Identifiability population kinetics

C. Population Kinetic Analysis Identifiability Issues Conclusions... 

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... 

Although these two rate components can be identified in all nerves examined to date, the rates and the precise compositions varies among nerve populations. For example, SCa and SCb are readily resolved as discrete waves moving down optic axons, but differences in rate are smaller in the motor axons of sciatic nerve so the two peaks overlap. Moreover, virtually all tubulin moves as a single peak in SCa in optic axons, but significant amounts of tubulin move at both SCa and SCb rates in sciatic motor axons [32]. In each nerve, certain polypeptides may be used to define the kinetics for a given slow component of axonal transport. For SCa, those signature polypeptides are the NF triplet proteins, while actin, clathrin and calmodulin serve a similar role for SCb. 

All distribution curves are bimodal with maxima at P = 60 and 400. At lower temperatures longer chains are formed. Since there is no gradual shift of the maximum with temperature it must be assumed that the chain grows by at least two different active chain ends, the population of which is strongly temperature dependent. The chemical nature of these chain ends cannot be deduced by the kinetic data. However, it seems reasonable to infer that we are dealing with the same carbene and radical intermediates which have been identified in the photopolymerization of diacetylenes at low temperatures by Sixl and coworkers... 

Mechanism and Kinetics. The most detailed study of the reaction mechanism has been made by Wachs and Madix. They used isotopic tracers and flash desorption to study the species produced when methanol is adsorbed on an oxygen-doped copper (110) single-crystal surface. While the results of such a study are of considerable interest, they are not necessarily representative of a copper catalyst continuously exposed to reaction conditions. From the desorption spectra, methanol shows exchange only of the hydroxy-hydrogen surface methoxide was identified as the most populous surface intermediate. As formaldehyde and hydrogen also appeared to be produced from the same intermediate, the mechanism (21)—(24) was proposed for the selective reaction ... 

The early kinetic model by Smith and Ewart was based on Harkin s mechanistic understanding of the batch process. The particle population balances were written for a stationary state assuming that the rate of formation of particles with n radicals equals the rate of their disappearance (see equation at the bottom of this page). Where / , is the rate of radical entry into a particle (m /sec) is the rate constant for radical exit (m/sec) S is the particle surface area (m ) ktp is the rate constant for bimolecular termination in the particles (m /sec) and o is the particle volume. According to Smith and Ewart three limiting cases can be identified ... 

Prior to initiating a population pharmacokinetic analysis, an accurate representahon of the underlying pharmacokinehcs, the so-called structural model, must be made. Kinetic phenomena can be described by differenhal equations or via implicit or explicit integrated forms, typically with time as the independent variable. As with the eshmahon of any model, we are concerned with identifying the best values for parameters 9i, 02,..., O, of a model by minimizing or maximizing some objective function. For example, some function y that is expressed in terms of several 0 terms and an independent variable X, such as... 

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