Model population kinetics

Pharmacokinetic/pharmacodynamic model using nonlinear, mixed-effects model in two compartment, best described time course of concentration strong correlation with creatinine clearance predicted concentration at the efi ect site and in reduction of heart rate during atrial fibrillation using population kinetic approach... 

Parametric uncertainty A great number of bacterial species carry out the transformations of organic load and nutrients in wastewater treatment processes without direct or easily comprehensible relationships between the microbial populations and viability. The role of each bacterial species is fuzzy [30], and aspects such as cellular physiology and its modeling are not easily understood from external measurements [18], [68]. As a first consequence, the kinetics of these transformations is often poorly or inadequately known [66]. Extensive efforts to model the kinetics have been undertaken, but these have not been successful to elucidate how yield coefficients, kinetic parameters and the bacterial population distribution change as a function of both, the influent composition and the operating conditions. 

We can also use chemical kinetics to attempt to model populations of living systems such as single-celled organisms or plant, animal, and human populations. We describe the density of individuals (species A) as Ca, which might be in individualsA olume in a three-dimensional... 

Comparative Toxicokinetics. A limited number of studies exist regarding the comparative toxicokinetics of orally administered silver compounds in rats, dogs, monkeys, and humans. A more complete comparison of the absorption and elimination of silver in humans and rats may be warranted given that much of the toxicokinetic data comes from rats. It would also be useful to acquire data on the comparative toxicokinetics of various silver compounds in several species of experimental animals and in humans following inhalation and dermal exposure in order to model the kinetics of silver deposition across different exposure scenarios and within sensitive populations. 

State selective dielectronic recombination rate coefficients from Li-like ions to Be-like ions (C, O, Ne, Fe ions) and for carbon L-shell ions have been calculated [10-13]. These data are used to develop collisional-radiative models including dielectronic recombination to excited states [14-17]. The population kinetics of L-shell ions and atoms have been developed and their results have been applied to plasma diagnostics. 

Min and Ray (1978) have compared the predictions of the population balance model wiA the experimental results obtained by Gerrens (1959) on poly(methyl methacrylate) latexes. The correspondence between theory and experiment is qualitatively acceptable, and the same kinetic parameters model the kinetic behavior of the polymerization process (see Fig. 5). Again, the PSD was measured at the conclusion of the polymerization reaction, raising once more the problem of cancelling errors in the theory. Min and Ray (1978) used literature values for all but two of the rate coefficients... 

The mathematical modeling of polymerization reactions can be classified into three levels microscale, mesoscale, and macroscale. In microscale modeling, polymerization kinetics and mechanisms are modeled on a molecular scale. The microscale model is represented by component population balances or rate equations and molecular weight moment equations. In mesoscale modeling, interfacial mass and heat transfer... 

Unfortunately, there has been minimal work on identifiability issues with respect to population kinetic analysis. The current work on identifiability of kinetic models (Jacquez, 1985 belli and DiStefano, 1980 Cobelli and Saccomani, 1990) focuses on estimation for an individual experiment. With regard to population analysis and Bayesian estimation of parameters for an individual from the population, it is the population analysis step for which identifiability issues need to be considered. Once a prior distribution... 

The rationale of cancer chemotherapy is based on ceU growth, differentiation, and apoptotic mechanisms of the cell. Carcinogenesis is actuaUy a multistep process that occurs within years. This is because the human cell has many defense mechanisms for protecting DNA. The number of ceUs in an individual is controlled by ceU division and apoptotic systems. DNA mutations that affect the genes that control either cell cycle (cell division) or apoptosis result in an excessive number of mutated cells and that is cancer. Nowadays, there are a few cancer cell population kinetics hypotheses (i.e., Norton-Simon, Gompertzian model) and... 

S Kinetic Emission Model The Kinetic Emission model proposed by Joyes (.loyes 1963, 1969a, 1969b) was developed to explain the yield trends exhibited by the positive multiply charged atomic ions from elements lighter than Phosphorus. This mechanism describes the formation of multiply charged ions as being formed as a result of the de-excitation of core holes present in the sputtered atomic/ionic populations, i.e. an auto-ionization process. 

Mixed Populations. Considerable literature has evolved on mixed populations kinetics. Virtually every possible biological interaction from the classical prey-predator model of Lotka (35) to various forms of commensalism, synergism, etc. have been modelled. Virtually all models end up exhibiting stable oscillations. Solutions are often expressed in triangular phase plane plots of the limiting substrate and the two species. Invariably the plots have a limit cycle as one of the stable steady state solutions. From this one gains the impression that oscillatory behavior is the norm rather than the exception in biological reactors. 

The A and B coefficients can be used in a kinetic equation model to follow the time evolution of the populations of the corresponding levels ... 

The simplest model of time-dependent behavior of a neutron population in a reactor consists of the point kinetics differential equations, where the space-dependence of neutrons is disregarded. The safety of reactors is greatly enhanced inherently by the existence of delayed neutrons, which come from radioactive decay rather than fission. The differential equations for the neutron population, n, and delayed neutron emitters, are... 

Measuring Protein Sta.bihty, Protein stabihty is usually measured quantitatively as the difference in free energy between the folded and unfolded states of the protein. These states are most commonly measured using spectroscopic techniques, such as circular dichroic spectroscopy, fluorescence (generally tryptophan fluorescence) spectroscopy, nmr spectroscopy, and absorbance spectroscopy (10). For most monomeric proteins, the two-state model of protein folding can be invoked. This model states that under equihbrium conditions, the vast majority of the protein molecules in a solution exist in either the folded (native) or unfolded (denatured) state. Any kinetic intermediates that might exist on the pathway between folded and unfolded states do not accumulate to any significant extent under equihbrium conditions (39). In other words, under any set of solution conditions, at equihbrium the entire population of protein molecules can be accounted for by the mole fraction of denatured protein, and the mole fraction of native protein,, ie. 

Correlations of nucleation rates with crystallizer variables have been developed for a variety of systems. Although the correlations are empirical, a mechanistic hypothesis regarding nucleation can be helpful in selecting operating variables for inclusion in the model. Two examples are (/) the effect of slurry circulation rate on nucleation has been used to develop a correlation for nucleation rate based on the tip speed of the impeller (16) and (2) the scaleup of nucleation kinetics for sodium chloride crystalliza tion provided an analysis of the role of mixing and mixer characteristics in contact nucleation (17). Pubhshed kinetic correlations have been reviewed through about 1979 (18). In a later section on population balances, simple power-law expressions are used to correlate nucleation rate data and describe the effect of nucleation on crystal size distribution. 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

The kinetics of culture media sterilisation describe the rate of destruction of microorganisms by steam using a fust-order chemical reaction rate model. As the population of microorganisms (N) decreases with time, the rate is defined by the following equation ... 

Model Deyelopment. Rachow and Timm (] ) derived working relationships for the kinetic mechanism described. Degree of polymerization is considered to be a continuous variable. For quenched samples a relationship correlating population density of associated polymer molecules as a function of time, degree of polymerization and environmental factors is... 

Figure 2. Kinetic schemes for Na channel gating (right) and the graphed time-course for single channels (solid lines, the higher position is open ) and for the population of many channels (broken line, the fraction open increases upwardly). Numbers at the arrows of the kinetic scheme are the rate constants, in 10 sec" The period of simulation is 5 msec. Computerized model courtesy of Dr. Daniel Chemoff.

The ability to detect discrete rovibronic spectral features attributed to transitions of two distinct conformers of the ground-state Rg XY complexes and to monitor changing populations as the expansion conditions are manipulated offered an opportunity to evaluate the concept of a thermodynamic equilibrium between the conformers within a supersonic expansion. Since continued changes in the relative intensities of the T-shaped and linear features was observed up to at least Z = 41 [41], the populations of the conformers of the He - lCl and He Br2 complexes are not kinetically trapped within a narrow region close to the nozzle orifice. We implemented a simple thermodynamic model that uses the ratios of the peak intensities of the conformer bands with changing temperature in the expansion to obtain experimental estimates of the relative binding energies of these complexes [39, 41]. 

Simkins S, M Alexander (1984) Models for mineralization kinetics with the variables of substrate concentration and population density. Appl Environ Microbiol 47 1299-1306. 

---