Analytical Model for Pixellated SPECT Detector Concepts

Abstract

Pixellated CZT detectors provide a new opportunity to improve the image quality of SPECT detector systems. Their performance has to be evaluated in terms of resolution and efficiency, in a similar way as done earlier for NaI detectors.We have developed an analytical model for spatial resolution and geometric efficiency of collimators specifically for pixellated CZT based detectors. We derive an exact description for static and rotating detector concepts, use NEMA performance criteria for detection efficiency, and adapt measures for spatial resolution of pixellated detectors, based on the sampling of the single pixel response function.Tradeoffs among resolution, efficiency, and signal-to-noise ratio (SNR) have been investigated for different applications. Our analysis shows that the concept of rotating collimators suffers from noise accumulation, except for purely hot spot imaging. We propose multi-pinhole, slat-slit or fan beam-slit collimators in a demagnification mode for optimum efficiency and image quality using pixellated solid-state detectors for SPECT cameras.

Towards a continuous crystal APD-based PET detector design

“…To fully harness the resolving power of these machines, the noise level in the reconstructed image should be sufficiently low. However, the squared signal-to-noise ratio SNR 2 is inversely proportional to the fourth power of the image pixel size [1]. Hence, when the image resolution is improved by a factor of 2, one needs 16 times more coincidence events to achieve the same variance in the reconstructed image.…”

The geometric response function for convergent slit-slat collimators

“…The direction of vector ( x p − x 0 , y p − y 0 , H + B ) is (cosϕ 0 cosγ 0 , cosϕ 0 sinγ 0 , sinϕ 0 ), so we can easily get, $$\begin{array}{cc}right{\xi }_0& left=\frac{x_p}{h}=\cot \theta =\cot {\varphi }_0\cos {\gamma }_0\\ right{\zeta }_0& left=-\frac{y_p}{F-b}=\cot \beta =\cot {\varphi }_0\sin {\gamma }_0.\end{array}$$ Then equation (37) becomes $$g_{\text{std}}=\frac{w{d}^2}{4\pi ah(d+t)}true\mid \frac{F+a}{F-b}true\mid {\sin }^3{\varphi }_0(1-∊)$$ and $$\epsilon =\frac{{\sin }^2{\varphi }_0}{4}true[(1-5{\cot }^2\theta {\sin }^2{\varphi }_0)\frac{w^2}{2h^2}+(1-5{\cot }^2\beta {\sin }^2{\varphi }_0){\left(\frac{d}{a}\frac{F+a}{F-b}\right)}^{2}true].$$ In most situations, the first term in equation (40) can give an accurate sensitivity estimation for the standard region, and the second term can be used to calculate the relative error. The first term of equation (40) is identical to equation (19) in (Wieczorek and Goedicke 2006) and to equation (24) in (Accorsi et al 2008). When the point source is in the principal line, the sensitivity formula is the geometric mean of the sensitivity for pinhole and cone-beam collimators (Metzler et al 2006, Cherry et al 2003).…”

“…The SS collimator has been used subsequently in other SPECT systems (Rogers et al 1988, Juni 2003, Walrand et al 2005, Chang et al 2006, Chang et al 2008). Recent publications have shown the theoretical and experimental performance of SS collimation (Wieczorek and Goedicke 2006, Metzler et al 2006). …”

Registered collimation for pixellated SPECT detectors

“…where D and p are inner width and pitch of the collimator hole, respectively while H is the septa height to be determined [4]. In order to get 0.2% efficiency which is about fourteen times higher than the counts from LEHR in Fig.…”

“…The results of Wieczorek et. al also proposed an analytical method to estimate system resolution of the collimator in [4]. Fig.…”