|06.07.2012||13:45||HS 9||Gabriel Wittum (Goethe University Frankfurt)||Modelling and Simulation of Biological Systems|
Biological systems are distinguished by their enormous complexity and variability. That is why mathematical modelling and computational simulation of those systems is very difficult, in particular thinking of detailed models which are based on first principles. The difficulties start with geometric modelling which needs to extract basic structures from highly complex and variable phenotypes, on the other hand also has to take the statistic variability into account. Moreover, the models of the processes running on these geometries are not yet well established, since these are equally complex and often couple many scales in space and time. Thus, simulating such systems always means to put the whole frame to test, from modelling to the numerical methods and software tools used for simulation. These need to be advanced in connection with validating simulation results by comparing them to experiments. To treat problems of this complexity, novel mathematical models, methods and software tools are necessary . In recent years, such models, numerical methods and tools have been developed, allowing to attack these problems. In the talk we consider two examples as paradigms for the process of modelling and simulation in biosciences. The first example is the diffusion of xenobiotics through human skin, the second one is the automatic reconstruction of neurons and nueclei by means of numerical methods for partial differential equations.
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