Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria

This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since - after establishing the invariance of observability under output injection - this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.

High resolution cortical bone thickness measurement from clinical CT data.

The distribution of cortical bone in the proximal femur is believed to be a critical component in determining fracture resistance. Current CT technology is limited in its ability to measure cortical thickness, especially in the sub-millimetre range which lies within the point spread function of today's clinical scanners. In this paper, we present a novel technique that is capable of producing unbiased thickness estimates down to 0.3mm. The technique relies on a mathematical model of the anatomy and the imaging system, which is fitted to the data at a large number of sites around the proximal femur, producing around 17,000 independent thickness estimates per specimen. In a series of experiments on 16 cadaveric femurs, estimation errors were measured as -0.01+/-0.58mm (mean+/-1std.dev.) for cortical thicknesses in the range 0.3-4mm. This compares with 0.25+/-0.69mm for simple thresholding and 0.90+/-0.92mm for a variant of the 50% relative threshold method. In the clinically relevant sub-millimetre range, thresholding increasingly fails to detect the cortex at all, whereas the new technique continues to perform well. The many cortical thickness estimates can be displayed as a colour map painted onto the femoral surface. Computation of the surfaces and colour maps is largely automatic, requiring around 15min on a modest laptop computer.

Insulin analog preparations and their use in children and adolescents with type 1 diabetes mellitus.

Standard or 'traditional' human insulin preparations such as regular soluble insulin and neutral protamine Hagedorn (NPH) insulin have shortcomings in terms of their pharmacokinetic and pharmacodynamic properties that limit their clinical efficacy. Structurally modified insulin molecules or insulin 'analogs' have been developed with the aim of delivering insulin replacement therapy in a more physiological manner. In the last 10 years, five insulin analog preparations have become commercially available for clinical use in patients with type 1 diabetes mellitus: three 'rapid' or fast-acting analogs (insulin lispro, aspart, and glulisine) and two long-acting analogs (insulin glargine and detemir). This review highlights the specific pharmacokinetic properties of these new insulin analog preparations and focuses on their potential clinical advantages and disadvantages when used in children and adolescents with type 1 diabetes mellitus. The fast-acting analogs specifically facilitate more flexible insulin injection timing with regard to meals and activities, whereas the long-acting analogs have a more predictable profile of action and lack a peak effect. To date, clinical trials in children and adolescents have been few in number, but the evidence available from these and from other studies carried out in adults with type 1 diabetes suggest that they offer significant benefits in terms of reduced frequency of nocturnal hypoglycemia, better postprandial blood glucose control, and improved quality of life when compared with traditional insulins. In addition, insulin detemir therapy is unique in that patients may benefit from reduced risk of excessive weight, particularly during adolescence. Evidence for sustained long-term improvements in glycosylated hemoglobin, on the other hand, is modest. Furthermore, alterations to insulin/insulin-like growth factor I receptor binding characteristics have also raised theoretical concerns that insulin analogs may have an increased mitogenic potential and risk of tumor development, although evidence from both in vitro and in vivo animal studies do not support this assertion. Long-term surveillance has been recommended and further carefully designed prospective studies are needed to evaluate the overall benefits and clinical efficacy of insulin analog therapy in children and adolescents with type 1 diabetes.