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PubMed1992

A general diffusion model for analyzing the efficacy of synaptic input to threshold neurons.

We describe a general diffusion model for analyzing the efficacy of individual synaptic inputs to threshold neurons. A formal expression is obtained for the system propagator which, when given an arbitrary initial state for the cell, yields the conditional probability distribution for the state at all later times. The propagator for a cell with a finite threshold is written as a series expansion, such that each term in the series depends only on the infinite threshold propagator, which in the diffusion limit reduces to a Gaussian form. This procedure admits a graphical representation in terms of an infinite sequence of diagrams. To connect the theory to experiment, we construct an analytical expression for the primary correlation kernel (PCK) which profiles the change in the instantaneous firing rate produced by a single postsynaptic potential (PSP). Explicit solutions are obtained in the diffusion limit to first order in perturbation theory. Our approximate expression resembles the PCK obtained by computer simulation, with the accuracy depending strongly on the mode of firing. The theory is most accurate when the synaptic input drives the membrane potential to a mean level more than one standard deviation below the firing threshold, making such cells highly sensitive to synchronous synaptic input.

Computer Simulation↗
PubMed2006

Genetic associations between clinical mastitis and somatic cell score in early first-lactation cows.

The objectives of this study were to examine genetic associations between clinical mastitis and somatic cell score (SCS) in early first-lactation cows, to estimate genetic correlations between SCS of cows with and without clinical mastitis, and to compare genetic evaluations of sires based on SCS or clinical mastitis. Clinical mastitis records from 15 d before to 30 d after calving and first test-day SCS records (from 6 to 30 d after calving) from 499,878 first-lactation daughters of 2,043 sires were analyzed. Results from a bivariate linear sire model analysis of SCS in cows with and without clinical mastitis suggest that SCS is a heterogeneous trait. Heritability of SCS was 0.03 for mastitic cows and 0.08 for healthy cows, and the genetic correlation between the 2 traits was 0.78. The difference in rank between sire evaluations based on SCS of cows with and without clinical mastitis varied from -994 to 1,125, with mean 0. A bivariate analysis with a threshold-liability model for clinical mastitis and a linear Gaussian model for SCS indicated that heritability of liability to clinical mastitis is at least as large as that of SCS in early lactation. The mean (standard deviation) of the posterior distribution of heritability was 0.085 (0.006) for liability to clinical mastitis and 0.070 (0.003) for SCS. The posterior mean (standard deviation) of the genetic correlation between liability to clinical mastitis and SCS was 0.62 (0.03). A comparison of sire evaluations showed that genetic evaluation based on SCS was not able to identify the best sires for liability to clinical mastitis. The association between sire posterior means for liability to clinical mastitis and sire predicted transmitting ability for SCS was far from perfect.

Analysis of Variance↗
PubMed1998

Murine strain differences in the volume effect and incidence of radiation-induced colorectal obstruction.

PURPOSE: Interindividual variation in the level of normal tissue damage after radiotherapy has been clinically observed. Murine models have suggested that there may be a genetic component to the variation in susceptibility of different radiation-induced normal tissue complications. Currently, there are no experimental data available describing interstrain differences in the "volume effect" for irradiated normal tissues, such as the colorectum. The aims of this study are to determine if there are strain differences in: 1. the incidence of colorectal obstruction; and 2. the volume effect, after irradiation of the colorectum using two mouse strains that are known to vary in their susceptibility for developing pulmonary fibrosis. METHODS AND MATERIALS: Various lengths (5.2 to 22.9 mm) of the colorectum of male C57B1/6 and C3Hf/Kam mice were irradiated with a single dose (30 Gy) of 137Cs gamma rays. Also, various doses (20 to 35 Gy) were given to a single length (22.9 mm) of colorectum. The incidence of obstruction was determined as a function of length and dose at 6 months after irradiation. The Threshold Probability model was fit to the length-response data. RESULTS: C57B1/6 mice developed colorectal obstruction at significantly higher incidence than C3Hf/Kam mice at all lengths after a single dose of 30 Gy. In addition, the data showed a strain difference in the threshold length of colorectum that had to be irradiated before obstructions were observed. CONCLUSION: Strain differences in the incidence of radiation-induced colorectal obstruction were observed, consistent with previous studies that showed a strain difference in radiation-induced pulmonary fibrosis. The presence of a threshold length of colorectum that was different for the two strains is consistent with the concept that there may be a critical threshold amount of colorectal tissue that can tolerate a high dose without complication, and that the dimensions of the threshold may vary among individuals.

Animals↗
PubMedDate not supplied

[A quantitative description of the cytostatic effects of chelators of transition metal ions (exemplified by picolinic acid and Fe2+)].

A mathematical model is proposed for the description of the cytostatic effects of the chelating agents of the transition metal ions on cell cultures. Chelate complexes of picolinic acid and bivalent iron ions, which play an important role in nucleic acid synthesis, were considered as an example. Kinetic equations of the theory of receptors were used for model construction. The best correspondence with the experimental dose-effect curves, obtained in the experiments on influence of various picolinic acid concentrations on division of the SPEV cultured cells, is provided by the model of threshold type. The parameters lying in the basis of the theory of receptors and relating the biological effect (cell division) to the number of ligand-receptor complexes were calculated.

Animals↗
PubMed1987

A model for thermal ablation of biological tissue using laser radiation.

We present a theory of thermal laser ablation based on the heat equation and on an energy balance equation derived from it. Ablation is assumed to be brought about by the heating and evaporation of tissue water. The model is three-dimensional, and scattering and the water-steam phase transition are explicitly taken into account. The model predicts threshold parameters and a steady-state ablation velocity in terms of the optical and thermal properties of the tissue and the laser beam intensity and spot diameter.

Biophysical Phenomena↗
PubMed2006

Spatiotemporal consequences of relaxation time scales in threshold-coupled systems.

We study a class of models incorporating threshold-activated coupling on a lattice of chaotic elements. In such systems, the relaxation time allowed between chaotic updates determines the intrinsic driving rate due to the local chaos, and we show that there exists an inverse cascade from fixed spatial profiles to spatiotemporal chaos, as the relaxation time grows shorter. We analyze how this spectrum of spatiotemporal transitions arises from the competing time scales of the local chaos and the propagation of coupling.

Journal Article↗
PubMed1989

A model for the peripheral auditory nervous system of the grassfrog.

A model is presented which incorporates several data from the literature on isolated parts of the peripheral auditory nervous system into a coherent model. The usefulness of the model lies in the fact that it describes the functional properties of eighth nerve fibres and dorsal medullary nucleus neurons in response to monaural stimuli. The components are: a middle ear filter, transduction and tuning of the haircell, short-term adaptation, event generation with refractory properties, and coincidence detection. In a previous paper [Van Stokkum (1987), Hear. Res. 29, 223-235] a class of dorsal medullary nucleus neurons was described, which preferred fast intensity changes. Using a coincidence detection mechanism the proposed model reproduces the same preference. Variation of the parameters of the model successfully reproduces the range of response patterns which have been obtained from eighth nerve fibres and dorsal medullary nucleus neurons. With one set of parameters the output of the model in response to a set of spectrally and temporally structured stimuli qualitatively resembles the response of a single neuron. In this way the responses to the different stimuli are synthesized into a framework, which functionally describes the neuron.

Acoustic Stimulation↗
PubMedDate not supplied

Schistosomiasis models with density dependence and age of infection in snail dynamics.

New models for schistosomiasis are developed. These models incorporate several realistic features including drug treatment for human hosts, an infection age in snail hosts, density-dependent birth rate of snails, distribution of schistosomes within human hosts, and disease-induced mortality in both human and snail hosts. The qualitative and quantitative mathematical properties of the models are studied, their biological consequences and some control strategies are discussed, and the results of the new models are compared with those of simpler models. It is shown that the new model may have a bifurcation at which the unique endemic equilibrium changes the stability and stable periodic solutions exist. This is quite different from the simpler models. Explicit thresholds of treatment rate are established above which the infection will be controlled under certain levels. Evaluations of cost-effectiveness are also discussed by analyzing the sensitivity of the mean number of parasites per person to changes of other parameters.

Animals↗
PubMed2003

On vaccine efficacy and reproduction numbers.

We consider the impact of a vaccination programme on the transmission potential of the infection in large populations. We define a measure of vaccine efficacy against transmission which combines the possibly random effect of the vaccine on individual susceptibility and infectiousness. This definition extends some previous work in this area to arbitrarily heterogeneous populations with one level of mixing, but leads us to question the usefulness of the concept of vaccine efficacy against infectiousness. We derive relationships between vaccine efficacy against transmission, vaccine coverage and reproduction numbers, which generalize existing results. In particular we show that the projected reproduction number RV does not depend on the details of the vaccine model, only on its overall effect on transmission. Explicit expressions for RV and the basic reproduction number R0 are obtained in a variety of settings. We define a measure of projected effectiveness of a vaccination programme PE=1-(RV/R0) and investigate its relationship with efficacy against transmission and vaccine coverage. We also study the effective reproduction number Re(t) at time t. Monitoring Re(t) over time is an important aspect of programme surveillance. Programme effectiveness PE is less sensitive than RV or the critical vaccination threshold to model assumptions. On the other hand Re(t) depends on the details of the vaccine model.

Age Factors↗
PubMed2000

Dose-response and threshold-mediated mechanisms in mutagenesis: statistical models and study design.

The objective of this paper is to review the use, in mutagenesis, of various mathematical models to describe the dose-response relationship and to try to identify thresholds. It is often taken as axiomatic that genotoxic carcinogens could damage DNA at any level of exposure, leading to a mutation, and that this could ultimately result in tumour development. This has led to the assumption that for genotoxic chemicals, there is no discernible threshold. This assumption is increasingly being challenged in the case of aneugens. The distinction between 'absolute' and 'pragmatic' thresholds is made and the difficulties in determining 'absolute' thresholds using hypothesis testing approaches are described. The potential of approaches, based upon estimation rather than statistical significance for the characterization of dose-response relationships, is stressed. The achievement of a good fit of a mathematical model to experimental data is not proof that the mechanism supposedly underlying this model is operating. It has been argued, in the case of genotoxic chemicals, that any effects produced by a genotoxic chemical which augments that producing a background incidence in unexposed individuals will lead to a dose-response relationship that is non-thresholded and is linear at low doses. The assumptions underlying this presumption are explored in the context of the increasing knowledge of the mechanistic basis of mutagenicity and carcinogenicity. The possibility that exposure to low levels of genotoxic chemicals may induce and enhance defence and repair mechanisms is not easily incorporated into many of the existing mathematical models and should be an objective in the development of the next generation of biologically based dose-response (BB-DR) models. Studies aimed at detecting or characterizing non-linearities in the dose-response relationship need appropriate experimental designs with careful attention to the choice of biomarker, number and selection of dose levels, optimum allocation of experimental units and appropriate levels of replication within and repetition of experiments. The characterization of dose-response relationships with appropriate measures of uncertainty can help to identify 'pragmatic' thresholds based upon biologically relevant criteria which can help in the regulatory process.

Aneuploidy↗
PubMed2005

Does god play dice with schizophrenia? A probabilistic model for the understanding of causation in mental illness.

While the pure sciences have moved over the XX century from the certainties of the Laplacian mechanistic models to probabilistic ones, such as quantum physics, the attempts to explain the causation in mental illness are still stuck to deterministic frameworks which are deceptively reassuring, but also too simplistic to approach problems of such a complexity. The deterministic approach has led to several false leads that have affected research in the aetiology in mental illness, especially schizophrenia, and only moving to probabilistic models will allow an understanding of the causal processes. In this paper is challenged the almost universally accepted assumption that, to explain the lack of complete concordance amongst identical twins in schizophrenia, there is the need to resort to environmental aetiological agents. It is described instead how, using a probabilistic framework, a polygenic model without threshold can satisfactorily explain the data available so far without having to resort to environmental factors. The genes predisposing to schizophrenia, probably through a derailment of the neurodevelopment, would have a normal distribution in the general population, while the liability for the illness will increase exponentially with the number of risk genes, with a small minority of the population being at high risk. The average genetic liability to develop schizophrenia in individuals who later are affected by the disorder is around 50%. The adoption of a probabilistic model for the understanding of the inheritance of schizophrenia has therefore far reaching consequences, revolutionizing the interpretation of the twin studies, allowing a consistent model which does not require environmental interventions in the aetiology of schizophrenia and offering a framework to make sense of findings from the epidemiological research which are not satisfactorily explained by the deterministic models adopted so far.

Genetic Predisposition to Disease↗
PubMed1990

The membrane skeleton of erythrocytes. A percolation model.

The spectrin network on the cytoplasmic surface of the erythrocyte membrane is modeled as a triangular lattice of spectrin tetramers. This network obstructs lateral diffusion of proteins and provides mechanical reinforcement to the membrane. These effects are treated in a systematic and unified manner in terms of a percolation model. The diffusion coefficient is obtained as a function of the fraction of normal spectrin tetramers for both static and fluctuating barriers. The elasticity of the network is calculated as a function of the fraction of normal spectrin and the ratio of bending to stretching energies. For static barriers, elasticity and lateral diffusion are incompatible: if a network is connected enough to be elastic, it is connected enough to block long-range lateral diffusion. The elasticity and the force required for mechanical breakdown go to zero at the percolation threshold; experimental evidence suggests the existence of a stability threshold at or near the percolation threshold. The model is qualitatively applicable to other cells with membrane skeletons, such as epithelial cells, in which localization of membrane proteins is essential to differentiation.

Algorithms↗
PubMed1989

The quantitative relationship between nutritional effects on preweaning growth and behavioral development in mice.

Our objective was to establish whether nutritional effects on the behavioral development of preweaning mouse pups were linearly related to effects on body and brain growth or whether there was a threshold effect, with behavior being affected only by nutritional extremes. We also used a standardized scale of development to compare the relative magnitude of such effects on morphological and behavioral measures. The level of nutrient availability was manipulated continuously by rearing the pups in litter sizes ranging from 3 to 12. On Day 32 post-conception, measures were taken of body weight, brain weight, thickness of the cerebellar external granular layer (EGL), and behavioral development. The relationship between litter size and body weight, brain weight, and behavioral development was best described by a linear regression model; no threshold effect was apparent. By comparing measures on animals from different litter sizes at the same age (32 days) to standard developmental curves over a wide range of ages, we found that for every additional pup in a litter, body growth was retarded by the equivalent of 1.28 days, brain weight by 0.44 day, and behavioral development by 0.07 day. Although the variation in nutrient availability provided by this range of litter sizes does result in a linear relationship between growth and behavioral development, there is nevertheless considerable sparing of function.

Animals↗
PubMed2006

A model for predicting feed intake of growing animals during exposure to pathogens.

A general model is proposed for predicting the effects of subclinical pathogen challenges of different doses and virulence on the relative feed intake (RFI) of animals. The RFI is defined as the feed intake (FI, kg/d) of the animal challenged by a pathogen divided by its FI in the same state had it not been challenged. Actual FI can be predicted from the RFI and the animal's state. The RFI was assumed to be affected only when animals were naïve to a particular pathogen (i.e., had not previously experienced it) and when the challenge dose was above a predetermined threshold. The model is for the period from recognition of a pathogen through acquisition and subsequent expression of immunity. The way in which RFI changes with time is described by 5 main parameters and is based on data for RFI during different pathogen challenges of a range of hosts. Lag time (L, d) is the delay from a pathogen challenge until any effects on RFI are seen. Reduction time (R, d) describes the time it takes for the lowest value of RFI (lambda) to be achieved. The duration time (D, d) describes the time that lambda is maintained for, and rho (RFI/d) describes the rate of recovery of RFI until RFI = 1. There is no compensatory intake, and RFI is always < or = 1. The effects of host resistance on the values of the model parameters are proposed. Attempts were made to parameterize the model; when data were scarce, initial parameter values were derived on conceptual grounds. Predictions of the effects of pathogen dose, virulence, and host resistance are described and discussed. When comparing the responses in RFI for different genotypes, it is crucial to define the pathogen challenge (in terms of dose and virulence) and the degree of resistance of different hosts. Possible interactions between dose, virulence, and resistance were explored. Feed intake of healthy and challenged animals, at a time, may be different once the challenged animal has recovered (RFI = 1). The issue of reductions in FI during pathogen challenges is important for nutritionist and animal breeders. The large variation that has been observed for reductions in FI during pathogen challenges may be a viable point of selection. The points highlighted will aid selection strategies by quantifying the effects of pathogen dose and virulence, and time, on the FI of challenged animals. The proposed model may be integrated with other models of growth to predict animal performance during exposure to pathogens.

Animal Diseases↗
PubMed1984

[Effect of nootropic agents on the lowering of the spasm threshold after a single ethanol application].

We used the effect of ethanol on the convulsion threshold as model of injuriousness to analyse the CNS protective efficacy of nootropics. The CD50 of picrotoxine in mice was significantly diminished in comparision with the controls between 5 and 6 hours after 66 mmol/kg ethanol administered intraperitoneally and between 7 and 8 h after 92.4 mmol/kg. In this moment the administered ethanol was already eliminated; the effect is explained as a reversible consequence of the previous ethanol exposition. The influence of nootropics was examined. Piracetam (0.7 mmol/kg i.p.) as well as methylglucaminorotate (MGO) (0.68 mmol/kg-1 i.p.) suppressed the ethanol effect on the convulsibility, pyritinol (0.82 mmol/kg) was ineffective, and meclophenoxate (1.02 mmol/kg) by itself decreased the convulsions threshold.

Animals↗
PubMed2003

Effective size in management and conservation of subdivided populations.

A numerical method for computing the eigenvalue variance effective size of a subdivided population connected by any fixed pattern of migration is described. Using specific examples it is shown that total effective size of a subdivided population can become less than the sum of the subpopulation sizes as a result of directionalities in the pattern of migration. For an extension of the model with threshold harvesting and local deterministic logistic population dynamic we consider the problem of maximizing the total harvesting yield with constraints on the total effective size. For some simple source-sink systems and more complicated population structures where subpopulations differ in their degree of isolation, it is shown to be optimal, for a given total effective size, to raise the harvesting thresholds relatively more in small and in isolated populations. Finally, we show how the method applies to populations which are supplemented, either intentionally or unintentionally. It is shown that the total effective size can be reduced by several orders of magnitude if the captive component of a population is much smaller than the wild component, even with symmetric backward migration.

Animals↗
PubMed2002

De Vries-Weber gain control and dark adaptation in human vision.

Thresholds for seeing light from a stimulus are determined by a mechanism that pairs subliminal excitations from both halves of a twin unit. Such excitations stem from a package of k > or = 1 receptor responses. A half-unit contains one red or one green cone and P rods. The receptor's "Weber machine" controls the receptor's gain. Each half of a twin unit contains a "de Vries machine," which controls the half's k number. In the dark the receptor's dark noise events reset its Weber machine and the receptor's relation to its de Vries machine. A pairing product for light perception also represents a direction event. The local time signs of the two subliminal excitations are crucial for the polarity, size, and pace of the direction event. In relation to the time when and the area in which the stimulus is presented, these signs have average latency periods that depend on intensity and average locations that depend on movement. Polarity depends on which of the two subliminal excitations happens to arrive first at the twin's pairing facility. The intra- and inter-twin pairings in a persepton for the perceptions of light, edge and movement and the probability summation of the pairing products of the mutually independent three sets of twins of the retrinet improve intensity discrimination. Cross-pairings of intra-receptor pairings in red and green cones of a trion for yellow improve visual discrimination further. Discrimination of stimuli that exploit the model's entire summation mechanisms and pairing facilities represents "what the perfect human eye sees best." For the model this threshold of modulation in quantum absorption is the ideal limit that is prescribed by statistical physics. The lateral and meta interaction in a twin unit enhance the contrast of an edge and of a temporal transient. The precision of the local time sign of a half's stimulation determines the spatiotemporal hyperfunctions for location and speed. The model's design for the perfect retinal mosaic consists of red twins situated along clockwise and counterclockwise spirals and green twins along circles that are concentric with the fovea. The model's descriptions of discrimination, adaptation, and hyperfunctions agree with experimental data.

Dark Adaptation↗