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 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. 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 20T or more. 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 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.
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 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 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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.
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, the 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].
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 will use a “Compton” 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 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 below we list the properties of some non-conventional positron emitters, their endpoint
energies and nominal x coordinate of the annihilation point distribution in tissue from Levin and Hoffman [2]. In
cases marked with an asterisk we have used a linear approximation to scale the Levin and Hoffman data by
taking into account the maximum positron energy. In Table 1 we list both the FWHM and the FWTM of the x
coordinate of the annihilation point distribution as a measure of the effect of positron range. The result on
image resolution due to positron range should fall somewhere between these two measures. Many of these
sources are being used or considered for use in PET applications.
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Positron
Emitter
Max  Energy
(keV)
F-18
Kagan, Harris
Coincident 's
Annihilation Point x
coordinate in
Tissue FWHM (mm)
Annihilation Point x
coordinate in Tissue
FWTM (mm)
635
0.102
1.03
C-11
970
0.188
1.86
N-13
1190
0.282
2.53
I-124
1535, 2138
0.50
4.5*
O-15
1720
0.50
4.14
Ga-68
1899
0.6*
4.6*
Tc-94m
2438
0.8*
6.2*
603, 723, 909, 1691
871, 869
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 and others the embedding of the PET FOV
presents a method for high resolution scanners to achieve sub-millimeter image resolution. Although the submillimeter 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
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the resolution improvements at different field strengths but also to aid in the design scanners and for
generating data to compare with measurements. The construction of a small scanner will unveil the general
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
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. The idea of this system is that photons from positron annihilation Compton scatter in the silicon
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.
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
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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 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
that there was no space between them (separation between F-18 lines: 0.4mm). The measured resolution of
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 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 2: 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.
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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. 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 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.
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 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 2.3mm
to roughly 0.6mm.
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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
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 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
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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Bloomfield, P.M., R. Myers, S.P. Hume, T.J. Spinks, A.A. Lammertsma, and T. Jones, Threedimensional performance of a small-diameter positron emission tomograph. Physics in Medicine and
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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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K. Resource Sharing
Not applicable.
L. Consultants
Not applicable.
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