Combined Adomian/Alienor methods for solving adaptive control problems in chemotherapy

Abstract

Purpose

To show how the combined Adomian/Alienor methods for solving adaptive control problems can successfully be applied to chemotherapy.

Design/methodology/approach

Problem formulation is first developed and combined mathematical methods (Adomian/Alienor) are used for the solution of non‐linear differential equations/systems with unknown parameters and without discretization or linearization. The approach is applied to biological systems and in particular the drug/tumour two compartment model is addressed.

Findings

A general abstract framework for the identification and the control of a non‐linear evolution system has been developed. It was found that it is possible to identify and control a system using a powerful technique based on a combination of the Adomian/Alienor methods. This produced a methodology which showed its superiority over the traditional methods in that as a result of their implementation we can predict and optimize the individual dosage in the described application.

Research limitations/implications

The combined techniques proved to be successful for the optimization of drug administration where account is taken of effectiveness, usefulness and safety. Further research collaboration between multidisciplinary scientists and practitioners directed towards more insight into drug/cancerous cells behaviour is required.

Practical implications

An alternative to other classical techniques to solve control/identification problems has been produced.

Originality/value

New combined technique given which is superior to traditional ones for certain therapeutic cases.

Citation

Zaidi, Z., Twizell, E.H., Cherruault, Y. and Meulemans, A. (2005), "Combined Adomian/Alienor methods for solving adaptive control problems in chemotherapy", Kybernetes, Vol. 34 No. 7/8, pp. 1223-1236. https://doi.org/10.1108/03684920510605993