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Accurate analytical expressions for collimator resolution and sensitivity are important tools in the optimization of SPECT systems. However, presently known expressions for the sensitivity of converging collimators either diverge near the focal point or focal line(s), or are only valid on the collimator axis. As a result, these expressions are unsuitable to calculate volumetric sensitivity for e.g. short-focal length collimators that focus inside the object to enhance sensitivity. To also enable collimator optimization for these geometries, we here present non-diverging sensitivity formulas for astigmatic, cone beam and fan beam collimators that are applicable over the full collimator's field-of-view. The sensitivity was calculated by integrating previously derived collimator response functions over the full detector surface. Contrary to common approximations, the varying solid angle subtended by different detector pixels was fully taken into account which results in a closed-form non-diverging formula for the sensitivity. We validated these expressions using ray-tracing simulations of a fan beam and an astigmatic cone beam collimator and found close agreement between the simulations and the sensitivity expression. The largest differences with the simulation were found close to the collimator, where sensitivity depends on the exact placement of holes and septa, while our expression represents an average over all possible placements as is common practice for analytical sensitivity expressions. We checked that average differences between the analytical expression and simulations reduced to less than 1% of the maximum sensitivity when we averaged our simulations over different septa locations. Moreover, we found that our new expression reduced to the traditional diverging formula under certain assumptions. Therefore, the newly derived sensitivity expression may enable the optimization of converging collimators for a wide range of applications, in particular when the focus is close to, or in, the object of interest.

Planar molecular breast imaging (MBI) is rapidly gaining in popularity in diagnostic oncology. To add 3D capabilities, we introduce a novel molecular breast tomosynthesis (MBT) scanner concept based on multi-pinhole collimation. In our design, the patient lies prone with the pendant breast lightly compressed between transparent plates. Integrated webcams view the breast through these plates and allow the operator to designate the scan volume (e.g. a whole breast or a suspected region). The breast is then scanned by translating focusing multi-pinhole plates and NaI(Tl) gamma detectors together in a sequence that optimizes count yield from the volume-of-interest. With simulations, we compared MBT with existing planar MBI. In a breast phantom containing different lesions, MBT improved tumour-to-background contrast-to-noise ratio (CNR) over planar MBI by 12% and 111% for 4.0 and 6.0 mm lesions respectively in case of whole breast scanning. For the same lesions, much larger CNR improvements of 92% and 241% over planar MBI were found in a scan that focused on a breast region containing several lesions. MBT resolved 3.0 mm rods in a Derenzo resolution phantom in the transverse plane compared to 2.5 mm rods distinguished by planar MBI. While planar MBI cannot provide depth information, MBT offered 4.0 mm depth resolution. Our simulations indicate that besides offering 3D localization of increased tracer uptake, multi-pinhole MBT can significantly increase tumour-to-background CNR compared to planar MBI. These properties could be promising for better estimating the position, extend and shape of lesions and distinguishing between single and multiple lesions.

The recently developed versatile emission computed tomography (VECTor) technology enables high-energy SPECT and simultaneous SPECT and PET of small animals at sub-mm resolutions. VECTor uses dedicated clustered pinhole collimators mounted in a scanner with three stationary large-area NaI(Tl) gamma detectors. Here, we develop and validate dedicated image reconstruction methods that compensate for image degradation by incorporating accurate models for the transport of high-energy annihilation gamma photons. Ray tracing software was used to calculate photon transport through the collimator structures and into the gamma detector. Input to this code are several geometric parameters estimated from system calibration with a scanning 99mTc point source. Effects on reconstructed images of (i) modelling variable depth-of-interaction (DOI) in the detector, (ii) incorporating photon paths that go through multiple pinholes ('multiple-pinhole paths' (MPP)), and (iii) including various amounts of point spread function (PSF) tail were evaluated. Imaging 18F in resolution and uniformity phantoms showed that including large parts of PSFs is essential to obtain good contrast-noise characteristics and that DOI modelling is highly effective in removing deformations of small structures, together leading to 0.75 mm resolution PET images of a hot-rod Derenzo phantom. Moreover, MPP modelling reduced the level of background noise. These improvements were also clearly visible in mouse images. Performance of VECTor can thus be significantly improved by accurately modelling annihilation gamma photon transport.