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PubMed2006

A bivariate quantitative genetic model for a threshold trait and a survival trait.

Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.

Bayes Theorem↗
PubMed1985

The inheritance of spontaneous amyloidosis development in mice: a model for hereditary threshold metabolic disorders.

To study the inheritance of spontaneous amyloidosis development in mice, we crossed the LLC strain (with a high incidence) with the A/J strain (with a low incidence) and with the HLC strain (with a zero incidence of amyloidosis). We produced the F1 and a backcross generation to each parental strain in each cross. Examination of the spleen, liver, and kidneys of each mouse for the presence of amyloid was made between age 15 and 18 months. The data fit neither a dominant nor a recessive single gene hypothesis for the development of amyloidosis. In consideration of amyloidosis as a hereditary threshold character, we developed an additive gene model. Subsequently, a test for fitness of the observed percentages to the expected percentages in the backcross generations was made according to this model. The observed percentages of amyloidosis in the spleens, livers, and individual mice agreed with the expected percentages in the LLC X A/J crosses but not in the LLC X HLC crosses. Therefore, we conclude that for the development of amyloidosis, a difference exists at one locus between LLC and A/J and at more than one locus between LLC and HLC. The probability of development of amyloidosis in an individual depends on the effects of the genes at these loci. For hereditary metabolic disorders that cannot be explained by either a single dominant or recessive gene hypothesis, this genetic model may be useful to test whether the development of the disease is due to additive effects of genes.

Amyloidosis↗
PubMed2004

History, development, and future of the progressively lowered stress threshold: a conceptual model for dementia care.

Behavioral symptoms associated with dementia are a major concern for the person who experiences them and for caregivers who supervise, support, and assist them. The knowledge and skill of formal and informal caregivers affects the quality of care they can provide and their ability to cope with the challenges of caregiving. Nurses are in an excellent position to provide training to empower caregivers with the knowledge and skills necessary to reduce and better manage behaviors. This article reviews advances in geriatric nursing theory, practice, and research based on the Progressively Lowered Stress Threshold (PLST) model that are designed to promote more adaptive and functional behavior in older adults with advancing dementia. For more than 17 years, the model has been used to train caregivers in homes, adult day programs, nursing homes, and acute care hospitals and has served as the theoretical basis for in-home and institutional studies. Care planning principles and key elements of interventions that flow from the model are set forth, and outcomes from numerous research projects using the PLST model are presented.

Aged↗
PubMed1995

Dose-dependent anticonvulsant and proconvulsant effects of nitric oxide synthase inhibitors on seizure threshold in a cortical stimulation model in rats.

In the central nervous system, nitric oxide (NO) is increasingly being considered as a trans-synaptic retrograde messenger, being involved for instance in cellular responses to stimulation of glutamate receptors of the NMDA subtype. Thus, compounds that modify NO production, such as NO synthase inhibitors, may provide a means of altering NMDA receptor function. The functional consequences of NO synthase inhibition are, however, complicated by the fact that NO not only serves as a messenger to activate guanylyl cyclase and so to raise cGMP in target cells in response to NMDA receptor stimulation but also to induce feedback inhibition of the NMDA receptor via a redox modulatory site on the receptor complex. This may explain the contrasting results obtained previously with NO synthase inhibitors in animal models of ischaemia and seizures. In the present study, we tried to resolve the reported discrepancies about the effects of NO synthase inhibitors in seizure models by studying such drugs at various doses in a novel model of cortical seizure threshold. In this model, the threshold for seizures in rats is determined at short time intervals by applying ramp-shaped electrical pulse-trains directly to the cerebral cortex, allowing one to determine the time course of anti- or proconvulsant drug effects in individual rats. Two NO synthase inhibitors, NG-nitro-L-arginine and NG-nitro-L-arginine methyl ester, were compared with a clinically effective antiepileptic drug, i.e. valproate.(ABSTRACT TRUNCATED AT 250 WORDS)

Amino Acid Oxidoreductases↗
PubMed1987

Threshold dose-response models in toxicology.

After a brief discussion of the threshold concept in toxicology, we consider models for the estimation of thresholds in the case where the observed response is binary or quantal. A generalization of the four-parameter Tukey-lambda family of distributions is proposed as a useful class of models for threshold estimation. Properties of these models are discussed and the process of model fitting and evaluation is illustrated using a number of data sets. The discussion includes consideration of background or spontaneous response, and comparison with other models. One of these is the linear-plateau or hockey-stick model, which has been used in a number of toxicological studies.

Animals↗
PubMed1993

Reduction of structured population models to threshold-type delay equations and functional differential equations: a case study.

It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability.

Age Factors↗
PubMed1997

Temperature thresholds and statistical modelling of larval Wuchereria bancrofti (Filariidea:Onchocercidae) developmental rates.

Developmental rates for Wuchereria bancrofti larvae maturing in the vector Aedes polynesiensis were estimated by analysing stage-frequency data consisting of counts of larval stages in mosquitoes reared at 20, 22.5, 25, 27.5, 30 and 32 degrees C. Base temperatures (i.e. low temperature thresholds) for W. bancrofti development were estimated by the x-intercept method and the model of Lactin et al. (1995). Resulting values were similar with both methods and were approximately 12.5 degrees C for microfilariae (mf) in thorax, approximately 17 degrees C for L1, 15.5 degrees C for L2 and 16.5 degrees C for L3. Upper thresholds estimated by the Lactin et al. model were 29.3 degrees C for mf, 29.1 degrees C for L1, 32.2 degrees C for L2 and 31.5 degrees C for L3. In addition, an original method was devised for computing the L3 upper threshold, by modelling L3 length shrinkage with temperature. It gave a value of 31.4 degrees C. At 32 degrees C, L2 and L3 stages exhibited altered morphology, larvae being shorter and wider than expected. The model of Lactin et al. described adequately the non-linear relationship between developmental rate and temperature, but a linear degree-day approach may be applied for temperatures below 27-28 degrees C.

Aedes↗
PubMed1997

Genetic analysis of discrete reproductive traits in sheep using linear and nonlinear models: II. Goodness of fit and predictive ability.

The performance of linear and nonlinear sire and animal models in the analyses of reproductive traits (fertility, litter size, and ovulation rate) in two sheep populations (Rambouillet and Finnsheep) was compared in terms of goodness of fit and predictive ability. Linear sire (LSM) and animal (LAM) models were used with all traits. Nonlinear models were the threshold, Poisson, and negative binomial. Threshold sire (TSM) and animal (TAM) models were also used with all traits. Litter size and ovulation rate were analyzed also with Poisson and negative binomial sire (PSM and NBSM, respectively) and animal (PAM and NBAM, respectively) models. Variance components were those reported in the companion article. For PAM a new set of variance components derived from estimates found with the linear animal model also was used (PAM-L). Mean squares error (MSE) and correlations between fitted and observed values were used to assess goodness of fit. Predictive ability was assessed by partitioning the data sets for the different traits into two subsets with the restriction that all levels of fixed effects were represented in each subset. Parameters from one subset were employed to predict observations in the other, and then MSE and correlations between observed and predicted values were used as criteria for model comparison. Within estimation procedure, breed, and trait, goodness of fit of sire and animal models was similar. Linear and threshold models resulted in similar fit, and both outperformed Poisson and negative binomial models. In terms of predictive ability, linear and threshold models performed only slightly better than Poisson and negative binomial models. Goodness of fit and predictive ability generally were better when models included permanent environmental effects.

Animals↗
PubMed1999

Satiety threshold: a quantitative model of maintained cocaine self-administration.

The intervals between self-injections of cocaine by rats are defined by an equation that contains only three parameters: the dose of cocaine administered, the elimination half-life of cocaine, and an amount of cocaine in the body, which we have termed the cocaine satiety threshold. This latter parameter is defined as the maximal level of cocaine at which the probability of self-administration approximates one and above which the probability of self-administration is low. The mathematical model generated mean values for the satiety threshold and the functional elimination half-life of cocaine of approximately 1.7 mg/kg (i.v.) and 8.2 min, respectively. Therefore, the simple equations presented here permit the measurement of the pharmacokinetics and pharmacodynamics of cocaine using self-administration behavior as a bioassay. Our satiety model predicts that when cocaine levels are maintained above the satiety threshold, rats would not self-administer cocaine. The elimination rate of cocaine at the satiety threshold was calculated to be approximately 2 microg kg(-1) s(-1). Therefore, an infusion of cocaine at this rate should maintain cocaine levels fractionally above the satiety threshold. A continuous infusion of cocaine at this rate prevented cocaine self-administration for the duration of the infusion, thereby confirming the validity of the satiety model. These equations provide a quantitative description of cocaine self-administration and contain no subjective terms, implying that concepts such as "craving", drug "wanting" and "liking" and "reinforcement", used in psychologically oriented models, are not necessary for descriptions of this behavior in rats.

Animals↗
PubMed1991

Variable threshold as a model for selective attention, (de)sensitization, and anesthesia in associative neural networks.

We study the influence of a variable neuronal threshold on fixed points and convergence rates of an associative neural network in the presence of noise. We allow a random distribution in the activity levels of the patterns stored, and a modification to the standard Hebbian learning rule is proposed for this purpose. There is a threshold at which the retrieval ability, including the average final overlap and the convergence rate, is optimized for patterns with a particular activity level at a given noise level. This type of selective attention to one class of patterns with a certain activity level may be obtained at the cost of reducing the retrieval ability of the network for patterns with different activity levels. The effects of a constant threshold independent of noise, time, and pattern are discussed. For high-(low-) activity patterns, the average final overlap is shown to be increased at high noise levels and decreased at low noise levels by a negative (positive) constant threshold, whereas a positive (negative) threshold always reduces the final average overlap. When the magnitude of the constant threshold exceeds a critical value, there is no retrieval. Rates of convergence towards the stored pattern with negative (positive) thresholds are greater than those with positive (negative) thresholds. These results are related to (de)sensitization and anesthesia. For certain threshold values and patterns with certain activity levels, hysteresis appears in the plot of the average final overlap versus the noise level, even for first order interactions. We make the analogy between the pattern-dependent neuronal threshold proposed in the present paper and the "task-related" modulation in neuronal excitability determined by cognitive factors, such as the attentional state of a higher animal. A constant threshold is associated with overall changes in neuronal excitability caused, e.g., by various drugs and physical injuries. Neurophysiological evidence of a dynamically variable neuronal threshold, such as accommodation and potentiation, is presented.

Anesthesia↗
PubMed2002

Overcoming the phage replication threshold: a mathematical model with implications for phage therapy.

Prior observations of phage-host systems in vitro have led to the conclusion that susceptible host cell populations must reach a critical density before phage replication can occur. Such a replication threshold density would have broad implications for the therapeutic use of phage. In this report, we demonstrate experimentally that no such replication threshold exists and explain the previous data used to support the existence of the threshold in terms of a classical model of the kinetics of colloidal particle interactions in solution. This result leads us to conclude that the frequently used measure of multiplicity of infection (MOI), computed as the ratio of the number of phage to the number of cells, is generally inappropriate for situations in which cell concentrations are less than 10(7)/ml. In its place, we propose an alternative measure, MOI(actual), that takes into account the cell concentration and adsorption time. Properties of this function are elucidated that explain the demonstrated usefulness of MOI at high cell densities, as well as some unexpected consequences at low concentrations. In addition, the concept of MOI(actual) allows us to write simple formulas for computing practical quantities, such as the number of phage sufficient to infect 99.99% of host cells at arbitrary concentrations.

Bacteriophage M13↗
PubMed2006

Comment on "Auditory-nerve first-spike latency and auditory absolute threshold: a computer model" [J. Acoust. Soc. Am. 119, 406-417 (2006)].

A recent paper by Meddis [J. Acoust. Soc. Am. 119, 406-417 (2006)] shows that an existing model of the auditory nerve [Meddis and O'Mard, J. Acoust. Soc. Am. 117, 3787-3798 (2005)] is consistent with experimentally-measured first-spike latencies in the auditory nerve [Heil and Neubauer, J. Neurosci. 21, 7404-7415 (2001)]. The paper states that this consistency emerges because in the model, the calcium concentration inside the inner hair cell builds up over long periods of time (up to at least 200 ms) during tone presentation. It further states that integration over long time-scales happens despite the very short time constants (< 1 ms) used for the calcium dynamics. This letter demonstrates that these statements are incorrect. It is shown by simulation that calcium concentration inside the hair cell stage of the Meddis model rapidly reaches a steady state within a few milliseconds of a stimulus onset, exactly as expected from the short time-constant in the simple first-order differential equation used to model the calcium concentration. The success of the Meddis model in fitting experimental data actually confirms earlier results [Krishna, J. Comput. Neurosci. 13, 71-91 (2002a)] that show that the experimental data are a natural result of stochasticity in the synaptic events leading up to spike-generation in the auditory nerve; integration over long time scales is not necessary to model the experimental data.

Action Potentials↗
PubMed2004

Prediction of myelinated nerve fiber stimulation thresholds: limitations of linear models.

Computer models of neurons are used to simulate neural behavior, and are important tools for designing neural prostheses. Computation time remains an issue when simulating large numbers of neurons or applying models to real time applications. Warman et al. developed a method to predict excitation thresholds for axons using linear models and a predetermined critical voltage. We calculated threshold prediction error as a function of the location of an extracellular electrode using two different axon models to examine further threshold prediction using linear models. Threshold prediction error was low (<3% error) under the conditions examined by Warman et al., but under more general conditions, threshold prediction error was as high as 23.6%. Linear models were limited as effective tools for single fiber threshold prediction because accuracy was dependent on the nonlinear and linear models used, and any parameter that affected the extracellular potential distribution. Threshold prediction could be improved by appropriately choosing the membrane conductance of the linear model, but determination of an optimal conductance was computationally expensive. Finally, although single fiber threshold prediction error was partially masked when considering the input-output (I/O) properties of populations of axons, relatively large errors still occurred in population I/O curves generated with linear models.

Axons↗
PubMed2004

Modeling associative recognition: a comparison of two-high-threshold, two-high-threshold signal detection, and mixture distribution models.

A 2-high-threshold signal detection (HTSDT) model, a mixture distribution (SON) model, and 2-high-threshold (HT) models with responses distributed over 1 or several response categories were fit to results of 6 experiments from 2 studies on associative recognition: R. Kelley and J. T. Wixted (2001) and A. P. Yonelinas (1997). HTSDT assumes that associative recognition is based on conscious recollection and familiarity assessment, whereas according to SON and HT, associative information results in a shift of familiarity. The modeling results cast doubt on the prominent role of conscious recollection, and as far as models are valid, parameter estimation suggests 2 processes in associative recognition: a shift in familiarity that is due to associative information and the determination of the source of familiarity of pairs.

Association↗
PubMed1991

Reproduction numbers and thresholds in stochastic epidemic models. I. Homogeneous populations.

We compare threshold results for the deterministic and stochastic versions of the homogeneous SI model with recruitment, death due to the disease, a background death rate, and transmission rate beta cXY/N. If an infective is introduced into a population of susceptibles, the basic reproduction number, R0, plays a fundamental role for both, though the threshold results differ somewhat. For the deterministic model, no epidemic can occur if R0 less than or equal to 1 and an epidemic occurs if R0 greater than 1. For the stochastic model we find that on average, no epidemic will occur if R0 less than or equal to 1. If R0 greater than 1, there is a finite probability, but less than 1, that an epidemic will develop and eventuate in an endemic quasi-equilibrium. However, there is also a finite probability of extinction of the infection, and the probability of extinction decreases as R0 increases above 1.

Computer Simulation↗
PubMed2002

A simple model of long-term spike train regularization.

A simple model of spike generation is described that gives rise to negative correlations in the interspike interval (ISI) sequence and leads to long-term spike train regularization. This regularization can be seen by examining the variance of the kth-order interval distribution for large k (the times between spike i and spike i + k). The variance is much smaller than would be expected if successive ISIs were uncorrelated. Such regularizing effects have been observed in the spike trains of electrosensory afferent nerve fibers and can lead to dramatic improvement in the detectability of weak signals encoded in the spike train data (Ratnam & Nelson, 2000). Here, we present a simple neural model in which negative ISI correlations and long-term spike train regularization arise from refractory effects associated with a dynamic spike threshold. Our model is derived from a more detailed model of electrosensory afferent dynamics developed recently by other investigators (Chacron, Longtin, St.-Hilaire, & Maler, 2000;Chacron, Longtin, & Maler, 2001). The core of this model is a dynamic spike threshold that is transiently elevated following a spike and subsequently decays until the next spike is generated. Here, we present a simplified version-the linear adaptive threshold model-that contains a single state variable and three free parameters that control the mean and coefficient of variation of the spontaneous ISI distribution and the frequency characteristics of the driven response. We show that refractory effects associated with the dynamic threshold lead to regularization of the spike train on long timescales. Furthermore, we show that this regularization enhances the detectability of weak signals encoded by the linear adaptive threshold model. Although inspired by properties of electrosensory afferent nerve fibers, such regularizing effects may play an important role in other neural systems where weak signals must be reliably detected in noisy spike trains. When modeling a neuronal system that exhibits this type of ISI correlation structure, the linear adaptive threshold model may provide a more appropriate starting point than conventional renewal process models that lack long-term regularizing effects.

Action Potentials↗
PubMed1987

Simple test of the Multifactorial-Polygenic Model with sex dependent thresholds.

Under the Multifactorial-Polygenic Model, a sex difference in population incidence implies higher risk in relatives of low risk sex probands than in those of high risk sex probands. The relationship between sex ratio in population incidence and expected relative risk (RR) to first-degree relatives of probands of the low risk sex vs the high risk sex under the Multifactorial-Polygenic Model was examined. Five observations were made from this analysis: as the sex ratio increases, the expected RR increases for each combination of incidence and r, the liability correlation between relatives, RRs are higher for low risk sex relatives than for high risk sex relatives at each combination of incidence, r, and sex ratio, the expected RR increases as r increases at each incidence and sex ratio, and variation in population incidence has little effect on RR at a given sex ratio and r, and the expected RRs are small, rarely exceeding two-fold. The quantitative relationship between sex ratio and RR provides the basis for a simple test of the Multifactorial-Polygenic Model when two different sex or severity thresholds can be identified.

Epidemiologic Methods↗