Micro-scale particle tracking using hybrid detectors

Positron Emission Particle Tracking (PEPT) techniques allow the tracking of a radioactive tracer particle moving within a system of flow, enabling non-invasive study of dynamic systems. On the micro-scale, PEPT performance is limited by the achievable activity in radiolabelling a suitable tracer particle, and the fixed geometry of conventional detector systems. To enable application of PEPT towards these scales advanced instrumentation is required, and a hybrid detection system has been developed combining scintillator and semiconductor devices. A bismuth germanate oxide (BGO) scintillator array consisting of 1024 detector elements derived from CTI/Siemens PET scanners (512 pixels of 6.75 x 6.25 x 30 mm3 and 512 pixels of 4.1 x 4.0 x 30 mm3) forms a field of view of 150 x 196 x 101 mm3. A pair of pixelated cadmium zinc telluride room temperature semiconductors (9680 pixels of 1.8 x 1.8 x 0.5 mm3) form a high spatial resolution region of 62 x 42 x 20 mm3 placed within the larger field of view. The design choice maximizes absolute efficiency by merit of the scintillators and enhances spatial resolution through the semiconductors. Energy and timing resolutions of the BGO elements were determined, and sensitivity profiles of the system modelled numerically, enabling the characterization of the system absolute efficiency and spatial resolution. The results suggest the applicability of PEPT in the study of microscale flows for the first time, including investigating flows in capillaries and micro-fluidic devices.


Introduction
Positron emission tomography (PET) imaging is a powerful non-invasive technique in which fluid tracer distributions can be imaged over time in biological systems, with use cases in medicine to characterise disease, alongside research into the systems and techniques used [1].Based on PET, positron emission particle tracking (PEPT) [2] was developed to study dynamic systems, with applications in the fields of engineering to medicine [2,3,4].By labeling a single tracer particle with a positron emitting radionuclide, tracking can be performed within a system to high spatial and temporal resolution, from which the tracer trajectory can be accurately reconstructed with an associated uncertainty.A desire to study micro-scale phenomena in PEPT, e.g.flows, has lead to the development of advanced instrumentation to account for performance limitations of existing systems.The fixed geometries of existing PEPT detection systems limit absolute efficiencies, and micro-scale tracer particles are necessarily limited in their activities given the difficulty in fabrication.As a result, the conventionally achievable location rates are inadequate to study dynamic (fast moving, cm/s) particles.Previous work [5] with semiconductor detectors has demonstrated the applicability of PEPT on the micro-scale, however the achievable location rates and field-of-view (FOV) were limited.In this work, a modular scintillator array offering improved absolute efficiencies has been constructed to supplement the semiconductor array.Characterisation of the system has been performed, extending previous work [6] and leading towards the development of a hybrid PEPT system for the study of micro-scale phenomena.

The Positron Emission Particle Tracking (PEPT) technique
PEPT relies on positron annihilation, where positron emission from a tracer particle is followed by annihilation, producing two approximately back-to-back 511 keV photons.When these photons are detected in time coincidence, a line-of-response (LOR) can be defined, ideally describing the 3D line along which the annihilation occurred.However, not all LORs arise from true coincidence events, and corrupt LORs are reconstructed where one or both photons were detected originating from an unassociated decay, or after scattering.An iterative leastsquares minimisation algorithm [2] isolates true coincidences and determines the instantaneous position of the tracer particle over time with an associated uncertainty, using many LORs per location.The spatial resolution of a PEPT system can be described by u( P ) = w/ √ T where u( P ) is the 3D location uncertainty on a measured PEPT location P , w is the spatial resolution of the positron camera, and T is the true coincidence rate [7].To improve upon the spatial resolution as required for micro-scale PEPT, a detector pixel size reduction or energy resolution improvement can reduce w, whereas an increase in system absolute efficiency or tracer activity can increase T , noting activity is limited in practice.Existing PEPT systems make use of scintillator devices, leveraging their favourable efficiency and time resolution to perform highspeed tracking, with spatial resolution suitable for typical applications.Semiconductor detectors offer smaller pixel sizes and improved energy resolution, although have relatively poor detection efficiency and time resolution.The Polaris system [8] at UCT, consisting of pixelated cadmium zinc telluride (CZT) semiconductor crystals, has been investigated for PEPT, achieving submillimetre tracking of a low activity tracer particle [5].However, event rates and the FOV were limited, leading to the development of a hybrid system combining semiconductor and scintillator devices.Characterisation of a modular scintillator array optimised to support Polaris is reported here, where high quality characterisation allows for dynamic position and timing corrections per crystal, yielding high precision tracking.

Detector Geometry
A modular scintillator array has been constructed from detector blocks of segmented 8 x 8 bismuth germanate oxide (BGO) scintillator crystals from Siemens ECAT 951 and EXACT HR+ PET scanners.Both block types have the same pixel count and similar intrinsic efficiency, with differing dimensions.The HR+ detector block has smaller pixels (4.0 x 4.1 x 30 mm 3 ) than the 951 detector block (6.25 x 6.75 x 30 mm 3 ), leading to improved spatial resolution, whereas the overall size increase of the 951 detector block improves its geometric efficiency.A hybrid system combining these blocks can therefore optimise their relative advantages for micro-scale tracking.
A high spatial resolution central region is achieved by placing the HR+ blocks and the Polaris system centrally, while the achievable system FOV and absolute efficiency is improved by placing the 951 blocks surrounding the central region.One module of the BGO array is shown in figure 1, with the HR+ blocks placed in a central square surrounded by 951 blocks.The full hybrid geometry consists of two such modules opposing to provide a FOV of 150 x 196 x 101 mm 3 , with the Polaris system placed perpendicularly between the two to provide a central high spatial resolution region of 62 x 42 x 20 mm 3 .A numerical model of the sensitivity profile of the system was used to determine the optimal geometry for the BGO elements of the system, aiming for a centrally uniform sensitivity profile to avoid deadtime limiting hotspots and to allow uniformity of PEPT measurements over the volume.Several detector configurations were tested, and an optimal geometry consisting of four HR+ and four 951 detector blocks per module was found, having the best central uniformity with results shown in figure 1.
A set of 3D printed frames were produced to align the BGO detector modules.A significant contribution to the location uncertainty budget is the precision in the relative placement of the individual detector elements, and these frames allow for precise and reproducible block placement.The spatial resolution of the 3D printer, being approximately 0.4 mm and 0.15 mm in the horizontal and vertical directions, is taken into account in LOR reconstruction.

Energy and temporal resolutions
To achieve micro-scale spatial resolution, low-noise detection is required.Two parameters ensuring limited noise are the energy and timing coincidence windows, and by optimising these windows the fraction of corrupt LORs can be reduced.The energy window, defined by the lower and upper level discriminators (LLD and ULD), dictates whether a detected photon is discarded based on deposited energy, selecting photons which are likely to have arisen from annihilation.
To accurately set the discriminators to minimise the detection of scattered or random photons, an understanding of the detector energy resolution is required.For a single 951 detector block, anodes from the four photomultiplier tubes were connected to preamplifier and amplifier systems, with signals summed and then digitised to produce a pulse height spectrum.An energy calibration was performed using standard gamma photon-emitting calibration sources, and a Gaussian function was fitted to the annihilation photopeak from Na-22.The energy resolution was determined to be 30.51± 0.48% at 511 keV.Choosing the energy window such that 99% of the annihilation photopeak was encompassed, the LLD was set as 338.9 ± 3.3 keV and the ULD as 678.4 ± 3.3 keV.This choice of discriminators excludes most scattered photons, reducing corrupt LORs, with the LLD approximately aligning with the expected 340 keV Compton edge.When two photons with appropriate energies are detected (i.e.singles events) within a time period of 2τ , with τ limited by the system time resolution, they are considered coincident.The random coincidence rate scales linearly with τ , thus optimisation of this window is required, using the time resolution of the system to select τ to maximise the true coincidence rate while limiting corrupt LORs.To determine the time resolution of the 951 blocks, singles events were recorded in two coincident modules, and a systematic time delay was added to one of the modules.As the delay is varied from zero to ±256 ns, the number of true coincidences decrease until only random coincidences remain, generating a Gaussian curve when τ is lower than the time resolution of the system.As τ increases, the Gaussian curves plateau as all true coincidences lie within the window and the proportion of random coincidences increases linearly, as seen in figure 2 (right).Fitting a Gaussian function to the 2τ = 8 ns curve, a time resolution, given by the standard deviation of the distribution, of 4.24 ± 0.03 ns was determined.The energy and time resolutions of the HR+ series detector block were determined to agree with the values calculated for the 951 series block [9], implying these parameters are fixed by materials rather than geometry.

Conclusions and future work
Advances have been made in the development of a hybrid PEPT camera system, combining scintillator and semiconductor devices, for application to small-scale systems with micron-scale tracking precision.Construction of a modular BGO array has begun, using a numerically modelled sensitivity profile and 3D printed frames to enable the precise placement of detector modules.Energy and timing resolutions of the scintillator elements have been determined, allowing for the optimisation of system parameters for low-noise detection.Characterisation of the hybrid camera spatial resolution and detection efficiency have been made and deadtime parameters will follow, allowing for the study of micro-scale phenomena using PEPT.

Figure 1 .
Figure 1.(Left) The geometry of a single optimal BGO detector module placed on its 3D printed frame, with HR+ (left) and 951 (right) detector blocks shown without their protective casing alongside.Dimensions are given in mm.(Right) A plan view of the simulated sensitivity profile integrated along the vertical axis.Corresponding profiles are shown alongside at varying depths, with the uniform mean highlighted in bold.Profiles are drawn to scale.

Figure 2 .
Figure 2. (Left) Calibrated energy spectra of three sources measured by a 951 detector block, with Gaussian curves fitted to the photopeaks.Optimal LLD and ULDs are shown as dashed vertical lines.(Right) The coincidence rate as a function of time delay added to a coincident module, plotted for various coincidence windows 2τ with the 24 ns case fitted in colour.Dashed vertical lines indicate window boundaries and the randoms contribution is shaded green.