Theoretical bounds and optimal configurations for multi-pinhole SPECT

Abstract

Abstract-The pinhole geometry in SPECT has an inherent trade-off between resolution and sensitivity. High resolution requires a small aperture which on the other hand directly reduces the rate of detected photons. Recent systems overcome this to some extent by using multiple pinholes spread out around the imaging object, effectively increasing the sensitivity with a factor equal to the number of pinholes. The images of each pinhole must fit on the detector without overlap. This creates another trade-off between resolution, sensitivity and the field-ofview (FOV) of the system.The present work analytically analyzes the properties of the multi-pinhole SPECT geometry. Optimal configurations are identified and characterized. One of the main results is that there exists a theoretical upper bound for the sensitivity given the resolution and the FOV. This upper bound is proportional to the square of the resolution and inversely proportional to the square FOV diameter. This means that if we want to improve the resolution by a factor of ten, the sensitivity will go down a factor 100, unless we decrease the FOV an equal amount. The bound can not be broken even if the detector sphere is infinitely large.One important parameter when designing a system is how close it will be to its theoretical bound. The closer to the bound the more extreme the system will be, in terms of size and number of pinholes. A moderate distance away from the bound the proportions of the system are more realistic.

Theoretical Bounds and System Design for Multipinhole SPECT

“…Through an approximation using a first-order Taylor expansion they identify two regimes, one for low-resolution and one for high-resolution detectors. For low-resolution detectors they arrive at the same upper bound as in (21). For high-resolution detectors, they find an increase in the maximum sensitivity by a factor of .…”

“…To express it in terms of the system resolution we use (1) to write in terms of and , and plug it into (17), resulting in (20) This expression is maximized when and hence . By also letting grow enough, i.e., grows faster than , we can get arbitrary close to (21) which is the upper bound for the system sensitivity given the system resolution and the FOV.…”

“…In the present work, parts of which first appeared in [21], we use a similar analytic model and provide a theoretical analysis of some of the fundamental properties of multipinhole SPECT design. In particular, we derive the theoretical upper bound for the sensitivity given the system resolution and field-of-view (FOV), when the images do not overlap on the detector.…”