Modeling plasma processes assumptions

The advantages of using non-compartmental methods for calculating pharmacokinetic parameters, such as systemic clearance (CZg), volume of distribution (Vd(area))/ systemic availability (F) and mean residence time (MRT), are that they can be applied to any route of administration and do not entail the selection of a compartmental pharmacokinetic model. The important assumption made, however, is that the absorption and disposition processes for the drug being studied obey first-order (linear) pharmacokinetic behaviour. The first-order elimination rate constant (and half-life) of the drug can be calculated by regression analysis of the terminal four to six measured plasma... 

A great deal can be learned about the absorption process by applying Eqs. (40) and (41) to plasma concentration versus time data. Since there is no model assumption with regard to the absorption process, the calculated values of At/Vd can often be manipulated to determine the kinetic mechanism that controls absorption. This is best illustrated by an example. 

From the above it can be concluded that in many instances the introduction of an artificial radionuclide into the environment provides us with a natural tracer experiment. Indeed, this is the basis for the application of deterministic compartmental models, based on tracer kinetics, to radioecology (Whicker and Schultz, 1982). This approach is largely based on the assumption that radionuclide movements will exhibit first order kinetics although the existence of naturally-occurring tracees (stable isotopes) at relatively high abundance may result in more complex concentration-dependent kinetics. Furthermore, nutrient analogues may exert even more complex effects on processes such as radioion absorption across root plasma membranes this will become evident later in the chapter. 

Many attempts have been made to quantify SIMS data by using theoretical models of the ionization process. One of the early ones was the local thermal equilibrium model of Andersen and Hinthome [36-38] mentioned in the Introduction. The hypothesis for this model states that the majority of sputtered ions, atoms, molecules, and electrons are in thermal equilibrium with each other and that these equilibrium concentrations can be calculated by using the proper Saha equations. Andersen and Hinthome developed a computer model, C ARISMA, to quantify SIMS data, using these assumptions and the Saha-Eggert ionization equation [39-41]. They reported results within 10% error for most elements with the use of oxygen bombardment on mineralogical samples. Some elements such as zirconium, niobium, and molybdenum, however, were underestimated by factors of 2 to 6. With two internal standards, CARISMA calculated a plasma temperature and electron density to be used in the ionization equation. For similar matrices, temperature and pressure could be entered and the ion intensities quantified without standards. Subsequent research has shown that the temperature and electron densities derived by this method were not realistic and the establishment of a true thermal equilibrium is unlikely under SIMS ion bombardment. With too many failures in other matrices, the method has fallen into disuse. 

The kinetic model (4) developed for analysis of the XPS data is based on a system in which the modification of a surface layer of thickness d occurs via both direct and radiative energy transfer processes, while beneath this layer only radiative energy transfer processes are considered to be important. This assumption derives from the fact that the U.V. and vacuum U.V. radiation, emitted from the plasma, is expected to penetrate the... 

The core of the nucleation model proposed in Refs. [362, 363] is an assumption based on the experimental data that epitaxially oriented nucleation sites are formed in the SiC layer of about 10-nm thickness during the bias treatment. These sites are exposed at the SiC surface, while plasma etching of SiC is occurring during both the BEN treatment and the successive diamond growth process. The model of nucleation process is schematically depicted in Figure 11.57 ... 

The one-compartment bolus IV injection model is mathematically the simplest of aU PK models. Drug is delivered directly into the systemic circulation by a rapid injection over a very short period of time. Thus the bolus rV injection offers a near perfect example of an instantaneous absorption process. Representation of the body as a single compartment implies that the distribution process is essentially instantaneous as well. The exact meaning of the assumptions inherent in this model are described in the next section. Model equations are then introduced that allow the prediction of plasma concentrations for drugs with known PK parameters, or the estimation of PK parameters from measured plasma concentrations. Situations in which the one-compartment instantaneous absorption model can be used to reasonably approximate other types of drug delivery are described later in Section 10.7.5. 

The premise of noncompartmental PK analysis is to utilize a universal approach to analyze plasma concentration data without making assumptions about a specific number of model compartments or type of absorption process. This generally involves fitting the measured plasma concentration data to an equation in the form of a sum of multiple exponential terms ... 

The pres it understanding of processes in the interior of stars is the result of combined efforts from many scientific disciplines such as hydrodynamics, plasma physics, nuclear physics, nuclear chemistry and not least astrophysics. To understand what is going on in the inaccessible interior of a star we must make a model of the star which explains the known data mass, diameter, luminosity, surface temperature and surface composition. The development of such a model normally starts with an assumption of how elemental conqx)sition varies with distance from the center. By solving the difierential equations for pressure, mass, tenq>erature, luminosity and nuclear reactions from the surface (where these parameters are known) to the star s center and adjusting the elemental composition model until zero mass and zero luminosity is obtained at the center one arrives at a model for the star s interior. The model developed then allows us to extrapolate the star s evolution backwards and forwards in time with some confidence. Figure 17.4 shows results from such modelling of the sun. 

In the past, although much effort has been expended to predict residual coating stresses by modeling the life expectancy of the TBCs, problems were encountered by the assumption of a continuum theory and the non-consideration of elastic finite elements, nonlinear processes, and the general fractal nature of plasma-sprayed coatings (Heimann, 2008). 

---