Models eliminating parameters from

In the following section, the calculation of the VolSurf parameters from GRID interaction energies will be explained and the physico-chemical relevance of these novel descriptors demonstrated by correlation with measured absorption/ distribution/metabolism/elimination (ADME) properties. The applications will be shown by correlating 3D molecular structures with Caco-2 cell permeabilities, thermodynamic solubilities and metabolic stabilities. Special emphasis will be placed on interpretation of the models by multivariate statistics, because a rational design to improve molecular properties is critically dependent on an understanding of how molecular features influence physico-chemical and ADME properties. 

The structural submodel describes the central tendency of the time course of the antibody concentrations as a function of the estimated typical pharmacokinetic parameters and independent variables such as the dosing regimen and time. As described in Section 3.9.3, mAbs exhibit several parallel elimination pathways. A population structural submodel to mechanistically cover these aspects is depicted schematically in Fig. 3.14. The principal element in this more sophisticated model is the incorporation of a second elimination pathway as a nonlinear process (Michaelis-Menten kinetics) into the structural model with the additional parameters Vmax, the maximum elimination rate, and km, the concentration at which the elimination rate is 50% of the maximum value. The addition of this second nonlinear elimination process from the peripheral compartment to the linear clearance process usually significantly improves the fit of the model to the data. Total clearance is the sum of both clearance parts. The dependence of total clearance on mAb concentrations is illustrated in Fig. 3.15, using population estimates of the linear (CLl) and nonlinear clearance (CLnl) components. At low concentra-... 

In order to estimate the model parameters from the data equation, we also need to specify the rate of drug elimination from the central compartment (Vi). The rate of elimination from this compartment, dE/dt, is given by the equation... 

Pharmacokinetic models to describe, as a function of formaldehyde air concentration, the rate of formation of formaldehyde-induced DNA-protein cross links in different regions of the nasal cavity have been developed for rats and monkeys (Casanova et al. 1991 Heck and Casanova 1994). Rates of formation of DNA-protein cross links have been used as a dose surrogate for formaldehyde tissue concentrations in extrapolating exposure-response relationships for nasal tumors in rats to estimate cancer risks for humans (EPA 1991a see Section 2. 4.3). The models assume that rates of cross link formation are proportional to tissue concentration of formaldehyde and include saturable and nonsaturable elimination pathways, and that regional and species differences in cross link formation are primarily dependent on anatomical parameters (e g., minute volume and quantity of nasal mucosa) rather than biochemical parameters. The models were developed with data from studies in which... 

Maitre et al. (15) proposed an improvement on the traditional approach. The approach consists of using individual Bayesian posthoc PK or PK/PD parameters from a population modeling software such as NONMEM and plotting these parameter estimates against covariates to look for any possible model parameter covariate relationship. The individual model parameter estimates are obtained using a base model—a model without covariates. The covariates are in turn tested to determine individual significant covariate predictors, which are in turn used to form a full model. The final irreducible model is obtained by backward elimination. The drawback for this approach is the same as that for the traditional approach. 

One of the most common transformations is the natural logarithmic transformation of multiplicative models. Many pharmacokinetic parameters, such as area under the curve (AUC) and maximal concentration, are log-normal in distribution (Lacey et al., 1997), and hence, using the Ln-transformation results in approximate normality. The rationale is as follows (Westlake, 1988). For a drug that has linear kinetics and elimination occurs from the central compartment (the usual assumptions for a noncompartmental analysis) then... 

Standard linear regression and method of residual analyses of two-compartment IV infusion (zero-order absorption) data is limited to samples collected during the postinfusion period. Plasma concentrations during the infusion period do not lend themselves to a linear analysis for a two-compartment model. Estimation of parameters from measured postinfusion plasma samples is quite similar to the two-compartment bolus IV (instantaneous absorption) case. Proper parameter evaluation ideally requires at least three to five plasma samples be collected during the distribution phase, and five to seven samples be collected during the elimination phase. Area under the curve (AUC) calculations can also be used in evaluating some of the model parameters. 

Quite interestingly, it was shown in the more recent study [108] that a subset of 34 compounds whose biological data had been obtained with racemic mixtures led to very poor models when treated on its own. Consistently, the statistical parameters of models for the total data set were also improved when such racemates were eliminated from the data set, i.e. not considered in the model building process. 

III. PCA was applied to eliminate some parameters from the model fitted through approach II. In consequence, it was assumed that the sites are in quasi-steady state and that AC, EC, MCC and CE are in adsorption equilibrium. It was also assumed that kinetic constants for reactions 4 and 8, and 1 and 2 are not independent and are related through a linear relation. 

The structural information contained in the ARRs, i.e. the information on which ARR depends on which component parameters can be obtained directly by inspection of causal paths in a diagnostic bond graph [1]. There is no need to derive equations and to eliminate unknowns in order to set up a mode-dependent FSM. To that end, causal paths from model inputs to inputs of sensor elements are considered. Elements that are traversed on these causal paths contribute to the ARR of a residual related to a sensor element. An output of a source or an element that is followed directly or indirectly by switches on the causal path to a sensor element provides an entry in the FSM equal to the product of the switch states. 

The mechanistic model (of Table II of the previous chapter) was developed by successive approximations. First, only those reactions assumed to be most important were used in the model, and later secondary reaction steps were added until good predictions were obtained of the experimental results. In the previous chapter of the book, the parameters for the various reaction steps are reported. The major reactions for pyrolyses of both ethane and propane are grouped in Table II (1). When ethane is pyrolyzed, the propane reactions are. pf relatively minor importance and eliminating them from the model has little effect on the ethane pyrolysis predictions. When propane is pyrolyzed, however, significantly better predictions result when the ethane reactions are included and the entire set of reactions are employed. 

Ruckenstein and Huber [6] worked out a different model by trying to eliminate the shielding parameter and the problems associated with it. They introduced a global interaction parameter, Amicelle surface tension and was claimed to be an experimentally determinable parameter from hydrocarbon-polymer solution surface tension measurements. The use of macroscopic parameters such as the surface tension to describe local molecular interactions between the micelle core and its environment has been criticised recently [7]. Furthermore, the surface tension depends on the polymer concentration therefore, it is not determined unambiguously at which composition the surface tension should be measured. 

Figure 3 displays both models for the albedo-temperature relation. Any such o(T) destroys the linearity in (1). One way to proceed is to eliminate Tj from (1) and rearrange in the form a2(T2> = L(T2,...), in which the right hand side is linear in T2 and depends on the parameters in the problem. Intersections between the L lines and the 02 curve determine solutions for T2. Figure 3 shows that for fixed parameters there can be one or three solutions. The single solution is always stable. Of the three solutions, the middle one is always unstable and therefore will not be found in nature. 

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