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1
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Comparison of six models of antiangiogenic therapy

100%
Świerniak A.
Applicationes Mathematicae
|
2009
|
tom 36
|
nr 3
333-348
EN
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.
2
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Non-cooperative game approach to multi-robot planning

64%
Gałuszka A., Świerniak A.
International Journal of Applied Mathematics and Computer Science
|
2005
|
tom 15
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nr 3
359-367
EN
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 that solves the problem described above is proposed and its computational complexity is analyzed. To make the plan precise, non-cooperative strategies are used.
3
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Different models of chemotherapy taking into account drug resistance stemming from gene amplification

64%
Śmieja J., Świerniak A.
International Journal of Applied Mathematics and Computer Science
|
2003
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tom 13
|
nr 3
297-305
EN
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, can have any form, the other is infinite dimensional and tridiagonal. A methodology of the analysis of such models, based on system decomposition, is presented. An optimal control problem is defined in the l^1 space. In order to derive necessary conditions for optimal control, the model description is transformed into an integro-differential form. Finally, biomedical implications of the obtained results are discussed.
4
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Continuity of solutions of Riccati equations for the discrete-time JLQP

64%
Czornik A., Świerniak A.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
|
nr 4
539-543
EN
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.
5
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On the discrete time-varying JLQG problem

64%
Czornik A., Świerniak A.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
|
nr 2
203-207
EN
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 are available.
6
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Regulation of p53 by siRNA in radiation treated cells: Simulation studies

51%
Puszyński K., Jaksik R., Świerniak A.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 4
1011-1018
EN
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 correlation between the radiation dose and the number of apoptotic cancer cells, radiation has to be limited because of extensive side effects. Therefore, additional control signals whose role will be to maximize the cancer cells death-ratio while minimizing the radiation dose and by that the potential side effects are worth considering. In this work we present the results of simulation studies showing possibilities of single gene regulation by small interfering RNA (siRNA) that can increase radio-sensitivity of malignant cells showing aberrations in the p53 signaling pathway, responsible for DNA damage-dependant apoptosis. By blocking the production of the p53 inhibitor Mdm2, radiation treated cancer cells are pushed into the apoptotic state on a level normally achievable only with high radiation doses. The presented approach, based on a simulation study originating from experimentally validated regulatory events, concerns one of the basic problems of radiotherapy dosage limitations, which, as will be shown, can be partially avoided by using the appropriate siRNA based control mechanism.
7
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Optimal Control in a Model of Chemotherapy-induced Radiosensilisation

51%
Bajger P., Fujarewicz K., Świerniak A.
Mathematica Applicanda
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2019
|
tom 47
|
nr 1
EN
  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 increase in survival time over a sequential treatment. We then revisit in more detail a question of measuring the synergy between the therapies by means of isobolograms, a common experimental technique for measuring the additivity of two treatments.
8
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Optimal control for a class of compartmental models in cancer chemotherapy

51%
Świerniak A., Ledzewicz U., Schättler H.
International Journal of Applied Mathematics and Computer Science
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2003
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tom 13
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nr 3
357-368
EN
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.
9
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Content available

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

39%
Wołkowicz S., Fujarewicz K., Kurpas M., Łakomiec K., Śmieja J., Suwiński R., Świerniak A.
Mathematica Applicanda
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2019
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tom 47
|
nr 2
PL
The paper presents a novel approach to 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 estimated by a neural network based regressor, constituting the second component of the hybrid model. Estimation is based on data from mass spectrometry of patient blood plasma samples. Comparison of clinical and simulation-based survival curves is used to evaluate the quality of the model.
EN
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 to evaluate the quality of the model.
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