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

In this contribution, we present the symbolic time course equations corresponding to a general model of a linear compartmental system, closed or open, with or without traps and with zero input. The steady state equations are obtained easily from the transient phase equations by setting the time --> infinity. Special attention has been given to the open systems, for which an exhaustive kinetic analysis has been developed to obtain important properties. Besides, the results have been particularized to open systems without traps and an alternative expression for the distribution function of exit times has been provided. We have implemented a versatile computer program, that is easy to use and with a user-friendly format of the input of data and the output of results. This computer program allows the user to obtain all the information necessary to derive the symbolic time course equations for closed or open systems as well as for the derivation of the distribution function of exit times.