Steklov problem on differential forms

In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\Lambda$ is shown to be self-adjoint on the subspace of coclosed forms and to have purely discrete spectrum there.We investigate properies of eigenvalues of $\Lambda$ and prove a Hersch-Payne-Schiffer type inequality relating products of those eigenvalues to eigenvalues of Hodge Laplacian on the boundary. Moreover, non-trivial eigenvalues of $\Lambda$ are always at least as large as eigenvalues of Dirichlet-to-Neumann map defined by Raulot and Savo. Finally, we remark that a particular case of $p$-forms on the boundary of $2p+2$-dimensional manifold shares a lot of important properties with the classical Steklov eigenvalue problem on surfaces.Comment: 18 page

The transmethylation cycle in the brain of Alzheimer patients

Homocysteine accumulation, frequently observed in plasma of AD patients, may be a sign of a reduced activity of the brain methionine-homocysteine transmethylation cycle. S-Adenosylmethionine (SAM) is the main methyl donor in several transmethylation reactions. The demethylated product of SAM, S-adenosylhomocysteine (SAH), is hydrolyzed to yield homocysteine, which can be remethylated to methionine by transfer of a methyl group of 5- methyltetrahydrofolate (5-MTHF). A reduced activity of the transmethylation cycle in the brain may result in hypomethylation of the promoter of the presenilin 1 (PS1) gene, which will lead to overexpression of presenilin 1 and, consequently, to increased Aβ1-42 (Aβ42) formation. Brain transmethylation was studied in 30 patients with 'probable' AD and 28 age-matched non-demented controls by measuring the cerebrospinal fluid (CSF) levels of SAM, SAH and 5-MTHF. 5-MTHF was determined by HPLC with electrochemical detection, while SAM and SAH were assayed by stable isotope dilution tandem mass spectrometry. We found no statistical differences between AD patients and controls for 5-MTHF, SAM and SAH levels, and the SAM/SAH-ratio in CSF. These findings argue against a possible change in methylation of the promoter and expression of PS1

Total tau and phosphorylated tau 181 levels in the cerebrospinal fluid of patients with frontotemporal dementia due to P301L and G272V tau mutations

Background: Frontotemporal dementia (FTD) is a pathologically heterogeneous group of presenile neurodegenerative disorders, with or without the deposition of hyperphosphorylated tau protein in affected brain regions. Mutations in the tau gene have been found in the familial form of FTD, linked to chromosome 17q21-22, showing a spectrum of tauopathy. Objective: To evaluate levels of total tau, phosphorylated tau 181 (Ptau-181), and amyloid-β 1-42 in the cerebrospinal fluid (CSF) of patients with FTD, with special emphasis on FTD due to tau mutations. Design: Case-control study. Setting: Outpatient neurology clinics at 2 university medical centers, in Rotterdam and Amsterdam (the Netherlands). Patients: Twenty-six patients with FTD (9 with tau mutations 7 P301L and 2 G272V), 18 patients with Alzheimer disease (AD), and 13 nondemented controls. Methods: Total tau, Ptau-181, and amyloid-β1-42 levels in CSF, obtained by lumbar puncture, were determined by sandwich enzyme-linked immunosorbent assay. Patients were diagnosed after clinical examination, neuropsychologic evaluation, and neuroimaging. Differences between patient groups were statistically evaluated using nonparametric tests. Results: Although CSF levels of total tau were mildly increased in FTD patients compared with nondemented controls (P = .05), median CSF total tau levels were low in the subgroup with tau mutations compared with AD patients. Furthermore, CSF levels of Ptau-181 and amyloid-β1-42 were not different in FTD patients, including the patients with tau mutations, compared with nondemented controls. Conclusions: The tauopathy in P301L and G272V does not appear to be associated with an evident increase in CSF levels of Ptau-181 in FTD patients with these tau mutations, in contrast with findings in patients with AD

Amyloid β 38, 40, and 42 species in cerebrospinal fluid: More of the same?

Various C-terminally truncated amyloid β peptides (Aβ) are linked to Alzheimer's disease (AD) pathogenesis. Cerebrospinal fluid (CSF) concentrations of Aβ38, Aβ40, and Aβ42 were measured by enzyme-linked immunosorbent assay in 30 patients with AD and 26 control subjects. CSF Aβ42 levels was decreased in patients with AD, whereas CSF Aβ38 and Aβ40 levels were similar in patients with AD and control subjects. All three Aβ peptides were interrelated, particularly CSF Aβ38 and Aβ40. Diagnostic accuracy of CSF Aβ42 concentrations was not improved by applying the ratios of CSF Aβ42 to Aβ38 or Aβ40

Decision tree supports the interpretation of CSF biomarkers in Alzheimer's disease

Introduction: We developed and validated a clinically applicable decision tree for the use of cerebrospinal fluid biomarkers in the diagnosis of Alzheimer's disease (AD). Methods: Subjects with probable AD (n = 1004) and controls (n = 442) were included. A decision tree was modeled using Classification And Regression Tree analysis in a training cohort (AD n = 221; controls n = 221) and validated in an independent cohort (AD n = 783; controls n = 221). Diagnostic performance was compared to previously defined cutoffs (amyloid β 1-42 375 pg/ml). Results: Two cerebrospinal fluid AD biomarker profiles were revealed: the “classical” AD biomarker profile (amyloid β 1-42: 647-803 pg/ml; tau >374 pg/ml) and an “atypical” AD biomarker profile with strongly decreased amyloid β 1-42 (<647 pg/ml) and normal tau concentrations (<374 pg/ml). Compared to previous cutoffs, the decision tree performed better on diagnostic accuracy (86% [84-88] vs 80% [78-83]). Discussion: Two cerebrospinal fluid AD biomarker profiles were identified and incorporated in a readily applicable decision tree, which improved diagnostic accuracy

Effects of processing and storage conditions on amyloid β (1-42) and tau concentrations in cerebrospinal fluid: Implications for use in clinical practice

Background: Reported concentrations of amyloid β (1-42) (Aβ42) and tau in cerebrospinal fluid (CSF) differ among reports. We investigated the effects of storage temperature, repeated freeze/thaw cycles, and centrifugation on the concentrations of Aβ42 and tau in CSF. Methods: Stability of samples stored at -80 °C was determined by use of an accelerated stability testing protocol according to the Arrhenius equation. Aβ42 and tau concentrations were measured in CSF samples stored at 4, 18, 37, and -80 °C. Relative CSF concentrations (%) of the biomarkers after one freeze/thaw cycle were compared with those after two, three, four, five, and six freeze/thaw cycles. In addition, relative Aβ42 and tau concentrations in samples not centrifuged were compared with samples centrifuged after 1, 4, 48, and 72 h. Results: Aβ42 and tau concentrations were stable in CSF when stored for a long period at -80 °C. CSF Aβ42 decreased by 20% during the first 2 days at 4, 18, and 37 °C compared with -80 °C. CSF tau decreased after storage for 12 days at 37 °C. After three freeze/thaw cycles, CSF Aβ42 decreased 20%. CSF tau was stable during six freeze/thaw cycles. Centrifugation did not influence the biomarker concentrations. Conclusions: Repeated freeze/thaw cycles and storage at 4, 18, and 37 °C influence the quantitative result of the Aβ42 test. Preferably, samples should be stored at -80 °C immediately after collection