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Coupled analytical and numerical approach to uncovering new regulatory mechanisms of intracellular processes

100%
Śmieja J.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
|
nr 4
781-788
EN
The paper deals with the analysis of signaling pathways aimed at uncovering new regulatory processes regulating cell responses. First, general issues of comparing simulation and experimental data are discussed, and various aspects of data normalization are covered. Then, a model of a particular signaling pathway, induced by Interferon-β, is briefly introduced. It serves as an example illustrating how mathematical modeling can be used for inferring the structure of a regulatory system governing the dynamics of intracellular processes. In this pathway, experimental results suggest that a hitherto unknown process is responsible for a decrease in the levels of one of the important molecules used in the pathway. Then, equilibrium points of the model are analyzed, allowing the rejection of all but one explanation of the phenomena observed experimentally. Numerical simulations confirm that the model can mimic the dynamics of the processes in the pathway under consideration. Finally, some remarks about the applicability of the method based on an analysis of equilibrium points are made.
2
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Different models of chemotherapy taking into account drug resistance stemming from gene amplification

63%
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.
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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
|
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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