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PubMed2002

Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters.

We critically review and classify models of single-species population dynamics subject to the demographic Allee effect with emphasis on non-spatial, deterministic approach. Inclusion of spatial movement and stochastic phenomena does not substantially change the behaviour; stochasticity only "blurs" step-like character of the Allee effect into a sigmoidal form. The outcome of all non-spatial, deterministic models is either unconditional extinction, extinction-survival scenario (ES), or unconditional survival. Three major model classes are recognized: (1) one-dimensional heuristic models, (2) one-dimensional models with mating probability and fixed sex ratio, and (3) two-sex models with variable adult sex ratio. Each class is characterized by the shape of extinction boundary which separates extinction from survival in the ES scenario. The latter two classes may give better predictions of extinction thresholds than heuristic models but require specific information and are data intensive. In one-dimensional models with fixed sex ratio, population cannot survive if density/number of males decreases below some threshold while there is no such restriction on females. Individual-based models seem to be most capable of explaining mechanisms leading to the Allee effect.

Animals↗

PubMed1997

An indirect method for absorption rate estimation: flurothyl-induced seizures.

This paper develops a method to estimate a minimal amount of flurothyl necessary to induce the seizures (the seizure threshold). A simple mathematical model is proposed which permits one to determine the drug absorption rate from the amount which has been administered and from the measured latency to onset of seizure. Experimental animal (rats) were exposed to a continuous intake of flurothyl in two different situations: either being alone in the airtight chamber or sharing it in a pair. In the latter case, we assume that the two rats uniformly share the infused drug. Our calculations estimate that approximately 20 microliters of flurothyl is necessary to induce twitches, whereas 25 microliters of flurothyl is the dose required for the induction of clonic seizures. The model can be used to estimate the threshold amounts of any drug producing obvious behavioral changes irrespective of the route of administration.

Absorption↗

PubMed1991

Hearing impairment related to plasma quinine concentration in healthy volunteers.

1. Hearing impairment was investigated in six healthy volunteers who received oral doses of 5, 10 and 15 mg kg-1 quinine single-blind and in random order. 2. The plasma concentration of quinine was followed for 48 h and the time course was fitted by a linear one compartment pharmacokinetic model. 3. Hearing thresholds were measured by pure tone audiometry. There was a delay between impairment in hearing and change in plasma quinine concentration. Thus the method of effect compartment modelling was applied. 4. The effect on hearing (L), measured as a shift in hearing threshold (dB), was used to estimate the rate constant for elimination of drug from the assumed effect compartment (ke0) and two parameters specifying the effect model (gamma and k). The effect model applied was L = 10 (log k + gamma x log Ce) where Ce is the calculated drug concentration in the effect compartment. This model is a logarithmic transform of a power expression equivalent to the Hill equation at the lower end of the effect range. In all experiments where there was a clear effect on hearing, convergence on a set of parameter estimates occurred, but inter- and intraindividual variability was large. The mean value of ke0 was 3.32 +/- 5.93 h-1 s.d., for gamma it was 1.73 +/- 1.14 s.d. and for k it was 0.59 +/- 0.66 s.d.

Adult↗

PubMed1993

Histologic determination of the ischemic threshold of muscle in the canine compartment syndrome model.

Our objective was to define the critical tissue pressure at which irreversible muscle damage occurs and to compare our results to those thresholds advocated in the orthopaedic literature. A standard plasma infusion compartment syndrome model was created in a canine model. Four dogs were in each of four experimental groups with compartment pressure maintained as follows: (a) 30 mm Hg with support of diastolic blood pressure to a level > 50 mm Hg; (b) 20 mm Hg less than diastolic pressure; (c) 10 mm Hg less than diastolic blood pressure; (d) a level equal to the animal's diastolic blood pressure. All animals were sacrificed 14 days after the procedure. Histology revealed the following: (a) tissues pressurized to 30 mm Hg in a normotensive dog demonstrated no significant abnormalities; (b) tissues pressurized to 20 mm Hg less than diastolic revealed occasional cells undergoing regeneration but no evidence of infarction or fibrosis; (c) tissues pressurized to 10 mm Hg less than diastolic showed scattered small areas of infarction and fibrosis; and (d) tissues pressurized to diastolic blood pressure demonstrated more widespread infarction and scarring. The ischemic threshold of muscle, beyond which irreversible tissue damage occurs, is directly related to the difference in compartment and perfusion pressure. Our findings document this pressure to be 10 mm Hg less than diastolic blood pressure or within 30 mm Hg of mean arterial pressure. This data refutes the use of absolute tissue pressure values as a guide to the necessity of fasciotomy. To abort an impending compartment syndrome and avoid irreversible tissue injury and their sequelae, fasciotomy should be done if tissue pressure reaches within 10-20 mm Hg of diastolic pressure.

Animals↗

PubMed1981

Multiple-threshold transmission of affective disorders.

Data on bipolar and unipolar affective disorders were gathered on first-degree relatives of 255 patients with both illness types. As consistent with a model of continuous liability, bipolar probands were found to have more bipolar relatives and more relatives with any affective disorder than unipolar probands. Multiple-threshold models of inheritance were applied to the data using clinical polarity as a threshold determinant. The hypothesis of multifactorial inheritance was ruled out. Autosomal single-major-locus inheritance provided an acceptable fit to the data. It is proposed that separate genetic mechanisms for bipolar and unipolar disorders need not be present. The two illness types are represented in the model at different thresholds on a single continuum of genetic-environmental liability in which bipolar illness is claimed to be more deviant genetically than unipolar illness.

Bipolar Disorder↗

PubMed2005

Orientation discrimination in human vision: psychophysics and modeling.

We evaluated orientation discrimination thresholds using an external noise paradigm. Stimuli were spatiotemporal Gaussian patches of 2D orientation noise band-pass filtered in Fourier domain. Orientation acuity was measured for various combinations of stimulus spatial bandwidth, spatial frequency, and size as a function of orientation bandwidths of the stimuli. Stimulus contrast was matched in multiples of detection threshold. Consistent with the idea that stimulus orientation bandwidth acts as a source of external noise, orientation discrimination thresholds increased monotonically in all conditions with stimulus bandwidth. To interpret these results quantitatively, we first fitted a variance summation model to the data and derived the internal orientation noise, relative sampling efficiency, and orientation tuning of the mechanism underlying orientation discrimination. Due to the equivocal biological nature of these parameters for orientation discrimination, we investigated, with a modeling approach, how neural detectors characterized by a broad orientation tuning may support orientation discrimination. We demonstrated using the ideal-observer theory that while linear models, based on either unimodal filtering or center-surround opponency, predict the monotonic relationship between orientation discrimination threshold and orientation noise, a nonlinear model incorporating a broadband divisive inhibition in the orientation domain is a better candidate due to its contrast invariance. This model, using broad and similar orientation tuning for its excitatory and inhibitory inputs, accounts for the acute orientation acuity of human vision and proves to be robust despite the variance found in natural stimuli.

Discrimination, Psychological↗

PubMed2006

Rate coding and spike-time variability in cortical neurons with two types of threshold dynamics.

Neurons and dynamical models of spike generation display two different classes of threshold behavior: type 1 [firing frequency vs. current (f-I) relationship is continuous at threshold] and type 2 (discontinuous f-I). With steady current or conductance stimulation, regular-spiking (RS) pyramidal neurons and fast-spiking (FS) inhibitory interneurons in layer 2/3 of somatosensory cortex exhibit type 1 and type 2 threshold behaviors, respectively. We compared the postsynaptic firing variability of type 1 RS and type 2 FS cells, during naturalistic, fluctuating conductance input. In RS neurons, increasing the level of independently random, shunting inhibition caused a monotonic increase in spike reliability, whereas in FS interneurons, there was an optimum level of shunting inhibition for achieving the most reliable spike generation and the most precise spike-time encoding. This was observed over a range of different degrees of synchrony, or correlation, in the input. RS cells displayed a progressive rise in spike jitter during natural-like transient burst inputs, whereas for FS cells, jitter was mostly kept low. Furthermore, RS cells showed encoding of the input level in the spike shape, whereas FS cells did not. These differences between the two cell types are consistent with a role of RS neurons as rate-coding integrators, and a role of FS neurons as resonators controlling the coherence of synchronous firing.

Action Potentials↗

PubMed1999

Mutants of glucokinase cause hypoglycaemia- and hyperglycaemia syndromes and their analysis illuminates fundamental quantitative concepts of glucose homeostasis.

AIMS/HYPOTHESIS: Mutations of the glucokinase gene cause hyperglycaemia or hypoglycaemia. A quantitative understanding of these defects of glucose homeostasis linked to the glucokinase gene was lacking. Therefore a database of kinetic variables of wild-type and 20 missense mutants of glucokinase was developed and used in mathematical modelling to predict the thresholds for glucose-stimulated insulin release. METHODS: Recombinant human glucokinase was generated in E. coli. The k(cat), glucose S(0.5), ATP K(m), and Hill number of glucokinase were determined. Inhibition by Stearoyl CoA and glucokinase regulatory protein and thermal stability were assayed for all mutants kinetically similar to wild-type glucokinase. A mathematical model predicting the threshold for glucose-stimulated insulin release was constructed. This model is based on the two substrate kinetics of glucokinase and the kinetic variables of the database. It is assumed that both glucokinase gene alleles are equally expressed in beta-cells and that induction of glucokinase occurs as a function of basal blood glucose. RESULTS: Large changes, varying greatly between mutants were found in nearly all variables. Glucokinase flux at threshold for glucose-stimulated insulin release was about 25 % of total phosphorylating potential in the normal beta-cell and this was used to predict thresholds for the mutant heterozygotes. Clinical data for maturity onset diabetes of the young type linked to the glucokinase gene and familial hyperinsulinaemic hypoglycaemia linked to the glucokinase gene and the glucokinase kinetic data of this study were used to test the model. The model predicts fasting blood glucose between 3 and 7 mmol/l in these cases. CONCLUSION/INTERPRETATION: A kinetics database of wild-type and 20 mutants of glucokinase was developed. Many kinetic differences were found for the mutants. The mathematical model to calculate the threshold for glucose-stimulated insulin release predicts fasting blood glucose between 3 and 7 mmol/l in subjects with glucokinase gene mutations. [Diabetologia 42: 1175-1186]

Adaptor Proteins, Signal Transducing↗

PubMed1995

Triggered electromyographic threshold for accuracy of pedicle screw placement. An animal model and clinical correlation.

STUDY DESIGN: This study consisted of a laboratory investigation of triggered electromyographic stimulation of pedicle screws placed in a pig spine, with a correlative prospective clinical series of lumbosacral pedicle screws stimulated in a similar fashion. OBJECTIVES: To determine the threshold of stimulus intensity necessary to confirm accuracy of lumbar pedicle screw placement via a triggered electromyographic peripheral response. SUMMARY OF BACKGROUND DATA: Documentation of lumbar pedicle screw placement is imperative to perform proper spinal instrumentation and to avoid perioperative complications. Previous electrophysiologic techniques using stimulation of a pedicle opening or pedicle screw with peripheral recording of electromyographic activity from the lower extremity muscles have been used to identify varying threshold values that indicate a break in the bony pedicle wall. METHODS: Six adult pigs had 107 pedicle screws placed bilaterally into the pedicles of the lumbar spine. These screws were stimulated with an ascending stimulus intensity until a peripheral triggered electromyographic response was recorded. Pedicle screws were placed in the pig either entirely in the pedicle (Group A), medial to the pedicle without direct contact to the nerve root and dura (Group B), or purposely medial to the pedicle with direct contact to the nerve root and dura (Group C). A correlative clinical series of 233 pedicle screws placed in 54 patients had a similar intraoperative neurophysiologic technique. RESULTS: In the animal model, the mean threshold differences were: Group A screws 21.9 mA, Group B screws 8.5 mA, and Group C screws 4.2 mA (P < 0.05). Ninety-three percent of the clinical Group A screws had threshold stimuli less than 8.0 mA, whereas Groups B and C screws had a mean threshold of 3.3 mA. CONCLUSIONS: Triggered electromyographic stimulation is a valuable aid to determine appropriate placement of pedicle screws. We recommend the following interpretation of threshold stimulus intensity: > 8 mA--screw entirely in the pedicle; 4.0-8.0 mA--potential for pedicle wall defect; < 4.0 mA--strong likelihood of pedicle wall defect with potential for nerve root and dura contact.

Animals↗

PubMed2000

Estimating particulate matter-mortality dose-response curves and threshold levels: an analysis of daily time-series for the 20 largest US cities.

Numerous studies have shown a positive association between daily mortality and particulate air pollution, even at concentrations below regulatory limits. These findings have motivated interest in the shape of the exposure-response relation. The authors have developed flexible modeling strategies for time-series data that include spline and threshold exposure-response models; they apply these models to daily time-series data for the 20 largest US cities for 1987-1994, using the concentration of particulate matter <10 microm in aerodynamic diameter (PM10) as the exposure measure. The spline model showed a linear relation without indication of threshold for PM10 and relative risk of death for all causes and cardiorespiratory causes; by contrast, for other causes, the risk did not increase until approximately 50 microg/m3 PM10. For all-cause mortality, a linear model without threshold was preferred to the threshold model and to the spline model, using the Akaike information criterion (AIC). The findings were similar for cardiovascular and respiratory deaths combined. By contrast, for causes other than cardiovascular and respiratory, a threshold model was more competitive with a threshold value estimated at 65 microg/m3. These findings indicate that linear models without a threshold are appropriate for assessing the effect of particulate air pollution on daily mortality even at current levels.

Air Pollutants↗

PubMed2004

Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights.

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Phys. Rev. Lett. 89, 258702 (2002)]. Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering, and short path lengths are produced for many types of weight distributions. Thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2. It contrasts with the class of growth models with preferential attachment, which is marked by competitiveness and baseline scaling exponent 3.

Journal Article↗

PubMed1990

Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity.

We have developed a model for the representation of stereo disparity by a population of neurons that is based on tuning curves similar in shape to those measured physiologically (Poggio and Fischer, 1977). Signal detection analysis was applied to the model to generate predictions of depth discrimination thresholds. Agreement between the model and human psychophysical data was possible in this model only when the population size representing disparity in a small patch of visual field was in the range of about 20-200 units. Interval encoding and rate encoding were found to be inconsistent with these data. Psychophysical data on stereo interpolation (Westheimer, 1986a) suggest that there are short-range excitatory and long-range inhibitory interactions between disparity-tuned units at nearby spatial locations. We extended our population model of disparity coding at a single spatial location to include such lateral interactions. When there was a small disparity gradient between stimuli at 2 locations, units in the intermediate, unstimulated position developed a pattern of activity corresponding to the average of the 2 lateral disparities. When there was a large disparity gradient, units at the intermediate position developed a pattern of activity corresponding to an independent superposition of the 2 lateral disparities, so that both disparities were represented simultaneously. This mixed population pattern may underlie the perception of depth discontinuities and transparent surfaces. Similar types of distributed representations may be applicable to other parameters, such as orientation, motion, stimulus size, and motor coordinates.

Depth Perception↗

PubMed1980

Incorporation of background in dose-response models.

Dose-response models are generally classified as either threshold-tolerance or mechanism models. These models are briefly reviewed and their impact upon low-dose estimation is discussed. The concept of independent versus additive backgrounds is explored. The mathematical implications are considered with the conclusion that additive background implies linearity and that the assumption of total independence of background is required to justify nonlinearity at low doses. This finding has important implications to low-dose extrapolations for the purpose of risk estimation.

Animals↗

PubMed2002

Treat or test first? Decision analysis of empirical antiviral treatment of influenza virus infection versus treatment based on rapid test results.

BACKGROUND: neuraminidase (NA) inhibitors have recently become available for treatment of influenza. Rapid antigen detection assays at 'point-of-care' may improve the accuracy of clinical diagnosis, but the value of these techniques in assisting with the appropriate use of antivirals remains controversial. OBJECTIVE: to compare the diagnostic utilities of two management strategies for influenza, empirical antiviral therapy versus therapy based on a positive rapid test result in pre-epidemic and epidemic periods. STUDY DESIGN: a threshold decision analytic model was designed to compare these competing strategies and sensitivity analysis performed to examine the impact of diagnostic variables on the expected utility of the decision with a range of prior probabilities of infection between 1 and 50%. RESULTS: on the basis of the calculated sensitivity (77%) and specificity (95%) of a point-of-care test for influenza, pre-treatment testing was preferred and cost-effective in non-epidemic stage of the influenza cycle. The alternative strategy of empirical treatment produces a higher utility value during epidemics, but may result in overuse of antivirals for low-risk populations. The two strategies had equivalent efficacy when the probability of influenza was 42%. CONCLUSIONS: Patients with flu-like illness, who present outside the influenza outbreak and are considered to be at low risk for influenza-related complications, should be tested to confirm the diagnosis before starting antiviral treatment with a NA inhibitor. The most important variables in the model were the accuracy of the clinical diagnosis and the pre-test probability of influenza. A threshold probability of influenza of 42% would dictate changing from the rapid testing strategy to a 'treat regardless' strategy.

Antiviral Agents↗

PubMed1993

Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos.

To contribute to a deeper understanding of M-phase control in eukaryotic cells, we have constructed a model based on the biochemistry of M-phase promoting factor (MPF) in Xenopus oocyte extracts, where there is evidence for two positive feedback loops (MPF stimulates its own production by activating Cdc25 and inhibiting Wee1) and a negative feedback loop (MPF stimulates its own destruction by indirectly activating the ubiquitin pathway that degrades its cyclin subunit). To uncover the full dynamical possibilities of the control system, we translate the regulatory network into a set of differential equations and study these equations by graphical techniques and computer simulation. The positive feedback loops in the model account for thresholds and time lags in cyclin-induced and MPF-induced activation of MPF, and the model can be fitted quantitatively to these experimental observations. The negative feedback loop is consistent with observed time lags in MPF-induced cyclin degradation. Furthermore, our model indicates that there are two possible mechanisms for autonomous oscillations. One is driven by the positive feedback loops, resulting in phosphorylation and abrupt dephosphorylation of the Cdc2 subunit at an inhibitory tyrosine residue. These oscillations are typical of oocyte extracts. The other type is driven by the negative feedback loop, involving rapid cyclin turnover and negligible phosphorylation of the tyrosine residue of Cdc2. The early mitotic cycles of intact embryos exhibit such characteristics. In addition, by assuming that unreplicated DNA interferes with M-phase initiation by activating the phosphatases that oppose MPF in the positive feedback loops, we can simulate the effect of addition of sperm nuclei to oocyte extracts, and the lengthening of cycle times at the mid-blastula transition of intact embryos.

Animals↗

PubMed2003

Strategic management of non-point source pollution from sewage sludge.

In the UK, the recycling of sewage sludge to land is expected to double by 2006 but the security of this route is threatened by environmental concerns and health scares. Strategic investment is needed to ensure sustainable and secure sludge recycling outlets. At present, the security of this landbank for sludge recycling is determined by legislation relating to nutrient rather than potentially toxic elements (PTEs) applications to land--especially the environmental risk linked to soil phosphorus (P) saturation. We believe that not all land has an equal risk of contributing nutrients derived from applications to land to receiving waters. We are currently investigating whether it is possible to minimise nutrient loss by applying sludge to land outside Critical Source Areas (CSAs) regardless of soil P Index status. Research is underway to develop a predictive and spatially-sensitive, semi-distributed model of critical thresholds for sludge application that goes beyond traditional "end-of-pipe" or "edge-of-field" modelling, to include hydrological flow paths and delivery mechanisms to receiving waters from non-point sources at the catchment scale.

Conservation of Natural Resources↗

PubMed1979

Sensitivity variations in the visual system, contrast resolution and eye movements.

Attention is drawn to the fact that under normal visual conditions the sensitivity of the receptor units of the visual system are subject to spatial and temporal variations, and that consequently in performing pattern recognition the visual cortex has to discriminate between external luminance structure and internal sensitivity structure. It is suggested that eye movements are the method by which this discrimination is performed. In a simplified model analysis it is shown that eye movements are a suitable mechanism for this discrimination. Implications of this model for detection threshold and stabilized retinal images are discussed. A new interpretation of the adaptation to sine wave grids is given.

Eye Movements↗

PubMed1999

Comparative analgesic effects of H-wave therapy and transcutaneous electrical nerve stimulation on pain threshold in humans.

OBJECTIVE: To assess the comparative analgesic efficacy of H-wave therapy (HWT) and transcutaneous electrical nerve stimulation (TENS) using a mechanical model of pain threshold measurement. STUDY DESIGN: Forty-eight healthy human volunteers (24 women, 24 men) were recruited and randomly assigned into one of six experimental groups; control, HWT (placebo, 2Hz, or 60Hz), or TENS (placebo or 110Hz). For each subject, mechanical pain threshold (MPT) measurements were recorded at three standardized recording points marked on the dorsal web space of the dominant hand. Two MPT measurements were recorded at each point at the following time intervals: before treatment was initiated (baseline), after each of three consecutive 10-minute periods of stimulation (HWT or TENS), and at four intervals within 30 minutes after stimulation. In the control and placebo groups MPT measurements were recorded at similar time intervals. RESULTS: Difference scores, calculated from patients' baseline values, were analyzed by ANOVA for each of the three recording points. Although results showed a significant increase in MPT levels in all three stimulation groups when compared with their relative placebo (indicating a hypoalgesic effect), no differences were observed between the different modalities or HWT frequencies. Significant hypoalgesia continued for 5 minutes after stimulation. CONCLUSION: The findings showed that HWT and TENS provided localized hypoalgesia during stimulation and for up to 5 minutes after it. No frequency- or modality-specific effects were observed between the groups.

Adult↗