Time course equations of the amount of substance in a linear compartmental system and their computerized derivation

García-Meseguer, María José; Labra, J.A. Vidal de; Garcı́a-Cánovas, Francisco; Havsteen, B.; García-Moreno, Manuela; Varón, R.

doi:10.1016/s0303-2647(01)00116-2

Cited by 13 publications

(25 citation statements)

References 27 publications

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“…When obtaining the general symbolic kinetic equations for linear compartmental systems, like those analyzed herein, and as described in previous contributions [10,30], neither the properties of matrix K nor its characteristic polynomial D(λ) relating to the distribution of system compartments into classes, as described in this paper, have been considered. These equations involve all the initial amounts of substance and all the fractional transfer coefficients in the compartmental system, regardless of the compartment for which we need to know the temporal evolution of the amount of substance and the compartments where the material is injected at t = 0.…”

Section: Resultsmentioning

confidence: 99%

“…In each section, the standard definitions and nomenclature that are commonly employed in the literature on closed compartmental systems have been used [8,10,11,26,28,33,37,42] and will prove useful in the following analysis: n: Number of compartments in the system. X 1, X 2,..., X n : Each n compartment in the system.…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…The study of the matrix associated with linear compartmental systems is an indispensable bridge between the structural and the kinetic studies of linear compartmental systems [10,30,43].…”

Section: Matrix Of the System And Some Of Its Propertiesmentioning

confidence: 99%

“…Next, we revise the additional definitions and notations on compartmental systems [10,11,30] needed to make progress in the paper. To support this task, we will use the compartmental system shown in Fig.…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…In this way, explicit general equations describing the evolution of any compartment of a linear system, either closed or open, were obtained. Moreover, Garcia-Meseguer et al [10] implemented a software, COEFICOM, developed in MS Visual BASIC, that provides the expressions of these coefficients as a function of the fractional transfer coefficients.…”

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confidence: 99%

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Linear compartmental systems. I. kinetic analysis and derivation of their optimized symbolic equations

et al. 2012

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The study of many biological systems requires the application of a compartmental analysis, together with the use of isotopic tracers, parameter identification and methods to evaluate the mean parameters. For all this, the kinetic equations of the compartmental system as a function of its parameters are needed. In this paper, we present some considerations on the diagrams of connectivity of linear compartmental systems and obtain new properties from the matrix corresponding to the ordinary first-order linear differential equation systems which describe their kinetic behaviour. Using these properties, symbolic equations are obtained in a simplified form. These equations provide the instantaneous amount of substance in any compartment of the system when zero input is injected into one or more of the system compartments, 1599 solely as a function of those parameters of compartmental systems which really have an influence on the sought expression. This is unlike what happens in the other symbolic equations obtained in a previous contribution that included all the fractional transfer coefficients involved in the compartmental system, regardless of whether or not they had an influence on the instantaneous amount of substance.

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Section: Resultsmentioning

confidence: 99%

Section: Notation and Definitionsmentioning

confidence: 99%

“…The study of the matrix associated with linear compartmental systems is an indispensable bridge between the structural and the kinetic studies of linear compartmental systems [10,30,43].…”

Section: Matrix Of the System And Some Of Its Propertiesmentioning

confidence: 99%

Section: Notation and Definitionsmentioning

confidence: 99%

mentioning

confidence: 99%

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Linear compartmental systems. I. kinetic analysis and derivation of their optimized symbolic equations

et al. 2012

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Computerized evaluation of mean residence times in multicompartmental linear system and pharmacokinetics

Villalba¹,

Barbero²,

Díaz‐Sierra³

et al. 2010

J Comput Chem

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Deriving mean residence times (MRTs) is an important task both in pharmacokinetics and in multicompartmental linear systems. Taking as starting point the analysis of MRTs in open or closed (Garcia-Meseguer et al., Bull Math Biol 2003, 65, 279) multicompartmental linear systems, we implement a versatile software, using the Visual Basic 6.0 language for MS-Windows, that is easy to use and with a user-friendly format for the input of data and the output of results. For any multicompartmental linear system of up to 512 compartments, whether closed or open, with traps or without traps and with zero input in one or more of the compartments, this software allows the user to obtain the symbolic expressions, in the most simplified form, and/or the numerical values of the MRTs in any of its compartments, in the entire system or in a part of the system. As far as we known from the literature, such a software has not been implemented before. The advantage of the present software is that it reduces on the work time needed and minimizes the human errors that are frequent in compartmental systems even those that are relatively staightforward. The software bioCelTer, along with instructions, can be downloaded from http://oretano.iele-ab.uclm.es/~fgarcia/bioCelTer/.

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Linear compartmental systems: II—A software to obtain the symbolic kinetic equations

et al. 2012

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Software has been implemented in this work to take full advantage of the characteristics of current operating systems and to provide the optimized symbolic kinetic equations for the linear compartmental systems derived in part I of this series. This software, called RM-w2011, is implemented using the C# language and runs under Windows XP, Vista and 7. It is applicable to any linear compartmental system, closed or open, and with a zero input in one or more of its compartments. Apart from the optimized equations that the software provides, if so desired, non optimized equations are offered to compare the advantage of using optimized equations while using non optimized ones, whenever they do not coincide. Moreover, the software circumvents the limitations of other previous software tools that operated with non optimized symbolic equations.

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Time course equations of the amount of substance in a linear compartmental system and their computerized derivation

Cited by 13 publications

References 27 publications

Linear compartmental systems. I. kinetic analysis and derivation of their optimized symbolic equations

Linear compartmental systems. I. kinetic analysis and derivation of their optimized symbolic equations

Computerized evaluation of mean residence times in multicompartmental linear system and pharmacokinetics

Linear compartmental systems: II—A software to obtain the symbolic kinetic equations

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