Optimal Delivery of Chemotherapeutic Agents in
Cancer
Pinky Dua
a
, Vivek Dua
b
, Efstratios N. Pistikopoulos
a
a
Centre for Process Systems Engineering, Department of Chemical Engineering,
Imperial College London, South Kensington Campus, London SW7 2AZ, United
Kingdom
b
Centre for Process Systems Engineering, Department of Chemical Engineering,
University College London, Torrington Place, London WC1E 7JE, United Kingdom
Abstract
In this paper, derivation of the optimal chemotherapy schedule is formulated and solved
as a dynamic optimization problem. For this purpose two models representing the
tumour growth kinetics are considered. The dynamic optimization problem for the first
model, which is cell cycle non-specific, takes into account multiple time characteristics,
drug resistance and toxicity. The discontinuity in the model is formulated by
introducing integer variables. For the second model, which is cell cycle specific, the
tumour growth is modelled via two compartments: proliferating and resting
compartment.
Keywords: Drug Delivery Systems, Cancer, Chemotherapy, Optimal Control, Mixed
Integer Dynamic Optimization
1. Introduction
Cancer is a collective term that describes a group of diseases characterized by
uncontrolled and unregulated growth of cells leading to invasion of surrounding tissues
and spreading to the parts of the body that are distant from the site of origin. There are
around 200 types of cancer and cancers of lungs, breast, bowel and prostrate are the
most common ones. There are three main stages in the process of carcinogenesis:
initiation, promotion and progression. The normal cell changes to an initiated cell and
then to cancer differentiated cell and finally invades and spreads to the surrounding
cells.
The simplest mathematical model describes the entire cell cycle as a uniform entity,
where all the cells contained in a tumour are of the same type. The cell cycle non-
specific models consist of one compartment so that the effect of the anticancer agents is
same on all the cells. However these models fail to describe the action of cycle specific
drugs due to their over-simplified nature. The more detailed multi-compartment models
(cell cycle specific models) are considered for this purpose. Here the cell cycle is
divided into compartments depending on the types of cells that are affected by the drug.
Chemotherapy is one of the most commonly used treatments for cancer that uses
anticancer or cytotoxic drugs to destroy or kill cancer cells. The suitability of
chemotherapy and the choice of drugs depend on many factors including the type of
cancer, the location of the origin of the cancer in the body, how mature the cancer cells
are and whether the cancer cells have spread to the other parts of the body.
Chemotherapy targets dividing cells which does not only include cancer cells but any
and 9th International Symposium on Process Systems Engineering
W. Marquardt, C. Pantelides (Editors)
© 2006 Published by Elsevier B.V.
16th European Symposium on Computer Aided Process Engineering
1643