Principal Investigator/Program Director (Last, First, Middle):
Kagan, Harris
C.1 PET with submillimeter spatial resolution
Figure 2 shows two views of the high resolution PET experimental setup used to acquire preliminary data [92].
The mechanics of the proposed system are similar to this system and constructed from non-magnetic
materials. Two 512-pad (32x16 array, 1.4mm x 1.4mm x 1mm thick) silicon detectors were oriented
horizontally to image a single slice. The detectors of the porposed system are the same detectors used here.
To cut down background radiation, sources were placed in a shielded cavity and collimated with tungsten to a
1.5mm slice. The idea of this system is that photons from positron annihilation Compton scatter in the silicon
pad detectors and the resulting Compton electron will be measured in the silicon pad detector. To collect the
scattered photon for possible energy discrimination and additional timing information, the silicon detectors were
flanked by four BGO scintillation detector modules scavenged from a CTI 931 PET scanner. No position
information was available from these BGO detectors (although different scintillation detectors could provide
additional position information). For the results described in this section the BGO scintillation detector system
was not used. Because the detectors do not record the full sinogram, the object must be rotated using the
computer controlled rotation stage on the instrument (For the updated instrument proposed in Section D.2
both the object and eventually the detectors will be capable of rotating around the tomograph axis for
maximum flexibility in data acquisition relative to the orientation of the B-field.)
Using a laser, detectors were aligned in a plane parallel to that of the slit using pitch and roll adjustments. The
Figure 2: Experimental setup for high resolution PET data acquisitions. Left: disassembled showing silicon detectors,
tungsten slice collimation, shielded source cavity, and rotating table. Laser is used to align silicon detectors coplanar
with tungsten slit. Right: assembled device showing source shielding, protective plastic boxes for silicon detectors and
position-insensitive BGO detectors (“end-caps”) for improved timing and energy resolution.
1mm thickness of each detector was then centered vertically on the open slit. Line sources were imaged at
several rotational positions in the field-of-view and a ML calibration method was used to estimate the unknown
geometric parameters of the instrument (detector positions, axis-of-rotation, etc.) Because of the large timewalk with our present version of the silicon detector readout electronics, which uses a 200 ns shaper in the
fast-channel, a 200 ns time-window was used. Detectors were biased slightly less than depletion (due to bias
supply limits) and were operated at a triggering threshold of ~20keV. Depending on the maximum distance of
source activity from the isocenter, increments of the rotation stage for data acquisition ranged from 1º to 30º.
For the initial studies we acquired an equal number of events at each view with each silicon detector read out
in serial mode with all pads being readout.
Figure 3 shows the initial results from the tomograph in Fig. 2 compared with those from the Concorde
MicroPET R4. Shown at the left is an image of two hematocrit tubes filled with F-18 FDG acquired using the
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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 650µm (axial) FWHM (0.42µl). In contrast to systems
without DOI resolution, performance is nearly constant across the FOV. To demonstrate that this is no
resolution-recovery “trick” of the reconstruction, each pair of sources is apparent in the corresponding
sinogram (Fig. 2, right). Recently, detectors having 1mm x 1mm x 1mm elements have been fabricated and
should allow intrinsic resolution of approximately 650 µm FWHM including the effect of acolinearity.
This result clearly demonstrates that prototype PET system is capable of achieving high (sub-millimeter) spatial
resolutions. The significant remaining question is whether it is feasible for the detectors to operate in a large
magnetic field. This is addressed in Section C.3.
Figure 3: F-18 sources in two adjacent hematocrit tubes on-axis for MicroPET R4 (left) and for four pairs at 5mm, 10mm,
15mm, and 20mm off-axis for the high resolution PET test system shown in Fig 1 (center). Tubes have an internal
diameter of 1.1mm and wall thickness of 0.2mm. MicroPET reconstructed using MAP algorithm; prototype high resolution
PET using maximum likelihood with a simple system matrix that does not account for finite detector size. Resolution
correcting for source size is approximately 1.6mm FWHM for MicroPET R4 and 800µm FWHM for the new instrument.
Image at right is efficiency-corrected sinogram demonstrating the intrinsically high spatial resolution. Each hematocrit
tube in each pair is evident at the appropriate projection angle.
In the upcoming period we propose to use the above PET technique within its realm of applicability as a high
resolution imaging tool to address the issue of positron range on image resolution. The results of this
investigation should be applicable to all high resolution PET systems capable of operation at high magnetic
field-strengths.
C.2 Reduction of positron range in magnetic fields
The importance of the positron distance of flight has been discussed in Section B. Here we discuss our
preliminary simulation work using EGS-4 of the effect of strong magnetic fields on positron range. While the
total distance traveled by a positron between emission and annihilation is not affected by an external magnetic
field, the positrons no longer move in straight lines between scatter interactions with the material they travel
through. The Lorentz force acts on the moving positrons forcing them onto a helical path thereby reducing the
range which is defined as the distance between emission and annihilation points. The size of this effect
depends on the direction of the positron relative to the magnetic field direction. It is largest for positrons
traveling perpendicular to the direction of the magnetic field. Figure 4 shows simulated positron range
distributions for different positron emitters in both water and lung tissue. Each configuration was simulated with
and without a 7-T magnetic field. The reduction in range is clearly visible in Figure 4. The size of the effect
depends both on the positron energy and the density of the material the positrons travel through. In order to
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obtain quantitative results we project the range distribution onto an axis perpendicular to the magnetic field
direction. An example for positrons emitted by Ga-68 in water is shown in Figure 5. Cusp-like distributions are
observed in these studies similar to studies without magnetic field but with significantly reduced tails.
Numerical results for different positron emitters are listed in Table 2. A substantial reduction in range can be
obtained for radionuclides with large positron energies such as Tc-94m or Ga-68 but even for F-18 the average
positron range can be reduced by strong magnetic fields in particular in less dense media such as lung tissue.
In Water
No Magnetic Field
In Lung Tissue
7 T Magnetic Field
No Magnetic Field
7 T Magnetic Field
F-18
Ga-68
Tc-94m
Figure 4: Simulated positron range distributions for F-18, Ga-68 and Tc-94m in water and lung tissue with
and without a magnetic field. The range distribution is projected onto a plane perpendicular to the direction
of the magnetic field.
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Figure 5: Positron distance of flight in water for Ga-68, (a) without magnetic field, (b) projected onto a plane
perpendicular to a 7-T magnetic field, (c) projected onto a plane parallel to a 7-T magnetic field, and (d) range
projection onto an axis parallel and perpendicular to an 7-T magnetic field.
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Isotope
Max. Positron
Energy [KeV]
F-18
635
C-11
N-13
O-15
Ga-68
Tc-94m
Tissue
FWHM
[mm]
FWTM
[mm]
Water
0.16
0.80
Lung
0.32
1.08
Water
0.32
1.20
Lung
0.48
1.52
Water
0.40
1.44
Lung
0.64
1.76
Water
0.60
1.96
Lung
0.88
2.24
Water
0.80
2.20
Lung
1.00
2.48
Water
1.12
2.80
Lung
1.20
2.84
970
1190
1720
1899
1428
Table 2 Simulated positron range in water and lung tissue for different positron-emitters in a 7T magnetic field
perpendicular to the image plane.
We conclude that embedding the PET FOV in a large magnetic field (7T) should reduce the positron range
distribution in water and lung tissue and this effect should be observable with a PET system with sub-millimeter
resolution.
C.3 Magnetic field compatibility of proposed detectors
In order to identify the issues associated with high field operation of a Compton PET system, we tested a
silicon detector hybrid module similar to that which we propose to use for this investigation and similar to that
used for the results in Section C.1. This module is shown is Figure 6. The silicon detector had 512-pads
(32x16 array, 1.4mm x 1.4mm x 1mm thick) and was readout via four VaTaGP3 ASIC’s. We chose to measure
the pulse height spectrum of Am-241 to look for an effect due to the magnetic field. We initially setup to
acquire an Am-241 spectrum in the 8T magnetic of the Ohio State University MRI facility. Within one minute of
operation the hybrid failed. Upon further investigation we discovered that three wire bonds to the integrated
circuit had broken on the high current lines which power the digital readout. These are shown in the right
image of Figure 6. To understand this result we constructed a wire bond test system and operated it in the 8T
magnetic field. We put 133mA through the test wire bonds which is roughly twice the peak current the real
wires bonds have during readout operation.
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Figure 6: Left Image: Photograph of the silicon detector module tested in an 8T magnetic field. Right Image: Photograph
of the three broken wires (first, fourth, and sixth ones in) after the initial test in the 8T field.
In the real device the current in the bond wires changes in magnitude with frequency. We found that for DC
and high frequency operation we could not reproduce the breaking of bonds. However at roughly the readout
frequency of the ASIC we were able to break bonds. Our solution was to encapsulate the wire bonds of the
test setup. Upon testing this configuration we found that we did not break a wire bond after 18 hrs of
continuous testing at the same frequency which previously had broken bonds.
Figure 7: The Am-241 pulse height spectra obtained using a silicon pad detector and VaTaGP3 electronics operating in
0T (red curve) and 8T (black curve) magnetic fields.
We repaired the broken detector system, encapsulated the wire bonds and took Am-241 spectra at 0, 2, 4, 6,
and 8T. The total time in the 8T magnetic field was 8 hrs. No wire bonds were broken during the test nor were
any other problems observed. For these tests the detector was operated at 100V and at a trigger threshold of
approximately 20keV and each data run was a fixed number of events. Figure 7 shows the Am-241 results for
data runs taken at 0T (red curve) and 8T (black curve). We observe no difference in the spectra obtained at
0T and at 8T. That the raw spectra appear nearly identical indicates that the trigger efficiency and energy
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resolution did not change in the magnetic field. We conclude that the proposed silicon detector system will
operate and have the same performance in the 7T field as we measure on the bench at 0T.
C.4 Method for reducing effects of positron range in 3D
As evident from the information above, while the magnetic field improves spatial resolution by reducing range
in directions transverse to the field, it has little to no effect on the range of positrons emitted with significant
momentum parallel to the magnetic field vector. The point spread functions resulting from this static magnetic
confinement may actually exhibit worse imaging performance than using no confinement at all. To visualize
this, refer to the projections of Monte Carlo generated PSFs for I-124 shown in Figure 8. The leftmost image is
a planar projection of the PSF with no applied magnetic field. It has a sharp central peak and broad, diffuse
Distance (mm)
0 Tesla
9 Tesla XZ-Plane
9 Tesla XY-Plane
-4
-4
-4
-3
-3
-3
-2
-2
-2
-1
-1
-1
0
0
0
1
1
1
2
2
2
3
3
3
-4
-2
0
2
-4
-2
0
2
Distance (mm)
-4
-2
0
2
Figure 8. Projections of the PSF due to range of I-124 positrons in water. Left: No magnetic confinement; PSF is
isotropic. Center: Orientation of B-field vector is parallel to bottom of page. Note long tails extending in z-direction.
Right: Orientation of B-field is into the page.
tails that tend to average any out-of-plane structures resulting in an additional background “haze” in the slice
being viewed. At 9T, projections of the resulting PSFs in two orthogonal directions are shown at the center
and right. If one is viewing slices in the X-Y plane (rightmost image), resolution of in-plane structures will
obviously be much better than with no magnetic field. However, notice the sharpness of the tails of the
response function in the X-Z projection (center). Rather than a diffuse background, these sharp tails will
generate artifacts in the slice being viewed from structures in adjacent planes. In short, while positron range
will be reduced and images will exhibit improved spatial resolution, artifacts will be worse than with no
magnetic field.
The solution—one that will improve spatial resolution in 3D to essentially that shown in the X-Y projection of
Figure 8—is to acquire PET measurements in multiple orientations of the magnetic field vector relative to the
object. It is of course difficult to change the orientation of a 9T magnet but it is much easier to orient the object
in two or more directions relative to the magnetic field.
The next significant question is once such PET information is obtained, how should it be reconstructed? The
answer is particularly straightforward: a single estimate of the distribution of radiotracer is obtained by
considering all measurements simultaneously. Specifically, the sets of projection data from each B-field
orientation are combined using a maximum likelihood (or penalized likelihood or maximum a posteriori) image
reconstruction that accounts correctly for uncertainties in the measurements. Although resolution recovery—
assuming the system response is modeled correctly—is possible for all the above cases, the situation in which
at least two orientations (preferably orthogonal) of a strong magnetic are used will provide a noise-resolution
tradeoff superior to either the use of no field or a field oriented in only one direction.
For the reconstructed images shown below, we assume the probability mass function of the measurements
can be represented as a conditionally Poisson model where the conditioning is with respect to the unknown
object:
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 A 
y 
 b 
y   ~ PoissonA   λ  b   
 

 

(1)
where y = [y11,…,y1N]T and y = [y21,…,y2N]T represent the recorded events for two orientations, which may
be binned into histograms (or “sinograms”) or instead may be just a list of the endpoints of each recorded
coincidence (or other information-preserving transformation of the data). The matrices A and A represent the
aperture function or system response of the tomograph in the two orientations of the magnetic field. For
example, with the magnetic field vector parallel to the axis of the PET instrument, A would model a response
function that has low uncertainty due to positron range in the x-y plane and high uncertainty along the axis of
the tomograph. In contrast, A—if the magnetic field vector is perpendicular to the previous orientation—
would model low uncertainty along the tomograph axis and high uncertainty in some orthogonal direction. The
symbol λ=[λ1,…,λM]T is a discrete representation of the object—e.g., voxels. More orientations of the field
can be accommodated in the above model by augmenting the composite system matrix (in square brackets in
(1)) with an additional A accounting for the correct orientation of the magnetic field relative to the object. As in
similar models for PET the vectors b represent additive interference due to randoms and scatter.
Once the reconstruction problem has been set up in this fashion, numerous methods can be used to obtain the
estimate, the EM-algorithm being a particularly suitable choice for solving for the corresponding maximum
likelihood or penalized maximum likelihood estimate. The key things to note are that (1) both sets of
measurements arise from a single, unknown object λ that must be estimated, and (2) the system model must
account for the PSF induced by the positron range for each orientation of the magnetic field.
Calculations of image effect of range reduction
The PSF for I-124 positron annihilations in water shown in Figure 8 was used to blur data from the simulated
resolution phantom (rod diameters 4.8, 4.0, 3.2, 2.4, 1.6, and 1.2 mm) . One million detected annihilations
were recorded in a simulated single-slice PET scanner with resolution similar to the instrument that will be
used for the experiments described in Section D, and then reconstructed using a maximum likelihood method
(EM algorithm) that modeled the spatial resolution of the PET system but not the range of the positron. The
corresponding image is shown in Figure 9 left below.
Figure 9.
Left: Reconstructed PET images for
simulated data corresponding to resolution phantom
filled with I-124 resolution phantom with no magnetic
field. Right: Same phantom at 9T field strength with
magnetic field vector perpendicular to the page. Both
datasets have one million detected events. Intrinsic
resolution of the PET scanner implied in the simulations
is ~700µm FWHM—similar to the instrument that will be
used in the proposed investigation. This represents the
ideal situation: artifacts from out-of-plane activity are
non-existent
The PSF modeling I-124 positron range at 9T field was also calculated and used to blur the phantom assuming
the constant axis of the phantom (direction along rods) was oriented parallel to the B-field. This case will give
the best resolution for such a phantom but it is unrealistic in practice since real objects tend not to have a
constant activity distribution along one direction. Again, one million detected events were used to reconstruct
the image in Figure 9 on the right. Notice the significantly improved spatial resolution. As noted, in reality this
case is somewhat unrealistic (except for micro-Jaszczak phantoms!).
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Figure 10. Left: Orientation
of B-field parallel to bottom
of page. Center: orientation
of B-field perpendicular to
bottom of page. Right:
Reconstruction from both
orientations.
Using the proposed acquisition and reconstruction method, datasets were simulated in two orientations of the
B-field relative to the object; each orientation contains a mean of 500K events (1M total) and data were
reconstructed using the ML technique described above. The leftmost image of Figure 10 is a reconstruction
corresponding to a B-field to the right, the image in the center is a reconstruction from data acquired when the
B-field is pointing toward the bottom of the page, and finally, the reconstruction on the right is made using both
field orientations. These preliminary results are encouraging but the proposed work will quantify the actual
advantages in terms of better noise-resolution tradeoffs as well as freedom from artifacts due to structures in
adjacent planes using magnetic range confinement.
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