Laminar distribution of the pathological changes in sporadic frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy:a quantitative study using polynomial curve fitting

Aims: Previous data suggest heterogeneity in laminar distribution of the pathology in the molecular disorder frontotemporal lobar degeneration (FTLD) with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy (FTLD-TDP). To study this heterogeneity, we quantified the changes in density across the cortical laminae of neuronal cytoplasmic inclusions, glial inclusions, neuronal intranuclear inclusions, dystrophic neurites, surviving neurones, abnormally enlarged neurones, and vacuoles in regions of the frontal and temporal lobe. Methods: Changes in density of histological features across cortical gyri were studied in 10 sporadic cases of FTLD-TDP using quantitative methods and polynomial curve fitting. Results: Our data suggest that laminar neuropathology in sporadic FTLD-TDP is highly variable. Most commonly, neuronal cytoplasmic inclusions, dystrophic neurites and vacuolation were abundant in the upper laminae and glial inclusions, neuronal intranuclear inclusions, abnormally enlarged neurones, and glial cell nuclei in the lower laminae. TDP-43-immunoreactive inclusions affected more of the cortical profile in longer duration cases; their distribution varied with disease subtype, but was unrelated to Braak tangle score. Different TDP-43-immunoreactive inclusions were not spatially correlated. Conclusions: Laminar distribution of pathological features in 10 sporadic cases of FTLD-TDP is heterogeneous and may be accounted for, in part, by disease subtype and disease duration. In addition, the feedforward and feedback cortico-cortical connections may be compromised in FTLD-TDP. © 2012 The Authors. Neuropathology and Applied Neurobiology © 2012 British Neuropathological Society.

White matter pathology in progressive supranuclear palsy (PSP):a quantitative study of 8 cases

Aims: To quantify white matterpathology in progressive supranuclear palsy (PSP). Material: Histological sections of white matter of 8 PSP and 8 control cases \Method: Densities and spatial patterns of vacuolation, glial cell nuclei, and glial inclusions (GI) were measured in 8cortical and subcortical fiber tracts. Results: No GI wereobserved in control fiber tracts. Densities of vacuoles and glial cell nuclei were greater in PSP than in controls. In PSP, density of vacuoles was greatest in the alveus, frontopontine fibers (FPF), and central tegmental tract (CTT), and densities of glial cell nuclei were greater in cortical than subcortical regions.The highest densities of GI were observed in the basal ganglia, FPF, cerebellum, andsuperior frontal gyrus (SFG). Vacuoles, glialcells and GI were distributed randomly, uniformly,in regularly distributed clusters, or in large clusters across fiber tracts. GI wermore frequently distributed in regular clusters than the vacuoles and glial cell nuclei.Vacuoles, glial cell nuclei, and GI were not spatially correlated. Conclusions: The data suggest significant degeneration of white matter in PSP, vacuolation being related to neuronal loss in adjacent gray matterregions,GI the result of abnormal tau released from damaged axons, and gliosis a responseto these changes. © 2013.

Two-dimensional viscoelastic discrete triangular system with negative-stiffness components

Potential applications of high-damping and high-stiffness composites have motivated extensive research on the effects of negative-stiffness inclusions on the overall properties of composites. Recent theoretical advances have been based on the Hashin-Shtrikman composite models, one-dimensional discrete viscoelastic systems and a two-dimensional nested triangular viscoelastic network. In this paper, we further analyze the two-dimensional triangular structure containing pre-selected negative-stiffness components to study its underlying deformation mechanisms and stability. Major new findings are structure-deformation evolution with respect to the magnitude of negative stiffness under shear loading and the phenomena related to dissipation-induced destabilization and inertia-induced stabilization, according to Lyapunov stability analysis. The evolution shows strong correlations between stiffness anomalies and deformation modes. Our stability results reveal that stable damping peaks, i.e. stably extreme effective damping properties, are achievable under hydrostatic loading when the inertia is greater than a critical value. Moreover, destabilization induced by elemental damping is observed with the critical inertia. Regardless of elemental damping, when the inertia is less than the critical value, a weaker system instability is identified.

Anomalies in stiffness and damping of a 2D discrete viscoelastic system due to negative stiffness components

The recent development of using negative stiffness inclusions to achieve extreme overall stiffness and mechanical damping of composite materials reveals a new avenue for constructing high performance materials. One of the negative stiffness sources can be obtained from phase transforming materials in the vicinity of their phase transition, as suggested by the Landau theory. To understand the underlying mechanism from a microscopic viewpoint, we theoretically analyze a 2D, nested triangular lattice cell with pre-chosen elements containing negative stiffness to demonstrate anomalies in overall stiffness and damping. Combining with current knowledge from continuum models, based on the composite theory, such as the Voigt, Reuss, and Hashin-Shtrikman model, we further explore the stability of the system with Lyapunov's indirect stability theorem. The evolution of the microstructure in terms of the discrete system is discussed. A potential application of the results presented here is to develop special thin films with unusual in-plane mechanical properties. © 2006 Elsevier B.V. All rights reserved.

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

Intragranular nucleation of austenite

The mechanism of intragranular nucleation of austenite in a duplex stainless steel (Fe-23.1 Cr-6.1 Ni-3.1 Mo-O.165 N-0.017 C, wt.%) weld metal and heat-affected zone (HAZ) has been examined. In the weld metal the acicular austenite is found to nucleate intragranularly on inclusions and subsequent plates form sympathetically resulting in a fine interlocked microstructure. Austenite plates adopt the Kurdjumov-Sachs orientation relationship with the ferrite matrix and grow with diffusion-controlled mechanism as evident from partitioning of substitutional alloying elements. At least one set of fine intrinsic dislocations on the austenite/ferrite interphase interfaces is observed suggesting that the boundaries are semi-coherent. The high cooling rates involved in the HAZ result in a supersaturated ferrite matrix where precipitation of intragranular austenite occurs as a result of reheating associated with subsequent passes. Austenite particles in the HAZ nucleate preferentially away from gain boundary austenite allotriomorphs indicating that intragranular precipitation is favoured by the supersaturated matrix.

Variations in dentate gyrus pathology in neurodegenerative disease

The dentate gyrus (DG) is an important part of the hippocampal formation and is believed to be involved in a variety of brain functions including episodic and spatial memory and the exploration of novel environments. In several neurodegenerative disorders, significant pathology occurs in the DG which may be involved in the development of clinical dementia. Based on the abundance of pathological change, neurodegenerative disorders could be divided into three groups: (1) those in which high densities of neuronal cytoplasmic inclusions (NCI) were present in DG granule cells, e.g., Pick’s disease (PiD), frontotemporal lobar degeneration with TDP-43-immunoreactive inclusions (FTLD-TDP), and neuronal intermediate filament inclusion disease (NIFID), (2) those in which aggregated protein deposits were distributed throughout the hippocampal formation including the molecular layer of the DG, e.g., Alzheimer’s disease (AD), Down’s syndrome (DS), and variant Creutzfeldt-Jakob disease (vCJD), and (3) those in which in there was significantly less pathology in the DG, e.g., Parkinson’s disease dementia (PD-Dem), dementia with Lewy bodies (DLB), progressive supranuclear palsy (PSP), corticobasal degeneration (CBD), multiple system atrophy (MSA), and sporadic CJD (sCJD). Hence, DG pathology varied significantly among disorders which could contribute to differences in clinical dementia. Pathological differences among disorders could reflect either differential vulnerability of the DG to specific molecular pathologies or variation in the degree of spread of pathological proteins into the hippocampal formation from adjacent regions.

Cortical degeneration in frontotemporal lobar degeneration with TDP-43 proteinopathy caused by progranulin gene mutation

Familial frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43 kDa (TDP-43) proteinopathy (FTLD-TDP) is most commonly caused by progranulin (GRN) gene mutation. To characterize cortical degeneration in these cases, changes in density of the pathology across the cortical laminae of the frontal and temporal lobe were studied in seven cases of FTLD-TDP with GRN mutation using quantitative analysis and polynomial curve fitting. In 50% of gyri studied, neuronal cytoplasmic inclusions (NCI) exhibited a peak of density in the upper cortical laminae. Most frequently, neuronal intranuclear inclusions (NII) and dystrophic neurites (DN) exhibited a density peak in lower and upper laminae, respectively, glial inclusions (GI) being distributed in low densities across all laminae. Abnormally enlarged neurons (EN) were distributed either in the lower laminae or were more uniformly distributed across the cortex. The distribution of all neurons present varied between cases and regions, but most commonly exhibited a bimodal distribution, density peaks occurring in upper and lower laminae. Vacuolation primarily affected the superficial laminae and density of glial cell nuclei increased with distance across the cortex from pia mater to white matter. The densities of the NCI, GI, NII, and DN were not spatially correlated. The laminar distribution of the pathology in GRN mutation cases was similar to previously reported sporadic cases of FTLD-TDP. Hence, pathological changes initiated by GRN mutation, and by other causes in sporadic cases, appear to follow a parallel course resulting in very similar patterns of cortical degeneration in FTLD-TDP.

Corticobasal degeneration and dementia

Corticobasal degeneration is a rare, progressive neurodegenerative disorder which significantly impairs movement. The most common initial symptom is asymmetric limb clumsiness with or without accompanying rigidity or tremor. Subsequently, the disease progresses to affect gait and there is a slow progression to influence ipsilateral arms and legs. Apraxia and dementia are the most common cortical signs. Clinical diagnosis of the disorder is difficult as the symptoms resemble those of related neurodegenerative disorders. Histopathologically, there is widespread neuronal and glial pathology including tau-immunoreactive neuronal cytoplasmic inclusions, neuropil threads, oligodendroglial inclusions, astrocytic plaques, together with abnormally enlarged ‘ballooned’ neurons. Corticobasal degeneration has affinities both with the parkinsonian syndromes including Parkinson’s disease, progressive supranuclear palsy, and multiple system atrophy and with the fronto-temporal dementias. Treatment of corticobasal degeneration involves managing and reducing the effect of symptoms.

Pathology of the dentate gyrus in neurodegenerative disease

The dentate gyrus (DG) is an important part of the hippocampal formation and is believed to be involved in a variety of brain functions including episodic and spatial memory and the exploration of novel environments. In several neurodegenerative disorders, significant pathology occurs in the DG which may be involved in the development of clinical dementia. Based on the abundance of pathological change, neurodegenerative disorders can be divided into three groups: (1) those in which high densities of neuronal cytoplasmic inclusions (NCI) are present in DG granule cells, e.g., Pick’s disease (PiD), frontotemporal lobar degeneration with TDP-43-immunoreactive inclusions (FTLD-TDP), and neuronal intermediate filament inclusion disease (NIFID), (2) those in which aggregated protein deposits are distributed throughout the hippocampal formation including the molecular layer of the DG, e.g., Alzheimer’s disease (AD), Down’s syndrome (DS), and variant Creutzfeldt-Jakob disease (vCJD), and (3) those in which in there is significantly less pathology in the DG, e.g., Parkinson’s disease dementia (PD-Dem), dementia with Lewy bodies (DLB), progressive supranuclear palsy (PSP), corticobasal degeneration (CBD), multiple system atrophy (MSA), and sporadic CJD (sCJD). Hence, DG pathology varies significantly among disorders which could contribute to differences in clinical dementia. Pathological differences among disorders could reflect either differential vulnerability of the DG to specific molecular pathologies or variation in the degree of spread of pathological proteins into the hippocampal formation from adjacent regions.

A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

Stability of the Iteration Method for non Expansive Mappings

The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.

Comparative quantitative study of ‘signature’ pathological lesions in the hippocampus and adjacent gyri of 12 neurodegenerative disorders

The hippocampus (HC) and adjacent gyri are implicated in dementia in several neurodegenerative disorders. To compare HC pathology among disorders, densities of ‘signature’ pathological lesions were measured at a standard location in eight brain regions of 12 disorders. Principal components analysis of the data suggested that the disorders could be divided into three groups: (1) Alzheimer’s disease (AD), Down’s syndrome (DS), sporadic Creutzfeldt–Jakob disease, and variant Creutzfeldt–Jakob disease in which either β-amyloid (Aβ) or prion protein deposits were distributed in all sectors of the HC and adjacent gyri, with high densities being recorded in the parahippocampal gyrus and subiculum; (2) Pick’s disease, sporadic frontotemporal lobar degeneration with TDP-43 immunoreactive inclusions, and neuronal intermediate filament inclusion disease in which relatively high densities of neuronal cytoplasmic inclusions were present in the dentate gyrus (DG) granule cells; and (3) Parkinson’s disease dementia, dementia with Lewy bodies, progressive supranuclear palsy, corticobasal degeneration, and multiple system atrophy in which densities of signature lesions were relatively low. Variation in density of signature lesions in DG granule cells and CA1 were the most important sources of neuropathological variation among disorders. Hence, HC and adjacent gyri are differentially affected in dementia reflecting either variation in vulnerability of hippocampal neurons to specific molecular pathologies or in the spread of pathological proteins to the HC. Information regarding the distribution of pathology could ultimately help to explain variations in different cognitive domains, such as memory, observed in various disorders.

Viability Kernels of Higher Order

AMS subject classification: Primary 34A60, Secondary 49K24.

Quantitative pathological changes in the cerebellum of multiple system atrophy

Multiple system atrophy (MSA) is a rare neurodegenerative disorder associated with parkinsonism, ataxia, and autonomic dysfunction. Its pathology is primarily subcortical comprising vacuolation, neuronal loss, gliosis, and α-synuclein-immunoreactive glial cytoplasmic inclusions (GO). To quantify cerebellar pathology in MSA, the density and spatial pattern of the pathological changes were studied in α-synuclein-immunolabelled sections of the cerebellar hemisphere in 10 MSA and 10 control cases. In MSA, densities of Purkinje cells (PC) were decreased and vacuoles in the granule cell layer (GL) increased compared with controls. In six MSA cases, GCI were present in cerebellar white matter. In the molecular layer (ML) and GL of MSA, vacuoles were clustered, the clusters exhibiting a regular distribution parallel to the edge of the folia. Purkinje cells were randomly or regularly distributed with large gaps between surviving cells. Densities of glial cells and surviving neurons in the ML and surviving cells and vacuoles in the GL were negatively correlated consistent with gliosis and vacuolation in response to neuronal loss. Principal components analysis (PCA) suggested vacuole densities in the ML and vacuole density and cell losses in the GL were the main source of neuropathological variation among cases. The data suggest that: (1) cell losses and vacuolation of the GCL and loss of PC were the most significant pathological changes in the cases studied, (2) pathological changes were topographically distributed, and (3) cerebellar pathology could influence cerebral function in MSA via the cerebello-dentato-thalamic tract.