the primary culprit
for discrepancies between performance predicted by the bound and that actually obtained in experiment. As
noted below, discrepancies will be traced and fixed by modifying the model.
There are several other degradations that should be accounted for in the system model including dead-time,
scatter, and random coincidences. Fortunately, because of the data acquisition geometry, the count rate is
likely to be moderate and the non-linear effects and inherent modeling difficulties with dead-time will not likely
be a significant issue. These will be ignored unless they prove to be non-negligible. Moreover, Comptonscatter is not likely to be significant in the single-slice geometry. Its effect will, in any case, be estimated using
Monte Carlo modeling techniques described above. As for random coincidences, even though pulse-height
based time-walk correction will be used; time resolution will still be rather sloppy mandating a wide coincidence
window. Although the count rate will typically be low, randoms estimation and correction will still be necessary
and will be performed either by the spoiled timing method (i.e., one channel is delayed enough that there are
essentially no true coincidences in the time window) or the singles method (b = 2S1S2τw, where S1 and S2 are
the singles rates in each detector and τw is the width of the coincidence window).
Assuming the system matrix adequately reflects reality, images reconstructed by the following post-smoothed,
maximum penalized likelihood method will asymptotically achieve the limiting performance.1
λˆ pml  arg max y T log Aλ  b   1T Aλ  b    λ T λ
λ
λˆ opt  Sf 0  λˆ pml
Here y represents the measured PET data, 1 is a vector of ones the size of y, A, b, and α are the same as in
the bound calculation, and S(f0) represents the post-smoothing operation with the desired PSF as the kernel.
Bound predictions in terms of variance at a given PSF will be compared with sample statistics obtained from
repeated measurements using the high resolution PET setup under at different magnetic field strengths and
using different phantoms and radionuclides. The PSF at desired points in reconstructions from experimental
data will be estimated using a perturbation technique in which a weak simulated point source at the desired
location is projected through the system matrix and added to the averaged experimental data. Both the
1
Asymptotic performance in this case means as the number of recorded events becomes large. In practice, this tends to be the
situation for all but very low count PET studies at usable levels of resolution enhancement.
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experimental data with and without this probe source are then reconstructed and the resulting images
subtracted leaving an estimate of the reconstructed PSF at the chosen location. The norm of the difference
between this PSF and the desired PSF provides an estimate of δ and the variance at each point in the
reconstruction will be estimated from point-wise sample variance in the multiple reconstructions resulting from
data taken for a specific nuclide, field strength, and object. In this manner it will be possible to trace out the
noise-resolution tradeoff curve from experimental data for comparison with the M-UCRB predictions. Errors in
the sample statistics will be estimated using bootstrapping methods [90]. This study serves primarily as a
sanity check—we expect that the performance predicted by the bound will be close to that actually achieved
assuming that the measurement statistics are high enough. The primary reason for discordance with
predictions will be that the system model used for both the bound calculations and reconstructions is not an
accurate reflection of reality. If this is the case, the discrepancies will be located and fixed.
E. Human Subjects
None.
F. Vertebrate Animals
None.
G. Select Agent Research
None.
H. References
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I. Multiple PI Leadership Plan
Not applicable.
J. Consortium / Contractual Arrangements
This proposal is a collaborative effort between The Ohio State University and The University of Michigan. Neal
Clinthorne of the University of Michigan has written a segment of this proposal with respect to image
reconstruction and analysis necessary for the quantification of the effects of the large magnetic field on a PET
scanner and his budget has been separately presented and justified. Substantial coordination of our efforts will
be accomplished via Internet communications as has been the case in preparing this proposal and in
coordinating our ongoing projects. The travel budget has been set up so that there are 1-2 day face-to-face
meetings of the key investigators at least twice per year. Furthermore, personnel from the University of
Michigan frequently travel to Ohio State University, which is a 2 ½ hour drive and vice versa.
Below we attach a University of Michigan Face Page, a letter of support from Prof. N. Clinthorne, a statement
of work for the University of Michigan, detailed yearly budgets and justification, and the University of Michigan
checklist.
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Kagan, Harris
K. Resource Sharing
Not applicable.
L. Consultants
Not applicable.
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