The reinfection threshold

Thresholds in transmission are responsible for critical changes in infectious disease epidemiology. The epidemic threshold indicates whether infection invades a totally susceptible population. The reinfection threshold indicates whether self-sustained transmission occurs in a population that has developed a degree of partial immunity to the pathogen (by previous infection or vaccination). In models that combine susceptible and partially immune individuals, the reinfection threshold is technically not a bifurcation of equilibria as correctly pointed out by Breban and Blower. However, we show that a branch of equilibria to a reinfection submodel bifurcates from the disease-free equilibrium as transmission crosses this threshold. Consequently, the full model indicates that levels of infection increase by two orders of magnitude and the effect of mass vaccination becomes negligible as transmission increases across the reinfection threshold.     

Evidence that the metabolic acidosis threshold is the anaerobic threshold

We evaluated maximal O2 uptake (VO2max), the metabolic acidosis threshold determined by the V-slope analysis [plot of CO2 output (VCO2) as a function of oxygen uptake (VO2)], the ratio of increase in VO2 to work rate increment (delta VO2/delta WR), the upper slope (S2) of the V-slope analysis, and the VO2 for work below and above the metabolic acidosis threshold to determine whether the changes in O2 transport caused by increased carboxyhemoglobin (HbCO) affected these parameters and variables. Ten normal subjects (aged 32.8 +/- 7.1 yr) performed symptom-limited incremental exercise tests in a ramp pattern on a cycle ergometer while breathing air and air with added carbon monoxide to cause HbCO to be approximately 11% and 20%. VO2max decreased by 11.6 and 19.3%, the metabolic acidosis threshold decreased by 11.9 and 19.6%, delta VO2/delta WR decreased by 8.9 and 14.0%, and S2 increased by 13.6 and 21.8% when HbCO was increased to 11 and 20%, respectively. Most importantly, VO2 was unchanged related to work rate below the metabolic acidosis threshold during the tests with increased HbCO but was reduced at the work rates above the metabolic acidosis threshold. These findings are consistent with the concept that the metabolic acidosis threshold is synonymous with an anaerobic threshold, i.e., the latter demarcating the VO2 above which the contracting muscles are not adequately supplied with O2 but below which they are.     

Scaling threshold characters

A simple method of scaling ordered categorical responses having a joint distribution with an underlying normal variable is presented. Scores are developed that maximize heritability of the observed variate and that in the class of scores based on polychotomies: (1) maximize the correlation between score and the underlying genetic value to be predicted, and (2) minimize mean-square prediction error. Several examples suggest little is lost, in terms of heritability, by using equally spaced scores. The proposed scaling method discriminates among candidates for selection that would be tied if equally spaced scores are used and sometimes yields different rankings of candidates.     

Determination of taste threshold

A linear inverse relation links the HCl solution molarity to both the absolute HCl solution intake, and the ratio of the HCl solution to the total fluid intake. The last algebraic relation allows the taste threshold to be estimated.     

The relationship between anaerobic threshold and electromyographic fatigue threshold in college women

The purpose of this study was to investigate the relationship between anaerobic threshold (Th(an)) and muscle fatigue threshold (EMGFT) as estimated from electromyographic (EMG) data taken from the quadriceps muscles (vastus lateralis) during exercise on a cycle ergometer. The subjects in this study were 20 female college students, including highly trained endurance athletes and untrained sedentary individuals, whose fitness levels derived from their maximal oxygen consumption ranged from 24.9 to 62.2 ml.kg-1.min-1. The rate of increase in integrated EMG (iEMG) activity as a function of time (iEMG slope) was calculated at each of four constant power outputs (350, 300, 250, 200 W), sufficiently high to bring about muscle fatigue. The iEMG slopes so obtained were plotted against the exercise intensities imposed, resulting in linear plots which were extrapolated to zero slope to give an intercept on the power axis which was in turn interpreted as the highest exercise intensity sustainable without electromyographic evidence of neuromuscular fatigue (EMGFT). The Th(an) was estimated from gas exchange parameters during an incremental exercise test on the same cycle ergometer. The mean results indicated that oxygen uptake (VO2) at Than was 1.39 l.min-1, SD 0.44 and VO2 at EMGFT was 1.33 l.min-1, SD 0.57. There was no significant difference between these mean values (P greater than 0.05) and there was a highly significant correlation between VO2 at Than and VO2 at EMGFT (r = 0.823, P less than 0.01).(ABSTRACT TRUNCATED AT 250 WORDS)     

Validation of the hedonic threshold methodology in determining the hedonic rejection threshold

The hedonic thresholds methodology was recently proposed which allows for determination of two new sensorial thresholds, the compromised acceptance threshold and the hedonic rejection threshold (HRT). For a new methodology to be accepted by the scientific community, its ability to produce reliable results must be demonstrated. Thus, this study sought to validate this new methodology when used to calculate the HRT. In order to do so, the analytical performance indices of precision (repeatability, intermediate precision, and reproducibility), accuracy and robustness for the results for the HRT calculation were measured. The results of seven experiments demonstrated that the methodology possesses high repeatability, intermediate precision and robustness, and satisfactory accuracy and reproducibility. It was therefore concluded that the HRT determination methodology satisfactorily met the analytical performance criteria evaluated, therefore generating reliable results.

Practical applications

The hedonic thresholds methodology (HTM) has numerous applications, including the application of a more severe thermal treatment to obtain greater microbial or enzymatic inactivation, the determination of food shelf life based on its sensory acceptance, the reduction of specific, expensive ingredients in food formulations, reduction of ingredients that are harmful to health when consumed in excess (e.g., sucrose, sodium, and fat), determination of the maximum “defect” threshold that may be present in food and others. The HTM is a recently proposed methodology; therefore, the reliability of the values of the hedonic rejection threshold must be validated, calculated via the HTM. Reliability of the HRT results was confirmed when HTM validation was performed. Thus, the methodology can undoubtedly be applied for the intended purpose.     

Pattern-specific contrast threshold elevation

Visual channels are defined psychophysically; stimuli that interact share information in the same channel, and those that do not interact are processed in different channels. Channels are often investigated by means of adaptation to one stimulus, testing contrast threshold elevation with one (or more) others. Much recent work has tested the tuning of channels for orientation and spatial frequency, using simple line gratings. This study examined the pattern-specificity of such adaptation, testing the hypothesis that the fundamental operators of the Lie Transformation Group Theory of Neuropsychology (LTG/NP) define psychophysical channels. In Experiment I the three basic pattern pairs of LTG/NP were used as adaptation and test stimuli in a conventional contrast threshold-elevation experiment. Threshold elevation was pattern-specific, thus supporting the hypothesis. In subsequent experiments various 'fractured' patterns, and patterns generated by combinations of Lie operators were used both for adaptation and test. The results were mixed; some supported the original hypothesis, but many did not. Relations between local contour orientations in adaptation and test patterns could explain some results, but not all. The hypothesis that adaptation occurs to the oriented spatial-frequency components of the test patterns, on the other hand, gave a good fit to the data. It is concluded that there is pattern-specificity in contrast threshold elevation, but it is a form of specificity that can be explained without recourse to a model of geometrical pattern processing, at least for the simple patterns used here.     

Acceleration-sensitivity threshold of Physarum

Free-living cells show distinct gravisensitivities and often use the gravity ('g') vector for their spatial orientation. The rhythmic contractions of the ameboid Myxomycete (acellular slime mold) Physarum polycephalum are a sensitive parameter which can be modified by external stimuli. Space experiments and ground-based 0 x g simulation studies established that the contraction period transiently decreases after a transition from 1 x g to 0 x g with a back-regulating process starting after 30 min. For determination of the threshold of acceleration sensitivity, a slow-rotating centrifuge microscope (NIZEMI--Niedergeschwindigkeits-Zentrifugenmikroskop) was used, providing in space accelerations from 0 x g to 1.5 x g. A stepwise acceleration increase revealed that the lowest acceleration level capable of inducing a response was 0.1 x g. The response to the acceleration increase was an increase in contraction period, in contrast to a stimulus deprivation, which led to a period decrease. The time schedule of the acceleration responses and back-regulating process seems to be fixed, suggesting that every acceleration being above the threshold can induce a complete response-regulation process. The low acceleration-sensitivity threshold favors rather large and dense cell organelles as candidates for the gravity receptor in Physarum.     

Some biochemical threshold mechanisms

Certain arrangements of enzymatic (bimolecular) subsystems lead to characteristic threshold-type response. Two simple cases of such systems are studied here in terms of steady state behavior and explicit relationships between system and curve parameters. It is found that the curvature of the threshold curve is directly related to the equivalent Michaelis constant and, in the case of saturated threshold curve, the slope of the curve at the idealized threshold is limited by the ratio of saturation to threshold. This slope may be appreciably increased up to a stepwise response at the threshold if a multisubstrate complex of the enzyme is the only species which affects the enzyme mediated transport.     

Anaerobic threshold in rats

• 1.1. The aim of this study was to find out whether the anaerobic threshold (AT) can be estimated in rats running at increasing speed and if so what is the reproducibility of the measurements.
• 2.2. Lactate (LA) concentrations in blood taken from 11 rats were determined during a discontinued, multistage treadmill exercise test repeated four times in each animal.
• 3.3. It was found that blood LA changes vs speed have an exponential pattern with a distinct, rapid rise at the speed above 25 m/min which corresponds to blood LA of approx. 4 mmol/1.
• 4.4. The variation coefficient of the speed at which AT occurred in individual animals ranged between 10 and 20%.
• 5.5. These results offer a potential application of AT determination in the animal studies concerning mechanisms controlling exercise metabolism.

     

Allee threshold and extinction threshold for spatially explicit metapopulation dynamics with Allee effects

In this paper, we investigate a spatially explicit metapopulation model with Allee effects. We refer to the patch occupancy model introduced by Levins (Bull Entomol Soc Am 15:237–240, 1969) as a spatially implicit metapopulation model, i.e., each local patch is either occupied or vacant and a vacant patch can be recolonized by a randomly chosen occupied patch from anywhere in the metapopulation. When we transform the model into a spatially explicit one by using a lattice model, the obtained model becomes theoretically equivalent to a “lattice logistic model” or a “basic contact process”. One of the most popular or standard metapopulation models with Allee effects, developed by Amarasekare (Am Nat 152:298–302, 1998), supposes that those effects are introduced formally by means of a logistic equation. However, it is easier to understand the ecological meaning of associating Allee effects with this model if we suppose that only the logistic colonization term directly suffers from Allee effects. The resulting model is also well defined, and therefore we can naturally examine it by Monte Carlo simulation and by doublet and triplet decoupling approximation. We then obtain the following specific features of one-dimensional lattice space: (1) the metapopulation as a whole does not have an Allee threshold for initial population size even when each local population follows the Allee effects; and (2) a metapopulation goes extinct when the extinction rate of a local population is lower than that in the spatially implicit model. The real ecological metapopulation lies between two extremes: completely mixing interactions between patches on the one hand and, on the other, nearest neighboring interactions with only two nearest neighbors. Thus, it is important to identify the metapopulation structure when we consider the problems of invasion species such as establishment or the speed of expansion.     

Stroke rehabilitation reaches a threshold

Motor training with the upper limb affected by stroke partially reverses the loss of cortical representation after lesion and has been proposed to increase spontaneous arm use. Moreover, repeated attempts to use the affected hand in daily activities create a form of practice that can potentially lead to further improvement in motor performance. We thus hypothesized that if motor retraining after stroke increases spontaneous arm use sufficiently, then the patient will enter a virtuous circle in which spontaneous arm use and motor performance reinforce each other. In contrast, if the dose of therapy is not sufficient to bring spontaneous use above threshold, then performance will not increase and the patient will further develop compensatory strategies with the less affected hand. To refine this hypothesis, we developed a computational model of bilateral hand use in arm reaching to study the interactions between adaptive decision making and motor relearning after motor cortex lesion. The model contains a left and a right motor cortex, each controlling the opposite arm, and a single action choice module. The action choice module learns, via reinforcement learning, the value of using each arm for reaching in specific directions. Each motor cortex uses a neural population code to specify the initial direction along which the contralateral hand moves towards a target. The motor cortex learns to minimize directional errors and to maximize neuronal activity for each movement. The derived learning rule accounts for the reversal of the loss of cortical representation after rehabilitation and the increase of this loss after stroke with insufficient rehabilitation. Further, our model exhibits nonlinear and bistable behavior: if natural recovery, motor training, or both, brings performance above a certain threshold, then training can be stopped, as the repeated spontaneous arm use provides a form of motor learning that further bootstraps performance and spontaneous use. Below this threshold, motor training is "in vain": there is little spontaneous arm use after training, the model exhibits learned nonuse, and compensatory movements with the less affected hand are reinforced. By exploring the nonlinear dynamics of stroke recovery using a biologically plausible neural model that accounts for reversal of the loss of motor cortex representation following rehabilitation or the lack thereof, respectively, we can explain previously hard to reconcile data on spontaneous arm use in stroke recovery. Further, our threshold prediction could be tested with an adaptive train-wait-train paradigm: if spontaneous arm use has increased in the "wait" period, then the threshold has been reached, and rehabilitation can be stopped. If spontaneous arm use is still low or has decreased, then another bout of rehabilitation is to be provided.