Single-photon emission computed tomography (SPECT) is based on the detection of individual γ-rays emitted from a radiotracer distribution within a subject. An Anger camera detects the γ-rays with a scintillation crystal and associated electronics after passing through a collimator (1). The collimator aperture permits the passage of γ-rays from specific directions, and the pattern of photon interactions in the scintillation crystal forms a 2D projection image of the tracer distribution in the subject. A series of projection images acquired from different angles can be subsequently used to reconstruct the 3D radiotracer distribution in a tomographic image.

The design of the collimator in terms of hole size, material, and overall geometry, among other factors, affects the spatial resolution and sensitivity of a SPECT system. Several designs exist, including but not limited to parallel-hole, slanthole, converging and diverging, fanbeam, and pinhole collimators (2). Therefore, the choice of collimator design is application-dependent for channelling photons of different energies, magnifying or minifying images, or selecting between image quality and imaging speed. Although parallel-hole and fanbeam collimators are conventionally used when imaging small fields-of-view (FOVs), pinhole collimators can provide a superior resolution-sensitivity trade-off (3). In addition to the successful application of pinhole SPECT systems in small animal imaging, there has been a resurgence in the use of pinhole collimators for clinical cardiac and brain studies and when imaging small FOVs (4).

While pinhole SPECT has regained popularity in clinical and preclinical investigations of molecular imaging agents, no open-source software solutions are available for reconstructing pinhole SPECT datasets. However, recent efforts have led to the integration of a 3D SPECT system matrix modelling library for pinhole collimators into the open-source Software for Tomographic Image Reconstruction (STIR). The STIR package is an object-oriented library implemented in C++ that provides a framework for research in the processing and reconstruction of emission tomography studies (5). Initially written to support positron emission tomography (PET) data, STIR was previously extended to handle SPECT data with parallel- and converging-hole collimators (6,7). This was achieved by integrating parts of the SPECT Reconstruction Library (developed at the University of Barcelona) into STIR (8–11). The expansion of STIR’s support for pinhole collimators marks the first open-source platform for reconstructing pinhole SPECT datasets, which is important for advancing molecular imaging techniques and technologies.

This work aims to demonstrate the capabilities of STIR’s support for pinhole SPECT datasets. The pinhole code uses a similar implementation strategy as the previously integrated SPECT collimator modelling. The library enables corrections for attenuation and the spatially variant collimator–detector response by incorporating their effects into the system matrix.

Similar to the original SPECTUB implementation, the new pinhole SPECT implementation is referred to as PinholeSPECTUB and includes a dedicated reader for pinhole SPECT projection data in Interfile format (12), with some adaptations as pinhole collimators are not supported in Interfile. The pinhole SPECT Interfile reader utilises the projection matrix size, pixel scaling factor, and detector radius defined at the face of the scintillation crystal. System matrix calculation is executed with the ProjMatrixByBinPinholeSPECTUB projector class derived from the existing STIR ProjMatrixByBin class, and detector and collimator parameter files are utilised in addition to the usual STIR parameter file. The parameter files are text files that use an Interfile-like syntax. They are composed of keywords corresponding to the names of the various reconstructions and matrix parameters with the values entered next to them. Sample parameter files for configuring the PinholeSPECTUB projector can be found in the Appendix, and a detailed description of all parameters can be found in STIR’s documentation.

The detector file defines the intrinsic resolution for point spread function (PSF) correction, scintillation crystal attributes for depth of interaction (DOI) correction, and orbit information for the acquisition (i.e., number of orbits, number of angles, initial angle, angular increment—positive for counterclockwise and negative for clockwise rotation, and axial position with respect to the reconstructed volume). Note that only circular camera orbits are supported at this time. The collimator file defines the radius of rotation and geometry for cylindrical or polygonal collimators (i.e., the detector element exposed by the pinhole, hole position, shape—rectangular or round, size, tilt, and acceptance angle). An illustration of the pinhole SPECT system matrix geometry for a polygonal collimator setup is shown in Figure 1.

The system matrix weights the contribution of each image voxel along the line of response (LOR) to each detector element. Corrections can be made for increased system matrix accuracy by modelling the effects of intrinsic PSF, DOI, and attenuation (ATT) when configuring the STIR parameter file. When PSF correction is disabled, a geometrical approach is applied by considering the projection of the pinhole on the detector. This provides higher computational speed and a reduced memory requirement compared to the PSF approach, but is less accurate. When PSF correction is enabled, the projection of the hole is convolved with the PSF in detector space to account for the blurring effects of the camera. Values parsed from the parameter file define the number of standard deviations to be considered in the PSF, along with the subsampling factor to temporarily reduce PSF resolution for increased calculation accuracy, before downsampling the final PSF to the bin size. Furthermore, when PSF or DOI corrections are enabled, an additional parsed parameter sets the spatial sampling interval for PSF and DOI distributions.

Enabling DOI correction subdivides the scintillation crystal using Bresenham’s line algorithm (13) to calculate the crystal attenuation and DOI along the LOR. If DOI correction is disabled, half the crystal thickness is added to the detector radius. When attenuation correction is enabled, a simple correction can be applied where the same attenuation factor is applied for the whole PSF, or a full correction can be performed where different attenuation factors are applied for each bin of the PSF (7). Further improvements to speed and memory can be made with image masking using the default cylinder, an attenuation map, or a mask file. The default cylinder is based on the object radius in the image volume. It is essential to set the object radius greater than or equal to the size of the object in the attenuation map or mask file when masking, as the matrix weights are calculated according to this value. Failure to do so will result in an error. The projection matrix can be kept in memory or calculated per projection angle. In the latter case, the memory is released before starting calculations on a new angle, reducing memory requirements but increasing computation time for iterative reconstruction algorithms.

To test the pinhole-SPECT implementation in STIR, the Spark silicon-photomultiplier (SiPM)-based preclinical SPECT system was used with a single-pinhole (SPH) collimator (Cubresa Inc., Winnipeg, Canada). Previous work characterised the system with the National Electrical Manufacturers Association (NEMA) NU 1-2018 Standards for Performance Measurements of Gamma Cameras, and a corresponding Geant4 Application for Tomographic Emission (GATE) Monte Carlo model was validated (14). Excellent agreement was found between measurement and simulation, with differences on the order of a few percent, supporting the accuracy and detailed analysis of simulated data in this study.

The Spark has a fixed rotation range of 270^∘ from a starting angle of 180^∘. Angular increments of 3^∘ were used for data acquisition based on NEMA’s specification (15). GATE simulation results (16) were output to Rapid Object-Oriented Technology (ROOT) format (17) and converted to Cubresa’s list mode format. Projection data with 0.5 mm bins were generated from measured and simulated list mode data using a 30%-wide energy window centered at 140 keV. Projection images were then converted from Cubresa’s format to Interfile format for use with STIR. Parameter files were configured as necessary with a full attenuation correction model, a PSF subsampling factor of 1, a maximum number of PSF standard deviations of 2, and a spatial resolution of 0.1 mm when sampling distributions in PSF or DOI corrections. Unless explicitly stated, images were reconstructed in the entire FOV using an object radius of r=23.0 mm.

Simulations and image reconstructions were performed on an HP Z820 workstation operating Ubuntu 18.04.5 LTS with two Intel Xeon E5-2630 2.3 GHz hexa-core CPUs and 64 GB of 1600 MHz DDR3 memory. The SPH-SPECT data for quantitative image assessment were simulated with GATE v9.0, while qualitative image assessment used in vivo data. Tomographic images were reconstructed with STIR v5.1.0 on a single CPU core as the PinholeSPECTUB projector class has not yet been configured to use the OpenMP or Message Passing Interface capabilities of STIR, which would allow several computations to be performed in parallel. Note that pre-corrected projection data is expected to be input into the projection matrix. Therefore, measured data were corrected with energy, linearity, and uniformity calibrations, while simulated data required no calibration.

The purpose of this study was to demonstrate and test the integration of a pinhole SPECT library in STIR using simulated and measured data. The aim was not to optimise reconstruction parameters for the γ-camera used in this study. Altogether, the SPH-SPECT images reconstructed with STIR showed appreciable image quality with radioactive source distributions true to their physical geometry. As discussed in the previous SPECTUB publication, reconstruction requires tuning of (sub)iterations for OSEM and MLEM algorithms or penalisation factors for OS-OSL-MRP and OS-SPS-QP algorithms based on the object size, activity, and background (6). In the present study, PSF correction improved image quality as seen in resolution, uniformity, and variability figures of merit. Although the inclusion of attenuation modelling improves system matrix accuracy, its present application in a preclinical setting shows minimal effects. In general, further improvements to image quality could be achieved with application-specific post-reconstruction image filtering (25).

Apart from the photon energy dependence in attenuation correction, PSF and DOI corrections include energy-specific factors for intrinsic resolution and crystal attenuation, respectively, to improve system matrix accuracy. When DOI correction is disabled, interactions in the scintillator are assumed to occur at half the crystal depth. An energy-dependent modification could apply a corresponding mean or median depth of interaction. This would affect reconstruction quality, and relatively small pinhole acceptance angles and degrees of parallax would be most accurate in the uncorrected case, while DOI correction would be required otherwise.

Unfortunately, DOI correction degrades image quality due to a bug affecting small angles from the pinhole axis. This results in a loss of counts where pinhole axes intersect rather than a distortion of the reconstructed radioactivity distribution, as illustrated in Figure 7. In our results, this caused a significant separation between maximum and minimum intensity values and resulted in uniformity quickly approaching 100%. When calculating CV, this caused an increased standard deviation and reduced mean, corresponding to greater variability in the cylindrical volume. However, the resolution calculated with DOI correction and reported in Figure 5 was negligibly affected since the resolution was reported as the average of all x and y FWHMs, and the axial line source was only affected in a fraction of the 3.5 mm-thick slice at the isocenter. More specifically, the mean relative standard error from all subiterations calculated with Eq. (2) was 9% for DOI-corrected matrices and 8% otherwise, which shows consistent resolution with minor variations throughout the tomographic FOV. Future work aims to correct the DOI bug.

The computational costs were comparable to STIR’s parallel- and converging-hole SPECTUB projector class. Matrices were chosen to be similar in size to those in the previous SPECTUB publication in (6), where projection and reconstruction matrix sizes were 1.1% and 3.2% larger, respectively. When storing the pinhole SPECT matrix in memory, computations required up to 3× more RAM and 4.7× more CPU time than the parallel-hole SPECT case, except for PSF correction, which required 1.7× less RAM and 1.2× less CPU time. When calculating the matrix per projection, memory requirements were nearly identical, and computations took up to 6× longer using the PinholeSPECTUB projector, except for PSF correction which required 1.3× less RAM and 1.1× less CPU time. The general increase in computation cost can be attributed to pinhole SPECT LORs that intersect more voxels at non-orthogonal angles than a parallel-hole collimator, and the differences in PSF correction can be attributed to the correction applied in detector space for the PinholeSPECTUB projector versus object space for the SPECTUB projector.

The integrated software is included in STIR release 5.1.0. Further extensions could expand the software to support non-circular orbits, improve energy dependence, model keel-edge or lofthole pinholes, enable parallel computing, and correct for knife-edge penetration. In addition, camera designs can be readily explored with the PinholeSPECTUB projector for single- and multi-pinhole collimators in terms of magnification, detector coverage, multiplexing, and pinhole geometry for optimal FOV, sensitivity, and detection efficiency without degrading spatial resolution (26). The Synergistic Image Reconstruction Framework (SIRF) (27) has also been extended to use these new STIR capabilities, allowing the use of SIRF’s advanced optimisation algorithms. Additional possibilities with the software include scatter correction, motion-compensated image reconstruction, synergistic image reconstruction, dynamic imaging, and multi-tracer protocols. Ongoing work aims to utilise the pinhole SPECT SIRF extension for multi-tracer protocols. The method under development requires multiple energy-dependent system matrices to simultaneously reconstruct distributions from a multi-radionuclide SPECT acquisition. However, this is currently not possible with STIR’s SPECT projectors, as the weight matrix is defined as a global variable that only allows for one unique matrix during reconstruction. Therefore, the next steps will replace any global variables with local ones.

Pinhole SPECT is becoming increasingly important in clinical and preclinical investigations of molecular imaging agents. We have demonstrated the pinhole SPECT modelling tool capabilities in the open-source STIR package. Tomographic image quality was evaluated qualitatively and quantitatively using several figures of merit and iterative reconstruction algorithms with and without system matrix corrections. Our results showed measurable and indicative image quality suitable for in vivo applications. This shows that STIR can be configured for complex pinhole SPECT scanner geometries and used with many reconstruction algorithms.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The animal study was reviewed and approved by Dalhousie University Committee for Laboratory Animals.

MS wrote the ProjMatrixByBinPinholeSPECTUB class to integrate the prototype pinhole SPECT system matrix estimation software into STIR, with assistance from KT. MS also extended its integration to SIRF, performed data collection, image reconstruction, analysis, and wrote the manuscript. CF wrote the prototype pinhole SPECT system matrix estimation software. KE and BFH were involved in the development of the software. KB and KT contributed to study interpretation. All authors contributed to the article and approved the submitted version.

MS was supported by a Nova Scotia Graduate Scholarship, and KB was supported by an NSERC grant (499115-2016). The prototype code was partly developed with support from the EC FP7 INSERT project (HEALTH-F5-2012-305311). STIR is partly maintained by the Collaborative Computational Project in Synergistic Reconstruction for Biomedical Imaging (CCP SyneRBI) through an EPSRC grant (EP/T026693/1). BFH acknowledges support from the NIHR UCLH Biomedical Research Centre.