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At least 19 recordsLinked to original sources
PubMed1986

On the spatial spread of rabies among foxes.

We present a simple model for the spatial spread of rabies among foxes and use it to quantify its progress in England if rabies were introduced. The model is based on the known ecology of fox behaviour and on the assumption that the main vector for the spread of the disease is the rabid fox. Known data and facts are used to determine real parameter values involved in the model. We calculate the speed of propagation of the epizootic front, the threshold for the existence of an epidemic, the period and distance apart of the subsequent cyclical epidemics which follow the main front, and finally we quantify a means for control of the spatial spread of the disease. By way of illustration we use the model to determine the progress of rabies up through the southern part of England if it were introduced near Southampton. Estimates for the current fox density in England were used in the simulations. These suggest that the disease would reach Manchester within about 3.5 years, moving at speeds as high as 100 km per year in the central region. The model further indicates that although it might seem that the disease had disappeared after the wave had passed it would reappear in the south of England after just over 6 years and at periodic times after that. We consider the possibility of stopping the spread of the disease by creating a rabies 'break' ahead of the front through vaccination to reduce the population to a level below the threshold for an epidemic to exist. Based on parameter values relevant to England, we estimate its minimum width to be about 15 km. The model suggests that vaccination has considerable advantages over severe culling.

Animals↗
PubMed2026

Reconstructing the early spatial spread of pandemic respiratory viruses in the United States.

Understanding the geographic spread of emerging respiratory viruses is critical for pandemic preparedness, yet the early spatiotemporal dynamics of the 2009 H1N1 pandemic influenza and severe acute respiratory syndrome coronavirus 2 in the United States remain unclear. While mobility and genomic data have revealed important aspects of pandemic spatial spread, several key questions remain: Did the two pandemics follow similar spatial transmission routes? How rapidly did they spread across the United States? What role did stochastic processes play in early spatial transmission? To address these questions, we integrated high-resolution disease data with a robust, data-efficient inference framework combining air travel, commuting flows, and pathogen superspreading potentials to reconstruct their spatial spread across US metropolitan areas. The two pandemics exhibited distinct transmission pathways across locations; however, both pandemics established local circulation in most metropolitan areas within weeks, driven by several shared transmission hubs. Early spatial spread was more strongly associated with air travel than with commuting, though stochastic dynamics introduced substantial uncertainty in transmission routes, creating challenges for timely detection and control. Simulations indicate that broad wastewater surveillance coverage beyond top transmission hubs coupled with effective infection control may slow initial spatial expansion. Our findings highlight the rapid, stochastic spread of pandemic respiratory pathogens and the difficulties of early outbreak containment.

Humans↗
PubMed1985

A simple model for the spatial spread and control of rabies.

A simple mathematical model for the spatial spread of rabies is presented. It models the dynamics of the front of an epizootic wave. We show how the model can be used to estimate the minimum width (in kilometers) of a break, that is, a region in which a control scheme is employed in order to stop the spatial progression of the rabies wave front. A simple expression is derived for the surviving fox population, after the passage of the epizootic, in terms of measurable parameters of the model.

Animals↗
PubMed1987

Spatial spread of adaptation within the cone network of turtle retina.

1. The spatial characteristics of adaptation were studied in the red-sensitive cones of the snapping turtle retina using intracellular microelectrodes. Light responses elicited with slit-shaped test and adapting stimuli revealed that test response amplitudes and adaptation decline similarly with distance from the impaled cone. The spatial spread of adaptation and the light response cannot be accounted for by scattered light and must therefore result from electrical coupling between cones. 2. The reduction in the amplitude of the test response correlated strongly with the magnitude of the sustained hyperpolarization induced by the adapting fields. This dependence of adaptation on membrane potential was independent of the spatial configuration of the adapting field. 3. The time courses of flash responses were monotonically related to the membrane potential induced by adapting stimuli and were also independent of adapting field configuration. 4. Adapting slits imaged on the cone receptive field centres uniformly depressed sensitivity without altering the shape of the field or its exponential fall-off. Since the membrane potential evoked by the adapting slit falls off exponentially, the invariance of receptive field shape implies that the spread of adaptation cannot be attributed solely to voltage-dependent desensitization of the transduction apparatus in the cones. Therefore a substantial part of the membrane potential dependency of adaptation probably results from a shunting of signals across the plasma membrane of the cone. 5. Full field backgrounds depressed sensitivity but did not alter the receptive field profiles. On the model of electrical coupling proposed by Lamb & Simon (1976), this suggests that to the extent that the voltage-dependent desensitization results from an increased conductance and hence an increased shunt of the signals at the plasma membrane, there must be a concomitant increase in the conductance of the electrical pathways linking cones to one another.

Action Potentials↗
PubMed1977

A model for the spatial spread of an epidemic.

We set up a deterministic model for the spatial spread of an epidemic. Essentially, the model consists of a nonlinear integral equation which has an unique solution. We show that this solution has a temporally asymptotic limit which describes the final state of the epidemic and is the minimal solution of another nonlinear integral equation. We outline the asymptotic behaviour of this minimal solution at a great distance from the epidemic's origin and generalize D. G. Kendall's pandemic threshold theorem (1957).

Disease Outbreaks↗
PubMed1989

Spatial spread of in-field afferent inhibition in the cat's spinocervical tract.

1. Extracellular microelectrode recordings were made from twenty-three spinocervical tract (SCT) cells in the lumbar spinal cord of cats anaesthetized with chloralose and paralysed with gallamine triethiodide. Excitation and inhibition of the cells were elicited by applying small brief (4 mN, 60 ms) localized jets of air to the clipped hair in and around the receptive fields. 2. Receptive field extents ranged from 40 to 180 mm. Excitation occurred in the period 30-130 ms after the start of the stimulus, and in-field afferent inhibition from 130 ms up to 700 ms or more. The inhibition was manifest as a reduction in background discharge and as a reduction in responsiveness to a test stimulus which followed a conditioning stimulus. 3. When the conditioning stimulus was spatially separated from the test stimulus, the degrees of in-field afferent inhibition depended on the spatial separation, even when both were within the excitatory receptive field. The spatial spread of in-field afferent inhibition was limited to 100 mm or less. 4. In two units only, afferent inhibition was produced from a narrow strip just outside the excitatory receptive field. In the other units, it could only be produced from within the excitatory receptive field. 5. The results suggest that the inhibitory input to SCT cells is organized in subdomains no more than 100 mm across, which may correspond to the receptive fields of interneurones between the primary afferent fibres and the SCT cells.

Afferent Pathways↗
PubMed1987

Natural boundaries for the spatial spread of directed visual attention.

The spatial characteristics of directed attention were studied using spatial precues in a suprathreshold luminance detection task. Visual response times to probe flashes presented at various distances from the presumed focus of attention provided the dependent measure. The variation in response times with distance from the attentional focus was used to create spatial maps of the expectancy effect. The results indicate that, in an uncluttered visual field, the effects of precuing are widely distributed, and that the principal transitions in performance tend to occur either at the horizontal meridian, the vertical meridian, or both meridians, depending on the locus of the observers' expectancy.

Attention↗
PubMed1985

Spatial spread of light-induced sensitization in rod photoreceptors exposed to low external calcium.

Light sensitizes rods that have been desensitized by exposure to low external calcium. Yoshikami and Hagins [Biophys. Soc. Abstr. 15, 169a (1975)] suggested that desensitization in low external calcium results from exposure of intracellular calcium binding sites subsequent to depletion of internal calcium, and that background light sensitizes in this situation by releasing calcium to occupy those binding sites. In this view, it might be expected that light-induced sensitization would be spatially restricted to the illuminated region of the outer segment. However, in the present experiments, background illumination at one end of the outer segment potentiated responses to test flashes at the other end; resensitization was global rather than local. Patch-clamp recordings from the outer segment showed that the spread of internal transmitter was longitudinally restricted. Therefore, the sensitizing effect of background light is apparently not mediated via the internal transmitter, as required in the calcium-depletion explanation described above.

Animals↗
PubMed1989

On the spatial spread of the grey squirrel in Britain.

We present a diffusion-competition model to describe the interaction between the externally introduced grey squirrel and the indigenous red squirrel in Britain. We estimate the model parameters from field data. Solution of the model predicts waves of grey squirrel invasion with speed of invasion typical of that observed in the field. Numerical solution of the model on a two-dimensional domain gives population distributions qualitatively similar to those observed. We suggest that competition alone could account for the observed displacement of the red squirrel by the grey in large regions of Britain. The solutions are qualitatively similar to those for a single species spreading in the absence of competition. The quantitative difference is because competition slows down the speed of advance of the invading species.

Animals↗
PubMed1992

The mass angular scattering power method for determining the kinetic energies of clinical electron beams.

A method for determining the kinetic energy of clinical electron beams is described. The method is based on the measurement in air of the spatial spread of a pencil electron beam which is produced from the broad clinical electron beam. As predicted by the Fermi-Eyges theory, the dose distribution measured in air on a plane, perpendicular to the incident direction of the initial pencil electron beam, is Gaussian. The square of its spatial spread is related to the mass angular scattering power which in turn is related to the kinetic energy of the electron beam. The measured spatial spread may thus be used to determine the mass angular scattering power, which is then used to determine the kinetic energy of the electron beam from the known relationship between mass angular scattering power and kinetic energy. Energies obtained with the mass angular scattering power method agree with those obtained with the electron range method. The angular scattering power method is relatively cumbersome, but allows us to determine the kinetic energies of electron beams from first principles, in contrast to the empirical methods based on range measurements in water.

Electrons↗
PubMedDate not supplied

The effect of angular spread on the intensity distribution of arbitrarily shaped electron beams.

Knowledge of the relative intensity distribution at the patient's surface is essential for pencil beam calculations of three-dimensional dose distributions for arbitrarily shaped electron beams. To calculate the relative intensity distribution, the spatial spread resulting from angular spread is convolved with a two-dimensional step function whose shape corresponds to the applicator aperture. Two different approaches to obtain angular spread or the equivalent spatial spread are investigated. In the first method, the pencil beam angular spread is assumed to be Gaussian in shape. The angular spread constants (sigma theta) are then obtained from the slopes of measured intensity profiles. In the second method, the angular spread, in the form of an array of numerical values, is obtained by the deconvolution of measured intensity profiles. After obtaining the angular spread, the calculation for convolution is done in a number of parallel planes normal to the central axis at various distances from the electron collimator. Intensity at any arbitrary point in space is computed by interpolating between intensity distributions in adjacent planes on either side of the point. The effects of variations in angular spread as a function of field size for two treatment machines, one with a scanned electron beam and the other with a scattering foil, have been studied. The consequences of assuming angular spread to be of Gaussian shape are also examined. The electron intensity calculation techniques described in this paper apply primarily to methods of dose calculations that employ pencil beams generated using Monte Carlo simulations.

Electrons↗
PubMed1992

The rod-cone shift and its effect on ganglion cells in the cat's retina.

We examined how several characteristics of cat retinal ganglion cells--receptive field size, spatial resolution, and centre-surround antagonism--change with background illumination. Spectral sensitivity was also measured to see how these changes depend on the rod-cone shift. The radius of the centre mechanism changed very little across the mesopic range. The absence of a change can be attributed to the connections rods make with cones, and to the small spatial spread of rods which connect to a cone. The highest spatial frequency to which a cell could respond dropped sharply with falling background illumination. This loss of spatial resolution is due partly to increasing receptive field size, and partly to loss of contrast gain. Centre-surround antagonism approached zero as background illumination fell. The loss of antagonism could have been due to either a change in the subtractive relationship between centre and surround, or due to a loss of surround strength relative to centre strength; the latter was shown to be the case.

Adaptation, Ocular↗
PubMed1985

The absence of spread of adaptation between rod photoreceptors in turtle retina.

Adaptation by weak backgrounds and the spatial spread of desensitization between rods was studied in the snapping turtle retina, Chelydra serpentina. Intracellular membrane potentials were recorded from these photoreceptors in an eyecup preparation. The kinetics and sensitivity of rod responses were changed significantly by large, very dim backgrounds. For the twenty-five most sensitive rods where the dark-adapted flash sensitivity, SDF, was greater than 1.0 mV/Rh*, Rh* being the number of effective photo-isomerizations per rod, the background intensity required to halve the amplitude of the linear range response averaged 0.21 Rh* s-1. The time-to-peak of the test responses was reduced up to 50% by these dim backgrounds. The desensitizing effects of full field backgrounds of various intensities on the responses to large test spots were measured. The dependence of incremental flash sensitivity, SF, on background intensity, IB, followed the form (FORMULA: SEE TEXT) where I0 is the background intensity which halved SDF. The same intensity dependence held for slit-shaped background fields that desensitized responses to small test spots. The desensitizing effects of large, very dim flashed and continuous backgrounds took several seconds to appear and decay to dark levels. This in conjunction with the sparsity of photons suggests, that the desensitization from a single photoisomerization can persist for several seconds. A comparison of the desensitizing effects of spot and annular backgrounds revealed that small spot backgrounds superimposed on the centered test spots desensitized rods more effectively than annular fields. This finding held true even when annular patterns produced a greater maintained hyperpolarization in the rods. Thus, there was no unique relationship between desensitization and the steady maintained hyperpolarization evoked by a background field. The dependence of adaptation on distance from the impaled rod was determined with slit-shaped background fields placed at different positions across the rod's receptive field. The desensitizing effect of displaced slit stimuli was found to decline much more rapidly with distance than excitation. Displacing the slit by 20 micron from the centre reduced its desensitizing effect by more than 1 log unit. In contrast, excitation fell to about 80% at the same distance (lambda ranging from 50 to 70 micron). The fall off of desensitization with distance matched the calculated fall off with distance of light scatter from a slit. No difference was noted in the kinetics of test responses in the presence of equally desensitizing, superimposed and displaced slits.(ABSTRACT TRUNCATED AT 400 WORDS)

Adaptation, Ocular↗
PubMedDate not supplied

Comparison of methods to determine electron pencil beam spread in tissue-equivalent media.

This study has intercompared the predictions of Fermi-Eyges theory for the rms spatial spread (sigma) of an electron pencil beam scattering in muscle-, lung- and bone-equivalent media with those of; two range straggling modifications to the theory, Monte Carlo simulations, and an empirical method based on broad beam penumbra. Systematic differences among the results obtained by these methods for the values of sigma have been identified. Monte Carlo simulations are lower than the predictions of Fermi-Eyges theory for sigma at all depths whereas the broad beam penumbra method results are in reasonable agreement with Fermi-Eyges theory at depths less than approximately 0.7 times the range of the incident electrons. All of the methods investigated have an increasing discrepancy from the predictions of Fermi-Eyges theory with depth, especially close to the end of the electron range. The two range-straggling modifications to Fermi-Eyges theory developed for soft tissue do not agree with either measured or Monte Carlo results for sigma in homogeneous scattering media of lung and bone.

Bone and Bones↗
PubMed1988

Effects of blur and eccentricity on differential spatial displacement discrimination.

Differential spatial displacement discrimination thresholds were determined for stimuli consisting of blobs with Gaussian spatial and temporal contrast envelopes. The stimuli were presented at detection threshold luminance contrast. The tasks were similar to the two-point discrimination acuity task and the three-dot alignment hyperacuity task. Thresholds were determined as a function of eccentricity along the horizontal meridian of the visual field (from 45 degrees nasal to 65 degrees temporal). The spatial spread or blur parameter of the blobs was adopted as a scale parameter. The results show that the performance of the visual system in differential spatial displacement discrimination tasks becomes progressively more homogeneous for a progressive increase in the blur parameter of the stimuli. Scaling (i) the three-blob alignment results with estimates of the cortical magnification factor and (ii) the two-blob separation discrimination results with their corresponding neural blur parameter shows an impressive isotropy and blur scale-invariance for the mechanisms mediating differential spatial displacement discrimination across the visual field. These results are interpreted in terms of a scaled sampling lattice model of the visual system, in combination with an automatic scale-selection mechanism.

Adult↗
PubMed1989

A model for spatiotemporal frequency responses in the X cell pathway of the cat's retina.

A linear model is described for the cat eye's signal-processing pathway, from the visual stimulus at the cornea, to cones, to X-type ganglion cells. The model contains elements representing the eye's optics, phototransduction, gain control, spatiotemporal processing by cell layers, and pure delay. Centre-surround antagonism in the model arises through the presence of a centre element producing a small spatial spread of signals, and an antagonistic element producing a larger spread. Two arrangements were tried, feedforward and feedback, in which the antagonistic element's output was subtracted from the centre element's output, and input, respectively. The model was fitted to empirical spatial and temporal frequency responses collected by Frishman et al. (1987), and accounted qualitatively for these data in the feedback, but not the feedforward, arrangement. The model's centre pathway comprises a cascade of low-pass spatial filters, as does the surround pathway. As a consequence, the spatial frequency responses for these two pathways closely approximate Gaussian functions of spatial frequency, and the spatial frequency response of the complete model at low temporal frequency closely matches that of the difference of Gaussians model.

Adaptation, Ocular↗
PubMed1975

Prognostic significance of primary site after radiotherapy in non-Hodgkin's lymphomata.

In contrast to Hodgkin's lymphomata, non-Hodgkin's lymphomata originate in approximately a fourth of the cases in extranodal organs and sites. The prognosis of patients with primary extranodal organ involvement of the non-Hodgkin's lymphomata is similar to that of patients with primary lumph node involvement of the Hodgkin's and non-Hodgkin's lymphomata, dependent on the special spreading of the disease corresponding to the 4 stages of the Ann Arbor classification. This applies to the primary involvement of a single lymph node region (Stage I) or a single extralymphatic organ or site (stage IE) as well as to further stages of spreading within the lymphatic system (Stages II and III) including secondary localized involvement of an extralymphatic organ and site (Stages IIE and IIIE). The same qualitative dependence of the prognosis of Hodgkin's and non-Hodgkin's lymphomata on the spatial spreading, corresponding to the Ann Arbor concept, legitimizes, in spite of some quantitative differences, the application of the Ann Arbor classification system to all malignant lymphomata.

Hodgkin Disease↗