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PubMed2000

Enhancement of epidemic spread by noise and stochastic resonance in spatial network models with viral dynamics.

We extend a previous dynamical viral network model to include stochastic effects. The dynamical equations for the viral and immune effector densities within a host population of size n are bilinear, and the noise is white, additive, and Gaussian. The individuals are connected with an n x n transmission matrix, with terms which decay exponentially with distance. In a single individual, for the range of noise parameters considered, it is found that increasing the amplitude of the noise tends to decrease the maximum mean virion level, and slightly accelerate its attainment. Two different spatial dynamical models are employed to ascertain the effects of environmental stochasticity on viral spread. In the first model transmission is unrestricted and there is no threshold within individuals. This model has the advantage that it can be analyzed using a Fokker-Planck approach. The noise is found both to synchronize and uniformize the trajectories of the viral levels across the population of infected individuals, and thus to promote the epidemic spread of the virus. Quantitative measures of the speed of spread and overall amplitude of the epidemic are obtained as functions of the noise and virulence parameters. The mean amplitude increases steadily without threshold effects for a fixed value of the virulence as the noise amplitude sigma is increased, and there is no evidence of a stochastic resonance. However, the speed of transmission, both with respect to its mean and variance, undergoes rapid increases as sigma changes by relatively small amounts. In the second, more realistic, model, there is a threshold for infection and an upper limit to the transmission rate. There may be no spread of infection at all in the absence of noise. With increasing noise level and a low threshold, the mean maximum virion level grows quickly and shows a broad-based stochastic resonance effect. When the threshold within individuals is increased, the mean population virion level increases only slowly as sigma increases, until a critical value is reached at which the mean infection level suddenly increases. Similar results are obtained when the parameters of the model are also randomized across the population. We conclude with a discussion and a description of a diffusion approximation for a model in which stochasticity arises through random contacts rather than fluctuation in ambient virion levels.

Epidemiologic Methods↗

PubMed1992

Relationship of the train-of-four ratio to plasma atracurium concentration.

The electromyographic response to a short infusion of atracurium 0.25 mg kg-1 was recorded using the train-of-four (TOF) technique, and the plasma atracurium concentration profile measured, in 10 healthy patients. The TOF ratio (T4:T1) was depressed over a time course which did not conform to the predictions of an effect compartment model; the fit of such a model, when possible, was associated with large residual errors. In contrast, the absolute height of the fourth response of the TOF (T4:T0) may be fitted by a standard effect compartment model with smaller errors. This residual error was reduced further on fitting a threshold effect compartment model to the data set T4:T0. The parameter values of such a model were related closely to those for the first response (T1:T0). The kinetics of the effect compartments for the first and fourth response of the TOF were similar, whilst the CPss50 for the fourth response was approximately 67% that for the first response.

Adolescent↗

PubMed1992

The contributions of figure and ground textures to segmentation.

Several models of texture segmentation use spatial gradients in the activity of early filters to locate texture boundaries. The models assume that these filters are identical to those involved in the detection and discrimination of near threshold patterns. The models differ in how activity gradients from different types of filters are combined. We examined this question by measuring the respective contributions of a figure and a ground texture to segmentation. Vertical and horizontal line segments were used to construct two perfectly discriminable textures and these textures were used to construct four types of displays. Each display contained an obliquely oriented figure, but the displays differed in the way this figure was defined. Displays consisted of either (1) a horizontally textured figure on a blank background, (2) a blank figure on a vertically textured background, (3) a horizontally textured figure on a vertically textured background or (4) a figure with a mixed texture (50% vertical lines, 50% horizontal lines) on a blank background. In a two-alternative forced-choice experiment, observers were asked to judge the figure's orientation (right or left oblique), and the contrast of the textures was varied across trials. The resulting psychometric functions for segmentation were very similar for the four types of displays, suggesting ways in which a simple model of segmentation should be modified.

Contrast Sensitivity↗

PubMed1972

A threshold distribution hypothesis for packet storage of insulin and its mathematical modeling.

Phases of insulin release were studied in the perfused pancreas during a variety of glucose stimulation patterns. Patterns included staircase stimulations, constant prolonged single steps, restimulations, and ramp functions. Except at low concentrations, prolonged single steps of glucose elicited early spikes of insulin and a slowly rising second phase. Total insulin in the initial spikes increased with higher glucose concentrations. However, the time-related pattern of these spikes was similar in all cases; ratios of initial secretion rate to total insulin released were constant. Total insulin released in this early phase approximated a sigmoidal function of glucose concentration; mathematical differentiation of this function gave a skewed bell-shaped distribution curve. Staircase stimulations caused insulin to be released as a series of transient spikes which did not correlate with the increment of glucose but rather to the available insulin for a given glucose concentration minus that released in previous steps. The sum of total insulin released as spikes in a staircase series leading to a given glucose concentration was the same as when that concentration was used as a single step. Interrupted prolonged glucose infusions indicated the second phase of insulin release could prime the pancreas and that the first and second phases were interrelated. When glucose was perfused as ramp functions of slow, increasing, concentration, phasic response disappeared.A previous two-compartmental model was expanded to include a threshold or sensitivity distribution hypothesis. This hypothesis proposes that labile insulin is not stored in a homogeneous form but as packets with a bell-shaped distribution of thresholds to glucose. These packets respond quickly when their threshold levels to glucose are reached or exceeded. Data from single step stimulations were utilized for constructing a mathematical model which simulated satisfactorily the various stimulation patterns.

Animals↗

PubMedDate not supplied

A threshold limit theorem for a multitype epidemic model.

The asymptotic final size distribution of a multitype Martin-Löf process, a discrete-time SIR model for the spread of an infectious disease in a closed multitype population, is derived for the case of large total population size. When all subgroups are of comparable size and the infection pattern is irreducible, a threshold behavior is obtained, and the asymptomatic distributions for small and large outbreaks can be found. As an important corollary we get a threshold limit theorem for a class of continuous-time SIR models with several types.

Communicable Diseases↗

PubMed2001

Receptor dose in digital fluorography: a comparison between theory and practice.

A method of identifying the dose per image when quantum mottle no longer dominates the image statistics is presented as a first step towards quantitative optimization in native and subtracted digital fluorography. The method is based on measurements of threshold contrast over a range of receptor doses and the application of a simple model of the threshold contrast detection task to estimate the magnitude of system noise sources. The point at which system and quantum noise sources are equal in magnitude is proposed as the practical upper limit for dose per image. The method is applied to a typical digital fluorography system and the results are placed into the context of the range of dose per image values found from a regional survey of digital fluorography units. While there is broad agreement between the dose per image values in the survey with values predicted from the experimental method, the considerable spread in survey doses suggests there are instances where the use of a high dose per image is unjustified.

Dose-Response Relationship, Radiation↗

PubMed2003

Thermal modeling of millimeter wave damage to the primate cornea at 35 GHz and 94 GHz.

Recent data on damage to the primate cornea from exposure to millimeter wave radiation are interpreted in terms of a simple thermal model. The measured temperature increases during the exposures (duration 1-5 s, 35 or 94 GHz, 2-7 W cm(-2)) agree with the model within the variability of the data. The thresholds for damage to the cornea (staining of the corneal epithelium by fluorescein and corneal edema) correspond to temperature increases of about 20 degrees C at both irradiation frequencies. Within the limits of the one-dimensional model, thresholds for thermal damage to the cornea can be predicted for a range of exposure conditions.

Animals↗

PubMed2003

Genetic linkage analysis of a dichotomous trait incorporating a tightly linked quantitative trait in affected sib pairs.

Many complex diseases are usually considered as dichotomous traits but are also associated with quantitative biological markers or quantitative risk factors. For such dichotomous traits, although their associated quantitative traits may not directly underly the diagnosis of the disease status, if the associated quantitative trait is also linked to the chromosomal regions linked to the dichotomous trait, then joint analysis of dichotomous and quantitative traits should be more efficient than consideration of them separately. Previous studies have focused on the situation when a dichotomous trait can be modeled by a threshold process acting on a single underlying normal liability distribution. However, for many complex disorders, including most psychiatric disorders, diagnosis is generally based on a set of binary or discrete criteria. These traits cannot be modeled on the basis of a threshold process acting on an underlying continuous trait. We propose a likelihood-based method that efficiently combines such a discrete trait and an associated quantitative trait in the analysis, using affected-sib-pair data. Our simulation studies suggest that joint analysis increases the power to detect linkage of dichotomous traits. We also apply the proposed new method to an asthma genome-scan data set and incorporate the total serum immunoglobulin E level in the analysis.

Asthma↗

PubMed2004

Variations in excitability of single human motor axons, related to stochastic properties of nodal sodium channels.

Threshold variability of single human motor axons was studied by delivering 0.1 ms constant current stimuli of randomly varied intensity over the ulnar nerve at the elbow, and recording all-or-none potentials from flexor carpi ulnaris. In nine normal subjects, a single unit was tested with 8-11,000 stimuli at intervals of 0.5 s. After allowing for slow changes in excitability, the probability of excitation was in all cases well fitted by a cumulative Gaussian function. The relative spread (RS) of thresholds (S.D./mean) averaged 1.65 +/- 0.26% (mean +/- S.D., n = 9). When threshold was tested 20 ms after the start of a polarizing current, RS increased on depolarization and decreased on hyperpolarization. The product RS x mean threshold also increased on depolarization, especially when threshold was reduced by more than 50%. When the mean was reduced by 90%, RS increased above 50% and the axon sometimes fired spontaneously. Threshold variability was simulated by a computer model of a single node of Ranvier, in which the variability arose because of the stochastic behaviour of nodal sodium channels. The observed values of RS, and potential dependence of RS, were well modelled by a node with 60,000 sodium channels, of which about 1% were modelled as persistent sodium channels. Threshold variations in the model at resting potential were not primarily due to fluctuations in the state of the node before the stimulus was delivered, but rather to the variable activation of channels by the stimulus pulse. On depolarization, however, current through (mainly persistent) sodium channels caused appreciable fluctuations in membrane potential, which increased RS and the probability of spontaneous firing.

Adult↗

PubMed1998

A mathematical model for the determination of the optimum value of the treatment threshold for a continuous risk factor.

Hypercholesterolemia or hypertension are continuous risk factors for coronary heart disease. When a preventive action is carried out against such a risk factor, it is necessary to specify a risk factor level value, named the treatment threshold, above which a subject should be treated. But a non-arbitrary determination of this threshold value is impossible from the epidemiological data. A method for the non-arbitrary determination of the treatment threshold value is presented, based upon mathematical modelling of the clinical and economics consequences of the prevention policy in the whole population. In a cost-effectiveness approach, the model was used to estimate the cost per coronary event prevented according to the threshold value for blood cholesterol. It was found that a minimum in this outcome proposed as the optimum treatment threshold. It is possible, from a public health point of view, to determine an optimum, non-arbitrary treatment threshold value in the prevention of coronary heart disease with cholesterol-lowering interventions. The model proposed here could be useful in decision making processes.

Anticholesteremic Agents↗

PubMed2005

Applying a mathematical model to training adaptation in a distance runner.

This study investigated physiological and psychological correlates of the positive and negative components of a systems model in a well-trained male middle-distance runner. In the systems model, performance at any given point in time is seen as the difference between two antagonistic components, fitness and fatigue, which represent the positive and negative adaptation to training, respectively. Each component comprises a set of parameters unique to the individual, which were estimated by fitting model-predicted performance to performance measured weekly throughout a 12-week training period. The model fitness component was correlated with extrapolated VO(2max) (ml.kg(-1).min(-1)), running economy (RE) (VO(2) at 17 km.h(-1)), and running speed (km.h(-1)) at ventilatory threshold (VTRS). The model fatigue component was correlated with the fatigue subset of the profile of mood states (POMS). The fit between model and actual performance was significant (r(2)=0.92, P< 0.01). In the case of fitness, both VTRS (r=0.94, P=0.0001) and RE (r=-0.61, P=0.04) were significantly correlated with the model fitness component. There was also a moderate correlation between the fatigue subset of the POMS and the fatigue component (r=0.75, p< 0.05). In summary, this is the first time VTRS and the POMS have been used in an attempt to validate the model components. The findings of the present study support previous validation attempts using biochemical and hormonal markers of fitness and fatigue.

Adaptation, Physiological↗

PubMed1987

Point spread functions and detail detection.

Point spread functions, intended to characterize local spatial transfer of the visual system, can be obtained psychophysically using a perturbation technique. Data of such point spread functions are shown for three experimental conditions: foveally at adaptation levels of 1200 and 10 Td, and in the parafovea at an eccentricity of 2 deg using a 1200 Td adaptation level. The results are consistent with earlier findings (Blommaert, F. J.J. and Roufs, J.A.J. 1981, Vision Res. 21, 1223-1233). On the basis of such point spread functions a simplified multiple unit model was constructed, the parameters of which were fitted to thresholds of discs with varying diameter. Threshold predictions from this model for annuli, thin lines and broad lines were found to be in fair quantitative agreement with experimental results. It is argued that for a certain class of slender stimuli, including alphanumeric characters, thresholds can be described with a single channel model containing only the experimentally determined point spread function as a basic component.

Humans↗

PubMed2001

Measurement and prediction of thermal behavior and acute assessment of injury in a pig model of renal cryosurgery.

PURPOSE: To analyze in vivo end temperatures and histologic injury in a standardized cryo-iceball using a porcine kidney model in order to establish the threshold temperature for tissue ablation. To evaluate the ability to predict end temperatures using a thermal finite element model. MATERIALS AND METHODS: A single freeze/thaw cryolesion was created in five pig kidneys and the temperature history recorded. End temperature was calculated using a thermal finite element model. The threshold temperature for tissue injury was established by directly correlating end temperature and histologic injury. RESULTS: Reproducible geometry and temperature profiles of the cryo-iceball were found. End temperature could be accurately predicted through thermal modeling, and correlation with histologic injury revealed a threshold temperature of -16.1 degrees C for complete tissue ablation. CONCLUSION: Thermal modeling may accurately predict end temperature within a cryo-iceball. Provided threshold temperatures for tissue destruction are known, modeling may become a powerful tool in cryosurgery, improving the assessment of damage in normal and malignant tissue.

Animals↗

PubMed2006

Bayes factor for testing the genetic background of quantitative threshold traits.

The recent development of the Bayes factor methodology to test between nested competing models has allowed to evaluate the genetic component of continuous traits through a methodology based on the reparameterization of a variance component model in terms of intra-class correlation. In this study, we present a modification of that procedure to compare between threshold models that only differ in a bounded variable. An extra data-augmentation step is required to sample liability, an underlying continuous variable related with phenotypic records through an adequate number of thresholds. In this context, we describe a procedure to sample from a truncated multivariate normal distribution with non-null covariances between records, taking as starting point the Cholesky factorization and the inclusion of linear restrictions. The method was tested by computer simulations with satisfactory results.

Animals↗

PubMed1994

Diversity and virulence thresholds in AIDS.

We propose a model for the interaction between human immunodeficiency virus and the immune system. Two differential equations describe the interactions between one strain of virus and one clone of T lymphocytes. We use the model to generalize earlier results pertaining to the AIDS diversity threshold [Nowak, M. A., Anderson, R. M., McLean, A. R., Wolfs, T. F. W., Goudsmit, J. and May, R. M. (1991) Science 254, 963-969]. Our model has (i) a stable steady state corresponding to the "controlled" persistence of the virus and (ii) a region corresponding to AIDS. The separatrix between the two regimes is formed by the stable manifold of a saddle point. We define a dimensionless "virulence" parameter which combines the infectivity and antigenicity of a virus strain. We derive analytically two parameter conditions involving virulence. The first corresponds to a saddle-node bifurcation which causes AIDS due to the loss of the stable equilibrium. The second corresponds to a global bifurcation which causes AIDS due to a change in the basins of attraction. Incorporating diversity into the model, we derive a diversity threshold corresponding to the saddle-node bifurcation. In this threshold condition diversity and virulence have an equivalent effect. By studying the effect of diversity on the critical virulence that is required for a new mutant to cause AIDS, we again establish that diversity and virulence are equivalent parameters. Because in our model increasing diversity decreases the critical virulence, the strain that eventually causes AIDS need not be a virulent one.

Acquired Immunodeficiency Syndrome↗

PubMed2006

Phonation threshold pressure across the pitch range: preliminary test of a model.

This study sought to examine the specific relationship between phonation threshold pressure (PTP) and voice fundamental frequency (F(0)) across the pitch range. A published theoretical model of this relationship described a quadratic equation, with PTP increasing exponentially with F(0). Prospective data from eight adults with normal, untrained voices were collected. Subjects produced their quietest phonation at 10 randomly ordered pitches from 5% to 95% of their semitone pitch range at 10% intervals. Analysis included curve fitting for individual and group data, as well as comparisons to the previous model. The group data fit a quadratic function similar to that proposed previously, but the specific quadratic coefficient and constant values differed. Four of the individual subjects' data were best fit by quartic functions, two by quadratic functions, and one by a linear function. This preliminary study indicates that PTP may be minimal at a "comfortable" pitch rather than the lowest pitch tested, and that, for some individuals, PTP may be slightly elevated during the passaggio between modal and falsetto vocal registers. These data support the general form of the theoretical PTP-F(0) function for these speakers, and indicate the possibility of potential refinements to the model. Future studies with larger groups of male and female subjects across a wider age range may eventually reveal the specific nature of the function.

Adult↗

PubMed1998

The effects of different envelope patterns and uncertainty for the detection of a tone added to SAM complex tonal maskers.

Thresholds for the detection of a tone added in-phase to the carrier of a fully modulated SAM tone were measured. In some conditions the signal was added to a single SAM tone, and in other conditions the signal was added to the sum of three or more SAM tones. Level equalization ensured that the addition of the tonal signal did not lead to increases in energy. When multiple SAM tone maskers were used, a small number of reproducible maskers were tested, each masker being composed of SAM tones with a variety of relative modulator phases. The maskers were either fixed across intervals and trials, roved across trials but fixed across intervals, or randomly chosen across both intervals and trials. The frequency separation between the signal-centered and off-frequency SAM tones was also varied. For small signal-centered/off-frequency SAM tone frequency separations, a separation ratio of 1.3, thresholds in the fixed condition depend on the relative modulator phases, and a simple mixture model reasonably predicted thresholds in the roving condition based on thresholds in the fixed condition for two of the three observers. For signal-centered/off-frequency SAM tone frequency separation factor of 1.68, effects of relative modulator phases were not obtained. Thresholds in the target-alone condition were generally superior to thresholds measured with the comodulated masker. Comodulated thresholds were better than target-alone thresholds only when level equalization was not used, and so the addition of the signal led to increases in level.

Acoustic Stimulation↗

PubMed2006

The psychological and physiological responses of sedentary individuals to prescribed and preferred intensity exercise.

OBJECTIVES: Affective valence responses to exercise may influence adherence. According to a newly proposed dual-mode model, affective responses have been proposed to vary depending on whether exercise is undertaken above or below the anaerobic threshold. With the model in mind, the study objectives were to explore the impact of an above-lactate, below-lactate, and self-selected exercise condition on acute affective responses in sedentary individuals. DESIGN: Using a repeated measures design, 12 volunteers participated in two prescribed intensity exercise conditions (above and below-lactate threshold) and one self-selected intensity exercise condition. The three conditions were randomized. METHOD: An incremental walking protocol was used to identify exercise intensities that would elicit above- and below-lactate threshold work rates for each participant. The exercise conditions were completed on different days and each lasted for 20 minutes. Physiological and affective responses were recorded pre-exercise, during exercise, and post-exercise. RESULTS: Affective responses were more negative in the above-lactate condition during exercise compared with the below-lactate and self-selected conditions. There were no differences between the conditions post-exercise. Participants exercised around the lactate threshold and at a significantly higher intensity in the self-selected compared with the below-lactate condition. Inter-individual variability in responses was greatest below the lactate threshold, with similar levels of variability in the self-selected and above-lactate conditions. CONCLUSIONS: Data are consistent with the proposals of the dual-mode model and support the use of self-selected intensity with sedentary individuals to promote positive affective responses.

Adult↗