SPECT electronic collimation resolution enhancement using chi-square minimization

A fully coupled binary biochemical reactive-diffusion model with analytic solution

Coupled multicomponent biochemical reactive diffusion underlies a variety of biological signalling processes and pharmacokinetic applications, such as paracrine signalling involving "cocktails" comprised of growth promoter/inhibitor factors and proteases associated with tumor angiogenesis, invasion and metastasis, extravascular drug delivery, and polymeric controlled-release drug codelivery design. Here, we present a model and develop a new analytic solution to illustrate the spatiotemporal behavior associated with fully coupled binary biochemical reactive diffusion. The complete coupling renders the solution appreciably more complex in structure and behavior than solutions for unicomponent or partially coupled models. Concentration behavior is illustrated by the computational simulation of binary-species tumor angiogenesis factor reactive-diffusion in the extravascular tissue matrix. The computational results indicate that (a) steady-state concentration profiles are achieved within 1 h of a change in factor production; (b) in the steady state, the spatial profiles of the two components tend to be similar; (c) exceedingly steep concentration gradients, involving several orders-of-magnitude differences in concentration over a few tenths of a millimeter, can occur in the vicinity of boundary sources due to inter-species reaction; (d) the concentration profiles of the two species differ from unicomponent predictions due to the simultaneous mass interchange between the two species. The analytic solution predictions are also used to provide a first-ever validation of a time-dependent, binary-component Crank-Nicholson numerical solution. The ability to quantitatively model interacting and often strongly varying concentration levels as a function of time and position can serve as a powerful complementary tool to experimental analyses for assessing disease state and interventional pharmacological efficacy, especially when the spatial scales on which in vivo behavior occurs taxes the limits of imaging capabilities.

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

The widely applied single-interaction analytic expression characterizing the energy resolution component of the angular resolution precision for an electronically collimated point source is extended to include multiple-interaction Compton scatter sequences as well as sequences terminated by photoelectric absorption. The analytic formulation is developed using the statistical variance of the mean for components comprising composite, multivariate resolution precision estimators. It is demonstrated that enhanced resolution precision in the incident interaction scatter angle is attained when use is made of information from multiple interactions. An improvement in the resolution precision of up to approximately 40% is observed for triple Compton scatter. Comparison of the analytic estimates with Monte Carlo/chi-square results shows good agreement.