A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

Nuclear and cytoplasmic expression of survivin in 67 surgically resected pancreatic cancer patients

Pancreatic cancer is one of the most aggressive gastrointestinal cancer with less than 10% long-term survivors. The apoptotic pathway deregulation is a postulated mechanism of carcinogenesis of this tumour. The present study investigated the prognostic role of apoptosis and apoptosis-involved proteins in a series of surgically resected pancreatic cancer patients. All patients affected by pancreatic adenocarcinoma and treated with surgical resection from 1988 to 2003 were considered for the study. Patients' clinical data and pathological tumour features were recorded. Survivin and Cox-2 expression were evaluated by immunohistochemical staining. Apoptotic cells were identified using the TUNEL method. Tumour specimen of 67 resected patients was included in the study. By univariate analysis, survival was influenced by Survivin overexpression. The nuclear Survivin overexpression was associated with better prognosis (P=0.0009), while its cytoplasmic overexpression resulted a negative prognostic factor (P=0.0127). Also, the apoptotic index was a statistically significant prognostic factor in a univariate model (P=0.0142). By a multivariate Cox regression analysis, both the nuclear (P=0.002) and cytoplasmic (P=0.040) Survivin overexpression maintained the prognostic statistical value. This is the first study reporting a statistical significant prognostic relevance of nuclear and cytoplasmic Survivin overexpression in pancreatic cancer. In particular, patients with high nuclear Survivin staining showed a longer survival, whereas patients with high cytoplasmic Survivin staining had a shorter overall survival

Status Update and Interim Results from the Asymptomatic Carotid Surgery Trial-2 (ACST-2)

Objectives: ACST-2 is currently the largest trial ever conducted to compare carotid artery stenting (CAS) with carotid endarterectomy (CEA) in patients with severe asymptomatic carotid stenosis requiring revascularization. Methods: Patients are entered into ACST-2 when revascularization is felt to be clearly indicated, when CEA and CAS are both possible, but where there is substantial uncertainty as to which is most appropriate. Trial surgeons and interventionalists are expected to use their usual techniques and CE-approved devices. We report baseline characteristics and blinded combined interim results for 30-day mortality and major morbidity for 986 patients in the ongoing trial up to September 2012. Results: A total of 986 patients (687 men, 299 women), mean age 68.7 years (SD ± 8.1) were randomized equally to CEA or CAS. Most (96%) had ipsilateral stenosis of 70-99% (median 80%) with contralateral stenoses of 50-99% in 30% and contralateral occlusion in 8%. Patients were on appropriate medical treatment. For 691 patients undergoing intervention with at least 1-month follow-up and Rankin scoring at 6 months for any stroke, the overall serious cardiovascular event rate of periprocedural (within 30 days) disabling stroke, fatal myocardial infarction, and death at 30 days was 1.0%. Conclusions: Early ACST-2 results suggest contemporary carotid intervention for asymptomatic stenosis has a low risk of serious morbidity and mortality, on par with other recent trials. The trial continues to recruit, to monitor periprocedural events and all types of stroke, aiming to randomize up to 5,000 patients to determine any differential outcomes between interventions. Clinical trial: ISRCTN21144362. © 2013 European Society for Vascular Surgery. Published by Elsevier Ltd. All rights reserved

Second asymptomatic carotid surgery trial (ACST-2): a randomised comparison of carotid artery stenting versus carotid endarterectomy

Background: Among asymptomatic patients with severe carotid artery stenosis but no recent stroke or transient cerebral ischaemia, either carotid artery stenting (CAS) or carotid endarterectomy (CEA) can restore patency and reduce long-term stroke risks. However, from recent national registry data, each option causes about 1% procedural risk of disabling stroke or death. Comparison of their long-term protective effects requires large-scale randomised evidence. Methods: ACST-2 is an international multicentre randomised trial of CAS versus CEA among asymptomatic patients with severe stenosis thought to require intervention, interpreted with all other relevant trials. Patients were eligible if they had severe unilateral or bilateral carotid artery stenosis and both doctor and patient agreed that a carotid procedure should be undertaken, but they were substantially uncertain which one to choose. Patients were randomly allocated to CAS or CEA and followed up at 1 month and then annually, for a mean 5 years. Procedural events were those within 30 days of the intervention. Intention-to-treat analyses are provided. Analyses including procedural hazards use tabular methods. Analyses and meta-analyses of non-procedural strokes use Kaplan-Meier and log-rank methods. The trial is registered with the ISRCTN registry, ISRCTN21144362. Findings: Between Jan 15, 2008, and Dec 31, 2020, 3625 patients in 130 centres were randomly allocated, 1811 to CAS and 1814 to CEA, with good compliance, good medical therapy and a mean 5 years of follow-up. Overall, 1% had disabling stroke or death procedurally (15 allocated to CAS and 18 to CEA) and 2% had non-disabling procedural stroke (48 allocated to CAS and 29 to CEA). Kaplan-Meier estimates of 5-year non-procedural stroke were 2·5% in each group for fatal or disabling stroke, and 5·3% with CAS versus 4·5% with CEA for any stroke (rate ratio [RR] 1·16, 95% CI 0·86–1·57; p=0·33). Combining RRs for any non-procedural stroke in all CAS versus CEA trials, the RR was similar in symptomatic and asymptomatic patients (overall RR 1·11, 95% CI 0·91–1·32; p=0·21). Interpretation: Serious complications are similarly uncommon after competent CAS and CEA, and the long-term effects of these two carotid artery procedures on fatal or disabling stroke are comparable. Funding: UK Medical Research Council and Health Technology Assessment Programme