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An optimal input design using the sensitivity criterion for parametric identification of pharmacokinetic models

Kalicka R., Pietrenko-Dąbrowska A.

Biocybernetics and Biomedical Engineering

2005

Vol. 25, no. 2

3-18

The parametric approach to the identification of the SISO state space compartmental models of pharmacokinetic systems is presented. The model structure is formulated basing on the a priori knowledge. The initial parameter estimates are calculated on the base of the output measurements collected during the intuitive experiment. They are used for designing the optimal input, which ensures the best accuracy of the parameter estimates. The sensitivity criterion is adopted and presented in terms of nonlinear programming problem with constraints. Two classes of optimal inputs are considered: equidose and equienergy inputs. The results obtained with optimal and standard inputs are presented and compared.

Optimal Control for a Class of Compartmental Models in Cancer Chemotherapy

Świerniak A., Ledzewicz U., Schättler H.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 3

357-368

We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are analyzed, which consider a blocking agent and a recruiting agent, respectively. In Model B a blocking agent which slows down cell growth during the synthesis allowing in consequence the synchronization of the neoplastic population is added. In Model C the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal. Then sharp necessary and sufficient optimality conditions for bang-bang controls are given for the general class of models P and illustrated with numerical examples.