SPECT electronic collimation resolution enhancement using chi-square minimization

Abstract

An electronic collimation technique is developed which utilizes the chi-square goodness-of-fit measure to filter scattered gammas incident upon a medical imaging detector. In this data mining technique, Compton kinematic expressions are used as the chi-square fitting templates for measured energy-deposition data involving multiple-interaction scatter sequences. Fit optimization is conducted using the Davidon variable metric minimization algorithm to simultaneously determine the best-fit gamma scatter angles and their associated uncertainties, with the uncertainty associated with the first scatter angle corresponding to the angular resolution precision for the source. The methodology requires no knowledge of materials and geometry. This pattern recognition application enhances the ability to select those gammas that will provide the best resolution for input to reconstruction software. Illustrative computational results are presented for a conceptual truncated-ellipsoid polystyrene position-sensitive fibre head-detector Monte Carlo model using a triple Compton scatter gamma sequence assessment for a 99mTc point source. A filtration rate of 94.3% is obtained, resulting in an estimated sensitivity approximately three orders of magnitude greater than a high-resolution mechanically collimated device. The technique improves the nominal single-scatter angular resolution by up to approximately 24 per cent as compared with the conventional analytic electronic collimation measure.

Analytic treatment of resolution precision in electronically collimated SPECT imaging involving multiple-interaction gamma rays

“…The analytic solutions were calculated using the average source-to-first-scatter distance d1 for all sequences computed by the accompanying chi-square calculation. As the chi-square results in figure 5 of Durkee et al (1998a) and figure 3 of Durkee et al (1998b) show, the bin-average d 1 tends to increase as θ 1 increases, perhaps by a few centimetres. This behaviour tends to increase the spatial resolution precision as θ 1 increases.…”

A Fully Coupled Binary Biochemical Reactive-diffusion Model with Analytic Solution

“…The presence of these concentration distributions impacts pharmacological effectiveness and disease state associated with tumor angiogenesis, invasive and metastatic behavior, and possibly desmoplasia (Anderson & Chaplain, 1998;Liotta & StetlerStevenson, 1993;Weinberg & Hanahan, 1996). Improvements in modelling (Forni, 1996) and data acquisition (Jain, 1987;Durkee et al, 1998a, b;Mason et al, 1999) are needed to better quantify multicomponent biochemical reactivediffusive concentration behavior associated with disease and improve therapeutic efficacy. (and theoretical estimates of error bounds) that are valid at only a finite number of spatial and temporal points (Hennart, 1973).…”