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PubMed1996

Competition in a spatially heterogeneous environment: modelling the risk of spread of a genetically engineered population.

In recent years regulations have been developed to address the risks of releasing genetically engineered organisms into the natural environment. These risks are generally considered to be proportional to the exposure multiplied by the hazard. Exposure is, in part, determined by the spatial spread of the organisms, a component of risk suited to mathematical analysis. In this paper we exampine a mathematical model describing the spread of organisms introduced into a hetereogeneous environment, focusing on the risk of spread and plausibility of containment strategies. Two competing populations are assumed, one the natural species and the other an engineered species or strain, both of which move randomly in a spatially heterogenous environment consisting of alternating favourable and unfavourable patches. The classical Lotka-Volterra competition model with diffusion is used. Analyses of the possible spread and invasion of engineered organisms are thus reduced to finding periodic travelling wave solutions to the model equations. We focus on whether a very small number of engineered organisms can spatially invade a natural population. Initially we investigate the problem for spatially periodic diffusion coefficients and demonstrate that, under the right circumstances and a large enough unfavourable patch, invasion does not succeed. However, if spatially periodic carrying capacities are assumed along with spatially varying diffusion rates, the situation is far more complex. In this case containment of the engineered species is no longer only a simple function of the unfavourable patch length. By using perturbation solutions to the nonuniform steady states, approximate invasion conditions are obtained.

DNA, Recombinant↗
PubMed2006

Nonparaxial fields with maximum joint spatial-directional localization. I. Scalar case.

In paraxial optics, the spatial and angular localization of a beam are usually characterized through second moments in intensity. For these measures, Gaussian beams have the property of achieving a minimum angular spread for a given spatial spread (or beam waist). For wide-angle fields, however, the standard measures of spatial and angular localization become inappropriate, and new definitions must be used. Previously proposed definitions [J. Opt. Soc. Am. A 17, 2391 (2000)] are adopted, and the scalar monochromatic wave fields that achieve a minimum angular spread for a given spatial spread are found.

Journal Article↗
PubMed1993

Spatial aspects of vertical phoria adaptation.

Vergence adaptation to vertical disparity spreads to unadapted directions of gaze. The spatial spread function for prism adaptation was estimated from aftereffects of a vertical disparity presented at a single position. Constraints limiting the spatial spread of adaptation were investigated with two stimuli of opposite disparity (hyper and hypo), presented at two different eye positions with a separation that varied from 6 to 18 deg in either the horizontal or vertical meridian. On average, phoria adaptation to the single point paradigm spread uniformly across the entire 18 deg test field. A resolution limit for adaptation to the two point paradigm was demonstrated by a reduction of phoria aftereffects with decreasing target separation (crowding). Vertical phoria aftereffects were reduced more by horizontal than by vertical crowding. A disparity gradient limit was demonstrated for a fixed target separation by a reduction of gain (phoria change/stimulus disparity) with increasing stimulus disparity.

Adaptation, Ocular↗
PubMed2005

The spread of infectious diseases in spatially structured populations: an invasory pair approximation.

The invasion of new species and the spread of emergent infectious diseases in spatially structured populations has stimulated the study of explicit spatial models such as cellular automata, network models and lattice models. However, the analytic intractability of these models calls for the development of tractable mathematical approximations that can capture the dynamics of discrete, spatially-structured populations. Here we explore moment closure approximations for the invasion of an SIS epidemic on a regular lattice. We use moment closure methods to derive an expression for the basic reproductive number, R(0), in a lattice population. On lattices, R(0) should be bounded above by the number of neighbors per individual. However, we show that conventional pair approximations actually predict unbounded growth in R(0) with increasing transmission rates. To correct this problem, we propose an 'invasory' pair approximation which yields a relatively simple expression for R(0) that remains bounded above, and also predicts R(0) values from lattice model simulations more accurately than conventional pair and triple approximations. The invasory pair approximation is applicable to any spatial model, since it takes into account characteristics of invasions that are common to all spatially structured populations.

Animals↗
PubMed2001

Bayesian 2-D deconvolution: effect of using spatially invariant ultrasound point spread functions.

Observed ultrasound images are degraded representations of the-true tissue reflectance. The specular reflections at boundaries between regions of different tissue types are blurred, and the diffuse scattering within homogenous regions causes speckle because of the oscillating nature of the transmitted pulse. To reduce both blur and speckle, we have developed algorithms for the restoration of simulated and real ultrasound images based on Markov random field models and Bayesian statistical methods. The algorithm is summarized here, although a more detailed description can be found in our companion paper [1]. Because the point spread function (psf) is unknown, we investigate the effects of using incorrect frequencies and sizes for the model psf during the restoration process. First, we degrade the images either with a known simulated psf or a measured psf. Then, we use different psf shapes during restoration to study the robustness of the method. We found that small variations in the parameters characterizing the psf, less than +/- 25% change in frequency, width, or length, still yielded satisfactory results. When altering the psf more than this, the restorations were not acceptable. The restorations were particularly sensitive to large increases in the restoring psf frequency. Thus, 2-D Bayesian restoration using a fixed psf may yield acceptable results as long as the true variant psfs have not varied too much during imaging.

Bayes Theorem↗
PubMed1977

Spatial frequency and light-spread descriptions of visual acuity and hyperacuity.

Resolution (visual acuity) and differential spatial localization (hyperacuity) targets were selected to allow rigorous psychophysical measurements as well as ready expression of both their spatial frequency spectrum and their retinal image light distribution. Thresholds were about 1 arc min for acuity and 4-6 arc sec for hyperacuity. As is consistent with the reciprocal relationship between the space and spatial frequency domains, the small locally restricted spatial differences between just distinguishable patterns are represented in the frequency domain by equally small differences, which are distributed over the entire spatial frequency spectrum. While they occur in many test situations, phase variations of spatial frequency components are not necessary for achieving optimum acuity and hyperacuity.

Female↗
PubMed2004

Micropatterning of proteins and mammalian cells on biomaterials.

Controlling the spatial organization of cells is vital in engineering tissues that require precisely defined cellular architectures. For example, functional nerves or blood vessels form only when groups of cells are organized and aligned in very specific geometries. Yet, scaffold designs incorporating spatially defined physical cues such as microscale surface topographies or spatial patterns of extracellular matrix to guide the spatial organization and behavior of cells cultured in vitro remain largely unexplored. Here we demonstrate a new approach for controlling the spatial organization, spreading, and orientation of cells on two micropatterned biomaterials: chitosan and gelatin. Biomaterials with grooves of defined width and depth were fabricated using a two-step soft lithography process. Selective attachment and spreading of cells within the grooves was ensured by covalently modifying the plateau regions with commercially available protein resistant triblock copolymers. Precise spatial control over cell spreading and orientation has been observed when human microvascular endothelial cells are cultured on these patterned biomaterials, suggesting the potential of this technique in creating tissue culture scaffolds with defined chemical and topographical features.

Biocompatible Materials↗
PubMed1994

Effects of activation sequence on the spatial distribution of repolarization properties.

The electrotonic effects of activation spread on the spatial distribution of repolarization properties were studied in animal experiments and with computer simulations. Refractory periods (RPs) were measured at 36 sites within a 1.0 cm2 region of the epicardial surface of the canine pulmonary conus during 37 drives in 11 experiments. In each experiment three or four sites along the perimeter of the region bounding the RP test sites were driven. Activation propagated uniformly during some and nonuniformly during other drives in the same animals. In general, RPs were distributed uniformly when activation spread uniformly and nonuniformly when activation spread nonuniformly. The authors observed RP differences as large as 16 ms between sites with 2 mm separation during drive from some epicardial sites in these normal canine hearts. Indices of nonuniformity of activation and of relative RP values were used to quantify the relation between nonuniformity of activation spread and the spatial distribution of the RP. There was a significant negative correlation between nonuniformity of activation and RP indices during the 19 drives in which activation spread nonuniformly. This indicated that RPs were relatively long at sites where activation spread decelerated and relatively short at sites where activation spread accelerated. When nonuniform activation spread was simulated by introducing high-resistance barriers in a model with fixed anisotropic conductivities, there were marked spatial variations in action potential duration. The spatial variations in action potential duration were negatively correlated to acceleration and deceleration of activation spread. The major new finding of this study is that the spatial distributions of RPs are markedly affected by activation spread. Since both characteristics of activation sequence and nonuniformity of RP distributions have roles in reentrant arrhythmias, the findings suggest that some sites of origin of premature activity may be more arrhythmogenic than others. The findings may also explain why ventricular tachycardia can sometimes be initiated from one but not from other sites in patients undergoing electrophysiologic testing.

Action Potentials↗
PubMed1983

Temporal-spatial-social parameters in the spread of contagious disease.

A conceptual theoretical model was built on the basis of prominent concepts of the generally accepted knowledge on the spread of contagious disease. Subsequently, the model was applied to a real epidemic of variola minor (the mild form of smallpox) and four phases of the epidemic were disclosed. The phases discriminated themselves through their relationships to invasion of certain city subdivisions and rural districts and particularly, through the type of social units involved and the type of persons introducing the disease into these units. Introduction of variola minor into day schools with further spread in classes passed across a threshold which led to a boosting of the number of households affected and of the area involved in the epidemic. The phase of maximal spread corresponded to this operation of day schools as diffusion agencies. The temporal-spatial-social correspondence suggests that phases of the epidemic did occur as a result of periodic variation of the mechanism of spread.

Brazil↗
PubMed2006

Epidemiology of bovine brucellosis in Northern Ireland between 1990 and 2000.

Between 1990 and 2000, 317 herds of cattle in Northern Ireland were identified as being seropositive to Brucella abortus, and 68 per cent of them were attributed to transmission from neighbouring herds or to local spread. Of particular significance were three primary outbreaks in 1997, which resulted in significant secondary and tertiary spread. Three spatial clusters were identified, corresponding to two of the primary outbreaks, and the herd density and within-herd spread were highest in the largest cluster. Abortions in an infected herd and the disease-risk status of the disclosure test were positively associated with an increased within-herd prevalence.

Animals↗
PubMed1994

Changes in energy metabolites, cGMP and intracellular pH during cortical spreading depression.

The spatial and temporal distribution of cerebral metabolites and pHi were examined in the cortex during spreading depression. Acidification and marked depression in the energy status of the tissue was evident at the wavefront of spreading depression. In its aftermath, the residual activation of glycolysis and accumulation of cGMP persisted for minutes after a relatively rapid restoration of high-energy phosphates and pHi.

Adenosine Triphosphate↗
PubMed1992

The spread of a parasitic infection in a spatially distributed host population.

Starting from a stochastic model for the spread of a parasitic infection in a spatially distributed host population we describe the way to a continuum formulation by a deterministic model in terms of a nonlinear partial differential equation and an integro-differential equation. The hosts are assumed to occupy fixed spatial positions, whereas the parasites are mobile, however can propagate only within the hosts. To perform the continuum limit we suppose that the size Nh of the host population, the size Np of the parasite population, and the ratio Np/Nh tend to infinity. Accordingly, the parameters determining the time evolution of the host and parasite populations are rescaled suitably.

Cells, Cultured↗
PubMed2006

Measurement of the spatial response of a detector pixel.

In order to measure the internal spatial response of a pixel in a detector, it is scanned by a beam smaller than its size. This becomes difficult as the wave length grows and becomes comparable to the pixel size, such as in the infra red. To overcome this difficulty, a special phase mask which makes the beam narrower was designed, constructed, and tested successfully. The mask was made from five alternating transparent rings, where the rings had half a wave phase difference between them. The beam was scanned with and without the mask in two dimensions in fine steps by a much smaller detector and its response was taken. The spot width dropped by 19% at half its height and by 42% at tenth its height, a significant narrowing. The scan was repeated with the full detector pixel. That beam scan served as a deconvolution kernel and allowed us to find the pixel point spread function (spatial response), the pixel modulation transfer function and the optical cross talk between the pixels.

Journal Article↗
PubMed2006

Estimating transmission intensity for a measles epidemic in Niamey, Niger: lessons for intervention.

The objective of this study is to estimate the effective reproductive ratio for the 2003-2004 measles epidemic in Niamey, Niger. Using the results of a retrospective and prospective study of reported cases within Niamey during the 2003-2004 epidemic, we estimate the basic reproductive ratio, effective reproductive ratio (RE) and minimal vaccination coverage necessary to avert future epidemics using a recent method allowing for estimation based on the epidemic case series. We provide these estimates for geographic areas within Niamey, thereby identifying neighbourhoods at high risk. The estimated citywide RE was 2.8, considerably lower than previous estimates, which may help explain the long duration of the epidemic. Transmission intensity varied during the course of the epidemic and within different neighbourhoods (RE range: 1.4-4.7). Our results indicate that vaccination coverage in currently susceptible children should be increased by at least 67% (vaccine efficacy 90%) to produce a citywide vaccine coverage of 90%. This research highlights the importance of local differences in vaccination coverage on the potential impact of epidemic control measures. The spatial-temporal spread of the epidemic from district to district in Niamey over 30 weeks suggests that targeted interventions within the city could have an impact.

Age Distribution↗
PubMed2000

JNK and decapentaplegic signaling control adhesiveness and cytoskeleton dynamics during thorax closure in Drosophila.

One of the fundamental events in metamorphosis in insects is the replacement of larval tissues by imaginal tissues. Shortly after pupariation the imaginal discs evaginate to assume their positions at the surface of the prepupal animal. This is a very precise process that is only beginning to be understood. In Drosophila, during embryonic dorsal closure, the epithelial cells push the amnioserosa cells, which contract and eventually invaginate in the body cavity. In contrast, we find that during pupariation the imaginal cells crawl over the passive larval tissue following a very accurate temporal and spatial pattern. Spreading is driven by filopodia and actin bridges that, protruding from the leading edge, mediate the stretching of the imaginal epithelia. Although interfering with JNK (Jun N-terminal kinase) and dpp (decapentaplegic) produces similar phenotypic effects suppressing closure, their effects at the cellular level are different. The loss of JNK activity alters the adhesion properties of larval cells and leads to the detachment of the imaginal and larval tissues. The absence of dpp signaling affects the actin cytoskeleton, blocks the emission of filopodia, and promotes the collapse of the leading edge of the imaginal tissues. Interestingly, these effects are very similar to those observed after interfering with JNK and dpp signaling during embryonic dorsal closure.

Animals↗
PubMed1998

Modulation of the frequency of spontaneous sarcoplasmic reticulum Ca2+ release events (Ca2+ sparks) by myoplasmic [Mg2+] in frog skeletal muscle.

The modulation by internal free [Mg2+] of spontaneous calcium release events (Ca2+ "sparks") from the sarcoplasmic reticulum (SR) was studied in depolarized notched frog skeletal muscle fibers using a laser scanning confocal microscope in line-scan mode (x vs. t). Over the range of [Mg2+] from 0.13 to 1.86 mM, decreasing the [Mg2+] induced an increase in the frequency of calcium release events in proportion to [Mg2+]-1.6. The change of event frequency was not due to changes in [Mg-ATP] or [ATP]. Analysis of individual SR calcium release event properties showed that the variation in event frequency induced by the change of [Mg2+] was not accompanied by any changes in the spatiotemporal spread (i.e., spatial half width or temporal half duration) of Ca2+ sparks. The increase in event frequency also had no effect on the distribution of event amplitudes. Finally, the rise time of calcium sparks was independent of the [Mg2+], indicating that the open time of the SR channel or channels underlying spontaneous calcium release events was not altered by [Mg2+] over the range tested. These results suggest that in resting skeletal fibers, [Mg2+] modulates the SR calcium release channel opening frequency by modifying the average closed time of the channel without altering the open time. A kinetic reaction scheme consistent with our results and those of bilayer and SR vesicle experiments indicates that physiological levels of resting Mg2+ may inhibit channel opening by occupying the site for calcium activation of the SR calcium release channel.

Adenine Nucleotides↗
PubMed2000

Proton stopping powers averaged over beam energy spectra.

Stopping powers averaged over the proton energy spectra at various depths in water and a tissue-like material were calculated for proton beams with initial energies between 50 and 250 MeV. The analysis was made for proton beams with a spread-out Bragg peak (SOBP) to assess in particular the variations of stopping power with depth in the SOBP plateau region. Nuclear interactions were accounted for in determination of the proton energy spectra. In modulated beams, stopping power varies considerably with depth along the plateau region of the spread-out peak. Moreover, stopping powers at the same water depth may differ from each other by up to 20% if referring to modulated or non-modulated beams. Calculations of water-air mass stopping power ratios were also performed, with and without the inclusion of nuclear interactions, for modulated and non-modulated beams. The stopping power ratios do not depend significantly on proton energy, and this makes the effect of accounting for nuclear interactions in proton fluence calculation negligible. For the same reason the stopping power ratios for modulated beams do not appreciably differ from those referred to non-modulated beams with the same Emax at the same depth in water. The present results also show that the dependence of stopping power on energy spread and spatial divergence for proton beams is not negligible in some conditions. Some conclusions are drawn on the possibility of using the residual range as a descriptor of the proton beam quality for different experimental beam conditions.

Algorithms↗
PubMed2001

Organization of junctional proteins in proliferating cat corneal endothelium during wound healing.

PURPOSE: To evaluate for the first time cell junctional protein organization in proliferating corneal endothelial cells during in vivo wound healing. METHODS: A total of 16 cats (32 eyes) were used in this study. A single 3-mm diameter (n = 24) or 1- to 2-mm diameter (n = 8) scrape injury was created in the central corneal endothelium of each eye. Twenty-four, 48, 72 hours or 5 days after scrape injury, eyes were collected for in situ double- or triple-labeling with phalloidin, anti-ZO-1, alpha-catenin, beta-catenin, and MIB-1 (monoclonal antibody to Ki67, a marker for actively cycling cells) and were imaged using confocal laser microscopy. RESULTS: In 3-mm diameter injuries, endothelial cells completely resurfaced the wound 48 to 72 hours after scrape injury; smaller wounds resurfaced by 48 hours. Ki67 staining was negative 24 hours after scrape injury in all cases. Ki67-positive cells were observed in the central region of the wounds after 48 and 72 hours, and mitotic figures and pairs of postmitotic cells were observed. On day 5, Ki67-positive cells were rarely detected, and no mitotic figures were observed. In the wound area, a significant increase in cell area and a reduction in hexagonality were observed in cycling cells after 48 and 72 hours. Normal apical, pericellular staining of f-actin, ZO-1, alpha-catenin, and beta-catenin was partially maintained at all times during wound healing of small and large wounds. Double-labeling confirmed that these proteins were also present along the apical cell border in Ki67-positive cells. CONCLUSIONS: After in vivo scrape injury, proliferation is limited temporally and spatially to spreading endothelial cells within the wound. Cell junctional connections appear to be maintained in actively cycling cells during healing.

Actins↗