Mathematical modeling of cell signaling pathways has become a very important and challenging problem in recent years. The importance comes from possible applications of obtained models. It may help us to understand phenomena appearing in single cells and cell populations on a molecular level. Furthermore, it may help us with the discovery of new drug therapies. Mathematical models of cell signaling pathways take different forms. The most popular way of mathematical modeling is to use a set of nonlinear...
DNA microarrays provide a new technique of measuring gene expression, which has attracted a lot of research interest in recent years. It was suggested that gene expression data from microarrays (biochips) can be employed in many biomedical areas, e.g., in cancer classification. Although several, new and existing, methods of classification were tested, a selection of proper (optimal) set of genes, the expressions of which can serve during classification, is still an open problem. Recently we have...
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...
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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