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This paper introduces a novel compartmental model describing the excretion of 18F-fluoro-deoxyglucose (FDG) in the renal system and a numerical method based on the maximum likelihood for its reduction. This approach accounts for variations in FDG concentration due to water re-absorption in renal tubules and the increase of the bladder's volume during the FDG excretion process. From the computational viewpoint, the reconstruction of the tracer kinetic parameters is obtained by solving the maximum likelihood problem iteratively, using a non-stationary, steepest descent approach that explicitly accounts for the Poisson nature of nuclear medicine data. The reliability of the method is validated against two sets of synthetic data realized according to realistic conditions. Finally we applied this model to describe FDG excretion in the case of animal models treated with metformin. In particular we show that our approach allows the quantitative estimation of the reduction of FDG de-phosphorylation induced by metformin.

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BackgroundCompartmental analysis is a standard method to quantify metabolic processes using fluorodeoxyglucose-positron emission tomography (FDG-PET). For liver studies, this analysis is complex due to the hepatocyte capability to dephosphorylate and release glucose and FDG into the blood. Moreover, a tracer is supplied to the liver by both the hepatic artery and the portal vein, which is not visible in PET images. This study developed an innovative computational approach accounting for the reversible nature of FDG in the liver and directly computing the portal vein tracer concentration by means of gut radioactivity measurements.MethodsTwenty-one mice were subdivided into three groups: the control group ‘CTR’ (n = 7) received no treatment, the short-term starvation group ‘STS’ (n = 7) was submitted to food deprivation with free access to water within 48 h before imaging, and the metformin group ‘MTF’ (n = 7) was treated with metformin (750 mg/Kg per day) for 1 month. All mice underwent a dynamic micro-PET study for 50 min after an 18F-FDG injection. The compartmental analysis considered two FDG pools (phosphorylated and free) in both the gut and liver. A tracer was carried into the liver by the hepatic artery and the portal vein, and tracer delivery from the gut was considered as the sole input for portal vein tracer concentration. Accordingly, both the liver and gut were characterized by two compartments and two exchange coefficients. Each one of the two two-compartment models was mathematically described by a system of differential equations, and data optimization was performed by applying a Newton algorithm to the inverse problems associated to these differential systems.ResultsAll rate constants were stable in each group. The tracer coefficient from the free to the metabolized compartment in the liver was increased by STS, while it was unaltered by MTF. By contrast, the tracer coefficient from the metabolized to the free compartment was reduced by MTF and increased by STS.ConclusionsData demonstrated that our method was able to analyze FDG kinetics under pharmacological or pathophysiological stimulation, quantifying the fraction of the tracer trapped in the liver or dephosphorylated and released into the bloodstream.

In this paper we explain the linear sampling method and its performances in various scattering conditions by means of an analysis of the far-field equation based on the principle of energy conservation. Specifically, we consider the conservation of energy along the flow strips of the Poynting vector associated with the scattered field whose far-field pattern is one of the two terms in the far-field equation. The behavior of these flow lines is numerically investigated and theoretically described. Appropriate assumptions on the flow lines, based on the numerical results, allow characterizing a set of approximate solutions of the far-field equation which can be used to visualize the boundary of the scatterer in the framework of the linear sampling method. In particular, under the same assumptions, we can show that Tikhonov regularized solutions belong to this set of approximate solutions for appropriate choices of the regularization parameter.

ObjectivesThe present study aims to verify the relationship between glucose consumption and uptake of 18F-2-deoxy-glucose (FDG) in the skeletal muscle (SM) of experimental models of streptozotocin-induced diabetes mellitus (STZ-DM).MethodsThe study included 36 Balb/c mice. Two weeks after intraperitoneal administration of saline (control group, n = 18) or 150 mg streptozotocin (STZ-DM group, n = 18), the two cohorts were submitted to an oral glucose tolerance test and were further subdivided into three groups (n = 6 each): untreated and treated with metformin (MTF) at low or high doses (10 or 750 mg/kg daily, respectively). Two weeks thereafter, all mice were submitted to dynamic micro–positron emission tomography (PET) imaging after prolonged fasting. After sacrifice, enzymatic pathways and response to oxidative stress were evaluated in harvested SM.ResultsOn PET imaging, the FDG uptake rate in hindlimb SM was significantly lower in nondiabetic mice as compared with STZ-DM–untreated mice. MTF had no significant effect on SM FDG uptake in untreated mice; however, its high dose induced a significant decrease in STZ-DM animals. Upon conventional analysis, the SM standard uptake value was higher in STZ-DM mice, while MTF was virtually ineffective in either control or STZ-DM models. This metabolic reprogramming was not explained by any change in cytosolic glucose metabolism. By contrast, it closely agreed with the catalytic function of hexose-6P-dehydrogenase (H6PD; i.e., the trigger of a specific pentose phosphate pathway selectively located within the endoplasmic reticulum). In agreement with this role, the H6PD enzymatic response to both STZ-DM and MTF matched the activation of the NADPH-dependent antioxidant responses to the increased generation of reactive oxygen species caused by chronic hyperglycemia. Ex vivo analysis of tracer kinetics confirmed that the enhanced SM avidity for FDG occurred despite a significant reduction in glucose consumption, while it was associated with increased radioactivity transfer to the endoplasmic reticulum.ConclusionsThese data challenge the current dogma linking FDG uptake to the glycolytic rate. They instead introduce a new model considering a strict link between the uptake of this glucose analog, H6PD reticular activity, and oxidative damage in diabetes, at least under fasting condition.