Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics.

In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to be a (secondary) linear instability mechanism. Furthermore, we develop a more precise analysis of cancellations in the resonance mechanism, which yields a modified exponent in the high frequency regime. This allows us, in addition, to remove a logarithmic constraint on the perturbations present in prior works by Bedrossian, Deng and Masmoudi, and to construct solutions which are initially in a Gevrey class for which the velocity asymptotically converges in Sobolev regularity but diverges in Gevrey regularity.

Corona again? SSC after a severe COVID-disease.

Secondary sclerosing cholangitis (SSC) is a severe complication of intensive care treatment in critically ill patients. It is characterized by rapid onset and severe chlolestasis with elevation of gGT. In contrast to primary sclerosing cholangitis, SSC-CIP has a distinct and timely well defined trigger and can have a rapid progress to cirrhosis and liver failure. In context of the COVID-19-pandemic, there are reports about patients, who developed SSC after a severe COVID-infection and intensive care treatment.We report on a 62-year old patient without any relevant pre-existing illnesses, who suffered from severe COVID-19 pneumonia with the need for long term ventilation. In the course of the disease he developed a critical-illness-polyneuropathy a pronounced cholestasis. After recovery from COVID-pneumonia, the PNP regressed but the cholestasis progressed. MRCP showed only irregular intrahepatic bile ducts, while EUS showed echogenic intraductal longitudinal structures characteristic for intraductal casts and for SSC-CIP. This was confirmed with ERC, where the complete necrotic bile ducts could be extracted and retrieved for histological and molecular analysis.The patient was included in a scheduled ERC-program to prevent a progress of SSC and the concomitant cirrhosis.SSC is an often missed diagnosis, which obviously can also occur in COVID-patients. In case of elevated liver function tests with cholestasis, EUS might be the key diagnostic method to characterize intraductal casts and identify those patients who should undergo ERC.

A prospective comparison of the diagnostic accuracy of ERCP, MRCP, CT, and EUS in biliary strictures.

BACKGROUND: The differential diagnosis of biliary strictures remains a challenge. This study evaluated magnetic resonance cholangiopancreatography (MRCP) as a new procedure in comparison with the established methods of diagnosis including ERCP or percutaneous transhepatic cholangiography (PTC), CT, and EUS. METHODS: Fifty patients (21 men, 29 women, mean age 65.7 years) with jaundice but no pain suspected to have biliary strictures were enrolled in this prospective study. MRCP, ERCP/PTC, CT, and EUS were performed prospectively; images and videotapes (EUS) of these tests were reviewed blindly under standardized conditions. Reference standards for comparison were surgery, a biopsy confirming malignancy, or the clinical course during follow-up (at least 12 months) in cases without histopathologic proof of malignancy. RESULTS: Seven patients ultimately proved to have jaundice caused by parenchymal liver disease and 43 had a biliary stricture (17 benign, 26 malignant). Forty patients underwent all 4 imaging tests. There were 10 patients in whom patient-specific problems precluded some procedures but who were included in an intention-to-diagnose analysis. The sensitivity and specificity for diagnosis of malignancy in the 50 patients were as follows: 85% / 75% for ERCP/PTC, 85% / 71% for MRCP, 77% / 63% for CT, and 79% / 62% for EUS, with similar values in the 40 patients who underwent all 4 imaging methods. The combination of MRCP and EUS improved specificity. CONCLUSIONS: Although MRCP provides the same imaging information as direct cholangiography, it has limited specificity for the diagnosis of malignant strictures. In the differential diagnosis of biliary strictures, several tests including ERCP-guided tissue diagnosis are still required, and MRCP has only a limited clinical role.