This example deals with a model described in E. Walter, Identifiability of State Space Models. Berlin, Germany:Springer-Verlag, 1982. The model is shown in Fig. 3. All fluxes are assumed linear except some leaving compartment 3. In particular, parameters $k_{13}$, $k_{23}$, and $k_{43}$ are assumed to be parametrically linearly controlled by the arrival compartment, i.e. $k_{13}(x_1) = k_{13}x_1$, $k_{23}(x_2) = k_{23}x_2$ and $k_{43}(x_4) = k_{43}x_4$.
A prerequisite for well-posedness of parameter estimation of biological and physiological systems is a priori global identifiability, a property which concerns uniqueness of the solution for the unknown model parameters. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature but no solution exists in the general case. Here, the authors present a new algorithm for testing global identifiability of nonlinear dynamic models, based on differential algebra. The characteristic set associated to the dynamic equations is calculated in an efficient way and computer algebra techniques are used to solve the resulting set of nonlinear algebraic equations. The algorithm is capable of handling many features arising in biological system models, including zero initial conditions and time-varying parameters. Examples of usage of the algorithm for analyzing a priori global identifiability of nonlinear models of biological and physiological systems are presented.
This example deals with a model describing the control of insulin on glucose utilization in humans. The model is shown in Fig. 2. The experiment consists of an impulse input of glucose labeled with a tracer and of the measurement in plasma of glucose, labeled glucose and insulin concentrations. The measured insulin concentration acts as model input $u$, while the model output $y$ is the measured tracer glucose concentration. The control by insulin on the glucose system is exerted by insulin in a remote compartment $(x_3)$. The glucose system is described by two compartments which represent, respectively, glucose in rapidly $(x_1)$ and slowly equilibrating tissues $(x_2)$ which include the muscle tissues. Insulin control is exerted on glucose utilization in compartment 3 (insulin-dependent tissues) while glucose utilization in compartment 1 refers to insulin-independent tissues.
A prerequisite for well-posedness of parameter estimation of biological and physiological systems is a priori global identifiability, a property which concerns uniqueness of the solution for the unknown model parameters. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature but no solution exists in the general case. Here, the authors present a new algorithm for testing global identifiability of nonlinear dynamic models, based on differential algebra. The characteristic set associated to the dynamic equations is calculated in an efficient way and computer algebra techniques are used to solve the resulting set of nonlinear algebraic equations. The algorithm is capable of handling many features arising in biological system models, including zero initial conditions and time-varying parameters. Examples of usage of the algorithm for analyzing a priori global identifiability of nonlinear models of biological and physiological systems are presented.
The two compartment model describes the kinetics of a drug in the human body. The drug is injected into the blood (compartment 1) where it exchanges linearly with the tissues (compartment 2); the drug is irreversibly removed with a nonlinear saturative characteristic from compartment 1 and with a linear one from compartment 2. The I/O experiment takes place in compartment 1.
A prerequisite for well-posedness of parameter estimation of biological and physiological systems is a priori global identifiability, a property which concerns uniqueness of the solution for the unknown model parameters. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature but no solution exists in the general case. Here, the authors present a new algorithm for testing global identifiability of nonlinear dynamic models, based on differential algebra. The characteristic set associated to the dynamic equations is calculated in an efficient way and computer algebra techniques are used to solve the resulting set of nonlinear algebraic equations. The algorithm is capable of handling many features arising in biological system models, including zero initial conditions and time-varying parameters. Examples of usage of the algorithm for analyzing a priori global identifiability of nonlinear models of biological and physiological systems are presented.
