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Optimal inputs in pharmacokinetics model's identification

Pietrenko-Dąbrowska A., Kalicka R.

Biocybernetics and Biomedical Engineering

2006

Vol. 26, no. 3

3-14

The paper presents optimal input design for parametric identification of the SISO state space compartmental models of pharmacokinetic systems. The adopted objective function is the trace of the Fisher information matrix (the sensitivity criterion). The class of equienergy admissible inputs is concemed, as rate-dependent side effects occur for many medicines. The optimal input design problem is a nonlinear programming problem with constraint. The problem is solved using Kuhn-Tucker necessary conditions. SeveraI compartmental models were examined. The optimal inputs of different shapes were obtained and compared.

Properties of D-optimal sampling schedule for compartmental models

Kalicka R., Bochen D.

Biocybernetics and Biomedical Engineering

2005

Vol. 25, no. 1

23-36

Software allowing visualization of D-optimal objective function distribution over multidimensional time space was designed and implemented. The analysis was performed for one, two and three-compartmental models. Outputs of the models have form of sums of exponential terms. The exemplary objective functions distribution and searching algorithm are presented. The obtained results show that objective function for D-optimal solution has no local extremes. The problem under investigation has one globally optimal solution.

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.