Ahmet S. Ayan

Derivation and Validation of a Sensitivity Formula for Slit-Slat Collimation

An analytic formula is derived for the sensitivity of collimators achieving transverse collimation with a slit and axial collimation with a slat assembly whose septa may be parallel or focus on a line. The formula predicts sin3 phi dependence on the incidence angle and, in the particular case of parallel slats, 1/h dependence on the distance from the slit. More complex expressions for sensitivity that do not diverge at points near the slit or the focal line of the slat assembly are also derived. The predictions of the formulas are checked against simple cases for which solutions are available from direct calculation as well as against Monte Carlo simulation and published experimental data. Agreement is good in all cases analyzed. An approximate penetration model is also introduced: it involves the use of a sensitivity-effective slit width and septal length. Its predictions are compared to simulation results. Agreement was found to be compatible with statistical fluctuation (plusmn0.3%) for geometric sensitivity and better than 3 % of total sensitivity in the worst case of septa designed for high-energy (364.5 keV) photons.

Verification of the sensitivity and resolution dependence on the incidence angle for slit?slat collimation

Single photon emission computed tomography (SPECT) can be performed with various collimator types, which have an inherent tradeoff between the properties of sensitivity, resolution, field of view and complete sampling. Slit-slat collimation, which has seen recent interest in the literature, combines a slit parallel to the axis of rotation of a gamma camera with a set of septa perpendicular to the slit. This collimator geometry exhibits properties that may enhance some SPECT imaging applications, specifically imaging of the breast, limbs and medium-sized animals. However, a complete description of its system response is critical for a comparison to other collimator types and for accurate reconstruction of projection data. Herein, experimental and Monte Carlo methods are used to determine the sensitivity and transaxial and axial resolutions as a function of the incidence angle theta, which is the angle formed by the line from the photon source to the center of the slit and the plane of the slit, to compare to theoretical expectations. Four configurations are investigated by varying the slit width, septal spacing and septal height. Monte Carlo sensitivity data not modeling penetration and scatter exhibit a sin(3)theta dependence. Experimental and Monte Carlo-derived sensitivity data modeling scatter and penetration are consistent with each other and have a sin(x)theta dependence, where x is greater than 3. Transaxial resolution data show a small dependence on theta, and axial resolution data are consistent with no angular dependence.

Slit-Slat and Multi-Slit-Slat Collimator Design and Experimentally Acquired Phantom Images From a Rotating Prototype

We have previously found and validated expressions for slit-slat (SS) geometric efficiency and resolution. These expressions have suggested that SS may be a good choice for imaging midsize objects or objects that are long axially since i) the geometric efficiency increases near the slit as h -1 [instead of h -2 for pinhole (PIN) and either decreases near the collimator for fan-beam (FB) or remains constant for parallel-beam (PB)], where h is the distance from a point to the slit plane; (ii) the transverse resolution is comparable to that of PIN, which is better than that of FB and PB for small objects; iii) the axial resolution is worse than that of PIN since there is no axial magnification; iv) there is a large axial field of view, unlike PIN, which is likely to be useful when imaging midsize or long objects; and v) there is no need for three-dimensional orbits (e.g., helical) since each slice is complete (like PB and FB). We have developed a rotating prototype SS collimator that is capable of single-slit or multi-slit acquisition of data. The focal length (FL) is shorter than that of a typical PIN since increasing the FL requires taller slats to maintain resolution; taller slats reduce geometric efficiency. A lead rectangular box was used to provide support and shielding around the slit-slat collimator. Lead slats, spaced with Rohacell foam, were mounted in an assembly with 3 mm pitch. We have performed preliminary characterization with point sources and acquired micro hot- and cold-rod phantoms and a deluxe Jaszczak phantom. The projections have been reconstructed using a maximum likelihood expectation maximization algorithm and show good resolution. Comparisons indicate that SS is more sensitive than PB and FB for the same resolution for objects with smaller diameter. The advantage of SS over PB and FB increases as the desired resolution improves. SS can also be used in configurations that yield projections that have nonisotropic resolution; it is possible for SS to achieve transverse resolutions that are unreachable by PB, since PB does not magnify, and by FB, since its magnification factor for small objects is much smaller than that of SS. Experimental results show that the resolution of the reconstructed phantoms is consistent with theoretical expectations.

Analytic Derivation and Monte Carlo Validation of a Sensitivity Formula for Slit-Slit Collimation With Penetration

A slit-slit collimator consists of two orthogonal slits and can be conceptualized as a generalized pinhole. Since the two slits are independent of each other, there can be independent axial and transaxial acceptance angles. A small axial acceptance angle may help mitigate axial blurring with circular orbits, allowing multiple copies axially. In addition, since the two slit planes can be placed at different distances with respect to the source, a better detector usage can be achieved, especially in the case of detectors and imaged objects with different aspect ratios. In this paper, an analytical expression is derived for the sensitivity of slit-slit collimation including effective slit widths for photon penetration. An analytical expression for sensitivity is necessary in order to accurately model the system response. This expression could also be useful for comparing a slit-slits sensitivity performance with others. When the effective slit width is used instead of the geometric slit width, the derived analytical expression accurately accounts for photon penetration of the aperture. The derived expression for the sensitivity was validated by Monte Carlo simulation for both geometric and penetrative cases.

Analytical derivation and experimental verification of a sensitivity formula for slit-slat SPECT collimation

The formula g = wd2/[4pia(d+t)h] sin2thetas is derived for the sensitivity of a slit-slat collimator. Both Monte Carlo and experimental data confirm the expected dependence of g on the parameters, especially the distance from the plane of the slit h and the off-axis angle thetas. To refine agreement, a formula for the sensitivity-equivalent slit width is derived to account for slit penetration. At least at low energy its predictions agree well with Monte Carlo data and its use improves agreement with experimental data.

Axial Resolution of Helical-Orbit Pinhole SPECT With Synchronized and Unsynchronized Motion

Pinhole SPECT imaging is widely used in small-animal imaging. Helical orbits provide better sampling and axial resolution compared to circular ones; however, the unsynchronized axial translation of the imaged object and the camera rotation may cause blurring in the image resulting in poorer resolution. In this study, we investigated the axial resolution for synchronized and unsynchronized motions with a small phantom (Ultra-Micro-Defrise) that closely mimics the size of a mouse. We applied angular-dependent axial mechanical shift corrections that substantially improved axial resolution in this regime. Further, we developed custom-designed electronic circuitry to achieve synchronization of the SPECT scanner and the imaged object. The results show that synchronized motion improves axial resolution especially when the angular step of the scanners rotation is large.

Experimental Measurement of Axial and Transaxial Resolutions of a Slit-Slat Collimator and Comparison to Theoretical Expectations

A slit-slat collimator combines a slit parallel to the axis of rotation of a gamma camera with a set of parallel septa evenly spaced in the axial direction. Since the system geometry is similar to pinhole and parallel beam, it is expected that transaxial resolution is described by pinhole relationships and axial resolution is described by parallel-beam relationships. Axial and transaxial resolutions were investigated analytically, through Monte Carlo simulations, and experimentally. A prototype slit-slat collimator was constructed from pre-existing materials. Point source data were collected over a range of source positions, and for values of the slit width, septal spacing, and septal height that varied by factors of two. Experimental FWHM resolutions agree with the theoretical and MC results.

Comparison of Circular and Polygonal Planar Orbits for Pinhole and Slit-Slat SPECT

Analytic formulas and Monte Carlo simulation are used to calculate and compare the sensitivity of circular and polygonal orbits at different points in the Field of View (FoV) for both pinhole and slit-slat collimation. Results show that for a given slit-slat collimator an N-sided polygonal orbit tangent to the FoV generally provides average sensitivity lower than the tightest circular orbit consistent with the same aperture angle, but with better spatial resolution that can be traded for sensitivity for a constant-resolution comparison. This generally results in a slight advantage for the polygonal orbit. However, this advantage depends on the clearance that must be allowed between the orbit and the FoV and decreases quickly, vanishing when even a few millimeters of space are left, which in practice is necessary to accommodate mechanical constraints. For a pinhole collimator the advantage for the tangent polygonal orbit is more consistent, but similar conclusions are reached again when clearance is considered. A direct comparison at constant resolution between slit-slat and pinhole collimation in a single transverse plane is shown to be possible with parameters typical of small-animal imaging applications only for detectors with excellent intrinsic resolution; in this case, pinhole collimation is shown to be more sensitive in magnifying geometries, but reduced axial FoV and increased axial blurring should also be considered for a more complete comparison.

Reconstruction of Phantom SPECT Scans Acquired with a Slit-Slat Collimator

A slit-slat collimator merges the properties of pinhole and fan-beam collimation. The slit allows high sensitivity and fine resolution for points near the slit, as does a pinhole. The slats, which are normal to the axis of rotation, provide axial collimation, resulting in nearly independent axial slices and complete sampling for points for circular orbits. The collimator differs from pinhole in that a circular orbit is sufficient to avoid axial-blurring artifacts from incomplete sampling. It differs from fan-beam in that both the best resolution and best sensitivity are obtained near the collimator, whereas fan-beams sensitivity is best at the focal line. In this study, the SPECT performance of an early prototype collimator is evaluated. The collimator was placed on a lead box attached to a gamma camera. Micro hot-rod and cold-rod phantoms and a mini cold-rod phantom were rotated about a line parallel to the slats normal. Two different slit widths, 1.0 mm and 3.0 mm, were used. The projections were reconstructed slice by slice using an MLEM algorithm (50 iterations). The configuration of this early prototype allowed only a large radius of rotation (80 mm), hurting sensitivity and resolution. Despite this, the reconstruction was able to resolve 3.2 mm hot rods and 4.0 mm cold rods when the slit width was 3 mm. Hot rods of diameter 1.6 were resolved using the 1 mm slit, although sensitivity was reduced by a factor of 3. These resolutions are consistent with theoretical expectations for the resolutions at these configurations. The properties of this collimator make it a good choice for scanning mid-size objects.

First experimental results from a prototype rotating slit-slat collimator

We have previously found and validated expressions for slit-slat (SS) geometric efficiency and resolution. These expressions have suggested that SS may be a good choice for imaging mid-size objects or objects that are long axially since (i) the geometric efficiency increases near the slit as h−1 (instead of h−2 for pinhole (PIN) and either decreasing near the collimator for fan-beam (FB) or constant for parallel-beam (PB)), where h is the distance from a point to the slit plane; (ii) the transverse resolution is comparable to PIN, which is better than FB and PB for small objects; (iii) the axial resolution is worse than PIN since there is no axial magnification; (iv) there is a large axial FOV, unlike PIN, which is likely to be useful when imaging mid-size or long objects; and (v) there is no need for 3D orbits (e.g., helical) since each slice is complete (like PB and FB).