Using an Observer in a Sliding Mode for Modeling Antiangiogenic Therapy

Abstract

Currently, a slew of biomedical system models have been proposed, but in certain cases their real-world application is a challenge.This is because in these models not all state variables can be measured. The task of restoring the state vector, which is to obtain estimates for its non-measurable components, can be solved by control theory methods, in which it is formulated as the task of constructing a state observer.The article analyses Russian and foreign publications available in the field concerned to consider the problem of observer applications to biological systems. One of the types of state observers, an observer operating in a sliding mode in particular, is under consideration. The procedure to construct it for biological systems is shown by an example of a tumor growth model in which treatment is based on blocking the processes of angiogenesis.For a nonlinear dynamic system describing the tumor growth in the process of antiangiogenic therapy, its normal form is shown and a nonlinear state observer in sliding modes is constructed. As the measurable system output, a variable appropriate to the tumor volume was selected. The estimate of the total vector of the system state, obtained by the observer, is used to build state feedback that stabilises the program trajectory. Mathematical modelling, which shows that, in principle, in sliding modes an observer can be used for control of biological systems, proves the theoretical principles.

Keywords

• state observer
• observer in a sliding mode
• normal form
• control
• antiangiogenesis