The spatial pattern of the vacuolation ('spongiform change') in the cerebral cortex in variant Creutzfeldt-Jakob disease (vCJD)

The spatial pattern of the vacuolation ('spongiform change') was studied in areas of the cerebral cortex in 11 cases of variant Creutzfeldt-Jakob disease (vCJD). The vacuoles were evenly distributed along the cortex in 40/106 (38%) areas studied and randomly distributed in 6/106 (5.6%) areas. In 22/106 (21%) areas, the vacuoles were aggregated into clusters, 50 - 1600 μm in diameter and which were distributed in a regular pattern parallel to the pia mater. In 38/106 (36%) areas, large clusters of vacuoles, at least 1600 μm in diameter, were present. No significant differences in spatial patterns were observed between the different cortical regions or between the upper and lower laminae. In addition, age at onset and duration of the disease had no significant affect on spatial patterns. The spatial distribution of the vacuolation contrasts with that reported in sporadic CJD (sCJD) suggesting a different pattern of cortical degeneration in vCJD.

Spatial pattern of prion protein deposits in patients with sporadic Creutzfeldt–Jakob disease

The spatial pattern of the prion protein (PrP) deposits was studied in the cerebral cortex and cerebellum in 10 patients with sporadic Creutzfeldt–Jakob disease (CJD). In all patients the PrP deposits were aggregated into clusters and, in 90% of cortical areas and in 50% of cerebellar sections, the clusters exhibited a regular periodicity parallel to the tissue boundary; a spatial pattern also exhibited by ß-amyloid (Aß) deposits in Alzheimer's disease (AD). In the cerebral cortex, the incidence of regular clustering of the PrP deposits was similar in the upper and lower cortical laminae. The sizes of the PrP clusters in the upper and lower cortex were uncorrelated. No significant differences in mean cluster size of the PrP deposits were observed between brain regions. The size, location and distribution of the PrP deposit clusters suggest that PrP deposition occurs in relation to specific anatomical pathways and supports the hypothesis that prion pathology spreads through the brain via such pathways. In addition, the data suggest that there are similarities in the pathogenesis of extracellular protein deposits in prion disease and in AD.

The spatial pattern of senile plaques, neurofibrillary tangles and A4 deposits in Alzheimer's disease

The spatial patterns of senile plaques (SP) and neurofibrillary tangles (NFT) as visualised using the Gallyas stain and of discrete A4 protein deposits were determined in coronal serial sections from a variety of brain regions in six elderly patients with Alzheimer's disease (AD). These lesions showed clustering in virtually all tissues examined with many of the clusters being regularly spaced. These spatial patterns were compared with the clustering observed for SP and NFT stained by the Glees and Marsland method in the same tissues. The data suggest that on average, while the regular clusters of A4 deposits and NFT were of approximately the same mean diameter (3600 microns), clusters of both Glees and Gallyas SP were approximately half this diameter (1800 - 2000 microns). If SP develop in local areas of the brain where both A4 deposition and neurofibrillary changes have occurred, the data suggest that the SP clusters would represent the region of overlap of the A4 deposits and neurofibrillary changes. Various hypothese are advocated to explain the regular clsuetring of the A4 deposits.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

The spatial pattern of the vacuolation in patients with sporadic Creutzfeldt-Jakob disease

The spatial pattern of the vacuolation ('spongiform change') was studied in the upper and lower laminae of the cerebral cortex, the CA1/CA2 sectors of the hippocampus and the molecular layer of the cerebellum in 11 cases of sporadic Creutzfeldt-Jakob disease (CJD). Individual vacuoles were grouped into clusters, 50 to >1600 μm in diameter and, in the majority of tissue sections, the vacuole clusters were distributed with regular periodicity parallel to the tissue boundary. The size of the vacuole clusters was positively correlated with patient age in the lower laminae of the occipital cortex and the inferior temporal gyrus (ITG) and negatively correlated with age in the hippocampus. In addition, the size of the vacuole clusters was positively correlated with disease duration in the upper laminae of the ITG. The size and distribution of the vacuole clusters suggests that the vacuolation in CJD reflects the degeneration of specific brain pathways and supports the hypothesis that prion pathology may spread through the brain along well defined anatomical pathways. (C) 2000 Elsevier Science Ireland Ltd.

The spatial pattern of discrete beta-amyloid deposits in Alzheimer's disease reflects synaptic disconnection

The spatial pattern of discrete beta-amyloid (A beta) deposits was studied in the superficial laminae of cortical fields of different types and in the hippocampus in 6 cases of Alzheimer's disease (AD). In 41/42 tissues examined, discrete A beta deposits were aggregated into clusters and in 34/41 tissues (25/34 of the cortical tissues), there was evidence for a regular periodicity of the A beta deposit clusters parallel to the tissue boundary. The dimensions of the clusters varied from 400 to > 12,800 microns in different tissues. Although the A beta deposit clusters were larger than predicted, the regular periodicity suggests that they develop in relation to groups of cells associated with specific projections. This would be consistent with the hypothesis that the distribution of discrete A beta deposits in AD could reflect progressive synaptic disconnection along interconnected neuronal pathways. This implies that amyloid deposition could be a response to, rather than a cause of, synaptic disconnection in AD.

Spatial pattern analysis of beta-amyloid (A beta) deposits in Alzheimer disease by linear regression

The spatial patterns of discrete beta-amyloid (Abeta) deposits in brain tissue from patients with Alzheimer disease (AD) were studied using a statistical method based on linear regression, the results being compared with the more conventional variance/mean (V/M) method. Both methods suggested that Abeta deposits occurred in clusters (400 to <12,800 mu m in diameter) in all but 1 of the 42 tissues examined. In many tissues, a regular periodicity of the Abeta deposit clusters parallel to the tissue boundary was observed. In 23 of 42 (55%) tissues, the two methods revealed essentially the same spatial patterns of Abeta deposits; in 15 of 42 (36%), the regression method indicated the presence of clusters at a scale not revealed by the V/M method; and in 4 of 42 (9%), there was no agreement between the two methods. Perceived advantages of the regression method are that there is a greater probability of detecting clustering at multiple scales, the dimension of larger Abeta clusters can be estimated more accurately, and the spacing between the clusters may be estimated. However, both methods may be useful, with the regression method providing greater resolution and the V/M method providing greater simplicity and ease of interpretation. Estimates of the distance between regularly spaced Abeta clusters were in the range 2,200-11,800 mu m, depending on tissue and cluster size. The regular periodicity of Abeta deposit clusters in many tissues would be consistent with their development in relation to clusters of neurons that give rise to specific neuronal projections.

The spatial pattern of beta-amyloid (Abeta) deposits in Alzheimer’s disease patients is related to apolipoprotein genotype

The spatial patterns of the diffuse, primitive, and classic beta-amyloid (Abeta) deposits was studied in the frontal and temporal cortex in cases of Alzheimer’s disease (AD) expressing different apolipoprotein (Apo E) genotypes. No significant differences in the density of the three Abeta deposit subtypes were observed in individuals expressing genotypes e2/3 and e3/3 compared with those expressing e3/4 and e4/4. In all patients, Abeta deposit subtypes occurred in the tissue in clusters. Chi-square contingency analyses of the data suggested that the cluster size of the diffuse and classic Abeta deposits was unrelated to Apo E genotype. However, the primitive (‘neuritic’) type Abeta deposits occurred more frequently in smaller, denser clusters in individuals expressing genotypes e3/4 and e4/4 compared with those expressing e2/3 and e3/3. Hence, the presence of the e4 allele may be associated with a more specific pattern of neuronal degeneration in the frontal and temporal cortex in AD.

The usefulness of spatial pattern analysis in understanding the pathogenesis of neurodegenerative disorders, with particular reference to plaque formation in Alzheimer's disease

Discrete, microscopic lesions are developed in the brain in a number of neurodegenerative diseases. These lesions may not be randomly distributed in the tissue but exhibit a spatial pattern, i.e., a departure from randomness towards regularlity or clustering. The spatial pattern of a lesion may reflect its development in relation to other brain lesions or to neuroanatomical structures. Hence, a study of spatial pattern may help to elucidate the pathogenesis of a lesion. A number of statistical methods can be used to study the spatial patterns of brain lesions. They range from simple tests of whether the distribution of a lesion departs from random to more complex methods which can detect clustering and the size, distribution and spacing of clusters. This paper reviews the uses and limitations of these methods as applied to neurodegenerative disorders, and in particular to senile plaque formation in Alzheimer's disease.

The relationship between the spatial pattern of senile plaques and neurofibrillary tangles in Alzheimer's disease

The topographic pattern of senile plaques (SP) and neurofibrillary tangles (NFT) was studied in silver stained coronal sections of neocortex and hippocampus in ten cases of Alzheimer's disease (AD). Both lesions showed evidence of clustering in the tissue with many of the clusters being regularly spaced. The patterns of SP and NFT were compared 1) in the same cortical zone, 2) between upper and lower zones of the cortex and 3) in regions connected by either association fibres or the perforant path. Correlations between the lesions in the same cortical zone were found in 20% of the layers examined while correlations between upper and lower zones occurred in 64% of cortical regions examined. There was evidence that NFT in upper and lower cortex may be in register in some tissues. In addition, positive correlations were found between upper NFT and lower SP and negative correlations between upper SP and lower NFT in some tissues. Regular clustering of lesions was also observed in brain regions connected to one another suggesting that they develop on functinally related sets of neurons.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

A spatial pattern analysis of beta-amyloid (Abeta) deposition in the temporal lobe in Alzheimer's disease

To determine the factors influencing the distribution of -amyloid (Abeta) deposits in Alzheimer's disease (AD), the spatial patterns of the diffuse, primitive, and classic A deposits were studied from the superior temporal gyrus (STG) to sector CA4 of the hippocampus in six sporadic cases of the disease. In cortical gyri and in the CA sectors of the hippocampus, the Abeta deposits were distributed either in clusters 200-6400 microm in diameter that were regularly distributed parallel to the tissue boundary or in larger clusters greater than 6400 microm in diameter. In some regions, smaller clusters of Abeta deposits were aggregated into larger 'superclusters'. In many cortical gyri, the density of Abeta deposits was positively correlated with distance below the gyral crest. In the majority of regions, clusters of the diffuse, primitive, and classic deposits were not spatially correlated with each other. In two cases, double immunolabelled to reveal the Abeta deposits and blood vessels, the classic Abeta deposits were clustered around the larger diameter vessels. These results suggest a complex pattern of Abeta deposition in the temporal lobe in sporadic AD. A regular distribution of Abeta deposit clusters may reflect the degeneration of specific cortico-cortical and cortico-hippocampal pathways and the influence of the cerebral blood vessels. Large-scale clustering may reflect the aggregation of deposits in the depths of the sulci and the coalescence of smaller clusters.

Excitation of higher spatial harmonics by a moving light pattern in sillenites

We investigate numerically the dependence of higher harmonics of the space-charge field on the detuning frequency between the pump waves, which form a running interference pattern. Bistability and hysteresis of harmonics are predicted for a contrast of the interference pattern m =(0.25-0.3). For contrasts m˜1 and small detuning frequencies we show the existence of a narrow resonance, connected with the nonlinear excitation of a slowly decreasing sequence of spatial harmonics. For experiments we use a BSO crystal in the optical configuration which avoids nonlinear optical distortions. The experimental data show good qualitative agreement with theory.