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Spatial speckle characterization by Brownian motion analysis.

It is well known that the interactions between coherent monochromatic radiation and a scattering medium induce a speckle phenomenon. The spatial and temporal statistics of this speckle are employed to analyze many applications in laser imaging. The direct exposure of a photographic film, without a lens to the backscattered radiation, gives a speckle pattern. The main problem lies in the determination of those parameters which can efficiently characterize this pattern. In this paper, we present a fractal-theory-based stochastic approach to approximate the diffusion. In our opinion, this method is more appropriate for the classification of this nonlinear and nonstationary phenomenon than the classical frequency-based approach. The paper also presents several applications of this method which have employed for characterization of different test media.

Journal Article↗

Spatial smoothing of autocorrelations to control the degrees of freedom in fMRI analysis.

In the statistical analysis of fMRI data, the parameter of primary interest is the effect of a contrast; of secondary interest is its standard error, and of tertiary interest is the standard error of this standard error, or equivalently, the degrees of freedom (df). In a ReML (Restricted Maximum Likelihood) analysis, we show how spatial smoothing of temporal autocorrelations increases the effective df (but not the smoothness of primary or secondary parameter estimates), so that the amount of smoothing can be chosen in advance to achieve a target df, typically 100. This has already been done at the second level of a hierarchical analysis by smoothing the ratio of random to fixed effects variances (Worsley, K.J., Liao, C., Aston, J.A.D., Petre, V., Duncan, G.H., Morales, F., Evans, A.C., 2002. A general statistical analysis for fMRI data. NeuroImage, 15:1-15); we now show how to do it at the first level, by smoothing autocorrelation parameters. The proposed method is extremely fast and it does not require any image processing. It can be used in conjunction with other regularization methods (Gautama, T., Van Hulle, M.M., in press. Optimal spatial regularisation of autocorrelation estimates in fMRI analysis. NeuroImage.) to avoid unnecessary smoothing beyond 100 df. Our results on a typical 6-min, TR = 3, 1.5-T fMRI data set show that 8.5-mm smoothing is needed to achieve 100 df, and this results in roughly a doubling of detected activations.

Algorithms↗

Ultrasonic motion analysis system--measurement of temporal and spatial gait parameters.

The duration of stance and swing phase and step and stride length are important parameters in human gait. In this technical note a low-cost ultrasonic motion analysis system is described that is capable of measuring these temporal and spatial parameters while subjects walk on the floor. By using the propagation delay of sound when transmitted in air, this system is able to record the position of the subjects' feet. A small ultrasonic receiver is attached to both shoes of the subject while a transmitter is placed stationary on the floor. Four healthy subjects were used to test the device. Subtracting positions of the foot with zero velocity yielded step and stride length. The duration of stance and swing phase was calculated from heel-strike and toe-off. Comparison with data obtained from foot contact switches showed that applying two relative thresholds to the speed graph of the foot could reliably generate heel-strike and toe-off. Although the device is tested on healthy subjects in this study, it promises to be extremely valuable in examining pathological gait. When gait is asymmetrical, walking speed is not constant or when patients do not completely lift their feet, most existing devices will fail to correctly assess the proper gait parameters. Our device does not have this shortcoming and it will accurately demonstrate asymmetries and variations in the patient's gait. As an example, the recording of a left hemiplegic patient is presented in the discussion.

Acoustics↗

CORSICA: correction of structured noise in fMRI by automatic identification of ICA components.

When applied to functional magnetic resonance imaging (fMRI) data, spatial independent component analysis (sICA), a data-driven technique that addresses the blind source separation problem, seems able to extract components specifically related to physiological noise and brain movements. These components should be removed from the data to achieve structured noise reduction and improve any subsequent detection and analysis of signal fluctuations related to neural activity. We propose a new automatic method called CORSICA (CORrection of Structured noise using spatial Independent Component Analysis) to identify the components related to physiological noise, using prior information on the spatial localization of the main physiological fluctuations in fMRI data. As opposed to existing spectral priors, which may be subject to aliasing effects for long-TR data sets (typically acquired with TR >1 s), such spatial priors can be applied to fMRI data, regardless of the TR of the acquisitions. By comparing the proposed automatic selection to a manual selection performed visually by a human operator, we first show that CORSICA is able to identify the noise-related components for long-TR data with a high sensitivity and a specificity of 1. On short-TR data sets, we validate that the proposed method of noise reduction allows a substantial improvement of the signal-to-noise ratio evaluated at the cardiac and respiratory frequencies, even in the gray matter, while preserving the main fluctuations related to neural activity.

Biometry↗

On semi-blind source separation using spatial constraints with applications in EEG analysis.

Blind source separation (BSS) techniques, such as independent component analysis (ICA), are increasingly being used in biomedical signal processing applications, including the analysis of multichannel electroencephalogram (EEG) and magnetoencephalogram (MEG) signals. These methods estimate a set of sources from the observed data, which reflect the underlying physiological signal generating and mixing processes, noise and artifacts. In practice, BSS methods are often applied in the context of additional information and expectations regarding the spatial or temporal characteristics of some sources of interest, whose identification requires complicated post-hoc analysis or, more commonly, manual selection by human experts. An alternative would be to incorporate any available prior knowledge about the source signals or locations into a semi-blind source separation (SBSS) approach, effectively by imposing temporal or spatial constraints on the underlying source mixture model. This work is concerned with biomedical applications of SBSS using spatial constraints, particularly for artifact removal and source tracking in EEG analysis, and provides definitions of different types of spatial constraint along with general guidelines on how these can be implemented in conjunction with conventional BSS methods.

Algorithms↗

Genetic microstructure in two Spanish cat populations. II: gametic disequilibrium and spatial autocorrelation.

In a previous publication, we described some aspects of the microgenetic structure of two Spanish cat populations (in Barcelona and Alicante). In the present study, the possible existence ofgametic disequilibrium and spatial genetic structure for these populations, at the coat colour pattern and length genes O, A, T D, L, S and W, was analyzed. There was little gametic disequilibrium between pairs of these loci, despite certain pairs that showed significant systematic gametic disequilibrium (a-d and O-S), which appears to show the action of natural selection on domestic cat populations. Nevertheless, we believe that the major cause of the small amount of gametic disequilibrium found was probably a combination of gene drift and gene flow. The results obtained here were clearly in disagreement with those of Hedrick (1985), who concluded that epistatic selection was the cause of the gametic disequilibrium that he found in cat populations. We also found that although Hardy-Weinberg equilibrium could not be demonstrated, the gametic disequilibrium statistics were not affected by this fact, adding credence to the estimates obtained. We found no genetic spatial structure inside the city of Barcelona, as shown by analysis of the spatial autocorrelation of the individual loci, and analysis of the coordinates of the two first axes of a multidimensional scale. However, some gametic disequilibrium statistics showed certain spatial patterns, which leads us to consider the possibility of several evolutionary processes acting upon some of Barcelona's cat colonies.

Alleles↗

[Analysis on variation of urinary iodine of children by spatial autoregressive model].

OBJECTIVE: To study spatial autocorrelation and spatial variation of urinary iodine of children and to provide references for statistical data analysis of spatial disease. METHODS: Taking urinary iodine as response variable, salt iodine and altitude as independent variable, linear regression and spatial autoregressive models were made. RESULTS: 69.8%, 32.8%, 43.9% variations of children urinary iodine were caused by salt iodine, altitude and spatial autocorrelation in 1995, 1997 and 1999, took altitude away, 57.6%, 21.4%, 18.8% of variations of urinary iodine were caused by other spatial factors. Positive correlation was showed between the level of urinary iodine and salt iodine, negative correlation was showed between urinary iodine and altitude. CONCLUSION: There was higher clustering in the geographical location among urinary iodine of children, the level of urinary iodine had been decreased since 1995. This implied that status of nutrition had been improved and one of most effective way to control iodine deficiency disorders was through universal salt iodization.

Altitude↗

Spatial patterns of malaria in the Amazon: implications for surveillance and targeted interventions.

A measure of local spatial association, G(i)*(d), is applied to test for the presence of malaria clusters in a colonization area in the Brazilian Amazon. Clusters of high and low malaria rates at different moments in time are identified. They suggest unambiguous spatial patterns of transmission, most likely linked to the social and natural habitat. Results imply that a comprehensive identification of the determinants of malaria transmission requires a spatial framework of analysis, and that control strategies must be spatially targeted and guided by a surveillance system that constantly learns the specificities of local transmission and adapts interventions to them.

Brazil↗

[Spatial heterogeneity of demersal fish in East China Sea].

Quantitative analysis for the spatial distribution of fish is one of the important methods in fishery or fish ecology research. In this paper, the indexes Geary c and Moran I for the density distribution of demersal fish were calculated, and the semivariograms were drawn. The values of Geary c and Moran I were 0.38 and 0.52, respectively, and the C0/C0 + C was 59.9%, which meant that the distribution had a medium spatial autocorrelation with anisotropy, and the heterogeneity caused by random was a little higher than that caused by spatial autocorrelative process. The annual fluctuation of density was caused by the spatial autocorrelation and the random, because the density was significantly positively correlated with the values of C, C0 and C + C0, respectively.

Algorithms↗

Microbial communities and their interactions in biofilm systems: an overview.

Several important advances have been made in the study of biofilm microbial populations relating to their spatial structure (or architecture), their community structure, and their dependence on physicochemical parameters. With the knowledge that hydrodynamic forces influence biofilm architecture came the realization that metabolic processes may be enhanced if certain spatial structures can be forced. An example is the extent of plasmid-mediated horizontal gene transfer in biofilms. Recent in situ work in defined model systems has shown that the biofilm architecture plays a role for genetic transfer by bacterial conjugation in determining how far the donor cells can penetrate the biofilm. Open channels and pores allow for more efficient donor transport and hence more frequent cell collisions leading to rapid spread of the genes by horizontal gene transfer. Such insight into the physical environment of biofilms can be utilized for bioenhancement of catabolic processes by introduction of mobile genetic elements into an existing microbial community. If the donor organisms themselves persist, bioaugmentation can lead to successful establishment of newly introduced species and may be a more successful strategy than biostimulation (the addition of nutrients or specific carbon sources to stimulate the authochthonous population) as shown for an enrichment culture of nitrifying bacteria added to rotating disk biofilm reactors using fluorescent in situ hybridization (FISH) and microelectrode measurements of NH4+, NO2-, NO3-, and O2. However, few studies have been carried out on full-scale systems. Bioaugmentation and bioenhancement are most successful if a constant selective pressure can be maintained favoring the promulgation of the added enrichment culture. Overall, knowledge gain about microbial community interactions in biofilms continues to be driven by the availability of methods for the rapid analysis of microbial communities and their activities. Molecular tools can be grouped into those suitable for ex situ and in situ community analysis. Non-spatial community analysis, in the sense of assessing changes in microbial populations as a function of time or environmental conditions, relies on general fingerprinting methods, like DGGE and T-RFLP, performed on nucleic acids extracted from biofilm. These approaches have been most useful when combined with gene amplification, cloning and sequencing to assemble a phylogenetic inventory of microbial species. It is expected that the use of oligonucleotide microarrays will greatly facilitate the analysis of microbial communities and their activities in biofilms. Structure-activity relationships can be explored using incorporation of 13C-labeled substrates into microbial DNA and RNA to identify metabolically active community members. Finally, based on the DNA sequences in a biofilm, FISH probes can be designed to verify the abundance and spatial location of microbial community members. This in turn allows for in situ structure/function analysis when FISH is combined with microsensors, microautoradiography, and confocal laser scanning microscopy with advanced image analysis.

Bacteria↗

Spatio-temporal growth dynamics of a subAlpine Pinus uncinata stand in the French Alps.

Natural forests are characterised by a high level of both spatial and temporal heterogeneity. The major processes involved in the creation and maintenance of forest heterogeneity in temperate climates are small-sized canopy disturbances. The resulting openings also modify the growth conditions for the remaining trees. The analysis of tree growth responses using dendrochronological techniques allows the reconstruction of the time sequence of the disturbances. The radial growth analysis is coupled here with both a spatial analysis and a demographic analysis of the forest structure. The age classes are temporally organised in cohorts and spatially distributed in spatial aggregates. The analysis of the most documented disturbance event allowed us to determine the size of the disturbance response patch (between 0.036 and 0.073 ha) and the duration of the disturbance (six years). We considered that this small-scale disturbance event may have been caused by the fall of a single tree and has freed the surrounding trees of its competition.

Altitude↗

Spatial distribution functions as a tool in the analysis of ribonucleic acids hydration--molecular dynamics studies.

The spatial distribution functions (SDFs) determined as three-dimensional density distribution of hydrogen and oxygen atoms of water in a local coordinate system linked with RNA molecule are used to study details of the spatial structure of aqueous solution around selected parts of RNA duplexes: r(CGCGCG)2 and 2'-O-Me(CGCGCG)2. The influence of the 2'-O-methylation on the hydration pattern of RNA helical fragments is visualized at the atomic level.

Base Pairing↗

Spatial statistical modeling of disease outbreaks with particular reference to the UK foot and mouth disease (FMD) epidemic of 2001.

In this paper we examine issues relating to the analysis of spatially-referenced disease data. Initially, we discuss the use of exploratory statistical tools such as density estimation and nonparametric regression. We then consider the need for descriptive epidemic models in space, time, and space-time models for epidemic dynamics. Implicitly space-time must be considered in any analysis of the spatial structure of epidemics. The use of Bayesian models for disease spread is discussed and applied to the recent foot and mouth outbreak in the UK.

Animals↗

Geostatistical analysis of disease data: accounting for spatial support and population density in the isopleth mapping of cancer mortality risk using area-to-point Poisson kriging.

BACKGROUND: Geostatistical techniques that account for spatially varying population sizes and spatial patterns in the filtering of choropleth maps of cancer mortality were recently developed. Their implementation was facilitated by the initial assumption that all geographical units are the same size and shape, which allowed the use of geographic centroids in semivariogram estimation and kriging. Another implicit assumption was that the population at risk is uniformly distributed within each unit. This paper presents a generalization of Poisson kriging whereby the size and shape of administrative units, as well as the population density, is incorporated into the filtering of noisy mortality rates and the creation of isopleth risk maps. An innovative procedure to infer the point-support semivariogram of the risk from aggregated rates (i.e. areal data) is also proposed. RESULTS: The novel methodology is applied to age-adjusted lung and cervix cancer mortality rates recorded for white females in two contrasted county geographies: 1) state of Indiana that consists of 92 counties of fairly similar size and shape, and 2) four states in the Western US (Arizona, California, Nevada and Utah) forming a set of 118 counties that are vastly different geographical units. Area-to-point (ATP) Poisson kriging produces risk surfaces that are less smooth than the maps created by a naïve point kriging of empirical Bayesian smoothed rates. The coherence constraint of ATP kriging also ensures that the population-weighted average of risk estimates within each geographical unit equals the areal data for this unit. Simulation studies showed that the new approach yields more accurate predictions and confidence intervals than point kriging of areal data where all counties are simply collapsed into their respective polygon centroids. Its benefit over point kriging increases as the county geography becomes more heterogeneous. CONCLUSION: A major limitation of choropleth maps is the common biased visual perception that larger rural and sparsely populated areas are of greater importance. The approach presented in this paper allows the continuous mapping of mortality risk, while accounting locally for population density and areal data through the coherence constraint. This form of Poisson kriging will facilitate the analysis of relationships between health data and putative covariates that are typically measured over different spatial supports.

Cluster Analysis↗

Use of spatial models for community program evaluation of changes in alcohol outlet distribution.

Alcohol outlets have geographic and spatial characteristics which are important for researchers to consider when planning and evaluating community prevention programs. Community-level data used in monitoring alcohol problems across community areas and over time exhibit spatial dependencies. Statistical procedures which depend on assumptions of independence may fail to give proper results in such a situation. Specific statistical techniques have been developed which adjust for the effects of spatial dependencies in measures across geography. This paper provides an example of the creation and use of computer Geographic Information Systems to display community alcohol outlets and alcohol-involved problems and the use of statistical analysis techniques which account for such spatial dependencies over time. This paper introduces the concepts, terminology, and justification for considering spatial analysis in community prevention planning, research and evaluation. The selection of a geographical unit of analysis will be discussed. Finally, as a demonstration, a variety of spatial statistics are applied to community spatial data for evaluation.

Alcohol Drinking↗

Geostatistical analysis of disease data: visualization and propagation of spatial uncertainty in cancer mortality risk using Poisson kriging and p-field simulation.

BACKGROUND: Smoothing methods have been developed to improve the reliability of risk cancer estimates from sparsely populated geographical entities. Filtering local details of the spatial variation of the risk leads however to the detection of larger clusters of low or high cancer risk while most spatial outliers are filtered out. Static maps of risk estimates and the associated prediction variance also fail to depict the uncertainty attached to the spatial distribution of risk values and does not allow its propagation through local cluster analysis. This paper presents a geostatistical methodology to generate multiple realizations of the spatial distribution of risk values. These maps are then fed into spatial operators, such as in local cluster analysis, allowing one to assess how risk spatial uncertainty translates into uncertainty about the location of spatial clusters and outliers. This novel approach is applied to age-adjusted breast and pancreatic cancer mortality rates recorded for white females in 295 US counties of the Northeast (1970-1994). A public-domain executable with example datasets is provided. RESULTS: Geostatistical simulation generates risk maps that are more variable than the smooth risk map estimated by Poisson kriging and reproduce better the spatial pattern captured by the risk semivariogram model. Local cluster analysis of the set of simulated risk maps leads to a clear visualization of the lower reliability of the classification obtained for pancreatic cancer versus breast cancer: only a few counties in the large cluster of low risk detected in West Virginia and Southern Pennsylvania are significant over 90% of all simulations. On the other hand, the cluster of high breast cancer mortality in Niagara county, detected after application of Poisson kriging, appears on 60% of simulated risk maps. Sensitivity analysis shows that 500 realizations are needed to achieve a stable classification for pancreatic cancer, while convergence is reached for less than 300 realizations for breast cancer. CONCLUSION: The approach presented in this paper enables researchers to generate a set of simulated risk maps that are more realistic than a single map of smoothed mortality rates and allow the propagation of cancer risk uncertainty through local cluster analysis. Coupled with visualization and querying capabilities of geographical information systems, animated display of realizations can highlight areas that depart consistently from the general behavior observed across the region, guiding further investigation and control activities.

Cluster Analysis↗

Multiplex FISH analysis of a six-species bacterial biofilm.

Established procedures use different and seemingly incompatible experimental protocols for fluorescent in situ hybridization (FISH) with Gram-negative and Gram-positive bacteria. The aim of this study was to develop a procedure, based on FISH and confocal laser scanning microscopy (CLSM), for the analysis of the spatial organization of in vitro biofilms containing both Gram-negative and Gram-positive oral bacteria. Biofilms composed of the six oral species Actinomyces naeslundii, Candida albicans, Fusobacterium nucleatum, Streptococcus oralis, Streptococcus sobrinus, and Veillonella dispar were grown anaerobically for 64.5 h at 37 degrees C on hydroxyapatite disks preconditioned with saliva. Conditions for the simultaneous in situ hybridization of both Gram-negative and Gram-positive bacteria were sought by systematic variation of fixation and exposure to lysozyme. After fixation and permeabilization biofilms were labeled by FISH with 16S rRNA-targeted oligonucleotide probes ANA103 (for the detection of A. naeslundii), EUK116 (C. albicans), FUS664 (F. nucleatum), MIT447 and MIT588 (S. oralis), SOB174 (S. sobrinus), and VEI217 (V. dispar). Probes were used as 6-FAM, Cy3 or Cy5 conjugates, resulting in green, orange-red or deep-red fluorescence of target cells, respectively. Thus, with two independent triple-hybridizations with three probes carrying different fluorescence-tags, all six species could be visualized. Results show that the simultaneous investigation by FISH of complex biofilms composed of multiple bacterial species with differential Gram-staining properties is possible. In combination with the optical sectioning properties of CLSM the technique holds great promise for the analysis of spatial alterations in biofilm composition in response to environmental challenges.

Biofilms↗

Cellular and paracellular resistances of the Necturus proximal tubule.

Individual resistances of the apical cell membrane Ra, the basolateral cell membrane, Rbl, and the paracellular shunt, Rs, were determined in the Necturus proximal tubule using a set of three electrical parameters. Four electrical parameters were measured: the transepithelial resistance, (Rte), the apical and basolateral cell membrane resistance in parallel, (Rz free-flow tubules), the basolateral cell membrane resistance in oil-filled tubules, (Rz oil-filled), and the ratio of apical and basolateral cell membrane resistance (Ra/Rbl). Rte was determined from an analysis of the spatial decay of luminal voltage following luminal current injection. Rz free-flow and Rz oil-filled were measured by the analysis of the spatial decay of intracellular voltage deflections following cellular current injection in free flow and oil-filled tubules, respectively. Ra/Rbl was estimated from the ratio of voltage deflections across the apical and basolateral cell membranes following transepithelial current injection. In addition, the magnitude of cellular and luminal cable interactions was evaluated, by comparing the spatial decay of voltage deflections in the cell and in the lumen following intracellular current injection. The combined cell membrane resistance (Ra + Rbl) is between one to two orders of magnitude greater than the paracellular resistance. This result supports the view that the Necturus proximal tubule is a leaky epithelium.

Animals↗