Simulated one-pass list-mode: an approach to on-the-fly system matrix calculation

Virtual cylindrical PET for efficient DOI image reconstruction with sub-millimetre resolution

Objective.Image reconstruction in high resolution, narrow bore PET scanners with depth of interaction (DOI) capability presents a substantial computational challenge due to the very high sampling in detector and image space. The aim of this study is to evaluate the use of a virtual cylinder in reducing the number of lines of response (LOR) for DOI-based reconstruction in high resolution PET systems while maintaining uniform sub-millimetre spatial resolution.Approach.Virtual geometry was investigated using the awake animal mousePET as a high resolution test case. Using GEANT4 Application for Tomographic Emission (GATE), we simulated the physical scanner and three virtual cylinder implementations with detector size 0.74 mm, 0.47 mm and 0.36 mm (vPET1, vPET2 and vPET3, respectively). The virtual cylinder condenses physical LORs stemming from various crystal pairs and DOI combinations, and which intersect a single virtual detector pair, into a single virtual LOR. Quantitative comparisons of the point spread function (PSF) at various positions within the field of view (FOV) were compared for reconstructions based on the vPET implementations and the physical scanner. We also assessed the impact of the anisotropic PSFs by reconstructing images of a micro Derenzo phantom.Main results.All virtual cylinder implementations achieved LOR data compression of at least 50% for DOI PET reconstruction. PSF anisotropy in radial and tangential profiles was chiefly influenced by DOI resolution and only marginally by virtual detector size. Spatial degradation introduced by virtual cylinders was most prominent in the axial profile. All virtual cylinders achieved sub-millimetre volumetric resolution across the FOV when 6-bin DOI reconstructions (3.3 mm DOI resolution) were performed. Using vPET2 with 6 DOI bins yielded nearly identical reconstructions to the non-virtual case in the transaxial plane, with an LOR compression factor of 86%. Resolution modelling significantly reduced the effects of the asymmetric PSF arising from the non-cylindrical geometry of mousePET.Significance.Narrow bore and high resolution PET scanners require detectors with DOI capability, leading to computationally demanding reconstructions due to the large number of LORs. In this study, we show that DOI PET reconstruction with 50%-86% LOR compression is possible using virtual cylinders while maintaining sub-millimetre spatial resolution throughout the FOV. The methodology and analysis can be extended to other scanners with DOI capability intended for high resolution PET imaging.

Motion compensation using origin ensembles in awake small animal positron emission tomography

In emission tomographic imaging, the stochastic origin ensembles algorithm provides unique information regarding the detected counts given the measured data. Precision in both voxel and region-wise parameters may be determined for a single data set based on the posterior distribution of the count density allowing uncertainty estimates to be allocated to quantitative measures. Uncertainty estimates are of particular importance in awake animal neurological and behavioral studies for which head motion, unique for each acquired data set, perturbs the measured data. Motion compensation can be conducted when rigid head pose is measured during the scan. However, errors in pose measurements used for compensation can degrade the data and hence quantitative outcomes. In this investigation motion compensation and detector resolution models were incorporated into the basic origin ensembles algorithm and an efficient approach to computation was developed. The approach was validated against maximum liklihood-expectation maximisation and tested using simulated data. The resultant algorithm was then used to analyse quantitative uncertainty in regional activity estimates arising from changes in pose measurement precision. Finally, the posterior covariance acquired from a single data set was used to describe correlations between regions of interest providing information about pose measurement precision that may be useful in system analysis and design. The investigation demonstrates the use of origin ensembles as a powerful framework for evaluating statistical uncertainty of voxel and regional estimates. While in this investigation rigid motion was considered in the context of awake animal PET, the extension to arbitrary motion may provide clinical utility where respiratory or cardiac motion perturb the measured data.

List-mode image reconstruction for positron emission tomography using tetrahedral voxels

Image space decomposition based on tetrahedral voxels are interesting candidates for use in emission tomography. Tetrahedral voxels provide many of the advantages of point clouds with irregular spacing, such as being intrinsically multi-resolution, yet they also serve as a volumetric partition of the image space and so are comparable to more standard cubic voxels. Additionally, non-rigid displacement fields can be applied to the tetrahedral mesh in a straight-forward manner. So far studies incorporating tetrahedral decomposition of the image space have concentrated on pre-calculated, node-based, system matrix elements which reduces the flexibility of the tetrahedral approach and the capacity to accurately define regions of interest. Here, a list-mode on-the-fly calculation of the system matrix elements is described using a tetrahedral decomposition of the image space and volumetric elements-voxels. The algorithm is demonstrated in the context of awake animal PET which may require both rigid and non-rigid motion compensation, as well as quantification within small regions of the brain. This approach allows accurate, event based, motion compensation including non-rigid deformations.

Spatially Variant Resolution Modelling for Iterative List-Mode PET Reconstruction

A spatially variant resolution modelling technique is presented which estimates the system matrix on-the-fly during iterative list-mode reconstruction. This is achieved by redistributing the endpoints of each list-mode event according to derived probability density functions describing the detector response function and photon acollinearity, at each iteration during the reconstruction. Positron range is modelled using an image-based convolution. When applying this technique it is shown that the maximum-likelihood expectation maximisation (MLEM) algorithm is not compatible with an obvious acceleration strategy. The image space reconstruction algorithm (ISRA), however, after being adapted to a list-mode based implementation, is well-suited to the implementation of the model. A comparison of ISRA and MLEM is made to confirm that ISRA is a suitable alternative to MLEM. We demonstrate that this model agrees with measured point spread functions and we present results showing an improvement in resolution recovery, particularly for off-centre objects, as compared to commercially available software, as well as the standard technique of using a stationary Gaussian convolution to model the resolution, for equal iterations and only slightly higher computation time.