A posteriori error estimates for elliptic problems in two and three space dimensions

Let $u \in H$ be the exact solution of a given selfadjoint elliptic boundary value problem, which is approximated by some $\tilde u \in \mathcal{S}$, $\mathcal{S}$ being a suitable finite-element space. Efficient and reliable a posteriors estimates of the error $\| {u - \tilde u} \|$, measuring the (local) quality of $\tilde u$, play a crucial role in termination criteria and in the adaptive refinement of the underlying mesh. A well-known class of error estimates can be derived systematically by localizing the discretized defect problem by using domain decomposition techniques. In this paper, we provide a guideline for the theoretical analysis of such error estimates. We further clarify the relation to other concepts. Our analysis leads to new error estimates, which are specially suited to three space dimensions. The theoretical results are illustrated by numerical computations

Adaptive multilevel-methods for obstacle problems in three space dimensions

We consider the discretization of obstacle problems for second order elliptic differential operators in three space dimensions by piecewise linear finite elements. Linearizing the discrete problems by suitable active set strategies, the resulting linear sub-problems are solved iteratively by preconditioned cg-iterations. We propose a variant of the BPX preconditioner and prove an O(j) estimate for the resulting condition number To allow for local mesh refinement we derive semi-local and local a posteriori error estimates. The theoretical results are illustrated by numerical computations

Validation of the German Revised Addenbrooke's Cognitive Examination for Detecting Mild Cognitive Impairment, Mild Dementia in Alzheimer's Disease and Frontotemporal Lobar Degeneration

Background/Aims: The diagnostic accuracy of the German version of the revised Addenbrooke's Cognitive Examination (ACE-R) in identifying mild cognitive impairment (MCI), mild dementia in Alzheimer's disease (AD) and mild dementia in frontotemporal lobar degeneration (FTLD) in comparison with the conventional Mini Mental State Examination (MMSE) was assessed. Methods: The study encompasses 76 cognitively healthy elderly individuals, 75 patients with MCI, 56 with AD and 22 with FTLD. ACE-R and MMSE were validated against an expert diagnosis based on a comprehensive diagnostic procedure. Statistical analysis was performed using the receiver operating characteristic method and regression analyses. Results: The optimal cut-off score for the ACE-R for detecting MCI, AD, and FTLD was 86/87, 82/83 and 83/84, respectively. ACE-R was superior to MMSE only in the detection of patients with FTLD {[}area under the curve (AUC): 0.97 vs. 0.92], whilst the accuracy of the two instruments did not differ in identifying MCI and AD. The ratio of the scores of the memory ACE-R subtest to verbal fluency subtest contributed significantly to the discrimination between AD and FTLD (optimal cut-off score: 2.30/2.31, AUC: 0.77), whereas the MMSE and ACE-R total scores did not. Conclusion: The German ACE-R is superior to the most commonly employed MMSE in detecting mild dementia in FTLD and in the differential diagnosis between AD and FTLD. Thus it might serve as a valuable instrument as part of a comprehensive diagnostic workup in specialist centres/clinics contributing to the diagnosis and differential diagnosis of the cause of dementia. Copyright (C) 2010 S. Karger AG, Base

Cerebrospinal Fluid Cortisol and Dehydroepiandrosterone Sulfate, Alzheimer's Disease Pathology, and Cognitive Decline.

Elevated cortisol levels have been reported in Alzheimer's disease (AD) and may accelerate the development of brain pathology and cognitive decline. Dehydroepiandrosterone sulfate (DHEAS) has anti-glucocorticoid effects and it may be involved in the AD pathophysiology. To investigate associations of cerebrospinal fluid (CSF) cortisol and DHEAS levels with (1) cognitive performance at baseline; (2) CSF biomarkers of amyloid pathology (as assessed by CSF Aβ levels), neuronal injury (as assessed by CSF tau), and tau hyperphosphorylation (as assessed by CSF p-tau); (3) regional brain volumes; and (4) clinical disease progression. Individuals between 49 and 88 years (n = 145) with mild cognitive impairment or dementia or with normal cognition were included. Clinical scores, AD biomarkers, brain MRI volumetry along with CSF cortisol and DHEAS were obtained at baseline. Cognitive and functional performance was re-assessed at 18 and 36 months from baseline. We also assessed the following covariates: apolipoprotein E (APOE) genotype, BMI, and education. We used linear regression and mixed models to address associations of interest. Higher CSF cortisol was associated with poorer global cognitive performance and higher disease severity at baseline. Cortisol and cortisol/DHEAS ratio were positively associated with tau and p-tau CSF levels, and negatively associated with the amygdala and insula volumes at baseline. Higher CSF cortisol predicted more pronounced cognitive decline and clinical disease progression over 36 months. Higher CSF DHEAS predicted more pronounced disease progression over 36 months. Increased cortisol in the CNS is associated with tau pathology and neurodegeneration, and with decreased insula and amygdala volume. Both CSF cortisol and DHEAS levels predict faster clinical disease progression. These results have implications for the identification of patients at risk of rapid decline as well as for the development of interventions targeting both neurodegeneration and clinical manifestations of AD

Novel Psychoactive Substances 14Recent Progress on Neuropharmacological Mechanisms of Action for Selected Drugs

A feature of human culture is that we can learn to consume chemical compounds, derived from natural plants or synthetic fabrication, for their psychoactive effects. These drugs change the mental state and/or the behavioral performance of an individual and can be instrumentalized for various purposes. After the emergence of a novel psychoactive substance (NPS) and a period of experimental consumption, personal and medical benefits and harm potential of the NPS can be estimated on evidence base. This may lead to a legal classification of the NPS, which may range from limited medical use, controlled availability up to a complete ban of the drug form publically accepted use. With these measures, however, a drug does not disappear, but frequently continues to be used, which eventually allows an even better estimate of the drug 19s properties. Thus, only in rare cases, there is a final verdict that is no more questioned. Instead, the view on a drug can change from tolerable to harmful but may also involve the new establishment of a desired medical application to a previously harmful drug. Here, we provide a summary review on a number of NPS for which the neuropharmacological evaluation has made important progress in recent years. They include mitragynine ( 1CKratom 1D), synthetic cannabinoids (e.g., 1CSpice 1D), dimethyltryptamine and novel serotonergic hallucinogens, the cathinones mephedrone and methylone, ketamine and novel dissociative drugs, ;3-hydroxybutyrate, ;3-butyrolactone, and 1,4-butanediol. This review shows not only emerging harm potentials but also some potential medical applications

Anatomy, morphology and evolution of the patella in squamate lizards and tuatara (Sphenodon punctatus)

The patella (kneecap) is the largest and best-known of the sesamoid bones, postulated to confer biomechanical advantages including increasing joint leverage and reinforcing the tendon against compression. It has evolved several times independently in amniotes, but despite apparently widespread occurrence in lizards, the patella remains poorly characterised in this group and is, as yet, completely undescribed in their nearest extant relative Sphenodon (Rhynchocephalia). Through radiography, osteological and fossil studies we examined patellar presence in diverse lizard and lepidosauromorph taxa, and using computed tomography, dissection and histology we investigated in greater depth the anatomy and morphology of the patella in 16 lizard species and 19 Sphenodon specimens. We have found the first unambiguous evidence of a mineralised patella in Sphenodon, which appears similar to the patella of lizards and shares several gross and microscopic anatomical features. Although there may be a common mature morphology, the squamate patella exhibits a great deal of variability in development (whether from a cartilage anlage or not, and in the number of mineralised centres) and composition (bone, mineralised cartilage or fibrotendinous tissue). Unlike in mammals and birds, the patella in certain lizards and Sphenodon appears to be a polymorphic trait. We have also explored the evolution of the patella through ancestral state reconstruction, finding that the patella is ancestral for lizards and possibly Lepidosauria as a whole. Clear evidence of the patella in rhynchocephalian or stem lepidosaurian fossil taxa would clarify the evolutionary origin(s) of the patella, but due to the small size of this bone and the opportunity for degradation or loss we could not definitively conclude presence or absence in the fossils examined. The pattern of evolution in lepidosaurs is unclear but our data suggest that the emergence of this sesamoid may be related to the evolution of secondary ossification centres and/or changes in knee joint conformation, where enhancement of extensor muscle leverage would be more beneficial.Sophie Regnault, Marc E. H. Jones, Andrew A. Pitsillides, John R. Hutchinso

A monotone multigrid solver for two body contact problems in biomechanics

The purpose of the paper is to apply monotone multigrid methods to static and dynamic biomechanical contact problems. In space, a finite element method involving a mortar discretization of the contact conditions is used. In time, a new contact-stabilized Newmark scheme is presented. Numerical experiments for a two body Hertzian contact problem and a biomechanical application are reported

Plasma neurofilament light and phosphorylated tau 181 as biomarkers of Alzheimer's disease pathology and clinical disease progression.

To assess the performance of plasma neurofilament light (NfL) and phosphorylated tau 181 (p-tau181) to inform about cerebral Alzheimer's disease (AD) pathology and predict clinical progression in a memory clinic setting. Plasma NfL and p-tau181, along with established cerebrospinal fluid (CSF) biomarkers of AD pathology, were measured in participants with normal cognition (CN) and memory clinic patients with cognitive impairment (mild cognitive impairment and dementia, CI). Clinical and neuropsychological assessments were performed at inclusion and follow-up visits at 18 and 36 months. Multivariate analysis assessed associations of plasma NfL and p-tau181 levels with AD, single CSF biomarkers, hippocampal volume, and clinical measures of disease progression. Plasma NfL levels were higher in CN participants with an AD CSF profile (defined by a CSF p-tau181/Aβ <sub>1-42</sub> > 0.0779) as compared with CN non-AD, while p-tau181 plasma levels were higher in CI patients with AD. Plasma NfL levels correlated with CSF tau and p-tau181 in CN, and with CSF tau in CI patients. Plasma p-tau181 correlated with CSF p-tau181 in CN and with CSF tau, p-tau181, Aβ <sub>1-42</sub> , and Aβ <sub>1-42</sub> /Aβ <sub>1-40</sub> in CI participants. Compared with a reference model, adding plasma p-tau181 improved the prediction of AD in CI patients while adding NfL did not. Adding p-tau181, but not NfL levels, to a reference model improved prediction of cognitive decline in CI participants. Plasma NfL indicates neurodegeneration while plasma p-tau181 levels can serve as a biomarker of cerebral AD pathology and cognitive decline. Their predictive performance depends on the presence of cognitive impairment

Plasma neurofilament light and phosphorylated tau 181 as biomarkers of Alzheimer's disease pathology and clinical disease progression.

BACKGROUND: To assess the performance of plasma neurofilament light (NfL) and phosphorylated tau 181 (p-tau181) to inform about cerebral Alzheimer's disease (AD) pathology and predict clinical progression in a memory clinic setting. METHODS: Plasma NfL and p-tau181, along with established cerebrospinal fluid (CSF) biomarkers of AD pathology, were measured in participants with normal cognition (CN) and memory clinic patients with cognitive impairment (mild cognitive impairment and dementia, CI). Clinical and neuropsychological assessments were performed at inclusion and follow-up visits at 18 and 36 months. Multivariate analysis assessed associations of plasma NfL and p-tau181 levels with AD, single CSF biomarkers, hippocampal volume, and clinical measures of disease progression. RESULTS: Plasma NfL levels were higher in CN participants with an AD CSF profile (defined by a CSF p-tau181/Aβ1-42 > 0.0779) as compared with CN non-AD, while p-tau181 plasma levels were higher in CI patients with AD. Plasma NfL levels correlated with CSF tau and p-tau181 in CN, and with CSF tau in CI patients. Plasma p-tau181 correlated with CSF p-tau181 in CN and with CSF tau, p-tau181, Aβ1-42, and Aβ1-42/Aβ1-40 in CI participants. Compared with a reference model, adding plasma p-tau181 improved the prediction of AD in CI patients while adding NfL did not. Adding p-tau181, but not NfL levels, to a reference model improved prediction of cognitive decline in CI participants. CONCLUSION: Plasma NfL indicates neurodegeneration while plasma p-tau181 levels can serve as a biomarker of cerebral AD pathology and cognitive decline. Their predictive performance depends on the presence of cognitive impairment