A. Specific Aims. Principal Investigator/Program Director (Last, First, Middle): Kagan, Harris

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1 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 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 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

2 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 keV window and an absolute efficiency of ~1.2% for a keV 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 8μl. Biomedical scientists have a strong desire for spatial resolutions less than 1mm FWHM in 3D so that tracer concentration in volumes as small as 1μl 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]

3 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]. 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 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 the * cases 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.

4 Positron Emitter Max β+ Energy (kev) Coincident γ's (kev) Annihilation Point x coordinate in Tissue FWHM (mm) Annihilation Point x coordinate in Tissue FWTM (mm) F No C N I , , 723, 909, * O Ga No 0.6* 4.6* Tc-94m , * 6.2* 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 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

5 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 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. 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.

6 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 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.

7 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. 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].

8 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 2.5mm 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 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

9 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. 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 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 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 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.

10 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. 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.

11 -4 0 Tesla -4 9 Tesla XZ-Plane -4 9 Tesla XY-Plane Distance (mm) Distance (mm) 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. 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: y y A b ~ Poisson λ + (1) A b where y = [y 11,,y 1N ] T and y = [y 21,,y 2N ] 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=[λ 1,,λ M ] 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.

12 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. 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!). 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 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. 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

13 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 O- 15 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 Compton-PET system with an inherent resolution across the FOV of roughly 800μm. 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. 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.

14 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. 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-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

15 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. 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 Cramèr- Rao bound [89]. Given a desired PSF f 0 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 f 0 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 f 0 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: δ σ 2 i δ = f = f o f T 1 fo ( αi + F) F( αi + F) 1 α( αi + F) fo 1 ( αi + F) Ffo 1 f o