Naum Khutoryansky

A new approach to building explicit time‐marching stencil computation schemes for the transient two‐dimensional acoustic wave equation is implemented. It is based on using Poisson's formula and its three time level modification combined with polynomial stencil interpolation of the solution at each time‐step and exact integration. The time‐stepping algorithm consists of two explicit stencil computation procedures: a first time‐step procedure incorporating the initial conditions and a two‐step scheme for the second and next time‐steps. Three particular explicit stencil schemes (with 5, 9, and 13 space points) are constructed using this approach. Their stability regions are presented. All of the obtained first time‐step computation expressions are different from those used in conventional finite‐difference methods. Accuracy advantages of the new schemes in comparison with conventional finite‐difference schemes are demonstrated by simulation using an exact benchmark solution.

A novel approach to building explicit stencil computation schemes for the transient 2D scalar wave equation is proposed and implemented. It is based on using the integral representation formula (Poisson's formula) that provides the exact solution u(x,t) (where x ∈ R 2 , t is time) of the initial-value problem for the transient 2D scalar wave equation at t > 0 through the initial conditions for both u and v = ∂ u/∂t. For the purpose of constructing a two-step time-marching algorithm, an additional integral representation formula for the sum u(x,t * + τ) + u(x,t * − τ) is provided, with τ being a time step and t * ≥ τ. It is shown that integrals in the two representation formulas are easily calculated if the initial conditions and u(x,t *) as functions of spatial coordinates are approximated by stencil interpolation polynomials in the neighborhood of any point x i j in a 2D Cartesian grid {(ih, jh), (i, j) ∈ Z 2 } where h is a grid spacing. As a result, if a uniform time grid {t k = kτ, k ∈ N} is chosen, the proposed time-marching algorithm consists of two numerical procedures: (a1) the calculation of u(x i j ,t 1), at the very first time-step through the initial values of both u and v at stencil nodes; (a2) the calculation of u(x i j ,t n+1), n ≥ 1 at the second and next time-steps through a generated two-step scheme. Three computational stencils (with 5, 9 and 13 space points) are built using the proposed approach. Their stability is discussed. More attention is given to stencils with five and nine space points. The obtained numerical schemes are compared with corresponding finite-difference methods available in the literature. Simulation comparison results are presented for two benchmark problems that have exact solutions. It is demonstrated by simulation that using the new first time-step calculation procedure (a1) instead of the conventional one can lead to a significant improvement of accuracy including later time-steps.

An approach to building explicit time-marching stencil computation schemes for the transient 2D acoustic wave equation without using finite-difference approximations is proposed and implemented. It is based on using the integral representation formula (Poisson's formula) that provides the exact solution of the initial-value problem for the transient 2D scalar wave equation at any time point through the initial conditions. For the purpose of constructing a two-step time-marching algorithm, a modified integral representation formula involving three time levels is also employed. It is shown that integrals in the two representation formulas are exactly calculated if the initial conditions and the sought solution at each time level as functions of spatial coordinates are approximated by stencil interpolation polynomials in the neighborhood of any point in a 2D Cartesian grid. As a result, if a uniform time grid is chosen, the proposed time-marching algorithm consists of two numerical procedures: 1) the solution calculation at the first time-step through the initial conditions; 2) the solution calculation at the second and next time-steps using a generated two-step numerical scheme. Three particular explicit stencil schemes (with five, nine and 13 space points) are built using the proposed approach. Their stability regions are presented. The obtained stencil expressions are compared with the corresponding finite-difference schemes available in the literature. Their novelty features are discussed. Simulation results with new and conventional schemes are presented for two benchmark problems that have exact solutions. It is demonstrated that using the new first time-step calculation procedure instead of the conventional one can provide a significant improvement of accuracy even for later time steps.

(2013). Evidence supporting an association between hypoglycemic events and depression. Current Medical Research and Opinion: Vol. 29, No. 12, pp. 1609-1615.

Clopidogrel (Plavix®) therapy, although effective for minimizing risk of thrombotic events, is also associated with potential bleeding risk. Recombinant activated FVII (rFVIIa, NovoSeven®) induces hemostasis in hemophilia patients with inhibitors (alloantibodies) and has been proposed as potential treatment for mitigating clopidogrel therapy-mediated bleeding. In this single-center, randomized, placebo-controlled, double-blind, dose-escalation, exploratory phase I trial, we assessed the safety and effects of rFVIIa in reversing clopidogrel-enhanced bleeding in an experimentally induced punch biopsy in healthy subjects. Efficacy assessments included the reversal of bleeding characteristics (bleed duration [BD], the primary end point and blood loss volume [BV] induced by punch biopsy, and thromboelastograph [TEG®] parameters) with rFVIIa or placebo after clopidogrel treatment. A significant number of subjects (56%) had limited response to clopidogrel (defined as ≤30% platelet aggregation inhibition) and were discontinued from study. The remaining subjects continued and had 4 biopsies. Of 40 subjects randomized, 37 were evaluated for efficacy. Clopidogrel treatment increased BD and BV compared with the baseline biopsy. Recombinant FVIIa (10 and 20 μg/kg) significantly mitigated the clopidogrel-induced effects on BV (P = 0.007 and P = 0.001, respectively). Early trial termination limited the evaluation of effects of higher rFVIIa doses. Subgroup analyses of subjects biopsied by the same physician demonstrated significant reduction of clopidogrel-induced BD with 20 μg/kg rFVIIa (P = 0.048). Ex vivo analysis of rFVIIa demonstrated clotting dynamics presented by parameters time to clot onset (TEG®-R) and clot angle (TEG®-A) (P < 0.005). In this clinical study, rFVIIa (10 and 20 μg/kg) reversed the effect of clopidogrel on blood loss.

The use of warfarin has a well-known bleeding risk. Recombinant activated factor VII (rFVIIa) is a non–plasma-derived, rapid-acting, and rapidly infused potential treatment. This randomized, single-center, placebo-controlled, double-blinded, dose-escalation, exploratory phase 1 trial assessed safety and effects of rFVIIa in reversing warfarin-induced changes in bleeding and coagulation parameters, using a punch biopsy–induced bleeding model in healthy subjects. The effects of warfarin (experiment 1) and rFVIIa (5-80 μg/kg; experiment 2) were evaluated. Outcomes were bleeding duration, blood loss, coagulation parameters, and safety. Warfarin treatment significantly increased bleeding duration and blood loss from pretreatment (experiment 1, 12 subjects). However, these parameters after rFVIIa treatment were not significantly different from placebo (experiment 2, 85 subjects). Mean activated partial thromboplastin time, prothrombin time, and international normalized ratio were reduced from warfarin-elevated levels. rFVIIa (80 μg/kg) significantly reversed warfarin effects on all thromboelastography parameters, compared with placebo (P < .05), and returned the thrombin generation speed to baseline. There were no thromboembolic or serious adverse events. In this exploratory trial, the reversal of warfarin effects was observed in the thromboelastography, thrombin generation, and clotting assays. However, this reversal did not translate to improvements in the bleeding model parameters evaluated in the punch biopsy model. Trial registration is exempt (phase 1).

The objective of this study was to establish effects of liraglutide on the QTc interval. In this randomized, placebo‐controlled, double‐blind crossover study, 51 healthy participants were administered placebo, 0.6, 1.2, and 1.8 mg liraglutide once daily for 7 days each. Electro cardiograms were recorded periodically over 24 hours at the end of placebo and highest dosing periods. Four different models for QT correction were used: QTci, as the primary endpoint, and QTciL, QTcF, and QTcB as secondary endpoints. The upper bound of the 1‐sided 95% confidence interval for time‐matched, baseline‐corrected, placebo‐subtracted QTc intervals was 60 ms. The authors conclude that liraglutide caused no clinically relevant increases in the QTc interval.

To investigate the relationship between changes in glycated haemoglobin (HbA(1c)) and postprandial glucose excursions on 1,5-anhydroglucitol (1,5-AG) in patients with Type 2 diabetes, utilizing the differential effects between biphasic insulin aspart 30 (BIAsp 30) or insulin glargine (IGlar) on postprandial glucose (PPG) levels. 1,5-AG was measured using the GlycoMark assay at baseline and after 12 and 28 weeks in the INITiation of Insulin to reach HbA(1c) Target (INITIATE) study of 233 patients randomized to either BIAsp 30 or IGlar. Baseline 1,5-AG was low and not significantly different (4.9 +/- 3.5 and 4.3 +/- 2.6 microg/ml in the BIAsp 30 and IGlar groups, respectively). After 28 weeks, the levels of 1,5-AG were higher in the BIAsp 30 than in the IGlar group (13.4 vs. 11.1 microg/ml, P = 0.008) and change from baseline was 25% greater with BIAsp 30 than IGlar (8.4 vs. 6.7 microg/ml, P = 0.011). 1,5-AG levels increased as a function of decreasing HbA(1c) or the average change in postprandial plasma glucose (PPG(ave)) with significant relationships for 1,5-AG/ HbA(1c) vs. HbA(1c) or 1,5-AG/PPG(ave )vs. PPG(ave) (both P < 0.0001), respectively. As reported in previous publications, 1,5-AG reflects ambient glycaemic control and increases with reductions in HbA(1c) and postprandial glucose. The greater reductions in postprandial excursion achieved with BiAsp 30 compared with glargine were associated with greater increases in 1,5-AG. Even moderate elevations in HbA(1c) substantially lower 1,5-AG, suggesting that it can be most discriminating in identifying patients with excessive postprandial glucose excursions at HbA(1c) levels that approach the upper end of the normal range.

Randomized, placebo-controlled, double-blind, multicenter, Phase IIa study. To assess the safety and efficacy of recombinant-activated Factor VII (rFVIIa) in major spinal surgery. Spinal fusion surgery can cause substantial blood loss and blood product transfusions. Recombinant FVIIa is approved for treatment of bleeding in patients with coagulation abnormalities and has been shown to reduce blood loss and transfusion requirements in surgery in patients with no underlying coagulopathy. Forty-nine patients undergoing fusion of 3 or more vertebral segments were randomized and treated on losing 10% of their estimated blood volume (with total expected surgical blood loss ≥ 20%) and received 3 doses (2-hour intervals) of placebo (n = 13) or 30, 60, or 120 μg/kg rFVIIa (n = 12 per group). The primary endpoint was safety. A priori-defined efficacy endpoints included blood loss and transfusion requirements between placebo and each rFVIIa dose group, adjusted for surgery duration, number of segments fused, and estimated blood volume. Serious adverse events did not occur at any greater frequency in any of the treatment groups. One patient (3 × 30 μg/kg rFVIIa) with advanced cerebrovascular disease (undiagnosed, trial exclusion criterion) died 6 days after surgery due to an ischemic stroke. Mean blood loss was as follows: 2270 mL for placebo; 1909, 1262, and 1868 mL for 3 × 30, 3 × 60, and 3 × 120 μg/kg rFVIIa, respectively (differences not statistically significant). Mean adjusted surgical blood loss was as follows: 2536 mL for placebo; 1120, 400, and 823 mL for 3 × 30, 3 × 60, and 3 × 120 μg/kg rFVIIa, respectively (P ≤ 0.001). Mean surgical transfusion volume was reduced by 27% to 50% with rFVIIa treatment (not significant). The mean adjusted surgical transfusion volume was reduced by 81% to 95% with rFVIIa treatment (P ≤ 0.002). No safety concerns were indicated for the use of rFVIIa in patients at all doses tested; rFVIIa reduced adjusted blood loss and adjusted transfusions during spinal surgery.

OBJECTIVE—A randomized, parallel-group, open-label, multicenter 16-week clinical trial compared efficacy and safety of repaglinide monotherapy and nateglinide monotherapy in type 2 diabetic patients previously treated with diet and exercise. RESEARCH DESIGN AND METHODS—Enrolled patients (n = 150) had received treatment with diet and exercise in the previous 3 months with HbA_1c >7 and ≤12%. Patients were randomized to receive monotherapy with repaglinide (n = 76) (0.5 mg/meal, maximum dose 4 mg/meal) or nateglinide (n = 74) (60 mg/meal, maximum dose 120 mg/meal) for 16 weeks. Primary and secondary efficacy end points were changes in HbA_1c and fasting plasma glucose (FPG) values from baseline, respectively. Postprandial glucose, insulin, and glucagon were assessed after a liquid test meal (baseline, week 16). Safety was assessed by incidence of adverse events or hypoglycemia. RESULTS—Mean baseline HbA_1c values were similar in both groups (8.9%). Final HbA_1c values were lower for repaglinide monotherapy than nateglinide monotherapy (7.3 vs. 7.9%). Mean final reductions of HbA_1c were significantly greater for repaglinide monotherapy than nateglinide monotherapy (−1.57 vs. −1.04%; P = 0.002). Mean changes in FPG also demonstrated significantly greater efficacy for repaglinide than nateglinide (−57 vs. −18 mg/dl; P < 0.001). HbA_1c values 1c and FPG values after 16 weeks of therapy.