Quantitative methods in neuropathology

The last decade has seen a considerable increase in the application of quantitative methods in the study of histological sections of brain tissue and especially in the study of neurodegenerative disease. These disorders are characterised by the deposition and aggregation of abnormal or misfolded proteins in the form of extracellular protein deposits such as senile plaques (SP) and intracellular inclusions such as neurofibrillary tangles (NFT). Quantification of brain lesions and studying the relationships between lesions and normal anatomical features of the brain, including neurons, glial cells, and blood vessels, has become an important method of elucidating disease pathogenesis. This review describes methods for quantifying the abundance of a histological feature such as density, frequency, and 'load' and the sampling methods by which quantitative measures can be obtained including plot/quadrat sampling, transect sampling, and the point-quarter method. In addition, methods for determining the spatial pattern of a histological feature, i.e., whether the feature is distributed at random, regularly, or is aggregated into clusters, are described. These methods include the use of the Poisson and binomial distributions, pattern analysis by regression, Fourier analysis, and methods based on mapped point patterns. Finally, the statistical methods available for studying the degree of spatial correlation between pathological lesions and neurons, glial cells, and blood vessels are described.

Spatial patterns of the tau pathology in progressive supranuclear palsy

Progressive supranuclear palsy (PSP) is characterized neuropathologically by neuronal loss, gliosis, and the presence of tau-immunoreactive neuronal and glial cell inclusions affecting subcortical and some cortical regions. The objectives of this study were to determine (1) the spatial patterns of the tau-immunoreactive pathology, viz., neurofibrillary tangles (NFT), oligodendroglial inclusions (GI), tufted astrocytes (TA), and Alzheimer's disease-type neuritic plaques (NP) in PSP and (2) to investigate the spatial correlations between the histological features. Post-mortem material of cortical and subcortical regions of eight PSP cases was studied. Spatial pattern analysis was applied to the NFT, GI, TA, NP, abnormally enlarged neurons (EN), surviving neurons, and glial cells. NFT, GI, and TA were distributed either at random or in regularly distributed clusters. The EN and NP were mainly randomly distributed. Clustering of NFT and EN was more frequent in the cortex and subcortical regions, respectively. Variations in NFT density were not spatially correlated with the densities of either GI or TA, but were positively correlated with the densities of EN and surviving neurons in some regions. (1) NFT were the most widespread tau-immunoreactive pathology in PSP being distributed randomly in subcortical regions and in regular clusters in cortical regions, (2) GI and TA were more localized and exhibited a regular pattern of clustering in subcortical regions, and (3) neuronal and glial cell pathologies were not spatially correlated. © 2012 Springer-Verlag.

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

Objective: To quantify the neuronal and glial cell pathology in the hippocampus and the parahippocampal gyrus (PHG) of 8 cases of progressive supranuclear palsy (PSP). Material: tau-immunolabeled sections of the temporal lobe of 8 diagnosed cases of PSP. Method: The densities of lesions were measured in the PHG, CA sectors of the hippocampus and the dentate gyrus (DG) and studied using spatial pattern analysis. Results: Neurofibrillary tangles (NFT) and abnormally enlarged neurons (EN) were most frequent in the PHG and in sector CA1 of the hippocampus, oligodendroglial inclusions (“coiled bodies”) (GI) in the PHG, subiculum, sectors CA1 and CA2, and neuritic plaques (NP) in sectors CA2 and CA4. The DG was the least affected region. Vacuolation and GI were observed in the alveus. No tufted astrocytes (TA) were observed. Pathological changes exhibited clustering, the lesions often exhibiting a regular distribution of the clusters parallel to the tissue boundary. There was a positive correlation between the degree of vacuolation in the alveus and the densities of NFT in CA1 and GI in CA1 and CA2. Conclusion: The pathology most significantly affected the output pathways of the hippocampus, lesions were topographically distributed, and hippocampal pathology may be one factor contributing to cognitive decline in PSP.

A quantitative study of the pathological changes in the cerebellum in 15 cases of variant Creutzfeldt–Jakob disease (vCJD)

Aims: To determine in the cerebellum in variant Creutzfeldt–Jakob disease (vCJD): (i) whether the pathology affected all laminae; (ii) the spatial topography of the pathology along the folia; (iii) spatial correlations between the pathological changes; and (iv) whether the pathology was similar to that of the common methionine/methionine Type 1 subtype of sporadic CJD. Methods: Sequential cerebellar sections of 15 cases of vCJD were stained with haematoxylin and eosin, or immunolabelled with monoclonal antibody 12F10 against prion protein (PrP) and studied using spatial pattern analysis. Results: Loss of Purkinje cells was evident compared with control cases. Densities of the vacuolation and the protease-resistant form of prion protein (PrPSc) (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 regularly distributed along the folia with larger clusters of vacuoles and diffuse plaques in the GL. There was a negative spatial correlation between the vacuoles and the surviving Purkinje cells in the ML. There was a positive spatial correlation between the vacuoles and diffuse PrPSc plaques in the ML and GL. Conclusions: (i) all laminae were affected by the pathology, the GL more severely than the ML; (ii) the pathology was topographically distributed along the folia especially in the Purkinje cell layer and ML; (iii) pathological spread may occur in relation to the loop of anatomical connections involving the cerebellum, thalamus, cerebral cortex and pons; and (iv) there were pathological differences compared with methionine/methionine Type 1 sporadic CJD.

Diffuse beta-amyloid (A beta) deposits and neurons: in situ secretion or diffusion of A beta?

The association between diffuse-type beta -amyloid (AP) deposits and neuronal cell bodies in Alzheimer's disease (AD) and Down's syndrome (DS) could result from the secretion of AP from clusters of neurons in situ or the diffusion of A beta from cell processes, glial cells or blood vessels. To decide between these hypotheses, spatial pattern analysis was used to study the relationship between the degree of clustering of neuronal cell bodies and the presence of diffuse deposits in the temporal lobe of patients with DS. Significant clustering of neuronal cell bodies was present in 17/24 (71%) of brain areas studied. in addition, in 23/24 (96%) of brain areas, there was a positive correlation between the presence of diffuse deposits and the density of neurons. Hence, the data support the hypothesis that diffuse deposits develop in situ mainly as a result of the secretion of A beta by local clusters of neurons rather than by significant diffusion. Furthermore, the size of a diffuse deposit is likely to be determined by the number of neurons within a cluster which secrete A beta. The number and density of neurons could also be a factor determining the evolution of a diffuse into a mature amyloid deposit.

Is the clustering of neurofibrillary tangles in Alzheimer's patients related to the cells of origin of specific cortico-cortical projections?

The spatial pattern of cellular neurofibrillary tangles (NFT) was studied in the supra- and infragranular layers of various cortical regions in cases of Alzheimer's disease (AD). The objective was to test the hypothesis that NFT formation was associated with the cells of origin of specific cortico-cortical projections. The novel feature of the study was that pattern analysis enabled the dimension and spacing of NFT clusters along the cortical ribbon to be estimated. In the majority of brain regions studied, NFT occurred in clusters of neurons which were regularly spaced along the cortical strip. This pattern is consistent with the predicted distribution of the cells of origin of specific cortico-cortico projections. Mean NFT cluster size varied from 250 to > 12800 microns in different cortical tissues suggesting either variation in the size of the cell clusters or a dynamic process in the development of NFT in relation to these cell clusters. The formation of NFT in cell clusters which may give rise to the feed-forward and feed-back cortico-cortical projections suggests a possible route of spread of NFT pathology in AD between cortical regions and from the cortex to subcortical areas.

Factors associated with lobe division in the lichen Parmelia conspersa (Ehrh. ex. Ach.)Ach.

The factors associated with lobe division were studied in thalli of the lichen Parmelia conspersa (Ehrh. ex Ach.)Ach. Lobe division was studied in sequences of adjacent lobes using spatial pattern analysis. In five large thalli, lobe division within the thallus margin was randomly distributed. Correlations between the degree of lobe division, the radial growth of the lobe and lobe morphology were studied in six thalli. Lobe division was positively correlated with either lobe width or area in four thalli. Correlations were observed with radial growth or morphology of the adjacent lobes in two thalli. Dividing and non-dividing lobes were removed from large thalli and glued to pieces of slate with their tips either at the same level or in front of neighbouring lobes. Dividing lobes divided more rapidly when their tips were glued in front of their neighbours. The levels of ribitol, arabitol and mannitol were measured within a 2 mm region of the tip in dividing and non-dividing lobes on four occasions in 1994. Carbohydrate levels were significantly increased in dividing compared with non-dividing lobes. In addition, the mean size of the algal cells was greater in non-dividing compared with dividing lobes especially at the lobe base. However, the percentage of zoosporangia and aplanosporangia did not vary significantly in dividing and non-dividing lobes. These results suggest that: 1) the pattern of lobe division within the thallus margin may be random, 2) lobe division may be determined by lobe size and the location of the lobe tip relative to the neighbouring lobes and 3) there may be an increase in the productivity of lobes associated with lobe division.

The two forms of visuo-spatial perspective taking are differently embodied and subserve different spatial prepositions

We set out to distinguish level 1 (VPT-1) and level 2 (VPT-2) perspective taking with respect to the embodied nature of the underlying processes as well as to investigate their dependence or independence of response modality (motor vs. verbal). While VPT-1 reflects understanding of what lies within someone else’s line of sight, VPT-2 involves mentally adopting someone else’s spatial point of view. Perspective taking is a high-level conscious and deliberate mental transformation that is crucially placed at the convergence of perception, mental imagery, communication, and even theory of mind in the case of VPT-2. The differences between VPT-1 and VPT-2 mark a qualitative boundary between humans and apes, with the latter being capable of VPT-1 but not of VPT-2. However, our recent data showed that VPT-2 is best conceptualized as the deliberate simulation or emulation of a movement, thus underpinning its embodied origins. In the work presented here we compared VPT-2 to VPT-1 and found that VPT-1 is not at all, or very differently embodied. In a second experiment we replicated the qualitatively different patterns for VPT-1 and VPT-2 with verbal responses that employed spatial prepositions. We conclude that VPT-1 is the cognitive process that subserves verbal localizations using “in front” and “behind,” while VPT-2 subserves “left” and “right” from a perspective other than the egocentric. We further conclude that both processes are grounded and situated, but only VPT-2 is embodied in the form of a deliberate movement simulation that increases in mental effort with distance and incongruent proprioception. The differences in cognitive effort predict differences in the use of the associated prepositions. Our findings, therefore, shed light on the situated, grounded and embodied basis of spatial localizations and on the psychology of their use.

A stable graph-based representation for object recognition through high-order matching

Many Object recognition techniques perform some flavour of point pattern matching between a model and a scene. Such points are usually selected through a feature detection algorithm that is robust to a class of image transformations and a suitable descriptor is computed over them in order to get a reliable matching. Moreover, some approaches take an additional step by casting the correspondence problem into a matching between graphs defined over feature points. The motivation is that the relational model would add more discriminative power, however the overall effectiveness strongly depends on the ability to build a graph that is stable with respect to both changes in the object appearance and spatial distribution of interest points. In fact, widely used graph-based representations, have shown to suffer some limitations, especially with respect to changes in the Euclidean organization of the feature points. In this paper we introduce a technique to build relational structures over corner points that does not depend on the spatial distribution of the features. © 2012 ICPR Org Committee.

Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point

Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution.

Using generative models for handwritten digit recognition

We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B-splines with Gaussian ``ink generators'' spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. (1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. (2) During the process of explaining the image, generative models can perform recognition driven segmentation. (3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. (4) Unlike many other recognition schemes it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is it requires much more computation than more standard OCR techniques.

A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.

Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

Multiple system atrophy (MSA): Topographic distribution of the alpha-synuclein-associated pathological changes

To study the topographic distribution of the pathology in multiple system atrophy (MSA). Pattern analysis was carried out using a-synuclein immunohistochemistry in 10 MSA cases. The glial cytoplasmic inclusions (GCI) were distributed randomly or in large clusters. The neuronal inclusions (NI) and abnormal neurons were distributed in regular clusters. Clusters of the NI and abnormal neurons were spatially correlated whereas the GCI were not spatially correlated with either the NI or the abnormal neurons. The data suggest that the GCI represent the primary change in MSA and the neuronal pathology develops secondary to the glial pathology.

Bayesian classification with Gaussian processes

We consider the problem of assigning an input vector to one of m classes by predicting P(c|x) for c=1,...,m. For a two-class problem, the probability of class one given x is estimated by s(y(x)), where s(y)=1/(1+e-y). A Gaussian process prior is placed on y(x), and is combined with the training data to obtain predictions for new x points. We provide a Bayesian treatment, integrating over uncertainty in y and in the parameters that control the Gaussian process prior the necessary integration over y is carried out using Laplace's approximation. The method is generalized to multiclass problems (m>2) using the softmax function. We demonstrate the effectiveness of the method on a number of datasets.