Measuring the spatial arrangement patterns of pathological lesions in histological sections of brain tissue

The development of abnormal protein aggregates in the form of extracellular plaques and intracellular inclusions is a characteristic feature of many neurodegenerative diseases such as Alzheimer's disease (AD), Creutzfeldt-Jakob disease (CJD) and the fronto-temporal dementias (FTD). An important aspect of a pathological protein aggregate is its spatial topography in the tissue. Lesions may not be randomly distributed within a histological section but exhibit spatial pattern, a departure from randomness either towards regularity or clustering. Information on the spatial pattern of a lesion may be useful in elucidating its pathogenesis and in studying the relationships between different lesions. This article reviews the methods that have been used to study the spatial topography of lesions. These include simple tests of whether the distribution of a lesion departs significantly from random using randomized points or sample fields, and more complex methods that employ grids or transects of contiguous fields and which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters. The usefulness of these methods in elucidating the pathogenesis of protein aggregates in neurodegenerative disease is discussed.

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.

Integrated approach to project feasibility analysis:a case study

Feasibility studies of industrial projects consist of multiple analyses carried out sequentially. This is time consuming and each analysis screens out alternatives based solely on the merits of that analysis. In cross-country petroleum pipeline project selection, market analysis determines throughput requirement and supply and demand points. Technical analysis identifies technological options and alternatives for pipe-line routes. Economic and financial analysis derive the least-cost option. The impact assessment addresses environmental issues. The impact assessment often suggests alternative sites, routes, technologies, and/or implementation methodology, necessitating revision of technical and financial analysis. This report suggests an integrated approach to feasibility analysis presented as a case application of a cross-country petroleum pipeline project in India.

Changes in the clustering patterns of beta-amyloid (Abeta) with age in Down's syndrome

The spatial distribution patterns of the diffuse, primitive, and classic beta-amyloid (Abeta) deposits were studied in areas of the medial temporal lobe in 12 cases of Down's Syndrome (DS) 35 to 67 years of age. Large clusters of diffuse deposits were present in the youngest patients; cluster size then declined with patient age but increased again in the oldest patients. By contrast, the cluster sizes of the primitive and classic deposits increased with age to a maximum in patients 45 to 55 and 60 years of age respectively and declined in size in the oldest patients. In the parahippocampal gyrus (PHG), the clusters of the primitive deposits were most highly clustered in cases of intermediate age. The data suggest a developmental sequence in DS in which Abeta is deposited initially in the form of large clusters of diffuse deposits that are then gradually replaced by clusters of primitive and classic deposits. The oldest patients were an exception to this sequence in that the pattern of clustering resembled that of the youngest patients.

A statistical method for the identification and aggregation of regional linguistic variation

This paper introduces a method for the analysis of regional linguistic variation. The method identifies individual and common patterns of spatial clustering in a set of linguistic variables measured over a set of locations based on a combination of three statistical techniques: spatial autocorrelation, factor analysis, and cluster analysis. To demonstrate how to apply this method, it is used to analyze regional variation in the values of 40 continuously measured, high-frequency lexical alternation variables in a 26-million-word corpus of letters to the editor representing 206 cities from across the United States.

Spatial tuning studies of the pattern evoked electroretinogram

The locus of origin of the pattern evoked electroretinogram, (PERG), has been the subject of considerable discussion. A novel approach was adopted in this study to further elaborate the nature of the PERG evoked by pattern onset/offset presentation. The PERG was found to be linearly related to stimulus contrast and in particular was linearly related to the temporal contrast of the retinal image, when elicited by patterns of low spatial frequency. At high spatial frequencies the retinal image contrast is significantly reduced because of optical degradation. This is described by the eye's modulation transfer function (MTF). The retinal contrast of square wave grating and chequerboard patterns of increasing spatial frequency were found by filtering their Fourier transforms by the MTF. The filtered pattern harmonics were then resynthesised to constitute a profile of retinal image illuminance from which the temporal and spatial contrast of the image could be calculated. If the PERG is a pure illuminance response it should be spatially insensitive and dependent upon the temporal contrast of stimulation. The calculated loss of temporal contrast for finer patterns was expressed as a space-averaged temporal contrast attentuation factor. This factor, applied to PERGs evoked by low spatial frequency patterns, was used to predict the retinal illuminance response elicited by a finer pattern. The predicted response was subtracted from the recorded signal and residual waveform was proposed to represent specific activity. An additional correction for the attenuation of spatial contrast was applied to the extracted pattern specific response. Pattern specific responses computed for different spatial frequency patterns in this way are the predicted result of iso-contrast pattern stimulation. The pattern specific responses demonstrate a striking bandpass spatial selectivity which peaks at higher spatial frequencies in the more central retina. The variation of spatial sensitivity with eccentricity corresponds closely with estimated ganglion receptive field centre separation and psychophysical data. The variation of retinal structure with eccentricity, in the form of the volumes of the nuclear layers, was compared with the amplitudes of the computed retinal illuminance and pattern specific responses. The retinal illuminance response corresponds more closely to the outer and inner nuclear layers whilst the pattern specific response appears more closely related to the ganglion cell layer. In general the negative response transients correspond to the more proximal retinal layers. This thesis therefore supports the proposed contribution of proximal retinal cell activity to the PERG and describes techniques which may be further elaborated for more detailed studies of retinal receptive field dimensions.

Analysis of spatial patterns in histological sections of brain tissue using a method based on regression

A method of determining the spatial pattern of any histological feature in sections of brain tissue which can be measured quantitatively is described and compared with a previously described method. A measurement of a histological feature such as density, area, amount or load is obtained for a series of contiguous sample fields. The regression coefficient (β) is calculated from the measurements taken in pairs, first in pairs of adjacent samples and then in pairs of samples taken at increasing degrees of separation between them, i.e. separated by 2, 3, 4,..., n units. A plot of β versus the degree of separation between the pairs of sample fields reveals whether the histological feature is distributed randomly, uniformly or in clusters. If the feature is clustered, the analysis determines whether the clusters are randomly or regularly distributed, the mean size of the clusters and the spacing of the clusters. The method is simple to apply and interpret and is illustrated using simulated data and studies of the spatial patterns of blood vessels in the cerebral cortex of normal brain, the degree of vacuolation of the cortex in patients with Creutzfeldt-Jacob disease (CJD) and the characteristic lesions present in Alzheimer's disease (AD). Copyright (C) 2000 Elsevier Science B.V.

Analysis of spatial patterns in histological sections of brain tissue

A method is described which enables the spatial pattern of discrete objects in histological sections of brain tissue to be determined. The method can be applied to cell bodies, sections of blood vessels or the characteristic lesions which develop in the brain of patients with neurodegenerative disorders. The density of the histological feature under study is measured in a series of contiguous sample fields arranged in a grid or transect. Data from adjacent sample fields are added together to provide density data for larger field sizes. A plot of the variance/mean ratio (V/M) of the data versus field size reveals whether the objects are distributed randomly, uniformly or in clusters. If the objects are clustered, the analysis determines whether the clusters are randomly or regularly distributed and the mean size of the clusters. In addition, if two different histological features are clustered, the analysis can determine whether their clusters are in phase, out of phase or unrelated to each other. To illustrate the method, the spatial patterns of senile plaques and neurofibrillary tangles were studied in histological sections of brain tissue from patients with Alzheimer's disease.

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 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.

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.

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.