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Journal of Mathematical Chemistry

, Volume 50, Issue 6, pp 1598–1624 | Cite as

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

  • Francisco Garcia-Sevilla
  • Manuela Garcia-Moreno
  • Milagros Molina-Alarcon
  • María J. Garcia-Meseguer
  • José M. Villalba
  • Enrique Arribas
  • Ramón Varon
Original Paper
First Online:
Received:
Accepted:

Abstract

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, 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.

Keywords

Compartmental system Linear Open–closed Kinectics Symbolic equations 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Francisco Garcia-Sevilla
    • 1
  • Manuela Garcia-Moreno
    • 2
  • Milagros Molina-Alarcon
    • 3
  • María J. Garcia-Meseguer
    • 3
  • José M. Villalba
    • 4
  • Enrique Arribas
    • 5
  • Ramón Varon
    • 2
    • 6
  1. 1.Department of Electrical Engineering, Electronics, Automation and Communications, Technical School of Industrial EngineeringUniversity of Castilla-La ManchaAlbaceteSpain
  2. 2.Department of Physical Chemistry, Technical School of Industrial EngineeringUniversity of Castilla-La ManchaAlbaceteSpain
  3. 3.Nursing Department, School of NursingUniversity of Castilla-La ManchaAlbaceteSpain
  4. 4.Department of Medical Science, Faculty of MedicineUniversity of Castilla-La ManchaAlbaceteSpain
  5. 5.Applied Physics DepartmentHigh School of Informatics EngineeringAlbaceteSpain
  6. 6.Escuela de Ingenieros IndustrialesUniversidad de Castilla-La ManchaAlbaceteSpain

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