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Measuring spatial effects in time to event data: a case study using months from angiography to coronary artery bypass graft (CABG).

The application of Bayesian hierarchical models to measure spatial effects in time to event data has not been widely reported. This case study aims to estimate the effect of area of residence on waiting times to coronary artery bypass graft (CABG) and to assess the role of important individual specific covariates (age, sex and disease severity). The data involved all patients with definite coronary artery disease who were referred to one cardiothoracic unit from five contiguous health authorities covering 488 electoral wards (areas). Time to event was the waiting time in months from angiography (diagnosis) to CABG (event). A number of discrete time survival models were fitted to the data. A discrete baseline hazard was estimated by fitting waiting time non-parametrically into the models. Ward was fitted as a spatial effect using a Gaussian Markov random field prior. Individual specific covariates considered were age, sex and number of diseased vessels. The recently proposed DIC criteria was used for comparing models. Results showed a marked spatial effect on time to bypass surgery after including age, sex and disease severity in the model. Notably this spatial effect was not apparent when these covariates were not included in the model. The observed small area spatial variation in time to CABG warrants further investigation.

Bayes Theorem↗

A hierarchical model for spatially clustered disease rates.

Maps of regional disease rates are potentially useful tools in examining spatial patterns of disease and for identifying clusters. Bayes and empirical Bayes approaches to this problem have proven useful in smoothing crude maps of disease rates. In recent years, models including both spatially correlated random effects and spatially unstructured random effects have been very popular. The spatially correlated random effects have been proposed in an attempt to capture a general clustering in the data. As an alternative, we propose replacing the spatially structured random effect with fixed clustering effects associated with particular areas. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm for posterior inference is described. We illustrate the model using the well-known New York leukaemia data.

Cluster Analysis↗

Spatial ability and lateralization in the haptic modality.

Two experiments examined the relation between spatial visualization ability and spatial lateralization using a unimanual haptic task with random shapes as stimuli. High spatial ability was not associated with enhanced right hemisphere functioning. However, spatial ability considered in the context of sex differences (Experiment 1) and level of verbal ability (Experiment 2) did yield interactions with the laterality (i.e., hand) variable, at least for first-list data. In Experiment 2, verbal ability also interacted with the gender and hand variables and in the same crossed ability-sex manner as was found for spatial ability in Experiment 1. It is concluded that cognitive abilities, including the relation between abilities, may be associated with the extent to which the right cerebral hemisphere mediates tactuospatial performance and that this association may differ for males and females.

Adult↗

Hippocampal involvement in spatial and working memory: a structural MRI analysis of patients with unilateral mesial temporal lobe sclerosis.

Forty-seven patients with unilateral temporal lobe epilepsy (TLE) were investigated on the Nine-Box Maze. The task was designed to compare working memory and spatial mapping theories of the functions of the hippocampus and provide measures of spatial, object, working, and reference memory. The results extended our previous findings in a larger group of patients. Spatial memory deficits across both working and reference memory conditions were found in patients with a right epileptogenic focus. There was no evidence of an object working memory deficit, but a nonlateralized impairment in object reference memory was revealed, which is consistent with our previous findings. The pattern of results was confirmed in a subgroup of 33 patients with unilateral atrophy localized to the hippocampus and parahippocampal gyrus, as verified by volumetric analysis of magnetic resonance images. In addition spatial memory errors significantly correlated with volumetric measures of mesial temporal lobe structures and not with measures of the remaining temporal cortex. In contrast, object reference memory errors correlated with volumetric measures of the temporal cortex and not with mesial temporal lobe structures. These findings support a specialized role for the right hippocampal region in spatial memory.

Adult↗

Models of infectious diseases in spatially heterogeneous environments.

Most models of dynamics of infectious diseases have assumed homogeneous mixing in the host population. However, it is increasingly recognized that heterogeneity can arise through many processes. It is then important to consider the existence of subpopulations of hosts, and that the contact rate within subpopulations is different than that between subpopulations. We study models with hosts distributed in subpopulations as a consequence of spatial partitioning. Two types of models are considered. In the first one there is direct transmission. The second one is a model of dynamics of a mosquito-borne disease, with indirect transmission, and applicable to malaria. The contact between subpopulations is achieved through the visits of hosts. Two types of visit are considered: a first one in which the visit time is independent of the distance travelled, and a second one in which visit time decreases with distance. There are two types of spatial arrangement: one dimensional, and two dimensional. Conditions for the establishment of the disease are obtained. Results indicate that the disease becomes established with greater difficulty when the degree of spatial partition increases, and when visit time decreases. In addition, when visit time decreases with distance, the establishment of the disease is more difficult when the spatial arrangement is one dimensional than when it is two dimensional. The results indicate the importance of knowing the spatial distribution and mobility patterns to understand the dynamics of infectious diseases. The consequences of these results for the design of public health policies are discussed.

Animals↗

Nearest-neighbor analysis of spatial point patterns: application to biomedical image interpretation.

Analysis of the spatial distributions of objects is fundamental to biomedical image interpretation. Nearest-neighbor (NN) methods are generally used to assess whether objects are arranged at random or in a deterministic manner. Simple standard NN techniques, however, may fail to identify complex spatial organizations. To overcome this problem the present study proposes a NN iterative algorithm that enables deterministic spatial patterns to be detected by identifying the distances between objects for which there is the greatest deviation from randomness and hence the amplitude of the areas of maximum reciprocal influence between objects. The performance of the algorithm is evaluated by applying it to both manufactured and experimental data. The manufactured date example showed that the proposed procedure produced neither false positives or negatives. The method proved to be extremely sensitive, detecting even small deviations from randomness. The experimental analysis was applied to the study of the spatial distribution of apopototic structures in malignant neoplastic tissue. It showed that the apopototic cells and bodies are characterized by a complex spatial pattern, and aggregate closely.

Algorithms↗

Role of Mimeticism and Spatiality in Textual Recall.

Four experiments were conducted to investigate the role of map spatiality and icon mimeticism in facilitating text recall. A secondary goal was to explore an assumption of the conjoint retention hypothesis, that the visuospatial component of working memory is involved in retrieving map information. We manipulated display conditions to evaluate the separate and combined effects of map spatiality and icon mimeticism on text recall. We also utilized a concurrent task paradigm to assess both the recognition of spatial displays and the recall of map feature information. The results of all four experiments point to the mimeticism of icons as the key attribute of maps for facilitating recall, rather than the spatial layout of the map when visual displays and text are presented simultaneously during encoding. We also found no evidence indicating that maps are processed in a more spatial manner than are lists. Copyright 2000 Academic Press.

Journal Article↗

Linguistic and conceptual control of visual spatial attention.

A theory of voluntary, top-down control of visual spatial attention is presented that explains how linguistic cues like "above," "below," "left," and "right" are used to direct attention from one object to another. The theory distinguishes between perceptual and conceptual representations of space and views attention as a set of mechanisms that establish correspondences between the representations. Spatial reference frames play an important part in this analysis. The theory interprets reference frames as mechanisms of attention, similar to spatial indices but with more computational power. The theory was tested in 11 experiments that assessed the importance of linguistic distinctions between classes of spatial relations (basic, deictic, and intrinsic) and examined the flexibility with which subjects manipulated spatial reference frames.

Attention↗

Quantification of Spatial Correlation in Porous Media and Its Effect on Mercury Porosimetry.

In many porous media the grains are packed in a disordered manner, rather than in regular lattices. Theoretical treatments of the properties of these media often assume that because there is no regular lattice, the pore space between grains is completely spatially disordered. Here we present an analysis of a real granular medium (a close packing of equal spheres) which shows that, contrary to the popular assumption, the pore space is spatially correlated. The origin of this pore space correlation is the strong spatial correlation of grain locations, which is a feature of all dense granular media. Our analysis relies on physically representative network models of the pore space constructed from knowledge of the grain locations. Simulated drainage experiments on these networks agree with mercury porosimetry experiments in simple sandstones, whereas simulations in uncorrelated but otherwise identical networks do not. Thus the spatial correlation inherent in the pore space of simple porous media significantly affects mercury porosimetry. Deriving pore size distributions from mercury porosimetry without considering spatial correlation can give misleading results. The likelihood of error is compounded if such pore size distributions are used to estimate transport coefficients such as permeability, diffusivity, and electrical conductivity.

Journal Article↗

Sex differences in spatial cognition, computational fluency, and arithmetical reasoning.

Alternative explanations for the male advantage in arithmetical reasoning, as measured by the ability to solve complex word problems, include a male advantage in spatial cognition and a male advantage in computational fluency. The current study was designed to test these competing hypotheses. To this end, 113 male and 123 female undergraduates were administered arithmetical computations and arithmetical reasoning tests, along with an IQ test and a test of spatial cognition. There was no sex difference on the IQ test, but males showed significantly higher mean scores on the arithmetical computations, arithmetical reasoning, and spatial cognition measures. A series of structural equation models indicated that individual differences in arithmetical reasoning were related to individual differences in IQ, spatial abilities, and computational fluency. Moreover, the results suggested that the male advantage in arithmetical reasoning is mediated by the male advantages in both computational fluency and spatial cognition.

Adolescent↗

Mapping the spin-density and lineshape distribution of free radicals using 4D spectral-spatial EPR imaging.

The development and application of four-dimensional spectral-spatial electron paramagnetic resonance imaging (EPRI) techniques for unambiguous determination of spectral shape and spin distribution of paramagnetic samples are described. Strategies for optimizing acquisition and computation times, image resolution, and data presentation are described. The feasibility of studying small linewidth differences of approximately 0.1 G in samples of up to 25 mm in size was tested by computer simulations and by measurements on phantoms containing 0.5 mM nitroxide spin label. One thousand projections were used to reconstruct 32 x 32 x 32 x 32 pixel images. Similar 4D imaging experiments were performed on an isolated rat heart infused with a suspension of glucose char. The 4D image of the rat heart clearly showed the three-dimensional spatial structure of the heart and the spectral shape at each spatial point. Thus, we have demonstrated, for the first time, that 4D spectral-spatial EPRI could be performed on lossy biological samples or tissues at L-band frequencies, enabling the mapping of spectral information over the entire three-dimensional spatial structure of the object.

Animals↗

The scale-invariant spatial clustering of leukemia in San Francisco.

This study tests the hypothesis of scale-invariant self-similar clustering of childhood leukemia cases over the San Francisco spatial area. The spatial distribution of leukemia cases has been investigated over seven scales of observation. A power-law relation of the variance to the mean of aggregates (quadrats) was used to detect possible scale-invariant self-similar clustering. The spatial distribution of leukemia cases (incidence from 1946 to 1964) was well fitted by a power-law function. The follow-up of clustering from the first years of case notification (1946) confirmed a scale-invariant self-similar spatial pattern with a stable power-law slope from 1952 onward. This pattern was shown to pertain specifically to school-age leukemia cases. Younger cases had a random distributional pattern over space. Observation and simulations of the distributional patterns revealed memory-keeping of historical (the pre-1953 era) fractal-like conditions. Based on a comparison of the leukemia fractal dimension with that of the city residential data, it is speculated that the current scale-invariant self-similar spatial clustering of the leukemia cases reflects the onset of the historical fractal patterning of the city residences at a particular time point in the past.

Child↗

Human primary auditory cortex: cytoarchitectonic subdivisions and mapping into a spatial reference system.

The transverse temporal gyrus of Heschl contains the human auditory cortex. Several schematic maps of the cytoarchitectonic correlate of this functional entity are available, but they present partly conflicting data (number and position of borders of the primary auditory areas) and they do not enable reliable comparisons with functional imaging data in a common spatial reference system. In order to provide a 3-D data set of the precise position and extent of the human primary auditory cortex, its putative subdivisions, and its topographical intersubject variability, we performed a quantitative cytoarchitectonic analysis of 10 brains using a recently established technique for observer-independent definition of areal borders. Three areas, Te1.1, Te1.0, and Te1.2, with a well-developed layer IV, which represent the primary auditory cortex (Brodmann area 41), can be identified along the mediolateral axis of the Heschl gyrus. The cell density was significantly higher in Te1.1 compared to Te1.2 in the left but not in the right hemisphere. The cytoarchitectonically defined areal borders of the primary auditory cortex do not consistently match macroanatomic landmarks like gyral and sulcal borders. The three primary auditory areas of each postmortem brain were mapped to a spatial reference system which is based on a brain registered by in vivo magnetic resonance imaging. The integration of a sample of postmortem brains in a spatial reference system allows one to estimate the spatial variability of each cytoarchitectonically defined region with respect to this reference system. In future, the transfer of in vivo structural and functional data into the same spatial reference system will enable accurate comparisons of cytoarchitectonic maps of the primary auditory cortex with activation centers as established with functional imaging procedures.

Adult↗

Reorganization of frontal systems used by alcoholics for spatial working memory: an fMRI study.

Chronic alcoholism is associated with impairment in sustained attention and visual working memory. Thus, alcoholics have reduced ability, but not necessarily inability, to perform these executive tasks, assumed to be subserved by regions of prefrontal cortex. To identify neural substrates associated with this impairment, we used functional MRI (fMRI) to determine whether alcoholics invoke the same or different brain systems as controls when engaged in working memory tasks that the two groups were able to perform at equivalent levels. The fMRI spatial working memory paradigm instructed subjects to respond with a button press when a target position was either in the center of the field (match to center) or matched the spatial position of one presented two items previously (match 2-back) or to rest. Using whole-brain fMRI, alcoholics showed diminished activation frontal cortical systems compared to controls (bilateral dorsolateral prefrontal cortex) when responding 2-back vs rest. In the center vs rest contrast, the control group compared with the alcoholic group activated a large expanse of prefrontal cortex (including Brodmann areas 9, 10, and 45), whereas there was significantly greater activation by the alcoholic group relative to the control group localized more posteriorly and inferiorly in the frontal cortex (area 47). Examination of within group activation patterns revealed two different patterns of activation: the control group exhibited activation of the dorsal ("Where?") stream for visual spatial working memory processing, whereas the alcoholic group exhibited activation of the ventral ("What?") stream and declarative memory systems to accomplish the spatial working memory task. The differences in the pattern of brain activations exhibited by the alcoholic and control groups, despite equivalence in behavioral performance, is consistent with a functional reorganization of the brain systems invoked by alcoholic individuals or invocation of an inappropriate brain system when engaged in a visual spatial task requiring working memory.

Adult↗

Improved parametric image generation using spatial-temporal analysis of dynamic PET studies.

The value of parametric images that represent both spatial distribution and quantification of the physiological parameters of tracer kinetics has long been recognized. However, the inherent high noise level of pixel kinetics of dynamic PET makes it unsuitable to generate parametric images of the microparameters of tracer kinetic model by conventional weighted nonlinear least squares (WNLS) fitting. Based on the concept that both spatial and temporal information should be integrated to improve parametric image quality, a nonlinear ridge regression with spatial constraint (NLRRSC) parametric imaging algorithm was proposed in this study. For NLRRSC, a term that penalizes local spatial variation of parameters was added to the cost function of WNLS fitting. The initial estimates and spatial constraint were estimated by component representation model (CRM) with cluster analysis. A hierarchical cluster with average linkage method was used to extract components. The ridge parameter was determined by linear ridge regression theory at each iteration, and a modified Gauss-Newton algorithm was used for minimizing the cost function. Results from a computer simulation showed that the percent mean square error of estimates obtained by NLRRSC can be decreased by 60-80% compared to that of WNLS. The parametric images estimated by NLRRSC are significantly better than the ones generated by WNLS. A highly correlated linear relationship was found between the ROI values calculated from the microparametric images generated by NLRRSC and estimates from ROI kinetic fitting. NLRRSC provided a reliable estimate of glucose metabolite uptake rate with a comparable image quality compared to Patlak analysis. In conclusion, NLRRSC is a reliable and robust parametric imaging algorithm for dynamic PET studies.

Algorithms↗

Dissociation of hippocampal and striatal contributions to spatial navigation in the water maze.

Two experiments were conducted to compare the effects of fornix/fimbria and caudate-putamen lesions in Long-Evans hooded rats (Rattus norvegicus) trained on two water maze tasks that differed in the type of spatial localization required for optimum solution. In Experiment 1, the lesioned rats and surgical controls were trained on the standard place task in the water maze (Morris, 1981) and given two postacquisition tests (a platform removal probe and platform relocation test). In Experiment 2, rats with similar lesions and control rats were trained on a modified cue navigation task. Fornix/fimbria lesions impaired a late stage of place task acquisition but did not impair acquisition of the cue task. Caudate-putamen lesions resulted in a severe place acquisition impairment and a transient cue acquisition impairment, both of which were characterized by an initial tendency to swim near the wall of the pool. Post-hoc analyses of the direction and angles of departure from the start points suggested that rats with fornix/fimbria lesions used non-allocentric spatial strategies to solve the place task. These rats also demonstrated a significantly weakened spatial bias for the former training quadrant on the platform removal probe and reduced flexibility in navigating to a novel platform location on the platform relocation test. In contrast, rats with caudate-putamen lesions showed a significant spatial bias for the former training quadrant but failed to cross the exact location within the quadrant where the platform was formerly positioned. The results suggest that the hippocampus mediates the allocentric spatial component of the water maze place task while the dorsomedial striatum may play an important role in the acquisition of the procedural aspects of both place and cue versions of the task.

Animals↗

Spatial and space-time correlations in systems of subpopulations with stochastic migration.

The great majority of models of the population genetics of subdivided populations have made the simplifying assumption that the gene frequencies in migrant groups are deterministic. The present paper examines models which more closely mimic natural conditions, in which the gene frequencies in migrant groups are subject to stochastic effects. It is shown that some types of stochastic migration can cause dramatic changes in spatial correlations and variance. These changes depend on how the stochastic migration effects in the gene frequency recursion equations are shared among nearby subpopulations during the same generation. Only for cases where the effects are completely unshared are the equilibrium spatial and space-time correlations among adult subpopulations unaffected, but the variance is always inflated. The analyses here use novel methods, by recasting population genetic migration-drift models as space-time autoregressive moving average (STARMA) processes. Recent theorems for STARMA processes are employed for finding the spatial correlations, and for the first time in population genetics theory the complete set of space-time correlations, for systems with general patterns of migration rates and numbers of spatial dimensions. The space-time correlations provide a uniquely detailed description of a system, and thus form a link between observed spatial autocorrelation statistics and the underlying space-time population genetic process. STARMA theoretical processes have direct statistical analogues that can be applied for process identification, parameter estimation, model fitting, and forecasting in real systems.

Animals↗

Population persistence and spatially limited social interaction.

We investigate the persistence of a population composed of socially interacting individuals living in a lattice structured habitat and the effect of spatially limited social interaction, reproduction, and migration. Both cooperative interaction (enhancing the survivorship of neighboring individuals) and competitive interaction (reducing it) are examined. Mathematical analysis based on pair approximation (or doublet decoupling approximation) and computer simulation are used. Results are: If migration rate is not very large, the population tends to form clusters of individuals (clumped distribution) due to spatially limited reproduction. Although cooperative interaction is more effective in a spatially structured population, the population is more difficult to persist than in the corresponding population without spatial structure, because the shortage of nearest neighbor vacant sites reduces reproduction. Migration of individuals reduces the clumping of the spatial pattern. Pair approximation predicts the equilibrium density fairly accurately when the predicted density is sufficiently high (i.e., more than 40% sites are occupied). If the predicted density is low however, the pair approximation overestimates the equilibrium population level. To overcome this disagreement, we examined improved pair approximation.

Bias↗