On the isoperimetric problem for the Laplacian with Robin and Wentzell boundary conditions

Doctor of PhilosophyWe consider the problem of minimising the eigenvalues of the Laplacian with Robin boundary conditions $\frac{\partial u}{\partial \nu} + \alpha u = 0$ and generalised Wentzell boundary conditions $\Delta u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$ with respect to the domain $\Omega \subset \mathbb R^N$ on which the problem is defined. For the Robin problem, when $\alpha > 0$ we extend the Faber-Krahn inequality of Daners [Math. Ann. 335 (2006), 767--785], which states that the ball minimises the first eigenvalue, to prove that the minimiser is unique amongst domains of class $C^2$. The method of proof uses a functional of the level sets to estimate the first eigenvalue from below, together with a rearrangement of the ball's eigenfunction onto the domain $\Omega$ and the usual isoperimetric inequality. We then prove that the second eigenvalue attains its minimum only on the disjoint union of two equal balls, and set the proof up so it works for the Robin $p$-Laplacian. For the higher eigenvalues, we show that it is in general impossible for a minimiser to exist independently of $\alpha > 0$. When $\alpha < 0$, we prove that every eigenvalue behaves like $-\alpha^2$ as $\alpha \to -\infty$, provided only that $\Omega$ is bounded with $C^1$ boundary. This generalises a result of Lou and Zhu [Pacific J. Math. 214 (2004), 323--334] for the first eigenvalue. For the Wentzell problem, we (re-)prove general operator properties, including for the less-studied case $\beta 0$ establish a type of equivalence property between the Wentzell and Robin minimisers for all eigenvalues. This yields a minimiser of the second Wentzell eigenvalue. We also prove a Cheeger-type inequality for the first eigenvalue in this case

RANTES/CCL5 and Risk for Coronary Events: Results from the MONICA/KORA Augsburg Case-Cohort, Athero-Express and CARDIoGRAM Studies

BACKGROUND: The chemokine RANTES (regulated on activation, normal T-cell expressed and secreted)/CCL5 is involved in the pathogenesis of cardiovascular disease in mice, whereas less is known in humans. We hypothesised that its relevance for atherosclerosis should be reflected by associations between CCL5 gene variants, RANTES serum concentrations and protein levels in atherosclerotic plaques and risk for coronary events. METHODS AND FINDINGS: We conducted a case-cohort study within the population-based MONICA/KORA Augsburg studies. Baseline RANTES serum levels were measured in 363 individuals with incident coronary events and 1,908 non-cases (mean follow-up: 10.2±4.8 years). Cox proportional hazard models adjusting for age, sex, body mass index, metabolic factors and lifestyle factors revealed no significant association between RANTES and incident coronary events (HR [95% CI] for increasing RANTES tertiles 1.0, 1.03 [0.75-1.42] and 1.11 [0.81-1.54]). None of six CCL5 single nucleotide polymorphisms and no common haplotype showed significant associations with coronary events. Also in the CARDIoGRAM study (&gt;22,000 cases, &gt;60,000 controls), none of these CCL5 SNPs was significantly associated with coronary artery disease. In the prospective Athero-Express biobank study, RANTES plaque levels were measured in 606 atherosclerotic lesions from patients who underwent carotid endarterectomy. RANTES content in atherosclerotic plaques was positively associated with macrophage infiltration and inversely associated with plaque calcification. However, there was no significant association between RANTES content in plaques and risk for coronary events (mean follow-up 2.8±0.8 years). CONCLUSIONS: High RANTES plaque levels were associated with an unstable plaque phenotype. However, the absence of associations between (i) RANTES serum levels, (ii) CCL5 genotypes and (iii) RANTES content in carotid plaques and either coronary artery disease or incident coronary events in our cohorts suggests that RANTES may not be a novel coronary risk biomarker. However, the potential relevance of RANTES levels in platelet-poor plasma needs to be investigated in further studies

RANTES/CCL5 and risk for coronary events: Results from the MONICA/KORA Augsburg case-cohort, Athero-express and CARDIoGRAM studies

Background: The chemokine RANTES (regulated on activation, normal T-cell expressed and secreted)/CCL5 is involved in the pathogenesis of cardiovascular disease in mice, whereas less is known in humans. We hypothesised that its relevance for atherosclerosis should be reflected by associations between CCL5 gene variants, RANTES serum concentrations and protein levels in atherosclerotic plaques and risk for coronary events. Methods and Findings: We conducted a case-cohort study within the population-based MONICA/KORA Augsburg studies. Baseline RANTES serum levels were measured in 363 individuals with incident coronary events and 1,908 non-cases (mean follow-up: 10.2±

Adaptations of the 3T3-L1 adipocyte lipidome to defective ether lipid catabolism upon Agmo knockdown

Little is known about the physiological role of alkylglycerol monooxygenase (AGMO), the only enzyme capable of cleaving the 1-O-alkyl ether bond of ether lipids. Expression and enzymatic activity of this enzyme can be detected in a variety of tissues including adipose tissue. This labile lipolytic membrane-bound protein uses tetrahydrobiopterin as a cofactor, and mice with reduced tetrahydrobiopterin levels have alterations in body fat distribution and blood lipid concentrations. In addition, manipulation of AGMO in macrophages led to significant changes in the cellular lipidome, and alkylglycerolipids, the preferred substrates of AGMO, were shown to accumulate in mature adipocytes. Here, we investigated the roles of AGMO in lipid metabolism by studying 3T3-L1 adipogenesis. AGMO activity was induced over 11 days using an adipocyte differentiation protocol. We show that RNA interference-mediated knockdown of AGMO did not interfere with adipocyte differentiation or affect lipid droplet formation. Furthermore, lipidomics revealed that plasmalogen phospholipids were preferentially accumulated upon Agmo knockdown, and a significant shift toward longer and more polyunsaturated acyl side chains of diacylglycerols and triacylglycerols could be detected by mass spectrometry. Our results indicate that alkylglycerol catabolism has an influence not only on ether-linked species but also on the degree of unsaturation in the massive amounts of triacylglycerols formed during in vitro 3T3-L1 adipocyte differentiation

Consensus recommendations for histological criteria of autoimmune hepatitis from the International AIH Pathology Group : Results of a workshop on AIH histology hosted by the European Reference Network on Hepatological Diseases and the European Society of Pathology

Background &amp; Aims: Diagnostic histological criteria for autoimmune hepatitis (AIH) have not been clearly established. Previously published criteria focused mainly on chronic AIH, in which inflammatory changes mainly occur in portal/periportal regions and may not be applicable to acute presentation of AIH, in which inflammatory changes are typically predominantly lobular in location. International consensus criteria for the diagnosis and assessment of disease severity in both acute and chronic AIH are thus urgently needed. Methods: Seventeen expert liver pathologists convened at an international workshop and subsequently used a modified Delphi panel approach to establish consensus criteria for the histopathological diagnosis of AIH. Results: The consensus view is that liver biopsy should remain standard for diagnosing AIH. AIH is considered likely, if there is a predominantly portal lymphoplasmacytic hepatitis with more than mild interface activity and/or more than mild lobular hepatitis in the absence of histological features suggestive of another liver disease. AIH is also considered likely if there is predominantly lobular hepatitis with or without centrilobular necroinflammation and at least one of the following features: portal lymphoplasmacytic hepatitis, interface hepatitis or portal-based fibrosis, in the absence of histological features suggestive of another liver disease. Emperipolesis and hepatocellular rosettes are not regarded as being specific for AIH. Conclusions: The criteria proposed in this consensus statement provide a uniform approach to the histological diagnosis of AIH, which is relevant for patients with an acute as well as a chronic presentation and to more accurately reflect the current understanding of liver pathology in AIH. © 2022 John Wiley &amp; Sons A/S. Published by John Wiley &amp; Sons Lt

Complexity of ballooned hepatocyte feature recognition: Defining a training atlas for artificial intelligence-based imaging in NAFLD

Background &amp; Aims: Histologically assessed hepatocyte ballooning is a key feature discriminating non-alcoholic steatohepatitis (NASH) from steatosis (NAFL). Reliable identification underpins patient inclusion in clinical trials and serves as a key regulatory-approved surrogate endpoint for drug efficacy. High inter/intra-observer variation in ballooning measured using the NASH CRN semi-quantitative score has been reported yet no actionable solutions have been proposed. Methods: A focused evaluation of hepatocyte ballooning recognition was conducted. Digitized slides were evaluated by 9 internationally recognized expert liver pathologists on 2 separate occasions: each pathologist independently marked every ballooned hepatocyte and later provided an overall non-NASH NAFL/NASH assessment. Interobserver variation was assessed and a ‘concordance atlas’ of ballooned hepatocytes generated to train second harmonic generation/two-photon excitation fluorescence imaging-based artificial intelligence (AI). Results: The Fleiss kappa statistic for overall interobserver agreement for presence/absence of ballooning was 0.197 (95% CI 0.094–0.300), rising to 0.362 (0.258–0.465) with a ≥5-cell threshold. However, the intraclass correlation coefficient for consistency was higher (0.718 [0.511–0.900]), indicating ‘moderate’ agreement on ballooning burden. 133 ballooned cells were identified using a ≥5/9 majority to train AI ballooning detection (AI-pathologist pairwise concordance 19–42%, comparable to inter-pathologist pairwise concordance of between 8–75%). AI quantified change in ballooned cell burden in response to therapy in a separate slide set. Conclusions: The substantial divergence in hepatocyte ballooning identified amongst expert hepatopathologists suggests that ballooning is a spectrum, too subjective for its presence or complete absence to be unequivocally determined as a trial endpoint. A concordance atlas may be used to train AI assistive technologies to reproducibly quantify ballooned hepatocytes that standardize assessment of therapeutic efficacy. This atlas serves as a reference standard for ongoing work to refine how ballooning is classified by both pathologists and AI. Lay summary: For the first time, we show that, even amongst expert hepatopathologists, there is poor agreement regarding the number of ballooned hepatocytes seen on the same digitized histology images. This has important implications as the presence of ballooning is needed to establish the diagnosis of non-alcoholic steatohepatitis (NASH), and its unequivocal absence is one of the key requirements to show ‘NASH resolution’ to support drug efficacy in clinical trials. Artificial intelligence-based approaches may provide a more reliable way to assess the range of injury recorded as “hepatocyte ballooning”. © 202

ESCMID and ECMM joint clinical guidelines for the diagnosis and management of rare invasive yeast infections

The mortality associated with invasive fungal infections remains high with that involving rare yeast pathogens other than Candida being no exception. This is in part due to the severe underlying conditions typically predisposing patients to these healthcare-related infections (most often severe neutropenia in patients with haematological malignancies), and in part due to the often challenging intrinsic susceptibility pattern of the pathogens that potentially leads to delayed appropriate antifungal treatment. A panel of experts of the European Society of Clinical Microbiology and Infectious Diseases (ESCMID) Fungal Infection Study Group (EFISG) and the European Confederation of Medical Mycology (ECMM) undertook a data review and compiled guidelines for the diagnostic tests and procedures for detection and management of rare invasive yeast infections. The rare yeast pathogens were defined and limited to the following genera/species: Cryptococcus adeliensis, Cryptococcus albidus, Cryptococcus curvatus, Cryptococcus flavescens, Cryptococcus laurentii and Cryptococcus uniguttulatus (often published under the name Filobasidium uniguttulatum), Malassezia furfur, Malassezia globosa, Malassezia pachydermatis and Malassezia restricta, Pseudozyma spp., Rhodotorula glutinis, Rhodotorula minuta and Rhodotorula mucilaginosa, Sporobolomyces spp., Trichosporon asahii, Trichosporon asteroides, Trichosporon dermatis, Trichosporon inkin, Trichosporon jirovecii, Trichosporon loubieri, Trichosporon mucoides and Trichosporon mycotoxinivorans and ascomycetous ones: Geotrichum candidum, Kodamaea ohmeri, Saccharomyces cerevisiae (incl. S. boulardii) and Saprochaete capitatae (Magnusiomyces (Blastoschizomyces) capitatus formerly named Trichosporon capitatum or Geotrichum (Dipodascus) capitatum) and Saprochaete clavata. Recommendations about the microbiological investigation and detection of invasive infection were made and current knowledge on the most appropriate antifungal and supportive treatment was reviewed. In addition, remarks about antifungal susceptibility testing were made. © 2013 European Society of Clinical Microbiology and Infectious Diseases