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.

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.

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 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.

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.

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

To determine the factors influencing the distribution of β-amyloid (Aβ) deposits in Alzheimer's disease (AD), the spatial patterns of the diffuse, primitive, and classic Aβ 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 Aβ deposits were distributed either in clusters 200-6400 μm in diameter that were regularly distributed parallel to the tissue boundary or in larger clusters greater than 6400 μm in diameter. In some regions, smaller clusters of Aβ deposits were aggregated into larger 'superclusters'. In many cortical gyri, the density of Aβ 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 Aβ deposits and blood vessels, the classic Aβ deposits were clustered around the larger diameter vessels. These results suggest a complex pattern of Aβ deposition in the temporal lobe in sporadic AD. A regular distribution of Aβ 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.

Density and spatial pattern of the neuropathological changes in the cerebellum in the prion disease variant Creutzfeldt-Jakob disease (vCJD)

The objective of this chapter is to quantify the neuropathology of the cerebellar cortex in cases of the prion disease variant Creutzfeldt-Jakob disease (vCJD). Hence, sequential sections of the cerebellum of 15 cases of vCJD were stained with H/E, or immunolabelled with a monoclonal antibody 12F10 against prion protein (PrP) and studied using quantitative techniques and spatial pattern analysis. A significant loss of Purkinje cells was evident in all cases. Densities of the vacuolation and the protease resistant form of prion protein (PrPSc) in the form of diffuse and florid plaques were greater in the granule cell layer (GL) than the molecular layer (ML). In the ML, vacuoles and PrPSc plaques, occurred in clusters which were regularly distributed along the folia, larger clusters of vacuoles and diffuse plaques being present in the GL. There was a negative spatial correlation between the vacuoles and the surviving Purkinje cells in the ML and a positive spatial correlation between the clusters of vacuoles and the diffuse PrPSc plaques in the ML and GL in five and six cases respectively. A canonical variate analysis (CVA) suggested a negative correlation between the densities of the vacuolation in the GL and the diffuse PrPSc plaques in the ML. The data suggest: 1) all laminae of the cerebellar cortex were affected by the pathology of vCJD, the GL more severely than the ML, 2) the pathology was topographically distributed especially in the Purkinje cell layer and GL, 3) pathological spread may occur in relation to a loop of anatomical projections connecting the cerebellum, thalamus, cerebral cortex, and pons, and 4) there are differences in the pathology of the cerebellum in vCJD compared with the M/M1 subtype of sporadic CJD (sCJD).

What does the study of the spatial patterns of pathological lesions tell us about the pathogenesis of neurodegenerative disorders?

Discrete pathological lesions, which include extracellular protein deposits, intracellular inclusions and changes in cell morphology, occur in the brain in the majority of neurodegenerative disorders. These lesions are not randomly distributed in the brain but exhibit a spatial pattern, that is, a departure from randomness towards regularity or clustering. The spatial pattern of a lesion may reflect pathological processes affecting particular neuroanatomical structures and, therefore, studies of spatial pattern may help to elucidate the pathogenesis of a lesion and of the disorders themselves. The present article reviews first, the statistical methods used to detect spatial patterns and second, the types of spatial patterns exhibited by pathological lesions in a variety of disorders which include Alzheimer's disease, Down syndrome, dementia with Lewy bodies, Creutzfeldt-Jakob disease, Pick's disease and corticobasal degeneration. These studies suggest that despite the morphological and molecular diversity of brain lesions, they often exhibit a common type of spatial pattern (i.e. aggregation into clusters that are regularly distributed in the tissue). The pathogenic implications of spatial pattern analysis are discussed with reference to the individual disorders and to studies of neurodegeneration as a whole.

Spatial topography of the neurofibrillary tangles in cortical and subcortical regions in progressive supranuclear palsy

Objective: To study the topography of neurofibrillary tangles (NFT) in cortical and subcortical areas in progressive supranuclear palsy (PSP). Methods: Pattern analysis was carried out on tau-positive NFT in eight PSP cases. Results: Of the areas studied, NFT were randomly distributed in 68%, regularly distributed in 3%, and clustered in 29%. A regular distribution of clusters was more frequent in cortical than subcortical areas. Conclusion: NFT topography in subcortical areas was similar to inclusions in the synucleinopathy multiple system atrophy (MSA) but in cortical areas was comparable to other tauopathies. © 2006 Elsevier Ltd. All rights reserved.

Differences in the density and spatial distribution of florid and diffuse plaques in variant Creutzfeldt-Jakob disease (vCJD)

Objective: To determine whether in cases of variant Creutzfeldt-Jakob disease (vCJD), the florid-type plaques are derived from the diffuse plaques or whether the 2 plaque types develop independently. Material: Blocks of frontal, parietal, occipital and temporal neocortex and cerebellar cortex from 11 cases of vCJD. Method: The density, distribution and spatial pattern of the florid and diffuse plaques were determined in each brain region using spatial pattern analysis. Results: The density of the diffuse plaques was significantly greater than that of the florid plaques in most areas. The ratio of the diffuse to florid plaques varied between brain regions and was maximal in the molecular layer of the cerebellum. The densities of the florid and diffuse plaques were positively correlated in the parietal cortex, occipital cortex, the inferior temporal gyrus and the dentate gyrus. Plaque densities were not related to disease duration. In the cerebral cortex, the diffuse plaques were more commonly evenly distributed or occurred in large clusters along the cortex parallel to the pia mater compared with the florid plaques which occurred more frequently in regularly distributed clusters. Conclusion: The florid plaques may not be derived from the diffuse plaques, the 2 plaque types appearing to develop independently with unique factors involved in their pathogenesis.

Spatial patterns of the vacuolation in subcortical white matter in sporadic Creutzfeldt-Jakob disease (sCJD)

OBJECTIVE: To study the spatial patterns of the vacuolation ("spongiform change") in the subcortical white matter in the "classical" form of sporadic Creutzfeldt-Jakob disease (sCJD). MATERIAL: Frontal, parietal, occipital and temporal lobes of 11 cases of sCJD. METHOD: Spatial patterns were studied across the white matter at the base of the gyri using spatial pattern analysis. RESULTS: In the white matter of all gyri studied, vacuoles were aggregated into clusters, 50 to > 800 microm in diameter and in 22/37 (59%) of gyri, the clusters of vacuoles exhibited a regular distribution across the base of the gyri. In the remaining gyri, the vacuoles were aggregated into large clusters, at least 400 microm or 800 microm in diameter, but without evidence of a regular distribution. In a significant proportion of gyri, the spatial patterns of the vacuolation were similar to those reported previously for spongiform change and prion protein (PrP) deposits in the corresponding grey matter. CONCLUSIONS: Degeneration of the white matter and the formation of clusters of vacuoles may occur before the degeneration of the grey matter or could be a consequence of pathology affecting the cortico-cortical pathways.

The spatial arrangement patterns of senile plaques in senile dementia of the Alzheimer type (SDAT)

The spatial arrangement patterns of senile plaques have been studied in 10 micron cresyl violet stained sections cut from embedded portions of 20 brain regions from SDAT brains. Two studies are reported: an initial study using the Poisson distribution and a subsequent study using pattern analysis. The initial study indicated that plaques are arranged in discrete clumps in all brain regions when examined at x100 and x400 – suggesting that both small and larger scale clumping may be present. The pattern analysis study was applied to 8 cortical regions. This technique allows a more detailed study of pattern to be made. In all regions the technique revealed that the basic pattern of plaque arrangement is the regularly spaced discrete clump – which may be present on both large and small scales.

Spatial arrangement patterns of senile plaques in post-mortem senile dementia of the Alzheimer type brains

We have studied the spatial distribution of plaques in coronal and tangential sections of the parahippocampal gyrus (PHG), the hippocampus, the frontal lobe and the temporal lobe of five SDAT patients. Sections were stained with cresyl violet and examined at two magnifications (x100 and x400). in all cases (and at both magnifications) statistical analysis using the Poisson distribution showed that the plaques were arranged in clumps (x100: V/M = 1.48 - 4.49; x400 V/M = 1.17 - 1.95). this indicates that both large scale and small scale clumping occurs. Application of the statistical techniques of pattern analysis to coronal sections of frontal and temporal cortex and PHG showed. furthermore, that both large (3200-6400 micron) and small scale (100 - 400 micron) clumps were arranged with a high degree of regularity in the tissue. This suggests that the clumps of plaques reflect underlying neural structure.

A morphometric study of the spatial patterns of TDP-43 immunoreactive neuronal inclusions in frontotemporal lobar degeneration (FTLD) with progranulin (GRN) mutation

Mutations of the progranulin (GRN) gene are a major cause of familial frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43 kDa (TDP-43) proteinopathy (FTLD-TDP). We studied the spatial patterns of TDP-43 immunoreactive neuronal cytoplasmic inclusions (NCI) and neuronal intranuclear inclusions (NII) in histological sections of the frontal and temporal lobe in eight cases of FTLD-TDP with GRN mutation using morphometric methods and spatial pattern analysis. In neocortical regions, the NCI were clustered and the clusters were regularly distributed parallel to the pia mater; 58% of regions analysed exhibiting this pattern. The NII were present in regularly distributed clusters in 35% of regions but also randomly distributed in many areas. In neocortical regions, the sizes of the regular clusters of NCI and NII were 400-800 µm, approximating to the size of the modular columns of the cortico-cortical projections, in 31% and 36% of regions respectively. The NCI and NII also exhibited regularly spaced clustering in sectors CA1/2 of the hippocampus and in the dentate gyrus. The clusters of NCI and NII were not spatially correlated. The data suggest degeneration of the cortico-cortical and cortico-hippocampal pathways in FTLD-TDP with GRN mutation, the NCI and NII affecting different clusters of neurons.