Analytic determination of the resolution-equivalent effective diameter of a pinhole collimator

System calibration and statistical image reconstruction for ultra-high resolution stationary pinhole SPECT

For multipinhole single-photon emission computed tomography (SPECT), iterative reconstruction algorithms are preferred over analytical methods, because of the often complex multipinhole geometries and the ability of iterative algorithms to compensate for effects like spatially variant sensitivity and resolution. Ideally, such compensation methods are based on accurate knowledge of the position-dependent point spread functions (PSFs) specifying the response of the detectors to a point source at every position in the instrument. This paper describes a method for model-based generation of complete PSF lookup tables from a limited number of point-source measurements for stationary SPECT systems and its application to a submillimeter resolution stationary small-animal SPECT system containing 75 pinholes (U-SPECT-I). The method is based on the generalization over the entire object to be reconstructed, of a small number of properties of point-source responses which are obtained at a limited number of measurement positions. The full shape of measured point-source responses can almost be preserved in newly created PSF tables. We show that these PSFs can be used to obtain high-resolution SPECT reconstructions: the reconstructed resolutions judged by rod visibility in a micro-Derenzo phantom are 0.45 mm with 0.6-mm pinholes and below 0.35 mm with 0.3-mm pinholes. In addition, we show that different approximations, such as truncating the PSF kernel, with significant reduction of reconstruction time, can still lead to acceptable reconstructions.

The pinhole: gateway to ultra-high-resolution three-dimensional radionuclide imaging

Today the majority of clinical molecular imaging procedures are carried out with single-photon emitters and gamma cameras, in planar mode and single-photon emission computed tomography (SPECT) mode. Thanks to the development of advanced multi-pinhole collimation technologies, SPECT imaging of small experimental animals is rapidly gaining in popularity. Whereas resolutions in routine clinical SPECT are typically larger than 1 cm (corresponding to >1,000 microl), it has recently proved possible to obtain spatial resolutions of about 0.35 mm ( approximately 0.04 microl) in the mouse. Meanwhile, SPECT systems that promise an even better performance are under construction. The new systems are able to monitor functions in even smaller structures of the mouse than was possible with dedicated small animal positron emission tomography ( approximately 1 mm resolution, corresponding to 1 microl). This paper provides a brief history of image formation with pinholes and explains the principles of pinhole imaging and pinhole tomography and the basics of modern image reconstruction methods required for such systems. Some recently introduced ultra-high-resolution small animal SPECT instruments are discussed and new avenues for improving system performance are explored. This may lead to many completely new biomedical applications. We also demonstrate that clinical SPECT systems with focussing pinhole gamma cameras will be able to produce images with a resolution that may become superior to that of PET for major clinical applications. A design study of a cardiac pinhole SPECT system indicates that the heart can be imaged an order of magnitude faster or with much more detail than is possible with currently used parallel-hole SPECT (e.g. 3-4 mm instead of approximately 8 mm system resolution).

Optimizing multi-pinhole SPECT geometries using an analytical model

State-of-the-art multi-pinhole SPECT devices allow for sub-mm resolution imaging of radio-molecule distributions in small laboratory animals. The optimization of multi-pinhole and detector geometries using simulations based on ray-tracing or Monte Carlo algorithms is time-consuming, particularly because many system parameters need to be varied. As an efficient alternative we develop a continuous analytical model of a pinhole SPECT system with a stationary detector set-up, which we apply to focused imaging of a mouse. The model assumes that the multi-pinhole collimator and the detector both have the shape of a spherical layer, and uses analytical expressions for effective pinhole diameters, sensitivity and spatial resolution. For fixed fields-of-view, a pinhole-diameter adapting feedback loop allows for the comparison of the system resolution of different systems at equal system sensitivity, and vice versa. The model predicts that (i) for optimal resolution or sensitivity the collimator layer with pinholes should be placed as closely as possible around the animal given a fixed detector layer, (ii) with high-resolution detectors a resolution improvement up to 31% can be achieved compared to optimized systems, (iii) high-resolution detectors can be placed close to the collimator without significant resolution losses, (iv) interestingly, systems with a physical pinhole diameter of 0 mm can have an excellent resolution when high-resolution detectors are used.

Analytical derivation of the point spread function for pinhole collimators

The point spread function (PSF) of a pinhole collimator plays an important role in determining the resolution and characterizing the sensitivity of the accepted photons from a given point in the image space. The focus of this paper is to derive an analytical expression for the PSF of two different types of focusing pinhole collimators that are based on (1) right-circular double cones and (2) oblique-circular double cones. Conventionally, focusing pinhole collimators used in multi-pinhole SPECT were designed using right-circular double cones, as they were easier to fabricate. In this work, a novel focusing collimator consisting of oblique-circular double cones was designed and its properties were studied in detail with respect to right-circular double-cone based collimators. The main advantage of determining the PSF is the fact that they can be used to accurately model the PSF during the reconstruction, thereby improving the resolution of the reconstructed image. The PSF of the focusing collimators based on oblique-circular cones were found to be almost shift invariant for low and medium energy photons (below 200 keV). This property is very advantageous as algorithms such as slice-by-slice reconstruction can be used for resolution recovery thereby drastically reducing the reconstruction time. However, the PSF of focusing oblique-circular double cones (FOCDC) for higher energy photons were found to be asymmetric and hence need to be modelled more accurately during the reconstruction. On the other hand, the PSF for the right-circular cone based collimators were found to be asymmetric for all energy levels. However, due to the smaller acceptance angle used, the number of penetration photons was found to be far less than that observed for oblique-circular cones. This results in a smaller PSF making right-circular cone based collimators preferable for high-resolution small animal imaging, especially where very small pinhole diameters are used. The analytically derived PSF for both collimators were validated using a ray-tracing based Monte Carlo approach and found to agree well with a mean square error of less than 1%.

A geometric system model of finite aperture in small animal pinhole SPECT imaging

Accurate system modeling of the photon acquisition process is essential for optimizing quality in pinhole SPECT imaging. Conventional pinhole SPECT imaging assumes ideal pinhole geometry. However, neglect of pinhole finite aperture could lead to unfavorable quality degradations, such as positioning bias and image distortion. In this work, we develop a system model in which the aperture width of a pinhole collimator is explicitly included. The system model describes the probability of a single photon from its emission to detection. The probability value is calculated based on the effective intersection area resulting from a simulated cone-beam light source emitting from the image voxel, passing through a finite aperture, and reaching the detector's frontal face. The proposed model can be integrated with the ordered subsets expectation maximization (OSEM) algorithm for fast 3D statistical image reconstruction. Monte Carlo-based phantom experiments are used to evaluate the performance of the proposed system model compared to the ideal pinhole model. Reconstructed image results demonstrate that the proposed model can improve image quality in terms of reducing location bias and maintaining better contrast recovery.

Recent developments and future trends in nuclear medicine instrumentation

Molecular imaging using high-resolution single-photon emission computed tomography (SPECT) and positron emission tomography (PET) has advanced elegantly and has steadily gained importance in the clinical and research arenas. Continuous efforts to integrate recent research findings for the design of different geometries and various detector technologies of SPECT and PET cameras have become the goal of both the academic comcameras have become the goal of both the academic community and nuclear medicine industry. As PET has recently become of more interest for clinical practice, several different design trends seem to have developed. Systems are being designed for "low cost" clinical applications, very high-resolution research applications (including small-animal imaging), and just about everywhere in-between. The development of dual-modality imaging systems has revolutionized the practice of nuclear medicine. The major advantage being that SPECT/PET data are intrinsically aligned to anatomical information from the X-ray computed tomography (CT), without the use of external markers or internal landmarks. On the other hand, combining PET with Magnetic Resonance Imaging (MRI) technology is scientifically more challenging owing to the strong magnetic fields. Nevertheless, significant progress has been made resulting in the design of a prototype small animal PET scanner coupled to three multichannel photomultipliers via optical fibers, so that the PET detector can be operated within a conventional MR system. Thus, many different design paths are being pursued--which ones are likely to be the main stream of future commercial systems? It will be interesting, indeed, to see which technologies become the most popular in the future. This paper briefly summarizes state-of-the art developments in nuclear medicine instrumentation. Future prospects will also be discussed.

Resolution-effective diameters for asymmetric-knife-edge pinhole collimators

The effects of penetration are included in the formulas for the prediction of the resolution of pinhole collimators through the use of effective diameters. Expressions of the resolution-effective diameter for pinholes with a double-knife-edge (DKE) profile are available in the literature. In this paper the expressions applicable to asymmetric-knife-edge (AKE) profiles, which include the important case of the single-knife-edge (SKE), are presented. Results indicate that the simplest methods that are still accurate in the calculation of DKE effective diameters do not produce in general formulas with similar accuracy for AKE profiles, due to increased susceptibility to penetration. Especially at high energy (365 keV), for the SKE case more advanced formulas are necessary and were, therefore, derived.

Small animal SPECT and its place in the matrix of molecular imaging technologies

Molecular imaging refers to the use of non-invasive imaging techniques to detect signals that originate from molecules, often in the form of an injected tracer, and observe their interaction with a specific cellular target in vivo. Differences in the underlying physical principles of these measurement techniques determine the sensitivity, specificity and length of possible observation of the signal, characteristics that have to be traded off according to the biological question under study. Here, we describe the specific characteristics of single photon emission computed tomography (SPECT) relative to other molecular imaging technologies. SPECT is based on the tracer principle and external radiation detection. It is capable of measuring the biodistribution of minute (<10(-10) molar) concentrations of radio-labelled biomolecules in vivo with sub-millimetre resolution and quantifying the molecular kinetic processes in which they participate. Like some other imaging techniques, SPECT was originally developed for human use and was subsequently adapted for imaging small laboratory animals at high spatial resolution for basic and translational research. Its unique capabilities include (i) the ability to image endogenous ligands such as peptides and antibodies due to the relative ease of labelling these molecules with technetium or iodine, (ii) the ability to measure relatively slow kinetic processes (compared with positron emission tomography, for example) due to the long half-life of the commonly used isotopes and (iii) the ability to probe two or more molecular pathways simultaneously by detecting isotopes with different emission energies. In this paper, we review the technology developments and design tradeoffs that led to the current state-of-the-art in SPECT small animal scanning and describe the position SPECT occupies within the matrix of molecular imaging technologies.

Resolution- versus sensitivity-effective diameter in pinhole collimation: experimental verification

To account for photon penetration, the formulae used to calculate the geometric resolution of a pinhole collimator use an effective diameter d(e) rather than the physical diameter of the aperture. The expressions commonly used for d(e), however, were originally derived to include penetration in sensitivity calculations. To predict the full width at half maximum (FWHM) resolution of the point-spread function (PSF) of a knife-edge pinhole collimator, we have previously proposed simple expressions for a resolution-effective diameter d(re). Unlike those for d(e), expressions for d(re) predict both a dependence on the polar angle of the source (theta) and a non-isotropic PSF. In this paper, the new theory was tested by measuring experimentally the FWHM of the PSF. Results confirm the theoretical predictions that (a) d(re) provides the best estimates of the experimental FWHM as a function of theta and of the direction in the plane of the pinhole, (b) Paix's expression for d(e) tends to overestimate the FWHM, (c) Anger's is a better approximation, but still cannot predict the dependence on theta, and (d) the FWHM decreases with decreasing theta, i.e. resolution improves for sources at the edge of the field-of-view.

Optimal number of pinholes in multi-pinhole SPECT for mouse brain imaging—a simulation study

This study simulates a multi-pinhole single-photon emission computed tomography (SPECT) system using the Monte Carlo method, and investigates different multi-pinhole designs for quantitative mouse brain imaging. Prior approaches investigating multi-pinhole SPECT were not often optimal, as the number and geometrical arrangement of pinholes were usually chosen empirically. The present study seeks to optimize the number of pinholes for a given pinhole arrangement, and also for the specific application of quantitative neuroreceptor binding in the mouse brain. An analytical Monte Carlo simulation based method was used to generate the projection data for various count levels. A three-dimensional ordered-subsets expectation-maximization algorithm was developed and used to reconstruct the images, incorporating a realistic pinhole model for resolution recovery and noise reduction. Although artefacts arising from overlapping projections could be a major problem in multi-pinhole reconstruction, the cold-rod phantom study showed minimal loss of spatial resolution in multi-pinhole systems, compared to a single-pinhole system with the same pinhole diameter. A quantitative study of neuroreceptor binding sites using a mouse brain phantom and low activity (37 MBq) showed that the multi-pinhole system outperformed the single-pinhole system by maintaining the mean and lowering the variance in the measured uptake ratio. Multi-pinhole collimation can be used to reduce the injected dose and thereby reduce the radiation exposure to the animal. Results also suggest that the nine-pinhole configuration shown in this paper is a good choice for mouse brain imaging.

Molecular imaging of small animals with a triple-head SPECT system using pinhole collimation

Pinhole collimation yields high sensitivity when the distance from the object to the aperture is small, as in the case of imaging small animals. Fine-resolution images may be obtained when the magnification is large since this mitigates the effect of detector resolution. Large magnifications in pinhole single-photon emission computed tomography (SPECT) may be obtained by using a collimator whose focal length is many times the radius of rotation. This may be achieved without truncation if the gamma camera is large. We describe a commercially available clinical scanner mated with pinhole collimation and an external linear stage. The pinhole collimation gives high magnification. The linear stage allows for helical pinhole SPECT. We have used the system to image radiolabeled molecules in phantoms and small animals.

Determination of mechanical and electronic shifts for pinhole SPECT using a single point source

The effects of uncompensated electronic and mechanical shifts may compromise the resolution of pinhole single photon emission computed tomography. The resolution degradation due to uncompensated shifts is estimated through simulated data. A method for determining the transverse mechanical and axial electronic shifts is described and evaluated. This method assumes that the tilt of the detector and the radius of rotation (ROR) are previously determined using another method. When this assumption is made, it is possible to determine the rest of the calibration parameters using a single point source. A method that determines the electronic and mechanical shifts as well as the tilt has been previously described; this method requires three point sources. It may be reasonable in most circumstances to calibrate tilt much less frequently than the mechanical shifts since the tilt is a property of the scanner whereas the mechanical shift may change every time the collimator is replaced. An alternative method for determining the ROR may also be used. Lastly, we take the view that the transverse electronic shift and the focal length change slowly and find these parameters independently.

Design and simulation of a high-resolution stationary SPECT system for small animals

Exciting new SPECT systems can be created by combining pinhole imaging with compact high-resolution gamma cameras. These new systems are able to solve the problem of the limited sensitivity-resolution trade-off that hampers contemporary small animal SPECT. The design presented here (U-SPECT-III) uses a set of detectors placed in a polygonal configuration and a cylindrical collimator that contains 135 pinholes arranged in nine rings. Each ring contains 15 gold pinhole apertures that focus on the centre of the cylinder. A non-overlapping projection is acquired via each pinhole. Consequently, when a mouse brain is placed in the central field-of-view, each voxel in the cerebrum can be observed via 130 to 135 different pinholes simultaneously. A method for high-resolution scintillation detection is described that eliminates the depth-of-interaction problem encountered with pinhole cameras, and is expected to provide intrinsic detector resolutions better than 150 microm. By means of simulations U-SPECT-III is compared to a simulated dual pinhole SPECT (DP-SPECT) system with a pixelated array consisting of 2.0 x 2.0 mm NaI crystals. Analytic calculations indicate that the proposed U-SPECT-III system yields an almost four times higher linear and about sixty times higher volumetric system resolution than DP-SPECT, when the systems are compared at matching system sensitivity. In addition, it should be possible to achieve a 15 up to 30 times higher sensitivity with U-SPECT-III when the systems are compared at equal resolution. Simulated images of a digital mouse-brain phantom show much more detail with U-SPECT-III than with DP-SPECT. In a resolution phantom, 0.3 mm diameter cold rods are clearly visible with U-SPECT-III, whereas with DP-SPECT the smallest visible rods are about 0.6-0.8 mm. Furthermore, with U-SPECT-III, the image deformations outside the central plane of reconstruction that hamper conventional pinhole SPECT are strongly suppressed. Simulation results indicate that future pinhole SPECT systems are likely to bring about significant improvements in radio-molecular imaging of small animals.