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

Abstract

PurposeTo 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/approachThe 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.FindingsBoth stated results were proved and any open linear bicompartmental system whether homogeneous or not, of the type I is identifiable.Research limitations/implicationsIn 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 implicationsContributes to the identification of linear and non‐linear bicompartmental systems which are of biocybernetical significance.Originality/valueThe two proven results are new and applicable.