New results about the identifiability of linear open bicompartmental homogeneous system and the identification of open Michaelis-Menten system by a linear approach

摘要

Purpose - To prove two results. Namely that if in a linear homogeneous bicompartmental system one compartment is measured then it is indefinable. The second one is related to the identification of non-linear compartmental models by mean of a linear method. Design/methodology/approach - The first result is generalized to linear non-homogeneous bicompartmental systems of Michaelis-Menten M-M systems). The second one is related to the identification of a non-linear compartmental model. The obtained linear system is not homogeneous and must be generalized to nonhomogeneous systems. Then the Jacobian matrix associated to the M-M systems is identified and the M-M parameters are deduced by continuity from the Cauchy problem's solution. Findings - Both stated results were proved and any open linear bicompartmental system whether homogeneous or not, of the type I is identifiable. Research limitations/implications - In compartmental analysis the exchange hypothesis allows us to represent a model of any phenomenon depending on time. Many phenomena require "the enzyme reactions" leading to the M-M laws. These laws assert that the quantity of matter going from compartment can be defined and M-M constants prescribed. This research considers both homogeneous and nonhomogeneous Systems cases. Practical implications - Contributes to the identification of linear and non-linear bicompartmental systems which are of biocybernetical significance. Originality/value - The two proven results are new and applicable.