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J.M. Villalba (Universidad de Castilla-la Mancha, Spain), R. Varón (Universidad de Castilla-la Mancha, Spain), E. Arribas (Universidad de Castilla-la Mancha, Spain), R. Diaz-Sierra (UNED, Spain), F. Garcia-Sevilla (Universidad de Castilla-La Mancha, Spain), F. Garcia-Molina (Universidad de Murcia, Spain), M. Garcia-Moreno (Universidad de Castilla-la Mancha, Spain) and M. J. Garcia-Meseguer (Universidad de Castilla-la Mancha, Spain)

Source Title: Advanced Methods and Applications in Chemoinformatics: Research Progress and New Applications

Copyright: © 2012
|Pages: 32
DOI: 10.4018/978-1-60960-860-6.ch016

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TopIn the analysis of any linear compartmental system consisting of compartments *X _{1}, X_{2},…X_{n}*, there are two problems that must be solved: (1) The forward problem, i.e. to ascertain how the system behaves kinetically for given inputs, assuming connectivity between the compartments and that the values of the non-null fractional transfer coefficients,

The solution of the forward problem, together with the specific inputs of the substance made, leads to knowledge of the kinetic behavior of the compartmental system under study, i.e. the time variation of the amount of substance in each compartment.

The forward problem requires choosing both a model of the connectivity structure of the compartmental system and a mathematical model to acquire the kinetic behavior of the system. Mathematical model may be the residence time concept or the corresponding set of differential equations (Weiss, 1992). The first mathematical model gives time-independent kinetic parameters such as *exit* and *transit times, MRT*, *occupancy*, *turnover time* and *half-life* (Anderson, 1983; Jacquez, 1985; Jacquez, 1999). The second mathematical model furnishes the time course of the amount of substance in any compartment of the system after a specific input in one or more compartments is made (Garcia-Meseguer et al., 2001; Jacquez, 2002; Rescigno, 1956; Rescigno, 1999; Rescigno, 2004; Varon et al., 1995a). From the results obtained with the second mathematical model, the parameters provided by the first method can also be obtained (Anderson, 1983; Garcia-Meseguer et al., 2003; Jacquez, 1985; Jacquez, 1999; Varon, Garcia-Meseguer, Valero, Garcia-Moreno, & Garcia-Canovas, 1995). In this section the second mathematical model mentioned above is used.

The compartmental systems are considered closed if there is no interchange of substance between any compartment of the system and the environment; otherwise they are named open systems. A compartment or a set of interconnected compartment, from which substance cannot leave, is named a simple trap, i.e. material is “trapped” (Anderson, 1983; Jacquez, 1985).

From structural point of view of the compartmental systems and according to Rescigno (1956) one compartment X* _{i}* is precursor of another, X

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