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Comparison of six models of antiangiogenic therapy

Andrzej Świerniak — 2009

Applicationes Mathematicae

Six models of antiangiogenic therapy are compared and analyzed from control-theoretic point of view. All of them consist of a model of tumor growth bounded by the capacity of a vascular network developed by the tumor in the process of angiogenesis and different models of dynamics of this network, and are based on the idea proposed by Hahnfeldt et al. Moreover, we analyse optimal control problems resulting from their use in treatment protocol design.

Non-cooperative game approach to multi-robot planning

Adam GałuszkaAndrzej Świerniak — 2005

International Journal of Applied Mathematics and Computer Science

A multi-robot environment with a STRIPS representation is considered. Under some assumptions such problems can be modelled as a STRIPS language (for instance, a Block World environment) with one initial state and a disjunction of goal states. If the STRIPS planning problem is invertible, then it is possible to apply the machinery for planning in the presence of incomplete information to solve the inverted problem and then to find a solution to the original problem. In the paper a planning algorithm...

On the discrete time-varying JLQG problem

Adam CzornikAndrzej Świerniak — 2002

International Journal of Applied Mathematics and Computer Science

In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators...

Continuity of solutions of Riccati equations for the discrete-time JLQP

Adam CzornikAndrzej Świerniak — 2002

International Journal of Applied Mathematics and Computer Science

The continuity of the solutions of difference and algebraic coupled Riccati equations for the discrete-time Markovian jump linear quadratic control problem as a function of coefficients is verified. The line of reasoning goes through the use of the minimum property formulated analogously to the one for coupled continuous Riccati equations presented by Wonham and a set of comparison theorems.

Different models of chemotherapy taking into account drug resistance stemming from gene amplification

Jarosław ŚmiejaAndrzej Świerniak — 2003

International Journal of Applied Mathematics and Computer Science

This paper presents an analysis of some class of bilinear systems that can be applied to biomedical modelling. It combines models that have been studied separately so far, taking into account both the phenomenon of gene amplification and multidrug chemotherapy in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix whose form allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension,...

Optimal control for a class of compartmental models in cancer chemotherapy

Andrzej ŚwierniakUrszula LedzewiczHeinz Schättler — 2003

International Journal of Applied Mathematics and Computer Science

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...

Regulation of p53 by siRNA in radiation treated cells: Simulation studies

Krzysztof PuszyńskiRoman JaksikAndrzej Świerniak — 2012

International Journal of Applied Mathematics and Computer Science

Ionizing radiation activates a large variety of intracellular mechanisms responsible for maintaining appropriate cell functionality or activation of apoptosis which eliminates damaged cells from the population. The mechanism of such induced cellular death is widely used in radiotherapy in order to eliminate cancer cells, although in some cases it is highly limited by increased cellular radio-resistance due to aberrations in molecular regulation mechanisms of malignant cells. Despite the positive...

Optimal Control in a Model of Chemotherapy-induced Radiosensilisation

Piotr BajgerKrzysztof FujarewiczAndrzej Świerniak — 2019

Mathematica Applicanda

  In this work, we consider a simple mathematical model of radiochemotherapy which includes a term responsible for radiosensitization. We focus on finding theoretically optimal controls which maximise tumour cure probability for a finite, fixed therapeutic horizon. We prove that the optimal controls for both therapies are of 0-bang type, a result which is not altered by the inclusion of the radiosensilization term. By means of numerical simulations, we show that optimal control offers a moderate...

Prediction of lung cancer patients’ response to combined chemo-radiotherapy using a personalized hybrid model

The paper presents a novel approach to the prediction of the combined therapy outcome for non-small lung cancer patients. A hybrid model is proposed, consisting of two parts. The first one is a mathematical model of tumor response to therapy, whose parameters are expressed as linear function of data from massspectrometry of patient blood plasma samples. These linear functions constitute thesecond component of the hybrid model. A comparison of clinical and simulation-based survival curves is used...

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