New advances on the Lyapunov constants of some families of planar differential systems

This note presents some advances regarding the Lyapunov constants of some families of planar polynomial differential systems, as a first step toward the resolution of the center and cyclicity problems. First, a parallelization approach is computationally implemented to achieve the 14th Lyapunov constant of the complete cubic family. Second, a technique based on interpolating some specific quantities so as to reconstruct the structure of the Lyapunov constants is used to study a Kukles system, some fifth-degree homogeneous systems, and a quartic system with two invariant lines

Favorable Vascular Profile is an Independent Predictor of Outcome

Background and purposeWe hypothesized that a favorable vascular profile (FVP) defined as anatomic intactness of the Circle of Willis combined with a stable cerebral perfusion pressure (mean arterial blood pressure>65 mm Hg) is a prerequisite for collateral recruitment and maintenance and may improve outcome. We performed post hoc analyses of a subset of the Safety and Efficacy of NeuroFlo Technology in Ischemic Stroke (SENTIS) trial data set to identify whether FVP is associated with independent outcome.MethodsSENTIS was a randomized, controlled device trial comparing hemodynamic augmentation with the NeuroFlo device to best medical treatment. We identified all patients from the primary dataset (n=515 patients) with available intracranial vascular imaging at baseline. Vascular imaging data were read blind to clinical and treatment data. We performed univariate and multivariate analyses to identify predictors of independent outcome (modified Rankin Scale 0-2) at 90 days.ResultsA total of 192/515 SENTIS subjects had available baseline vascular imaging (91 treated/101 controls). Baseline characteristics did not differ between groups. Overall, FVP was seen in 89.6% of patients and predicted independent outcome in univariate (odds ratio, 7.46; 95% confidence interval, 1.68-33.18; P=0.0082) and multiple logistic regression analyses (odds ratio, 10.22; 95% confidence interval, 1.78-58.57; P=0.0091). Aside from FVP, only baseline National Institutes of Health Stroke Scales (NIHSS; odds ratio, 0.74; 95% confidence interval, 0.67-0.82, P<0.0001) entered the predictive model. There was no interaction with randomization to treatment or control.ConclusionsFVP and baseline NIHSS independently predicted outcome in this subset of the SENTIS population. FVP is a novel parameter to predict outcome of acute stroke patients and further studies will establish its potential role for selection of optimal candidates for hemodynamic augmentation. Clinical Trial Registration Information- URL: http://www.clinicaltrials.gov. Unique identifier: NCT00119717