TY - BOOK

T1 - Identifiability of deterministic differential models in state space

T2 - An implementation for a computer

AU - Pohjanpalo, Hannu

PY - 1982

Y1 - 1982

N2 - In this work the problem of identifiability of parameters
in models with an a priori known structure is considered.
The models are assumed to be presented in strictly
deterministic differential equations in state space, and
in the general case the equations may be nonlinear.
Although the methodology is applicable to a large variety
of models, special attention, especially in examples, was
paid to compartmental structures.
Different approaches to the problem, found in literature,
are reviewed. In particular, the method utilizing the
Taylor series expansion of the solution of the
differential equations, as functions of the unknown
parameters, is described, and was elaborated a step
further to obtain a simple criteria for local
identifiability.
The most prominent part of the present work is evidencing
that the algorithms derived for evaluating local
identifiability can be programmed for a computer. The
models for which the described implementation can be
applied can have polynomial nonlinearities in the state
components, in time, and in the parameters. In addition,
external binding equations and different initial
conditions can be included in an analysis of a given
model under a given experimentation. The measurements can
be defined as direct observations of the state
components, or, which is usual in compartmental systems,
as sums of state components.
The computer implementation has been utilized except for
analyzing single models, also for performing a systematic
study on biologically justified open three-compartment
models with one compartment Langmuir saturative. The
results of the analysis along with those obtained for the
corresponding linear models showed that the nonlinearity
often brings along local identifiability.

AB - In this work the problem of identifiability of parameters
in models with an a priori known structure is considered.
The models are assumed to be presented in strictly
deterministic differential equations in state space, and
in the general case the equations may be nonlinear.
Although the methodology is applicable to a large variety
of models, special attention, especially in examples, was
paid to compartmental structures.
Different approaches to the problem, found in literature,
are reviewed. In particular, the method utilizing the
Taylor series expansion of the solution of the
differential equations, as functions of the unknown
parameters, is described, and was elaborated a step
further to obtain a simple criteria for local
identifiability.
The most prominent part of the present work is evidencing
that the algorithms derived for evaluating local
identifiability can be programmed for a computer. The
models for which the described implementation can be
applied can have polynomial nonlinearities in the state
components, in time, and in the parameters. In addition,
external binding equations and different initial
conditions can be included in an analysis of a given
model under a given experimentation. The measurements can
be defined as direct observations of the state
components, or, which is usual in compartmental systems,
as sums of state components.
The computer implementation has been utilized except for
analyzing single models, also for performing a systematic
study on biologically justified open three-compartment
models with one compartment Langmuir saturative. The
results of the analysis along with those obtained for the
corresponding linear models showed that the nonlinearity
often brings along local identifiability.

M3 - Report

SN - 951-38-1397-5

T3 - Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports

BT - Identifiability of deterministic differential models in state space

PB - VTT Technical Research Centre of Finland

CY - Espoo

ER -