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S. Parragh:
"Modelle zur Bestimmung des aortalen Blut usses basierend auf Optimalitätsbedingungen";
Supervisor: F. Breitenecker; Institut für Analysis und Scientific Computing, 2013; final examination: 2013-06-05.

The hemodynamics in the human body is determined by blood
ow and pressure, which
depend on the mechanism of the heart and the properties of the vessels. Therefore,
the analysis of blood
ow and pressure can yield valuable insights into the status of
the cardiovascular system of a speci c person. Especially parameters, which are derived
from aortic pressure and
ow curves, are considered to be important indicators of cardiovascular
risk. But the measurement of the data needed is di cult. Validated methods
already exist for transfering peripheral blood pressure curves to central ones. The aim
of this work is to study models for the determination of the aortic
ow curve.
First, so called Windkessel models are presented, which describe the relation between
central pressure and
ow via linear ordinary di erential equations. In these models
the
ow represents the input and the pressure the output. Special attention is given
to the model parameters and their interpretation as well as to the model assumptions.
Next, the concept of optimality in the context of the cardiovascular system is explained.
By adding an optimality criterion to the Windkessel model, a feedback mechanism is
established, which allows to calculate both pressure and
ow at the same time if the
model parameters are known. Subsequently, some mathematical basics of optimization
are introduced, which can be used to solve the optimization problem resulting from the
model plus feedback mechanism. Di erent approaches and results found in literature
are discussed and nally, the results of my model experiments are presented.
The results show that it is indeed possible to generate
ow curves with this approach,
which resemble phyisiological ones. But they also show that the models plus feedback
mechanism react sensitively to any violation of the assumptions the Windkessel models
are based on. Thus the constraints and boundary conditions in the optimization problem
have to be chosen very carefully. However, when they are all taken into account, the
identi cation of the model parameters from a given pressure curve seems feasible