Drug Targeting Organ-Specific Strategies

13.2 Pharmacokinetics and Pharmacodynamics, Modelling, Simulation, and Data Analysis 347
chosen should be sufficiently small, and the fitting procedure may be repeated with a different
set of initial estimates, or a different minimizing algorithm.
13.2.8.4 Identification of Model Parameters
The procedure to obtain the best fitting set of model parameters (Section 13.2.8.3) can be
performed only if each model parameter is uniquely identifiable from the measurements
[35–38]. This implies that the same set of model parameters is obtained, irrespective of the
initial set (Section 13.2.8.3). In some cases one or more model parameters cannot be identified
uniquely, because the measurement data do not contain enough ‘information’ on that
particular parameter, for example:
• In the model depicted in Figure 13.1, the parameters CL 10 and CL 20 cannot be obtained
uniquely if only measurement data from compartment 1 are available. There is an infinite
number of parameter sets yielding exactly the same concentration profile in compartment
1. Only if certain constraints are imposed (for example, CL 20 = 0 or CL 20 = CL 10), can the
model parameters be identified uniquely.
• In the case of Michaelis–Menten kinetics (Eq. 13.4), Vmax xy and Km xy cannot be assessed
uniquely if the concentration C x is far below the value of Km xy; in that case, Eq. 13.4 reduces
to Eq. 13.3, and only one parameter CL xy, or the ratio Vmax xy/Km xy can be calculated
uniquely.
• In the model shown in Figure 13.1, if CL 12 is very large compared to CL 10, and if no data
shortly after administration of a bolus dose are available, the model would behave as a single
compartment model, and CL 12 will not identifiable; also, only the sum of the volumes
rather than both volumes separately can be assessed.
The problem of identification grows rapidly with increasing complexity of the model. In
some cases this problem can be solved by an appropriate experimental design. As a general
rule, the problem is reduced if the concentrations in compartments other than the central
plasma compartment can be measured. Also, simultaneous measurement of drug and
drug–carrier conjugate or pro-drug is a condition for identification of the models described
in Section 13.3.
Jacquez and Perry [37] developed the program IDENT to investigate the identification of
model parameters. In most cases, problems of identification can be detected by inspection of
the standard errors of the model parameters (the standard error of a model parameter is a
measure of the credibility of the parameter value, which is provided by the most fitting programs).
A high standard error (for example, more than 50% of the parameter value) indicates
that the parameter value cannot be assessed from the data, most likely due to an identification
problem. In that case, the parameter value itself is meaningless, and thus the parameter
set should be discarded (see Section 13.2.8.5).