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%0 Thesis %A da Cunha Orfao, Sandra Maria %T Mathematical approaches to modelling and controlling blood thrombin formation %C Aachen %I Publikationsserver der RWTH Aachen University %M RWTH-CONV-123347 %P 240 S. : graph. Darst. %D 2007 %Z Aachen, Techn. Hochsch., Diss., 2006 %X Chapter 1 is a brief description of the blood coagulation system. Besides making an excursion through the nomenclature and the principal properties, we are confronted with the pertinence of questions that are in nowadays object of discussion among the scientific community investigating the process of thrombin formation. Chapter 2 is a summary on what is known about the mathematical modelling of biochemical networks. There we present some of the formalism developed by Martin Feinberg and Rutherford Aris regarding structural aspects of such networks. In Chapter 3 we describe two of the most cited mathematical models for modelling a part of the blood coagulation system. These models are due to Stortelder, Hemker and Hemker (SHH) and to Jones and Mann (JM). The models comprise systems of nonlinear differential equations, where the reaction constants are taken as parameters and the physiological concentration of the different factors involved in the blood coagulation process are taken as initial values. To the description done belongs the presentation of the numerical solution and the analysis of the stoichiometry. Moreover, we interpreted the reaction scheme of (JM) as a graph and we observed the existence of loops and determined the number of connected components. Chapter 4 is devoted to the analysis of the dynamics of both systems by doing a qualitative analysis using results of the local theory of differential equations and nonlinear dynamical systems. Since the application of a drug can be of interest to reestablish hemostatic equilibrium it is very important to address the question of the controllability of the system. This was done in Chapter 5. There we started by analyzing the controllability of the linearized system from (SHH).The controllability of the non-linear system followed after identification of a flat output. Since physiologists may influence the system by adding thrombocytes to a sample of blood, we describe in Chapter 7 a possible mechanism of action for the platelets based on the knowledge gained from the previous analysis by extending the model from (SHH) as a first approach. The lag present in the course of thrombin concentration with time is imperceptible in the numerical results. Not excluding the possibility that this may be the case when a purified enzyme like RVV is used to trigger the system, we finished this chapter by proposing a new scheme for the extrinsic pathway as an extension of (SHH)'s model. So, we replace the purified enzyme RVV by the reactions that are thought to occur in the extrinsic pathway, including also inhibitory reactions. We hope that this work will help people working in the mathematical modelling of highly nonlinear biological or physiological systems to be aware of the difficulties inherent to such a task and to learn that apparently simple questions regarding mathematical aspects like stability or controllability of more general systems with several unknown parameters have to be handled properly. Moreover, we saw how classical mathematical theorems can be useful to gain more insights into complex phenomena that arise from the current practice of investigation of other disciplines. %K Dynamische Modellierung (SWD) %K Steuerbarkeit (SWD) %K Anwendung (SWD) %K Globale Stabilität (SWD) %K Lokale Asymptotik (SWD) %K Enzym (SWD) %K Chemische Reaktion (SWD) %K Reaktionsdynamik (SWD) %F PUB:(DE-HGF)11 %9 Dissertation / PhD Thesis %U https://publications.rwth-aachen.de/record/61712