On the evolution by fractional mean curvature

In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric quantities that yield preservation of certain quantities (such as positive fractional curvature) and smoothness of graphical evolutions.Comment: minor correction

Fractional flow reserve vs. angiography in guiding management to optimize outcomes in non-ST-segment elevation myocardial infarction: the British Heart Foundation FAMOUS-NSTEMI randomized trial

Aim: We assessed the management and outcomes of non-ST segment elevation myocardial infarction (NSTEMI) patients randomly assigned to fractional flow reserve (FFR)-guided management or angiography-guided standard care. Methods and results: We conducted a prospective, multicentre, parallel group, 1 : 1 randomized, controlled trial in 350 NSTEMI patients with ≥ coronary stenosis ≥30% of the lumen diameter assessed visually (threshold for FFR measurement) (NCT01764334). Enrolment took place in six UK hospitals from October 2011 to May 2013. Fractional flow reserve was disclosed to the operator in the FFR-guided group (n = 176). Fractional flow reserve was measured but not disclosed in the angiography-guided group (n = 174). Fractional flow reserve ≤0.80 was an indication for revascularization by percutaneous coronary intervention (PCI) or coronary artery bypass surgery (CABG). The median (IQR) time from the index episode of myocardial ischaemia to angiography was 3 (2, 5) days. For the primary outcome, the proportion of patients treated initially by medical therapy was higher in the FFR-guided group than in the angiography-guided group [40 (22.7%) vs. 23 (13.2%), difference 95% (95% CI: 1.4%, 17.7%), P = 0.022]. Fractional flow reserve disclosure resulted in a change in treatment between medical therapy, PCI or CABG in 38 (21.6%) patients. At 12 months, revascularization remained lower in the FFR-guided group [79.0 vs. 86.8%, difference 7.8% (−0.2%, 15.8%), P = 0.054]. There were no statistically significant differences in health outcomes and quality of life between the groups. Conclusion: In NSTEMI patients, angiography-guided management was associated with higher rates of coronary revascularization compared with FFR-guided management. A larger trial is necessary to assess health outcomes and cost-effectiveness

A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow

In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.Comment: 1 figur

Neckpinch singularities in fractional mean curvature flows

In this paper we consider the evolution of sets by a fractional mean curvature flow. Our main result states that for any dimension $n > 2$, there exists an embedded surface in $\mathbb R^n$ evolving by fractional mean curvature flow, which developes a singularity before it can shrink to a point. When $n > 3$ this result generalizes the analogue result of Grayson for the classical mean curvature flow. Interestingly, when $n = 2$, our result provides instead a counterexample in the nonlocal framework to the well known Grayson Theorem, which states that any smooth embedded curve in the plane evolving by (classical) MCF shrinks to a point

Fractional flow reserve-guided management in stable coronary disease and acute myocardial infarction: recent developments

Coronary artery disease (CAD) is a leading global cause of morbidity and mortality, and improvements in the diagnosis and treatment of CAD can reduce the health and economic burden of this condition. Fractional flow reserve (FFR) is an evidence-based diagnostic test of the physiological significance of a coronary artery stenosis. Fractional flow reserve is a pressure-derived index of the maximal achievable myocardial blood flow in the presence of an epicardial coronary stenosis as a ratio to maximum achievable flow if that artery were normal. When compared with standard angiography-guided management, FFR disclosure is impactful on the decision for revascularization and clinical outcomes. In this article, we review recent developments with FFR in patients with stable CAD and recent myocardial infarction. Specifically, we review novel developments in our understanding of CAD pathophysiology, diagnostic applications, prognostic studies, clinical trials, and clinical guidelines