Principal Investigator/Program Director (Last, First, Middle):
Kagan, Harris
A. Specific Aims
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 submillimeter spatial resolution with Compton PET methods. 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 submillimeter 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 the first question. One 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 until field strengths reach levels of 50T. This is undoubtedly due to scattering in
tissue. But for higher energy positron emitters (I-124 or Tc-94m), significant reductions are possible at field
strengths 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 predicted results for
Ge-68, the overall improvement 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 high
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.
The specific tasks we propose to evaluate the effect of a high spatial resolution detector 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.
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
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direction. The device will be based on 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 7T MRI facility 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 pair, 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 means 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
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
be reliably quantified [7]. This is especially true for imaging mice.
Problems with PET – spatial resolution
The spatial resolution in PET is limited by several factors including detector element size, inter-element scatter,
annihilation photon non-colinearity, depth-of-interaction of photons and positron range [2]. Although there have
been many efforts and much progress toward sub-millimeter spatial resolution in PET, the bulk of these 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 doppelganger, 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 is excellent, 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 some 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. However, these (with the exception of CZT, perhaps) lack the ability to
discriminate energy limiting their use with “dirty” positron emitters having coincident gammas such as Tc-94m
and I-124, which are becoming increasingly important radiolabels [58-60]
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Spatial resolution 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 can become severe at small diameters
exacerbating the problem of non-uniform transverse resolution. As for crystal depth, most small animal PET
systems presently use depths of 10mm or less. While this has a negative effect on efficiency, DOI effects are
tolerable—or at least they have been for first-generation scanners.
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]. DOI resolution, while a key ingredient in achieving high resolution across the FOV and
high efficiency, does not solve all problems.
Not as conveniently addressed is the fact that the most prevalent interaction of 511 keV photons in any
scintillator 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 scintillator resulting in mis-positioning (inter-crystal
scatter or ICS), or it may escape resulting in loss of efficiency. As detector resolution and efficiency improve
(smaller crystals, bigger blocks), we ultimately expect in a system incapable of independently recording each
interaction from a scattering event that only 17%, 11%, and 3.2% of events will be assigned to the correct
coincidence line-of-response for BGO, LSO, and NaI(Tl), respectively. Calculations by Rafecas et al. [79]
showed that if ICS events were included in their MADPET II data, efficiency jumped 35%—and that is for
identifiable ICS events.
ICS effects are less obvious in present small animal PET instruments for several reasons. First, the projection
of where the scattered photon is absorbed is often “close” to the projection of the initial interaction. One can
appreciate, however, that this may compromise performance in detectors having DOI capability [82]. Second,
each detector block is relatively inefficient with a high probability of scattered photon escape. This will either
have a positive or a neutral effect on mis-positioning depending on the detection threshold. As the efficiency
increases, ICS will become more problematic. Finally, it has been noted many times that ICS does not affect
resolution as quantified by the FWHM or even FWTM of the point spread function (PSF). While that’s true
increasingly smaller scintillation crystals will improve FWHM resolution—the more insidious effect is a several
millimeter tail of mis-positioned events that compromises noise performance. A recent study by Stickel, et al.
provides further confirmation that in a highly efficient detector, multiple interactions comprise the bulk of the
events potentially leading to a “haze” of mis-positioning [83].
As shown in Section C.1 the use of Compton PET allows sub-millimeter spatial resolutions to become
attainable by having a small device, limiting the effect of non-collinearity, with very high resolution detector
elements which are segmented to have DOI sensitivity. With such a system, the largest issue in image
resolution is positron range. Positron range depends on the maximum energy of the isotope used. While it is
not a large effect for F-18 it can be a substantial effect for other positron-emitters finding use in small animal
imaging such as I-124, O-15 and Tc-94m.
In Table 1 we list the properties of positron emitters, their endpoint energies and nominal ranges in tissue.
Many of these sources are being used or considered for use in PET applications.
Positron
Emitter
Max  Energy
(keV)
F-18
635
C-11
Coincident 
Range in Tissue
FWHM (mm)
Range in Tissue
FWTM (mm)
0.1
1.03
970
0.2
1.86
N-13
1190
0.3
2.53
I-124
1535, 2138
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No
Yes – 603, 723, 909, 1691
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O-15
1720
0.5
Ga-68
1899
No
Tc-94m
2438
Yes – 871, 869
4.14
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.
Opportunities to improve spatial resolution
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 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.
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.
The proposed work and how it moves toward long-term objective
The proposed work involves simulation of the PET performance in a magnetic field, construction 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 submillimeter PET image resolution for small animals. The detailed simulations 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. The construction of a small scanner will unveil the issues of
working in large magnetic fields. Having data from a system which we can understand and modify will allow us
to tailor the experiments to answer specific questions. Finally the quantification of results will determine which
of the next possible steps to take.
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 a large bore 7T magnetic. This 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 and testing of
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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
C.1 PET with submillimeter spatial resolution
Figure 1 shows two views of the high resolution PET experimental setup used to acquire preliminary data.
This proposed system is 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.
To cut down background radiation, sources were placed in a shielded cavity and collimated with tungsten to a
1.5mm slice. 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.
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 1: 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.
Figure 2 shows the initial results from the tomograph in Fig. 1 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
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that there was no space between them (separation between F-18 lines: 0.4mm). The measured resolution
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 plainvanilla maximum likelihood with no modeling of detector response. The two line sources in each pair are
clearly separated. Accounting for the source size, resolution is 800µm x 800µm x 500µm (axial) FWHM
(0.32µl). 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 significantly less than 800µm.
This result clearly demonstrates that the Compton PET concept is capable of achieving high (sub-millimeter)
spatial resolutions. The significant remaining questions are whether it is feasible to construct such a system to
operate in a large magnetic field, whether it is possible to scale the technology to appropriate sensitivities (i.e.,
equivalent or better than present commercial systems), and whether such an instrument can ultimately surpass
the noise-resolution tradeoff implicit in scintillator-based systems.
Figure 1: 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 summary, the high resolution PET concept has the potential for achieving good performance at deep submillimeter resolution but there remain significant challenges. These are being addressed in another
investigation. The major effort in the upcoming period will be to use above PET technique as a high resolution
imaging tool to address the issue of positron range on spatial resolution. Results of this investigation will 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 basic principles of positron range are discussed in Levin and Hoffman [2]. In Figure 3 we show the Levin
and Hoffman simulation of the positron range in water for F-18 (maximum energy 635keV) and O-15
(maximum energy 1720 keV). The scatter plot shows the positron annihilation distance in three dimensions
projected onto a plane. The histogram shows the positron annihilation distance projected on to a single axis.
As such quoted FWHM and FWTM represent lower limits to the positron range. In any case these curves
illustrate that the scale of positron range RMS is millimeters and that the positron range increases as the
maximum energy increases.
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Figure 3: Left Image: Calculated distribution of positron annihilation coordinates in water projected onto a plane for F-18
and O-15 sources. Right Image: Histogram of x coordinates from positron annihilation point distribution. Both figures are
from Levin and Hoffman [2].
We have performed simulations of the positron range in water for Tc-94m (maximum energy 2470 keV) using
EGS4 [xx] in both 0T and 9T magnetic fields. Figure 4 shows the positron annihilation point projected onto a
plane which is perpendicular to the axis of the magnetic field for 0T (left) and 9T (right) magnetic fields. We
observe the 9T magnetic field reduces the average (RMS) positron range by roughly a factor of 4 from roughly
2.5mm to roughly 0.5mm.
Figure 4: Calculated distribution of positron annihilation coordinates in water projected onto a plane which is perpendicular
to the magnetic field direction for Tc-94m in the presence of 0T (left) and 9T (right) magnetic field.
In Figure 5 we show the same distributions in the plane where one axis is parallel to the magnetic field
direction. In the direction perpendicular to the magnetic field direction we observe the reduced positron range
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as expected. In the direction parallel to the magnetic field the positron range is essentially the same
distribution as the 0T case.
Figure 5: Calculated distribution of positron annihilation coordinates in water projected onto a plane with one axis parallel
to the magnetic field for Tc-99m in the presence of 0T (left) and 9T (right) magnetic field.
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 any 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 show 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. 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.
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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.
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 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
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.
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.
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
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.
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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 that 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 account 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.
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.
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:
 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.
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Once the reconstruction problem has been set up in this fashion, numerous methods can be used for 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 on the left below.
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 on the right. Notice the significantly improved spatial resolution. As noted, in reality this
case is somewhat unrealistic (except for micro Jaszczak phantoms!).
Figure 9.
Right: Reconstructed PET images for
simulated data corresponding to resolution phantom
filled with I-124 resolution phantom with no magnetic
field. Left: 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
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.
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.
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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 lower 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 [2] 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)
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
ComptonD.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. A schematic view of the setup is
shown in Figure 8. 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 with tungsten 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 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. The detector system will be
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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 timewalk 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 9. 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.
Figure 9: 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.2.2 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-resolution PET measurements generated by the
Monte Carlo studies [86]. Generally, accurate models will have already been developed for the M-UCRB
calculations of Aim 1. Additional work is straightforward and will use as a basis the Matlab code already
developed for reconstruction only replacing the projection models for the data. Models will be altered as
necessary to accommodate changes in the system in the execution of Aim 3.
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
source. Random coincidences and misclassified event rates will be estimated using modeling techniques
developed in Aim 1. Finally 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
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locations in the FOV for the partial scanner ring. Both the partial scanner ring efficiency will be compared to
the corresponding Monte Carlo predictions.
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 microJaszczak hot- and
cold-spot phantoms with F-18 and F-18 in foam or tissue equivalent plastic will be performed. The goal of
these experiments is to collect data for estimating 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 estimated for experimental data and compared 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. Traditionally, this tradeoff has been ignored 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. [How will we evaluate it and
compare?]
E. Human Subjects
None.
F. Vertebrate Animals
None.
G. References
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H. 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. Finally, all
investigators involved in this application are members of the CIMA collaboration (see Resources section).
The proposal is supported by our colleagues in CERN in Geneva, Switzerland, the Institute for Particle Physics
(IFIC) at the University of Valencia, and Institut Jozef Stefan in Ljubljana, Slovenija. No financial support has
been requested for CERN, IJS or IFIC. Dr. Kagan from OSU frequently travels to CERN for long-term highenergy physics experiments and serves as a liaison connecting the efforts of the groups in Europe and the US.
Drs. Lacasta and Mikuz also frequently travel to CERN for physics experiments and this has proven to be an
effective coordination technique with IJS and IFIC. Although the financial component of the foreign institution
is substantial, it is not dominant. Further, it is the medical application in this case that is driving the technology
development.
I. Resource Sharing
Not applicable.
J. Consultants
Letters from the subcontractor have been attached (University of Michigan.).
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