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Aim: The effect of glucose-lowering agents on diabetes-related complications including cardiovascular (CV) events is of major importance. In the absence of a long-term study, we simulated such a trial using a mathematical model where subjects were given exenatide once-weekly (EQW), which has been shown to improve glycaemic control and reduce weight, systolic blood pressure (SBP) and lipids in patients with type 2 diabetes mellitus (T2DM). Methods: Using the Archimedes Model, we followed a simulated population derived from individuals with T2DM in NHANES who were drug-naive or on oral agents only. We modelled the effects of four treatment strategies including standard care (SC, maintaining levels of control seen in NHANES), intensive glycaemic control (IGC, target HbA1c < 7% with conventional antidiabetic agents) and two versions of EQW added to SC: one with glycaemic and weight reduction only (EQW-1) and one with additional improvements in SBP and lipids (EQW-2). EQW strategies were derived from 52-week clinical trial data. Endpoints included macrovascular and microvascular outcomes. Results: Simulated EQW treatment resulted in earlier benefit and 2–3 times greater relative reductions in major adverse CV events than IGC when compared to SC (6% relative reduction by year 20 for IGC vs. 12 and 17% for the EQW strategies). For microvascular complications, EQW showed comparable benefit to IGC for neuropathy but significantly greater impact on renal complications. Conclusions: This analysis shows that the novel drug EQW has the potential to greatly reduce CV events through its combined effects on glycaemia, weight and other CV risk factors.

The expansion of the solution of the Navier-Stokes equations for steady-state plane-parallel incompressible fluid flows in a series in powers of the Reynolds number and the subjection of this series to no-slip conditions on the rectilinear boundaries in the neighborhood of their intersection point leads to the asymptotic form of the solution in the neighborhood of that point. The use of the leading part of the asymptotic form obtained as the boundary condition at a certain distance from the corner point makes it possible to formulate boundary value problems for the Navier-Stokes equations in closed regions. Examples of the numerical solution of such problems illustrate the formation of infinite vortex systems in the neighborhood of the corner point on the boundary of the flow region.

On the basis of Stokes separated flows, examples of separated flows described by the Navier-Stokes equations of a viscous incompressible fluid are constructed. These flows are represented by series convergent in a certain non-zero neighborhood of a flat contour immersed in the flow. In this neighborhood, the series have the same structure as those for the basic Stokes flows. Examples of the regions in which the series segments chosen give only a slight deviation from the numerical solutions of the Navier-Stokes equations are presented. The comparison between inviscid separated flows (without the no-slip condition on the contour) and viscous flows of the same structure (with the no-slip condition) shows that the viscosity does not play a decisive role in the formation of separation or the type of streamline approach to or departure from the contour.

The governing equations are Maxwell's. The source of the current is either j = ey (z z0) (x)f(t) or e' (z z0) (r r0)f(t) (straight wire or loop of current, f(t) is a pulse). The conductivity (z) and permittivity "(z) are unknown in the medium (z > 0) and are known in the air (z 0, all x;y2R 2 on the surface z = 0. For t < 0 the system is at rest: the electromagnetic elds vanish. Given the data, an exact inversion procedure is described to nd (z) and "(z).