A study of prey-predator relations for mammals

In this paper, we present a prey-predator nonlinear model for mammals, consisting of large- and small-size prey species with group defence, in a partially protected habitat. If the prey size is small, then it is more prone to the predator at higher densities. Conversely, large prey size at higher densities tend to develop group defence. Therefore, the predator will be attracted towards that area where prey are less in number. A new physical constant has been introduced into the radiation-type condition on that part of the boundary where interaction between prey and predator takes place. This constant allows us to efficiently model group defence capabilities of the herds and its numerical values have to be determined for different pairs of prey-predator species from field observations. A way of measuring the constants involved in the model is suggested. Numerical results are provided and thoroughly discussed for a habitat of circular shape. The obtained results show that in the region away from the protected area, the density of large-size prey species is higher than that of small-size prey species, a fact that is in accordance with observations.     

An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect

We consider a single-species model of population dynamics allowing for migrations and the Allee effect. Two types of migration are taken into account: one caused by environmental factors (e.g., a passive transport with the wind or water current) and the other associated with biological mechanisms. While the first type is apparently density-independent, the speed of migration in the second one can depend on the population density. Mathematically, this model consists of a non-linear partial differential equation of advection-diffusion-reaction type. Using an appropriate change of variables, we obtain an exact solution of the equation describing propagation of travelling population fronts. We show that, depending on parameter values and thus on the relative intensity of density-dependent and density-independent factors, the direction of the propagation can be different thus describing either species invasion or species retreat.     

Effect of channel geometry on the electrostatic potential in acetylcholine channels

We study the effect of channel geometry on the potential barrier encountered by ions as they permeate the acetylcholine receptor channel. Among the various channel geometries which have been used to represent the acetylcholine receptor channel include the cylinder and the toroidal catenary. The main reasons for those choices appear to be the facilitation of separation of the Poisson equation, rather than biological considerations. We consider a novel and realistic acetylcholine channel geometry, and calculate the electrostatic potential profiles within it, and compare our results with results from other channel geometries.     

A mathematical model of quorum sensing in a growing bacterial biofilm

In a process called quorum sensing, bacteria monitor their population density via extracellular signaling molecules and modulate gene expression accordingly. This paper describes a one-dimensional model of a growing Pseudomonas aeruginosa biofilm. Quorum sensing has been included in the model by the addition of equations describing the production, degradation, and diffusion of acyl-homoserine lactones in the biofilm. In order for quorum sensing to initiate near the substratum, in accordance with experimental observations, model results suggest that cells in oxygen-deficient regions of the biofilm must still be synthesizing the signal compound. This result highlights the importance of careful study of the relationship between metabolic activity of the bacterium and signal synthesis. Received 11 March 2002/ Accepted in revised form 01 August 2002     

Methods and method evaluation for mycotoxins

Mycotoxins are metabolites of molds frequently found on and in agricultural commodities, food and feeds. Owing to their demonstrated acute, sub-acute and, in some cases, chronic toxicity, an effort has been made, worldwide, to control human and animal exposure to these toxic chemicals. This effort depends upon the availability of validated analytical methods for their detection and quantitation. This paper outlines the methodology available, and the procedures used to validate, i.e. evaluate, these methods based on the use of interlaboratory collaborative studies and the application of the HORRAT.     

A two-stage model for multiple time series data of counts

We propose a two-stage model for time series data of counts from multiple locations. This method fits first-stage model(s) using the technique of iteratively weighted filtered least squares (IWFLS) to obtain location-specific intercepts and slopes, with possible lagged effects via polynomial distributed lag modeling. These slopes and/or intercepts are then taken to a second-stage mixed-effects meta-regression model in order to stabilize results from various locations. The representation of the models from the stages into a combined mixed-effects model, issues of inference and choices of the parameters in modeling the lag structure are discussed. We illustrate this proposed model via detailed analysis on the effect of air pollution on school absenteeism based on data from the Southern California Children's Health Study.     

A semiparametric model for the analysis of recurrent-event panel data

In many longitudinal studies, interest focuses on the occurrence rate of some phenomenon for the subjects in the study. When the phenomenon is nonterminating and possibly recurring, the result is a recurrent-event data set. Examples include epileptic seizures and recurrent cancers. When the recurring event is detectable only by an expensive or invasive examination, only the number of events occurring between follow-up times may be available. This article presents a semiparametric model for such data, based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function. A random subject-specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data. Estimators are determined from quasi-likelihood estimating functions. Because only first- and second-moment assumptions are required for quasi-likelihood, the method is more robust than those based on the specification of a full parametric likelihood. Consistency of the estimators depends only on the assumption of the proportional intensity model. The semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators. As with semiparametric methods in survival analysis, the method provides useful diagnostics for specific parametric models, including a quasi-score statistic for testing specific baseline intensity functions. The techniques are used to analyze cancer recurrences and a pheromone-based mating disruption experiment in moths. A simulation study confirms that, for many practical situations, the estimators possess appropriate small-sample characteristics.     

Muscle contraction: energy rate equations in relation to efficiency and step-size distance

We derive the energy rate equation for muscle contraction. Our equation has only two parameters m, the maintenance heat rate and 1/S, the shortening heat coefficient. The impulsive model (previously described in earlier papers) provides a physical basis for parameter 1/S as well as for constants a and b in Hill’s force–velocity equation. We develop new theory and relate the efficiency and the step-size distance to our energy rate equation. Correlation between the efficiency and the step-size distance is established. The various numbers are listed in Table 1: we use data from five different muscles in the literature. In summary, our analysis strongly supports the impulsive model as the correct model of contraction.     

Local heating of human skin by millimeter waves: a kinetics study

Heating rates of human skin exposed locally to 42.25 GHz mm waves, coming from a waveguide (WG) opening or a YAV device designed for therapeutic application, were studied in vivo using infrared (IR) thermography. For both radiators, the power density distribution was described by a circularly symmetrical Gaussian type function on the exposed skin surface. Insertion of a small thermocouple (d = 0.1 mm) in the exposed area did not produce any significant artifact, either in the power density distribution or kinetics measurement, providing it was perpendicular to the E vector. The heating kinetics in the skin exposed with either the WG opening or the YAV device were well fitted to solutions of the 2-D bio-heat transfer equation for homogeneous tissue. Changes in irradiating beam size (1-8 mm) had no detectable effect on the initial (0.3-3.0 s) phase of the heating kinetics. However, the amplitude of the kinetics decreased substantially with decreasing the beam size. As the temperature rise in the time interval necessary for reliable measurement of the initial temperature rise rate was very small, an accurate experimental determination of specific absorption rate (SAR) becomes practically impossible at the low intensities normally used in our experiments. The correct SAR values may be found from fitting of the model to the heating kinetics. Bioelectromagnetics 24:571-581, 2003.