Comparison of thiamazole pharmacokinetics in healthy individuals and patients with hyperthyroidism]

Pharmacokinetic parameters of thiamazole in hyperthyroid patients (40 subjects with Graves-Basedow disease--32 female and 8 male patients) and in healthy individuals (8 subjects--5 women and 3 men) were compared. A one-compartment model was used for the analysis of examined pharmacokinetic parameters. Area under thiamazole concentration curve (AUC) and thiamazole peak plasma concentration (cmax) were significantly decreased in hyperthyroid patients in comparison with healthy individuals. An analysis of other pharmacokinetic parameters suggests that observed differences seem to depend upon lowered and retarded thiamazole absorption from the gut and acceleration of drug metabolism in hepatic microsomal system in hyperthyroid patients.     

Modeling the growth of individuals in crowded plant populations

Aims We present an improved model for the growth of individuals in plant populations experiencing competition.Methods Individuals grow sigmoidally according to the Birch model, which is similar to the more commonly used Richards model, but has the advantage that initial plant growth is always exponential. The individual plant growth models are coupled so that there is a maximum total biomass for the population. The effects of size-asymmetric competition are modeled with a parameter that reflects the size advantage that larger individual have over smaller individuals. We fit the model to data on individual growth in crowded populations of Chenopodium album .Important findings When individual plant growth curves were not coupled, there was a negative or no correlation between initial growth rate and final size, suggesting that competitive interactions were more important in determining final plant size than were plants' initial growth rates. The coupled growth equations fit the data better than individual, uncoupled growth models, even though the number of estimated parameters in the coupled competitive growth model was far fewer, indicating the importance of modeling competition and the degree of size-asymmetric growth explicitly. A quantitative understanding of stand development in terms of the growth of individuals, as altered by competition, is within reach.     

From individual behavior to metapopulation dynamics: unifying the patchy population and classic metapopulation models

Spatially structured populations in patchy habitats show much variation in migration rate, from patchy populations in which individuals move repeatedly among habitat patches to classic metapopulations with infrequent migration among discrete populations. To establish a common framework for population dynamics in patchy habitats, we describe an individual-based model (IBM) involving a diffusion approximation of correlated random walk of individual movements. As an example, we apply the model to the Glanville fritillary butterfly (Melitaea cinxia) inhabiting a highly fragmented landscape. We derive stochastic patch occupancy model (SPOM) approximations for the IBMs assuming pure demographic stochasticity, uncorrelated environmental stochasticity, or completely correlated environmental stochasticity in local dynamics. Using realistic parameter values for the Glanville fritillary, we show that the SPOMs mimic the behavior of the IBMs well. The SPOMs derived from IBMs have parameters that relate directly to the life history and behavior of individuals, which is an advantage for model interpretation and parameter estimation. The modeling approach that we describe here provides a unified framework for patchy populations with much movements among habitat patches and classic metapopulations with infrequent movements.     

Application of the Convection–Dispersion Equation to Modelling Oral Drug Absorption

Models of systemic drug absorption after oral administration are frequently based on a direct or a delayed first-order rate process. In practice, the use of the first-order approach to predict drug concentrations in blood plasma frequently yields a considerable mismatch between predicted and measured concentration profiles. This is particularly true for the upswing of the plasma concentration after oral administration. The current investigation explores an alternative model to describe the absorption rate based on the convection–dispersion equation describing the transport of chemicals through the GI tract. This equation is governed by two parameters, transport velocity and dispersion coefficient. One solution of this equation for a specific set of initial and boundary conditions was used to model absorption of paracetamol in a 22-year-old man after oral administration. The GI-tract passage rate in this subject was influenced by co-administration of drugs that stimulate or delay gastric emptying. The transport-limited absorption function is more accurate in describing the plasma concentration versus time curve after oral administration than the first-order model. Additionally, it provides a mechanistic explanation for the observed curve through the differences in GI-tract passage rate.     

Modelling and estimation of infectious diseases in a population with heterogeneous dynamic immunity

The paper presents a model for the evolution of an infectious disease in a population with individual-specific immunity. The immune state of an individual varies with time according to its own dynamics, depending on whether the individual is infected or not. The model involves a system of size-structured (first-order) PDEs that capture both the dynamics of the immune states and the transition between compartments consisting of infected, susceptible, etc. individuals. Due to the unavailability of precise data about the immune states of the individuals, the main focus in the paper is on developing a technique for set-membership estimations of aggregated quantities of interest. The technique involves solving specific optimization problems for the underlying PDE system and is developed up to a numerical method. Results of numerical simulations are presented for a benchmark model of SIS-type, potentially applicable to diseases like influenza and to various sexually transmitted diseases.     

Exterior exposure estimation using a one-compartment toxicokinetic model with blood sample measurements

Exposure assessment of individuals exposed to certain chemicals plays an important role in the analysis of occupational—as well as environmental-health problems. Biological monitoring, as an alternative to direct environmental measurements, may be applied to relate the exterior exposure with the amount of individual intake. In this paper, we estimate individuals’ (inhalation) exposure retrospectively from their blood concentrations via a simplified one-compartment toxicokinetic model. Considering stochastic variations to the toxicokinetic model, the solution to the resultant stochastic differential equation (SDE), together with measurement error, is transformed into a dynamic linear state-space model. The unknown model parameters and the mean inhalation concentration are then estimated via Markov Chain Monte Carlo (MCMC) simulations. The proposed method is used in the analysis of the styrene data (Wang et al. in Occup Environ Med 53:601–605, 1996) to backward estimate the inhalation concentration, assuming it is unknown. The data analysis showed that the internal stochastic variations, often ignored in toxicokinetic model analysis, outweighed in standard deviation almost twice that of the measurement error. Also, the simulation results showed that the method performed relatively well to the approach considering measurement error only.

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Contract/grant sponsor: National Science Council of Taiwan (NSC 93-2118-M-032-004); National Health Research Institutes of Taiwan (BS-096-PP-11).     

Buoyancy-induced mixing during wash and elution steps in expanded bed adsorption

Buoyancy-induced mixing occurs during expanded bed adsorption processes when the feed stream entering the bottom of the system has a lower density than that of the fluid above it. In the absence of a headspace, mixing in the expanded bed can be modeled as a single, well-mixed vessel, with first-order dynamics. In the presence of a headspace, the system exhibits second-order dynamics for the densities typically encountered in protein chromatography, and can be modeled as two well-mixed vessels (the expanded bed and the headspace) arranged in series. In this paper, the mixing dynamics of the expanded bed are described and a mathematical model of the system is presented. Experimental measurements of density changes during the dilution of sucrose and salt solutions in a STREAMLINE 25 column are presented. These show excellent agreement with predictions using the model. A number of strategies for wash and elution in expanded mode, both in the presence and absence of headspace, are discussed.     

Synchronization in a model of two inferior olive cells with variable electrotonic coupling

Synchronization was assessed in a model describing the dynamics of two inferior olive cells coupled electrotonically via gap junctions and surrounded with inhibitory synaptic terminals (modeled from first-order kinetics) that can block this coupling. Depending on the parameters, the system gives rise to various synchronization regimes: 1:1, 1:2, spike “time binding” etc. Even small changes of coupling parameters (coupling strength and decoupling delay) can quite significantly affect the regimes of synchronization between interacting neurons. In some cases, because of collective dynamics the activity of one cell is suppressed while the other cell remains active.     

Theoretical and experimental intravascular gas embolism absorption dynamics.

Multifocal cerebrovascular gas embolism occurs frequently during cardiopulmonary bypass and is thought to cause postoperative neurological dysfunction in large numbers of patients. We developed a mathematical model to predict the absorption time of intravascular gas embolism, accounting for the bubble geometry observed in vivo. We modeled bubbles as cylinders with hemispherical end caps and solved the resulting governing gas transport equations numerically. We validated the model using data obtained from video-microscopy measurements of bubbles in the intact cremaster microcirculation of anesthetized male Wistar rats. The theoretical model with the use of in vivo geometry closely predicted actual absorption times for experimental intravascular gas embolisms and was more accurate than a model based on spherical shape. We computed absorption times for cerebrovascular gas embolism assuming a range of bubble geometries, initial volumes, and parameters relevant to brain blood flow. Results of the simulations demonstrated absorption time maxima and minima based on initial geometry, with several configurations taking as much as 50% longer to be absorbed than would a comparable spherical bubble.     

A neural mass model based on single cell dynamics to model pathophysiology

Neural mass models are successful in modeling brain rhythms as observed in macroscopic measurements such as the electroencephalogram (EEG). While the synaptic current is explicitly modeled in current models, the single cell electrophysiology is not taken into account. To allow for investigations of the effects of channel pathologies, channel blockers and ion concentrations on macroscopic activity, we formulate neural mass equations explicitly incorporating the single cell dynamics by using a bottom-up approach. The mean and variance of the firing rate and synaptic input distributions are modeled. The firing rate curve (F(I)-curve) is used as link between the single cell and macroscopic dynamics. We show that this model accurately reproduces the behavior of two populations of synaptically connected Hodgkin-Huxley neurons, also in non-steady state.     

Deep learning and differential equations for modeling changes in individual-level latent dynamics between observation periods

When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction and differential equations for dynamic modeling of individual-level trajectories. However, such approaches so far assume that parameters of individual-level dynamics are constant throughout the observation period. Motivated by an application from psychological resilience research, we propose an extension where different sets of differential equation parameters are allowed for observation subperiods. Still, estimation for intra-individual subperiods is coupled for being able to fit the model also with a relatively small dataset. We subsequently derive prediction targets from individual dynamic models of resilience in the application. These serve as outcomes for predicting resilience from characteristics of individuals, measured at baseline and a follow-up time point, and selecting a small set of important predictors. Our approach is seen to successfully identify individual-level parameters of dynamic models that allow to stably select predictors, that is, resilience factors. Furthermore, we can identify those characteristics of individuals that are the most promising for updates at follow-up, which might inform future study design. This underlines the usefulness of our proposed deep dynamic modeling approach with changes in parameters between observation subperiods.     

Bayesian Analysis of Growth Curves Using Mixed Models Defined by Stochastic Differential Equations

Summary Growth curve data consist of repeated measurements of a continuous growth process over time in a population of individuals. These data are classically analyzed by nonlinear mixed models. However, the standard growth functions used in this context prescribe monotone increasing growth and can fail to model unexpected changes in growth rates. We propose to model these variations using stochastic differential equations (SDEs) that are deduced from the standard deterministic growth function by adding random variations to the growth dynamics. A Bayesian inference of the parameters of these SDE mixed models is developed. In the case when the SDE has an explicit solution, we describe an easily implemented Gibbs algorithm. When the conditional distribution of the diffusion process has no explicit form, we propose to approximate it using the Euler–Maruyama scheme. Finally, we suggest validating the SDE approach via criteria based on the predictive posterior distribution. We illustrate the efficiency of our method using the Gompertz function to model data on chicken growth, the modeling being improved by the SDE approach.     

Methods for analyzing panel studies of acute health effects of air pollution

New methods are presented for analyzing repeated binary health measurements of individuals exposed to varying levels of air pollution. The methods involve a separate logistic regression of response against environmental covariates for each individual. Parameters reflecting individual susceptibility to pollutants and weather are estimated using Cox's regression techniques (1970, 1972a). The individual parameters are combined to yield summary estimates of environmental effects. The approach does not require independence of successive health measurements. It is illustrated with data on asthma and air pollution in the Los Angeles area.     

Algal Population Growth Model Integrated with Toxicokinetics for Ecological Risk Assessment under Time-Varying Pesticide Exposure

An algal population growth model integrated with toxicokinetics was developed for assessing the effect of pesticides on population dynamics. This model is a simple one-compartment, first-order kinetic model in which toxicity (growth inhibition and mortality) depends on the intracellular effective concentration of a pesticide at a target site. The model's parameters were derived using an experimental study that investigated the effects of pretilachlor, bensulfuron-methyl, pentoxazone, and quinoclamine on the growth, mortality, and subsequent population recovery of the green alga Pseudokirchneriella subcapitata. Modeled and measured trajectories of algal population dynamics agreed well. The effect on population recovery was underestimated by the model that ignored the toxicokinetics. The four tested herbicides had a variety of toxicity characteristics and physicochemical properties, indicating the wide range of the model's applicability. Moreover, the developed model and the obtained model's parameters were extrapolated to predict long-term algal population dynamics under time-varying herbicide exposure. The calculated integral biomass lost compared with the control was considered a quantitative index of the population-level ecological risk. The model's prediction showed that the same exposure level (peak concentration is equivalent to EC50) indicated much different population-level effect depending on the herbicide.     

A calculator program for clinical application of the Bayesian method of predicting plasma drug levels

A pharmacokinetic program that allows individualization of drug dosage regimens through the Bayesian method is described. The program, which is designed for the Hewlett-Packard HP-41 CV calculator, is based upon the one-compartment open model with either instantaneous or zero-order absorption. Individualized estimation of the patient's kinetic parameters (clearance and volume of distribution) is performed by analyzing the plasma levels measured in the patient as well as considering the population data of the drug. After estimating the individual kinetic parameters by the Bayesian method, the program predicts the dosage regimen that will elicit the desired peak and trough plasma levels at steady state. For comparison purposes, the least-squares estimates for clearance and volume of distribution are calculated, and dosage prediction can also be made on the basis of the least-squares estimates. The least-squares estimates can be used to calculate population pharmacokinetic parameters according to the Standard Two-Stage method. Several examples of clinical use of the program are presented. The examples refer to patients with classic hemophilia who were treated with Factor VIII concentrates. In these patients, the Bayesian kinetic parameters of Factor VIII have been estimated through the calculator program. The Bayesian parameter estimates generated by the HP-41 have been compared with those determined by a Bayesian program (ADVISE) designed for microcomputers.     

Analysis and simulation of a stochastic, discrete-individual model of STD transmission with partnership concurrency

Deterministic differential equation models indicate that partnership concurrency and non-homogeneous mixing patterns play an important role in the spread of sexually transmitted infections. Stochastic discrete-individual simulation studies arrive at similar conclusions, but from a very different modeling perspective. This paper presents a stochastic discrete-individual infection model that helps to unify these two approaches to infection modeling. The model allows for both partnership concurrency, as well as the infection, recovery, and reinfection of an individual from repeated contact with a partner, as occurs with many mucosal infections. The simplest form of the model is a network-valued Markov chain, where the network's nodes are individuals and arcs represent partnerships. Connections between the differential equation and discrete-individual approaches are constructed with large-population limits that approximate endemic levels and equilibrium probability distributions that describe partnership concurrency. A more general form of the discrete-individual model that allows for semi-Markovian dynamics and heterogeneous contact patterns is implemented in simulation software. Analytical and simulation results indicate that the basic reproduction number R(0) increases when reinfection is possible, and the epidemic rate of rise and endemic levels are not related by 1-1/R(0), when partnerships are not point-time processes.