Brain single-photon emission CT physics principles.

The basic principles of scintigraphy are reviewed and extended to 3D imaging. Single-photon emission computed tomography (SPECT) is a sensitive and specific 3D technique to monitor in vivo functional processes in both clinical and preclinical studies. SPECT/CT systems are becoming increasingly common and can provide accurately registered anatomic information as well. In general, SPECT is affected by low photon-collection efficiency, but in brain imaging, not all of the large FOV of clinical gamma cameras is needed: The use of fan- and cone-beam collimation trades off the unused FOV for increased sensitivity and resolution. The design of dedicated cameras aims at increased angular coverage and resolution by minimizing the distance from the patient. The corrections needed for quantitative imaging are challenging but can take advantage of the relative spatial uniformity of attenuation and scatter. Preclinical systems can provide submillimeter resolution in small animal brain imaging with workable sensitivity.

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 sin(3) 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 (+/- 0.3%) 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.

Non-diverging analytic expression for the on-axis sensitivity of converging collimators: analytic derivation.

The expressions for the sensitivity of converging collimators found in the literature diverge at points near the focal locus of the collimator. In this paper, an analytical formula that does not diverge is derived and compared to that available in the literature. An analysis is provided to predict the cases in which use of the new formula is advisable. Since the first expression derived is rather complex, approximations were made to reach simpler formulae. The formulae derived can be used to define and extend the realm of applicability of the literature expression in the cases identified in their derivation.

Non-diverging analytic expression for the on-axis sensitivity of converging collimators: experimental verification.

The previous paper presented the derivation of an analytical formula for the sensitivity of converging collimators that does not diverge at the focal locus of the collimator. Its predictions, those from a simplified version, and those from the most commonly referenced formula are compared to Monte Carlo and experimental data. Agreement is excellent for all formulae far from the focal locus of the collimator, where it is markedly better for the new formula and its approximation. It is inferred that such formulae should be used in the cases identified by theory, namely around the focal locus of collimators of any focal length and over a substantial part of the field-of-view for short focal length collimators.

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.

Near-field artifact reduction in planar coded aperture imaging.

Coded apertures for imaging problems are typically based on arrays having perfect cross-correlation properties. These arrays, however, guarantee a perfect point-spread function in far-field applications only. When these arrays are used in the near-field, artifacts arise. We present a mathematical derivation capable of predicting the shape of such artifacts. The theory shows that methods used in the past to compensate for the effects of background nonuniformities in far-field problems are also effective in reducing near-field artifacts. The case study of a nuclear medicine problem is presented to show good agreement of simulation and experimental results with mathematical predictions.