Estimation population kinetics

Beal SL, Sheiner LB. Estimating population kinetics. CRC Crit Rev Biomed Eng 1982 8 195-222. 

Metabolism and pharmacokinetic studies have greater relevance when conducted in both sexes of young adult animals of the same species and strain used for other toxicity tests with the test substance. The number of animals used in metabolism and pharmacokinetic studies would be sufficient to reliably estimate population variability. This usually means a separate (but parallel) set of groups of animals in rodent studies. A single set of intravenous and oral dosing results from adult animals, when combined with some in vitro kinetic results, may provide an adequate data set for the design and interpretation of short-term, subchronic and chronic toxicity studies. 

Sheiner, L.B. Beal, S.L. Evaluation of methods for estimating population pharmacokinetic parameters. I. Biexponential model and experimental pharmacokinetic data. J. Pharmaco-kinet. Biopharm. 1981, 9 (5), 635-651. 

This ability is available in many software programs. NONMEM (Iconus, EUicott City, MD) has been widely used to estimate population models arising from both sparse and intensely sampled data. Other programs include WinNonMix (Pharsight Corp., Palo Alto, CA), Kinetica 2000 (Innaphase Corp, Philadelphia, PA), and Pop-Kinetics (SAAM Institute, Seattle, WA). ADAPT II and WinNonlin have focused on PK/PD models and have been combined with Bayesian approaches to estimate population models. 

Nucleation kinetics are often obtained from continuous experiments employing a mixed suspension, mixed product removal (MSMPR) crystallizer and the concepts of the population balances. This technique is also used to obtain crystal growth kinetics. The details of the population balance and its uses will be discussed in Chapter 4 of this volume. A review of methods to estimate nucleation kinetics from batch and continuous experiments can be found in Tavare (1995). 

This likelihood is calculated by weighting the parameter-dependent likelihood for each parameter value by the probability of the system parameters taking on that value. This likelihood is no longer a function of the system parameters but is a function of the population parameters. A likelihood for a several experiments (L(0)) may be calculated as a product of the likelihoods for the individual experiments. The job of the various population kinetic analysis algorithms is to estimate by finding the 6 that maximizes L 6). 

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... 

Bertoldo, A., Sparacino, G., and Cobelli, C. 2004. Population approach improves parameter estimation of kinetic models from dynamic PET data. IEEE Trans. Med. Imag., 23 297-306. 

Several authors have presented methods for the simultaneous estimation of crystal growth and nucleation kinetics from batch crystallizations. In an early study, Bransom and Dunning (1949) derived a crystal population balance to analyse batch CSD for growth and nucleation kinetics. Misra and White (1971), Ness and White (1976) and McNeil etal. (1978) applied the population balance to obtain both nucleation and crystal growth rates from the measurement of crystal size distributions during a batch experiment. In a refinement, Tavare and... 

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]. 

From the electronic populations on the vinylic hydrogens, the acidity of vinylic C—H was estimated to be higher in cyclopropenone than in cyclopropene (0.684 e/ 0.776 e). This agrees with kinetic measurements of the H-D-exchange at n-propyl cyclopropenone23 which showed an acidity of the vinylic C—H even higher than that of the acetylenic C—H in the reference compound propargyl alcohol. 

The interpretation of the stress dependent intensities is that the stress raises the energy of those B—H configurations with their axis along the direction of stress. The H has sufficient thermal energy at 100 K to reorient (Fig. 20b) the different orientations are populated according to their (stress-dependent) Boltzmann factors. Because the H can move at the measurement temperature (100 K) on the time scale of a Raman measurement (a few minutes) Herrero and Stutzmann (1988b) were able to estimate an upper limit for the barrier for H-motion. These authors assumed that the rate limiting step for H motion obeys first order kinetics and obtained Eb < 0.3 eV. 

The Rothamsted Carbon Model (RothC) uses a five pool structure, decomposable plant material (DPM), resistant plant materials (RPM), microbial biomass, humified organic matter, and inert organic matter to assess carbon turnover (Coleman and Jenkinson 1996 Guo et al. 2007). The first four pools decompose by first-order kinetics. The decay rate constants are modified by temperature, soil moisture, and indirectly by clay content. RothC does not include a plant growth sub-module, and therefore NHC inputs must be known, estimated, or calculated by inverse modeling. Skjemstad et al. (2004) tested an approach for populating the different pools based on measured values. 

An analysis is presented in this paper of the influence exerted on polymerisation kinetics by the complexing of carbocations with monomers. This had been brewing in the author s mind for a long time and had been mentioned in earlier works, and most other workers were aware of it to some extent. Curiously, few if any others had drawn the electrochemical conclusion that such a process would make meaningless the estimates of the population of paired cations in the reaction mixtures, because of the increase in the size of the cations resulting from such an association. 

Tavare and Garside ( ) developed a method to employ the time evolution of the CSD in a seeded isothermal batch crystallizer to estimate both growth and nucleation kinetics. In this method, a distinction is made between the seed (S) crystals and those which have nucleated (N crystals). The moment transformation of the population balance model is used to represent the N crystals. A supersaturation balance is written in terms of both the N and S crystals. Experimental size distribution data is used along with a parameter estimation technique to obtain the kinetic constants. The parameter estimation involves a Laplace transform of the experimentally determined size distribution data followed a linear least square analysis. Depending on the form of the nucleation equation employed four, six or eight parameters will be estimated. A nonlinear method of parameter estimation employing desupersaturation curve data has been developed by Witkowki et al (S5). 

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