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Results for “Spatial heterogeneity”

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PubMed2006

[Spatial heterogeneity of soil moisture in Shapotou sand-fixing artificial vegetation area].

To explore the characteristics of soil moisture heterogeneity in sand-fixing artificial vegetation area is of significance in vegetation recovery and environment control in arid regions. With the methods of traditional statistics and geo-statistics, this paper studied the heterogeneity of soil moisture in the layers from 0 to 200 cm in depth in Shapotou sand-fixing vegetation area. The results showed that the variation of soil moisture in layers of 160 to approximately 180 and 180 to approximately 200 cm was relatively larger, with the variation coefficient being 0.72 and 0.73, respectively, and the next was in top layer (0 to approximately 5 cm ), with a variation coefficient of 0.66. Semi-variance analysis showed that the autocorrelation of soil moisture spatial heterogeneity in total spatial heterogeneity was high, ranging from 87.7% to 99.9%. The scale of spatial heterogeneity in different soil layers was different, with the minimum in 60 to approximately 80 cm layer and the maximum in 20 to approximately 40 cm layer, but no regular changes being observed from surface to deep layers. The colorful contour maps of Kriging interpolation indicated that the variation of soil moisture was larger in 0 to approximately 140 cm layer than in 140 to approximately 200 cm layer. The correlation between semi-variance and distance in four directions of 0 degrees, 45 degrees ,90 degrees and 135 degrees was weak, suggesting that the variation of soil moisture was independent, random, and homogeneous.

Conservation of Natural Resources↗

PubMed2002

The effect of drinking water treatment on the spatial heterogeneity of micro-organisms: implications for assessment of treatment efficiency and health risk.

The effect of drinking water treatment (ferric coagulation, floc blanket clarification, rapid sand filtration) on the spatial heterogeneity of five species of micro-organism was studied at pilot scale. It was found that the spatial heterogeneity of vegetative bacteria (namely total coliform and heterotrophic (22 degrees C; 3 d) bacteria) was little affected by treatment. Indeed, counts of total coliform bacteria within 500 l volumes of treated water were Poisson distributed (i.e. showed minimum variation). In contrast, treatment appeared to increase the spatial heterogeneity (or clustering) of both aerobic spores indigenous to the raw water and Bacillus subtilis var niger spores added to the raw water. Furthermore, B. subtilis var niger spores added to the raw water were detected in the treated water 25 h after termination of spiking to the raw water. The effect on C. parvum oocysts added to the raw water could not be determined because few oocysts broke through treatment into the treated water. Indeed oocyst removals of 5-6 logs were apparent. "Species-specific" differences in the removal ratios were also demonstrated. It is concluded that audits for treatment processes based on single 100 ml "spot" samples for spores will tend to over-estimate the net spore removal and hence underestimate the public health risk. Spatial heterogeneity of counts in treated water contributes to explaining why no "ideal" surrogate has been identified for treatment plant performance.

Animals↗

PubMed2004

Temperature dependence of spatially heterogeneous dynamics in a model of viscous silica.

Molecular dynamics simulations are performed to study spatially heterogeneous dynamics in a model of viscous silica above and below the critical temperature of the mode coupling theory, T(MCT) . Specifically, we follow the evolution of the dynamic heterogeneity as the temperature dependence of the transport coefficients shows a crossover from non-Arrhenius to Arrhenius behavior when the melt is cooled. It is demonstrated that, on intermediate time scales, a small fraction of oxygen and silicon atoms are more mobile than expected from a Gaussian approximation. These highly mobile particles form transient clusters larger than that resulting from random statistics, indicating that the dynamics are spatially heterogeneous. An analysis of the clusters reveals that the mean cluster size is maximum at times intermediate between ballistic and diffusive motion, and the maximum size increases with decreasing temperature. In particular, the growth of the clusters continues into the crossover to Arrhenius behavior for the transport coefficients. These findings imply that the structural relaxation in silica cannot be understood as a statistical bond breaking process. Although the mean cluster sizes for silica are at the lower end of the spectrum of values reported in the literature for other model liquids, we find that spatially heterogeneous dynamics in models of strong and fragile glass formers are similar on a qualitative level. However, unlike the results for fragile liquids, we show that correlated particle motion along quasi-one-dimensional, stringlike paths is of little importance for the structural relaxation in this model of silica, suggesting that stringlike motion is suppressed by the presence of a network structure. To study transient clusters of localized particles, we calculate a generalized susceptibility corresponding to the self-part of a four-point time dependent density correlation function. We find that this generalized susceptibility is maximum on the time scale of the structural relaxation, where a strong increase of the peak height indicates a growing length of spatial correlations between localized particles upon cooling. Characterizing the local structural environments of the most mobile and the most immobile particles, respectively, we show that high particle mobility is facilitated by, but not limited to, the vicinity of defects in the network structure.

Journal Article↗

PubMed2003

[Spatial heterogeneity of Ulmus pumila open forest ecosystem in Otindag sandy land].

Ulmus pumila open forest ecosystem plays an important role in Otindag Sandy Land. Using biostatistics (U test and Pearson correlation analysis) and geostatistics (Semivariogram analysis and Kriging interpolation), the spatial heterogeneity of soil organic matter (SOM), soil total nitrogen (STN), soil pH (SpH), soil water content (SWC), and the correlations between them, as well as their relationships with herbaceous coverage (HC) and Ulmus pumila were studied. The results showed that spatial heterogeneity and spatial dependence were apparent in SOM, STN, SpH, SWC and HC. With Kriging interpolation in the sampling area, the contour maps for these properties were drawn. Using the contour maps, the relationship between Ulmus pumila and spatial heterogeneity of the studied properties was investigated. The possible reason for the formation of fertility island under the Ulmus pumila trees in the ecosystem was discussed.

Ecosystem↗

PubMed2004

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion.

BACKGROUND: Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach. METHODS: We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1) surface contact heating and (2) spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42 degrees C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image. RESULTS: The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45 degrees C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip. CONCLUSIONS: The heat transport system model of the skin was solved by exploiting the mathematical analogy between local thermal models and local electrical (charge transport) models, thereby allowing robust, circuit simulation software to obtain solutions to Kirchhoff's laws for the system model. Transport lattices allow systematic introduction of realistic geometry and spatially heterogeneous heat transport mechanisms. Local representations for both simple, passive functions and more complex local models can be easily and intuitively included into the system model of a tissue.

Blood Flow Velocity↗

PubMed2005

Spatial heterogeneity of DTPA-extractable zinc in cultivated soils induced by city pollution and land use.

The spatial heterogeneity of DTPA-extractable zinc in the cultivated soils of Shenyang suburbs in Liaoning Province of China was investigated, and its map was drawn by the methods of geostatistics combined with geographic information system. The data of soil DTPA-extractable zinc fitted normal distribution after logarithm transformation, and its semivariogram fitted a spherical model. The semivariogram indicated that the spatial dependence of soil DTPA-extractable zinc content was moderate, with the spatial dependence range of 1.69 km and the fractal dimension of 1.96. Stochastic factors contributed to 49.9% of the spatial variability, while structural factors contributed to 50.1% of it. The spatial heterogeneity of soil DTPA-extractable zinc shown by a kriged interpolation map was deeply influenced by stochastic factors such as city pollution, land use pattern and crop distributions. For example, the average content of Zn in vegetable garden soils was 2.5-4 times as much as in their originated soils, and was lower in paddy soils than in their originated soils. The areas with a higher content of soil DTPA-extractable zinc appeared in the near suburbs and the riverside along Hunhe River and the wastewater drainage of Xihe River, and the extremely high values in the near suburb of the city's residential area were a striking feature, indicating the key role of city pollution in the spatial heterogeneity of soil DTPA-extractable zinc. When recorded in the form of a soil pollution map, the results of such a survey make it possible to identify the unusually polluted areas, and to provide more information for precise agriculture and environmental control.

Agriculture↗

PubMed1985

Dependence of spatial heterogeneity of myocardial blood flow on mean blood flow rate in the rabbit heart.

The relationship between spatial heterogeneity of myocardial blood flow and the rate of perfusion was examined in anaesthetised-chest rabbits. Blood flow determinations employed the radioactive microsphere technique. Five tissue samples were obtained from each of four regions of the left ventricle: left septum, right septum, subendocardium and subepicardium. Standard deviation (SD) and the coefficient of variation (CV = SD/mean flow x 100), an index of spatial heterogeneity, were computed. A wide range of mean coronary flows was obtained in seven groups by inspiration of room air, 8% O2, 8% O2 and 10% CO2, 100% O2, 100% O2 and hyperventilation, and by administration of adenosine or chromomar HCl. Significant differences in CV were found between treatment groups at the upper and lower ends of the flow range. A significant positive linear correlation between overall SD and mean coronary flow was found (r = 0.760). A significant inverse linear relationship between CV and mean flow was found over the entire range of flows studied (r = -0.482). An improved correlation between CV of calculated coronary vascular resistance and mean vascular resistance (r = 0.742) amongst these treatments suggests that spatial heterogeneity is better described by the variability in calibre of large arterioles. This decreased heterogeneity accompanying high flows or reduced vascular resistance may be beneficial in terms of O2 supply and demand under conditions of myocardial stress.

Adenosine↗

PubMed2005

Global production increased by spatial heterogeneity in a population dynamics model.

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production. We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations.

Models, Theoretical↗

PubMed1998

Programs for assessment of spatial heterogeneity of regional organ blood flow.

Regional organ blood flow (RBF) is spatially heterogeneous. Relative dispersion (standard deviation S.D./mean) is often used to assess heterogeneity of RBF. Relative dispersion is a global measure of heterogeneity and is strongly influenced by the tissue sample size making comparisons between research groups inappropriate. Spatial correlation (s.c.) of blood flow is, on the other hand, averaged local self similarity. Both parameters change oppositely secondary to interventions. Fractal dimension (D) is a scale-independent measure of spatial heterogeneity and thus facilitates comparison of data. Programs for calculation of s.c. and D have not been published. We present two portable computer programs written in C+2 for calculating s.c. and D. The programs were validated with six computer generated data sets of known heterogeneity. The results were in agreement with data from the literature: we conclude that the programs accurately calculate spatial correlation and fractal dimension of 1-, 2-, or 3-dimensional perfusion matrices.

Humans↗

PubMedDate not supplied

[Statistical approaches to test for spatial heterogeneity of relative risks of cause-specific mortality in Alto Vicentino Municipalities (years 1991-2000)].

OBJECTIVE: To review the statistical approaches to test for spatial heterogeneity of relative risks. Three different statistical tests (Gail, Martuzzi-Hills and Potthoff-Whittinghill) are reviewed and applied--as motivating example--to the analysis of cause-specific mortality records (years: 1991-2000) of the Municipalities belonging to the Local Health Unit Alto Vicentino. METHODS: Spatial heterogeneity was found in 17 (Martuzzi-Hills) and 18 (Gail, Potthoff-Whittinghill) among 70 selected causes of death. Cohens Kappa test was chosen to assess the agreement among the tests (k = 0.596; p < or = 0.001). CONCLUSION: Spatial heterogeneity must be interpreted with great caution, taking into account the available evidence about risk factors for specific causes of death and carefully evaluating available exposure data.

Cardiovascular Diseases↗

PubMed2006

Spatial heterogeneity of personal exposure to airborne metals in French urban areas.

The spatial distribution of urban population exposures to ambient air particles was investigated as part of the Genotox'ER study conducted in four metropolitan areas (Grenoble, Paris, Rouen and Strasbourg) in France. In each city, 60 to 90 non-smoking adult and children volunteers were selected. Subjects lived in three different urban sectors: one highly exposed to traffic emissions, one influenced by local industrial sources, and a background urban environment. The Harvard Chempass multi-pollutant personal sampler was used to sample PM10 and PM2.5 particles during 48 h during two different seasons ('hot' and 'cold'). The elemental composition of the filters was analysed by Particle-Induced X-ray Emission (PIXE). Sixteen elements were found to be over the method detection limits: Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn and Pb. The relative concentrations of elements of crustal origin (Si, Al, Ca) were higher in the coarse fraction of PM10 filters, while elements associated with combustion processes (traffic emissions or industrial combustion) presented higher relative concentrations in the PM2.5 fraction (S, Ni, V, Pb). Spatial heterogeneity of elemental exposures by urban sector is substantial for some metals of health concern, with 20% to 90% greater exposure values, on average, in the traffic proximity or industrial sectors, compared to the background sector, for Fe, Zn, Cu, V and Cr. This spatial heterogeneity should not be overlooked in epidemiological or risk assessment studies.

Adolescent↗

PubMed2005

Influence of spatial heterogeneity on an emerging infectious disease: the case of dengue epidemics.

The importance of spatial heterogeneity and spatial scales (at a village or neighbourhood scale) has been explored with individual-based models. Our reasoning is based on the Chilean Easter Island (EI) case, where a first dengue epidemic occurred in 2002 among the relatively small population localized in one village. Even in this simple situation, the real epidemic is not consistent with homogeneous models. Conversely, including contact heterogeneity on different scales (intra-households, inter-house, inter-areas) allows the recovery of not only the EI epidemiological curve but also the qualitative patterns of Brazilian urban dengue epidemic in more complex situations.

Brazil↗

PubMed1988

Spatial heterogeneity of local blood flow and metabolite content in dog hearts.

Spatial variation (heterogeneity) of myocardial blood flow was studied under basal conditions in relation to four biochemical markers: creatine kinase (CK), lactate dehydrogenase (LDH), ATP, and glycogen. A total of 508 individual 0.5-g samples from the left ventricular free wall was studied in 12 dogs. Myocardial blood flow was measured by radioactive microspheres (15 micron diam) injected via a pigtail catheter into the left ventricle during light sedation (closed-chest flow measurements); following thoracotomy, a second set of microspheres was injected via a catheter into the left atrium (open-chest flow measurements, n = 5). In 27-54 samples/heart, myocardial blood flow, CK, LDH, protein, ATP, and glycogen were determined, permitting a direct correspondence between local blood flow and metabolic markers in each sample and an assessment of the spatial heterogeneity of flow and metabolite content. Correlations between myocardial blood flow per gram tissue and metabolite concentration per gram tissue in pooled data were weak but significant: partial correlation coefficients were 0.137 for CK (P = 0.024), 0.167 for LDH (P = 0.006), 0.341 for ATP (P less than 0.001), 0.123 for glycogen (P = 0.053), but not significant for protein vs. myocardial blood flow. The coefficient of variation, which defines the extent of spatial heterogeneity, averaged 20% for closed-chest flow measurements, 19% for open-chest flow measurements, 22% for CK, 17% for LDH, 15% for protein, 8% for ATP, and 18% for glycogen; these values are over and above the variability due to the technique error, indicating a definite physiological spatial variability. The correlation between local blood flow and the studied metabolites can only explain a minor portion of the spatial heterogeneity of myocardial blood flow. Although a physiological link between blood flow and metabolite content for small regions of the heart is demonstrated, the true local variability of blood flow may be modulated predominantly by other factors.

Adenosine Triphosphate↗

PubMed2002

Spatial heterogeneity and the stability of reaction states in autocatalysis.

The impact of stochasticity and spatial heterogeneity on the quadratic autocatalytic system is studied. In a nonspatial setting the reactive state of the system is found to be unstable in small volumes where internal fluctuations drive the system to the unreactive state. This phenomena is of potential importance to the stability of reactions in biological cells. A simple spatial model is constructed by linking N nonspatial models via migration of reactants controlled by a mixing rate lambda. Simulation of this stochastic process demonstrates the importance of such mixing in controlling the impact of internal fluctuations on the stability of the autocatalytic reaction. For high mixing rate the mean reactant levels in equilibrium correspond to the well-mixed deterministic system, although a significant degree of spatial heterogeneity remains. For intermediate mixing rates, mean reactant levels vary continuously with lambda, where the interaction of internal fluctuations with limited spatial mixing modifies the reactive states of the deterministic system. However, there is a threshold below which mixing is unable to control internal fluctuations which drive the system into the unreactive state. Thus a critical minimum level of communication between the cells is required to stabilize the reaction across the entire system. Approximate analytic results, obtained using moment-closure techniques, support these findings and demonstrate the relationship between the spatial stochastic and nonspatial deterministic models.

Biophysical Phenomena↗

PubMed2004

Index for spatial heterogeneity in breast cancer.

Histopathological heterogeneity in cancer is a general concern. Breast carcinoma heterogeneity is now widely admitted as a source of histological grading imprecision and reproducibility problems. Classically, homogeneity is defined as equivalent to stationarity. A measure of heterogeneity based on asymptotic properties of spatial statistics is developed. Long-range dependences in heterogeneous spatial processes make estimation of the proposed heterogeneity measure unreliable. A robust estimator based on the wavelet transform is presented; this bypasses long-range dependences. The estimator extends previous works on one-dimensional stochastic processes to two dimensions as appropriate for histopathological analysis. As a side result, the estimator gives confidence intervals for the heterogeneity measure that enables the formulation and validation of testable hypothesis on the observed histopathological samples. This approach is applied to the characterization of breast cancer tumours. We show that the heterogeneity measure for various blocks of a single tumour is invariable, even when various blocks differ in size and in number of marked nuclei.

Breast Neoplasms↗

PubMed2004

Impact of spatial heterogeneity on a predator-prey system dynamics.

This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium.

Animals↗

PubMed2000

Spatial heterogeneity in fasting and insulin-stimulated (18)F-2-deoxyglucose uptake in pigs with hibernating myocardium.

BACKGROUND: Previous studies of hibernating myocardium in the fasting state have shown regionally increased (18)F-2-deoxyglucose (FDG) uptake with a marked transmural gradient. We hypothesized that this adaptation to chronic ischemia might be associated with altered maximal FDG uptake. METHODS AND RESULTS: Pigs were instrumented with a 1.5-mm proximal left anterior descending artery (LAD) stenosis. Studies were conducted 106+/-4 days later on anesthetized animals with complete LAD occlusion and anteroapical dysfunction. In fasting animals (n=9), FDG uptake in dysfunctional LAD regions was 2-fold higher than in normally perfused myocardium (7.9+/-1.2 versus 4. 0+/-0.5 micromol x min(-1) x 100 g(-1), P<0.05), with a pronounced transmural gradient (endocardial/epicardial ratio 2.56+/-0.19 versus 1.25+/-0.03, P<0.05). Euglycemic, hyperinsulinemic clamp (insulin clamp, n=8) produced a 5- to 9-fold increase in FDG uptake, but there was no longer a regional difference in accumulation (LAD, 37. 8+/-4.2 versus normal, 36.4+/-5.1 micromol x min(-1) x 100 g(-1), P=NS) and the transmural distribution was uniform. FDG uptake in the fasting state varied inversely with coronary flow during vasodilation. In contrast, during insulin clamp there was no relation between FDG uptake and vasodilated flow, resulting in a reduced spatial heterogeneity in individual samples (relative dispersion=SD/mean; fasting, 52+/-5% versus insulin, 24+/-2%, P<0.05). CONCLUSIONS: In the fasting state, FDG uptake in pigs with hibernating myocardium was heterogeneous and was increased in dysfunctional regions with a marked transmural gradient and high spatial heterogeneity. In contrast, FDG uptake was more homogeneously distributed during insulin clamp with (1) uptake in dysfunctional myocardium similar to remote normal regions, (2) uniform transmural distribution, and (3) reduced spatial heterogeneity.

Animals↗

PubMedDate not supplied

Influence of spatially heterogeneous background activity on "hot object" quantitation in brain emission computed tomography.

PURPOSE: Our goal was to evaluate the influence of spatially heterogeneous background activity on "hot object" quantitation in brain emission CT. METHOD: We studied the effects of spatially heterogeneous background activity on hot object quantitative recovery in simulations of both spheres and realistic brain distributions (utilizing human MRI data). RESULTS: Significant underestimation of object activity concentration was seen for both cortical and subcortical hot objects, with increasing underestimation for increasing hot object/surrounding gray matter contrast. Significant "spill-in" of counts from surrounding activity was present. CONCLUSION: Hot objects are significantly influenced by both "spill-out" and "spill-in." Qualitative and quantitative analyses of such objects must explicitly consider both spill-out and spill-in; this implies a correction scheme that goes beyond simple division of the observed value by a conventional recovery coefficient.

Brain↗