Stephen Moore

Collimator design for single photon emission tomography

We discuss recent trends in collimator design and technology, with emphasis on theoretical and practical issues of importance for single photon emission tomography (SPET). The well-known imaging performance parameters of parallel-hole collimators are compared with those of fan-beam collimators, which have enjoyed considerable success in recent years, particularly for brain SPET. We review a simplistic approach to the collimator optimization problem, as well as more sophisticated “task-dependent” treatments and important considerations for SPET collimator design. Practical guidance is offered for understanding trade-offs that must be considered for clinical imaging. Finally, selective comparisons among different SPET systems and collimators are presented for illustrative purposes.

A volume-localized, two-dimensional NMR method for lactate-edited diffusion coefficient measurements using zero-quantum coherence-transfer spectroscopy

The noninvasive measurement of the self-diffusion coefficient of biological metabolites would be a powerful tool for evaluating the microenvironment of these compounds. The molecular displacement of in vivo metabolites is a complex function of, for example, cellular compartment size, active and passive transport across cell membranes, and immobilization due to adsorption processes (I), which are in turn associated with the biological activities of the cell and its immediate surroundings. Consequently, the study of metabolite diffusion would be important for understanding these processes and may prove useful in characterizing the disease state of a tissue or an organ. Diffusion-coefficient measurements of in vivo metabolites have recently been initiated using spin-echo NMR spectroscopy pulse sequences which contain diffusion-sensitive pulsed field gradients (1, 2). In addition to the classical Stejskal-Tanner spin-echo method (3), the stimulated-echo (STE) sequence (4), shown in Fig. 1, has been found to be particularly useful for applications to metabolites, which frequently have short T, but relatively long T, relaxation times. For the STE sequence in Fig. 1, molecular diffusion in the presence of the pulsed field gradients results in an attenuation of the echo signal amplitude given by

Barankin bound: a model of detection with location uncertainty

We have developed generalized ideal observer models relating human performance in detection tasks to physical properties of medical imaging systems, such as spatial resolution and noise power spectrum. Our approach treats detection as a special case of amplitude estimation, with certain other aspects of the signal, e.g., size or location, considered additional unknown parameters. The models are based on the Barankin lower bound on the precision with which the quantities of interest can be determined. We have found the Barankin bound to be particularly promising in predicting human performance in detection with location uncertainty. Its predictions differ from those of other proposed models in two respects. First, our results suggest that the degradation in performance due to location uncertainty depends on resolution. Second, we have shown analytically that for a given search area, the ratio of ideal observer performance when location is unknown to performance when location is known is nearly independent of signal size. This differs from previously proposed models which predict that the effect of location uncertainty depends on the ratio of signal size to search area, but agrees with the results of reported perceptual experiments testing this question.

X2 isocontours: predictors of performance in nonlinear estimation tasks at low SNR

Maximum-likelihood (ML) estimation is an established paradigm for the assessment of imaging system performance in nonlinear quantitation tasks. At high signal-to-noise ratio (SNR), maximum likelihood estimates are asymptotically normally distributed, unbiased, and efficient, thereby attaining the Cramer-Rao bound (CRB). Therefore, at high SNR the CRB is useful as a predictor of estimation performance. At low SNR, however, the achievable parameter variances are substantially larger than the CRB and the estimates are no longer Gaussian distributed. This implies that intervals derived from the CRB or other tighter symmetric variance bounds do not contain the appropriate fraction of the estimates expected from the normal distribution. We have derived the mathematical relationship between (chi) 2 and the expected probability density of the ML-estimates, and have justified the use of (chi) 2-isocontours to describe the estimates. We validates this approach by simulation of spherical objects imaged with a Gaussian PSF. The parameters, activity concentration and size, were estimated simultaneously by ML, and variances and covariances calculated over 1000 replications per condition. At low SNR, where the CRB is no longer achieved, (chi) 2-isocontours provide a robust predictor of the distribution of the ML- estimates. At high SNR, the (chi) 2-isocontours approach asymptotically the contour derived from the Fisher information matrix.