Model description:
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.
The system-experiment model is
$$\begin{align*} \dot{x}_1(t) &= - \left(k_{21} + \frac{V_M}{K_m + x_1}\right)x_1(t) + k_{12}x_2(t) + b_1u(t) \\ \dot{x}_2(t) &= k_{21}x_1(t) - (k_{02} + k_{12})x_2(t) \\ y(t) &= c_1x_1(t) \\ \end{align*}$$
The initial conditions are $x_1(0) = 0$ and $x_2(0) = 0$. System parameters are presented in the table below.
| $x_1$, $x_2$ | drug masses in compartment 1 and 2, respectively; |
| $u$ | drug input; | $y$ | measured drug outtup; |
| $k_{12}$, $k_{21}$ and $k_{02}$ | constant rate parameters; |
| $V_M$ and $K_m$ | classical Michaelis-Mentel parameters; |
| $b_1$ and $c_1$ | input and output parameters, respectively |
Type:
Form:
Model order:
2
Time domain:
Linearity:
Attachment:
Publication details:
| Title | Global identifiability of nonlinear models of biological systems |
| Publication Type | Journal Article |
| Year of Publication | 2001 |
| Authors | Audoly, S., Bellu G., D'Angio L., Saccomani M.P., and Cobelli C. |
| Journal | IEEE Transactions on Biomedical Engineering |
| Volume | 48 |
| Pagination | 55-65 |
| Date Published | Jan |
| ISSN | 0018-9294 |
| Keywords | a priori global identifiability, algebra, algorithm, Algorithm design and analysis, Algorithms, Biological, Biological system modeling, biological system models, Biological systems, Biology computing, characteristic set, computer algebra techniques, differential algebra, Glucose, Humans, Insulin, Models, nonlinear dynamic models, Nonlinear dynamical systems, Nonlinear Dynamics, Nonlinear equations, nonlinear models, parameter estimation, Pharmacokinetics, physiological models, physiological systems, solution uniqueness, Testing, Time varying systems, time-varying parameters, zero initial conditions |
| Abstract | 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. |
| DOI | 10.1109/10.900248 |