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

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