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

Resection of the mesopancreas (RMP): a new surgical classification of a known anatomical space

BACKGROUND: Prognosis after surgical therapy for pancreatic cancer is poor and has been attributed to early lymph node involvement as well as to a strong tendency of cancer cells to infiltrate into the retropancreatic tissue and to spread along the peripancreatic neural plexuses. The objective of our study was to classify the anatomical-surgical layer of the mesopancreas and to describe the surgical principles relevant for resection of the mesopancreas (RMP). Immunohistochemical investigation of the mesopancreatic-perineural lymphogenic structures was carried out with the purpose of identifying possible routes of metastatic spread. METHODS: Resection of the mesopancreas (RMP) was performed in fresh corpses. Pancreas and mesopancreas were separated from each other and the mesopancreas was immunohistochemically investigated. RESULTS: The mesopancreas strains itself dorsally of the mesenteric vessels as a whitish-firm, fatty tissue-like layer. Macroscopically, in the dissected en-bloc specimens of pancreas and mesopancreas nerve plexuses were found running from the dorsal site of the pancreatic head to the mesopancreas to establish a perineural plane. Immunohistochemical examinations revealed the lymphatic vessels localized in direct vicinity of the neuronal plexuses between pancreas and mesopancreas. CONCLUSION: The mesopancreas as a perineural lymphatic layer located dorsally to the pancreas and reaching beyond the mesenteric vessels has not been classified in the anatomical or surgical literature before. The aim to ensure the greatest possible distance from the retropancreatic lymphatic tissue which drains the carcinomatous focus can be achieved in patients with pancreatic cancer only by complete resection of the mesopancreas (RMP)

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

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