Structural Submodel

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- 

Mechanistically, the linear clearance pathway represents most probably the slow and nonspecific proteolytic degradation of mAbs in hepatic endothelial and reticu- 

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Various methods are available to estimate population parameters, but today the nonlinear mixed effects modeling approach is the most common one employed. Population analyses have been performed for mAbs such as basiliximab, daclizu-mab and trastuzumab, as well as several others in development, including clenolixi-mab and sibrotuzumab. Population pharmacokinetic models comprise three submodels the structural the statistical and covariate submodels (Fig. 3.13). Their development and impact for mAbs will be discussed in the following section. 

Robust models of ship NPU reactors use a cylinder model for geometric representation of reactor cores with different nuclear-physical properties. The heterogeneous structure of RC layers is considered using submodels of a reactor cell (fuel, cladding, moderator, control rods (CR)) and microcells (the bumup absorber (BA) of neutrons). 

A simple, quantitative, steady-state diffusion model (36) demonstrates the importance of physical processes in shaping the vertical distribution of phytoplankton. This model uses values of the eddy diffusion coefficient K from the theoretical model of James (35), which reproduces accurately the annual cycle of vertical temperature structure for this area of the Celtic Sea. The submodels for photosynthetic production, light, and grazing can be varied to any of the established models nutrient luxury or nutrient limitation of growth can be included. The model reproduces the main features of the UOR observations in the Celtic Sea and English Channel. 

It is conceivable that quantitative structure-activity (QSAR) approaches (e.g., TOPKAT see Chapter 7) could be applied to predict response levels for uncharacterized contaminants for use in the HI approach. Further, specific submodels existing (e.g., that for developmental toxicity) could be applied to estimate system-specific response levels for application in the IT D approach. To our knowledge, there are no computer-assisted programs available that can automate the prediction of toxicity for mixtures. Much of the reason may reside in the relative lack of empirical observations and characterizations of chemical interactions. Many QSAR approaches rely on training set approaches to the development of automated programs. Another impediment may be the many examples of the levels, types and biochemical bases for chemical interactions, the intricacies of which would benefit from an automated approach. This area is a useful area for exploration. 

Figure 2.36 displays the structure of the four submodels of the C EDM as well as their interdependencies on a coarse-grained level. As indicated in the figure, each submodel can be split into a domain-independent and a domain-specific part. Since the individual parts are represented as OWL ontologies, inclusion relations can be established between them by means of the OWL... 

In this subsection, we relate the different submodels used for the definition and realization of integrators to the overall structure of the layered process/product model., as sketched in Fig. 6.1. 

In this section, we mainly focus on process-related modeling and therefore we highlight the partial model Process Models (cf. Chap. 2). This submodel defines several modeling concepts to express important structures for work processes like activity class, input and output information, tool, goal and their relationships. For example, the Simulation reactor activity creates the information Reactor simulation result. This information is defined in the partial model Document model, which contains the information-related modeling concepts. The resource-related modeling concepts can be found in the CLiP partial model Actor model. 

The chapter is structured as follows. The first section reviews descriptions of organic phosphorus components in biogeochemical models of aquatic systems. This is followed by a review of frequently used model formulations for important processes affecting organic phosphorus in lakes, rivers, sediments, marine systems and sewage treatment plants. The next section contains a brief review of how to embed organic phosphorus submodels into biogeochemical models of aquatic systems. Then we analyse which processes have been con-... 

First of all are determined physicochemical processes enabling the solution of the set problem and are selected those laws of thermodynamics and kinetics or known empiric correlations, which formalize them and set sought for final data in correlation with available initial data in the studied system. Chemical processes in the geological medium are mutually associated by strict restrictions of charge neutrality, mass and energy conservation. Structurization of models in these conditions boils down to identification of cause and effect associations between various physicochemical processes and in the selection or derivation of equations describing them. Such structurization is intended for the creation of a system of interrelated equations, which characterize the physicochemical state of groimd water and may be considered as an independent physicochemical submodel. 

Among the outside factors the main role belongs to geological ones. They include the composition, properties and mutual position of deposits and rocks, their hydrogeological stratification. They affect ground water hydrodynamics but practically do not depend on it. In connection with this the geologic structure and properties of the host rocks may be considered an independent stationary submodel of the geologic structure... 

The geological submodel is a structural one as it determines spatial position of boundaries most important for modeling. They separate deposits and rock from each other, from the atmosphere, surface water. Such boxmdaries have rigid space coordinates and actually do not change their position in time. Parameters of this submodel characterize the composition of host deposits and rocks, porosity and permeability properties. A geological submodel may be constructed in coordinates x, y and 2 and graphically imaged in the forms of maps and vertical cross-sections. 

In the final analysis in the structure of most hydrogeochemical models are identified the following groups of mutually associated parameters, which form three submodels, inserted into one another as in Russian nesting dolls ... 

The content and interrelation of the above submodels determine the structure of the hydrogeochemical model as a whole the first one determines the substance of the hydrogeochemical model, the second and third, its conditions. At that, the hydro-geodynamical submodel characterizes variable conditions associated with ground water flow, the geological submodel characterizes unchangeable conditions in the forecast area. The content and interrelation of two former submodels determine the type of hydrogeochemical model as a whole. 

The geological submodel includes additional parameters, which do not change with time and characterize the structure, properties and composition of the geological medium, namely ... 

The hydro-geodynamic submodel requires additional initial data characterizing structure and properties of the flow streams, namely ... 

The use of k =6 is clearly applicable only to OPs and AChE as the response variable of Interest. For nonchollnergic effects, another dose-response submodel must be considered. The purpose of k was to suggest the utilization of a dermal absorption coefficient t project a measured topical dermal dose into an Internal dose which could be compared to the internal doses associated with other dose-response studies such as chronic feeding studies. K values have been derived from radioactive tracer studies (31) although these seem to have limited application to field conditions, and do not necessarily relate to the chemical structure of either the... 

The principles of metaboHc modeling can be consequently applied also for photobioprocesses to have a first structured model which has to be amended with specific submodels for photosynthesis and product formation. These principles include thinking on different process levels basically reactor and ceU level and appHcation of chemical reaction principles like balances, stoichiometry, and kinetics. In the following paragraphs this approach wiU be outlined and explained introducing a simple generic example. 

As mentioned before, in the early 1980 s, research activities on jprocess modelling started in the field of processing of thermosets and thermoset matrix composites [59-66]. The final objective of these activities has been the construction of a general processing model that could be adapted to different specific processes. In order to develop such general model several submodels are needed as shown in Fig. 20. The first submodel should describe the kinetics of the matrix chemical transfmmations, responsible of the final structure of the composite. The thermokinetic model predicts the exothermal heat of reaction and the degree of cure as a function of process time and temperature. 

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